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ESA-Prima Win
STEEL AND TIMBER DESIGN BENCHMARKS SCIA Scientific Application Group
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___________________________________________________________ Release : 3.20.xx Module : Manual : Design benchmarks Revision : June 2000
___________________________________________________________ SCIA Group n.v. Scientific Application Group Industrieweg 1007 B-3540 Herk-de-Stad (België) Tel.(+32) (0)13/55 17 75 Fax.(+32) (0)13/55 41 75 ___________________________________________________________ SCIA W+B Software b.v. Postbus 330 NL-6860 AH Oosterbeek (Nederland) Tel.(+31) 26-3338008 Fax.(+31) 26-3341949 ___________________________________________________________ SCIA sarl Parc Club des Prés Rue Papin 29 - F-59650 Villeneuve d'Asq (Frankrijk) Tel.(+33) (0) 3.20.04.10.60 Fax.(+33) (0) 3.20.04.03.36 ___________________________________________________________ SCIA GmbH Giesestraße 3 D 58636 Iserlohn (Duitsland) Tel.(+49) 2371-4944 Fax.(+49) 2371-4904
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ABOUT THIS BENCHMARKS All benchmarks are presented in the following form : Description Short description of the benchmark. Project data All necessary data to calculate the project. Reference The reference from which the results are taken or the analytical solution. Result Comparison between ESA-Prima Win and the reference result. Version Version number of the version with which the verification was done. Input file + calculation note Name of the corresponding ESA-Prima Win file. Modules Name of the commercial modules needed to calculate this example. Author Initials of the author of the benchmark Information in this document is subject to change without notice. No part of this document may be reproduced, stored in a retrieval system or transmitted, in any form or by any means, electronic or mechanical, for any purpose, without the express written permission of the publisher. SCIA Software is not responsible for direct or indirect damage as a result of imperfections in the documentation and/or software. Copyright 2000 SCIA Software. All rights reserved.
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TABLE OF CONTENTS The following benchmarks are available (the benchmarks are grouped according to the ESA-Prima Win modules) :
INTRODUCTION 10
1. STEEL CODE CHECK 11
1.1 PST.06.XX – 01 : CALCULATION OF BUCKLING RATIOS 11 1.2 PST.06.XX – 02 : CALCULATION OF BUCKLING RATIOS FOR CROSSING DIAGONALS 14 1.3 PST.06.01 – 01 : EC 3 STEEL CODE CHECK TUTORIAL FRAME 23 1.4 PST.06.01 – 02 : EC 3 STEEL CODE CHECK – WARPING CHECK 45 1.5 PST.06.01 – 03 : EC 3 STEEL CODE CHECK – WARPING CHECK 49 1.6 PST.06.01 – 04 : EC 3 STEEL CODE CHECK – WARPING CHECK 52 1.7 PST.06.01 – 05 : EC 3 STEEL CODE CHECK – WARPING CHECK 56 1.8 PST.06.01 – 06 : EC 3 STEEL CODE CHECK – TORSIONAL BUCKLING CHECK AND SHEAR
BUCKLING CHECK FOR COLD FORMED SECTIONS 60 1.9 PST.06.01 – 07 : EXAMPLE CODE CHECK AND CONNECTIONS ACCORDING TO EC3 : DESIGN OF
AN INDUSTRIAL TYPE BUILDING 68 1.10 PST.06.02 – 01 : DIN 18800 STEEL CODE CHECK (1) 119 1.11 PST.06.02 – 02 : DIN 18800 STEEL CODE CHECK (2) 125 1.12 PST.06.02 – 03 : DIN 18800 STEEL CODE CHECK (3) 131 1.13 PST.06.02 – 04 : DIN 18800 STEEL CODE CHECK (4) 136 1.14 PST.06.02 – 05 : DIN 18800 STEEL CODE CHECK TUTORIAL FRAME 141 1.15 PST.06.03 – 01 : NEN 6770/6771 STEEL CODE CHECK 156 1.16 PST.06.05 – 01 : AISC STEEL CODE CHECK TUTORIAL FRAME 159 1.17 PST.06.06 – 01 : CM 66 STEEL CODE CHECK TUTORIAL FRAME 176 1.18 PST.06.08 - 01 : SIA161 STEEL CODE CHECK TUTORIAL FRAME 197 1.19 PST.06.09 – 01 : BS5950 STEEL CODE CHECK TUTORIAL FRAME 208 1.20 PST.06.09 – 02 : BS5950 STEEL CODE OF PRACTICE FOR DESIGN 225 1.21 PST.06.10 – 01 : GBJ 17-88 STEEL CODE CHECK TUTORIAL FRAME 233 1.22 PST.06.11 – 01 : KOREAN STEEL CODE CHECK TUTORIAL FRAME 250
2. CONNECTIONS 263
2.1 PST.07.01 – 01 : CALCULATION OF A BASE PLATE 263 2.2 PST.07.01 – 02 : CALCULATION OF A BOLTED CONNECTION 272 2.3 PST.07.01 – 03 : CALCULATION OF A BOLTED CONNECTION 299 2.4 PST.07.01 – 04 : CALCULATION OF A BOLTED CONNECTION 305 2.5 PST.07.01 – 05 : CALCULATION OF WELDED CONNECTIONS 323 2.6 PST.07.01 – 06 : CALCULATION OF REQUIRED STIFFNESS 332 2.7 PST.07.01 - 07: BOLTED CONNECTION WITH COLUMN MINOR AXIS 340 2.8 PST.07.01 - 08: WELDED CONNECTION WITH COLUMN MINOR AXIS 349 2.9 PST.07.01 - 09: BOLTED CONNECTION 356 2.10 PST.07.02 – 01 : FRAME PINNED CONNECTION (PLATE WELDED ON THE WEB) 358 2.11 PST.07.02 – 02 : FRAME PINNED CONNECTION (PLATE BOLTED TO THE WEB) 365 2.12 PST.07.02 – 03 : FRAME PINNED CONNECTION (ANGLES) 378 2.13 PST.07.02 – 04 : FRAME PINNED CONNECTIONS (SHORT ENDPLATE) 391 2.14 PST.07.02 - 05 : FRAME PINNED CONNECTION (ANGLES) WITH COLUMN MINOR AXIS 399
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2.15 PST 07 03 01: HOLLOW SECTION JOINT DESIGN ANNEX K 408 2.16 PST 07 03 02: HOLLOW SECTION JOINT DESIGN ANNEX K 413 2.17 PST 07 03 03: HOLLOW SECTION JOINT DESIGN ANNEX K 418 2.18 PST 07 03 04: HOLLOW SECTION JOINT DESIGN ANNEX K 423 2.19 PST.07.03 -5: KLS TRUSS CONNECTION: WELDSIZE CALCULATION 428 2.20 PST.07.04 – 01 : BOLTED DIAGONAL CONNECTIONS 432
3. TIMBER 449
3.1 PTR.06.01 – 01 : EC 5 TIMBER CODE CHECK 449 3.2 PTR.06.01 – 02 : EC 5 TIMBER CODE CHECK 452 3.3 PTR.06.01 – 03 : EC 5 TIMBER CODE CHECK 455
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The ESA-Prima Win modules :
ESA-Prima Win Engineering Structural Analysis for Windows 95/98/NT/2000 - Rel.3.20 FEM = Finite Element Method
RC = Reinforced Concrete
ESA-Prima Win Base PRS.00 Base:
basic module for each ESA-Prima Win installation, including import/export of projects, libraries (profiles, plates, bolts and materials), document generation, gallery of drawings, rendering, manuals, online help and delivery materials
ESA-Prima Win: Basic Structural Analysis PRS.01 2D Frame :
linear static analysis of plane beam structures with loads in their plane
PRE.01 2D Wall (FEM ext.) : linear static analysis of plane wall structures in plane stress (ext. to PRS.01)
PRS.02 2D Grid : linear static analysis of grid structures with loads perpendicular to their plane
PRE.02 2D Plate (FEM ext.) : linear static analysis of plates with loads perpendicular to their plane (ext. to PRS.02)
PRS.11 3D Frame : linear static analysis of spatial beam structures (incl. funct. PRS.01 + PRS.02)
PRE.11 3D Shell (FEM ext.) : linear static analysis of spatial shells (incl. funct. PRE.01 + PRE.02) (ext. to PRS.11)
ESA-Prima Win: Pre-processors PRE.12 Intersec :
intersection of 2D/1D (shell/beam) and 2D/2D (shell/shell) macros
PRS.13 Graphical section : graphical input of cross-sections with arbitrary shape and different materials, thin-walled sections, DXF import of cross-sections
PRE.31 Influence surfaces : calculation of the influence surface of an internal force, deformation or reaction in plate or shell projects/
PRC.70 Beam : pre-processor for fast input of continuous beams, including predefined loadcases and automatic generation of combinations
PST.07.00 Connect : pre-processor for manual input of internal forces on a connection
ESA-Prima Win: Load generators PRS.62 Plane load :
automatic division of a surface load to the beams
PRE.63 Train load : defining of train loads and positioning on plane surfaces
PRS.65.01 Advanced Wind + Snow (EC 1) : advanced automatic generation of wind and snow on complex structures, according to EC 1
PRS.65.02 Wind + Snow (DIN 1055) : automatic generation of wind and snow loads according to DIN 1055
PRS.65.03 Advanced Wind + Snow + Slab (NEN 6702) : advanced automatic generation of wind, snow and slab loads on complex structures, according to NEN
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6702
PRS.65.07 Wind + Snow (CSN 730035) : automatic generation of wind and snow loads according to CSN 730035
PRS.66 Mobile loads Frame : one user defined group of mobile pointloads on frame structures, calculation of the envelope for the whole structure and the local course in a point of the structure
PRE.66 Mobile loads FEM : one user defined group of mobile pointloads on shell structures, calculation of the envelope for the whole structure (ext. to PRS.66)
PRS.67 Advanced mobile loads Frame : several groups of mobile loads with interference, user defined loadgroup of pointloads and uniformly distributed loads, loadgroups according to different codes
PRE.67 Advanced mobile loads FEM : several groups of mobile loads with interference, user defined loadgroup of pointloads and uniformly distributed loads, loadgroups according to different codes (ext. to PRS.67)
ESA-Prima Win: Advanced Structural Analysis PRS.22 2nd order Frame :
geometrical nonlinear analysis incl. modelling of geometric imperfections (initial deformations and member imperfections), prestressed beams
PRE.22 2nd order FEM : geometrical nonlinear analysis of shell structures, membrane effects (ext. to PRS.22)
PRS.25 Stability Frame : determination of the global buckling mode and buckling load, extraction of critical geometric imperfections, results can be used as input for PRS.22
PRE.25 Stability FEM : determination of the global buckling mode and buckling load (ext. to PRS.25)
PRS.28 Dynamics Frame : definition of eigenfrequencies and eigenmodes for frames
PRS.29 Dynamics Frame (ext.) : harmonic, spectral and time history analysis, seismic loads (ext. to PRS.28)
PRE.28 Dynamics FEM : definition of eigenfrequencies and eigenmodes for shells (ext. to PRS.28)
PRE.29 Dynamics FEM (ext.) : harmonic, spectral and time history analysis, seismic loads (ext. to PRE.28)
PRP.01 Dynamics package : PRS.28 + PRE.28 + PRS.29 + PRE.29
PRS.55 Building phases Frame : calculation of Frame structures in different phases : adding or removing supports, members, loadcases, changing cross section properties in different steps ; the history of internal forces is calculated
PRE.55 Building phases FEM : calculation of FEM structures in different phases : adding or removing supports, members, loadcases, changing cross section properties in different steps ; the history of internal forces is calculated (ext. to PRS.55)
PRS.80 Physical nonlinear conditions : analysis of structures with local physical nonlinearities: members with limited tension/compression, elimination of tension springs, gap elements, nonlinear supports
PRS.81 Physical nonlinear Frame (steel) : analysis of steel structures with plastic hinges (for EC, DIN, NEN)
PRS.82 Physical nonlinear Frame (concrete) : analysis of RC structures with physical nonlinearities: bending, creep (for EC, NEN, DIN, ÖNORM, CSN)
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PRE.82 Physical nonlinear FEM (concrete) : analysis of RC structures with physical nonlinearities: bending, creep (for EC, NEN, DIN, ÔNORM, CSN)
ESA-Prima Win: Steel Design PST.06.01 Steel Code Check (EC 3) :
stress and stability verification of steel members according to EC 3, with profile optimization
PST.06.02 Steel Code Check (DIN 18800) : stress and stability verification of steel members according to DIN 18800, with profile optimization
PST.06.03 Steel Code Check (NEN 6770/6771) : stress and stability verification of steel members according to NEN 6770/6771, with profile optimization
PST.06.04 Steel Code Check (Önorm 4300) : stress and stability verification of steel members according to Önorm 4300, with profile optimization
PST.06.05 Steel Code Check (AISC) : stress and stability verification of steel members according to AISC, with profile optimization
PST.06.06 Steel Code Check (CM 66) : stress and stability verification of steel members according to CM 66, with profile optimization
PST.06.07 Steel Code Check (CSN 731401) : stress and stability verification of steel members according to CSN 731401, with profile optimization
PST.06.08 Steel Code Check (SIA 161) : stress and stability verification of steel memebers according to SIA 161, with profile optimization
PST.06.09 Steel Code Check (BS 5950 - Part 1) : stress and stability verification of steel members according to BS 5950 - Part 1, with profile optimization
PST.06.10 Steel Code Check (CHIN GBJ 17-88) : stress and stability verification of steel members according to CHIN GBJ 17-88, with profile optimization
PST.06.11 Steel Code Check (KOR) : stress and stability verification of steel members according to KOR, with profile optimization
PST.07.01 Connect Frame - Rigid (EC 3 Revised annex J) : design, verification and drawing of bolted and welded steel frame connections according to EC 3 Revised annex J
PST.07.02 Connect Frame - Pinned (EC 3) : design, verification and drawing of hinged steel frame connections according to EC 3
PST.07.03 Truss connections : calculation of welded connections in trusses (tubes, rectangular hollow sections and I sections) acc. To EC 3 and CIDECT
PST.07.04 Bolted Diagonals : calculation of bolted diagonals in steel structures according to Eurocode 3 (bolts, net section)
PST.07.10 Expert system Connect Frame : intelligent selection of a steel frame connection from an extended library with DSTV, SPRINT and user defined connections.
PST.11 Project : general overview drawings for steel structures with annotations, detailed bill of material
ESA-Prima Win: Foundations
PRS.14 Foundation block stability : input of foundation blocks under colums, calculation of the resulting rigidity of the support (optionally in combination with Soilin for input of Ground layers), check of: bearing resistance, sliding and overturning.
PRE.32 Soilin : Iterative analysis of soil-structure interaction : calculation of soil parameters for structures on foundation plates
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ESA-Prima Win: Concrete Design
PRC.71.01 RC Beams & Columns Analysis (EC 2) : reinforcement analysis of concrete beams & columns according to EC 2
PRC.71.02 RC Beams & Columns Analysis (DIN 1045-1) : reinforcement analysis of concrete beams & columns according to DIN 1045-1
PRC.71.03 RC Beams & Columns Analysis (NEN 6720) : reinforcement analysis of concrete beams & columns according to NEN 6720
PRC.71.04 RC Beams & Columns Analysis (Önorm) : reinforcement analysis of concrete beams & columns according tot önorm
PRC.71.07 RC Beams & Columns Analysis (CSN) : reinforcement analysis of concrete beams & columns according to CSN
PRC.71.09 RC Beams & Columns Analysis (BS8110) : reinforcement analysis of concrete beams & columns according to British Standard 8110
PRC.71.10 RC Beams & Columns Analysis (GBJ 10-89) : reinforcement analysis of concrete beams & columns according to the Chinese code GBJ 10-89
PRC.72.01 RC Plates & Shells Analysis (EC 2) : reinforcement analysis of plates & shells according to EC 2
PRC.72.02 RC Plates & Shells Analysis (DIN 1045) : reinforcement design of plates & shells according to DIN 1045
PRC.72.03 RC Plates & Shells Analysis (NEN 6720) : reinforcement design of plates & shells according to NEN 6720
PRC.72.04 RC Plates & Shells Analysis (Önorm) : reinforcement design of plates & shells according to Önorm
PRC.72.07 RC Plates & Shells Analysis (CSN) : reinforcement design of plates & shells according to CSN
PRC.72.08 RC Plates & Shells Analysis (SIA) : reinforcement design of plates & shells according to SIA
PRC.72.09 RC Plates & Shells Analysis (BS8110) : reinforcement design of plates & shells according to British Standard 8110
PRC.72.10 RC Plates & Shells Analysis (GBJ 10-89) : reinforcement design of plates & shells according to the Chinese code GBJ 10-89
PRC.73 RC Beams & Columns Design & Drawings : reinforcement design for concrete beams & columns : conversion from theoretical to practical reinforcement, generation of drawings, generation of bill of material
PRC.74 RC Plates Design & Drawings : reinforcement design for concrete plates : conversion from theoretical to practical reinforcement, generation of drawings, generation of bill of material
PRC.75.01 Punching (Eurocode 2) : punching check for plates according to Eurocode 2
PRC.80 Prestress : calculation of the internal force distribution and time dependent deformation of 2D Frame structures with prestressed elements ; prestressing and poststressing ; calculation of losses (immediate and time-dependent)
ESA-Prima Win: Timber Design PTR.06.01 Timber Code Check (EC 5) :
stress and stability verification of timber members according to Eurocode 5, serviceability check including creep
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INTRODUCTION This verification report contains a series of benchmarks for the design modules of ESA-Prima Win. At least one relevant example of each module is checked and verified with results from the literature, with analytical results or with the result of a manual calculation.
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1. STEEL CODE CHECK 1.1 PST.06.xx – 01 : Calculation of buckling ratios Description Calculation of buckling ratios for columns of simple frames. Project data
Section Moment of inertia
[cm4] IPE240 3890 IPE270 5790 IPE360 16270 IPE400 23130 Reference [1] Eurocode 3 : Design of steel structures
Part 1-1 : General rules and rules for buildings ENV 1993-1-1:1992 Annex E : Buckling length of compression members
[2] G. Hünersen, E. Fritzsche Stahlbau in Beispielen Berechnungspraxis nach DIN 18 800 Teil 1 bis Teil 3 Werner Verlag GmbH & Co. KG – Dusseldorf 1995
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Calculation of buckling ratio according to EC3 – Annex E Stiffness coefficients Beam
K (I/L) [cm³]
1 40.68 2 40.68 3 46.26 4 7.78 5 12.97 6 9.73 7 7.78 8 12.97 9 9.73 10 9.65 11 6.48 12 9.65 Calculation buckling ratio’s with formula (E.7) Beam
Kc K1 K2 K11 K12 K21 K22 ηηηη1 ηηηη2 l/L
1 40.68 0 0 0 46.26 0 0 0.47 1.00 2.47 4 7.78 12.97 0 0 9.65 0 0 0.68 0.00 1.37 5 12.97 9.73 7.78 0 6.48 0 9.65 0.78 0.68 2.06 6 9.73 0 12.97 0 9.65 0 6.48 0.49 0.78 1.81 Result Beam EPW EC3
Annex E % Diff. Ref.[2] % Diff. Remark
1 2.35 2.47 4.86 % 2.30 2.17 % Example 6.6.1. from Ref.[2] 2 2.35 2.47 4.86 % 2.30 2.17 % Example 6.6.1. from Ref.[2] 4 1.21 1.37 11.68 % 1.15 5.22 % Example 6.6.4. from Ref.[2] 5 1.99 2.06 3.40 % 2.03 1.97 % Example 6.6.4. from Ref.[2] 6 1.79 1.81 1.10 % 2.30 22.17 % Example 6.6.4. from Ref.[2] 13 1.00 Standard Euler case: ratio = 1.00 14 2.02 Standard Euler case: ratio = 2.00 Version ESA-Prima Win 3.20.03 Input file + calculation note PST06xx01.epw Modules 2D Frame (PRS.01) EC 3 Steel code check (PST.06.01) Author
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CVL
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1.2 PST.06.xx – 02 : Calculation of buckling ratios for crossing diagonals Description Calculation of buckling ratios of crossing diagonals according to DIN18800 Teil 2, table 15. The buckling check of member 17 is performed. Project data See Input file.
12
34
56
78
9
10
11
12
13
14
15
16
17
18
19
20
The diagonal crossings are introduced by using the input option <Cross-Links>. The column sections are the cold formed RHS section SC140/140/8. The diagonal sections are the cold formed RHS section AC100/80/6. The weak axis of this section is in the calculation plane. Reference [1] DIN18800 Teil 2
Stahlbauten : Stabilitätsfälle, Knicken von Stäben und Stabwerken
See the chapter "Manual calculation" for the detailed calculation according to this reference. Result
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Type of result Manually ESA-Prima Win % Diff Unity check "Buckling check" - No "crossing diagonals"
1.03 1.03 0 %
Unity check "Buckling check" - With "crossing diagonals"
0.82 0.82 0 %
See the chapter "Calculation note" for the detailed output of ESA-Prima Win. Version ESA-Prima Win 3.20.03 Input file PST06xx02.epw Modules 2D Frame (PRS.01) EC3 Steel code check (PST.06.01)
Author CVL Manual calculation 1 For the section AC100/80/6, the following properties are valid : A 2020 mm² Iy 2800000 mm4 Iz 1960000 mm4 iy 37.23 mm iz 31.15 mm fy 235 N/mm² When the option “Crossing diagonals” is not active, the element 17 is considered as a hinged member. strong axis weak axis system length 3610 mm 3610 mm buckling ratio 1.0 1.0 buckling length 3610 mm 3610 mm slenderness 3610/37.23 = 96.9 3610/31.15 = 115.9 reduced slenderness 96.9/93.9 = 1.03 115.9/93.9 = 1.23 imperfection curve for cold formed section
b b
reduction factor 0.58 0.46 In the element, a normal compressive force NSd = 204.7 kN is acting. The capacity for the compressive force Nb,Rd is given by
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( )
kN5.1981.1
23520200.146.0Rd,Nb
fA46.0,58.0minRd,Nb
1M
yA
=⋅
⋅⋅=
γ
⋅⋅β⋅=
The resulting unity check is 204.7/198.5 = 1.03. See also Calculation note 1. Manual calculation 1 When the option “Crossing diagonals” is active, the element 17 is supported by the tension element nr.13. The buckling length sk around the weak axis is given by :
l5.0s
lI
lI1
lN4
lZ31
ls
k
31
31
1k
⋅≥
⋅
⋅+
⋅⋅⋅⋅
−
=
In this case, we have Z 151.6 kN N 204.7 kN l 3610 mm l1 3610 mm I 1960000 mm4 I1 1960000 mm4 This results in :
l5.0s
47.0l2
7.2044
6.15131
ls
k
k
⋅≥
⋅=⋅⋅
−=
strong axis weak axis system length 3610 mm 3610 mm buckling ratio 1.0 0.5 buckling length 3610 mm 1805 mm slenderness 3610/37.23 = 96.9 1805/31.15 = 57.9 reduced slenderness 96.9/93.9 = 1.03 57.9/93.9 = 0.62 imperfection curve for cold formed section
b b
reduction factor 0.58 0.83 In the element, a normal compressive force NSd = 204.7 kN is acting. The capacity for the compressive force Nb,Rd is given by
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( )
kN2501.1
23520200.158.0Rd,Nb
fA83.0,58.0minRd,Nb
1M
yA
=⋅
⋅⋅=
γ
⋅⋅β⋅=
The resulting unity check is 204.7/250 = 0.82. See also Calculation note 2. Calculation note 1
EC3 Code Check
Macro 11 Member 17 AC100/80/6 Fe 360 Loadcase 1 1.16
Basic data EC3
partial safety factor Gamma M0 for resistance of cross-sections 1.10
partial safety factor Gamma M1 for resistance to buckling 1.10
partial safety factor Gamma M2 for resistance of net sections 1.10
Material data
yield strength fy 235.00 MPa
tension strength fu 360.00 MPa
fabrication cold formed
SECTION CHECK
Width-to-thickness ratio for webs (Tab.5.3.1. a).
ratio 10.33 on position 0.00 m
ratio
maximum ratio 1 33.00
maximum ratio 2 38.00
maximum ratio 3 42.00
==> Class cross-section 1
Width-to-thickness ratio for internal flanges (Tab.5.3.1. b).
ratio 13.33 on position 0.00 m
ratio
maximum ratio 1 42.00
maximum ratio 2 42.00
maximum ratio 3 42.00
==> Class cross-section 1
The critical check is on position 1.80 m
Internal forces
NSd -204.78 kN
Vy.Sd 0.00 kN
Vz.Sd 0.60 kN
Mt.Sd -0.00 kNm
My.Sd 1.07 kNm
Mz.Sd 0.00 kNm
Only elastic check
Compression check
according to article 5.4.4. and formula (5.16)
Section classification is 3.
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Table of values
Nc.Rd 431.55 kN
unity check 0.47
Shear check (Vy)
according to article 5.4.6. and formula (5.20)
Section classification is 3.
Table of values
Vpl.Rd 110.73 kN
unity check 0.00
Shear check (Vz)
according to article 5.4.6. and formula (5.20)
Section classification is 3.
Table of values
Vpl.Rd 138.42 kN
unity check 0.00
Combined bending, axial force and shear force check
according to article Part 1-3 5.7 and formula (5.11a,5.11b,5.11c)
Section classification is 3.
Table of values
sigma N 101.38 MPa
sigma Myy 19.18 MPa
sigma Mzz 0.03 MPa
Tau z 0.00 MPa
Tau z 0.00 MPa
Tau t -0.00 MPa
ro 0.00 place 8
unity check 0.56
Element satisfies the section check !
STABILITY CHECK
Buckling parameters yy zz
type non-sway non-sway
Slenderness 96.84 115.75
Reduced slenderness 1.03 1.23
Buckling curve b b
Imperfection 0.34 0.34
Reduction factor 0.58 0.46
Length 3.61 3.61 m
Buckling factor 1.00 1.00
Buckling length 3.61 3.61 m
Critical Euler load 446.43 312.50 kN
Buckling check
according to article 5.5.1. and formula (5.45)
Table of values
Nb.Rd 198.86 kN
Beta A 1.00
unity check 1.03
Torsional-flexural buckling check
according to article ENV 1993-1-3 : 6.2.3 and formula (6.1) (6.4a-b)(6.5a-b)(6.6)
Table of values
Nb.Rd 198.86 kN
Beta A 1.00
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Table of values
Reduced slenderness 1.23
Reduction factor 0.46
sigma,cr,T 54735.22 MPa
sigma,cr,TF 154.70 MPa
Torsional buckling length 3.61 m
unity check 1.03
LTB check
according to article 5.5.2. and formula (5.48)
Table of values
Mb.Rd 11.96 kNm
Beta W 0.82
reduction 1.00
imperfection 0.49
Mcr 385.19 kNm
LTB
LTB length 3.61 m
k 1.00
kw 1.00
C1 1.35
C2 0.55
C3 1.73
load in center of gravity
unity check =0.09
Compression and bending check
according to article 5.5.4. and formula (5.53)
Table of values
ky 1.50
kz 1.50
muy -1.44
muz -1.73
BetaMy 1.30
BetaMz 1.30
unity check = 1.03 + 0.13 + 0.00 = 1.16
Compression, bending and LTB check
according to article 5.5.4. and formula (5.54)
Table of values
klt 0.92
kz 1.50
mult 0.09
muz -1.73
BetaMlt 1.30
BetaMz 1.30
unity check =1.03 + 0.08 + 0.00 = 1.11
Element does NOT satisfy the stability check !
Calculation note 2 EC3 Code Check
Macro 11 Member 17 AC100/80/6 Fe 360 Loadcase 1 0.96
Basic data EC3
partial safety factor Gamma M0 for resistance of cross-sections 1.10
partial safety factor Gamma M1 for resistance to buckling 1.10
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partial safety factor Gamma M2 for resistance of net sections 1.10
Material data
yield strength fy 235.00 MPa
tension strength fu 360.00 MPa
fabrication cold formed
SECTION CHECK
Width-to-thickness ratio for webs (Tab.5.3.1. a).
ratio 10.33 on position 0.00 m
ratio
maximum ratio 1 33.00
maximum ratio 2 38.00
maximum ratio 3 42.00
==> Class cross-section 1
Width-to-thickness ratio for internal flanges (Tab.5.3.1. b).
ratio 13.33 on position 0.00 m
ratio
maximum ratio 1 42.00
maximum ratio 2 42.00
maximum ratio 3 42.00
==> Class cross-section 1
The critical check is on position 1.80 m
Internal forces
NSd -204.78 kN
Vy.Sd 0.00 kN
Vz.Sd 0.60 kN
Mt.Sd -0.00 kNm
My.Sd 1.07 kNm
Mz.Sd 0.00 kNm
Only elastic check
Compression check
according to article 5.4.4. and formula (5.16)
Section classification is 3.
Table of values
Nc.Rd 431.55 kN
unity check 0.47
Shear check (Vy)
according to article 5.4.6. and formula (5.20)
Section classification is 3.
Table of values
Vpl.Rd 110.73 kN
unity check 0.00
Shear check (Vz)
according to article 5.4.6. and formula (5.20)
Section classification is 3.
Table of values
Vpl.Rd 138.42 kN
unity check 0.00
Combined bending, axial force and shear force check
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according to article Part 1-3 5.7 and formula (5.11a,5.11b,5.11c)
Section classification is 3.
Table of values
sigma N 101.38 MPa
sigma Myy 19.18 MPa
sigma Mzz 0.03 MPa
Tau z 0.00 MPa
Tau z 0.00 MPa
Tau t -0.00 MPa
ro 0.00 place 8
unity check 0.56
Element satisfies the section check !
STABILITY CHECK
Buckling parameters yy zz
type non-sway non-sway
Slenderness 96.84 57.87
Reduced slenderness 1.03 0.62
Buckling curve b b
Imperfection 0.34 0.34
Reduction factor 0.58 0.83
Length 3.61 3.61 m
Buckling factor 1.00 0.50
Buckling length 3.61 1.80 m
Critical Euler load 446.43 1249.95 kN
Remark : The buckling data around the weak axis are calculated
according to DIN 18800 T2 Tab.15 (case 1)
Table of values
Z 151.61 kN
L 3.61 m
L1 3.61 m
I 1.960000e+006 mm^4
I1 2.800000e+006 mm^4
Buckling check
according to article 5.5.1. and formula (5.45)
Table of values
Nb.Rd 249.16 kN
Beta A 1.00
unity check 0.82
Torsional-flexural buckling check
according to article ENV 1993-1-3 : 6.2.3 and formula (6.1) (6.4a-b)(6.5a-b)(6.6)
Table of values
Nb.Rd 249.16 kN
Beta A 1.00
Reduced slenderness 1.03
Reduction factor 0.58
sigma,cr,T 54735.22 MPa
sigma,cr,TF 221.01 MPa
Torsional buckling length 3.61 m
unity check 0.82
LTB check
according to article 5.5.2. and formula (5.48)
Table of values
Mb.Rd 11.96 kNm
Beta W 0.82
reduction 1.00
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Table of values
imperfection 0.49
Mcr 385.19 kNm
LTB
LTB length 3.61 m
k 1.00
kw 1.00
C1 1.35
C2 0.55
C3 1.73
load in center of gravity
unity check =0.09
Compression and bending check
according to article 5.5.4. and formula (5.53)
Table of values
ky 1.50
kz 1.45
muy -1.44
muz -0.86
BetaMy 1.30
BetaMz 1.30
unity check = 0.82 + 0.13 + 0.00 = 0.96
Compression, bending and LTB check
according to article 5.5.4. and formula (5.54)
Table of values
klt 1.00
kz 1.45
mult -0.03
muz -0.86
BetaMlt 1.30
BetaMz 1.30
unity check =0.82 + 0.09 + 0.00 = 0.91
Element satisfies the stability check !
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1.3 PST.06.01 – 01 : EC 3 Steel Code Check Tutorial Frame Description The unity check according to EC3 of members 4, 7 and macro 18 of the Tutorial Frame project are calculated manually. The result is compared with the result of ESA-Prima Win EC3 Steel code check. Project data See input file. Reference [1] Eurocode 3
Design of steel structures Part 1-1 : General rules and rules for buildings ENV 1993-1-1:1992
[2] Essentials of Eurocode 3 Design manual for Steel Structures in Building First edition 1991
[3] Construction Métallique et mixte acier-béton Volume 1 APK Edition Eyrolle
See the chapter "Manual calculation" for the detailed calculation according to this reference. Result
Type of result Manually ESA-Prima Win % Diff Max. unity check Member 4
0.63 0.63 0 %
Max. unity check Member 7
0.28 0.28 0 %
Max. unity check Macro 18
0.557 0.56 0 %
See the chapter "Calculation note" for the detailed output of ESA-Prima Win. Version ESA-Prima Win 3.20.03 Input file + calculation note PST060101.epw Modules 3D Frame (PRS.11) EC3 Steel code check (PST.06.01)
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Author CVL Manual calculation - Member 4 Critical check : Load Combination : 7 Section : x = 2.22 m in member 4 Beam type : HEB160
Steel : σe=235 2mmN
System length L : system length for member 4: Ly=Lz=5m Sway modes : Y-Y non-sway Z-Z non-sway The member is loaded through the shear centre. The effective length factors k and kw for LTB are taken as 1 (No end fixity and no special provision for warping fixity). Section Check Classification of the section (Table 5.3.1 EC3)
a) Width-to-thickness ratio for webs
By using Art. 3.2.2.1 (1)table 3.1. of EC3, we can determine the yield strength fy:
• Normal steel grade: Fe 360 • Nominal thickness of the element t ≤ 40 mm ⇒ Nominal value of yield strength: fy=235 N/mm2
⇒ 1f
235
y
=
=ε (Using Table 5.3.1. EC3)
The web of member is subjected to bending and compression in position x=0m. By using table 5.3.1.a of EC3, we find:
( )68
113
396138
104t
dw
=−α⋅ε⋅
≤== with 52.0ftd
N1
2
1
yw
Sd =
⋅⋅+⋅=α ⇒ WEB is CLASS 1
b) Width-to-thickness ratio for outstand flanges
By using table 5.3.1.c of EC3, we find in position x=0m:
101015.61380
tc
f=ε⋅≤== ⇒ FLANGES are CLASSE 1
The section HEB160 is a CLASS-1 section for the stability check, following the EC3 rules. Normal stress and shear stress (Art. 5.4.3.and 5.4.6. EC3)
The member 4 is subjected to a normal force NSd=-88700 N and a shear force VSd,y=20 N VSd,z=-2130N in the critical section. According to EC3 we can verify:
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N45.11600451.1
2351043.5fAN8870N
3
0M
yRd,cSd =
⋅⋅=
γ
⋅=≤−=
( ) 2ffy,v mm4598tr2t2hAtdAA =⋅⋅−⋅−−=⋅−= (Using Art.5.4.6. (2).d EC3)
( ) 2fwfz,v mm1764tr2ttb2AA =⋅⋅++⋅⋅−= (Using Art.5.4.6. (2).a EC3)
N16.56713131.1
2354598
3
fAV20V
0M
yvRd,ply,Sd =
⋅
⋅=
⋅γ
⋅=≤=
N07.21757731.1
2351764
3
fAV2130V
0M
yvRd,plz,Sd =
⋅
⋅=
⋅γ
⋅=≤−=
Unity Check : 101.0V
V and 101.0
N
N
RdPl,
z&ySd,
Rd,t
Sd ≤=≤= ⇒ Section OK for tension and shear
Combined bending, axial force and shear force
By using Art.5.4.7. (1), 5.4.8.1. (4), 5.4.9. (2) and 5.4.5.2. (1) of EC3 and table 5.17 of Essentials of EC3, we determined: NSd≤0.25Nt,Rd: low level of axial loads (Essentially by using Table 5.17 of Essential of EC3) VSd≤0.5Vpl,Rd: MNvy,Rd=My,Rd and MNVz,Rd=Mz,Rd (Essentially by using Table 5.17 of Essential of EC3)
with Nmm72.756272721.1
2351054.3fWM
5
0M
yRd,plPl,y
y =⋅⋅
=γ
⋅= (Using Art. 5.4.5.2. (1) EC3)
Nmm818.363181811.1
235107.1fWM
5
0M
yRd,plPl,z
z =⋅⋅
=γ
⋅= (Using Art. 5.4.5.2. (1) EC3)
We verify: 129.0M
M
M
M
Rd,NV
Sd,z
Rd,NV
Sd,y
zy
≤=
+
βα
(Using Art.5.4.8.1.(11) formula 5.35 EC3)
with: α=2 and β=1 for I section (Using Art. 5.4.8.1. (11) EC3) My,Sd=40650000 Nmm Mz,Sd=--600000 Nmm Stability Check: Check for bending, compression and LTB Calculation of Reduction factor in buckling mode: χy, χz, kLT
Reduction factors in buckling mode: 733.01
22yy
y
y
=λ−φ+φ
=χ (Using Art.5.5.1.2. Formula 5.46 EC3)
382.01
22zz
z
z
=λ−φ+φ
=χ (Using Art.5.5.1.2. Formula 5.46 EC3)
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with: • 1=ε (Using Art.5.5.1.2. EC3)
• 9.939.93f
E
y1 =ε⋅=⋅π=λ (Using Art.5.5.1.2. EC3)
• Slenderness: 836.73
AI
L
i
L
yyy ===λ (Using Art.5.5.1.2. (1) EC3)
571.123
AI
L
i
L
zzz ===λ (Using Art.5.5.1.2. (1) EC3)
• Section 1 CLASS 1A =β (Using Art.5.5.1.1. (1) EC3)
• To determine the equivalent uniform moment factor βy, βz and βMLT, we use the figure 5.5.3. in EC3 of EC3and the
moment diagram of member 4 around y and z axis between the relevant braced point. Since de moment diagram is parabolic around y axis and linear around z axis, we have:
Internal forces.Selected members : 4
0.0
Member : 4
5.0
My /kNm/
0.0
10.0
20.0
30.0
40.0
0.0
10.0
20.0
30.0
40.0
40.7
-0.1
βM,ψ=1.8 (ψ=0) βM,Q=1.3 MQmax=27.7 kNm ∆M=40.5 kNm
( ) 46.1M
M,MQ,M
Q,MMLT =β−β⋅
∆+β=β ΨΨ
46.1MLTMy =β=β
8.17.08.1Mz =Ψ⋅−=β
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• Reduced Slenderness: 786.0N
fAA
1
y
cr
yAy =β⋅
λ
λ=
⋅⋅β=λ (Using Art.5.5.1.2. (1) EC3)
315.1N
fAA
1
z
cr
yAz =β⋅
λ
λ=
⋅⋅β=λ (Using Art.5.5.1.2. (1) EC3)
• ( ) 578.0W
WW42
y,el
y,ely,plMyyy −=
−+−β⋅⋅λ=µ (Using Art.5.5.4. (1) EC3 for Class 1 section)
( ) 006.0W
WW42
z,el
z,elz,plMzzz =
−+−β⋅⋅λ=µ (Using Art.5.5.4. (1) EC3 for Class 1 section)
• 14.015.015.0 MLTzLT =−β⋅λ⋅=µ (Using Art.5.5.4. (2) EC3)
• 01.1fA
N1k
yy
Sdy
y=
⋅⋅χ
⋅µ−= (Using Art.5.5.4. (1) EC3 for Class 1 section)
0.1fA
N1k
yz
Sdz
z=
⋅⋅χ⋅µ
−= (Using Art.5.5.4. (1) EC3 for Class 1 section)
• 0.1fA
N1k
yz
SdLTLT =
⋅⋅χ
⋅µ−= (Using Art.5.5.4. (2) EC3)
• Buckling Curve “b” around y axis and “c” around z axis (table 5.5.3. EC3)
• By 5.5.1.2. (2) EC3, we find the imperfections factor: 49.0 34.0 zy =α=α
• ( )( ) 908.02.015.0 2yyyy =λ+−λ⋅α+⋅=φ (Using Art. 5.5.1.2. (1) EC3)
( )( ) 637.12.015.0 2zzzz =λ+−λ⋅α+⋅=φ (Using Art. 5.5.1.2. (1) EC3)
Calculation of Reduction factor in lateral-torsional buckling mode: χLT
Reduction factor for lateral torsional buckling: 89.01
2LT
2LTLT
LT =λ−φ+φ
=χ (Art.5.5.2. (2) EC3)
with : ( )( ) 7213.02.015.0 2LTLTLTLT =λ+−λ⋅α+⋅=φ (Art.5.5.2. (2) EC3) In this expression:
Imperfection for lateral –torsional buckling: αLT=0.21 for rolled section (Art.5.5.2.(3) EC3)
245.56
th
iL
20
11C
iL9.0
25.02
f
z1
zLT =
⋅+⋅
⋅=λ (Annexe F.2. (6) Formula F.26)
where: 57.123iL
y=
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3.12th
f= and 59.1C1 = (using Annexe F table F1.2. with k=1)
598.0M
fWw
1
5.0
cr
yy,plwLT
LT =β⋅λ
λ=
⋅⋅β=λ (Using Art.5.5.2.(5) EC3)
where: βw=1 (CLASS_1 Section) (Using Art.5.5.2. (1) EC3)
Buckling Check
The design buckling resistance of member 47, using article 5.5.1.1. (1) Formula 5.45 of EC3, is:
N36.443137fA
N8870N1M
yAminRd,bSd =
γ
⋅⋅β⋅χ=≤=
Unity Check: 102.0N
N
Rd,b
Sd ≤= ⇒Section OK for buckling due to compression
Compression and bending
The design buckling resistance moment of member 47, using article 5.5.2. of EC3, is :
Nmm72.67308272fW
M1M
yy,plwLTRd,b =
γ
⋅⋅β⋅χ=
with 1w =β for class-1 section
Unity Check : 161.0M
M
Rd,b
Sd ≤= ⇒Section OK for lateral-torsional buckling
Combined Compression and bending
The internal forces for the ultimate combination 7 in the critical section x=2.22m of member 4 are: NSd=-8.87 kN Vy,Sd=0.02 kN Vz,Sd=-2.13 kN My,Sd=40.65 kNm Mz,Sd=-0.06 kNm We consider that Vy,Sd 0 precision to be neglected. Normally we should perform a check for bending and axial tension according to article 5.5.3. of EC3 but the program doesn’t take account for the beneficial effect of the tension forces. Using article 5.5.4. and formula 5.52 of EC3, we must verify:
OK 156.00.054.002.0
1f
W
Mk
fW
Mk
fA
N
1M
yz.pl
sd.zz
1M
yy.pl
sd.yy
1M
ymin
sd
⇒≤=++
≤
γ⋅⋅+
γ⋅⋅+
γ⋅⋅χ
(Using Art.5.5.4. (1) EC3)
Combined Compression, bending and LTB
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We can perform exactly the same check than previously but considering lateral-torsional buckling as a potential failure mode by using Art.5.5.4. (2) formula 5.52 of EC3:
OK 163.00.061.002.0
1f
W
Mk
fW
Mk
fA
N
1M
yz.pl
sd.zz
1M
yy.plLT
sd.yLT
1M
yz
sd
⇒≤=++
≤
γ⋅⋅+
γ⋅⋅χ⋅+
γ⋅⋅χ
(Using Art.5.5.4. (2) EC3)
Manual calculation - Member 7 Critical check : Load Combination : 5 Section : x = 3 m Beam type : IPE270
Steel : σe=235 2mmN
Beam length : 6 m Sway modes : Y-Y non-sway Z-Z non-sway The member is loaded through the shear centre. The effective length factors k and kw for LTB. are taken as 1 (No end fixity and no special provision for warping fixity). Section check Classification of the section (Table 5.3.1 EC3)
a) Width-to-thickness ratio for webs
By using Art. 3.2.2.1. (1) table 3.1. of EC3, we can determine the yield strength fy:
• Normal steel grade: Fe 360 • Nominal thickness of the element t ≤ 40 mm ⇒ Nominal value of yield strength: fy=235 N/mm2
⇒ 1f
235
y
=
=ε (Using Table 5.3.1. EC3)
The web of member 7 is subjected both to bending and tension in section x=0.55 m. By using table 5.3.1.a of EC3, we find:
( )95.71
113
39627.336.6
6.219t
dw
=−α⋅ε⋅
≤== where 5.0ftd
N1
2
1
yw
Sd =
⋅⋅+⋅=α ⇒ WEB is CLASSE 1
b) Width-to-thickness ratio for outstand flanges
By using table 5.3.1.c of EC3, we find for section x=0 m:
1062.62.105.67
tc
f≤== ⇒ FLANGES are CLASSE 1
The IPE 270 section is a CLASS-1 section for the stability check.
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Combined bending, axial force and shear force
By using Art. 5.4.7. (1), 5.4.8. (4), 5.4.9. (2) and 5.4.5.2. (1) of EC3 and table 5.17 of Essentials of EC3, we determined : NSd≤0.25Nt,Rd: low level of axial load VSd≤0.5Vpl,Rd: MNvy,Rd=My,Rd and MNVz,Rd=Mz,Rd (essentially by using Table 5.17 of Essential of EC3)
with Nmm1034000001.1
2351084.4fWM
5
0M
yRd,plPl,y
y =⋅⋅
=γ
⋅= (Using Art. 5.4.5.2. (1) EC3)
Nmm27.207227271.1
235107.9fWM
4
0M
yRd,plPl,z
z =⋅⋅
=γ
⋅= (Using Art. 5.4.5.2. (1) EC3)
We verify: 102.0M
M
M
M
Rd,NV
Sd,z
Rd,NV
Sd,y
zy
≤=
+
βα
(Using 5.4.8.1. (11) formula 5.35 EC3)
with: α=2 and β=1 for I section (Using Art. 5.4.8.1. (11) EC3) My,Sd=14338660Nmm Mz,Sd≈0 Stability Check: Check for bending, compression and L.T.B. Calculation of Reduction factor in buckling mode: χy, χz, kLT
Reduction factor in buckling mode: 902.01
2y
2yy
y =λ−φ+φ
=χ (Using Art.5.5.1.2. Formula 5.46 EC3)
1903.01
22zz
z
z
=λ−φ+φ
=χ (Using Art.5.5.1.2. Formula5.46 EC3)
with : • 1=ε (Using Art.5.5.1.2. EC3)
• 9.939.93f
E
y1 =ε⋅=⋅π=λ (Using Art.5.5.1.2. EC3)
• Slenderness : 42.53
AI
L
i
L
yyy ===λ (Using Art.5.5.1.2. (1) EC3)
35.198
AI
L
i
L
zzz ===λ (Using Art.5.5.1.2. (1) EC3)
• Section 1 CLASS 1A =β (Using Art.5.5.1.1. (1) EC3)
• To determine the equivalent uniform factors βy, βz and βMLT, we use the figure 5.5.3. of EC3 and the moment
diagram of member 7 around y and z axis between the relevant braced point. Since the moment is have a parabolic shape around y axis and is linear around z axis, we have:
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3.1y =β
8.1z =β
3.1MLT =β (Figure 5.5.3.)
• Reduced slenderness : 568.0N
fAA
1
y
cr
yAy =β⋅
λ
λ=
⋅⋅β=λ (Using Art.5.5.1.2. (1) EC3)
11.2N
fAA
1
z
cr
yAz =β⋅
λ
λ=
⋅⋅β=λ (Using Art.5.5.1.2. (1) EC3)
• Buckling Curve “a” around y axis and “b” around z axis (Table 5.5.3. EC3)
• ( ) 666.0W
WW42
y,el
y,ely,plMyyy −=
−+−β⋅⋅λ=µ (Using Art.5.5.4. (1) EC3 for Class 1 section)
( ) 126.0W
WW42
z,el
z,elz,plMzzz −=
−+−β⋅⋅λ=µ (Using Art.5.5.4. (1) EC3 for Class 1 section)
• 2614.015.015.0 MLTzLT =−β⋅λ⋅=µ (Using Art.5.5.4. (1) EC3)
• 99.0fA
N1k
yy
Sdy
y=
⋅⋅χ
⋅µ−= (Using Art.5.5.4. (1) EC3 for Class 1 section)
99.0fA
N1k
yz
Sdz
z=
⋅⋅χ⋅µ
−= (Using Art.5.5.4. (1) EC3 for Class 1 section)
999.0fA
N1k
yz
SdLTLT =
⋅⋅χ
⋅µ−= (Using Art.5.5.4. (2) EC3)
• By using 5.5.1.2. (2) EC3, we find : 34.0 21.0 zy =α=α
• ( )( ) 699.02.015.0 2yyyy =λ+−λ⋅α+⋅=φ (Using Art. 5.5.1.2. (1) EC3)
( )( ) 05.32.015.0 2zzzz =λ+−λ⋅α+⋅=φ (Using Art. 5.5.1.2. (1) EC3)
Calculation of Reduction factor in lateral-torsional buckling mode: χLT
Reduction factor for lateral-torsional buckling: 48.01
2LT
2LTLT
LT =λ−φ+φ
=χ (Art.5.5.2. (2) EC3)
with: ( )( ) 431.12.015.0 2LTLTLTLT =λ+−λ⋅α+⋅=φ (Art.5.5.2. (2) EC3) In this expression:
Imperfection for lateral-torsional buckling:αLT=0.21 for rolled section (Art.5.5.2. (3) EC3)
163.120
th
iL
20
11C
iL9.0
25.02
f
z1
zLT =
⋅+⋅
⋅=λ (Annexe F.2. (6) Formula F.26)
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where: 35.198iL
y=
5.26th
f= and 132.1C1 = (using Annexe F table F1.2. with k=1)
279.1M
fWw
1
5.0
cr
yy,plwLT
LT =β⋅λ
λ=
⋅⋅β=λ (Using Art.5.5.2.(5) EC3)
where: βw=1 (CLASS_1 Section) (Using Art.5.5.2. (1) EC3) Buckling
To improve the security of the stability check, we consider that NSd=0 since the element is in tension and not in compression. The first term of is thus equal to 0. Compression and bending
The design buckling resistance moment of member 47, using article 5.5.2. of EC3, is:
Nmm49632000fW
M1M
yy,plwLTRd,b =
γ
⋅⋅β⋅χ=
with 1w =β for class-1 section
Unity Check : 1286.0M
M
Rd,b
Sd ≤= ⇒Section OK for lateral-torsional buckling
Combined Compression and bending
The internal forces for the ultimate combination 4 in the critical section x=3 m are: NSd=199.38N Vz,Sd=2250.05N My,Sd=14338660Nmm We consider that Vy,Sd and Mz,Sd approach the 0 precision to be neglected. Normally we should perform a check for bending and axial tension according to article 5.5.3. of EC3 but the program doesn’t take account for the beneficial effect of the tension forces. Using article 5.5.4. and formula 5.52 of EC3, we must verify:
OK 1137.00.0137.00.0
1f
W
Mk
fW
Mk
fA
N
1M
yz.pl
sd.zz
1M
yy.pl
sd.yy
1M
ymin
sd
⇒≤=++
≤
γ⋅⋅+
γ⋅⋅+
γ⋅⋅χ
(Using Art.5.5.4. (1) EC3)
Combined Compression, bending and LTB
We can perform exactly the same check than previously but considering lateral-torsional buckling as a potential failure mode by using Art.5.5.4. (2) formula 5.52 of EC3:
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OK 1286.00.0286.00.0
1f
W
Mk
fW
Mk
fA
N
1M
yz.pl
sd.zz
1M
yy.plLT
sd.yLT
1M
yz
sd
⇒≤=++
≤
γ⋅⋅+
γ⋅⋅χ⋅+
γ⋅⋅χ
(Using Art.5.5.4. (2) EC3)
Manual calculation - Macro 18 Critical check : Load Combination : 6 Section : x = 0 m in member 47 Beam type : T120/120/13
Steel : σe=235 2mmN
System length L : macro 18 is made of member 41 to 52 System length for member 41 to 52:
• Ly=1 m(member length) • Lz=6 m(Lateral restraint by middle-rafter) • LLTB=6 m(Lateral restraint by middle-rafter)
Sway modes: Y-Y non-sway Z-Z non-sway The macro is loaded through the shear centre. The effective length factors k and kw for LTB are taken as 1 (No end fixity and no special provision for warping fixity). Section check Classification of the section (Table 5.3.1 EC3)
Since EC3 Table 5.3.1 gives no formulas for T-section, we have to classify the T-section as a Class-3 section. This simplification is also done is the program. Normal stress and shear stress (Art. 5.4.3.and 5.4.6. EC3)
The member 47, the critical member of macro 18, is subjected to a normal force NSd=-38333N and shear forces VSd,y=-1.39N (can be neglected) VSd,z=-461.01N in the critical section. According to EC3 we can verify:
N63.6323631.1
2351096.2fAN38333N
3
0M
yRd,cSd =
⋅⋅=
γ
⋅=≤−=
098.19241531.1
23513120
3
fAV0V
0M
yvRd,ply,Sd =
⋅
⋅⋅=
⋅γ
⋅=≤≅
( )N12.17157013
31.1
2351313120
3
fAV01.461V
0M
yvRd,plz,Sd =⋅
⋅
⋅⋅−=
⋅γ
⋅=≤−=
Unity Check : 10.0V
V and 10604.0
N
N
RdPl,
z&ySd,
Rd,t
Sd ≤≅≤= ⇒ Section OK for tension and shear
Combined bending, axial force and shear force
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By using EC3 Part 1-3 Art. 5.7. we can verify that the Von Mises criteria is respected. To simplify the checking, we’ll consider only stress due to compression and due to bending:
63.213f
238.2628.1395.12
65.851066.3
27.569800
1096.2
72.38265
vI
M
A
N
0M
y
63
max
y
ySdMN y
=γ
≤=+=⋅
+⋅
=+=σ+σ
Stability Check : Check for bending, compression and L.T.B. Calculation of Reduction factor in buckling mode: χy, χz, kLT
To calculate the first and the second term, we have:
Reduction factors in buckling mode: 948.01
22yy
y
y
=λ−φ+φ
=χ (Using Art.5.5.1.2. Formula 5.46 EC3)
123.01
22zz
z
z
=λ−φ+φ
=χ (Using Art.5.5.1.2. Formula 5.46 EC3)
with: • 1=ε (Using Art.5.5.1.2. EC3)
• 9.939.93f
E
y1 =ε⋅=⋅π=λ (Using Art.5.5.1.2. EC3)
• Slenderness: 438.28
AI
L
i
L
y
y
yy ===λ (Using Article 5.5.1.2. (1) EC3)
673.244
AI
L
i
L
z
z
zz ===λ (Using Article 5.5.1.2. (1) EC3)
• Section 3 CLASS 1A =β (Using Article 5.5.1.1. (1) EC3)
• To determine the equivalent uniform moment factors βy βz and βML, we use the figure 5.5.3. of EC3 and the moment
diagram of member 47 around y and z axis between the relevant braced point. Since the moment diagram is linear, we have:
4.1
8.1M
M7.08.17.08.1
859.13.569800
6.480557.08.1
,M
,M7.08.17.08.1
MLT
47BeginMem,z
47EndMem,zMz
47BeginMemy
47EndMemyMy
=β
=
⋅−=Ψ⋅−=β
=
−⋅−=
⋅−=Ψ⋅−=β
• Reduce Slenderness: 302.0N
fAA
1
y
cr
yAy =β⋅
λ
λ=
⋅⋅β=λ (Using Art. 5.5.1.2. (1) EC3)
605.2N
fAA
1
z
cr
yAz =β⋅
λ
λ=
⋅⋅β=λ (Using Art. 5.5.1.2. (1) EC3)
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• ( ) 0851.042 Myyy −=−β⋅⋅λ=µ (Using Art. 5.5.4. (3) EC3 for Class 3 section)
( ) 042.142 Mzzz −=−β⋅⋅λ=µ (Using Art 5.5.4. (3) EC3 for Class 3 section)
• 397.015.015.0 MLTzLT =−β⋅λ⋅=µ (Using Art 5.5.4. (2) EC3 for Class 3 section)
• 004.1fA
N1k
yy
Sdyy =
⋅⋅χ
⋅µ−= (Using Art. 5.5.4. (1&3) EC3 for Class 3 section)
466.1fA
N1k
yz
Sdzz =
⋅⋅χ
⋅µ−= (Using Art. 5.5.4. (1&3) EC3 for Class 3 section)
• 822.0fA
N1k
yz
SdLTLT =
⋅⋅χ
⋅µ−= (Using Art. 5.5.4. (2) EC3 for Class 3 section)
• Buckling Curve “c” (table 5.5.3. EC3)
• By Article 5.5.1.2. (2) Table 5.5.1. of EC3, we find the imperfections factor: 49.0=α
• ( )( ) 57.02.015.0 2yyy =λ+−λ⋅α+⋅=φ (Using Art. 5.5.1.2.(1) EC3)
( )( ) 482.42.015.0 2zzz =λ+−λ⋅α+⋅=φ (Using Art. 5.5.1.2.(1) EC3)
Calculation of Reduction factor in lateral-torsional buckling mode: χLT
Reduction factor for lateral torsional buckling: 923.01
2LT
2LTLT
LT =λ−φ+φ
=χ (Art.5.5.2.(2) EC3)
with : ( )( ) 658.02.015.0 2LTLTLTLT =λ+−λ⋅α+⋅=φ (Art. 5.5.2. (2) EC3) In this expression:
Imperfection for lateral–torsional buckling: αLT=0.21 for rolled section (Art. 5.5.2.(3) EC3)
88.1C1 = (using Annexe F1.2. (6) with k=1 and Table F1.1.)
Iw=0 for T section
Nmm49.38919458IE
IGL
I
I
L
IEM
5.0
z2
t2LTB
z
w2LTB
z2
cr =
⋅⋅π
⋅⋅+⋅
⋅⋅π= (Using Annexe F F1.1.(1) Formula F.1 EC3)
5035.0M
fW5.0
cr
yy,plwLT =
⋅⋅β=λ (Using Art.5.5.2.(5) EC3)
where: βw= 443.0W
W
y,pl
y,el= (CLASS_3 Section) (Art. 5.5.2. (1) EC3)
Buckling Check
The design buckling resistance of member 47, using article 5.5.1.1. of EC3, is:
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N727.77780fA
N72.38265N1M
yAminRd,bSd =
γ
⋅⋅β⋅χ=≤=
Unity Check : 1491.0N
N
Rd,b
Sd ≤= ⇒ Section OK for buckling due to compression
Lateral torsional buckling check
The design buckling resistance moment of member 47, using article 5.5.2. of EC3, is:
Nmm811.8282571fW
M1M
yy,plwLTRd,b =
γ
⋅⋅β⋅χ=
with 443.0W
W
y,pl
y,elw ==β for class-3 section
Unity Check : 10775.0M
M
Rd,b
Sd ≤= ⇒ Section OK for lateral torsional buckling
Combined Compression and bending
The internal forces for the ultimate combination 6 in the critical section x=0 m of member 47 are: NSd=-38265.72N Vy,Sd=-1.39 Vz,Sd=-461.01N My,Sd=569800.27Nmm Mz,Sd=-9409.25Nmm Normally we should perform a check for bending and axial tension according to article 5.5.3. of EC3 but the program doesn’t take account for the beneficial effect of the tension forces. To perform the combined compression and bending check, we must verify:
OK 1 0.5570.0021 0.063 4919.0
1f
W
Mk
fW
Mk
fA
N
1M
yz.el
sd.zz
1M
yy.el
sd.yy
1M
ymin
sd
⇒≤=++
≤
γ⋅⋅+
γ⋅⋅+
γ⋅⋅χ
(Using Art. 5.5.4. (3) EC3)
Combined compression, bending and LTB
We can perform exactly the same check than previously but considering lateral-torsional buckling as a potential failure mode by using Art. 5.5.4. (4) formula 5.54:
OK 1 0.550.0021 0.056 4919.0
1f
W
Mk
fW
Mk
fA
N
1M
yz.el
sd.zz
1M
yy.elLT
sd.yLT
1M
yz
sd
⇒≤=++
≤
γ⋅⋅+
γ⋅⋅χ⋅+
γ⋅⋅χ
(Using Art. 5.5.4. (4) EC3)
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Calculation note - Member 4
EC3 Code Check
Macro 2 Member 4 HEB160 S 235 Ult. comb 7 0.63
Basic data EC3
partial safety factor Gamma M0 for resistance of cross-sections 1.10
partial safety factor Gamma M1 for resistance to buckling 1.10
partial safety factor Gamma M2 for resistance of net sections 1.10
Material data
yield strength fy 235.00 MPa
tension strength fu 360.00 MPa
fabrication rolled
SECTION CHECK
Width-to-thickness ratio for webs (Tab.5.3.1. a).
ratio 13.00 on position 0.00 m
ratio
maximum ratio 1 67.84
maximum ratio 2 78.12
maximum ratio 3 115.22
==> Class cross-section 1
Width-to-thickness ratio for outstand flanges (Tab.5.3.1. c).
ratio 6.15 on position 0.00 m
ratio
maximum ratio 1 10.00
maximum ratio 2 11.00
maximum ratio 3 15.11
==> Class cross-section 1
The critical check is on position 2.22 m
Internal forces
NSd -8.87 kN
Vy.Sd 0.02 kN
Vz.Sd -2.13 kN
Mt.Sd -0.00 kNm
My.Sd 40.65 kNm
Mz.Sd -0.06 kNm
Compression check
according to article 5.4.4. and formula (5.16)
Section classification is 1.
Table of values
Nc.Rd 1160.05 kN
unity check 0.01
Shear check (Vy)
according to article 5.4.6. and formula (5.20)
Section classification is 1.
Table of values
Vpl.Rd 567.13 kN
unity check 0.00
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Shear check (Vz)
according to article 5.4.6. and formula (5.20)
Section classification is 1.
Table of values
Vpl.Rd 217.58 kN
unity check 0.01
Combined bending, axial force and shear force check
according to article 5.4.9. and formula (5.35)
Section classification is 1.
Table of values
MNVy.Rd 75.63 kNm
MNVz.Rd 36.32 kNm
alfa 2.00 beta 1.00
unity check 0.29
Element satisfies the section check !
STABILITY CHECK
Buckling parameters yy zz
type sway non-sway
Slenderness 73.84 123.57
Reduced slenderness 0.79 1.32
Buckling curve b c
Imperfection 0.34 0.49
Reduction factor 0.73 0.38
Length 5.00 5.00 m
Buckling factor 1.00 1.00
Buckling length 5.00 5.00 m
Critical Euler load 2064.33 737.02 kN
Buckling check
according to article 5.5.1. and formula (5.45)
Table of values
Nb.Rd 443.38 kN
Beta A 1.00
unity check 0.02
Torsional-flexural buckling check
according to article ENV 1993-1-3 : 6.2.3 and formula (6.1) (6.4a-b)(6.5a-b)(6.6)
Table of values
Nb.Rd 486.45 kN
Beta A 1.00
Reduced slenderness 1.32
Reduction factor 0.42
sigma,cr,T 868.53 MPa
sigma,cr,TF 135.73 MPa
Torsional buckling length 5.00 m
unity check 0.02
LTB check
according to article 5.5.2. and formula (5.48)
Table of values
Mb.Rd 66.72 kNm
Beta W 1.00
reduction 0.88
imperfection 0.21
Mcr 216.35 kNm
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LTB
LTB length 5.00 m
k 1.00
kw 1.00
C1 1.47
C2 0.25
C3 2.64
load in center of gravity
unity check =0.61
Compression and bending check
according to article 5.5.4. and formula (5.51)
Table of values
ky 1.01
kz 1.00
muy -0.71
muz 0.01
BetaMy 1.46
BetaMz 1.80
unity check = 0.02 + 0.54 + 0.00 = 0.56
Compression, bending and LTB check
according to article 5.5.4. and formula (5.52)
Table of values
klt 1.00
kz 1.00
mult 0.14
muz 0.01
BetaMlt 1.46
BetaMz 1.80
unity check =0.02 + 0.61 + 0.00 = 0.63
Element satisfies the stability check !
Calculation note - Member 7
Macro 4 Member 7 IPE270 S 235 Ult. comb 5 0.28
Basic data EC3
partial safety factor Gamma M0 for resistance of cross-sections 1.10
partial safety factor Gamma M1 for resistance to buckling 1.10
partial safety factor Gamma M2 for resistance of net sections 1.10
Material data
yield strength fy 235.00 MPa
tension strength fu 360.00 MPa
fabrication rolled
SECTION CHECK
Width-to-thickness ratio for webs (Tab.5.3.1. a).
ratio 33.27 on position 0.55 m
ratio
maximum ratio 1 71.95
maximum ratio 2 82.85
maximum ratio 3 124.00
==> Class cross-section 1
Width-to-thickness ratio for outstand flanges (Tab.5.3.1. c).
ratio 6.62 on position 0.55 m
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ratio
maximum ratio 1 10.00
maximum ratio 2 11.00
maximum ratio 3 15.08
==> Class cross-section 1
The critical check is on position 3.00 m
Internal forces
NSd 0.20 kN
Vy.Sd 0.00 kN
Vz.Sd 2.25 kN
Mt.Sd 0.00 kNm
My.Sd 14.34 kNm
Mz.Sd -0.00 kNm
Normal force check
according to article 5.4.3. and formula (5.13)
Table of values
Nt.Rd 980.59 kN
unity check 0.00
Shear check (Vz)
according to article 5.4.6. and formula (5.20)
Section classification is 1.
Table of values
Vpl.Rd 272.50 kN
unity check 0.01
Combined bending, axial force and shear force check
according to article 5.4.9. and formula (5.35)
Section classification is 1.
Table of values
MNVy.Rd 103.40 kNm
MNVz.Rd 20.72 kNm
alfa 2.00 beta 1.00
unity check 0.02
Element satisfies the section check !
STABILITY CHECK
Buckling parameters yy zz
type sway non-sway
Slenderness 53.42 198.35
Reduced slenderness 0.57 2.11
Buckling curve a b
Imperfection 0.21 0.34
Reduction factor 0.90 0.19
Length 6.00 6.00 m
Buckling factor 1.00 1.00
Buckling length 6.00 6.00 m
Critical Euler load 3333.46 241.82 kN
LTB check
according to article 5.5.2. and formula (5.48)
Table of values
Mb.Rd 51.47 kNm
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Table of values
Beta W 1.00
reduction 0.50
imperfection 0.21
Mcr 72.51 kNm
LTB
LTB length 6.00 m
k 1.00
kw 1.00
C1 1.13
C2 0.45
C3 0.53
load in center of gravity
unity check =0.28
Compression and bending check
according to article 5.5.4. and formula (5.51)
Table of values
ky 1.00
kz 1.00
muy -0.67
muz -0.29
BetaMy 1.30
BetaMz 1.80
unity check = 0.00 + 0.14 + 0.00 = 0.14
Compression, bending and LTB check
according to article 5.5.4. and formula (5.52)
Table of values
klt 1.00
kz 1.00
mult 0.26
muz -0.29
BetaMlt 1.30
BetaMz 1.80
unity check =0.00 + 0.28 + 0.00 = 0.28
Element satisfies the stability check !
Calculation note - Macro 18 EC3 Code Check
Macro 18 Member 47 T120/120/13 S 235 Ult. comb 6 0.56
Basic data EC3
partial safety factor Gamma M0 for resistance of cross-sections 1.10
partial safety factor Gamma M1 for resistance to buckling 1.10
partial safety factor Gamma M2 for resistance of net sections 1.10
Material data
yield strength fy 235.00 MPa
tension strength fu 360.00 MPa
fabrication rolled
SECTION CHECK
Width-to-thickness ratio for outstand flanges (Tab.5.3.1. c).
ratio 4.62 on position 0.00 m
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ratio
maximum ratio 1 10.00
maximum ratio 2 11.00
maximum ratio 3 15.11
==> Class cross-section 1
The critical check is on position 0.00 m
Internal forces
NSd -38.33 kN
Vy.Sd -0.00 kN
Vz.Sd -0.46 kN
Mt.Sd -0.00 kNm
My.Sd 0.57 kNm
Mz.Sd 0.01 kNm
Compression check
according to article 5.4.4. and formula (5.16)
Section classification is 3.
Table of values
Nc.Rd 632.36 kN
unity check 0.06
Shear check (Vy)
according to article 5.4.6. and formula (5.20)
Section classification is 3.
Table of values
Vpl.Rd 192.42 kN
unity check 0.00
Shear check (Vz)
according to article 5.4.6. and formula (5.20)
Section classification is 3.
Table of values
Vpl.Rd 171.57 kN
unity check 0.00
Combined bending, axial force and shear force check
according to article Part 1-3 5.7 and formula (5.11a,5.11b,5.11c)
Section classification is 3.
Table of values
sigma N 12.95 MPa
sigma Myy 13.28 MPa
sigma Mzz 0.02 MPa
Tau z -0.00 MPa
Tau z 0.00 MPa
Tau t 0.00 MPa
ro 0.00 place 10
unity check 0.12
Element satisfies the section check !
STABILITY CHECK
Buckling parameters yy zz
type non-sway non-sway
Slenderness 28.44 244.67
Reduced slenderness 0.30 2.61
Buckling curve c c
Imperfection 0.49 0.49
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Buckling parameters yy zz
Reduction factor 0.95 0.12
Length 1.00 6.00 m
Buckling factor 1.00 1.00
Buckling length 1.00 6.00 m
Critical Euler load 7585.78 102.48 kN
Buckling check
according to article 5.5.1. and formula (5.45)
Table of values
Nb.Rd 77.77 kN
Beta A 1.00
unity check 0.49
Torsional-flexural buckling check
according to article ENV 1993-1-3 : 6.2.3 and formula (6.1) (6.4a-b)(6.5a-b)(6.6)
Table of values
Nb.Rd 81.43 kN
Beta A 1.00
Reduced slenderness 2.61
Reduction factor 0.13
sigma,cr,T 1921.48 MPa
sigma,cr,TF 34.44 MPa
Torsional buckling length 1.00 m
unity check 0.47
LTB check
according to article 5.5.2. and formula (5.48)
Table of values
Mb.Rd 8.28 kNm
Beta W 1.00
reduction 0.92
imperfection 0.21
Mcr 38.92 kNm
LTB
LTB length 6.00 m
k 1.00
kw 1.00
C1 1.88
C2 0.00
C3 0.94
load in center of gravity
unity check =0.07
Compression and bending check
according to article 5.5.4. and formula (5.53)
Table of values
ky 1.01
kz 1.49
muy -0.09
muz -1.10
BetaMy 1.86
BetaMz 1.79
unity check = 0.49 + 0.06 + 0.00 = 0.56
Compression, bending and LTB check
according to article 5.5.4. and formula (5.54)
Table of values
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Table of values
klt 0.82
kz 1.49
mult 0.40
muz -1.10
BetaMlt 1.40
BetaMz 1.79
unity check =0.49 + 0.06 + 0.00 = 0.55
Element satisfies the stability check !
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1.4 PST.06.01 – 02 : EC 3 Steel Code Check – Warping check Description The elastic stresses, inclusive the warping check, is compared with literature results. Project data See input files. Reference [1] Eurocode 3
Design of steel structures Part 1-1 : General rules and rules for buildings ENV 1993-1-1:1992
[2] ENV 1993-1-3:1996 Eurocode 3 : Design of steel structures Part 1-3 : General rules – Supplementary rules for cold formed thin gauge members and sheeting CEN 1996
[3] Schneider Bautabellen mit Berechnungshinweisen und Beispielen 7. Auflage Werner-Verlag, 1986
Result Ref.[3], pp.8.14 EPW % Diff. Mx = 1500 kNcm Mxs = 15 kNm 0 % Mwa = -1.32 105 kNcm Mw = 13.20 kNm 0.08 % σT = 10.4 kN/cm² sigma warping = -104.12 N/mm² 0.12 % max σ =120 N/mm² composed stress = -119.81 N/mm² 0.16 % See the chapter "Calculation note" for the detailed output of ESA-Prima Win. Version ESA-Prima Win 3.20.03 Input file + calculation note PST060102.epw Modules 3D Frame (PRS.11) EC3 Steel code check (PST.06.01) Author CVL
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Calculation note EC3 Code Check
Macro 1 Member 1 HEM280 Fe 360 Loadcase 1 0.51
Basic data EC3
partial safety factor Gamma M0 for resistance of cross-sections 1.00
partial safety factor Gamma M1 for resistance to buckling 1.10
partial safety factor Gamma M2 for resistance of net sections 1.10
Material data
yield strength fy 235.00 MPa
tension strength fu 360.00 MPa
fabrication rolled
SECTION CHECK
Width-to-thickness ratio for webs (Tab.5.3.1. a).
ratio 10.59 on position 0.00 m
ratio
maximum ratio 1 72.00
maximum ratio 2 83.00
maximum ratio 3 124.00
==> Class cross-section 1
Width-to-thickness ratio for outstand flanges (Tab.5.3.1. c).
ratio 4.36 on position 0.00 m
ratio
maximum ratio 1 10.00
maximum ratio 2 11.00
maximum ratio 3 15.08
==> Class cross-section 1
The critical check is on position 0.00 m
Internal forces
NSd 0.00 kN
Vy.Sd 0.00 kN
Vz.Sd 20.00 kN
Mt.Sd -15.00 kNm
My.Sd -40.00 kNm
Mz.Sd 0.00 kNm
Warning : The unity check for pure torsion is 0.49 for Loadcase 1.
Shear check (Vz)
according to article 5.4.6. and formula (5.20)
Section classification is 1.
Table of values
Vpl.Rd 975.04 kN
unity check 0.02
Stress check (incl. warping and torsional moment)
according to article ENV 1993-1-3 : 5.7
Warping fixed at begin beam. 1
Warping free at end beam 1
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x(m) Mxp(kNm) Mxs(kNm) Mw(kNm2)
0.00 0.00 15.00 -13.20
0.20 2.91 12.09 -10.50
0.40 5.22 9.78 -8.32
0.60 7.04 7.96 -6.55
0.80 8.48 6.52 -5.11
1.00 9.58 5.42 -3.92
1.20 10.43 4.57 -2.93
1.40 11.04 3.96 -2.08
1.60 11.46 3.54 -1.33
1.80 11.70 3.30 -0.65
2.00 11.78 3.22 0.00
Table of values
Mxp (St.Venant Torque) 0.00 kNm
Mxs (warping torque) 15.00 kNm
Mw (bimoment) -13.20 kNm2
unity check 0.51
Direct stress check (5.11a)
sigma N 0.00 MPa
sigma Myy -15.69 MPa
sigma Mzz 0.00 MPa
sigma Warping -104.12 MPa
total stress -119.81 MPa
unity check 0.51
Shear stress check (5.11b)
Tau y 0.00 MPa
Tau z 0.00 MPa
Tau t 0.00 MPa
tau Warping 8.52 MPa
total stress 8.52 MPa
unity check 0.06
Composed stress check (5.11c)
sigma N 0.00 MPa
sigma Myy -15.69 MPa
sigma Mzz 0.00 MPa
sigma Warping -104.12 MPa
Tau y 0.00 MPa
Tau z 0.00 MPa
Tau t 0.00 MPa
tau Warping 0.00 MPa
Composed stress 119.81 MPa
unity check 0.46
Element satisfies the section check !
STABILITY CHECK
Buckling parameters yy zz
type non-sway sway
Slenderness 11.41 54.60
Reduced slenderness 0.12 0.58
Buckling curve b c
Imperfection 0.34 0.49
Reduction factor 1.00 0.80
Length 2.00 2.00 m
Buckling factor 0.73 2.02
Buckling length 1.47 4.05 m
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Buckling parameters yy zz
Critical Euler load 381807.03 16688.72 kN
LTB check
according to article 5.5.2. and formula (5.48)
Table of values
Mb.Rd 632.36 kNm
Beta W 1.00
reduction 1.00
imperfection 0.21
Mcr 21788.32 kNm
LTB
LTB length 2.00 m
k 1.00
kw 1.00
C1 1.88
C2 0.00
C3 0.94
load in center of gravity
unity check =0.06
Compression and bending check
according to article 5.5.4. and formula (5.51)
Table of values
ky 1.00
kz 1.00
muy 0.11
muz 0.30
BetaMy 1.80
BetaMz 1.80
unity check = 0.00 + 0.06 + 0.00 = 0.06
Compression, bending and LTB check
according to article 5.5.4. and formula (5.52)
Table of values
klt 1.00
kz 1.00
mult 0.01
muz 0.30
BetaMlt 1.80
BetaMz 1.80
unity check =0.00 + 0.06 + 0.00 = 0.06
Element satisfies the stability check !
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1.5 PST.06.01 – 03 : EC 3 Steel Code Check – Warping check Description The elastic stresses, inclusive the warping check, is compared with literature results. Project data See input files. Reference [1] Eurocode 3
Design of steel structures Part 1-1 : General rules and rules for buildings ENV 1993-1-1:1992
[2] ENV 1993-1-3:1996 Eurocode 3 : Design of steel structures Part 1-3 : General rules – Supplementary rules for cold formed thin gauge members and sheeting CEN 1996
[3] Dietrich von Berg Krane und Kranbahnen – Berechnung Konstruktion Ausführung B.G. Teubner, Stuttgart 1988
Result Ref.[3], pp.130 EPW % Diff. Mxw = 500 kNcm Mxs = 5 kNm 0 % Mw = 6.17 kNm² Mw = 6.19 kNm² 0.32 % σwxx = 12.9 kN/cm² sigma warping = 129.05 N/mm² 0.04 %
τS =0.68 kN/cm² tau warping = 6.78 N/mm² 0.29 % See the chapter "Calculation note" for the detailed output of ESA-Prima Win. Version ESA-Prima Win 3.20.03 Input file + calculation note PST060103.epw Modules 3D Frame (PRS.11) EC3 Steel code check (PST.06.01) Author CVL Calculation note
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EC3 Code Check
Macro 1 Member 1 HEB260 Fe 360 Loadcase 1 0.55
Basic data EC3
partial safety factor Gamma M0 for resistance of cross-sections 1.00
partial safety factor Gamma M1 for resistance to buckling 1.10
partial safety factor Gamma M2 for resistance of net sections 1.10
Material data
yield strength fy 235.00 MPa
tension strength fu 360.00 MPa
fabrication rolled
SECTION CHECK
The critical check is on position 3.00 m
Internal forces
NSd 0.00 kN
Vy.Sd 0.00 kN
Vz.Sd 0.00 kN
Mt.Sd -5.00 kNm
My.Sd 0.00 kNm
Mz.Sd 0.00 kNm
Warning : The unity check for pure torsion is 0.64 for Loadcase 1.
Stress check (incl. warping and torsional moment)
according to article ENV 1993-1-3 : 5.7
Warping free at begin beam 1
Warping free at end beam 1
x(m) Mxp(kNm) Mxs(kNm) Mw(kNm2)
0.00 4.09 0.91 0.00
0.60 3.98 1.02 0.57
1.20 3.64 1.36 1.27
1.80 2.98 2.02 2.27
2.40 1.85 3.15 3.79
3.00 0.00 5.00 6.19
3.00 -0.00 -5.00 6.19
3.60 -1.85 -3.15 3.79
4.20 -2.98 -2.02 2.27
4.80 -3.64 -1.36 1.27
5.40 -3.98 -1.02 0.57
6.00 -4.09 -0.91 0.00
Table of values
Mxp (St.Venant Torque) 0.00 kNm
Mxs (warping torque) 5.00 kNm
Mw (bimoment) 6.19 kNm2
unity check 0.55
Direct stress check (5.11a)
sigma N 0.00 MPa
sigma Myy 0.00 MPa
sigma Mzz 0.00 MPa
sigma Warping -129.05 MPa
total stress -129.05 MPa
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Direct stress check (5.11a)
unity check 0.55
Shear stress check (5.11b)
Tau y 0.00 MPa
Tau z 0.00 MPa
Tau t 0.00 MPa
tau Warping 6.78 MPa
total stress 6.78 MPa
unity check 0.05
Composed stress check (5.11c)
sigma N 0.00 MPa
sigma Myy 0.00 MPa
sigma Mzz 0.00 MPa
sigma Warping -129.05 MPa
Tau y 0.00 MPa
Tau z 0.00 MPa
Tau t 0.00 MPa
tau Warping 0.00 MPa
Composed stress 129.05 MPa
unity check 0.50
Element satisfies the section check !
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1.6 PST.06.01 – 04 : EC 3 Steel Code Check – Warping check Description The elastic stresses, inclusive the warping check, is compared with literature results. Project data See input files. Reference [1] Eurocode 3
Design of steel structures Part 1-1 : General rules and rules for buildings ENV 1993-1-1:1992
[2] ENV 1993-1-3:1996 Eurocode 3 : Design of steel structures Part 1-3 : General rules – Supplementary rules for cold formed thin gauge members and sheeting CEN 1996
[3] Kaltprofile 3. Auflage Verlag Stahleisen mbH, Düsseldorf 1982
Result Ref.[3], pp.68 EPW % Diff. MwT = 128.7 kNcm² Mw =130.34 kNcm² 1.27 % σB = 4.40 kN/cm² sigma Myy = 48.32 N/mm² 9.81 %
σw = 4.24 kN/cm² sigma warping = 42.91 N/mm² 1.20 % σ = 8.64 kN/cm² total stress = 91.23 N/mm² 5.59 % See the chapter "Calculation note" for the detailed output of ESA-Prima Win. Version ESA-Prima Win 3.20.03 Input file + calculation note PST060104.epw Modules 3D Frame (PRS.11) EC3 Steel code check (PST.06.01) Author CVL
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Calculation note
EC3 Code Check
Macro 1 Member 1 CC100/40/3 Fe 360 Loadcase 1 0.43
Basic data EC3
partial safety factor Gamma M0 for resistance of cross-sections 1.10
partial safety factor Gamma M1 for resistance to buckling 1.10
partial safety factor Gamma M2 for resistance of net sections 1.10
Material data
yield strength fy 235.00 MPa
tension strength fu 360.00 MPa
fabrication cold formed
SECTION CHECK
Width-to-thickness ratio for webs (Tab.5.3.1. a).
ratio 32.33 on position 18.00 cm
ratio
maximum ratio 1 72.00
maximum ratio 2 83.00
maximum ratio 3 124.00
==> Class cross-section 1
Width-to-thickness ratio for outstand flanges (Tab.5.3.1. c).
ratio 4.50 on position 18.00 cm
ratio
maximum ratio 1 10.00
maximum ratio 2 11.00
maximum ratio 3 16.97
==> Class cross-section 1
The critical check is on position 90.00 cm
Internal forces
NSd 0.00 kN
Vy.Sd 0.00 kN
Vz.Sd -0.00 kN
Mt.Sd -0.00 kNcm
My.Sd 81.00 kNcm
Mz.Sd 0.00 kNcm
Warning : The unity check for pure torsion is 0.67 for Loadcase 1.
Stress check (incl. warping and torsional moment)
according to article ENV 1993-1-3 : 5.7
Warping free at begin beam 1
Warping free at end beam 1
x(cm) Mxp(kNcm) Mxs(kNcm) Mw(kNcm2)
0.00 -2.03 -3.37 0.00
18.00 -1.90 -2.42 -51.74
36.00 -1.58 -1.66 -88.14
54.00 -1.13 -1.03 -112.20
72.00 -0.58 -0.50 -125.89
90.00 -0.00 0.00 -130.34
108.00 0.58 0.50 -125.89
126.00 1.13 1.03 -112.20
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x(cm) Mxp(kNcm) Mxs(kNcm) Mw(kNcm2)
144.00 1.58 1.66 -88.14
162.00 1.90 2.42 -51.74
180.00 2.03 3.37 0.00
Table of values
Mxp (St.Venant Torque) -0.00 kNcm
Mxs (warping torque) 0.00 kNcm
Mw (bimoment) -130.34 kNcm2
unity check 0.43
Direct stress check (5.11a)
sigma N 0.00 MPa
sigma Myy 48.32 MPa
sigma Mzz 0.00 MPa
sigma Warping 42.91 MPa
total stress 91.23 MPa
unity check 0.43
Shear stress check (5.11b)
Tau y 0.00 MPa
Tau z 0.00 MPa
Tau t 0.00 MPa
tau Warping 0.00 MPa
total stress 0.00 MPa
unity check 0.00
Composed stress check (5.11c)
sigma N 0.00 MPa
sigma Myy 48.32 MPa
sigma Mzz 0.00 MPa
sigma Warping 42.91 MPa
Tau y 0.00 MPa
Tau z 0.00 MPa
Tau t 0.00 MPa
tau Warping 0.00 MPa
Composed stress 91.23 MPa
unity check 0.39
Element satisfies the section check !
STABILITY CHECK
Buckling parameters yy zz
type non-sway sway
Slenderness 47.24 126.16
Reduced slenderness 0.50 1.34
Buckling curve b b
Imperfection 0.34 0.34
Reduction factor 0.88 0.41
Length 180.00 180.00 cm
Buckling factor 1.00 1.00
Buckling length 180.00 180.00 cm
Critical Euler load 520.10 72.93 kN
LTB check
according to article 5.5.2. and formula (5.48)
Table of values
Mb.Rd 232.11 kNcm
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Table of values
Beta W 1.00
reduction 0.67
imperfection 0.34
Mcr 481.80 kNcm
LTB
LTB length 180.00 cm
k 1.00
kw 1.00
C1 1.13
C2 0.45
C3 0.53
load in center of gravity
unity check =0.35
Compression and bending check
according to article 5.5.4. and formula (5.53)
Table of values
ky 1.00
kz 1.00
muy -0.70
muz -0.54
BetaMy 1.30
BetaMz 1.80
unity check = 0.00 + 0.23 + 0.00 = 0.23
Compression, bending and LTB check
according to article 5.5.4. and formula (5.54)
Table of values
klt 1.00
kz 1.00
mult 0.11
muz -0.54
BetaMlt 1.30
BetaMz 1.80
unity check =0.00 + 0.35 + 0.00 = 0.35
Element satisfies the stability check !
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1.7 PST.06.01 – 05 : EC 3 Steel Code Check – Warping check Description The elastic stresses, inclusive the warping check, is compared with literature results. Project data See input files. Reference [1] Eurocode 3
Design of steel structures Part 1-1 : General rules and rules for buildings ENV 1993-1-1:1992
[2] ENV 1993-1-3:1996 Eurocode 3 : Design of steel structures Part 1-3 : General rules – Supplementary rules for cold formed thin gauge members and sheeting CEN 1996
[3] Stahl im Hochbau 14. Auglage Band I/ Teil 2 Verlag Stahleisen mbH, Düsseldorf 1986
Comparison Ref.[3], pp.713 EPW % Diff. Mxs = 14.5 kNcm² Mxs =14.48 kNcm² 0 % σx = 9.26 kN/cm² sigma Myy = -92.59 N/mm² 0 %
σx’ = 3.03 kN/cm² sigma warping = -26.94 N/mm² 11.08 % σv = 12.30 kN/cm² composed stress = 120.11 N/mm² 2.35 % See the chapter "Calculation note" for the detailed output of ESA-Prima Win. Version ESA-Prima Win 3.20.03 Input file + calculation note PST060105.epw Modules 3D Frame (PRS.11) EC3 Steel code check (PST.06.01) Author CVL Calculation note
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EC3 Code Check
Macro 1 Member 1 UNP140 Fe 360 Loadcase 1 0.51
Basic data EC3
partial safety factor Gamma M0 for resistance of cross-sections 1.00
partial safety factor Gamma M1 for resistance to buckling 1.10
partial safety factor Gamma M2 for resistance of net sections 1.10
Material data
yield strength fy 235.00 MPa
tension strength fu 360.00 MPa
fabrication rolled
SECTION CHECK
Width-to-thickness ratio for webs (Tab.5.3.1. a).
ratio 14.29 on position 0.00 cm
ratio
maximum ratio 1 72.00
maximum ratio 2 83.00
maximum ratio 3 124.00
==> Class cross-section 1
Width-to-thickness ratio for outstand flanges (Tab.5.3.1. c).
ratio 6.00 on position 0.00 cm
ratio
maximum ratio 1 10.00
maximum ratio 2 11.00
maximum ratio 3 15.08
==> Class cross-section 1
The critical check is on position 0.00 cm
Internal forces
NSd 0.00 kN
Vy.Sd 0.00 kN
Vz.Sd 4.00 kN
Mt.Sd 14.48 kNcm
My.Sd -800.00 kNcm
Mz.Sd 0.00 kNcm
Warning : The unity check for pure torsion is 0.20 for Loadcase 1.
Shear check (Vz)
according to article 5.4.6. and formula (5.20)
Section classification is 3.
Table of values
Vpl.Rd 138.28 kN
unity check 0.03
Stress check (incl. warping and torsional moment)
according to article ENV 1993-1-3 : 5.7
Warping fixed at begin beam. 1
Warping free at end beam 1
x(cm) Mxp(kNcm) Mxs(kNcm) Mw(kNcm2)
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x(cm) Mxp(kNcm) Mxs(kNcm) Mw(kNcm2)
0.00 0.00 -14.48 448.86
20.00 -6.88 -7.60 235.46
40.00 -10.50 -3.98 123.51
60.00 -12.39 -2.09 64.78
80.00 -13.38 -1.10 33.97
100.00 -13.90 -0.58 17.80
120.00 -14.18 -0.30 9.30
140.00 -14.32 -0.16 4.80
160.00 -14.39 -0.09 2.38
180.00 -14.42 -0.06 0.98
200.00 -14.43 -0.05 0.00
200.00 -14.43 -0.05 0.00
Table of values
Mxp (St.Venant Torque) 0.00 kNcm
Mxs (warping torque) -14.48 kNcm
Mw (bimoment) 448.86 kNcm2
unity check 0.51
Direct stress check (5.11a)
sigma N 0.00 MPa
sigma Myy -92.59 MPa
sigma Mzz 0.00 MPa
sigma Warping -26.94 MPa
total stress -119.53 MPa
unity check 0.51
Shear stress check (5.11b)
Tau y 0.00 MPa
Tau z 3.68 MPa
Tau t 0.00 MPa
tau Warping 3.10 MPa
total stress 6.79 MPa
unity check 0.05
Composed stress check (5.11c)
sigma N 0.00 MPa
sigma Myy -92.59 MPa
sigma Mzz 0.00 MPa
sigma Warping -26.94 MPa
Tau y 0.00 MPa
Tau z 3.68 MPa
Tau t 0.00 MPa
tau Warping 3.10 MPa
Composed stress 120.11 MPa
unity check 0.46
Element satisfies the section check !
STABILITY CHECK
Buckling parameters yy zz
type non-sway sway
Slenderness 26.92 231.32
Reduced slenderness 0.29 2.46
Buckling curve c c
Imperfection 0.49 0.49
Reduction factor 0.96 0.14
Length 200.00 200.00 cm
Buckling factor 0.73 2.02
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Buckling parameters yy zz
Buckling length 146.62 404.89 cm
Critical Euler load 5833.16 79.02 kN
LTB check
according to article 5.5.2. and formula (5.48)
Table of values
Mb.Rd 1574.87 kNcm
Beta W 1.00
reduction 0.85
imperfection 0.21
Mcr 4287.03 kNcm
LTB
LTB length 200.00 cm
k 1.00
kw 1.00
C1 1.88
C2 0.00
C3 0.94
load in center of gravity
unity check =0.51
Compression and bending check
according to article 5.5.4. and formula (5.53)
Table of values
ky 1.00
kz 1.00
muy -0.11
muz -0.99
BetaMy 1.80
BetaMz 1.80
unity check = 0.00 + 0.43 + 0.00 = 0.43
Compression, bending and LTB check
according to article 5.5.4. and formula (5.54)
Table of values
klt 1.00
kz 1.00
mult 0.52
muz -0.99
BetaMlt 1.80
BetaMz 1.80
unity check =0.00 + 0.51 + 0.00 = 0.51
Element satisfies the stability check !
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1.8 PST.06.01 – 06 : EC 3 Steel Code Check – Torsional buckling check and Shear buckling check for cold formed sections Description The torsional buckling check and the shear buckling check are manually calculated, according to the regulations given in Ref.[2]. Project data See input files. Reference [1] Eurocode 3
Design of steel structures Part 1-1 : General rules and rules for buildings ENV 1993-1-1:1992
[2] ENV 1993-1-3:1996 Eurocode 3 : Design of steel structures Part 1-3 : General rules – Supplementary rules for cold formed thin gauge members and sheeting CEN 1996
See the chapter "Manual calculation" for a detailed calculation according to this reference. Result
Type of result Manually ESA-Prima Win % Diff Unity check LC 1 0.36 0.36 0 % Unity check LC 2 0.144 0.14 0 %
Version ESA-Prima Win 3.20.03 Input file + calculation note PST060106.epw Modules 3D Frame (PRS.11) EC3 Steel code check (PST.06.01) Author CVL Manual calculation - 1
The section CC120/40/3 is checked. The following properties are used : Ag 620 mm²
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iy 45.0 mm iz 14.0 mm y0 28.3 mm i0 55.0 mm E 210000 N/mm² G 80769 N/mm² It 1962 mm4 Cm 3.98 108 mm6 lT 2000 mm ly 1470 mm sw 117 mm t 3 mm This section is checked with the following geometry :
The section is classified in section class 3. For load case 1, the torsional buckling and torsional flexural buckling is checked (See Ref.[2], part 6.2.3) :
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( ) ( )[ ]
( ) ( )[ ]
116.10.1188
235f
²mm
N188),min(
²mm
N1881941942735.04²19419421941942
735.02
1
4²2
1
735.0²0.55
3.281²
i
y1
²mm
N1942
²45
1470210000²
²i
l
E²
²mm
N194
2000
e98.3210000²196280769
3032620
1
l
EC²GI
iA
1
²mm3032yiii
Acr
yb
TF,crT,crcr
TF,cr
T,cry,crT,cry,crT,cry,crTF,cr
0
0
y
yy,cr
T,cr
2
8
2T
mt2
0gT,cr
20
2z
2y
20
==βσ
=λ
=σσ=σ
=⋅⋅⋅−+−+⋅
=σ
σβσ−σ+σ−σ+σβ
=σ
=
−=
−=β
=
⋅π=
π=σ
=σ
⋅⋅π+⋅
⋅=
π+=σ
=++=
With the reduced slenderness and the buckling curve b, the reduction factor χ=0.53 is found. This results in the design buckling resistance Nb,Rd
kN2.701.1
620235153.0AfRd,Nb
1M
gyA =⋅⋅⋅
=γ
⋅⋅β⋅χ=
The unity check is 25/70.2 =0.36. See also calculation note 1. Manual calculation - 2 For load case 2, the shear buckling is checked according to Ref.[2] part 5.8. The relative web slenderness is
451.0210000
235
3
117346.0
E
f
t
s346.0 ybw
w
_
=⋅=⋅=λ
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The shear buckling strength fbv, is given by
²mm
N249
451.0
23548.0
f48.0f
w
_
ybbv ==
λ=
The shear buckling resistance Vb,Rd is given by
kN73.791.1
2493117ftsV
1M
bvwRd,b =
⋅⋅=
γ
⋅⋅=
The plastic shear resistance Vpl,Rd is given by
kN29.4331.1
2353117
3
ftsV
0M
ywRd,pl =
⋅⋅=
γ
⋅⋅=
The unity check is 6.24/43.29=0.144. See also calculation note 2. Calculation note 1
EC3 Code Check
Macro 1 Member 1 CC120/40/3 S 235 Loadcase 1 0.36
Basic data EC3
partial safety factor Gamma M0 for resistance of cross-sections 1.10
partial safety factor Gamma M1 for resistance to buckling 1.10
partial safety factor Gamma M2 for resistance of net sections 1.10
Material data
yield strength fy 235.00 MPa
tension strength fu 360.00 MPa
fabrication cold formed
SECTION CHECK
Width-to-thickness ratio for webs (Tab.5.3.1. a).
ratio 39.00 on position 0.00 cm
ratio
maximum ratio 1 33.00
maximum ratio 2 38.00
maximum ratio 3 42.00
==> Class cross-section 3
Width-to-thickness ratio for outstand flanges (Tab.5.3.1. c).
ratio 4.50 on position 0.00 cm
ratio
maximum ratio 1 10.00
maximum ratio 2 11.00
maximum ratio 3 15.08
==> Class cross-section 1
The critical check is on position 0.00 cm
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Internal forces
NSd -25.00 kN
Vy.Sd 0.00 kN
Vz.Sd 0.00 kN
Mt.Sd 0.00 kNcm
My.Sd 0.00 kNcm
Mz.Sd 0.00 kNcm
Compression check
according to article 5.4.4. and formula (5.16)
Section classification is 3.
Table of values
Nc.Rd 132.45 kN
unity check 0.19
Combined bending, axial force and shear force check
according to article 5.4.9. and formula (5.37)
Section classification is 3.
Table of values
sigma N 40.32 MPa
sigma Myy 0.00 MPa
sigma Mzz 0.00 MPa
ro 0.00 place 15
unity check 0.19
Element satisfies the section check !
STABILITY CHECK
Buckling parameters yy zz
type non-sway non-sway
Slenderness 32.52 104.52
Reduced slenderness 0.35 1.11
Buckling curve b b
Imperfection 0.34 0.34
Reduction factor 0.95 0.53
Length 200.00 200.00 cm
Buckling factor 0.73 0.73
Buckling length 146.62 146.62 cm
Critical Euler load 1214.84 117.63 kN
Buckling check
according to article 5.5.1. and formula (5.45)
Table of values
Nb.Rd 69.87 kN
Beta A 1.00
unity check 0.36
Torsional-flexural buckling check
according to article ENV 1993-1-3 : 6.2.3 and formula (6.1) (6.4a-b)(6.5a-b)(6.6)
Table of values
Nb.Rd 69.64 kN
Beta A 1.00
Reduced slenderness 1.12
Reduction factor 0.53
sigma,cr,T 194.03 MPa
sigma,cr,TF 188.70 MPa
Torsional buckling length 200.00 cm
unity check 0.36
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Compression and bending check
according to article 5.5.4. and formula (5.53)
Table of values
ky 1.03
kz 1.14
muy -0.14
muz -0.45
BetaMy 1.80
BetaMz 1.80
unity check = 0.36 + 0.00 + 0.00 = 0.36
Compression, bending and LTB check
according to article 5.5.4. and formula (5.54)
Table of values
klt 0.95
kz 1.14
mult 0.15
muz -0.45
BetaMlt 1.80
BetaMz 1.80
unity check =0.36 + 0.00 + 0.00 = 0.36
Element satisfies the stability check !
Calculation note 2
EC3 Code Check
Macro 1 Member 1 CC120/40/3 S 235 Loadcase 2 0.94
Basic data EC3
partial safety factor Gamma M0 for resistance of cross-sections 1.10
partial safety factor Gamma M1 for resistance to buckling 1.10
partial safety factor Gamma M2 for resistance of net sections 1.10
Material data
yield strength fy 235.00 MPa
tension strength fu 360.00 MPa
fabrication cold formed
SECTION CHECK
Width-to-thickness ratio for webs (Tab.5.3.1. a).
ratio 39.00 on position 20.00 cm
ratio
maximum ratio 1 72.00
maximum ratio 2 83.00
maximum ratio 3 124.00
==> Class cross-section 1
Width-to-thickness ratio for outstand flanges (Tab.5.3.1. c).
ratio 4.50 on position 20.00 cm
ratio
maximum ratio 1 10.00
maximum ratio 2 11.00
maximum ratio 3 16.60
==> Class cross-section 1
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The critical check is on position 200.00 cm
Internal forces
NSd 0.00 kN
Vy.Sd 0.00 kN
Vz.Sd -6.24 kN
Mt.Sd 0.00 kNcm
My.Sd -247.80 kNcm
Mz.Sd 0.00 kNcm
Shear check (Vz)
according to article ENV 1993-1-3 : 5.8 and formula (5.13) (5.14)
Section classification is 3.
Table of values
VRd (Sum min(Vpl,Rd,Vb,Rd)) 43.29 kN
unity check 0.14
Combined bending, axial force and shear force check
according to article 5.4.9. and formula (5.37)
Section classification is 3.
Table of values
sigma N 0.00 MPa
sigma Myy 115.05 MPa
sigma Mzz 0.00 MPa
ro 0.00 place 13
unity check 0.54
Element satisfies the section check !
STABILITY CHECK
Buckling parameters yy zz
type non-sway non-sway
Slenderness 32.52 104.52
Reduced slenderness 0.35 1.11
Buckling curve b b
Imperfection 0.34 0.34
Reduction factor 0.95 0.53
Length 200.00 200.00 cm
Buckling factor 0.73 0.73
Buckling length 146.62 146.62 cm
Critical Euler load 1214.84 117.63 kN
LTB check
according to article 5.5.2. and formula (5.48)
Table of values
Mb.Rd 263.94 kNcm
Beta W 1.00
reduction 0.59
imperfection 0.34
Mcr 480.20 kNcm
LTB
LTB length 200.00 cm
k 1.00
kw 1.00
C1 1.58
C2 0.66
C3 2.64
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load in center of gravity
unity check =0.94
Compression and bending check
according to article 5.5.4. and formula (5.53)
Table of values
ky 1.00
kz 1.00
muy -0.36
muz -0.45
BetaMy 1.48
BetaMz 1.80
unity check = 0.00 + 0.55 + 0.00 = 0.55
Compression, bending and LTB check
according to article 5.5.4. and formula (5.54)
Table of values
klt 1.00
kz 1.00
mult 0.10
muz -0.45
BetaMlt 1.48
BetaMz 1.80
unity check =0.00 + 0.94 + 0.00 = 0.94
Element satisfies the stability check !
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1.9 PST.06.01 – 07 : Example Code Check and Connections according to EC3 : Design of an industrial type building Description The example is based on the illustration given in Ref.[1] :
Chapter 12 : Worked Example 3 Design of an industrial type building
The example is calculated using EPW release 3.1. The results from EPW are printed in italics. The member design is based on ref.[2]. The connection design is based on ref.[3]. The following possibilities of EPW are illustrated : • the use of haunched sections in the analysis model • the automatic generation of SLS and ULS combinations according to EC3 • the stability analysis for the determination of the elastic critical load ratio • the implementation of the global frame imperfection • the member design for class 4 sections • the calculation of the moment capacity for the connections based on the component method • the check of the required stiffness for the beam connections
Reference [1] Frame design including joint behaviour
Volume 1 ECSC Contracts n° 7210-SA/212 and 7210-SA/320 January 1997
[2] ENV 1993-1-1:1992 Eurocode 3 Design of steel structures – Part 1-1 General rules and rules for buildings
[3] Eurocode 3 : Part 1.1. Revised annex J : Joints in building frames, ENV 1993-1-1/pr A2
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Version ESA-Prima Win 3.20.03 Input file + calculation note PST060107.epw Author CVL Contents 1. Frame geometry 2. Design assumptions 3. Loadings 3.1. Basic loadings 3.2. Load combinations 4. Analysis
4.1. Linear elastic analysis 4.2. Stability calculation 4.3. Elastic analysis with local non-linearties
5. Member check
5.1. SLS check 5.2. ULS check
5.2.1. Column check 5.2.2. Beam check
6. Connection design 6.1. Bolted beam-to-column connection
6.2. Bolted plate-to-plate connection 6.3. Base plate connection
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Worked example 1. Frame geometry A two bay pinned-base pitched portal frame (with haunches) for an industrial building is considered. The dimensions of the building are the following : width (centrellines) 2 x 23.5 m height 10 m length 60.5 m The portal frames, which are at 6 m intervals, have 8 m high columns and have rafters sloped at 7.7° with a centreline ridge height of 9.5 m above ground level. Haunches are used for the joints of the rafters to the columns. Hot-rolled standard sections are used for the members : IPE550 for the columns, IPE400 for the roof beams. For the steel elements (members, haunches, endplates, stiffeners) the steel S275 is used. Material
Name
S 275
Ultimate strength 430.00 MPa
Yield design 275.00 MPa
E modulus 210000.00 MPa
Poisson coeff. 0.30
Specific weight 7850.00 kg/m^3
Extensibility 0.012 mm/m.K
List of material
Group of members :
1/7
num. Name unit weight
kg/m
length
m
weight
kg
1 IPE550 105.50 24.00 2532.10
2 IPE400 66.30 47.38 4716.28
The total weight of the structure: 7248.38 kg
Surface for painting: 117.23 m^2
Nodes
node X
m
Y
m
Z
m
1 0.000 0.000 0.000
2 0.000 0.000 8.000
3 23.500 0.000 0.000
4 23.500 0.000 8.000
5 47.000 0.000 0.000
6 47.000 0.000 8.000
7 11.750 0.000 9.500
8 35.250 0.000 9.500
Members
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macro memb node 1 node 2 length
m
Rx
deg
profile
1 1 1 2 8.00 0.00 1 - IPE550
2 2 3 4 8.00 0.00 1 - IPE550
3 3 5 6 8.00 0.00 1 - IPE550
4 4 2 7 11.85 0.00 2 - IPE400
5 5 4 7 11.85 0.00 2 - IPE400
6 6 4 8 11.85 0.00 2 - IPE400
7 7 6 8 11.85 0.00 2 - IPE400
Profiles
Figure 1: IPE550
Profile num. 1 - IPE550
Material : 47 - S 275
A 1.344000e+004 mm^2
Ay/A 0.477 Az/A 0.435
Iy 6.712000e+008 mm^4 Iz 2.668000e+007 mm^4
Iyz 2.710505e-008 mm^4 It 1.232000e+006 mm^4
Iw 1.921780e+012 mm^6
Wely 2.441000e+006 mm^3 Welz 2.541000e+005 mm^3
Wply 2.780000e+006 mm^3 Wplz 4.000000e+005 mm^3
cy 105.00 mm cz 275.00 mm
iy 223.47 mm iz 44.55 mm
dy -0.00 mm dz 0.00 mm
Type for check: I section
Height 550.00 mm Width 210.00 mm
Thickness of flange 17.20 mm Thickness of web 11.10 mm
Radius 24.00 mm
Figure 2: IPE400
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Profile num. 2 - IPE400
Material : 47 - S 275
A 8.446000e+003 mm^2
Ay/A 0.509 Az/A 0.391
Iy 2.313000e+008 mm^4 Iz 1.318000e+007 mm^4
Iyz 0.000000e+000 mm^4 It 5.108000e+005 mm^4
Iw 4.968547e+011 mm^6
Wely 1.156000e+006 mm^3 Welz 1.464000e+005 mm^3
Wply 1.308000e+006 mm^3 Wplz 2.300000e+005 mm^3
cy 90.00 mm cz 200.00 mm
iy 165.49 mm iz 39.50 mm
dy -0.00 mm dz 0.00 mm
Type for check: I section
Height 400.00 mm Width 180.00 mm
Thickness of flange 13.50 mm Thickness of web 8.60 mm
Radius 21.00 mm
Variable profile
macro cross-section length
m
Parts position alignment size[original/changed]
mm
4 3 - I + I var (IPE400,400) 1.750 5 Begin Align Z+ 400/0
5 3 - I + I var (IPE400,400) 1.750 5 Begin Align Z+ 400/0
6 3 - I + I var (IPE400,400) 1.750 5 Begin Align Z+ 400/0
7 3 - I + I var (IPE400,400) 1.750 5 Begin Align Z+ 400/0
Supports
support boundary node type rot
deg
flexibility
kN/m-kNm/rad
funct
1 1 XZ
2 3 XZ
3 5 XZ
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1 2 3
4 5 6 7
Figure 3: Member numbers
1
2
3
4
5
6
7 8
Figure 4: Node numbers
IPE550
IPE550
IPE550
IPE400 IPE400 IPE400 IPE400
Figure 5: Profile assignment
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Figure 6: Column and haunched beam
2. Design assumptions The structure is unbraced in its plane. In the longitudinal direction of the building, bracing is provided, so that the purlins act as out-of-plane support points to the frame. The position of the purlins will be defined and checked in 0. Several analysis were carried out : a linear elastic analysis for the serviceabililty limit states and to retrieve the critical combinations, a stability calculation for determining the critical load which leads to sway/non-sway classification ,an elastic analysis with local non-linearties for implementing the frame imperfections, used for the ultimate limit states for member check and connection check. The traditional assumption that joints are rigid is adopted. This assumption is verified. 3. Loadings 3.1. Basic loadings While the loads given are typical for a building of this type, the values should be taken as indicative. The values are taken from Ref.[1]. The following load cases are considered : load case 1 and 2 G : Self weight and dead load load case 3 and 4 W : Wind load load case 5,6,7 and 8 S : Snow load
Loadcases
Case Name coeff Description
1 Self weight 1.00 Self weight
2 Self weight (cladding + roof) 1.00 Permanent
3 Wind W1 1.00 Variable - Wind Excl.
4 Wind W2 1.00 Variable - Wind Excl.
5 Snow S1 1.00 Variable - Snow Excl.
6 Snow S2 1.00 Variable - Snow Excl.
7 Snow S3 1.00 Variable - Snow Excl.
8 Snow S4 1.00 Variable - Snow Excl.
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Loadcases num. 2 - distributed loads
memb macro bound type dx
m
exY
m
exZ
m
X beg
end
Y beg
end
Z beg
end
1 force
kN/m
0.00 rel
1.00
0.00 0.00 glo
len
0.00
0.00
0.00
0.00
-1.20
-1.20
3 force
kN/m
0.00 rel
1.00
0.00 0.00 glo
len
0.00
0.00
0.00
0.00
-1.20
-1.20
4 force
kN/m
0.00 rel
1.00
0.00 0.00 glo
len
0.00
0.00
0.00
0.00
-1.60
-1.60
5 force
kN/m
0.00 rel
1.00
0.00 0.00 glo
len
0.00
0.00
0.00
0.00
-1.60
-1.60
6 force
kN/m
0.00 rel
1.00
0.00 0.00 glo
len
0.00
0.00
0.00
0.00
-1.60
-1.60
7 force
kN/m
0.00 rel
1.00
0.00 0.00 glo
len
0.00
0.00
0.00
0.00
-1.60
-1.60
-1.2
-1.2
-1.2
-1.2
-1.6
-1.6
-1.6
-1.6
-1.6
-1.6
-1.6
-1.6
Figure 7: Load case 2
Loadcases num. 3 - distributed loads
memb macro bound type dx
m
exY
m
exZ
m
X beg
end
Y beg
end
Z beg
end
1 force
kN/m
0.00 rel
1.00
0.00 0.00 glo
len
1.80
2.22
0.00
0.00
0.00
0.00
3 force
kN/m
0.00 rel
1.00
0.00 0.00 glo
len
3.12
4.15
0.00
0.00
0.00
0.00
4 force
kN/m
0.00 rel
1.00
0.00 0.00 loc
len
0.00
0.00
0.00
0.00
4.44
4.44
5 force
kN/m
0.00 rel
1.00
0.00 0.00 loc
len
0.00
0.00
0.00
0.00
3.47
3.47
6 force
kN/m
0.00 rel
1.00
0.00 0.00 loc
len
0.00
0.00
0.00
0.00
3.96
3.96
7 force
kN/m
0.00 rel
1.00
0.00 0.00 loc
len
0.00
0.00
0.00
0.00
3.86
3.86
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1.8
2.2
3.1
4.2
4.4
4.43.5
3.5
4.0
4.0
3.9
3.9
Figure 8: Load case 3
Loadcases num. 4 - distributed loads
memb macro bound type dx
m
exY
m
exZ
m
X beg
end
Y beg
end
Z beg
end
1 force
kN/m
0.00 rel
1.00
0.00 0.00 glo
len
4.28
5.70
0.00
0.00
0.00
0.00
3 force
kN/m
0.00 rel
1.00
0.00 0.00 glo
len
0.52
0.68
0.00
0.00
0.00
0.00
4 force
kN/m
0.00 rel
1.00
0.00 0.00 loc
len
0.00
0.00
0.00
0.00
0.96
0.96
6 force
kN/m
0.00 rel
1.00
0.00 0.00 loc
len
0.00
0.00
0.00
0.00
-0.48
-0.48
7 force
kN/m
0.00 rel
1.00
0.00 0.00 loc
len
0.00
0.00
0.00
0.00
0.48
0.48
4.3
5.7
0.5
0.7
1.0
1.0
-0.5
-0.5
0.5
0.5
Figure 9: Load case 4
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Loadcases num. 5 - distributed loads
memb macro bound type dx
m
exY
m
exZ
m
X beg
end
Y beg
end
Z beg
end
4 force
kN/m
0.00 rel
1.00
0.00 0.00 glo
len
0.00
0.00
0.00
0.00
-2.64
-2.64
5 force
kN/m
0.00 rel
1.00
0.00 0.00 glo
len
0.00
0.00
0.00
0.00
-2.64
-2.64
6 force
kN/m
0.00 rel
1.00
0.00 0.00 glo
len
0.00
0.00
0.00
0.00
-2.64
-2.64
7 force
kN/m
0.00 rel
1.00
0.00 0.00 glo
len
0.00
0.00
0.00
0.00
-2.64
-2.64
-2.6
-2.6
-2.6
-2.6
-2.6
-2.6
-2.6
-2.6
Figure 10: Load case 5
Loadcases num. 6 - distributed loads
memb macro bound type dx
m
exY
m
exZ
m
X beg
end
Y beg
end
Z beg
end
4 force
kN/m
0.00 rel
1.00
0.00 0.00 glo
len
0.00
0.00
0.00
0.00
-1.32
-1.32
5 force
kN/m
0.00 rel
1.00
0.00 0.00 glo
len
0.00
0.00
0.00
0.00
-2.64
-2.64
6 force
kN/m
0.00 rel
1.00
0.00 0.00 glo
len
0.00
0.00
0.00
0.00
-2.64
-2.64
7 force
kN/m
0.00 rel
1.00
0.00 0.00 glo
len
0.00
0.00
0.00
0.00
-1.32
-1.32
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-1.3
-1.3
-2.6
-2.6
-2.6
-2.6
-1.3
-1.3
Figure 11: Load case 6
Loadcases num. 7 - distributed loads
memb macro bound type dx
m
exY
m
exZ
m
X beg
end
Y beg
end
Z beg
end
4 force
kN/m
0.00 rel
1.00
0.00 0.00 glo
len
0.00
0.00
0.00
0.00
-1.32
-1.32
5 force
kN/m
0.00 rel
1.00
0.00 0.00 glo
len
0.00
0.00
0.00
0.00
-5.40
0.00
6 force
kN/m
0.00 rel
1.00
0.00 0.00 glo
len
0.00
0.00
0.00
0.00
-5.40
0.00
7 force
kN/m
0.00 rel
1.00
0.00 0.00 glo
len
0.00
0.00
0.00
0.00
-1.32
-1.32
-1.3
-1.3
-5.4
0.000
-5.4
0.000
-1.3
-1.3
Figure 12: Load case 7
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Loadcases num. 8 - distributed loads
memb macro bound type dx
m
exY
m
exZ
m
X beg
end
Y beg
end
Z beg
end
4 force
kN/m
0.00 rel
1.00
0.00 0.00 glo
len
0.00
0.00
0.00
0.00
-5.40
0.00
5 force
kN/m
0.00 rel
1.00
0.00 0.00 glo
len
0.00
0.00
0.00
0.00
-5.40
0.00
6 force
kN/m
0.00 rel
1.00
0.00 0.00 glo
len
0.00
0.00
0.00
0.00
-5.40
0.00
7 force
kN/m
0.00 rel
1.00
0.00 0.00 glo
len
0.00
0.00
0.00
0.00
-5.40
0.00
-5.4
0.000
-5.4
0.000
-5.4
0.000
-5.4
0.000
Figure 13: Load case 8
3.2. Load combination The simplified load combination cases of Ref.[2] – Chapter 2 are adopted. For the ultimate load limit state combinations : • 1.35 G + 1.50 W • 1.35 G + 1.50 S • 1.35 G + 1.35 W + 1.35 S For the serviceability limit state combinations : • 1.00 G + 1.00 W • 1.00 G + 1.00 S • 1.00 G + 0.90 W + 0.90 S 4. Analysis 4.1. Linear elastic analysis A linear elastic analysis is performed. This generates 18 possible ULS combinations and 7 possible SLS combinations.
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Combinations
Combi Norma Case coeff
1 EC-ultimate 1 Self weight 1.00
1 EC-ultimate 2 Self weight (cladding + roof) 1.00
1 EC-ultimate 3 Wind W1 1.00
1 EC-ultimate 4 Wind W2 1.00
1 EC-ultimate 5 Snow S1 1.00
1 EC-ultimate 6 Snow S2 1.00
1 EC-ultimate 7 Snow S3 1.00
1 EC-ultimate 8 Snow S4 1.00
2 EC-serviceability 1 Self weight 1.00
2 EC-serviceability 2 Self weight (cladding + roof) 1.00
2 EC-serviceability 3 Wind W1 1.00
2 EC-serviceability 4 Wind W2 1.00
2 EC-serviceability 5 Snow S1 1.00
2 EC-serviceability 6 Snow S2 1.00
2 EC-serviceability 7 Snow S3 1.00
2 EC-serviceability 8 Snow S4 1.00
Basic rules for generation of ultimate load combinations:
1 : 1.35*LC1 / 1.35*LC2
2 : 1.35*LC1 / 1.35*LC2 / 1.50*LC3 / 1.50*LC4
3 : 1.00*LC1 / 1.00*LC2 / 1.50*LC3 / 1.50*LC4
4 : 1.35*LC1 / 1.35*LC2 / 1.50*LC5 / 1.50*LC6 / 1.50*LC7 / 1.50*LC8
5 : 1.00*LC1 / 1.00*LC2 / 1.50*LC5 / 1.50*LC6 / 1.50*LC7 / 1.50*LC8
6 : 1.35*LC1 / 1.35*LC2 / 1.35*LC3 / 1.35*LC4 / 1.35*LC5 / 1.35*LC6 / 1.35*LC7
/ 1.35*LC8
7 : 1.00*LC1 / 1.00*LC2 / 1.35*LC3 / 1.35*LC4 / 1.35*LC5 / 1.35*LC6 / 1.35*LC7
/ 1.35*LC8
Basic rules for generation of serviceability load combinations:
1 : 1.00*LC1 / 1.00*LC2
2 : 1.00*LC1 / 1.00*LC2 / 1.00*LC3 / 1.00*LC4
3 : 1.00*LC1 / 1.00*LC2 / 1.00*LC5 / 1.00*LC6 / 1.00*LC7 / 1.00*LC8
4 : 1.00*LC1 / 1.00*LC2 / 0.90*LC3 / 0.90*LC4 / 0.90*LC5 / 0.90*LC6 / 0.90*LC7
/ 0.90*LC8
List of extremal ultimate load combinations
1/ 3 : +1.00*LC1+1.00*LC2+1.50*LC3
2/ 5 : +1.00*LC1+1.00*LC2+1.50*LC8
3/ 4 : +1.35*LC1+1.35*LC2+1.50*LC5
4/ 4 : +1.35*LC1+1.35*LC2+1.50*LC6
5/ 4 : +1.35*LC1+1.35*LC2+1.50*LC7
6/ 4 : +1.35*LC1+1.35*LC2+1.50*LC8
7/ 7 : +1.00*LC1+1.00*LC2+1.35*LC3+1.35*LC6
8/ 7 : +1.00*LC1+1.00*LC2+1.35*LC4+1.35*LC6
9/ 7 : +1.00*LC1+1.00*LC2+1.35*LC3+1.35*LC8
10/ 7 : +1.00*LC1+1.00*LC2+1.35*LC4+1.35*LC8
11/ 6 : +1.35*LC1+1.35*LC2+1.35*LC3+1.35*LC5
12/ 6 : +1.35*LC1+1.35*LC2+1.35*LC4+1.35*LC5
13/ 6 : +1.35*LC1+1.35*LC2+1.35*LC3+1.35*LC6
14/ 6 : +1.35*LC1+1.35*LC2+1.35*LC3+1.35*LC7
15/ 6 : +1.35*LC1+1.35*LC2+1.35*LC4+1.35*LC6
16/ 6 : +1.35*LC1+1.35*LC2+1.35*LC3+1.35*LC8
17/ 6 : +1.35*LC1+1.35*LC2+1.35*LC4+1.35*LC7
18/ 6 : +1.35*LC1+1.35*LC2+1.35*LC4+1.35*LC8
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List of extremal serviceability load combinations
1/ 2 : +1.00*LC1+1.00*LC2+1.00*LC3
2/ 2 : +1.00*LC1+1.00*LC2+1.00*LC4
3/ 3 : +1.00*LC1+1.00*LC2+1.00*LC5
4/ 3 : +1.00*LC1+1.00*LC2+1.00*LC6
5/ 3 : +1.00*LC1+1.00*LC2+1.00*LC8
6/ 4 : +1.00*LC1+1.00*LC2+0.90*LC4+0.90*LC5
7/ 4 : +1.00*LC1+1.00*LC2+0.90*LC4+0.90*LC8
Deformations in nodes. Global extreme
Linear static - dangerous or all combinations
Group of nodes :1/8
Group of serviceability combi :1/7
node combi Ux
[mm]
Uz
[mm]
Fiy
[mrad]
6 6 44.62 -0.18 1.10
2 3 -14.86 -0.19 2.06
7 1 32.83 19.17 -1.02
8 3 7.42 -59.93 0.63
5 6 0.00 -0.00 7.76
1 3 -0.00 -0.00 -3.73
Figure 14: Deformation SLS combination 3
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Figure 15: Deformation SLS combination 6
Internal forces on members. Member extreme
Linear static - dangerous or all combinations
Group of members :1/7
Group of ultimate combi :1/18
memb cr.nr combi dx
[m]
N
[kN]
Vz
[kN]
My
[kNm]
1 1 1 8.000 51.76 15.45 223.47
1 1 6 0.000 -107.44 -31.36 0.00
1 1 1 0.000 33.72 39.57 -0.00
1 1 12 8.000 -59.84 -48.67 -163.54
1 1 3 8.000 -81.91 -36.48 -291.84
2 1 1 8.000 80.81 14.35 114.78
2 1 6 0.000 -185.01 -0.00 0.00
2 1 1 0.000 72.37 14.35 0.00
2 1 6 8.000 -173.61 -0.00 -0.00
3 1 1 8.000 35.12 -32.21 -74.96
3 1 6 0.000 -107.44 31.36 -0.00
3 1 12 0.000 -102.60 44.25 -0.00
3 1 12 8.000 -78.25 37.82 329.42
4 2 1 11.845 25.35 2.34 -58.16
4 2 12 0.000 -55.85 53.20 -163.54
4 2 6 0.000 -41.63 78.45 -250.88
4 2 1 0.000 21.88 -49.39 223.47
4 2 3 0.000 -46.56 76.63 -291.84
5 2 1 11.845 25.13 4.11 -58.16
5 2 12 0.000 -56.88 76.65 -349.88
5 2 5 0.000 -37.14 82.24 -292.87
5 2 1 0.000 21.66 -30.38 100.44
5 2 3 11.845 -36.44 -2.67 119.09
6 2 1 11.845 41.26 -0.30 -47.11
6 2 3 0.000 -47.06 80.54 -338.10
6 2 5 0.000 -37.14 82.24 -292.87
6 2 1 0.000 37.80 -43.49 215.22
7 2 1 11.845 39.87 10.65 -47.11
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memb cr.nr combi dx
[m]
N
[kN]
Vz
[kN]
My
[kNm]
7 2 12 0.000 -47.42 72.83 -329.42
7 2 6 0.000 -41.63 78.45 -250.88
7 2 1 0.000 36.40 -30.76 74.96
7 2 3 10.836 -36.83 0.45 122.18
-291.8
223.5 114.8
-75.0
329.4
-291.8
223.5
-349.9
119.1
-338.1
215.2
-329.4
122.2
Figure 16: Extremes for My (ULS combinations)
4.2. Stability calculation For the stability check, the 5 critical combinations are used. The stability analysis determines the sway classification of the frame. With this calculation, the value of Vcr is obtained for the relevant load combination. This value can be used to evaluate the sensitivity of the structure to second-order effects. The critical (smallest and positive) load coefficient is found for combination 3 : 13.30. This value is compared with the results of Ref.[1] Method Critical load coefficient EPW 13.71 Ref.[1] 12.5 a) 1/0.073=13.69 Ref.[1] 12.5 b) 1/0.07=14.30 Ref.[1] 12.5 c) 13.20 Ref.[1] 12.5 d) 11.06 There 13.71 > 10.0, we can define the frame as non-sway. A second-order elastic analysis is not necessary. Stability combination
Combi Case coeff
1 1 Self weight 1.00
1 2 Self weight (cladding + roof) 1.00
1 3 Wind W1 1.50
2 1 Self weight 1.35
2 2 Self weight (cladding + roof) 1.35
2 5 Snow S1 1.50
3 1 Self weight 1.35
3 2 Self weight (cladding + roof) 1.35
3 7 Snow S3 1.50
4 1 Self weight 1.35
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Combi Case coeff
4 2 Self weight (cladding + roof) 1.35
4 8 Snow S4 1.50
5 1 Self weight 1.35
5 2 Self weight (cladding + roof) 1.35
5 4 Wind W2 1.35
5 5 Snow S1 1.35
Stability combination:
SC2, 1. critical load coefficient : 13.30
node Ux []
Uy []
Uz []
Fix []
Fiy []
Fiz []
1 0.00 0.00 -0.00 0.00 -267.37 0.00 2 -1947.34 0.00 -0.58 0.00 -194.97 0.00 3 -0.00 0.00 0.00 0.00 -297.78 0.00 4 -1986.87 0.00 0.00 0.00 -151.13 0.00 5 0.00 0.00 0.00 0.00 -267.36 0.00 6 -1947.29 0.00 0.58 0.00 -194.98 0.00 7 -1967.31 0.00 154.57 0.00 114.31 0.00 8 -1967.28 0.00 -154.78 0.00 114.32 0.00 9 -1955.89 0.00 66.36 0.00 -190.99 0.00 10 -1964.24 0.00 131.72 0.00 -185.92 0.00 11 -1972.33 0.00 195.05 0.00 -179.39 0.00 12 -1980.08 0.00 255.75 0.00 -170.90 0.00 13 -1987.40 0.00 313.04 0.00 -159.87 0.00 14 -1993.48 0.00 -51.72 0.00 -147.28 0.00 15 -1999.89 0.00 -101.92 0.00 -142.41 0.00 16 -2006.05 0.00 -150.17 0.00 -136.16 0.00 17 -2011.89 0.00 -195.91 0.00 -128.06 0.00 18 -2017.32 0.00 -238.40 0.00 -117.61 0.00 19 -1993.48 0.00 51.72 0.00 -147.28 0.00 20 -1999.89 0.00 101.92 0.00 -142.41 0.00 21 -2006.05 0.00 150.17 0.00 -136.16 0.00 22 -2011.89 0.00 195.91 0.00 -128.06 0.00 23 -2017.32 0.00 238.39 0.00 -117.60 0.00 24 -1955.84 0.00 -66.36 0.00 -190.99 0.00 25 -1964.19 0.00 -131.72 0.00 -185.93 0.00 26 -1972.28 0.00 -195.06 0.00 -179.40 0.00 27 -1980.03 0.00 -255.76 0.00 -170.91 0.00 28 -1987.35 0.00 -313.06 0.00 -159.88 0.00
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Figure 17: Stability deformation for combination 2
4.3. Elastic analysis with local non-linearties The 5 critical combinations are used. The sway imperfections are derived from the following formula :
1n
12.0k
1n
15.0k
kk
cs
cc
0sc
≤+=
≤+=
φ=φ
For the actual structure we have nc=3 (number of columns per plane) and ns=1 (number of story in the frame). nc 3 ns 1 kc 0.913 ks 1.000 φ0 1/200
φ 1/219 The initial deformation at the eaves is 8000/219=36,5 mm, at the ridge 9500/219=43,4 mm. These are introduced as initial deformation in the local non-linearities. Therefore non-linear combinations are defined.
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Figure 18: Global frame imperfections
Initial deformation num. 1
node X
mm
Y
mm
2 36.50 0.00
4 36.50 0.00
6 36.50 0.00
7 43.40 0.00
8 43.40 0.00
Nonlinear combination
Combi Group of
init. deformations
Group of
init. curvatures
Case coeff
C 1 1 0 1 Self weight 1.00
C 1 1 0 2 Self weight (cladding + roof) 1.00
C 1 1 0 3 Wind W1 1.50
C 2 1 0 1 Self weight 1.35
C 2 1 0 2 Self weight (cladding + roof) 1.35
C 2 1 0 5 Snow S1 1.50
C 3 1 0 1 Self weight 1.35
C 3 1 0 2 Self weight (cladding + roof) 1.35
C 3 1 0 7 Snow S3 1.50
C 4 1 0 1 Self weight 1.35
C 4 1 0 2 Self weight (cladding + roof) 1.35
C 4 1 0 8 Snow S4 1.50
C 5 1 0 1 Self weight 1.35
C 5 1 0 2 Self weight (cladding + roof) 1.35
C 5 1 0 4 Wind W2 1.35
C 5 1 0 5 Snow S1 1.35
Internal forces on members. Member extreme
Nonlinear calculation, local nonlinearities Group of members :1/7
Group of nonlinear combinations :1/5
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memb cr.nr non. c. dx
[m]
N
[kN]
Vz
[kN]
My
[kNm]
1 1 1 8.000 51.71 15.23 222.04
1 1 4 0.000 -107.28 -30.86 -0.00
1 1 1 0.000 33.78 39.44 0.00
1 1 5 8.000 -59.79 -48.32 -160.34
1 1 2 8.000 -81.77 -36.09 -288.27
2 1 1 8.000 80.84 14.01 112.24
2 1 4 0.000 -184.96 0.84 -0.00
2 1 1 0.000 72.40 14.05 0.00
3 1 1 8.000 35.07 -32.41 -76.20
3 1 4 0.000 -107.56 31.84 0.00
3 1 5 0.000 -102.64 44.68 0.00
3 1 5 8.000 -78.31 38.14 332.46
4 2 1 11.845 25.35 2.45 -58.13
4 2 5 0.000 -55.74 52.94 -160.34
4 2 4 0.000 -41.57 78.15 -247.29
4 2 1 0.000 21.88 -49.26 222.04
4 2 2 0.000 -46.50 76.34 -288.27
5 2 1 11.845 25.15 3.99 -58.13
5 2 5 0.000 -56.84 76.89 -352.73
5 2 3 0.000 -37.12 82.46 -295.61
5 2 1 0.000 21.68 -30.48 101.60
5 2 2 11.845 -36.46 -2.36 119.09
6 2 1 11.845 41.28 -0.18 -46.99
6 2 2 0.000 -47.00 80.24 -334.76
6 2 3 0.000 -37.14 81.97 -289.91
6 2 1 0.000 37.82 -43.36 213.84
7 2 1 11.845 39.92 10.54 -46.99
7 2 5 0.000 -47.42 73.07 -332.46
7 2 4 0.000 -41.66 78.71 -254.27
7 2 1 0.000 36.45 -30.85 76.20
7 2 2 10.836 -36.85 0.72 121.66
-288.3
222.0 112.2
-76.2
332.5
-288.3
222.0
-352.7
119.1
-334.8
213.8
-332.5
121.7
Figure 19 : Extremes for my (for non-linear ULS combinations)
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5. Member check 5.1. SLS check We use the SLS results from 0. The limit for the maximum vertical deflection of the roof under SLS is :
mm5.117200
23500
200
Lmax ==≤δ
Since the vertical deflection of 59.93 < 117.5 mm, the condition is satisfied. The limit for the horizontal displacement (SLS) of a portal frame without gantry crane is :
mm3.53150
8000
150
hhoriz ==≤δ
Since the maximum lateral displacement is 44.62 mm < 53.3 mm, the condition is satisfied. 5.2. ULS check The results of the unity checks are as follows :
0.81 0.46 0.91
0.71
0.95 0.85 0.88
Figure 20 : Steel code unity checks
5.2.1. Column check
Macro Member Section Position
m
Combi sect. chk. stab chk.
1 1 IPE550 8.00 2 0.17 0.81
2 2 IPE550 8.00 5 0.05 0.46
3 3 IPE550 8.00 5 0.23 0.91
The critical column is member 3.
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Given the results in 0, we can define the frame as non-sway in the plane. Outside the plane we use a buckling factor of 1.0. At the support, the IPE550 is only charged by pure compression. This results in a class 4 classification. The detailed results are as follows : EC3 Code Check
Macro 1 Member 1 IPE550 S 275 Combi 2 0.81
Basic data EC3
partial safety factor Gamma M0 for resistance of cross-sections 1.10
partial safety factor Gamma M1 for resistance to buckling 1.10
partial safety factor Gamma M2 for resistance of net sections 1.10
Material data
yield strength fy 275.00 MPa
tension strength fu 430.00 MPa
fabrication rolled
SECTION CHECK Width-to-thickness ratio for webs (Tab.5.3.1. a).
ratio 42.13 on position 0.00 m
ratio
maximum ratio 1 30.51
maximum ratio 2 35.13
maximum ratio 3 38.83
==> Class cross-section 4
Width-to-thickness ratio for outstand flanges (Tab.5.3.1. c).
ratio 6.10 on position 0.00 m
ratio
maximum ratio 1 9.24
maximum ratio 2 10.17
maximum ratio 3 13.94
==> Class cross-section 1
The critical check is on position 8.00 m
Internal forces
NSd -81.77 kN
Vy.Sd 0.00 kN
Vz.Sd -36.09 kN
Mt.Sd 0.00 kNm
My.Sd -288.27 kNm
Mz.Sd 0.00 kNm
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Compression check
according to article 5.4.4. and formula (5.16)
Section classification is 1.
Table of values
Nc.Rd 3360.00 kN
unity check 0.02
Shear check (Vz)
according to article 5.4.6. and formula (5.20)
Section classification is 1.
Table of values
Vpl.Rd 1043.92 kN
unity check 0.03
Combined bending, axial force and shear force check according to article 5.4.9. and formula (5.35)
Section classification is 1.
Table of values
MNVy.Rd 695.00 kNm
MNVz.Rd 100.00 kNm
alfa 2.00 beta 1.00
unity check 0.17
Element satisfies the section check !
STABILITY CHECK
Calculation effective area properties with direct method.
Properties
sectional area A eff 11919.4 mm^2 mm^2
Shear area Vy eff 7224.0 mm^2 Vz eff 4695.4 mm^2
radius of gyration iy eff 231.7 mm iz eff 47.2 mm
moment of inertia Iy eff 639646575.6 mm^4 Iz eff 26606961.0 mm^4
elastic section modulus Wy eff 2325987.5 mm^3 Wz eff 253399.6 mm^3
Eccentricity eny -0.0 mm enz 0.0 mm
Buckling parameters yy zz
type non-sway non-sway
Slenderness 28.72 179.55
Reduced slenderness 0.31 1.95
Buckling curve a b
Imperfection 0.21 0.34
Reduction factor 0.97 0.22
Length 8.00 8.00 m
Buckling factor 0.80 1.00
Buckling length 6.42 8.00 m
Critical Euler load 33781.93 864.02 kN
Buckling check
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according to article 5.5.1. and formula (5.45)
Table of values
Nb.Rd 654.18 kN
Beta A 0.89
unity check 0.13
Torsional-flexural buckling check according to article ENV 1993-1-3 : 6.2.3 and formula (6.1) (6.4a-b)(6.5a-b)(6.6)
Table of values
Nb.Rd 654.18 kN
Beta A 0.89
Reduced slenderness 1.95
Reduction factor 0.22
sigma,cr,T 231.76 MPa
sigma,cr,TF 64.29 MPa
Torsional buckling length 8.00 m
unity check 0.13
LTB check according to article 5.5.2. and formula (5.48)
Table of values
Mb.Rd 405.59 kNm
Beta W 0.84
reduction 0.70
imperfection 0.21
Mcr 702.71 kNm
LTB
LTB length 8.00 m
k 1.00
kw 1.00
C1 1.88
C2 0.00
C3 0.94
load in center of gravity
unity check =0.71
Compression and bending check according to article 5.5.4. and formula (5.56)
Table of values
ky 1.00
kz 1.09
muy -0.12
muz -0.78
BetaMy 1.80
BetaMz 1.80
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unity check = 0.03 + 0.50 + 0.00 = 0.53
Compression, bending and LTB check
according to article 5.5.4. and formula (5.57)
Table of values
klt 0.96
kz 1.09
mult 0.38
muz -0.78
BetaMlt 1.80
BetaMz 1.80
unity check =0.13 + 0.68 + 0.00 = 0.81
Element satisfies the stability check !
5.2.2. Beam check To prevent the LTB, the purlins in the beam have to be positioned as follows :
ab
cd
e
f
g
Figure 21 : Position of purlins
The top flange of the beam is held by purlins at the points a, b, c, d and e. At the points f and g, the lower flange of the beam is held by LTB bracings. EC3 Code Check
Macro Member Section Position
m
Loadcase sect. chk. stab chk.
4 4 IPE400 1.75 2 0.26 0.71
5 5 IPE400 1.75 5 0.49 0.95
6 6 IPE400 1.75 2 0.40 0.85
7 7 IPE400 1.75 5 0.43 0.88
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The detailed results from critical beam nr 5 are as follows :
EC3 Code Check
Macro 5 Member 5 IPE400 S 275 Loadcase 5 0.95
Basic data EC3
partial safety factor Gamma M0 for resistance of cross-sections 1.10
partial safety factor Gamma M1 for resistance to buckling 1.10
partial safety factor Gamma M2 for resistance of net sections 1.10
Material data
yield strength fy 275.00 MPa
tension strength fu 430.00 MPa
fabrication rolled
SECTION CHECK Width-to-thickness ratio for webs (Tab.5.3.1. a).
ratio 38.49 on position 2.76 m
ratio
maximum ratio 1 61.50
maximum ratio 2 70.82
maximum ratio 3 103.88
==> Class cross-section 1
Width-to-thickness ratio for outstand flanges (Tab.5.3.1. c).
ratio 6.67 on position 2.76 m
ratio
maximum ratio 1 9.24
maximum ratio 2 10.17
maximum ratio 3 13.94
==> Class cross-section 1
The critical check is on position 1.75 m
Internal forces
NSd -55.27 kN
Vy.Sd 0.00 kN
Vz.Sd 64.62 kN
Mt.Sd 0.00 kNm
My.Sd -229.07 kNm
Mz.Sd 0.00 kNm
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Section properties
A 8.446000e+003 mm^2
Ay/A 0.509 Az/A 0.391
Iy 2.313000e+008 mm^4 Iz 1.318000e+007 mm^4
Iyz 0.000000e+000 mm^4 It 5.108000e+005 mm^4
Iw 4.968547e+011 mm^6
Wely 1.156000e+006 mm^3 Welz 1.464000e+005 mm^3
Wply 1.308000e+006 mm^3 Wplz 2.300000e+005 mm^3
cy 200.00 mm cz 90.00 mm
dy -0.00 mm dz 0.00 mm
Compression check
according to article 5.4.4. and formula (5.16)
Section classification is 1.
Table of values
Nc.Rd 2111.50 kN
unity check 0.03
Shear check (Vz) according to article 5.4.6. and formula (5.20)
Section classification is 1.
Table of values
Vpl.Rd 616.19 kN
unity check 0.10
Combined bending, axial force and shear force check according to article 5.4.9. and formula (5.35)
Section classification is 1.
Table of values
MNVy.Rd 327.00 kNm
MNVz.Rd 57.50 kNm
alfa 2.00 beta 1.00
unity check 0.49
Element satisfies the section check !
STABILITY CHECK
Buckling parameters yy zz
type non-sway sway
Slenderness 42.49 299.86
Reduced slenderness 0.49 3.45
Buckling curve a b
Imperfection 0.21 0.34
Reduction factor 0.93 0.08
Length 11.85 11.85 m
Buckling factor 0.59 1.00
Buckling length 7.03 11.85 m
Critical Euler load 9697.95 194.69 kN
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Warning: slenderness 299.86 is larger then 200.00 !
Buckling check
according to article 5.5.1. and formula (5.45)
Table of values
Nb.Rd 160.84 kN
Beta A 1.00
unity check 0.34
Torsional-flexural buckling check
according to article ENV 1993-1-3 : 6.2.3 and formula (6.1) (6.4a-b)(6.5a-b)(6.6)
Table of values
Nb.Rd 160.84 kN
Beta A 1.00
Reduced slenderness 3.45
Reduction factor 0.08
sigma,cr,T 198.77 MPa
sigma,cr,TF 23.05 MPa
Torsional buckling length 11.85 m
unity check 0.34
LTB check according to article 5.5.2. and formula (5.48)
Table of values
Mb.Rd 311.08 kNm
Beta W 1.00
reduction 0.95
imperfection 0.21
Mcr 2186.57 kNm
LTB
LTB length 1.75 m
k 1.00
kw 1.00
C1 1.20
C2 0.00
C3 1.00
negative influence of load position
unity check =0.74
Compression and bending check according to article 5.5.4. and formula (5.51)
Table of values
ky 1.00
kz 1.25
muy -0.06
muz -0.81
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Table of values
BetaMy 1.80
BetaMz 1.80
unity check = 0.03 + 0.70 + 0.00 = 0.73
Compression, bending and LTB check
according to article 5.5.4. and formula (5.52)
Table of values
klt 0.83
kz 1.25
mult 0.55
muz -0.81
BetaMlt 1.35
BetaMz 1.80
unity check =0.34 + 0.61 + 0.00 = 0.95
Element satisfies the stability check !
6. Connection design 6.1. Bolted beam-to-column connection
CD
IPE40010
10
7
Section CD
IPE550
13
13
7
11
1111
10
10
Figure 22: Beam-to-column connection
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End plate
180
779
2D Plate 20
40 100
65
590
60
6 x M-20 (DIN6914)
Figure 23: Endplate dimensions
Haunch
1426
523
30
311
IPE400
1519
Figure 24: Haunch dimensions
Stiffener
514
98
24 466
23
23
2D Plate 15
Figure 25: Stiffener dimensions
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The detailed calculation note for tension on the top side is as follows : Node 6 : bolted beam-to-column connection side AB
According to EC3, Revised Annex J
1. Input data
Column IPE550
h 550.00 mm
b 210.00 mm
tf 17.20 mm
tw 11.10 mm
r 24.00 mm
fy 275.00 MPa
fu 430.00 MPa
Connected beam IPE400
h 400.00 mm
b 180.00 mm
tf 13.50 mm
tw 8.60 mm
r 21.00 mm
fy 275.00 MPa
fu 430.00 MPa
Haunch under IPE400
hc 355.52 mm
lc 1498.30 mm
b 180.00 mm
tf 13.50 mm
tw 8.60 mm
weld ab 13.00 mm
weld ac 8.00 mm
Partial safety factors
Gamma M0 1.10
Gamma M1 1.10
Gamma Mb 1.25
Gamma Ms 1.10
Gamma Mw 1.25
Stiffener
Stiffener in tension zone
No. pos.[mm] fy[MPa]
1 744.08 275.00
End plate
h 779.00 mm
b 180.00 mm
t 20.00 mm
fy 275.00 MPa
fu 430.00 MPa
Bolts M-20 (DIN6914)
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Bolts M-20 (DIN6914)
type prestressed
grade 10.9
fu 1000.00 MPa
As 245.00 mm^2
do 22.00 mm
S 32.00 mm
e 35.00 mm
h head 13.00 mm
h nut 16.00 mm
Bolt position
row y[mm] spacing[mm]
1 715.00 100.00
2 655.00 100.00
3 65.00 100.00
Internal forces
Combination number 5
N -47.17 kN
Vz 71.26 kN
My -312.53 kNm
Tension top
2. Design moment resistance MRd
2.1. Design resistance of basic components
2.1.1. Column web panel in shear (J.3.5.2.)
Vwp,Rd data
Vwp,Rd 939.53 kN
Beta 1.00
Avc 7232.52 mm^2
2.1.2. Column web in compression (J.3.5.3.)
Fc,wc,Rd data
Fc,wc,Rd 495.28 kN
beff 263.87 mm
twc 11.10 mm
ro1 0.91
ro2 0.73
ro 0.91
kwc 1.00
lambda_rel 1.07
dc 467.60 mm
2.1.3. Haunch in compression
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Fc,h,Rd data
Fc,h,Rd 570.50 kN
bhf 180.00 mm
bhi 524.14 mm
alfa 20.15 deg
2.1.4. Design tension resistance of bolt row
(effective lengths in mm, resistance in kN)
Bt,Rd = 176.40 kN
2.1.4.1. Column flange
kfc = 1.00
row p (p1+p2) alfa e m n e1
1 0.0+30.0 8.00 55.00 25.25 31.56 64.00
2 30.0+295.0 - 55.00 25.25 31.56 -
3 295.0+ 0.0 - 55.00 25.25 31.56 -
row leff,cp,i leff,nc,i
1 158.65 202.00
2 158.65 169.75
3 158.65 169.75
row leff,cp,g leff,nc,g leff,cp,ge1 leff,nc,ge1 leff,cp,ge2 leff,nc,ge2
1 - - - - 139.33 147.12
2 650.00 325.00 139.33 114.87 669.33 379.87
3 - - 669.33 379.87 - -
For individual bolt row:
row leff,1 leff,2 leff Ft,fc,Rd Ft,wc,Rd ro
1 158.65 202.00 202.00 327.48 570.50 1.00
2 158.65 169.75 169.75 306.49 570.50 1.00
3 158.65 169.75 169.75 306.49 570.50 1.00
For bolt group:
group leff,1 leff,2 leff Ft,fc,Rd Ft,wc,Rd ro
1- 1 158.65 202.00 202.00 327.48 570.50 1.00
1- 2 262.00 262.00 262.00 562.54 570.50 1.00
1- 3 852.00 852.00 852.00 1058.40 570.50 1.00
2.1.4.2. Endplate
row p (p1+p2) alfa e m n
1 0.0+30.0 6.31 40.00 37.78 40.00
2 30.0+295.0 5.42 40.00 37.78 40.00
3 295.0+ 0.0 6.31 40.00 37.78 40.00
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row leff,cp,i leff,nc,i
1 237.38 238.28
2 237.38 204.76
3 237.38 238.28
row leff,cp,g leff,nc,g leff,cp,ge1 leff,nc,ge1 leff,cp,ge2 leff,nc,ge2
1 - - - - 178.69 167.72
2 - - 178.69 134.20 - -
3 - - 708.69 432.72 - -
For individual bolt row:
row leff,1 leff,2 leff Ft,ep,Rd Ft,wb,Rd
1 237.38 238.28 238.28 334.61 512.31
2 204.76 204.76 204.76 313.06 440.24
3 237.38 238.28 238.28 334.61 512.31
For bolt group:
group leff,1 leff,2 leff Ft,ep,Rd Ft,wb,Rd
1- 1 237.38 238.28 238.28 334.61 512.31
1- 2 301.92 301.92 301.92 556.95 649.13
3- 3 237.38 238.28 238.28 334.61 512.31
2.2. Determination of Mj,Rd
row h[mm] Ft[kN]
1 697.58 327.48
2 637.58 167.79
3 47.58 0.00
Mj,Rd = 335.43 kNm
Mj,Rd = 335.43 kNm (inclusive normal force)
2.3.Determination of Mj,Rd for compressed haunch at beam
data
alfa 12.87 deg
Af 2430.00 mm^2
Ad 1599.60 mm^2
Me 289.00 kNm
Mj,Rd 289.00 kNm
MSd -217.03 kNm
3. Design shear resistance VRd
VRd data
VRd 290.93 kN
ks 1.00
n 1.00
slip factor 0.30
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VRd data
Fp,Cd 171.50 kN
Ft,Sd -7.86 kN
Fs,Rd 48.49 kN
VRd beam 1336.90 kN
4. Stiffness calculation
4.1. Design rotational stiffness
row k3[mm] k4[mm] k5[mm] k7[mm] keff[mm]
1 37.43 2.44 21.15 7.58 1.63
2 30.86 2.82 16.92 7.58 1.73
Sj data
Sj 49308.21 kNm/rad
Sj,ini 121752.72 kNm/rad
z 667.99 mm
mu 2.47
k1 4.11 mm
k2 4.38 mm
keq 3.35 mm
4.2. Stiffness classification
Stiffness data
E 210000.00 MPa
Ib 231300000.45 mm^4
Lb 23710.00 mm
frame type unbraced
S1 51215.73 kNm/rad
S2 1024.31 kNm/rad
System RIGID
4.3 Check of stiffness requirement
Stiffness data
Fi y infinity kNm/rad
Stiffness modification coef. 2.00
Sj,app infinity kNm/rad
Sj,lower boundary 49167.10 kNm/rad
Sj,upper boundary infinity kNm/rad
Sj,ini is inside the boundaries.
The actual joint stiffness is conform with the joint stiffness of the analysis model.
4.4 Ductility classification
The failure mode is not situated in the column shear zone.
In the endplate we have the following :
0.36 sqrt(fub/fy) d < t <= 0.53 sqrt(fub/fy) d
This results in an intermediate classification for ductility : class 2.
5. Unity checks
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Unity checks
MSd/MjRd 0.93
VSd/VRd 0.24
The connection satisfies.
6. Design calculations
6.1. Calculation weldsize af / Minimum thickness th for stiffener in column
data
MRd 335.43 kNm
Gamma 1.70
h 744.83 mm
FRd 765.58 kN
NT,Rd 607.50 kN
N 607.50 kN
fu 430.00 MPa
BetaW 0.85
minimum af 5.90 mm
af 10.00 mm
Minimum th 13.50 mm
6.2. Calculation aw
data
Ft 531.89 kN
Fv 25.17 kN
lw 301.92 mm
fu 430.00 MPa
BetaW 0.85
minimum aw (a2) 4.00 mm
aw 7.00 mm
Sj,ini = 121752.72 kNm/radSj,MRd = 40741.06 kNm/rad
4.12 8.23 12.35 16.47
mrad
100.0
200.0
300.0
kNm
Figure 26: Moment-rotation diagramma
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In the present case, the length Lb for the stiffness classification is taken as the developed length of the rafter, i.e. 23.71 m. As shown in the previous output, the connection stiffness is conform with the analysis model.
Sj,ini
Sj,ini = 121752.72 kNm/rad
Sj,low
Sj,low = 49167.10 kNm/rad
Sj,upper
Sj,upper = infinity kNm/rad
1.38 2.75 4.13 5.51
mrad
100.0
200.0
300.0
kNm
Figure 27: Stiffness boundaries
The normal output for tension on the bottom side is as follows :
Node 2 : bolted beam-to-column connection side CD
According to EC3, Revised Annex J
1. Input data
Column IPE550
Connected beam IPE400
Haunch under IPE400
hc 355.52 mm
lc 1498.30 mm
b 180.00 mm
tf 13.50 mm
tw 8.60 mm
weld ab 13.00 mm
weld ac 8.00 mm
Partial safety factors
Gamma M0 1.10
Gamma M1 1.10
Gamma Mb 1.25
Gamma Ms 1.10
Gamma Mw 1.25
Stiffener
Stiffener in tension zone
No. pos.[mm] fy[MPa]
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No. pos.[mm] fy[MPa]
1 744.08 275.00
End plate
h 779.00 mm
b 180.00 mm
t 20.00 mm
fy 275.00 MPa
fu 430.00 MPa
Bolts M-20 (DIN6914)
type prestressed
grade 10.9
fu 1000.00 MPa
As 245.00 mm^2
do 22.00 mm
S 32.00 mm
e 35.00 mm
h head 13.00 mm
h nut 16.00 mm
Bolt position
row y[mm] spacing[mm]
1 715.00 100.00
2 655.00 100.00
3 65.00 100.00
Internal forces
Combination number 1
N 21.98 kN
Vz -48.16 kN
My 208.57 kNm
Tension bottom
2. Design moment resistance MRd
2.1. Design resistance of basic components
For individual bolt row:
Bt,Rd = 176.40 kN
row Ft,fc,Rd Ft,ep,Rd
3 306.49 313.06
2 306.49 313.06
1 327.48 334.61
data
Vwp,Rd 939.53 kN
Fc,wc,Rd 838.38 kN
Fc,fb,Rd 838.38 kN
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2.2. Determination of Mj,Rd
row h[mm] Ft[kN]
3 697.20 306.49
2 107.20 306.49
1 47.20 225.39
Mj,Rd = 257.18 kNm
Mj,Rd = 257.18 kNm (inclusive normal force)
3. Design shear resistance VRd
VRd =275.84 kN
4. Stiffness calculation
4.1. Design rotational stiffness
Sj data
Sj 69046.60 kNm/rad
Sj,ini 117210.28 kNm/rad
z 587.47 mm
mu 1.70
k1 4.68 mm
k2 -
keq 2.47 mm
4.2. Stiffness classification
Stiffness data
E 210000.00 MPa
Ib 231300000.45 mm^4
Lb 23710.00 mm
frame type unbraced
S1 51215.73 kNm/rad
S2 1024.31 kNm/rad
System RIGID
4.3 Check of stiffness requirement
Stiffness data
Fi y infinity kNm/rad
Stiffness modification coef. 2.00
Sj,app infinity kNm/rad
Sj,lower boundary 49167.10 kNm/rad
Sj,upper boundary infinity kNm/rad
Sj,ini is inside the boundaries.
The actual joint stiffness is conform with the joint stiffness of the analysis model.
4.4 Ductility classification
The failure mode is not situated in the column shear zone.
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In the endplate we have the following :
0.36 sqrt(fub/fy) d < t <= 0.53 sqrt(fub/fy) d
This results in an intermediate classification for ductility : class 2.
5. Unity checks
Unity checks
MSd/MjRd 0.81
VSd/VRd 0.17
The connection satisfies.
6. Design calculations
data
af 10.00 mm
aw 7.00 mm
Minimum th 13.50 mm
The configuration at the middle column is :
Figure 28: Bolted beam-to-column at middle column
6.2. Bolted plate-to-plate connection
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AB
IPE400
7
7
5
Section AB CD
IPE400
7
7
5
Section CD
87
10
87
10
Figure 29: plate-to-plate connection
End plate
180
500
2D Plate 20
40 100
46
95
295
6 x M-20 (DIN6914)
Figure 30: Endplate dimensions
Node 7 : bolted plate-to-plate connection
According to EC3, Revised Annex J
1. Input data
Right side
Connected beam IPE400
h 400.00 mm
b 180.00 mm
tf 13.50 mm
tw 8.60 mm
r 21.00 mm
fy 275.00 MPa
fu 430.00 MPa
End plate
h 500.00 mm
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End plate
b 180.00 mm
t 20.00 mm
fy 275.00 MPa
fu 430.00 MPa
Bolts M-20 (DIN6914)
type prestressed
grade 10.9
fu 1000.00 MPa
As 245.00 mm^2
do 22.00 mm
S 32.00 mm
e 35.00 mm
h head 13.00 mm
h nut 16.00 mm
Bolt position
row y[mm]
1 436.00 100.00
2 141.00 100.00
3 46.00 100.00
Left side
Connected beam IPE400
h 400.00 mm
b 180.00 mm
tf 13.50 mm
tw 8.60 mm
r 21.00 mm
fy 275.00 MPa
fu 430.00 MPa
End plate
h 500.00 mm
b 180.00 mm
t 20.00 mm
fy 275.00 MPa
fu 430.00 MPa
Partial safety factors
Gamma M0 1.10
Gamma M1 1.10
Gamma Mb 1.25
Gamma Ms 1.10
Gamma Mw 1.25
Internal forces
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Combination number 2
N -36.46 kN
Vz 2.36 kN
My 119.09 kNm
Tension bottom
2. Design moment resistance MRd
2.1. Design resistance of basic components
2.1.1.Beam flange and web in compression (J.3.5.4.) - Right side
Fc,fb,Rd data
Fc,fb,Rd 846.05 kN
section class 1
Mc,Rd 327.00 kNm
hb-tfb 386.50 mm
2.1.2. Beam flange and web in compression (J.3.5.4.) - Left side
Fc,fb,Rd data
Fc,fb,Rd 846.05 kN
section class 1
Mc,Rd 327.00 kNm
hb-tfb 386.50 mm
2.1.3. Design tension resistance of bolt row
(effective lengths in mm, resistance in kN)
Bt,Rd = 176.40 kN
2.1.3.1. Endplate - right side
row p (p1+p2) alfa e m
3 0.0+47.5 - 46.00 32.83 41.04
2 47.5+147.5 5.83 40.00 40.04 40.00
1 147.5+ 0.0 5.83 40.00 40.04 40.00
row leff,cp,i
3 90.00 90.00
2 251.60 233.40
1 251.60 233.40
row leff,cp,g leff,nc,g leff,cp,ge1 leff,nc,ge1 leff,cp,ge2
3 90.00 90.00 - - - -
2 - - - - 420.80 275.81
1 - - 420.80 275.81 - -
For individual bolt row:
row leff,1 leff,2 leff Ft,ep,Rd
3 90.00 90.00 90.00 256.91 -
2 233.40 233.40 233.40 322.10 501.81
1 233.40 233.40 233.40 322.10 501.81
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For bolt group:
group leff,1 leff,2 leff Ft,ep,Rd
3- 3 90.00 90.00 90.00 256.91 -
2- 2 233.40 233.40 233.40 322.10 501.81
2- 1 551.63 551.63 551.63 697.19 1186.00
2.1.3.2. Endplate - left side
row p (p1+p2) alfa e m
3 0.0+47.5 - 46.00 32.83 41.04
2 47.5+147.5 5.83 40.00 40.04 40.00
1 147.5+ 0.0 5.83 40.00 40.04 40.00
row leff,cp,i
3 90.00 90.00
2 251.60 233.40
1 251.60 233.40
row leff,cp,g leff,nc,g leff,cp,ge1 leff,nc,ge1 leff,cp,ge2
3 90.00 90.00 - - - -
2 - - - - 420.80 275.81
1 - - 420.80 275.81 - -
For individual bolt row:
row leff,1 leff,2 leff Ft,ep,Rd
3 90.00 90.00 90.00 256.91 -
2 233.40 233.40 233.40 322.10 501.81
1 233.40 233.40 233.40 322.10 501.81
For bolt group:
group leff,1 leff,2 leff Ft,ep,Rd
3- 3 90.00 90.00 90.00 256.91 -
2- 2 233.40 233.40 233.40 322.10 501.81
2- 1 551.63 551.63 551.63 697.19 1186.00
2.2. Determination of Mj,Rd
row h[mm] Ft[kN]
3 437.20 256.91
2 342.20 322.10
1 47.20 267.04
Mj,Rd = 235.15 kNm
Mj,Rd = 235.15 kNm (inclusive normal force)
3. Design shear resistance VRd
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VRd data
VRd 288.59 kN
ks 1.00
n 1.00
slip factor 0.30
Fp,Cd 171.50 kN
Ft,Sd -6.08 kN
Fs,Rd 48.10 kN
4. Stiffness calculation
4.1. Design rotational stiffness
row k5[mm] k5[mm] k7[mm]
3 17.29 17.29 7.19 3.93
2 24.72 24.72 7.19 4.55
1 24.72 24.72 7.19 4.55
Sj data
Sj 271519.93 kNm/rad
Sj,ini 271519.93 kNm/rad
z 370.81 mm
mu 1.00
keq 9.40 mm
4.2. Stiffness classification
Right side
Stiffness data
E 210000.00 MPa
Ib 231300000.45 mm^4
Lb 23710.00 mm
frame type unbraced
S1 51215.73 kNm/rad
S2 1024.31 kNm/rad
System RIGID
Left side
Stiffness data
E 210000.00 MPa
Ib 231300000.45 mm^4
Lb 23710.00 mm
frame type unbraced
S1 51215.73 kNm/rad
S2 1024.31 kNm/rad
System RIGID
4.3 Check of stiffness requirement
Right side
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Stiffness data
Fi y infinity kNm/rad
Stiffness modification coef. 3.00
Sj,app infinity kNm/rad
Sj,lower boundary 49167.10 kNm/rad
Sj,upper boundary infinity kNm/rad
Sj,ini is inside the boundaries.
The actual joint stiffness is conform with the joint stiffness of the analysis model.
Left side
Stiffness data
Fi y infinity kNm/rad
Stiffness modification coef. 3.00
Sj,app infinity kNm/rad
Sj,lower boundary 49167.10 kNm/rad
Sj,upper boundary infinity kNm/rad
Sj,ini is inside the boundaries.
The actual joint stiffness is conform with the joint stiffness of the analysis model.
4.4 Ductility classification
In the endplate we have the following :
0.36 sqrt(fub/fy) d < t <= 0.53 sqrt(fub/fy) d
This results in an intermediate classification for ductility : class 2.
5. Unity checks
Unity checks
MSd/MjRd 0.51
VSd/VRd 0.01
The connection satisfies.
6. Design calculations
6.1. Calculation af - Right side
data
MRd 235.15 kNm
Gamma 1.70
h 389.69 mm
FRd 1025.80 kN
NT,Rd 607.50 kN
N 607.50 kN
fu 430.00 MPa
BetaW 0.85
minimum af 5.90 mm
af 7.00 mm
6.2. Calculation aw - Right side
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data
Ft 322.10 kN
Fv 1.33 kN
lw 233.40 mm
fu 430.00 MPa
BetaW 0.85
minimum aw (a2) 3.00 mm
aw 5.00 mm
6.3. Calculation af - Left side
data
MRd 235.15 kNm
Gamma 1.70
h 389.69 mm
FRd 1025.80 kN
NT,Rd 607.50 kN
N 607.50 kN
fu 430.00 MPa
BetaW 0.85
minimum af 5.90 mm
af 7.00 mm
6.4. Calculation aw - Left side
data
Ft 322.10 kN
Fv 1.33 kN
lw 233.40 mm
fu 430.00 MPa
BetaW 0.85
minimum aw (a2) 3.00 mm
aw 5.00 mm
Sj,ini = 271519.93 kNm/radSj,MRd = 90856.36 kNm/rad
1.29 2.59 3.88 5.18
mrad
50.0
100.0
150.0
200.0
kNm
Figure 31: Moment-rotation diagramma
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6.3. Base plate connection
CD
IPE550
13 138
Section CD
1010
Figure 32: Baseplate connection
Baseplate
210
570
2D Plate 30
42 126
286
2 x M-24 (DIN601)
Figure 33: Baseplate dimensions
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102
448
Anchor:M-24 (DIN601)
Figure 34: Anchor dimensions
Node 3 : bolted baseplate connection
According to EC3, Annex L & Revised Annex J
1. Input data
Column IPE550
Partial safety factors
Gamma M0 1.10
Gamma M1 1.10
Gamma Mb 1.25
Gamma Mw 1.25
Gamma c 1.10
Gamma fr 1.10
Concrete block
fck_c 25.00 MPa
bond condition poor
Beta_j 0.66
kj 2.00
kfr 0.25
Baseplate
h 570.00 mm
b 210.00 mm
t 30.00 mm
fy 275.00 MPa
fu 430.00 MPa
Anchors M-24 (DIN601)
type straight
bar type high bond
grade 4.6
fu 400.00 MPa
As 353.00 mm^2
do 26.00 mm
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Anchors M-24 (DIN601)
S 36.00 mm
e 39.60 mm
h head 15.00 mm
h nut 19.00 mm
Anchor position
row y[mm] spacing[mm]
1 285.50 125.60
Internal forces
Combination number 1
N 72.40 kN
Vz 14.05 kN
My 0.00 kNm
Tension on right side.
Projected forces (Reactions)
N' = 72.40 kN
T' = 14.05 kN
2. Design compression resistance NRd,c
According to EC3, Annex L
NRd,c data
NRd,c 2357.91 kN
3. Design moment resistance MRd
According to EC3, Revised Annex J
3.1 Design resistance of basic components
For individual anchor row:
Bt,Rd = 101.66 kN
row
1 203.33
data
Fc,base,Rd 486.36 kN
Fc,fb,Rd 1304.43 kN
3.2 Determination of Mj,Rd
row h[mm] Ft[kN]
1 265.90 203.33
Mj,Rd = 54.06 kNm
Mj,Rd = 54.06 kNm (inclusive normal force)
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4. Design tension resistance NRd,t
According to EC3, Revised Annex J
NRd,t = 203.33 kN
5. Design shear resistance VRd
VRd (friction included) 48.72 kN
6. Unity checks
Unity checks
NSd/NRd,t 0.36
MSd/MjRd 0.00
VSd/VRd 0.29
The connection satisfies.
7. Design Calculations.
7.1 Anchorage length.
Designed for Combination number 1
Anchorage data
l,anchor 448.11 mm
7.2. Calculation weldsize
data
af 13.00 mm
aw 8.00 mm
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1.10 PST.06.02 – 01 : DIN 18800 Steel code check (1) Description Stress and stability check of a member with normal force and bending moments and of a member in a simple frame. Project data The following examples of Ref.[1] are calculated : - 9.5.1. Träger mit konstanter Normalkraft - 9.5.3. Rahmenstiel mit Biege-und Normalkraftbeanspruchung Reference [1] G. Hünersen, E. Fritzsche
Stahlbau in Beispielen Berechnungspraxis nach DIN 18 800 Teil 1 bis Teil 3 Werner Verlag GmbH & Co. KG – Dusseldorf 1995
Result Member Example Type Ref[1] EPW % Diff. Remark 4 9.5.1.
Bending+Compression 0.51
0.52
0 %
4 9.5.1. Bending+LTB+Compression
0.99 0.97 3.00 % Difference due to different fabrication conditions for LTB check
2 9.5.3. Bending+LTB+Compression
0.97 0.98 1.03 % Some differences in internal forces for Second Order calculation with global imperfection.
See the chapter "Calculation note" for the detailed output of ESA-Prima Win. Version ESA-Prima Win 3.20.03 Input file + calculation note PST060201.epw Modules 2nd order Frame (PRS.22) DIN 18800 Steel code check (PST.06.02) Author CVL Calculation note
Macro 2 Member 2 IPE360 Steel 37 Comb 1 0.99
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Basic data DIN18800
partial safety factor Gamma M =1.10
Material data
Yield strenght fy,k 235.00 MPa
Tensile strength fu,k 360.00 MPa
fabrication rolled
SECTION CHECK - DIN18800 Teil 1.
Width-to-thickness ratio for webs
ratio 37.33 on position 0.00 m
ratio
maximum ratio PL-PL 32.34 (Tab. 18)
maximum ratio EL-PL 37.39 (Tab. 15)
maximum ratio EL-EL 66.00 (Tab. 12,13,14)
==> Class cross-section : plastic.
Width-to-thickness ratio for flanges
ratio 4.96 on position 4.00 m
ratio
maximum ratio PL-PL 9.10 (Tab. 18)
maximum ratio EL-PL 11.12 (Tab. 15)
maximum ratio EL-EL 15.91 (Tab. 12,13,14)
==> Class cross-section : plastic.
The critical check is on position 4.00 m
Internal forces
N -521.36 kN
Vy 0.00 kN
Vz 16.92 kN
Mt 0.00 kNm
My 78.49 kNm
Mz 0.00 kNm
Only elastic check
Normal force check
according to article (756) and formula (Bild 18)
Section classification isplastic.
Table of values
Npl.d 1553.78 kN
unity check 0.34
Shear check (Vz)
according to article (756) and formula (Bild 18)
Section classification isplastic.
Table of values
Vpl.d 342.70 kN
unity check 0.05
Plastic check around strong axis.
Combined bending, axial force and shear force check
according to article (757) and formula (Tab.16)
Section classification isplastic.
Table of values
alfa.pl.y 1.13
alfa.pl.z 1.25
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Table of values
unity check 0.66
Element satisfies the section check !
STABILITY CHECK - DIN18800 Teil 2.
Buckling parameters yy zz
type non-sway sway
Slenderness 21.89 105.78
Reduced slenderness 0.23 1.13
Buckling curve a b
Imperfection 0.21 0.34
Reduction factor 0.99 0.52
Length 4.00 4.00 m
Buckling factor 0.82 1.00
Buckling length 3.28 4.00 m
Critical Euler load 31468.15 1347.20 kN
Buckling check
according to article T2 (304) and formula (3)
Table of values
Kappa*Npl.d 807.42 kN
unity check 0.65
LTB check
according to article T2 (311) and formula (16)
unity check = 0.38
Table of values
KappaM*Mpl.d 208.13 kNm
KappaM 0.95
LambdaM_r 0.66
n 2.50
kn 1.00
Mkiy =548.06 kNm according to DIN18800 T.2 form.(19)
LTB
LTB length 4.00 m
Betaz 1.00
Beta0 1.00
Ksi 1.77
load in center of gravity
Compression and bending check
according to article T2 (314) and formula (24)
Table of values
Beta_m 1.00
delta_n 0.01
unity check =0.34 + 0.33 + 0.01 = 0.68
Compression, bending and LTB check
according to article T2 (320) and formula (27)
Table of values
ky 0.90
kz 0.93
ay 0.15
az 0.10
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Table of values
BetaMy 1.80
BetaMz 1.80
unity check =0.65 + 0.34 = 0.99
LTB parameters
Table of values
KappaM 0.95
LambdaM_r 0.66
n 2.50
kn 1.00
Lambda_v 105.78
Lambda_vr 1.13
KappaM_v 0.47
ip 0.15 m
c 0.23 m
Mkiy =548.06 kNm according to DIN18800 T.2 form.(19)
Element satisfies the stability check !
Macro 4 Member 4 IPE360 Steel 37 Comb 1 0.97
Basic data DIN18800
partial safety factor Gamma M =1.10
Material data
Yield strenght fy,k 235.00 MPa
Tensile strength fu,k 360.00 MPa
fabrication rolled
SECTION CHECK - DIN18800 Teil 1.
Width-to-thickness ratio for webs
ratio 37.33 on position 6.00 m
ratio
maximum ratio PL-PL 32.34 (Tab. 18)
maximum ratio EL-PL 37.39 (Tab. 15)
maximum ratio EL-EL 123.04 (Tab. 12,13,14)
==> Class cross-section : plastic.
Width-to-thickness ratio for flanges
ratio 4.96 on position 3.00 m
ratio
maximum ratio PL-PL 9.10 (Tab. 18)
maximum ratio EL-PL 11.12 (Tab. 15)
maximum ratio EL-EL 18.87 (Tab. 12,13,14)
==> Class cross-section : plastic.
The critical check is on position 3.00 m
Internal forces
N -150.00 kN
Vy 0.00 kN
Vz 26.00 kN
Mt 0.00 kNm
My 89.00 kNm
Mz 0.00 kNm
Only elastic check
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Normal force check
according to article (756) and formula (Bild 18)
Section classification isplastic.
Table of values
Npl.d 1553.78 kN
unity check 0.10
Shear check (Vz)
according to article (756) and formula (Bild 18)
Section classification isplastic.
Table of values
Vpl.d 342.70 kN
unity check 0.08
Plastic check around strong axis.
Combined bending, axial force and shear force check
according to article (757) and formula (Tab.16)
Section classification isplastic.
Table of values
alfa.pl.y 1.13
alfa.pl.z 1.25
unity check 0.41
Element satisfies the section check !
STABILITY CHECK - DIN18800 Teil 2.
Buckling parameters yy zz
type non-sway sway
Slenderness 40.08 158.67
Reduced slenderness 0.43 1.69
Buckling curve a b
Imperfection 0.21 0.34
Reduction factor 0.95 0.28
Length 6.00 6.00 m
Buckling factor 1.00 1.00
Buckling length 6.00 6.00 m
Critical Euler load 9384.82 598.76 kN
Buckling check
according to article T2 (304) and formula (3)
Table of values
Kappa*Npl.d 436.59 kN
unity check 0.34
LTB check
according to article T2 (311) and formula (16)
unity check = 0.67
Table of values
KappaM*Mpl.d 133.29 kNm
KappaM 0.61
LambdaM_r 1.19
n 2.50
kn 1.00
Mkiy =168.26 kNm according to DIN18800 T.2 form.(19)
LTB
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LTB
LTB length 6.00 m
Betaz 1.00
Beta0 1.00
Ksi 1.35
negative influence of load position
Compression and bending check
according to article T2 (314) and formula (24)
Table of values
Beta_m 1.00
delta_n 0.01
unity check =0.10 + 0.41 + 0.01 = 0.52
Compression, bending and LTB check
according to article T2 (320) and formula (27)
Table of values
ky 0.94
kz 1.04
ay 0.18
az -0.12
BetaMy 1.30
BetaMz 1.80
unity check =0.34 + 0.63 = 0.97
LTB parameters
Table of values
KappaM 0.61
LambdaM_r 1.19
n 2.50
kn 1.00
Lambda_v 158.67
Lambda_vr 1.69
KappaM_v 0.26
ip 0.15 m
c 0.28 m
Mkiy =168.26 kNm according to DIN18800 T.2 form.(19)
Element satisfies the stability check !
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1.11 PST.06.02 – 02 : DIN 18800 Steel Code Check (2) Description Stress and stability check of a simple beam. Project data The following example of Ref.[1] is calculated : - 10.6 Beispiel für Träger mit Druck und zweiachsiger Biegebeanspruchung Reference [1] G. Hünersen, E. Fritzsche
Stahlbau in Beispielen Berechnungspraxis nach DIN 18 800 Teil 1 bis Teil 3 Werner Verlag GmbH & Co. KG – Dusseldorf 1995
Result Member Example Type Ref[1] EPW % Diff. Remark 1 10.6.
Bending+Compression Method 1
0.76
0.77
0 %
1 10.6. Bending++Compression Method 2
0.66 0.71 6.06 %
1 10.6. Bending+LTB+Compression 0.99 0.99 0 % See the chapter "Calculation note" for the detailed output of ESA-Prima Win. Version ESA-Prima Win 3.20.03 Input file + calculation note PST060202.epw Modules 2D Frame (PRS.11) DIN 18800 Steel code check (PST.06.02) Author CVL Calculation note
Method 1
Macro 1 Member 1 IPE300 Fe 360 Loadcase 1 1.00
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Basic data DIN18800
partial safety factor Gamma M =1.10
Material data
Yield strenght fy,k 235.00 MPa
Tensile strength fu,k 360.00 MPa
fabrication rolled
SECTION CHECK - DIN18800 Teil 1.
Width-to-thickness ratio for webs
ratio 35.01 on position 5.00 m
ratio
maximum ratio PL-PL 32.34 (Tab. 18)
maximum ratio EL-PL 37.39 (Tab. 15)
maximum ratio EL-EL 129.60 (Tab. 12,13,14)
==> Class cross-section : plastic.
Width-to-thickness ratio for flanges
ratio 5.28 on position 2.50 m
ratio
maximum ratio PL-PL 9.10 (Tab. 18)
maximum ratio EL-PL 11.12 (Tab. 15)
maximum ratio EL-EL 18.84 (Tab. 12,13,14)
==> Class cross-section : plastic.
The critical check is on position 2.50 m
Internal forces
N -100.00 kN
Vy 0.00 kN
Vz 0.00 kN
Mt 0.00 kNm
My 40.63 kNm
Mz -3.13 kNm
Normal force check
according to article (756) and formula (Bild 18)
Section classification isplastic.
Table of values
Npl.d 1149.36 kN
unity check 0.09
Plastic check around both axis.
Combined bending, axial force and shear force check
according to article (757) and formula (40)(41)(42)
Section classification isplastic.
Table of values
alfa.pl.y 1.13
alfa.pl.z 1.25
unity check 0.21
Element satisfies the section check !
STABILITY CHECK - DIN18800 Teil 2.
Buckling parameters yy zz
type non-sway sway
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Buckling parameters yy zz
Slenderness 40.11 149.23
Reduced slenderness 0.43 1.59
Buckling curve a b
Imperfection 0.21 0.34
Reduction factor 0.95 0.31
Length 5.00 5.00 m
Buckling factor 1.00 1.00
Buckling length 5.00 5.00 m
Critical Euler load 6931.18 500.74 kN
Buckling check
according to article T2 (304) and formula (3)
Table of values
Kappa*Npl.d 357.98 kN
unity check 0.28
LTB check
according to article T2 (311) and formula (16)
unity check = 0.53
Table of values
KappaM*Mpl.d 76.69 kNm
KappaM 0.57
LambdaM_r 1.25
n 2.50
kn 1.00
Mkiy =94.49 kNm according to DIN18800 T.2 form.(19)
LTB
LTB length 5.00 m
Betaz 1.00
Beta0 1.00
Ksi 1.12
negative influence of load position
Compression and bending check
according to article T2 (321) and formula (28)
Table of values
ky 1.04
kz 1.47
ay -0.47
az -1.67
BetaMy 1.30
BetaMz 1.30
unity check =0.28 + 0.32 + 0.17 = 0.77
Compression, bending and LTB check
according to article T2 (323) and formula (30)
Table of values
ky 0.96
kz 1.47
ay 0.16
az -1.67
BetaMy 1.30
BetaMz 1.30
unity check =0.28 + 0.51 + 0.21= 1.00
LTB parameters
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Table of values
KappaM 0.57
LambdaM_r 1.25
n 2.50
kn 1.00
Lambda_v 149.23
Lambda_vr 1.59
KappaM_v 0.29
ip 0.13 m
c 0.23 m
Mkiy =94.49 kNm according to DIN18800 T.2 form.(19)
Element satisfies the stability check !
Method 2
Macro 1 Member 1 IPE300 Fe 360 Loadcase 1 1.00
Basic data DIN18800
partial safety factor Gamma M =1.10
Material data
Yield strenght fy,k 235.00 MPa
Tensile strength fu,k 360.00 MPa
fabrication rolled
SECTION CHECK - DIN18800 Teil 1.
Width-to-thickness ratio for webs
ratio 35.01 on position 5.00 m
ratio
maximum ratio PL-PL 32.34 (Tab. 18)
maximum ratio EL-PL 37.39 (Tab. 15)
maximum ratio EL-EL 129.60 (Tab. 12,13,14)
==> Class cross-section : plastic.
Width-to-thickness ratio for flanges
ratio 5.28 on position 2.50 m
ratio
maximum ratio PL-PL 9.10 (Tab. 18)
maximum ratio EL-PL 11.12 (Tab. 15)
maximum ratio EL-EL 18.84 (Tab. 12,13,14)
==> Class cross-section : plastic.
The critical check is on position 2.50 m
Internal forces
N -100.00 kN
Vy 0.00 kN
Vz 0.00 kN
Mt 0.00 kNm
My 40.63 kNm
Mz -3.13 kNm
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Normal force check
according to article (756) and formula (Bild 18)
Section classification isplastic.
Table of values
Npl.d 1149.36 kN
unity check 0.09
Plastic check around both axis.
Combined bending, axial force and shear force check
according to article (757) and formula (40)(41)(42)
Section classification isplastic.
Table of values
alfa.pl.y 1.13
alfa.pl.z 1.25
unity check 0.21
Element satisfies the section check !
STABILITY CHECK - DIN18800 Teil 2.
Buckling parameters yy zz
type non-sway sway
Slenderness 40.11 149.23
Reduced slenderness 0.43 1.59
Buckling curve a b
Imperfection 0.21 0.34
Reduction factor 0.95 0.31
Length 5.00 5.00 m
Buckling factor 1.00 1.00
Buckling length 5.00 5.00 m
Critical Euler load 6931.18 500.74 kN
Buckling check
according to article T2 (304) and formula (3)
Table of values
Kappa*Npl.d 357.98 kN
unity check 0.28
LTB check
according to article T2 (311) and formula (16)
unity check = 0.53
Table of values
KappaM*Mpl.d 76.69 kNm
KappaM 0.57
LambdaM_r 1.25
n 2.50
kn 1.00
Mkiy =94.49 kNm according to DIN18800 T.2 form.(19)
LTB
LTB length 5.00 m
Betaz 1.00
Beta0 1.00
Ksi 1.12
negative influence of load position
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Compression and bending check
according to article T2 (322) and formula (29)
Table of values
ky 0.79
kz 1.00
cy 0.79
cz 1.26
BetaMy 1.00
BetaMz 1.00
delta_n 0.05
unity check =0.28 + 0.24 + 0.15 + 0.05 = 0.71
Table of values
My 40.63 kNm
Mz 3.13 kNm
Compression, bending and LTB check
according to article T2 (323) and formula (30)
Table of values
ky 0.96
kz 1.47
ay 0.16
az -1.67
BetaMy 1.30
BetaMz 1.30
unity check =0.28 + 0.51 + 0.21= 1.00
LTB parameters
Table of values
KappaM 0.57
LambdaM_r 1.25
n 2.50
kn 1.00
Lambda_v 149.23
Lambda_vr 1.59
KappaM_v 0.29
ip 0.13 m
c 0.23 m
Mkiy =94.49 kNm according to DIN18800 T.2 form.(19)
Element satisfies the stability check !
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1.12 PST.06.02 – 03 : DIN 18800 Steel Code Check (3) Description Stress and stability check of two simple beams. Project data The following example of Ref.[1] is calculated : - A) Dachtragwerk mit zwei Trägerlagen 1/ Pfette (pp.50-51) - B) Dachtragwerk mit einer Trägerlage / Dachträger (pp.54-56) Reference [1] G. Kahlmeyer
Stahlbau nach DIN18800 (11.90) Bemessung und Konstruktion Träger – Stützen – Verbindungen Werner Verlag GmbH & Co. KG – Dusseldorf 1996
Result Member Example Type Ref[1] EPW % Diff. Remark 2 A)Pfette erf cθ,k
[kNm/m] 0.605
0.58
4.3 %
2 A)Pfette vorh cθ,k [kNm/m]
3.78 3.77 0.26 %
4 B)Träger cθM,k [kNm/m]
318 317.9 0 %
4 B)Träger cθA,k reduced [kNm/m]
3.1 3.1 0 %
4 B)Träger cθA,k [kNm/m]
8.72 5.81 33.37 % Error in Ref[1]
4 B)Träger erf cθ,k [kNm/m]
71.8 68.7 4.5 %
4 B)Träger It.id [cm4]
80.3 62.3 22.42 %
4 B)Träger unity check 0.99 1.072 8.28 % See the chapter "Calculation note" for detailed output of ESA-Prima Win. Version ESA-Prima Win 3.20.03 Input file + calculation note PST060203.epw Modules 2D Frame (PRS.01) DIN 18800 Steel code check (PST.06.02)
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Author CVL Calculation note Macro 1 Member 2 IPE180 Fe 360 Loadcase 1 0.18
Basic data DIN18800
partial safety factor Gamma M =1.10
Material data
Yield strenght fy,k 235.00 MPa
Tensile strength fu,k 360.00 MPa
fabrication rolled
SECTION CHECK - DIN18800 Teil 1.
Width-to-thickness ratio for webs
ratio 27.55 on position 3.00 m
ratio
maximum ratio PL-PL 64.68 (Tab. 18)
maximum ratio EL-PL 74.78 (Tab. 15)
maximum ratio EL-EL 347.65 (Tab. 12,13,14)
==> Class cross-section : plastic.
Width-to-thickness ratio for flanges
ratio 4.23 on position 3.00 m
ratio
maximum ratio PL-PL 9.10 (Tab. 18)
maximum ratio EL-PL 11.12 (Tab. 15)
maximum ratio EL-EL 33.83 (Tab. 12,13,14)
==> Class cross-section : plastic.
The critical check is on position 3.00 m
Internal forces
N 0.00 kN
Vy 0.00 kN
Vz 0.00 kN
Mt 0.00 kNm
My 5.74 kNm
Mz 0.00 kNm
Only elastic check
Normal stress check
according to article (747) and formula (33)
Section classification is elastic.
Table of values
Sigma 39.17 MPa
unity check 0.18
Element satisfies the section check !
STABILITY CHECK - DIN18800 Teil 2.
LTB check
according to article T2 (309) and formula (8)
unity check = 0.15
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S =28768.70
S > 10327.04 kN ==> fixed rotation axis
Table of values
k0 0.23
kv 0.35
c0Mk 93.07 kNm/m (form. 10)
c0Pk 45.44 kNm/m
c0Ak 4.31 kNm/m (form. 11a / 11b)
c0Ak 5.20 kNm/m ( Tab. 7 )
vorh ck 3.77 kNm/m
erf ck 0.58 kNm/m
LTB
LTB length 6.00 m
Betaz 1.00
Beta0 1.00
Ksi 1.29
load in center of gravity
direction : downward
Diaphragm data : 40/183/0.88
Table of values
I 277000.00 mm^4
K1 0.20 m/kN
K2 6.71 m^2/kN
Length 10.00 m
frame dist 2.50 m
k 4.00
assembling: positive
bolt position : underside
bolt pitch : br
Element satisfies the stability check !
Macro 2 Member 4 IPE300 Fe 360 Loadcase 1 1.08
Basic data DIN18800
partial safety factor Gamma M =1.10
Material data
Yield strenght fy,k 235.00 MPa
Tensile strength fu,k 360.00 MPa
fabrication rolled
SECTION CHECK - DIN18800 Teil 1.
Width-to-thickness ratio for webs
ratio 35.01 on position 3.64 m
ratio
maximum ratio PL-PL 64.68 (Tab. 18)
maximum ratio EL-PL 74.78 (Tab. 15)
maximum ratio EL-EL 172.81 (Tab. 12,13,14)
==> Class cross-section : plastic.
Width-to-thickness ratio for flanges
ratio 5.28 on position 3.64 m
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ratio
maximum ratio PL-PL 9.10 (Tab. 18)
maximum ratio EL-PL 11.12 (Tab. 15)
maximum ratio EL-EL 16.82 (Tab. 12,13,14)
==> Class cross-section : plastic.
The critical check is on position 3.64 m
Internal forces
N 0.00 kN
Vy 0.00 kN
Vz 3.96 kN
Mt 0.00 kNm
My 86.48 kNm
Mz 0.00 kNm
Shear check (Vz)
according to article (756) and formula (Bild 18)
Section classification isplastic.
Table of values
Vpl.d 253.35 kN
unity check 0.02
Plastic check around strong axis.
Combined bending, axial force and shear force check
according to article (757) and formula (Tab.16)
Section classification isplastic.
Table of values
alfa.pl.y 1.13
alfa.pl.z 1.25
unity check 0.64
Element satisfies the section check !
STABILITY CHECK - DIN18800 Teil 2.
LTB check
according to article T2 (311) and formula (16)
unity check = 1.08
S =24945.59
0.2 S < 19316.22 kN ==> free rotation axis
Table of values
k0 4.00
kv 1.00
c0Mk 317.89 kNm/m (form. 10)
c0Pk 64.95 kNm/m
c0Ak 5.81 kNm/m (form. 11a / 11b)
c0Ak 3.10 kNm/m ( Tab. 7 )
vorh ck 5.25 kNm/m
erf ck 68.68 kNm/m
Table of values
KappaM*Mpl.d 80.18 kNm
KappaM 0.60
LambdaM_r 1.21
n 2.50
kn 1.00
Mkiy =100.36 kNm according to DIN18800 T.2 form.(19)
It,id =202000.00 + 421255.62 =623255.61 mm^4
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LTB
LTB length 8.00 m
Betaz 1.00
Beta0 1.00
Ksi 1.12
negative influence of load position
direction : downward
Diaphragm data : 100/275/0.88
Table of values
I 1703000.00 mm^4
K1 0.22 m/kN
K2 21.41 m^2/kN
Length 13.50 m
frame dist 4.50 m
k 4.00
assembling: positive
bolt position : underside
bolt pitch : 2br
Element does NOT satisfy the stability check !
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1.13 PST.06.02 – 04 : DIN 18800 Steel Code Check (4) Description Stress and stability check of a slender section. Project data The example of Ref.[1] pp.B-Knick01-12. Reference [1] H. Owczarzak, M. Stracke
DIN188000 in Beispielen Seminarunterlagen zum Dortmunder Praxisseminar L S+S Februar 1997
Result Member Example Type Ref[1] EPW Remark 1 BKNICK Biegeknicken
without slender section option (only elastic check)
0.79
0.79
0 %
1 BKNICK Biegeknicken with slender section influence
0.98 0.99 1.00 %
See the chapter "Calculation note" for the detailed output of ESA-Prima Win. Version ESA-Prima Win 3.20.03 Input file + calculation note PST060204.epw Modules 2D Frame (PRS.01) DIN 18800 Steel code check (PST.06.02) Author CVL Calculation note
Macro 1 Member 1 SC450/450/8 St 37 Loadcase 1 0.79
Basic data DIN18800
partial safety factor Gamma M =1.10
Material data
Yield strenght fy,k 240.00 MPa
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Material data
Tensile strength fu,k 360.00 MPa
fabrication cold formed
SECTION CHECK - DIN18800 Teil 1.
Width-to-thickness ratio for webs
ratio 54.25 on position 5.00 m
ratio
maximum ratio PL-PL 32.00 (Tab. 18)
maximum ratio EL-PL 37.00 (Tab. 15)
maximum ratio EL-EL 45.01 (Tab. 12,13,14)
==> Class cross-section : slender section
The critical check is on position 5.00 m
Internal forces
N -1100.00 kN
Vy 0.00 kN
Vz 0.00 kN
Mt 0.00 kNm
My 156.25 kNm
Mz 0.00 kNm
Only elastic check
Normal stress check
according to article (747) and formula (33)
Section classification is elastic.
Table of values
Sigma 154.08 MPa
unity check 0.71
Element satisfies the section check !
STABILITY CHECK - DIN18800 Teil 2.
Buckling parameters yy zz
type non-sway non-sway
Slenderness 55.41 0.55
Reduced slenderness 0.60 0.01
Buckling curve b b
Imperfection 0.34 0.34
Reduction factor 0.84 1.00
Length 10.00 10.00 m
Buckling factor 1.00 0.01
Buckling length 10.00 0.10 m
Critical Euler load 9548.79 95483169.51 kN
Buckling check
according to article T2 (304) and formula (3)
Table of values
Kappa*Npl.d 2588.95 kN
unity check 0.42
Compression and bending check
according to article T2 (314) and formula (24)
Table of values
Beta_m 1.00
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Table of values
delta_n 0.06
unity check =0.42 + 0.31 + 0.06 = 0.79
Element satisfies the stability check !
Macro 1 Member 1 SC450/450/8 St 37 Loadcase 1 1.31
Basic data DIN18800
partial safety factor Gamma M =1.10
Material data
Yield strenght fy,k 240.00 MPa
Tensile strength fu,k 360.00 MPa
fabrication cold formed
SECTION CHECK - DIN18800 Teil 1.
Width-to-thickness ratio for webs
ratio 54.25 on position 5.00 m
ratio
maximum ratio PL-PL 32.00 (Tab. 18)
maximum ratio EL-PL 37.00 (Tab. 15)
maximum ratio EL-EL 45.01 (Tab. 12,13,14)
==> Class cross-section : slender section
The critical check is on position 5.00 m
Internal forces
N -1100.00 kN
Vy 0.00 kN
Vz 0.00 kN
Mt 0.00 kNm
My 156.25 kNm
Mz 0.00 kNm
Normal stress check
according to article DIN18800 T2 (707) and formula DIN18800 T1 (38)
Section classification is slender section
Table of values
A eff 13229.70 mm^2
Wy eff 1777830.58 mm^3
Wz eff 2004388.63 mm^3
ey 15.27 mm
ez -0.00 mm
Table of values
Sigma 180.48 MPa
unity check 0.83
Element satisfies the section check !
STABILITY CHECK - DIN18800 Teil 2.
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Buckling parameters yy zz
type non-sway non-sway
Slenderness 56.60 0.54
Reduced slenderness 0.61 0.01
Buckling curve b b
Imperfection 0.37 0.33
Reduction factor 0.73 1.00
Length 10.00 10.00 m
Buckling factor 1.00 0.01
Buckling length 10.00 0.10 m
Critical Euler load 8559.14 93472420.70 kN
Slender section check according to DIN18800 T2 / 7.
Calculation effective area properties for El-El (Art.7.3)
with direct method (sigmaD=fy,d) (position = 2.00 m
Table of values
sectional area A' 13229.7 mm^2
Shear area Vy' 6285.7 mm^2 Vz' 6944.0 mm^2
radius of gyration iy' 176.7 mm iz' 184.6 mm
moment of inertia Iy' 412942505.0 mm^4 Iz' 450987429.7 mm^4
elastic section modulus Wy' 1718637.0 mm^3 Wz' 2004388.6 mm^3
Eccentricity eny' 15.3 mm enz' -0.0 mm
Increasing bow imperf woy' 15.3 mm woz' 0.0 mm
Buckling factor k 4.0
Critical ratio b/t 54.2
Buckling check
according to article T2 (304) and formula (3)
Table of values
Kappa*Npl.d 2107.92 kN
unity check 0.52
Compression and bending check
according to article T2 (314) and formula (24)
Table of values
Beta_m 1.00
delta_n 0.05
unity check =0.52 + 0.42 + 0.05 = 0.99
Shear buckling check
in buckling field 5
according to article T3 (504) and formula (14)
Table of values
N -1100.00 kN
My 156.25 kNm
Mz 0.00 kNm
Vy 0.00 kN
Vz 0.00 kN
unity check =1.31 + 0.00 + 0.00 + 0.00 = 1.31
Table of values
a 1.11 m
b 0.43 m
t 8.00 mm
alfa 2.56
sigma_e 64.49 MPa
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Table of values
Psi 1.00
sigma_x 154.08 MPa
tau 0.00 MPa
k_sigma_x 4.00
k_tau 5.95
sigma_x_pi 257.96 MPa
tau_pi 383.74 MPa
lambda_p_sig 0.96
lambda_p_t 0.60
ro -24.22
kappa_x 0.80
kappa_tau 1.00
kappa_k 0.73
sigma_xPRd 127.51 MPa
tau_PRd 125.97 MPa
e1 1.41
e3 1.80
Element does NOT satisfy the stability check !
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1.14 PST.06.02 – 05 : DIN 18800 Steel Code Check Tutorial Frame Description Three members (beam, column and a truss beam) of the tutorial project of ESA-Prima win are calculated manually and compared with the results of EPW. Project data See input file. Reference [1] Din 18800 : 1990.11 (neu)
Stahlbauten [2] G. Hünersen, E. Fritzsche
Stahlbau in Beispielen Berechnungspraxis nach DIN 18 800 Teil 1 bis Teil 3 Werner Verlag GmbH & Co. KG – Dusseldorf 1995
See the chapter "Manual calculation" for the manual calculation according to this reference. Result Member/Macro Manual EPW member 7 0.24 0.24 0 % macro 11 0.31
0.71 0.31 0.75 (0.73)
0 % 1.41 %
macro 18 0.44 0.44 (0.49) 0 % See the chapter "Calculation note" for the detailed output of ESA-Prima Win. Version ESA-Prima Win 3.20.03 Input file + calculation note PST060205.epw Modules 3D Frame (PRS.11) DIN 18800 Steel code check (PST.06.02) Author CVL Manual calculation
1.14.1 Check of member 7.
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1.14.1.1 Buckling data First we will discuss the buckling data of this member.
1. System length L : since there are no intermediate restraints on this member the system length L = the full
member length for all buckling modes (L = 6m).
2. The member is loaded through the shear centre.
3. Sway modes: Y-Y: non-sway Z-Z: non-sway.
4. The effective length factors k and kw for L.T.B. are taken as 1 (No end-fixity and no special provision for warping fixity).
1.14.1.2 Check of IPE 270 section.
Now, we will discuss the different steps of a section check.
A. Classification of the section a) Width-to-thickness ratio for webs (using Tab. 18) : b/tw = 219.6 / 6.6 = 33.27 Actually, the web is subjected to bending and tension. But because of the small value of this tensile force (0.20 kN), we consider bending only. For this case, the maximal ratio for a class-1 (PL-PL) member is 64 Since 33.27 < 64 , the web is a class-1 element. b) Width-to-thickness ratio for outstand flanges (using Tab. 18) : b/tf = (64.2-15)/10.2 = 4.82 Max. ratio for a class-1 section flange subject to compression is 9. Since 6.62 < 9 , the flanges are a class 1 element. � Section IPE270 is a class-1 (PL-PL) section for the stability check. B. Stability check : Check for L.T.B. Since this check is the most critical check, we will only perform this check. Critical check = Ultimate combination 6 on position x=3m. Combination 4, member 7 on x =3.0 m : X = 0.20 kN (tension) My = 14.34 kNm Z = 2.25 kN (Shear) Normally, we should perform a check for bending and axial tension, according to Art. 5.5.3 but the program doesn’t take account for the beneficial effect of the tension force. Using Article T2 (311) and Formula 16 :
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M
k M
y
M pl y d. .
≤ 1
Substitution of values : • My = 14.34 kNm
• Determination of Mpl.y.d
• Mpl.y = 240 N/mm² x 484 cm³ = 116.16 kNm • γM1 = 1.1
� Mpl.y.d = 116.16 / 1.1 = 105.6
• Determination of κM :
Determination of λM,red = M
M
pl y
Ki y
.
.
• Mpl.y = 116.16 kNm • Determination of Mki.y :
h < 60 cm => Formula 20
� Mki.y = 50.53 kNm Or by using formula 19:
� Mki.y = 71.88 kNm (assumption: zp = 0, load in center of gravity)
Note 1: ζ = 1.12
Note 2: c² is calculated according to reference (2) :
cI
ll
l I
I
zz t
z
²
( )²( )² . ( )²
=+ω
ββ β
0 00 039
where: β0 = warping factor (default-value = 1), analogue to kw in EC3 βz = LTB factor (default-value = 1), analogue to k in EC3
� λM,red = 1.27 ( > 0.4 => Formula 18)
� Formula 18 => κM = 0.56 Unity check: = 0.24 � Section is o.k.
1.14.2 Check of macro 11
1.14.2.1 Buckling data First we will discuss the buckling data of this macro.
1. System length L : the beams on a height of 3m provide restraint to the column :
the system lengths for member 18: Ly = Lz = 3 m. the system lengths for member 19: Ly = Lz = 5 m.
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2. The member is loaded through the shear centre.
3. Sway modes: Y-Y: non-sway (bracing in roof-plane) Z-Z: non-sway
4. The effective length factors k and kw for L.T.B. are taken as 1 (No end-fixity and no special provision for warping fixity).
1.14.2.2 2.2. Check of HEB 160 section A. Classification of the section a) Width-to-thickness ratio for webs (using Tab. 18) : b/tw = 104 / 8 = 13 On position 0 m. of the beam, the web is subjected to compression only. For this case, the maximal ratio for a class-1 (PL-PL) member is 32. Since 13 < 32 , the web is a class-1 element. b) Width-to-thickness ratio for outstand flanges (using Tab. 18) : b/tf = (76-15)/13 = 4.69 Max ratio for a class-1 section flange subject to compression is 9. Since 4.69 < 9 , the flanges are a class 1 element. � Section HEB 160 is a class-1 (Pl. - Pl.) section for the stability check. B. Section check This check is executed at member 19 on position x = 0 m (start of member 19). Combination 6 : X =-69.74 kN (compression) My = 44.37 kNm Mz = -0.67 kNm => Can be neglected. Z = -8.87 kN (Shear) Y = 0.13 kN => Can be neglected. B.1. Normal force check Using article 756, Bild 18 : • NSd = 69.74 kN • Npl.d = A x fy / γM
= 5430 mm² x 240/1.1 N/mm² = 1184.73 kN
�Unity check: 69.74 / 1185 = 0.059 : Section is o.k. for Compression. B.2. Shear check
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Using article 756, Bild 18 : • Vz.Sd = 8.87 kN
• V
Af
pl z d
vy
M. . =
30γ
Av = h x s Av = 147 x 8 = 1176 mm² � Vpl.z.d = 148.14 kN � Unity check : 8.87/148.14 =0.06 : section is o.k. for shear. B.3. Combined bending, axial force and shear force check Using article 757. Since the small value of Mz , it is o.k. to neglect Mz => only major axis bending. Using Table 16 : Vz.sd / Vpl.z.d < 0.33 & N/Npl.d < 0.1
� So, the only condition to check is M/Mpl.d ≤ 1 • My.Sd = 44.4 kNm • Mpl.y.d = 240 N/mm² x 354 cm³ / 1.1 = 77.2 kNm Unity check: = 0.58 OR, by using Formula 40 • My
* = 74.61 kNm • My < My
* => Formula 41 • c1 = 0.637 x 10-3 • c2 = 1.011 • Mz / Mpl.zd
= 0.0189 Formula 41: = 0.308
�Section is o.k.
B.4. Stability check for Bending + Compression + L.T.B. Since this check is the most critical check, we will only perform this check. Critical check = Ultimate combination 6 on position x=0m of member 19. Combination 6, member 19 on x =0.0 m : X =-69.74 kN (compression) My = 44.4 kNm Mz = -0.67 kNm => Can be neglected. Using article Teil 2, 323 and formula 30 :
N
N
M
Mk
M
Mk
z pl d
y
M pl y d
yz
pl z d
zκ κ. . . . .
+ + ≤ 1
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Substitution of values: 1. First term:
• N = 69.74 kN • Npl.d = 1184.73 kN • Determination of κz (Formula 4)
• Determination of λκ,red: λKz = lz/iz
lz = Lz x k’z (k’z = buckling factor, calculated by the program)
k’z = 0.90 Lz = 500 cm � lz = 450 cm � λΚz = 261/4.05 = 111.11
� λ Kz= 111.11 / 92.9 = 1.19 > 0.2 => Formula 4b
κz = 1
2k k K+ −² λ
• Determination of k : • α = 0.34
� k = 1.45 � κz = 0.44 � First term = 0.134 2. Second term (L.T.B):
• My = 44.4 kNm • Mpl.y.d = 77.2 kNm • Calculation of ky : according to Article 320.
kN
Nay
z pl d
y= −1κ .
but ky ≤ 1
ay Kz M y= −015 015. ..λ β (but ≤0.9)
λ Kz = 1.19
Calculation of β M y. :
Using Table 11: with ψ = 0
� β M y. = 1.8 − 0.7ψ = 1.8
� ay = 0.171
� ky = 0.98 • Determination of κM :
Determination of λM,red = M
M
pl y
Ki y
.
.
• Mpl.y = 84.9 kNm • Determination of Mki.y :
Or by using formula 19:
� Mki.y = 260.39 kNm (Assumption: zp = 0, Load in center of gravity)
Note : c² is calculated according to reference (2)
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cI
ll
l I
I
zz t
z
²
( )²( )² . ( )²
=+ω
ββ β
0 00 039
where: β0 = warping factor (default-value = 1), analogue to kw in EC3 βz = LTB factor (default-value = 1), analogue to k in EC3
� λM,red = 0.57 ( > 0.4 => Formula 18)
� Formula 18 => κM = 0.98
� Second term = 0.575
3. Third term:
• Mz = 0.70 ≈ 0 � Third term is neglected since the small value of Mz
4. Unity check:
0.134 + 0.575 = 0.709 < 1 � Section HEB 160 is o.k.
1.14.3 Check of macro 18.
1.14.3.1 Buckling data First we will discuss the buckling data of this macro.
1. System length L : for each member :
Ly = member length = 1m. Lz = macrolength / 2 = 6 m. (Lateral restraint by middle-rafter) Lltb = macrolength / 2 = 6 m. (Lateral restraint by middle-rafter)
2. The member is loaded through the shear center.
3. Sway modes: Y-Y: non-sway Z-Z: non-sway (bracing in roof-plane)
4. The effective length factors k and kw for L.T.B. are taken as 1 (No end fixity and no special provision for warping fixity).
1.14.3.2 Check of T120/120/13 section A. Cassification of the section a) Width-to-thickness ratio for outstand flanges 1 (using table 5.3.1c of the code) : c/tf = 60/13 = 4.62
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Max ratio for a class-1 section for a rolled flange subject to compression is 10 ε = 10. Since 4.62 < 10, this flange is a class 1 element. b) Width-to-thickness ratio for outstand flanges 2 (using table 5.3.1c of the code) : c/tf =120/13 = 9.23 Max ratio for a class-1 section for a rolled flange subject to compression is 10 ε = 10. Since 9.23 < 10, this flange is a class 1 element. � Section T120/120/13 is a class-1 section . � Note : Since DIN 18800 gives no formulas for T-sections, we have to classify all T-sections as a Class-3 section. (This is also done by the program) B. Stability check : Compression critical buckling check Since this check is the most critical check, we will only perform this check. Critical check = Ultimate combination 1 on position x=0m. of member 46. Combination 5, member 47 on x =0.0 m : X = -38.23 kN (compression) My = 0.59 kNm => Can be neglected (only induced by the self-weight) Z = 0.49 kN (Shear) LTB is neglected, because of the small value of My = 0.59 kNm, induced by the self-weight. Using Article Teil2, 304 and Formula 3:
N
Nz pl dκ .
≤ 1
Substitution of values : • N = 38.23 kN • A = 2960 mm² • fy = 240 N/mm² • γM = 1.1 • => Npl.d = 645.8 kN • Determination of κz (Formula 4)
• Determination of λκ,red: λKz = lz/iz
lz = Lz x k’z (k’z = buckling factor, calculated by the program)
k’z = 0.94 Lz = 600 cm � lz = 564 cm � λΚz = 564/245 = 230.2
� λ Kz= 230.2 / 92.9 = 2.48 > 0.2 => Formula 4b
κz = 1
2k k K+ −² λ
• Determination of k : • α = 0.49
� k = 4.13 � κz = 0.135 Unity check :
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= 0.44
� Section is o.k.
Calculation note
Macro 4 Member 7 IPE270 Fe 360 Ult. comb 5 0.25
Basic data DIN18800
partial safety factor Gamma M =1.10
Material data
Yield strenght fy,k 235.00 MPa
Tensile strength fu,k 360.00 MPa
fabrication rolled
SECTION CHECK - DIN18800 Teil 1.
Width-to-thickness ratio for webs
ratio 33.27 on position 3.00 m
ratio
maximum ratio PL-PL 64.64 (Tab. 18)
maximum ratio EL-PL 74.74 (Tab. 15)
maximum ratio EL-EL 376.85 (Tab. 12,13,14)
==> Class cross-section : plastic.
Width-to-thickness ratio for flanges
ratio 4.82 on position 3.00 m
ratio
maximum ratio PL-PL 9.10 (Tab. 18)
maximum ratio EL-PL 11.12 (Tab. 15)
maximum ratio EL-EL 36.60 (Tab. 12,13,14)
==> Class cross-section : plastic.
The critical check is on position 3.00 m
Internal forces
N 0.20 kN
Vy 0.00 kN
Vz 2.25 kN
Mt 0.00 kNm
My 14.34 kNm
Mz -0.00 kNm
Normal force check
according to article (756) and formula (Bild 18)
Section classification isplastic.
Table of values
Npl.d 980.59 kN
unity check 0.00
Shear check (Vz)
according to article (756) and formula (Bild 18)
Section classification isplastic.
Table of values
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Table of values
Vpl.d 211.49 kN
unity check 0.01
Plastic check around strong axis.
Combined bending, axial force and shear force check
according to article (757) and formula (Tab.16)
Section classification isplastic.
Table of values
alfa.pl.y 1.13
alfa.pl.z 1.25
unity check 0.14
Element satisfies the section check !
STABILITY CHECK - DIN18800 Teil 2.
LTB check
according to article T2 (311) and formula (16)
unity check = 0.25
Table of values
KappaM*Mpl.d 58.52 kNm
KappaM 0.57
LambdaM_r 1.26
n 2.50
kn 1.00
Mkiy =71.89 kNm according to DIN18800 T.2 form.(19)
LTB
LTB length 6.00 m
Betaz 1.00
Beta0 1.00
Ksi 1.12
load in center of gravity
Element satisfies the stability check !
Macro 11 Member 19 HEB160 Fe 360 Ult. comb 7 0.75
Basic data DIN18800
partial safety factor Gamma M =1.10
Material data
Yield strenght fy,k 235.00 MPa
Tensile strength fu,k 360.00 MPa
fabrication rolled
SECTION CHECK - DIN18800 Teil 1.
Width-to-thickness ratio for webs
ratio 13.00 on position 5.00 m
ratio
maximum ratio PL-PL 32.34 (Tab. 18)
maximum ratio EL-PL 37.39 (Tab. 15)
maximum ratio EL-EL 159.24 (Tab. 12,13,14)
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==> Class cross-section : plastic.
Width-to-thickness ratio for flanges
ratio 4.69 on position 0.00 m
ratio
maximum ratio PL-PL 9.10 (Tab. 18)
maximum ratio EL-PL 11.12 (Tab. 15)
maximum ratio EL-EL 18.25 (Tab. 12,13,14)
==> Class cross-section : plastic.
The critical check is on position 0.00 m
Internal forces
N -69.74 kN
Vy 0.13 kN
Vz -8.86 kN
Mt -0.00 kNm
My 44.29 kNm
Mz -0.67 kNm
Normal force check
according to article (756) and formula (Bild 18)
Section classification isplastic.
Table of values
Npl.d 1160.05 kN
unity check 0.06
Shear check (Vy)
according to article (756) and formula (Bild 18)
Section classification isplastic.
Table of values
Vpl.d 513.11 kN
unity check 0.00
Shear check (Vz)
according to article (756) and formula (Bild 18)
Section classification isplastic.
Table of values
Vpl.d 145.05 kN
unity check 0.06
Plastic check around both axis.
Combined bending, axial force and shear force check
according to article (757) and formula (40)(41)(42)
Section classification isplastic.
Table of values
alfa.pl.y 1.14
alfa.pl.z 1.25
unity check 0.32
Element satisfies the section check !
STABILITY CHECK - DIN18800 Teil 2.
Buckling parameters yy zz
type non-sway non-sway
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Buckling parameters yy zz
Slenderness 62.23 112.56
Reduced slenderness 0.66 1.20
Buckling curve b c
Imperfection 0.34 0.49
Reduction factor 0.80 0.43
Length 5.00 5.00 m
Buckling factor 0.84 0.91
Buckling length 4.21 4.55 m
Critical Euler load 2906.37 888.26 kN
Buckling check
according to article T2 (304) and formula (3)
Table of values
Kappa*Npl.d 503.99 kN
unity check 0.14
LTB check
according to article T2 (311) and formula (16)
unity check = 0.60
Table of values
KappaM*Mpl.d 73.95 kNm
KappaM 0.98
LambdaM_r 0.57
n 2.50
kn 1.00
Mkiy =260.39 kNm according to DIN18800 T.2 form.(19)
LTB
LTB length 5.00 m
Betaz 1.00
Beta0 1.00
Ksi 1.77
load in center of gravity
Compression and bending check
according to article T2 (321) and formula (28)
Table of values
ky 1.01
kz 0.99
ay -0.13
az 0.05
BetaMy 1.80
BetaMz 1.80
unity check =0.14 + 0.59 + 0.02 = 0.75
Compression, bending and LTB check
according to article T2 (323) and formula (30)
Table of values
ky 0.98
kz 0.99
ay 0.17
az 0.05
BetaMy 1.80
BetaMz 1.80
unity check =0.14 + 0.58 + 0.02= 0.75
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LTB parameters
Table of values
KappaM 0.98
LambdaM_r 0.57
n 2.50
kn 1.00
Lambda_v 73.84
Lambda_vr 0.79
KappaM_v 0.67
ip 0.08 m
c 0.12 m
Mkiy =260.39 kNm according to DIN18800 T.2 form.(19)
Element satisfies the stability check !
Macro 18 Member 47 T120/120/13 Fe 360 Ult. comb 6 0.49
Basic data DIN18800
partial safety factor Gamma M =1.10
Material data
Yield strenght fy,k 235.00 MPa
Tensile strength fu,k 360.00 MPa
fabrication rolled
SECTION CHECK - DIN18800 Teil 1.
Width-to-thickness ratio for flanges
ratio 9.23 on position 1.00 m
ratio
maximum ratio PL-PL 9.10 (Tab. 18)
maximum ratio EL-PL 11.12 (Tab. 15)
maximum ratio EL-EL 52.26 (Tab. 12,13,14)
==> Class cross-section : plastic.
The critical check is on position 0.00 m
Internal forces
N -38.33 kN
Vy -0.00 kN
Vz -0.46 kN
Mt -0.00 kNm
My 0.57 kNm
Mz 0.01 kNm
Normal stress check
according to article (747) and formula (33)
Section classification is elastic.
Table of values
Sigma 26.25 MPa
unity check 0.12
Shear stress check
according to article (747) and formula (34)
Section classification is elastic.
Table of values
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Table of values
tau 0.76 MPa
unity check 0.01
Element satisfies the section check !
STABILITY CHECK - DIN18800 Teil 2.
Buckling parameters yy zz
type non-sway non-sway
Slenderness 28.44 229.99
Reduced slenderness 0.30 2.45
Buckling curve c c
Imperfection 0.49 0.49
Reduction factor 0.95 0.14
Length 1.00 6.00 m
Buckling factor 1.00 0.94
Buckling length 1.00 5.64 m
Critical Euler load 7585.78 115.98 kN
Warning: slenderness 229.99 is larger then 200.00 !
Buckling check
according to article T2 (304) and formula (3)
Table of values
Kappa*Npl.d 86.92 kN
unity check 0.44
LTB check
according to article T2 (311) and formula (16)
unity check = 0.05
Table of values
KappaM*Mpl.d 11.22 kNm
KappaM 0.98
LambdaM_r 0.56
n 2.50
kn 1.00
Mkiy =39.35 kNm
LTB
LTB length 6.00 m
Compression and bending check
according to article T2 (321) and formula (28)
Table of values
ky 0.95
kz 1.14
ay 0.80
az -0.32
BetaMy 1.86
BetaMz 1.79
unity check =0.44 + 0.05 + 0.00 = 0.49
Compression, bending and LTB check
according to article T2 (323) and formula (30)
Table of values
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Table of values
ky 0.84
kz 1.14
ay 0.36
az -0.32
BetaMy 1.40
BetaMz 1.79
unity check =0.44 + 0.04 + 0.00= 0.49
LTB parameters
Table of values
KappaM 0.98
LambdaM_r 0.56
n 2.50
kn 1.00
Lambda_v 43.46
Lambda_vr 0.46
KappaM_v 0.86
ip 0.04 m
c 0.08 m
Mkiy =39.35 kNm
Element satisfies the stability check !
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1.15 PST.06.03 – 01 : NEN 6770/6771 Steel Code Check Description The stability results for beam 5 of EPW are compared with the results given in Ref.[3], 1.5, pp.1.91-1.97 Project data See the input file. Reference [1] Staalconstructies TGB 1990
Basiseisen en basisrekenregels voor overwegend statisch belaste constructies NEN 6770, december 1991
[2] Staalconstructies TGB 1990 Stabiliteit NEN 6771, december 1991
[3] SG Cursus Rekenen met nieuwe normen januari 1992
Result EPW Ref.[3] Diff. l eff [m] 14.8 11.3 23.6 % ω kip 0.75 0.75 0 % unity check 0.47 0.46 2.12 % The difference in leff is due to the fact that for the calculation of the buckling ratio, EPW does not consider the occasional restraint in the hinged column foot. See the chapter "Calculation note" for the detailed output of ESA-Prima Win. Version ESA-Prima Win 3.20.03 Input file + calculation note PST060301.epw Modules 2D Frame (PRS.01) NEN 6770/6771 Steel code check (PST.06.03) Author CVL
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Calculation note
NEN CHECK 6770/6771
Macro 4 Member 5 IPE360 Fe 360 Loadcase 2 0.47
Basic data NEN6770/6771
partial safety factor Gamma M0 for resistance of cross-sections = 1.00
Material data
Yield strenght fy;rep 235.00 MPa
Tensile strength ft;rep 360.00 MPa
fabrication rolled
SECTION CHECK
Width-to-thickness ratio for webs (NEN 6771 Tab.1.a)
ratio 37.33 on position 0.00 m
ratio
maximum ratio 1 33.00
maximum ratio 2 38.00
maximum ratio 3 42.00
==> Class cross-section 2
Width-to-thickness ratio for outstand flanges (NEN 6771 Tab.1.c)
ratio 6.69 on position 0.00 m
ratio
maximum ratio 1 10.00
maximum ratio 2 11.00
maximum ratio 3 15.08
==> Class cross-section 1
The critical check is on position 0.00 m
Internal forces
Ns;d -94.21 kN
Vy;s;d 0.00 kN
Vz;s;d 13.08 kN
Mx;s;d 0.00 kNm
My;s;d 0.00 kNm
Mz;s;d 0.00 kNm
Compression check
according to article NEN6770 11.2.2. and formula (11.2-5)
Section classification is 2.
Table of values
Nc;u;d 1713.05 kN
unity check 0.05
Shear check (Vz)
according to article NEN6770 11.2.4. and formula (11.2-10) (11.2-14)
Section classification is 2.
Table of values
Vu;d 557.36 kN
unity check 0.02
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Element satisfies the section check !
STABILITY CHECK
Buckling parameters yy zz
type sway non-sway
Slenderness 99.13 153.28
Reduced slenderness 1.06 1.63
Buckling curve a b
Imperfection 0.21 0.34
Reduction factor 0.63 0.30
Length 5.80 5.80 m
Buckling factor 2.56 1.00
Buckling length 14.83 5.80 m
Critical Euler load 1537.59 643.03 kN
Buckling check
according to article NEN6771 12.1.1.1. and formula (12.1-1a) (12.1-1b)
Table of values
Nc;u;d 1713.05 kN
unity check 0.18
Compression and bending check
according to article NEN6771 12.3.1.2.1. and formula (12.3-1) (12.3-2)
Table of values
ny 16.32
nz 6.83
chi y 1.00
chi z 1.00
ey* 25.18 mm
ez* 12.78 mm
My2;s;d 75.86 kNm
Mz2;s;d 0.00 kNm
My1;s;d 0.00 kNm
Mz1;s;d 0.00 kNm
My;mid;s;d 37.93 kNm
Mz;mid;s;d 0.00 kNm
My;equ;s;d 64.48 kNm
Mz;equ;s;d 0.00 kNm
My;u;d 240.13 kNm
Mz;u;d 44.95 kNm
Fy;tot;s;d 94.21 kN
Fz;tot;s;d 94.21 kN
Nc;u;d 1713.05 kN
wkip 0.75
unity check = 0.05+0.39+0.00=0.45 (12.3-1)
unity check = 0.05+0.38+0.03=0.47 (12.3-2)
Torsional buckling check for bending and compression
according to article NEN6771 12.3.3. and formula
Table of values
wkip 0.75
unity check 0.05
Element satisfies the stability check !
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1.16 PST.06.05 – 01 : AISC Steel code Check Tutorial Frame Description The unity check according to AISC-LRFD of members 4, 7 and macro 18 of the Tutorial Frame project are calculated manually. The result is compared with the result of ESA-Prima Win LRFD Steel code check. Project data See input file. Reference Manual of Steel Construction Load & Resistance Factor Design Part 6, Specifications and Codes AISC, Volume I, Second Edition, 1995 See the chapter "Manual calculation" for the manual calculation according to this reference. Result
Type of result Manually ESA-Prima Win % Diff Max. unity check Member 4
0.479 0.48 0 %
Max. unity check Member 7
0.22 0.22 0 %
Max. unity check Macro 18
0.52 0.52 0 %
See the chapter "Calculation note" for the detailed output of ESA-Prima Win. Version ESA-Prima Win 3.20.03 Input file + calculation note PST060501.epw Modules 3D Frame (PRS.11) AISC-LRFD Steel code check (PST.06.05) Author NEM/CVL Manual calculation
1.16.1 Member 4 Critical check : Load Combination : 5 Section : x = 2.22 m in member 4
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Beam type : HEB160
Steel : σe=235 2mmN
Beam length : 5 m Sway modes : Y-Y non-sway Z-Z non-sway
The member is loaded through the shear center. The effective length factors k and kw for LTB. are taken as 1 (No end fixity and no special provision for warping fixity).
1.16.1.1 Classification of the section (Table B5.1) a) Widh-to-thickness ratio for webs The web of member 7 is subjected to flexural compression in section x=3 m. By using table B.5.1, we find :
0.208160
td
w==
Maximum ratio for compact section : 625.109ksi083.34
640
F
640
w,y
== ⇒ WEB is COMPACT SECTION
b) With-to-thickness ratio for outstand flanges By using table B.5.1., we find for section x=0 m:
15.62.102
160
tb
f==
Maximum ratio for compact section : 13.11ksi083.34
65
F
65
w,y
== ⇒ ⇒ FLANGES are COMPACT SECTION
The HEB 160 section is a COMPACT SECTION section.
1.16.1.2 Buckling parameters (Art. E.2.) The formulas used to calculate the slenderness and reduced slenderness in LRFD are the same as in Eurocode 3.
• Slenderness: 836.73
AI
L
i
L
yyy ===λ (Using Art.5.5.1.2. (1) EC3)
571.123
AI
L
i
L
zzz ===λ (Using Art.5.5.1.2. (1) EC3)
• 9.939.93f
E
y1 =ε⋅=⋅π=λ (Using Art.5.5.1.2. EC3)
• Section 1 CLASS 1A =β (Using Art.5.5.1.1. (1) EC3)
• Reduced Slenderness: 786.0N
fAA
1
y
cr
yAy =β⋅
λ
λ=
⋅⋅β=λ (Using Art.5.5.1.2. (1) EC3)
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315.1N
fAA
1
z
cr
yAz =β⋅
λ
λ=
⋅⋅β=λ (Using Art.5.5.1.2. (1) EC3)
1.16.1.3 Normal force (Art. E.1) The design strength for flexural buckling of compression in member 4 is calculated as following : we have: 85.0c =φ
N95.113F658.0F ycr
2c =⋅
= λ
N5.6187481043.595.113AFP 3gcrn =⋅⋅=⋅=
Unity Check : 11062.15.61874885.0
41.8560
P
P 2
nc
u ≤⋅=⋅
=⋅φ
− ⇒ Section OK for tension
1.16.1.4 Torsional buckling (Art.Appendix E.3.) The checking of member 4 of macro 2 for lateral torsional-buckling and flexural-torsional buckling is made in the following way: • 85.0c =φ
• 610ESA,ww mm10807236.4IC ⋅==
• 47ESA,yx mm1049.2II ⋅== 46
ESA,zy mm1089.8II ⋅==
• 45ESA,t mm1014.3IJ ⋅==
• ( )
N33.868II
1JG
lK
CEF
yx2
z
w2
e =+
⋅
⋅+
⋅⋅π=
• Equivalent slenderness: 52.0F
F
e
ye ==λ
• Nominal critical stress: 2yQ
cr mmN85.209F658.0QF
2e =⋅
⋅= λ⋅ with 1Q = and 5.1Qe ≤⋅λ
• Nominal resistance in compression: N31.1139504FAP crgn =⋅=
Unity Check : 11083.8P
P 3
nc
u ≤⋅=⋅φ
− ⇒ Section OK for LTB
1.16.1.5 Strong axis bending (Art.F1)
Using Article F1.2a Design for Flexure : DETERMINATION OF LB:
The laterally unsupported length of the compression flange: Lb = 5 m DETERMINATION OF LP (Formula F1-4):
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mm23.2079in593.1F
r300L
yf
yp ==
⋅=
with mm 40.46 in593.1A
I r ESA,z
y ===
ksi 34.08 Fyf =
Since Lb> Lp we can use Article F1.2. of LRFD code. Using Lateral-torsional buckling rules, we see that we have to determine the flexural design strength φbMn where: Reduction factor φb = 0.90 Mn = nominal strength
DETERMINATION OF LR : (Formula F1-6) mm16.13382in85.526FX11F
XrL 2
L2L
1yr ==++= with:
• FL = 24.08 ksi
• Determination of X1:(Formula F1-8): 2x
1 mmN43.38412329.5571
2
EGJA
SX ==
π=
• Sx :35
ESAy, mm1011.3 ³ni978.18 W ⋅==
• J : 445ESAt, in 0.7543 mm1014.3I =⋅=
• E : modulus of elasticity of steel = 2mmN210000ksi 30457.92 =
• G : Shear modulus of elasticity = 2mmN80769.2ksi 11200 =
• A : in² 8.416 mm² 105.43 3 =⋅ • Determination of X2: (Formula F1-9):
2
4642
x
y
w2 N
mm10247.310546.1GJ
S
I
C4X −− ⋅=⋅=
=
• 446ESAz,y in 21.35 mm108.89 I I =⋅==
• Cw = Warping constant = 6610w in 179.016 mm10.84 I =⋅=
Since Lb < Lr, we use Article F1.2b. to determine the critical value of the moment: Mn = Mcr ≤ Mp
DETERMINATION OF MN :(Formula F1-3) ( ) Nmm24.84048021LL
LLMMMC
pr
pbrppb =
−
−⋅−−⋅
where Nmm831900001054.3235WFZFM 5yESA,plyyp =⋅⋅=⋅=⋅=
( ) Nmm5.516618851011.3115.166WF,10FminSFM 5yESA,elywyfxLr =⋅⋅=⋅−=⋅=
Determination of Cb: Modification factor for non-uniform moment diagram (Formula F1-3):
12.1M3M4M3M5.2
M5.12C
CBAmax
maxb =
+++= with
• Nm32.35115 M max =
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• Nm58.32819 M A =
Nm93.22816 MC = (Absolute value of moment at ¼ and ¾ of the unbraced segment)
• Nmm3.34077 M B = (Absolute value at centreline of the unbraced segment)
The nominal flexural strength MN is the lowest value obtained according to the limit state of yielding, lateral torsional buckling and flange local buckling. In the present situation, MN=Mp.
Unity check : 1469.09.083190
11.35189
M
M
nb
ux ≤=⋅
=⋅φ
⇒ SECTION IS OK
1.16.1.6 Weak axis bending (Art.F1) The introduction of LRFD Chapter F specifies that lateral-torsional buckling limit state is not applicable to members subjected to bending about the minor axis. We just have to perform yielding control following Art. F1.1.
where Nmm39950000107.1235WFZFM 5zESA,plyyp =⋅⋅=⋅=⋅=
Unity check : 11061.19.039950
97.57
M
M 3
nb
uy ≤⋅=⋅
=⋅φ
− ⇒ SECTION IS OK
1.16.1.7 Shear stress (Art. A-F2.2. and F2.)
Web Area: 2www mm8328104thA =⋅=⋅=
Ratio: 260138104
th
w≤== and 27.27F
k187th
yw
v
w=⋅≤ with 5kv =
We find: N117312235000000000832.06.0FA6.0V ywwn =⋅⋅=⋅⋅=
9.0v =φ
Unity Check : 11073.1V
V 2
nv
u ≤⋅=⋅φ
− ⇒ Section OK for Shear Stress
1.16.1.8 Shear Stress Check (Art. H2.) For member under combined torsion, flexure, shear, and axial force, we have:
Shear stress given by ESA-Prima Win : 2uv mN29.1678698f =
Unity Check: 11032.1F6.0
f 2
y
uv ≤⋅=⋅φ⋅
− with 9.0=φ
1.16.1.9 Combined stresses (Art.H1.1.) Following Art. H1.1. of LRFD, we have, for a symmetric member in flexure and tension, the following check to perform:
N20.618232)LTBP;bucklingPmin(P nnn ==
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Unity Check : 479.0M
M
M
M
P2
P 2.0
P
P
nyb
y,u
nxb
x,u
n
u
nn
u =
⋅φ+
φ+
⋅φ⋅⇒≤
⋅φ⇒ Section OK
1.16.2 Member 7 Critical check : Load Combination : 6 Section : x = 3 m Beam type : IPE270
Steel : σe=235 2mmN
Beam length : 6 m Sway modes : Y-Y non-sway Z-Z non-sway The member is loaded through the shear centre. The effective length factors k and kw for L.T.B. are taken as 1 (No end fixity and no special provision for warping fixity).
1.16.2.1 Classification of the section (Table B5.1) a) Width-to-thickness ratio for webs The web of member 7 is subjected to flexural compression in section x=3 m. By using table B.5.1, we find:
909.406.6270
td
w==
Maximum ratio for compact section: 625.109ksi083.34
640
F
640
w,y
== ⇒ WEB is COMPACT SECTION
b) With-to-thickness ratio for outstand flanges By using table B.5.1., we find for section x=0 m:
61.62.102
135
tb
f==
Maximum ratio for compact section: 13.11ksi083.34
65
F
65
w,y
== ⇒ ⇒ FLANGES are COMPACT SECTION
The IPE 270 section is a COMPACT SECTION.
1.16.2.2 Normal force (Art. D.1) The design strength of tension in member 7 is calculated as following : For yielding in gross section : 9.0t =φ
10786501059.4235AFP 3gyn =⋅⋅=⋅=
Unity Check : 11082.110786509.0
28.177
P
P 4
nt
u ≤⋅=⋅
=⋅φ
− ⇒ Section OK for tension
1.16.2.3 Strong axis bending (Art.F1)
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Using Article F1.2a Design for Flexure : DETERMINATION OF LB:
The laterally unsupported length of the compression flange: Lb = 6 m DETERMINATION OF LP (Formula F1-4):
mm39.1554in19.61F
r300L
yf
yp ==
⋅=
with in 1.19 cm 30.2 ry ==
ksi 34.08 N/mm² 235 Fy ==
Since Lb> Lp we can use Article F1.2. of LRFD code. Using Lateral-torsional buckling rules, we see that we have to determine the flexural design strength φbMn where: Reduction factor φb = 0.90 Mn = nominal strength
DETERMINATION OF LR : (Formula F1-6) mm05.5521in36.217FX11F
XrL 2
L2L
1yr ==⋅++⋅
⋅= with:
• FL = 24.08 ksi
• Determination of X1:(Formula F1-8): 2x
1 mmN80.1827568.2650
2
AJGE
SX ==
⋅⋅⋅⋅
π=
• Sx :35
ESAy, mm104.29 ³ni179.26 W ⋅==
• J : in4 0.383 mm101.6 I 45ESAt, =⋅=
• E : modulus of elasticity of steel = 2mmN210000ksi 30457.92 =
• G : Shear modulus of elasticity = 2mmN23.80769ksi 11200 =
• A : in² 7.12 mm²104.59 3 =⋅
• Determination of X2: (Formula F1-9):
2
4532
x
y
w2 N
mm1048.710556.3JG
S
I
C4X −− ⋅=⋅=
⋅⋅⋅=
• 446ESAz,y in 10.09 mm104.2 I I =⋅==
• Cw = Warping constant = 6610w in 265.42 mm10.1277 I =⋅=
Since Lb > Lr, we use Article F1.2b. to determine the critical value of the moment: Mn = Mcr ≤ Mp
DETERMINATION OF MCR :(Formula F1-13) Nmm30.73427747
rL2
XX1
rL
2XSCMM
2
y
b
221
y
b
1xbncr =
⋅+
⋅⋅⋅==
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• Determination of Cb: Modification factor for non-uniform moment diagram(Formula F1-3):
1467.1M3M4M3M5.2
M5.12C
CBAmax
maxb =
⋅+⋅+⋅+⋅
⋅= with
• Nmm1015.1 M 7max ⋅=
• Nmm101.1 M M 7CA ⋅== (Absolute value of moment at ¼ and ¾ of the unbraced segment)
• Nmm105.1 M 7B ⋅= (Absolute value at centreline of the unbraced segment)
Unity check : 12255.09.030.73427747
76.14905676
M
M
nb
u ≤=⋅
=⋅φ
⇒ SECTION IS O.K.
1.16.2.4 Shear stress (Art.F2. and A-F2.2.)
Web Area: 2ww mm17826.6270tdA =⋅=⋅=
Ratio: 26027.336.66.219
th
w≤== and 11.34
F523
th26.27
F418
ywwyw
=≤≤=
We find: N57.205911
th
F418FA6.0
V
w
ywyww
n =
⋅⋅⋅
=
9.0v =φ
Unity Check : 10129.060.185335
05.2400
V
V
nv
u ≤==⋅φ
⇒ Section OK for Shear Stress
1.16.2.5 Shear stress (Art. H2.) For member under combined torsion, flexure, shear, and axial force, we have:
Shear stress given by ESA-PRIMAWIN: 2uv mmN52.1f =
Unity Check : 11018.7F
f 3
y
uv ≤⋅=⋅φ
− with 9.0=φ
1.16.2.6 Combined stresses (Art.H1.1.) Following Art. H1.1. of LRFD, we have, for a symmetric member in flexure and tension, the following check to perform :
Unity Check : 22.0M
M
M
M
P2
P 2.0
P
P
nyb
y,u
nxb
x,u
n
u
nn
u =
⋅φ+
φ+
⋅φ⋅⇒≤
⋅φ⇒ Section OK
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1.16.3 Macro 18 Critical check : Load Combination : 1 Section : x=0 m in member 47 Beam type : T120/120/13
Steel : σe=235 2mmN
Beam lengths : Ly = member length = 1 m Lz = macro length divided by 2 = 6m(Lateral restraint by middle-rafter) LLTB = macro length divided by 2 = 6m(Lateral restraint by middle-rafter) Sway mode : Y-Y non-sway Z-Z non-sway The member is loaded through the shear centre. The effective length factors k and kw for LTB. are taken as 1 (No end fixity and no special provision for warping fixity).
1.16.3.1 Classification of the section (Table B5.1) a) Width-to-thickness ratio for Legs The web of member 47 is subjected to flexural compression in section x=0 m. By using table B.5.1, we find:
61.4132
120
tb
w==
Maximum ratio for compact section: 018.13ksi083.34
76
F
76
w,y
== ⇒ LEG is NON-COMPACT SECTION
The T120/120/13 section is a NON-COMPACT SECTION.
1.16.3.2 Buckling parameter (Art. E.2.) The formulas used to calculate the slenderness and reduced slenderness in LRFD are the same as in Eurocode 3.
• 9.939.93f
E
y1 =ε⋅=⋅π=λ (Using Art.5.5.1.2. EC3)
• Slenderness: 438.28
AI
L
i
L
y
y
yy ===λ (Using Article 5.5.1.2. (1) EC3)
673.244
AI
L
i
L
z
z
zz ===λ (Using Article 5.5.1.2. (1) EC3)
• Section 3 CLASS 1A =β (Using Article 5.5.1.1. (1) EC3)
• Reduced Slenderness: 302.0N
fAA
1
y
cr
yAy =β⋅
λ
λ=
⋅⋅β=λ (Using Art. 5.5.1.2. (1) EC3)
605.2N
fAA
1
z
cr
yAz =β⋅
λ
λ=
⋅⋅β=λ (Using Art. 5.5.1.2. (1) EC3)
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1.16.3.3 Normal force (Art. D.1) The design strength for flexural buckling of compression in member 47 is calculated as follows : we have : 85.0c =φ
N37.30F877.0
F y2c
cr =⋅
λ=
N69.898961096.237.30AFP 3gcrn =⋅⋅=⋅=
Unity Check : 1463.069.8989685.0
69.35437
P
P
nc
u ≤=⋅
=⋅φ
⇒ Section OK for tension
1.16.3.4 Torsional buckling (Art.Appendix E.3.) The checking of member 47 of macro 18 for lateral torsional-buckling and flexural-torsional buckling is made in the following way: • 85.0c =φ
• 6ESA,ww mm0IC ==
• 46ESA,yx mm1066.3II ⋅== 46
ESA,zy mm1078.1II ⋅==
• 45ESA,t mm10834.1IJ ⋅==
• Co-ordinate of shear centre with respect to centroid: 0x0 = and mm59.27y0 =
• 98.50A
IIyxr yx2
020
20 =
+++=
• 707.0r
yx1H
20
20
20 =
+−=
• 762.2562
rLk
EF
2
x
xx
2
ex =
⋅
⋅π=
• 43.34
rLk
EF
2
y
yy
2
ey =
⋅
⋅π=
• ( )
283.1921rA
1JG
lk
CEF
20
2LTBz
w2
ez =⋅
⋅
⋅+
⋅
⋅⋅π=
• Equivalent slenderness: 349.0F
F
ez
ye ==λ
• Nominal critical stress: 2yQ
cr mmN27.223F658.0QF
2e =⋅
⋅= λ⋅ with 1Q = and 5.1Qe ≤⋅λ
• Nominal resistance in compression: N21.660885FAP crgn =⋅=
Unity Check : 110308.6P
P 2
nc
u ≤⋅=⋅φ
− ⇒ Section OK for LTB
1.16.3.5 Strong axis bending check (Art.F1.2c)
Using Article F1.2c Design for Flexure :
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DETERMINATION OF LB:
The laterally unsupported length of the compression flange: Lb = 6 m DETERMINATION OF MN :(Formula F1-13)
Nm62.9905
WFSFM,Nm62.9905B1BL
JGIEminMM elESA,yyxyr
2
b
ycrn
=
⋅=⋅==
++⋅
⋅⋅⋅⋅π==
with 120mm4.72ind with 143.0J
I
L
d3.2B
y
b
==−=⋅
⋅−=
Unity check : 10622.09.062.9905
24.553
M
M
nb
ux ≤=⋅
=⋅φ
⇒ SECTION is O.K.
1.16.3.6 Weak axis bending (Art.F1.1.) The introduction of LRFD Chapter F specifies that lateral-torsional buckling limit state is not applicable to members subjected to bending about the minor axis. We just have to perform yielding control following Art. F1.1. We remark that, for non-compact section, it’s more useful to calculate Mp with Wz,elESA. where Nm69.7004WFZFMM zESA,elyypn =⋅=⋅==
Unity check : 11041.39.069.7004
5.21
M
M 3
nb
uy ≤⋅=⋅
=⋅φ
− ⇒ SECTION IS OK
1.16.3.7 Shear Stress (Art. H2.) For member under combined torsion, flexure, shear, and axial force, we have:
Shear stress given by ESA-Prima Win : 2uv mmN83.0f =
Unity Check : 11092.3F
f 3
y
uv ≤⋅=⋅φ
− with 9.0=φ
1.16.3.8 Combined Stresses (Art.H1.1.) Following Art. H1.1. of LRFD, we have, for a symmetric member in flexure and tension, the following check to perform :
( ) N43.89874P,PminP LTB,nbuckling,nn ==
Unity Check : 5203.0M
M
M
M
9
8
P2
P 2.0
P
P
nyb
y,u
nxb
x,u
n
u
nn
u =
⋅φ+
φ⋅+
⋅φ⋅⇒≥
⋅φ⇒ Section OK
Calculation note - Member 4
AISC - LRFD Check
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Macro 2 Member 4 HEB160 Fe 360 Ult. comb 6 0.48
Material data
Yield stress Fy 235.00 MPa
Tensile stress Fu 360.00 MPa
fabrication rolled
Cfr. Table B5.1. ratio Compact Non-compact
Webs 20.00 107.08 166.15
Outstanding flanges 6.15 11.13 28.73
Section is classified as compact section.
Section is checked as compact section.
The critical check is on position 2.22 m
Axis definition :
- local x- axis in this code check is referring to the local y axis in EPW
- local y- axis in this code check is referring to the local z axis in EPW
Internal forces
Pu -8.55 kN
Vux 0.02 kN
Vuy -1.85 kN
Mut -0.00 kNm
Mux 35.23 kNm
Muy -0.06 kNm
Buckling parameters xx yy
type non-sway non-sway
Slenderness 73.84 123.57
Reduced slenderness 0.79 1.32
Length 5.00 5.00 m
Buckling factor 1.00 1.00
Buckling length 5.00 5.00 m
Buckling check
according to article E2 and formula (E2-1)
Table of values
Pn 618.23 kN
Pu 8.55 kN
Fcr 113.85 MPa
Resistance factor 0.85
unity check 0.02
Torsional buckling check
according to article A-E3. and formula (A-E3-1)
Table of values
Pn 1139.42 kN
Pu 8.55 kN
Fe 868.53 MPa
Equiv.slenderness 0.52
Resistance factor 0.85
unity check 0.01
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LTB data
Lb 5.00 m
Cb 1.12
Strong axis bending check
according to article F1.2a and formula (F1-2)
Table of values
Lr 13.38 m
Lp 2.08 m
Mp 83.19 kNm
Mr 51.83 kNm
Mcr 165.19 kNm
Mn 83.19 kNm
Mu 35.23 kNm
Resistance factor 0.90
unity check 0.47
Weak axis bending check
according to article F1. and formula -
Table of values
Mn 39.27 kNm
Mu 0.06 kNm
Resistance factor 0.90
unity check 0.00
Shear stress check
according to article A-F2.2. and formula (A-F2-1)
in buckling field 1
Table of values
a 5.00 m
h 0.10 m
tw 8.00 mm
kv 5.00
Vn 117.31 kN
Vu -1.85 kN
Resistance factor 0.90
unity check 0.02
Shear stress check
according to article H2.(b) and formula (H2-2)
Table of values
fuv 1.70 MPa
Resistance factor 0.90
unity check 0.01
Combined stresses check
according to article H1.2. and formula (H1-1b)
Table of values
Pn 618.23 kN
Mnx 83.19 kNm
Mny 39.27 kNm
Pu 8.55 kN
Mux 35.23 kNm
Muy 0.06 kNm
Res. factor compression 0.85
Res. factor flexure 0.90
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unity check = 0.01+0.47+0.00=0.48 (H1-1b)
Element satisfies the stability check !
Calculation note - Member 7
Macro 4 Member 7 IPE270 Fe 360 Ult. comb 7 0.22
Material data
Yield stress Fy 235.00 MPa
Tensile stress Fu 360.00 MPa
fabrication rolled
Cfr. Table B5.1. ratio Compact Non-compact
Webs 40.91 109.62 166.15
Outstanding flanges 6.62 11.13 28.73
Section is classified as compact section.
Section is checked as compact section.
The critical check is on position 3.00 m
Axis definition :
- local x- axis in this code check is referring to the local y axis in EPW
- local y- axis in this code check is referring to the local z axis in EPW
Internal forces
Pu 0.18 kN
Vux 0.00 kN
Vuy 2.40 kN
Mut 0.00 kNm
Mux 14.91 kNm
Muy -0.00 kNm
Normal force check
according to article D1 and formula (D1-1)
Table of values
Pn 1078.65 kN
Pu 0.18 kN
Resistance factor 0.90
unity check 0.00
LTB data
Lb 6.00 m
Cb 1.15
Strong axis bending check
according to article F1.2b and formula (F1-12)
Table of values
Lr 5.52 m
Lp 1.55 m
Mp 113.74 kNm
Mr 71.49 kNm
Mcr 74.23 kNm
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Table of values
Mn 74.23 kNm
Mu 14.91 kNm
Resistance factor 0.90
unity check 0.22
Shear stress check
according to article A-F2.2. and formula (A-F2-1)
in buckling field 1
Table of values
a 6.00 m
h 0.22 m
tw 6.60 mm
kv 5.00
Vn 204.36 kN
Vu 2.40 kN
Resistance factor 0.90
unity check 0.01
Shear stress check
according to article H2.(b) and formula (H2-2)
Table of values
fuv 1.52 MPa
Resistance factor 0.90
unity check 0.01
Combined stresses check
according to article H1.1. and formula (H1-1b)
Table of values
Pn 1078.65 kN
Mnx 74.23 kNm
Mny 22.00 kNm
Pu 0.18 kN
Mux 14.91 kNm
Muy 0.00 kNm
Res. factor tension 0.90
Res. factor flexure 0.90
unity check = 0.00+0.22+0.00=0.22 (H1-1b)
Element satisfies the stability check !
Calculation note - Macro 18
Macro 18 Member 47 T120/120/13 Fe 360 Ult. comb 2 0.52
Material data
Yield stress Fy 235.00 MPa
Tensile stress Fu 360.00 MPa
fabrication rolled
Cfr. Table B5.1. ratio Compact Non-compact
Outstanding flanges 4.62 - 13.02
Section is classified as non-compact section.
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Section is checked as non-compact section.
The critical check is on position 0.00 m
Axis definition :
- local x- axis in this code check is referring to the local y axis in EPW
- local y- axis in this code check is referring to the local z axis in EPW
Internal forces
Pu -35.48 kN
Vux -0.00 kN
Vuy -0.44 kN
Mut -0.01 kNm
Mux 0.55 kNm
Muy 0.02 kNm
Buckling parameters xx yy
type non-sway non-sway
Slenderness 28.44 244.67
Reduced slenderness 0.30 2.61
Length 1.00 6.00 m
Buckling factor 1.00 1.00
Buckling length 1.00 6.00 m
Warning: slenderness 244.67 is larger then 200.00 !
Buckling check
according to article E2 and formula (E2-1)
Table of values
Pn 89.87 kN
Pu 35.48 kN
Fcr 30.36 MPa
Resistance factor 0.85
unity check 0.46
Torsional buckling check
according to article A-E3. and formula (A-E3-1)
Table of values
Pn 89.61 kN
Pu 35.48 kN
Fe 34.52 MPa
Equiv.slenderness 2.61
Resistance factor 0.85
unity check 0.47
LTB data
Lb 6.00 m
Cb 4.04
Strong axis bending check
according to article F1.2c and formula (F1-15)
Table of values
Mcr 9.91 kNm
Mn 9.91 kNm
Mu 0.55 kNm
Resistance factor 0.90
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Table of values
unity check 0.06
Weak axis bending check
according to article F1. and formula -
Table of values
Mn 7.00 kNm
Mu -0.02 kNm
Resistance factor 0.90
unity check 0.00
Shear stress check
according to article H2.(b) and formula (H2-2)
Table of values
fuv 0.82 MPa
Resistance factor 0.90
unity check 0.01
Combined stresses check
according to article H1.2. and formula (H1-1a)
Table of values
Pn 89.61 kN
Mnx 9.91 kNm
Mny 7.00 kNm
Pu 35.48 kN
Mux 0.55 kNm
Muy -0.02 kNm
Res. factor compression 0.85
Res. factor flexure 0.90
unity check = 0.47+8/9(0.06+0.00) =0.52 (H1-1a)
Element satisfies the stability check !
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1.17 PST.06.06 – 01 : CM 66 Steel Code Check Tutorial Frame Description The unity check according to CM 66 of members 3, 7 and 46 of the Tutorial Frame project are calculated manually. The result is compared with the result of ESA-Prima Win CM66 Steel code check. Project data See input file. Reference Règles de calcul des constructions en acier ITBTP / CTICM Règles CM Décembre 1966 Editions Eyrolles 1982 See the chapter "Manual calculation" for the manual calculation according to this reference. Result
Type of result Manually ESA-Prima Win % Diff Max. unity check Member 3
0.392 0.4 0 %
Max. unity check Member 7
0.379 0.38 0 %
Max. unity check Member 46
0.426 0.43 0 %
See the chapter "Calculation note" for the detailed output of ESA-Prima Win. Version ESA-Prima Win 3.20.03 Input file + calculation note PST060601.epw Modules 3D Frame (PRS.11) CM66 Steel code check (PST.06.06) Author NEM/CVL Manual calculation
1.17.1 Member 3 Critical check : Load Combination : 9
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Section : x=0 m Beam Type : HEA180
Steel : σe=235 2mmN
Beam Length : 3 m Sway modes : Y-Y non-sway Z-Z non-sway
The member is loaded through the shear centre. We choose the ultimate loading case to compute and to verify the tutorial TUTCM66.epw. We must note capital letters are used to indicate ESA-Prima Win axis and small letter CM 66 axis.
1.17.1.1 Section Check A. Calculation of the plastic factor (Art.3,212-13,212) Using the table and figure 13,212 for H profile and Art.3,212 we have the following plastic factor :
ψx=1.06 (figure)
ψy=1.185 (table) B. Normal Stress (Art.1,3-3,3) The member is subjected to the following internal forces
X=-4861.09 N MX=-0.92Nm Y=-17.9 N MY=0 Nm Z=24198.37N MT=-1.2Nm
An= 0.00453 m2
By converting these internal forces according to the CM66 axis, we have N=-4861.09 N Mx=-0.92 Nm Ty=-17.9 N My=0 Nm Tz=24198.37 N Mt=-1.2 Nm
• Normal Stress (Art.1,312) : 2
net
N/m 3.107308800453.0
09.4861
A
N===σ
Unity Check : 11056.4235000000
3.1073088 3
e
≤⋅==σσ − ⇒ Section OK for Normal force
• Simple Bending (Art.3,2) The stresses due to the simple bending in the critical section x=0 in x&y direction are :
2y
y
yy
y
2x
x
xx
x
mN0
W
M
mN81.3147
000294.0
925.0
W
M
=ψ
=σ
−=−
=ψ
=σ
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Unity Check : 11057.4235000000
11.1076236 3
e
fyfx ≤⋅==σ
σ+σ+σ − ⇒ Section OK
B. Shear Stress (Art.1,3-3,3) The shear stress due to Y=-37.82N,Z=31960.09N and Mt=-0.002Nm is calculate by (Art.3,31) :
2tCenterShear,zCenter Shear,yCenter Shear
27wt
tt
253
4
xa
xxzCenterShear,z
Center Shear,y
mN27.26078441
mN14.48322
1049.1
006.02.1t
I
M
mN 12.26030119
1051.2106
1062.137.24198
Ie
ST
0
=τ+τ+τ=τ
−=⋅
⋅−=⋅=τ
=⋅⋅⋅
⋅⋅=
⋅
⋅=τ
=τ
−
−−
−
Unity Check: 117.054.1
e
≤=σ
τ⋅⇒ Section OK for shear stress
1.17.1.2 Stability Check A. Buckling Data (Art.3,401) The buckling parameters for members 3 subjected to compression are described in Art.3,401 and Art.3,411: • Bulking length: Lx= 1.8 m kxx=0.6 Ly= 2.1 m kyy=0.7 • Slenderness parameters:
48.46i
L 19.24
i
L
y
yy
x
xx ==λ==λ
• Euler critical loads and stresses:
m
N 079.959674558A
N
mN63.3544455672
A
N
N 748.4347325L
IEN N 19.16056384
L
IEN
2n
cryky2
n
crxkx
2
y2
cry2x
2
crxyx
==σ==σ
=⋅⋅π
==⋅⋅π
=
• Coefficients for Critical State:
13.1
1k 1
3.1
1k
31.894 04.3303
y
y1y
x
xx1
kyy
kxx
=−µ
−µ==
−µ
−µ=
=σ
σ=µ=
σ
σ=µ
• Buckling coefficients:
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b
ea
ef
Fig. 2
b
e
ef
Fig. 1
0946.165.05.065.05.0k
0212.165.05.065.05.0k
ky
e
2
ky
e
ky
ey
kx
e2
kx
e
kx
ex
=σ
σ−
σ
σ⋅++
σ
σ⋅+=
=σ
σ−
σ
σ⋅++
σ
σ⋅+=
B. Buckling Check (Art.3,411-3,441) B.1. Compression of full section beam (Art.3,44)
The method used in Art.3,411 to control the bucking phenomena is applicable to slender section only if the ratio width-to-thickness respected the rules presented in Art.3,441. We hall verify this rules both for the flanges and the web of the concerned section. Slenderness 75401.66 and 753.40 yx ≤=λ≤=λ (Art.3,441)
Flange: Outstand Element (Fig. 1): b = 0.087 m
ef = 0.0095 m
We verify 1587.15240
151578.9e
b
e
=σ
⋅≤=
Web: Internal Element (Fig.2): b = 0.152 ea=0.006
We verify 47.45240
4533.25e
b
e
=σ
⋅≤=
As we can see, we can apply the buckling check for this slender section as a full section. The unity check for compression is:
Unity Check : ( )
11099.4k,kmax 3
e
yx ≤⋅=σ
⋅σ − ⇒ Buckling Check OK in compression
B.2. Section subjected to compression and bending in the bucking direction (Art.3,5) The member 3 is subjected to several loads in the same direction. So, we apply the Art.3,516 to calculate the amplification coefficient of the stress flexion. We note that AM and Mmed are respectively the surface under the moment distribution and the moment in the middle of the buckling length.
0017.13.1
lM
A172.125.0
kx
2
medx
Mxx
fx =−µ
⋅−⋅−+µ
= with AMx=61794.45m2 and Mmedx=24291.99 Nm
994.03.1
lM
A172.125.0
ky
2
medy
Myy
fy =−µ
⋅−⋅−+µ
= with AMy=80.56m2 and Mmedy=26.85 Nm
We consider that σfx&y, described in Art.3,730, design the greater value of all the sections in the member submitted to a simple bending around x&y axis.
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24fy
y
maxyy
fy
2fx
x
maxxx
fx
mN58.438198
1003.119.1
71.53
W
M
mN 72.90680780
000294.007.1
36.28526
W
M
=⋅
=ψ
=σ
==ψ
=σ
−
C. LTB Check (Art.3,6) First, we have to calculate the LTB data described in Art.3,611 and Art.3,641-642-643. The coefficients B, C, D included in the kd and σd expressions are calculated in the following way: • The B coefficient (Art.3,643) is function of the load applied to the member. As we can see, the moment distribution in member 3 corresponds to the moment appearing in the case of uniform loads. On one side of this member, the moment equals 0. Using the table presented in Art. 3,643-21, we have, for loads applied to the shear center: B=1 • The C coefficient (Art.3,642-21) depends on the repartition of the loads on the member. In this case, we consider a uniform load:1.132 ≤C=1.7439≤1.88 • The D coefficient is calculate with the following expression:
33147.1h
l
I
J
E
G41D
2
2
y2
=⋅⋅⋅π
+=
with ( ) 2m
N2.9807692307612
EG =
ν+⋅= J=1.49 10-7 m4 h=0.171m
The member 3 is not subjected to loads between the supports, so that we use Art.3,611:
( ) e22
2
x
y2
d mN499.275892423CB1D
l
h
I
I
2.5
Eσ≥=⋅⋅−⋅⋅⋅
⋅π=σ ⇔ LTB Check is not necessary
D. Shear Buckling Check (Art.5,212) To prevent any risk of shear buckling, we have to control the relation Art.5,212-3 where h’a represents the free height of the web between the flanges, ea the width of the web, σ the normal stress in the critical section, d the distance between the stiffeners (here the length of the beam) and ra the rounding between web and flange. In this case, we have:
N37.24198T
m006.0e
m122.0r2t2hh
y
a
af'a
=
=
=⋅−⋅−=
The distance from the shear center to the two extreme fibers is:
'yfy v061.0rt
2
hv −==−−=
The normal stress taking as the maximum of two following values and the shear stress are:
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( )
2'aa
yy
221
25z
zz'z
y
yy'y0x,2
25z
zzz
y
yyy0x,1
mN51.33057882
he
Tm
N15.1075324,max
mN44.10708520.0
1051.2
92.0061.0
00391.0
09.4861
I
Mv
I
Mv
A
N
mN15.10753240.0
1051.2
92.0061.0
00453.0
09.4861
I
Mv
I
Mv
A
N
=⋅
=τ
=σσ
=+⋅
⋅−=⋅+⋅+=σ
=+⋅
⋅+=⋅+⋅+=σ
−=
−=
Considering that the beam is equipped with web stiffeners to improve the security, we have the following unity check to control:
Unity Check : 11024.110
h
e1000015.0
d4
h31
7
3144
'a
a
2
2
2'a
y2
≤⋅=⋅
⋅⋅
⋅
⋅+
τ+
σ
−− ⇒ Shear bucking check OK
E. Combined Moment & Normal Forces (Art.3,731) Following the Art.3,731, we calculate the unity check for combined moment and normal forces, taking into account that σfx&y design the greater stresses due to simple flexion (Art.3,730). Buckling in the x direction:
Unity Check : 1392.0kkkk
e
fxdfxfyfyy1 ≤=σ
⋅⋅σ+⋅σ+⋅σ⇒ OK
Buckling in the y direction:
Unity Check : 1392.0kkkk
e
fxdfxfyfyx1 ≤=σ
⋅⋅σ+⋅σ+⋅σ ⇒ OK
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1.17.2 Member 7 Critical check : Load Combination : 8 Section : x = 0 m Beam Type : IPE 240
Steel : σe=235 2mmN
Beam length : 6 m Sway modes : Y-Y sway Z-Z non-sway The member is loaded through the shear centre. We must note capital letters are used to indicate ESA-Prima Win axis and small letter CM 66 axis.
1.17.2.1 Section Check A. Calculation of the plastic factor (Art.3,212-13,212) Using the table and the figure 13,212 for I profile and Art.3,212 we have the following plastic factor :
ψx=1.06 (figure)
ψy=1.185 (table) B. Normal Stress (Art.1,3-3,3) The member is subjected to a normal force X=-2527,4939 N and a shear force Z=8615.80 N in the X=0 m section, considering that the moment approaches 0 precision.
X=-2527.5 N Z=8615.80 N
An= 0.00391 m2
• Normal Stress (Art.1,312): 2
net
N/m 43.64641900391.0
5.2527
A
N−=
−==σ
Unity Check : 11075.2235000000
34.646437 3
e
≤⋅==σσ − ⇒ Section OK for Normal force
• Simple Bending (Art.3,2) The stress due to the simple bending in the critical section x=0 equal zero, therefor:
Unity Check : 10.0e
y
fy
e
x
fx
≤=σ
ψσ
=σ
ψσ
⇒ Section OK for simple bending
C. Shear Stress (Art.1,3-3,3) The shear stress due to Y=8615.80 N is calculate by (Art.3,31):
253
4
xa
xz m
N 26.65867251089.3102.6
1083.180.8615
Ie
ST=
⋅⋅⋅
⋅⋅=
⋅
⋅=τ
−−
−
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Unity Check : 11031.454.1 2
e
z ≤⋅=σ
τ⋅ − ⇒ Section OK for shear stress
1.17.2.2 Stability Check A. Bucking Data (Art.3,401) We consider that σfx&y, described in Art.3,730, design the greater value of all the sections in the member submitted to a simple bending around x&y axis. Moreover, we get the normal tension X to 0, the program doesn’t taking account for the beneficial effect of tension forces.
0W
M
mN 8.44389482
1024.30591.1
18.15232
W
M
fy
y
maxyy
fy
24fx
x
maxxx
fx
≅ψ
=σ
=⋅
=ψ
=σ−
The buckling parameters for members subjected to compression are described in Art.3,401: • Bulking length (calculate by EC3): Lx= 6 m kxx=1
Ly= 6 m kyy=1
• Slenderness parameters: 6345.222i
L 1564.60
i
L
y
yy
x
xx ==λ==λ
• Euler critical loads and stresses:
m
N 43.41817505A
N
mN 64.572782028
A
N
N 44.163506L
IEN N 73.2239577
L
IEN
2n
cryky2
n
crxkx
2y
2
cry2x
2
crx
==σ==σ
=⋅⋅π
==⋅⋅π
=
• Coefficients for Critical State:
6891.64 05.886ky
ykx
x =σ
σ=µ=
σ
σ=µ (due to N=0)
0047.13.1
1k 0003.1
3.1
1k
y
y1y
x
xx1 =
−µ
−µ==
−µ
−µ=
• Buckling coefficients:
5624.765.05.065.05.0k
188.165.05.065.05.0k
ky
e
2
ky
e
ky
ey
kx
e2
kx
e
kx
ex
=σ
σ−
σ
σ⋅++
σ
σ⋅+=
=σ
σ−
σ
σ⋅++
σ
σ⋅+=
B. Buckling Check (Art.3,411-3,441) B.1. Compression of full section beam (Art.3,44)
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The method used in Art.3,411 to control the bucking phenomena is applicable to slender section only if the ratio width-to-thickness respected the rules presented in Art.3,441. We shall verify this rules both for the flange and the web of the concerned section.
• Slenderness 751564.60x ≤=λ (Art.3,441)
Flange: Outstand Element (Fig. 1): b = 0.0569 m ef = 0.0098 m
We verify 1587.15240
15806.5e
b
e
=σ
⋅≤=
Web: Internal Element (Fig.2): b = 0.2204 ea=0.00619
We verify 47.45240
456058.35e
b
e
=σ
⋅≤=
• Slenderness λy=222.62 ≥ 75 (Art.3,442):
Flange: Outstand Element (Fig. 1): b = 0.0569 m
ef = 0.0098 m
We verify 995.44240
7515806.5
e
b
e
=σ
⋅λ
⋅≤=
Web: Internal Element (Fig.2): b = 0.2204
ea=0.00619
We verify 985.134240
75456058.35
e
b
e
=σ
⋅λ
⋅≤=
As we can see, we can apply the buckling check for this section as a full section. The unity check for compression is:
Unity Check : ( )
11008.2k,kmax 2
e
yx ≤⋅=σ
⋅σ − ⇔ Buckling Check OK in compression
B.2. Section subjected to compression and bending in the bucking direction (Art.3,5) The member 7 is subjected to several loads in the same direction. So, we apply the Art.3,516 to calculate the amplification coefficient of the stress flexion. We note that AM and Mmed are respectively the surface under the moment distribution and the moment in the middle of the buckling length.
=−µ
⋅−⋅−+µ
=3.1
lM
A172.125.0
kx
2
medx
Mxx
fx 1.0014 with AMx=58073.37m2 and Mmedx=15232.18 Nm
b
ea
ef
Fig. 2
b ea
ef
Fig. 1
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0244.13.1
25.0k
y
yfy =
−µ
+µ=
To improve the security of the program, we’ve performed the calculation of AM. The program integrates the surface under the moment distribution by applying Simpson Method. We have verified this integration by applying this method manually.
C. LTB Check (Art.3,6) First, we have to calculate the LTB data described in Art.3,611 and Art.3,641-642-643. The coefficient B, C, D include in the kd expression are calculated in the following way: • The B coefficient (Art.3,643) is function of the load applied to the member. As we can see, the moment distribution in member 7 corresponds to the moment appearing in the case of a uniform loads. Using the table presented in Art. 3,643-
21, we have, for loads applied to the shear center: B=1 • The C coefficient (Art.3,642) depends on the repartition of the loads on the member. In this case, we consider a uniform load: C=1.13 • The D coefficient is calculate with the following expression:
329.2h
l
I
J
E
G41D
2
2
y2
=⋅⋅⋅π
+=
with ( ) 2m
N231.9807692307612
EG =
ν+⋅= J=1.29e-7 m4 Iy=2.84 10-6 m4 and h=0.24m
The member is symmetrically loaded and supported so that we use the expression Art.3,611 to calculate the LTB stress:
( ) e22
2
x
y2
d mN955.70843063CB1D
l
h
I
I
2.5
Eσ≤=⋅⋅−⋅⋅⋅
⋅π=σ
Total Surface
5110Nm 10117.89Nm
11923.53N
15232.4Nm
13626.89N
1533 m2
34733.79m2
29036.6m2
58073.3m2
6101.3m2
12713.8m2
20378.9m2 N
m
Simpson Method
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This relation implicated that a LTB check is necessary. The other LTB data are:
( )9677.1
1k1
kk
378.365.05.065.05.0k
mN41.99186648
E
55.1441I
I
CB
4
h
l
0e
d
0d
k
e2
k
e
k
e0
22
2
k
e
d
y
x0
0
=−⋅
σ
σ+
=
=σ
σ−
σ
σ⋅++
σ
σ⋅+=
=λ
⋅π=σ
=
σ
σ−⋅⋅
⋅⋅=λ
The unity check for LTB is given by (Art.3,611):
Unity Check : 10W
Mkk
fxe
y
m0x,xxd
e
dfx ≤=⋅σ
ψ⋅
=σ
⋅σ=
⇒ LTB check OK
D. Shear Buckling Check (Art.5,212) To prevent any risk of shear buckling, we have to control the relation Art.5,212-3 where h’a represents the free height of the web between the flanges, ea the width of the web, σ the normal stress in the critical section, d the distance between the stiffeners (here the length of the beam) and ra the rounding between web and flange. In this case, we have:
N80.8615T
m0062.0e
m1904.0r2t2hh
y
a
af'a
=
=
=⋅−⋅−=
The distance from the shear center to the two extreme fibers is:
'yfy v0952.0rt
2
hv −==−−=
The normal stress taking as the maximum of two following values and the shear stress are:
( )
2'aa
yy
221
2z
zz'z
y
yy'y0x,2
2z
zzz
y
yyy0x,1
mN51.7298556
he
Tm
N34.646437,max
mN34.646437
00391.0
57.2527
I
Mv
I
Mv
A
N
mN34.646437
00391.0
57.2527
I
Mv
I
Mv
A
N
=⋅
=τ
−=σσ
−=−
=⋅+⋅+=σ
−=−
=⋅+⋅+=σ
=
=
Considering that the beam is equipped with web stiffeners to improve the security, we have the following unity check to control :
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Unity Check : 11015.310
h
e1000015.0
d4
h31
7
5144
'a
a
2
2
2'a
y2
≤⋅=⋅
⋅⋅
⋅
⋅+
τ+
σ
−− ⇒ Shear bucking check OK
E. Combined Moment & Normal Forces (Art.3,731) Following the Art.3,731, we calculate the unity check for combined moment and normal forces (N=0 in this case), taking into account that σfx&y design the greater stresses due to simple flexion (Art.3,730). Buckling in the x direction:
Unity Check : 1379.0kkkk
e
fxdfxfyfyy1 ≤=σ
⋅⋅σ+⋅σ+⋅σ⇒ OK
Buckling in the y direction:
Unity Check : 1379.0kkkk
e
fxdfxfyfyx1 ≤=σ
⋅⋅σ+⋅σ+⋅σ ⇒ OK
1.17.3 Member 46 Critical check : Load Combination : 10 Section : x = 0 m Beam type : T120/120/13
Steel : σe=235 2mmN
Beam length : 1 m Sway modes : Y-Y non-sway Z-Z non-sway
The member is loaded through the shear centre. We must note capital letters are used to indicate ESA-Prima Win axis and small letter CM 66 axis.
1.17.3.1 Section Check A. Calculation of the plastic factor (Art.3,212-13,212) Using the table and the figure 13,212 for H profile and Art.3,212 we have the following plastic factor :
ψx=1.23 (figure)
ψy=1.20 (table)
B. Normal Stress (Art.1,3-3,3) The member is subjected to the following internal forces :
X=36858.06N MX=-46.07Nm Y=1.34 N MY=8.26Nm Z=748.86 N MT=7.06-6.74Nm
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An= 0.00453 m2
By converting these internal forces according to the CM66 axis, we have N=-36858.06 N Mx=-46.07Nm Tx=1.34 N My=8.26Nm Ty=748.86 N Mt=6.74Nm
• Normal Stress (Art.1,312) : 2
net
N/m 29.1245204700296.0
06.36858
A
N===σ
Unity Check : 11029.5235000000
29.12452047 2
e
≤⋅==σσ − ⇒ Section OK for Normal force
• Simple Bending (Art.3,2) The stress due to the simple bending in the critical section x=0 in x&y direction are :
y
y
yy
y
x
x
xx
x
W
M
W
M
ψ=σ
ψ=σ
Unity Check : 11054.5235000000
49.13035581 2
e
fyfx ≤⋅==σ
σ+σ+σ − ⇒ Section OK
C. Check Shear Stress (Art.1,3-3,3) The shear stress due to Tx=1.34N, Ty=748.86N and Mt=-46.07Nm is calculate by (Art.3,31):
2tzy mN05.1197693=τ+τ+τ=τ
Unity Check : 11084.754.1 3
e
≤⋅=σ
τ⋅ − ⇒ Section OK for shear stress
1.17.3.2 Stability Check A. Bucking Data (Art.3,401) The buckling parameters for members 3 subjected to compression are described in Art.3,401 and Art.3,411: • Buckling length: Lx= 1 m kxx=1
Ly= 5.64 m kyy=0.94 • Slenderness parameters:
204.230i
L 49.28
i
L
y
yy
x
xx ==λ==λ
• Euler critical loads and stresses:
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b
ea
ef
Fig. 2
b
e
ef
Fig. 1
m
N 63.39182227A
N
mN47.2562762818
A
N
N 39.115979L
IEN N 94.7585777
L
IEN
2n
cryky2
n
crxkx
2
y2
cry2x
2
crxyx
==σ==σ
=⋅⋅π
==⋅⋅π
=
• Coefficients for Critical State:
16.13.1
1k 1
3.1
1k
146.3 81.05212.11023673
47.2562762818
y
y1y
x
xx1
kyy
kxx
=−µ
−µ==
−µ
−µ=
=σ
σ=µ==
σ
σ=µ
• Buckling coefficients:
052.865.05.065.05.0k
03.165.05.065.05.0k
ky
e
2
ky
e
ky
ey
kx
e2
kx
e
kx
ex
=σ
σ−
σ
σ⋅++
σ
σ⋅+=
=σ
σ−
σ
σ⋅++
σ
σ⋅+=
B. Buckling Check (Art.3,411-3,441) B.1. Compression of full section beam (Art.3,44) The method used in Art.3,411 to control the bucking phenomena is applicable to slender section only if the ratio width-to-thickness respected the rules presented in Art.3,441. We shall verify this rules both for the flanges and the web of the concerned section. Slenderness 7549.28x ≤=λ (Art.3,441)
Flange: Outstand Element (Fig. 1): b=0.01135 m
ef=0.013 m
We verify 1587.15240
1573.8e
b
e
=σ
⋅≤=
Web: Internal Element (Fig.2): b=0.05349
ea=0.013
We verify 15.15240
1511.4e
b
e
=σ
⋅≤=
Slenderness 75204.230y ≥=λ (Art.3,441)
Flange: Outstand Element (Fig. 1): b=0.0107 m ef=0.013 m
We verify 52.46240
751523.8
e
b
e
y =σ
⋅λ
⋅≤=
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Web: Internal Element (Fig.2): b=0.05349
ea=0.013
We verify 52.46240
751511.4
e
b
e
y =σ
⋅λ
⋅≤=
As we can see, we can apply the buckling check for this slender section as a full section. The unity check for compression is:
Unity Check : ( )
1426.0k,kmax
e
yx ≤=σ
⋅σ ⇒ Buckling Check OK in compression
B.2. Section subjected to compression and bending in the bucking direction (Art.3,5) The member 46 is subjected to several loads in the same direction. So, we apply the Art.3,516 to calculate the amplification coefficient of the stress flexion. We note that AM and Mmed are respectively the surface under the moment distribution and the moment in the middle of the buckling length.
01.13.1
lM
A172.125.0
kx
2
medx
Mxx
fx =−µ
⋅−⋅−+µ
= with AMx=251.07m2 and Mmedx=251.07 Nm
84.13.1
lM
A172.125.0
ky
2
medy
Myy
fy =−µ
⋅−⋅−+µ
= with AMx=8.93 m2 and Mmedx=8.93 Nm
B.3. Combined Moment & Normal Forces (Art.3,731) Following the Art.3,731, we calculate the unity check for combined moment and normal forces, taking into account that σfx&y design the greater stresses due to simple flexion (Art.3,730). Buckling in the x direction :
Unity Check : 111.0kkkk
e
fxdfxfyfyy1 ≤=σ
⋅⋅σ+⋅σ+⋅σ⇒ OK
Buckling in the y direction:
Unity Check : 111.0kkkk
e
fxdfxfyfyx1 ≤=σ
⋅⋅σ+⋅σ+⋅σ ⇒ OK
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Calculation note - Member 3 CM66 Check
Macro 2 Member 3 HEA180 Fe 360 Ult. comb 10 0.40
Material data
Yield strength 235.00 MPa
Tensile strength 360.00 MPa
fabrication rolled
Section Check CM66
The critical check is on position 0.00 m
Axis definition :
- local x- axis in this code check is referring to the local y axis in EPW
- local y- axis in this code check is referring to the local z axis in EPW
Internal forces
N -4.85 kN
Tx -0.02 kN
Ty 24.24 kN
Mt -0.00 kNm
Mx -0.00 kNm
My 0.00 kNm
Normal stress check
according to article (3,1) (3,2)
Table of values
sigma 1.07 MPa
Psix 1.07
Psiy 1.19
unity check 0.00
Shear stress check
according to article (3,3)
Table of values
tau 26.15 MPa
unity check 0.17
Element satisfies the section check !
Stability check CM66
Buckling parameters xx yy
type non-sway non-sway
Length 3.00 3.00 m
Buckling factor 0.60 0.70
Buckling length 1.80 2.10 m
Slenderness 24.18 46.47
Critical Euler load 16056.38 4347.33 kN
Critical Euler stress 3544.46 959.67 MPa
mu 3312.21 896.79
Amplification factor k1 1.00 1.00
Buckling coefficient k 1.02 1.09
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Buckling check
according to article 3,411
Table of values
sigma 1.07 MPa
k 1.09
unity check 0.00
LTB parameters
LTB length l0 3.00 m
k 1.00
LTB length l 3.00 m
C 1.65
Beta 3.00
B 1.00
D 1.33
load in center of gravity
LTB check
according to article 3,611
Table of values
Sigma f 0.00 MPa
LTB factor kd 1.00
Sigma d 261.54 MPa
unity check 0.00
Compression, bending and LTB check
according to article 3,731
Table of values
sigma 1.07 MPa
Sigma fx 91.41 MPa
Sigma fy 0.45 MPa
LTB factor kd 1.00
Amplification factor kfx 1.00
Amplification factor kfy 1.00
AMx 62110500.09 kN mm^2
AMy 81800.44 kN mm^2
Mmed x 24.81 kNm
Mmed y 0.03 kNm
My max 28.62 kNm
Mz max 0.05 kNm
unity check 0.40
1.07+91.45+0.45=92.97 MPa
1.07+91.45+0.45=92.97 MPa
Shear buckling check
in buckling field 1
according to article 5,212-3
Table of values
sigma 0.11 daN/mm^2
tau 3.31 daN/mm^2
h'a 122.00 mm
ea 6.00 mm
d 3000.00 mm
unity check 0.00
Calculation note - Member 7
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Macro 4 Member 7 IPE240 Fe 360 Ult. comb 9 0.38
Material data
Yield strength 235.00 MPa
Tensile strength 360.00 MPa
fabrication rolled
Section Check CM66
The critical check is on position 0.00 m
Axis definition :
- local x- axis in this code check is referring to the local y axis in EPW
- local y- axis in this code check is referring to the local z axis in EPW
Internal forces
N -2.58 kN
Tx 0.00 kN
Ty 8.62 kN
Mt 0.00 kNm
Mx -0.00 kNm
My -0.00 kNm
Normal stress check
according to article (3,1) (3,2)
Table of values
sigma 0.66 MPa
Psix 1.06
Psiy 1.19
unity check 0.00
Shear stress check
according to article (3,3)
Table of values
tau 6.54 MPa
unity check 0.04
Element satisfies the section check !
Stability check CM66
Buckling parameters xx yy
type non-sway non-sway
Length 6.00 6.00 m
Buckling factor 1.00 1.00
Buckling length 6.00 6.00 m
Slenderness 60.15 222.63
Critical Euler load 2239.58 163.51 kN
Critical Euler stress 572.78 41.82 MPa
mu 869.62 63.49
Amplification factor k1 1.00 1.00
Buckling coefficient k 1.19 7.56
Warning: slenderness 222.63 is larger then 200.00 !
Buckling check
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according to article 3,411
Table of values
sigma 0.66 MPa
k 7.56
unity check 0.02
LTB parameters
LTB length l0 6.00 m
k 1.00
LTB length l 6.00 m
C 1.13
Beta 1.00
B 1.00
D 2.33
load in center of gravity
Compression, bending and LTB check
according to article 3,731
Table of values
sigma 0.66 MPa
Sigma fx 44.37 MPa
Sigma fy 0.00 MPa
LTB factor kd 1.99
Amplification factor kfx 1.00
Amplification factor kfy 1.02
AMx 58040926.24 kN mm^2
AMy 0.00 kN mm^2
Mmed x 15.23 kNm
Mmed y 0.00 kNm
My max 15.23 kNm
Mz max -0.00 kNm
unity check 0.38
0.66+88.50+0.00=89.16 MPa
0.66+88.50+0.00=89.16 MPa
Shear buckling check
in buckling field 1
according to article 5,212-3
Table of values
sigma 0.07 daN/mm^2
tau 0.73 daN/mm^2
h'a 190.40 mm
ea 6.20 mm
d 6000.00 mm
unity check 0.00
Calculation note - Member 46
Macro 18 Member 46 T120/120/13 Fe 360 Ult. comb 11 0.43
Material data
Yield strength 235.00 MPa
Tensile strength 360.00 MPa
fabrication rolled
Section Check CM66
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The critical check is on position 0.00 m
Axis definition :
- local x- axis in this code check is referring to the local y axis in EPW
- local y- axis in this code check is referring to the local z axis in EPW
Internal forces
N -36.87 kN
Tx 0.00 kN
Ty 0.75 kN
Mt 0.01 kNm
Mx -0.04 kNm
My 0.01 kNm
Normal stress check
according to article (3,1) (3,2)
Table of values
sigma 13.03 MPa
Psix 1.23
Psiy 1.20
unity check 0.06
Shear stress check
according to article (3,3)
Table of values
tau 1.19 MPa
unity check 0.01
Element satisfies the section check !
Stability check CM66
Buckling parameters xx yy
type non-sway non-sway
Length 1.00 6.00 m
Buckling factor 1.00 0.94
Buckling length 1.00 5.64 m
Slenderness 28.44 229.99
Critical Euler load 7585.78 115.98 kN
Critical Euler stress 2562.76 39.18 MPa
mu 205.73 3.15
Amplification factor k1 1.00 1.16
Buckling coefficient k 1.03 8.05
Warning: slenderness 229.99 is larger then 200.00 !
Buckling check
according to article 3,411
Table of values
sigma 12.46 MPa
k 8.05
unity check 0.43
Compression, bending and LTB check
according to article 3,731
Table of values
sigma 12.46 MPa
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Table of values
Sigma fx 10.39 MPa
Sigma fy 0.27 MPa
LTB factor kd 1.00
Amplification factor kfx 1.01
Amplification factor kfy 1.84
AMx 270071.33 kN mm^2
AMy 8945.17 kN mm^2
Mmed x 0.29 kNm
Mmed y 0.01 kNm
My max 0.55 kNm
Mz max -0.01 kNm
unity check 0.11
14.48+10.47+0.50=25.45 MPa
12.48+10.47+0.50=23.44 MPa
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1.18 PST.06.08 - 01 : SIA161 Steel Code Check Tutorial Frame Description The unity check according to SIA161 of members 7, 4 of the Tutorial Frame project are calculated manually. The result is compared with the result of ESA-Prima Win SIA161 Steel code check. Project data See input file. Reference SIA 161 Norme Edition 1990 Constructions métalliques Editeur: Société suisse des ingénieurs et des architectes Eurocode 3: Calcul des structures en acier Edition 1992 Essentials of Eurocode 3:Design Manual for Steel Structures in Building First Edition 1991 See the chapter "Manual calculation" for the manual calculation according to this reference. Result Member EPW Manually 4 section check 0.253 0.253 LTB 0.559 0.558 Flexion+normal force 0.48 0.48 7 section check 0.023 0.0234 LTB 0.33 0.3316 Flexion + normal force 0.37 0.37 See the chapter "Calculation note" for the detailed output of ESA-Prima Win. Version ESA-Prima Win 3.20.03 Input file + calculation note PST060801.epw Modules 3D Frame (PRS.11) SIA161 Steel code check (PST.06.08) Author NEM/CVL
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Manual calculation
1.18.1 Member 7
1.18.1.1 Classification of the section (Table 3. SIA161) A. Width-to-thickness ratio for webs By using Table 16a of SIA161, we can determine the yield strength fy:
• Normal steel grade: S275 • Nominal thickness of the element t ≤ 40 mm
⇒ Nominal value of yield strength: fy=275 N/mm2
The web of member 7 is subjected both to bending and tension in section x=0.55 m. By using Table 3. of SIA161, we find:
NAfN ypl 1075250=⋅= and 00.N
Nn
R
pl=
γ
=
( ) ( ) 326641142093700620
230 .f
En....
.t
tht
dyw
f
w=⋅⋅−⋅≤==−= ⇒ WEB is CLASSE 1 (PP Method)
B. Width-to-thickness ratio for flanges By using table 3. for outstand element, we find for section x=0 m
491038012600980
120.
f
E..
.
.
T
b
y
=⋅≤== ⇒ FLANGES are CLASSE 1 (Method PP)
The section IPE 240 is a plastic section for the stability check, following SIA 161 rules.
1.18.1.2 Check Normal Stress and shear stress (Art. 3.2.11.1 and Art. 4.13.6) The member 7 is subjected to a normal tension N=262.81N and a small shear forces Fvy=2250.05N in the critical section. According to SIA 161, we can verify: Unity Check:
Normal check: 110442
11003910275000000
81262 4 ≤⋅=⋅
=
γ⋅
−.
..
.fAF
R
y
Shear area: ( ) 2001427024000620 m...tbtA fwwz =⋅=−⋅=
Shear check: 110091
1178226604
052250
3
2 ≤⋅==
γ⋅
⋅=
γ
−.
...
fAV
VV
R
ywz
dz
R
zRd
dz
⇒ Section OK for tension and shear
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1.18.1.3 Combined bending, axial force (Art. 4.13.4.) By using Art. 4.13.4 (42), we can determine:
N.AfN ypl 1075250003910275000000 =⋅=⋅=
Nm.ZfM yyply 1006500003660275000000 =⋅=⋅= and Nm.ZfM zyplz 203501047275000000 5 =⋅⋅=⋅= −
5741
1
11 .
A
A w=
−=ξ and 212231
21
122 . .
A
A w=ξ⇒=
⋅−
=ξ
NmMM plzN,plz 20350==
( ) Nm.;minN
NM;MminM
R
pl
dplyplyN,ply 1006504712081210065012 ==
γ
−⋅ξ⋅=
115
11 .N
N;.max
R
pl
d =
γ
⋅=α
Unity check: 110342 2
2
≤⋅=
γ
+
γ
−
α
.M
MM
M
R
N,plz
dz
R
N,ply
dy
1.18.1.4 Stability Check: Check for bending, compression and L.T.B.
A. Calculation of Lateral Torsional Buckling (Art. 3.254)
Table 3 of SIA161 proposes the calculation of the critical LTB length to check if a LTB is necessary. In this case, we have:
ml.f
Eil D
yzcr 6531
3
212 =<=⋅
ψ−⋅⋅= where 0.1
M
M
max,d
min,d ==ψ ⇒ LTB check necessary
Before the calculation of the LTB resistant moment, we must determinate irc. irc is defined as the radius gyration of a section comprising the compression flange plus 1/3 of the compression web area, taken about an axis in the plane of the web. Before the calculation of the compression area and the compression inertia, we must calculate distribution and the height of compression stress due to the moment My: Level arm: m.a 11020=
Stress: 23139702047m
N.bottop =σ−=σ
Height in compression: m.h
bottop
wtop11020=
σ+σ
⋅σ
Reduced area: 2310403713
m.tb
tbA wcwcffr
−⋅=⋅
+⋅=
Reduced area: 4633
1041113612
m.tbbt
I wcwcffrc
−⋅=⋅
+⋅
=
Reduced radius giration: m.A
Ii
rc
rcrc 03170==
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0440.M
M
max,d
min,d −==ψ 13130051751 2 .... =ψ⋅+ψ⋅−=η
m.l
l DK 645=
η= 83177.
i
l
rc
KK ==λ
22
2
2965537559m
N.E
KDw =
λ
⋅π=σ 2923143952330
mN.IEKG
Wl zyD
Dv =⋅⋅⋅⋅⋅
π⋅η=σ
222 131158169049
mN.DwDvcrD =σ+σ=σ
4011.W
Zf
ycrD
yyD =
⋅σ
⋅=λ 4610
1
1450
54.
.
.D
=
λ+=ζ 295127005186
mN.f yD =⋅ζ=σ
Nm.ZM yDD 8946483=⋅σ=
Unity check : 133160 ≤=
γ
.M
M
R
D
dy => OK LTB check
B. Tension members with moments (Art. 4.142.(48)) The internal forces for the ultimate combination 4 in the critical section x=3 m are N=262.81 N (tension) and My=14014.607 Nm. As we don’t take into account the beneficial effect of tension force (N=0), we find:
N.l
IEN
Ky
ycry 732239577
2
2
=⋅⋅π
= and N.l
IEN
Kz
zcrz 44163506
2
2
=⋅⋅π
=
0.1y =ω and 14060 =⋅+=ωmax,dz
min,dzz M
M..
12
40 =⋅
+
γ
+=βb
cN
N.
R
pl
d
( ) kNm7.46MkNm89.41MM DyDN,Ry =η⋅ω<== NmMM plzN,Rz 20350==
Unity check: 137.0M
MM
M
R
N,Rz
dzz
R
N,Ry
dyy ≤=
γ
⋅ω+
γ
⋅ω
ββ
=> Stability check OK
1.18.2 Member 4
1.18.2.1 Classification of the section (Table 3. BS5950) A. Width-to-thickness ratio for webs By using Table 16a of SIA161, we can determine the yield strength fy:
• Normal steel grade: S275 • Nominal thickness of the element t ≤ 40 mm
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⇒ Nominal value of yield strength: fy=275 N/mm2
The web of member 4 is subjected both to bending and tension in section x=0 m. By using Table 3. of SIA161, we find:
NAfN ypl 1245750=⋅= and 00.N
Nn
R
pl=
γ
=
( ) ( ) 32664114291260060
16150 .f
En....
.t
tht
dyw
f
w=⋅⋅−⋅≤==−= ⇒ WEB is CLASSE 1 (PP Method)
B. Width-to-thickness ratio for outstand flanges By using table 3. for outstand element, we find for section x=0 m
491038047900950
090.
f
E..
.
.
T
b
y
=⋅≤== ⇒ FLANGES are CLASSE 1 (Method PP)
The section HEA 180 is a plastic section for the stability check, following SIA 161 rules.
1.18.2.2 Check Normal Stress and shear stress (Art. 3.2.11.1 Art. 4.13.6) The member 4 is subjected to a normal tension N=2276.208N and shear forces Vvy=18.6 N Vzz=-2151.64 N in the critical section. According to SIA 161, we can verify: Unity Check:
Normal check: 1102
11004530275000000
22276 3 ≤⋅=⋅
=
γ⋅
−
...
fAF
R
y
Shear area: ( ) 20034202 m.tbA fwy =⋅⋅=
( ) 20009690 m.tbtA fwwz =−⋅=
Shear check: 11083
1192542997
7618
3
5 ≤⋅==
γ⋅
⋅=
γ
−.
..
.fA
V
V
V
R
ywy
dy
R
yRd
dy
1105381
1141153849
752150
3
2 ≤⋅==
γ⋅
⋅=
γ
−.
...
fAV
VV
R
ywz
dz
R
zRd
dz
⇒ Section OK for tension and shear
1.18.2.3 Combined bending, axial force (Art. 4.13.4.) By using Art. 4.13.4 (42), we can determine:
N.AfN ypl 1245750004530275000000 =⋅=⋅=
Nm.ZfM yyply 891000003240275000000 =⋅=⋅= and Nm.ZfM zyplz 429000001560275000000 =⋅=⋅=
271
1
11 .
A
Aw=
−=ξ and 21121
21
122 . .
A
A w=ξ⇒=
⋅−
=ξ
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NmMM plzN,plz 42900==
NmMN
NM;MminM ply
R
pl
dplyplyN,ply 8910012 ==
γ
−⋅ξ⋅=
115
11 .N
N;.max
R
pl
d =
γ
⋅=α
Unity check: 12530
2
≤=
γ
+
γ
α
.M
MM
M
R
N,plz
dz
R
N,ply
dy
1.18.2.4 Stability Check: Check for bending, compression and L.T.B. A. Calculation of Lateral torsional Buckling (Art. 3.254)
Table 3 of SIA161 proposes the calculation of the critical LTB length to check if a LTB is necessary. In this case, we have:
ml.f
Eil D
yzcr 5492
3
212 =<=⋅
ψ−⋅⋅= where 0==ψ
max,d
min,d
M
M⇒ LTB check necessary
Before the calculation of the LTB resistant moment, we must determinate irc. irc is defined as the radius gyration of a section comprising the compression flange plus 1/3 of the compression web area, taken about an axis in the plane of the web. Before the calculation of the compression area and the compression inertia, we must calculate distribution and the height of compression stress due to the moment My: Height in compression: m.bwc 0760=
Reduced area: 200186203
m.tb
tbA wcwcffr =
⋅+⋅=
Reduced area: 4633
1061743612
m.tbbt
I wcwcffrc
−⋅=⋅
+⋅
=
Reduced radius gyration: m.A
Ii
rc
rrc 049790==
0==ψmax,d
min,d
M
M 411.=η
m.l
l DK 24=
η= 049790.
i
l
rc
KK ==λ
22
2
85290404639m
N.E
KDw =
λ
⋅π=σ 216461562551
mN.IEKG
Wl zyD
Dv =⋅⋅⋅⋅⋅
π⋅η=σ
222 87545320862
mN.DwDvcrD =σ+σ=σ
7450.W
Zf
ycrD
yyD =
⋅σ
⋅=λ 90
1
1450
54.
.
.D
=
λ+=ζ 273247248657
mN.f yD =⋅ζ=σ
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Nm.ZM yDD 5680108=⋅σ=
Unity check : 15580 ≤=
γ
.M
M
R
D
dy => OK LTB check
B. Tension members with moments (Art. 4.142. (48))
The internal forces for the ultimate combination 3 in the critical section x=2.22 m are N=2276.208 N (tension) and My=40699.02Nm Mz=52.11Nm. As we don’t take into account the beneficial effect of tension force (N=0), we find:
N.l
IEN
Ky
ycry 47812854
2
2
=⋅⋅π
= and N.l
IEN
Kz
zcrz 93299557
2
2
=⋅⋅π
=
0.1y =ω (transversal loading is present) and 14060 =⋅+=ωmax,dz
min,dzz M
M..
5112
40 .b
cN
N.
R
pl
d =⋅
+
γ
+=β
( ) kNm1.80MkNm52.72MM DyDN,Ry =η⋅ω<== NmMM plzN,Rz 42900==
Unity check: 10.048.0M
MM
M
R
N,Rz
dzz
R
N,Ry
dyy ≤+=
γ
⋅ω+
γ
⋅ω
ββ
=> Stability check OK
Calculation note SIA161 check
Macro 2 Member 4 HEA180 S 275 Ult. comb 4 0.56
Material data
Gamma_r 1.10
Design strength 275.00 MPa
fabrication rolled
SECTION CHECK
Width to thickness ratio for webs
ratio 26.92 on position 0.00 m
ratio
Maximum ratio 1 66.32
Maximum ratio 2 82.90
Maximum ratio 3 115.39
==>Class cross-section 1 (PP Method)
Width to thickness ratio for outstand flanges
ratio 9.47 on position 0.00 m
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ratio
Maximum ratio 1 10.50
Maximum ratio 2 12.44
Maximum ratio 3 15.48
==>Class cross-section 1 (PP Method)
The critical check is on position 2.22 m
Internal forces
Nd 2.28 kN
Vdy 0.02 kN
Vdz -2.15 kN
Mt -0.00 kNm
Mdy 40.70 kNm
Mdz -0.05 kNm
Normal force check
according to 3.2.11.1 and formula (1) && Table 4
Table of values
Nt_Rd 1245.75 kN
Unity check 0.00
Shear check (Vy)
according to 4.13.6 and formula (46)
Table of values
Avy 3420.00 mm^2
Vy_Rd 543.00 kN
Unity check 0.00
Shear check (Vz)
according to 4.13.6 and formula (46)
Table of values
Avz 969.00 mm^2
Vz_Rd 153.85 kN
Unity check 0.02
Combined bending and normal force
according to 4.13.4 and formula (42)
Table of values
xi_1 1.27
xi_2 1.12
Npl 1245.75 kN
alfa 1.10
MplyN 89.10 kNm
MplzN 42.90 kNm
Unity check 0.25
Element satisfies the section check !
STABILITY CHECK
Design strength 275.00 MPa
LTB
L ltb 5.00 m
eta 1.41
Lcr 2.50 m
k 1.00
kw 1.00
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LTB check
according to 3.254 and formula (19) & 3.254.1
Table of values
psi -0.00
eta 1.41
l_K 4.21 m
A reduced 1862.00 mm^2
I reduced 4617456.40 mm^4
i reduced 49.80 mm
LTB slender. 84.54
sigma_Dw 290.01 MPa
sigma_Dv 460.94 MPa
sigma_crD 544.59 MPa
lamda_D 0.75
zeta 0.90
sigma_D 247.18 MPa
M_D 80.09 kNm
Unity check 0.56
Compression and bending check
according to 4.14.2 and formula (48)
Table of values
My max 40.70 kNm
Mz max 0.09 kNm
N_cry 812.85 kN
N_crz 299.56 kN
N_Kz 236.35 kN
M_D(eta=1) 72.52 kNm
M_D(eta) 80.09 kNm
omega_y 1.00
omega_z 1.00
beta 1.51
M_Ry,N 72.52 kNm
M_Rz,N 42.90 kNm
Unity check 0.48
0.48 +0.00=0.48
No shear buckling check
Element satisfies the stability check !
SIA161 check
Macro 4 Member 7 IPE240 S 275 Ult. comb 5 0.37
Material data
Gamma_r 1.10
Design strength 275.00 MPa
fabrication rolled
SECTION CHECK
Width to thickness ratio for webs
ratio 37.13 on position 0.86 m
ratio
Maximum ratio 1 66.32
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ratio
Maximum ratio 2 82.90
Maximum ratio 3 115.27
==>Class cross-section 1 (PP Method)
Width to thickness ratio for outstand flanges
ratio 6.12 on position 0.86 m
ratio
Maximum ratio 1 10.50
Maximum ratio 2 12.44
Maximum ratio 3 15.48
==>Class cross-section 1 (PP Method)
The critical check is on position 3.00 m
Internal forces
Nd 0.26 kN
Vdy 0.00 kN
Vdz 2.25 kN
Mt 0.00 kNm
Mdy 14.01 kNm
Mdz -0.00 kNm
Normal force check
according to 3.2.11.1 and formula (1) && Table 4
Table of values
Nt_Rd 1075.25 kN
Unity check 0.00
Shear check (Vz)
according to 4.13.6 and formula (46)
Table of values
Avz 1427.24 mm^2
Vz_Rd 226.60 kN
Unity check 0.01
Combined bending and normal force
according to 4.13.4 and formula (42)
Table of values
xi_1 1.57
xi_2 1.20
Npl 1075.25 kN
alfa 1.10
MplyN 100.65 kNm
MplzN 20.35 kNm
Unity check 0.02
Element satisfies the section check !
STABILITY CHECK
Design strength 275.00 MPa
LTB
L ltb 6.00 m
eta 1.13
Lcr 1.01 m
k 1.00
kw 1.00
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LTB check
according to 3.254 and formula (19) & 3.254.1
Table of values
psi 1.00
eta 1.13
l_K 5.64 m
A reduced 1403.75 mm^2
I reduced 1411929.47 mm^4
i reduced 31.71 mm
LTB slender. 177.97
sigma_Dw 65.44 MPa
sigma_Dv 143.95 MPa
sigma_crD 158.13 MPa
lamda_D 1.40
zeta 0.46
sigma_D 126.98 MPa
M_D 46.47 kNm
Unity check 0.33
Compression and bending check
according to 4.14.2 and formula (48)
Table of values
My max 14.01 kNm
Mz max 0.00 kNm
N_cry 2239.58 kN
N_crz 163.51 kN
N_Kz 143.30 kN
M_D(eta=1) 41.89 kNm
M_D(eta) 46.47 kNm
omega_y 1.00
omega_z 1.00
beta 1.00
M_Ry,N 41.89 kNm
M_Rz,N 20.35 kNm
Unity check 0.37
0.37 +0.00=0.37
No shear buckling check
Element satisfies the stability check !
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1.19 PST.06.09 – 01 : BS5950 Steel Code Check Tutorial Frame Description The unity check according to BS5950 of members 7, 4 and 46 of the Tutorial Frame project are calculated manually. The result is compared with the result of ESA-Prima Win BS5950 Steel code check. Project data See input file. Reference British Standard BS5950 Part 1.: 1990 + Revised text 1992 Structural use of steelwork in building Part 1. Code of practice for design in simple and continuous construction: hot rolled sections Steelwork Design Guide to BS5950: Part 1: 1990 Volume 2 Worked examples (Revised edition) Eurocode 3: Calcul des structures en acier Edition 1992 Essentials of Eurocode 3:Design Manual for Steel Structures in Building First Edition 1991 See the chapter "Manual calculation" for the manual calculation according to this reference. Result
Type of result Manually ESA-Prima Win % Diff Max. unity check Member 7
0.4298 0.43 0 %
Max. unity check Member 4
0.67 0.67 0 %
Max. unity check Macro 46
0.429 0.43 0 %
Version ESA-Prima Win 3.20.03 Input file + calculation note PST060901.epw Modules 3D Frame (PRS.11) BS5950 Steel code check (PST.06.09) Author
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NEM/CVL Manual calculation
1.19.1 Member 7
1.19.1.1 Classification of the section (Table 7. BS5950) A. Width-to-thickness ratio for webs
By using Table 7 of BS5950, we can determine the yield strength fy:
• Normal steel grade: S275 • Nominal thickness of the element t ≤ 40 mm ⇒ Nominal value of yield strength: py=275 N/mm2
⇒ 1235
=
=ε
yf (Using Note 3. Table 7.)
The web of member 7 is subjected both to bending and tension in section x=0.55 m. By using Table 7. of BS5950, we find:
( )9678
6040
79730
26194 .
....t
dw
=α⋅+
ε⋅≤== with 000811 .
ftd
N
yw
Sd =
⋅⋅+=α ⇒ WEB is CLASSE 1
B. Width-to-thickness ratio for flanges By using table 7. for outstand element, we find for section x=0 m
575712600980
120...
.
.
T
b=ε⋅≤== ⇒ FLANGES are CLASSE 1
The section IPE 240 is a plastic section for the stability check, following BS5950 rules.
1.19.1.2 Check Normal Stress and shear stress (Art. 4.6.1. Art. 4.2.3) The member 7 is subjected to a normal tension F=262.81N and a small shear forces Fvy=2250.05N in the critical section. According to BS5950, we can verify: Unity Check:
Normal check: 110442003910275000000
81262 4 ≤⋅=⋅
=⋅
−..
.
pyA
F
Shear area: 2001488024000620 m...DtA wvy =⋅=⋅=
Shear check: 110169245520
052250
60
3 ≤⋅==⋅⋅
= −..
pA.
F
P
F
yvy
vy
vy
vy
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⇒ Section OK for tension and shear
1.19.1.3 Combined bending, axial force (Art. 4.8.2.) By using Art. 4.8.2. (1), we can determine: Fvy≤0.6Pvy (LOW SHEAR): ( ) ( ) Nm ;minpZ.;pSminM yxxyxxcx 10065010688710065021 ==⋅⋅⋅=
( ) ( ) Nm ;minpZ.;pSminM yyyyyycy 15609156092035021 ==⋅⋅⋅=
We verify: 1139480
21
≤=
+
.
M
M
M
Mz
cy
yz
cx
x using 4.8.2.
with z1=2.0 z2=1.0 Mx=14014.38 Nm My=0 Nm
1.19.1.4 Stability Check: Check for bending, compression and L.T.B.
A. Calculation of Lateral Torsional Buckling (Art. 4.3.7. Appendix B)
To determined LTB parameters, the rules prescribed by BS5950 are different for section with flange symmetrical about major or minor axis. As we’ll see, for a double symmetrical section as member 7, this distinction leads to the same results.
Slenderness: 0422302690
6.
.A
I
L
i
L
yyy ====λ
N=0.5 (symmetrical section)
Limiting equivalent slenderness: 7234402
12
.p
E.
yLO =
⋅π⋅=λ
92699010893
1086211
5
6
..
.
I
I
x
y =⋅
⋅−=−=γ
−
−
Torsional index: 682210291
00391202302056605660
71 ..
...
J
Ah.x s =
⋅⋅⋅=⋅⋅=
−
73221029110842
107763003912013211321
76
8
2 ...
...
JI
HA.x
y
=⋅⋅⋅
⋅⋅⋅=
⋅⋅
⋅=−−
−
Buckling parameter: 88404 4
1
22
2
1 .hA
Su
s
x =
⋅
γ⋅⋅=
88301077530039120
926990000366010842 41
82
2641
2
2
2 ...
...
HA
SIu
xy =
⋅⋅
⋅⋅⋅=
⋅
γ⋅⋅=
−
−
Slenderness factor: ( ) 6433020
114
21
21
22
1 .x
NNv =
ψ+
ψ+
λ⋅+−⋅⋅=
−
( ) 6439020
114
21
21
22
2 .x
NNv =
ψ+
ψ+
λ⋅+−⋅⋅=
−
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Equivalent slenderness: 85126111 .vun y,LTB =λ⋅⋅⋅=λ
81126222 .vun y,LTB =λ⋅⋅⋅=λ
Perry coefficient: ( ) 644900070 11 .. LO,LT,LT =λ−λ⋅=η
( ) 644600070 22 .. LO,LT,LT =λ−λ⋅=η
Plastic moment: Nm SpM xxyp 100650=⋅=
Elastic critical moment: Nm .ES
p
EMM
,LT
xx
y,LT
p,E 2147143
21
2
21
2
1 =λ
⋅π⋅=
⋅λ
⋅π⋅=
Nm .ES
p
EMM
,LT
yy
y,LT
p,E 9547172
22
2
22
2
2 =λ
⋅π⋅=
⋅λ
⋅π⋅=
Reduced LTB factor: ( )
93890972
1 111 .
MM ,E,LTP,b =
⋅+η+=φ
( )3289115
2
1 112 .
MM ,E,LTP,b =
⋅+η+=φ
Equivalent uniform moment: 60714014.MmM A =⋅=
Buckling resistance moment: ( )
Nm .MM
MMM
,p,E,b,b
P,E,b 0632587
21
112
11
11 =
⋅−φ+φ
⋅=
( )Nm .
MM
MMM
,p,E,b,b
P,E,b 5232603
21
222
21
22 =
⋅−φ+φ
⋅=
Unity check : 1429805232603
60714014
21
≤== ..
.
M
M
),min(,b
=> OK LTB check
B. Tension members with moments (Art. 4.8.3.3.2.) The internal forces for the ultimate combination 4 in the critical section x=3 m are: F=262.81 N (tension) Mx=14014.607 Nm Using the more precise approach described in article 4.8.3.3.2., we find: Maximum buckling moment around major axis:
Nm .P
F.M;
P
F.P
F
MminMcy
b
cx
cxcxax 7832585
501
501
1
=
⋅−⋅
⋅+
−
⋅=
Maximum buckling moment around minor axis:
Nm M
P
F.
P
F
MM cy
cy
cxcyay 20350
501
1
==
⋅+
−
⋅=
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Unity check: 1430 ≤=⋅
+⋅
.M
Mm
M
Mm
ay
y
ax
x => Stability check OK
1.19.2 Member 4
1.19.2.1 Classification of the section (Table 7. BS5950) A. Width-to-thickness ratio for webs
By using Table 7 of BS5950, we can determine the yield strength fy:
• Normal steel grade: S275 • Nominal thickness of the element t ≤ 40 mm ⇒ Nominal value of yield strength: py=275 N/mm2
⇒ 1235
=
=ε
yf (Using Note 3. Table 7.)
The web of member 7 is subjected both to bending and tension in section x=0.55 m. By using Table 7 of BS5950 and Art. 3.5.4., we find:
( )05477
611
1203320
00601220 .
R...
.t
dw
=⋅+ε⋅
≤==
where 5010877 3 ..p
Ry
web,m ≤⋅=σ
= − ⇒ WEB is plastic
B. Width-to-thickness ratio for outstand flanges
By using Table 7 of BS5950, we find for section x=0 m:
5959473900950
090 .....
Tb =ε⋅≤== ⇒ FLANGES are compact
The section HEA180 is a compact section for stabilty check, following BS5950 rules.
1.19.2.2 Check Normal Stress and shear stress (Art. 4.6.1. Art. 4.2.3) The member 7 is subjected to a normal compression F=7404.15 N and a shear force Fvy=2145.32 N in the critical section. According to BS5950, we can verify: Unity Check:
Normal check: 1109550045250275000000
157404 3 ≤⋅=⋅
=⋅
−..
.
pyA
F
Shear area: 2001026017100060 m...DtA wvy =⋅=⋅=
Shear check: 110261169290
322145
60
2 ≤⋅==⋅⋅
= −..
pA.
F
P
F
yvy
vy
vy
vy
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⇒ Section OK for tension and shear
1.19.2.3 Combined bending, axial force (Art. 4.8.3.2.) By using Art. 4.8.2. (1), we can determine: Fvy≤0.6Pvy (LOW SHEAR): ( ) ( ) Nm ;minpZ.;pSminM yxxyxxcx 89100970208910021 ==⋅⋅⋅=
( ) ( ) Nm ;minpZ.;pSminM yyyyyycy 33990339904290021 ==⋅⋅⋅=
We verify: 146610 ≤=
+
+
⋅.
M
M
M
M
pA
F
cy
z
cx
y
y
(Using 4.8.3.2.)
with: z1=2.0 z2=1.0 Mx=14014.38 Nm My=0 Nm
1.19.2.4 Stability Check: Check for bending, compression and L.T.B. A. Calculation of Buckling (Art. 4.7.5. Appendix C)
• Slenderness: 47.1070744.0
8
AI
L
i
L
xxx ====λ
3817704510
8.
.A
I
L
i
L
yyy ====λ
• Limiting slenderness: 3617202
12
.p
E.
yO =
⋅π⋅=λ
• Robertson constant: 55.a x = 8=ya
• Perry coefficient: ( ) 495800010 .a. Oxxx =λ−λ⋅⋅=η
( ) 2801610010 .a. LOyyy =λ−λ⋅⋅=η
• Euler strength: N/m² .E
px
Ex 341792835852
2
=λ
⋅π=
N/m² .E
py
Ey 31658733482
2
=λ
⋅π=
• Reduced buckling factor: ( )
822715933642
1.
pp Exxyx =
⋅+η+=φ
( )9421200886
2
1.
pp Eyyyy =
⋅+η+=φ
• Compressive strength: ( )
Nm .pp
ppp
yExxx
yExcx 307115196530
21
2
=⋅−φ+φ
⋅=
( )Nm .
pp
ppp
yEyyy
yEycy 5748028816
21
2
=⋅−φ+φ
⋅=
Unity Check: 1104339217330
157404 2 ≤⋅==⋅
−..
.
pA
N
minc
=> Section OK for buckling
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B. Calculation of Lateral Torsional Buckling (Art. 4.3.7. Appendix B)
To determined LTB parameters, the rules prescribed by BS5950 are different for section with flange symmetrical about major or minor axis. As we’ve seen in the benchmark concerning member 7 of TutBS5950.epw, this distinction gives the same results for double symmetrical section.
• Slenderness: 8611004510
5.
.A
I
L
i
L
yyy ====λ
• N=0.5 (symmetrical section)
• Limiting equivalent slenderness: 7234402
12
.p
E.
yLO =
⋅π⋅=λ
• 6314010512
1025911
5
6
..
.
I
I
x
y =⋅
⋅−=−=γ
−
−
• Torsional index: 9291510491
00452501615056605660
7.
.
...
J
Ah.x s =
⋅⋅⋅=⋅⋅=
−
• Buckling parameter: 83940
41
2
2
.HA
SIu
xy =
⋅
γ⋅⋅=
• Slenderness factor: ( ) 7356020
114
21
21
22
.x
NNv =
ψ+
ψ+
λ⋅+−⋅⋅=
−
• Equivalent slenderness: 34468.vun yLTB =λ⋅⋅⋅=λ
• Perry coefficient: ( ) 235300070 .. LOLTLT =λ−λ⋅=η
• Elastic critical moment: Nm .ES
p
EMM
,LT
yy
yLT
pE 41143767
22
2
2
2
=λ
⋅π⋅=
⋅λ
⋅π⋅=
• Reduced LTB factor: ( )
981333492
1.
MM ELTPb =
⋅+η+=φ
• Equivalent uniform moment: 60714014.MmM A =⋅=
• Buckling resistance moment: ( )
Nm .MM
MMM
pEbb
PEb 7362833
21
2
=⋅−φ+φ
⋅=
Unity check : 16507362833
9540683≤== .
.
.
M
M
b
=> OK LTB check
1.19.2.5 Tension members with moments (Art. 4.8.3.3.2.)
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The internal forces for the ultimate combination 6 in the critical section x=2.22 m are: F=7404.15 N (tension) Mx=14014.607 Nm Using the more precise approach described in article 4.8.3.3.2., we find: Maximum buckling moment around major axis:
( ) Nm 60702.29.;.minP
F.M;
P
F.P
F
MminMcy
b
cx
cxcxax ==
⋅−⋅
⋅+
−
⋅= 2960702188724850
150
1
1
Maximum buckling moment around minor axis: Nm .
P
F.
P
F
MM
cy
cxcyay 53640753
501
1
=
⋅+
−
⋅=
Unity check: 167320 ≤=⋅
+⋅
.M
Mm
M
Mm
ay
y
ax
x => Stability check OK
1.19.3 Member 47
1.19.3.1 Classification of the section (Table 7. BS5950):Stem of T-section By using Table 7 of BS5950, we can determine the yield strength fy:
• Normal steel grade: S275 • Nominal thickness of the element t ≤ 40 mm ⇒ Nominal value of yield strength: py=275 N/mm2
⇒ 1235
=
=ε
yf (Using Note 3. Table 7.)
The section of member 47 is subjected both to bending and tension in section x=0 m. By using Table 7. of BS5950, we find:
59592390130
120 .....
td
w=ε⋅≤== ⇒ Section is compact
1.19.3.2 Check Normal Stress and shear stress (Art. 4.6.1. Art. 4.2.3) The member 47 is subjected to a normal tension F=37369.5N and a small shear force Fvy=441.92N in the critical section. According to BS5950, we can verify:
Unity Check: Normal check: 110594002960275000000
537369 2 ≤⋅=⋅
=⋅
−..
.
pyA
F
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Shear area: 2001560 m.AA vyvx ==
Shear Check: 31071125740
92441
60
−⋅==⋅⋅
= ..
pA.
F
P
F
yvy
vy
vy
vy
⇒ Section OK for tension and shear
1.19.3.3 Combined bending, axial force (Art. 4.8.2.) By using Art. 4.8.2. (1), we can determine: Fvy≤0.6Pvy (LOW SHEAR): Nm pZM yxxcx 11550=⋅=
Nm .pZM yyycy 58167=⋅=
A elastic check of the stress in the critical section gives:
110299275000000
4525562183
275000000
2319532831295688285912624832 2 ≤⋅==−+
=σ+σ+σ −.
....
p y
mymxn
=> Section check OK for combined bending and normal force
1.19.3.4 Stability Check: Check for bending, compression and L.T.B.
A. Calculation of Buckling (Art. 4.7.5. Appendix C)
• Slenderness: 492803510
1.
.A
I
L
i
L
xxx ====λ
897924402450
1.
.A
I
L
i
L
yyy ====λ
• Limiting slenderness: 3617202
12
.p
E.
yO =
⋅π⋅=λ
• Robertson constant: 55.a x = 55.a y =
• Perry coefficient: ( ) 061200010 .a. Oxxx =λ−λ⋅⋅=η
( ) 251410010 .a. LOyyy =λ−λ⋅⋅=η
• Euler strength: N/m² .E
px
Ex 8225534898832
2
=λ
⋅π=
N/m² .E
py
Ey 28345580252
2
=λ
⋅π=
• Reduced buckling factor: ( )
3614923817322
1.
pp Exxyx =
⋅+η+=φ
( )058176401969
2
1.
pp Eyyyy =
⋅+η+=φ
• Compressive strength: ( )
Nm .pp
ppp
yExxx
yExcx 717257475453
21
2
=⋅−φ+φ
⋅=
( )Nm .
pp
ppp
yEyyy
yEycy 74829384290
21
2
=⋅−φ+φ
⋅=
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Unity Check: 14290586977
537369≤==
⋅.
.
.
pA
F
minc
=> Section OK for buckling
B. Calculation of Lateral Torsional Buckling (Art. 4.3.7. Appendix B) Using the formula of section with flange symmetrical about the minor axis, we find:
• Slenderness: 8141.
AI
L
i
L
yyy ===λ
• N=1
• Limiting equivalent slenderness: 7234402
12
.p
E.
yLO =
⋅π⋅=λ
• 51301 .I
I
x
y =−=γ
• Torsional index: 17810831
0029601135056605660
7.
.
...
J
Ah.x s =
⋅⋅⋅=⋅⋅=
−
• Buckling parameter: 635704 4
1
22
2
.hA
Su
s
x =
⋅
γ⋅⋅=
• Slenderness factor: ( ) 678020
114
21
21
22
.x
NNv =
ψ+
ψ+
λ⋅+−⋅⋅=
−
• Equivalent slenderness: 5917.vun yLTB =λ⋅⋅⋅=λ
• Perry coefficient: ( ) 000070 =η⇒≤λ−λ⋅=η LTLOLTLT .
• Elastic critical moment: Nm .ES
p
EMM
LT
xx
yLT
pE 75634678
2
2
2
2
=λ
⋅π⋅=
⋅λ
⋅π⋅=
• Reduced LTB factor: ( )
3753303742
1.
MM ELTPb =
⋅+η+=φ
• Equivalent uniform moment: 68553.MmM A =⋅=
• Buckling resistance moment: ( )
Nm MM
MMM
pEbb
PEb 26070
21
2
=⋅−φ+φ
⋅=
Unity check : 110122 2 ≤⋅= −.M
M
b
=> OK LTB check
1.19.3.5 Tension members with moments (Art. 4.8.3.3.2.) The internal forces for the ultimate combination 5 in the critical section x=0 m are: F=37369.5 N (tension) Mx=553.58 Nm Using the more precise approach described in article 4.8.3.3.2., we find: Maximum buckling moment around major axis:
( ) Nm 10721.08.;.minP
F.M;
P
F.P
F
MminMcy
b
cx
cxcxax ==
⋅−⋅
⋅+
−
⋅= 8314887081072150
150
1
1
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Maximum buckling moment around minor axis: Nm .
P
F.
P
F
MM
cy
cxcyay 563840
501
1
=
⋅+
−
⋅=
Unity check: 110425 2 ≤⋅=⋅
+⋅
−.ayM
yMm
axMxMm
=> Stability check OK
Calculation note - Member 4 BS 5950 Check
Macro 2 Member 4 HEA180 Grade 43 Ult. comb 7 0.67
Material data
Design strength 275.00 MPa
fabrication rolled
SECTION CHECK
Width to thickness ratio for webs
ratio 20.33 on position 0.00 m
ratio
Maximum ratio 1 77.05
Maximum ratio 2 94.04
Maximum ratio 3 118.79
==> Class cross-section Plastic
Width to thickness ratio for outstand flanges
ratio 9.47 on position 0.00 m
ratio
Maximum ratio 1 8.50
Maximum ratio 2 9.50
Maximum ratio 3 15.00
==> Class cross-section Compact
The critical check is on position 2.22 m
Axis definition :
- local x- axis in this code check is referring to the local y axis in EPW
- local y- axis in this code check is referring to the local z axis in EPW
Internal forces
F -7.40 kN
Fvx 0.04 kN
Fvy -2.15 kN
Mt -0.00 kNm
Mx 40.68 kNm
My -0.12 kNm
Compression check
according to article 4.7.4.
Table of values
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Table of values
Pc 1245.75 kN
Unity check 0.01
Shear check (Fvx)
according to article 4.2.3.
Table of values
Avx 3420.00 mm^2
Pvx 564.30 kN
Unity check 0.00
Shear check (Fvy)
according to article 4.2.3.
Table of values
Avy 1026.00 mm^2
Pvy 169.29 kN
Unity check 0.01
Combined bending, axial force and shear force check
according to article 4.8.3.2.(a)
Table of values
Mcx 89.10 kNm
Mcy 33.99 kNm
Unity check 0.47
Element satisfies the section check !
STABILITY CHECK
Buckling parameters xx yy
type non-sway non-sway
Buckling length 8.00 8.00 m
Length 8.00 8.00 m
Buckling factor 1.00 1.00
Slenderness 107.47 177.04
Euler strength pE 179.44 66.13 MPa
Robertson Constant 5.50 8.00
Perry factor a 0.50 1.28
Reduced buckling factor 271.68 212.80 MPa
Compressive strength pc 115.27 48.18 MPa
Buckling check
according to article 4.7.5. & Appendix C
Table of values
Pc 218.27 kN
Unity check 0.03
LTB
L ltb 5.00 m
k 1.00
m 1.00
n 1.00
Stabilizing load according to Art. 4.3.4. and Table 13.
LTB check
according to article 4.3.7. & Appendix B
Table of values
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Table of values
N factor 0.50
Slenderness 110.65
Torsional index x 15.94
Buckling parameter u 0.84
Slender. factor v 0.74
Equivalent slender. 68.31
Limiting equiv. slender. 34.73
Perry factor 0.24
Mcr elastic 143.90 kNm
Red. LTB factor 133.41 kNm
Mb 62.86 kNm
Max. MA 40.68 kNm
Equiv. uniform M 40.68 kNm
Unity check 0.65
Compression and bending check
according to article 4.8.3.3.2.
Table of values
Max 60.73 kNm
May 40.75 kNm
Unity check 0.67
0.67 +0.00=0.67
NO shear buckling check
Element satisfies the stability check !
Calculation note - Member 7
Macro 4 Member 7 IPE240 Grade 43 Ult. comb 5 0.43
Material data
Design strength 275.00 MPa
fabrication rolled
SECTION CHECK
Width to thickness ratio for webs
ratio 30.71 on position 0.86 m
ratio
Maximum ratio 1 78.96
Maximum ratio 2 97.92
Maximum ratio 3 120.06
==> Class cross-section Plastic
Width to thickness ratio for outstand flanges
ratio 6.12 on position 0.86 m
ratio
Maximum ratio 1 8.50
Maximum ratio 2 9.50
Maximum ratio 3 15.00
==> Class cross-section Plastic
The critical check is on position 3.00 m
Axis definition :
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- local x- axis in this code check is referring to the local y axis in EPW
- local y- axis in this code check is referring to the local z axis in EPW
Internal forces
F 0.26 kN
Fvx 0.00 kN
Fvy -2.25 kN
Mt 0.00 kNm
Mx 14.01 kNm
My -0.00 kNm
Normal force check
according to article 4.6.1.
Table of values
Pt 1075.25 kN
Unity check 0.00
Shear check (Fvy)
according to article 4.2.3.
Table of values
Avy 1488.00 mm^2
Pvy 245.52 kN
Unity check 0.01
Combined bending, axial force and shear force check
according to article 4.8.2.
Table of values
Mcx 100.65 kNm
Mcy 15.61 kNm
Unity check 0.14
Element satisfies the section check !
STABILITY CHECK
LTB
L ltb 6.00 m
k 1.00
m 1.00
n 1.00
Stabilizing load according to Art. 4.3.4. and Table 13.
LTB check
according to article 4.3.7. & Appendix B
Table of values
N factor 0.50
Slenderness 222.63
Torsional index x 22.68
Buckling parameter u 0.88
Slender. factor v 0.64
Equivalent slender. 126.85
Limiting equiv. slender. 34.73
Perry factor 0.64
Mcr elastic 47.14 kNm
Red. LTB factor 89.10 kNm
Mb 32.59 kNm
Max. MA 14.01 kNm
Equiv. uniform M 14.01 kNm
Unity check 0.43
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Compression and bending check
according to article 4.8.3.2.
Table of values
Max 32.59 kNm
May 20.35 kNm
Unity check 0.43
0.43 +0.00=0.43
NO shear buckling check
Element satisfies the stability check !
Calculation note - Macro 18
Macro 18 Member 47 T120/120/13 Grade 43 Ult. comb 6 0.43
Material data
Design strength 275.00 MPa
fabrication rolled
SECTION CHECK
Width to thickness ratio for outstand flanges
ratio 9.23 on position 0.00 m
ratio
Maximum ratio 1 8.50
Maximum ratio 2 9.50
Maximum ratio 3 19.00
==> Class cross-section Compact
The critical check is on position 0.00 m
Axis definition :
- local x- axis in this code check is referring to the local y axis in EPW
- local y- axis in this code check is referring to the local z axis in EPW
Internal forces
F -37.37 kN
Fvx -0.00 kN
Fvy -0.44 kN
Mt -0.01 kNm
Mx 0.55 kNm
My 0.01 kNm
Compression check
according to article 4.7.4.
Table of values
Pc 814.00 kN
Unity check 0.05
Shear check (Fvx)
according to article 4.2.3.
Table of values
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Table of values
Avx 1560.00 mm^2
Pvx 257.40 kN
Unity check 0.00
Shear check (Fvy)
according to article 4.2.3.
Table of values
Avy 1391.00 mm^2
Pvy 229.51 kN
Unity check 0.00
Combined bending, axial force and shear force check
according to article 4.8.3.2.(a)
Table of values
sigma n 12.62 MPa
sigma Mx 12.96 MPa
sigma My 0.02 MPa
Unity check 0.09
Element satisfies the section check !
STABILITY CHECK
Buckling parameters xx yy
type non-sway non-sway
Buckling length 1.00 6.00 m
Length 1.00 6.00 m
Buckling factor 1.00 1.00
Slenderness 28.44 244.67
Euler strength pE 2562.76 34.62 MPa
Robertson Constant 5.50 5.50
Perry factor a 0.06 1.25
Reduced buckling factor 1496.94 176.45 MPa
Compressive strength pc 257.56 29.43 MPa
Warning: slenderness 244.67 is larger then 200.00 !
Buckling check
according to article 4.7.5. & Appendix C
Table of values
Pc 87.12 kN
Unity check 0.43
LTB
L ltb 1.00 m
k 1.00
m 1.00
n 1.00
Stabilizing load according to Art. 4.3.4. and Table 13.
LTB check
according to article 4.3.7. & Appendix B
Table of values
N factor 1.00
Slenderness 40.78
Torsional index x 8.17
Buckling parameter u 0.60
Slender. factor v 0.68
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Table of values
Equivalent slender. 16.49
Limiting equiv. slender. 34.73
Perry factor 0.00
Mcr elastic 634.83 kNm
Red. LTB factor 328.87 kNm
Mb 22.90 kNm
Max. MA 0.55 kNm
Equiv. uniform M 0.55 kNm
Unity check 0.02
Compression and bending check
according to article 4.8.3.3.2.
Table of values
Max 10.72 kNm
May 3.84 kNm
Unity check 0.05
0.05 +0.00=0.05
NO shear buckling check
Element satisfies the stability check !
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1.20 PST.06.09 – 02 : BS5950 Steel Code of practice for design Description Calculation of m and n factor of BS5950. Project data See input file. Reference [1] British Standard BS5950 Part 1.: 1990 + Revised text 1992
Structural use of steelwork in building Part 1. Code of practice for design in simple and continuous construction: hot rolled sections
[2] Steelwork Design
Guide to BS5950: Part 1: 1990 Volume 2 Worked examples (Revised edition)
[3] Eurocode 3: Calcul des structures en acier
Edition 1992 [4] Essentials of Eurocode 3:Design Manual for Steel Structures in Building
First Edition 1991 See the chapter "Manual calculation" for the manual calculation according to this reference. Result Example in Ref[2]. Ref.[2] EPW % Diff. Example 2 Mb 397 kNm 397 kNm 0 % M reduced 381 kNm 379 kNm 0.50 % m 0.91 0.91 0 % n 1.00 1.00 0 % Example 3 Mb 450 kNM 451 kNm 0.20 % M reduced 419 kNm 418 kNm 0.20 % m 1.00 1.00 0 % n 0.94 0.94 0 % Example 4 Mb 184 kNm 185 kNm 0.50 % M reduced 126 124 kNm 1.60 % m 0.80 0.81 1.25 % n 1.00 1.00 0 % See the chapter "Calculation note" for the detailed output of ESA-Prima Win. Version ESA-Prima Win 3.20.03 Input file example 2 : PST060902a.epw example 3 : PST060902b.epw example 4 : PST060902c.epw
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Modules 3D Frame (PRS.11) BS5950 Steel code check (PST.06.10) Author NEM/CVL Manual calculation The next 3 examples treat the specific calculation of the equivalent uniform factor m and the equivalent slenderness factor n. BS5950 makes using of those values in LTB check to determine the LTB design moment resistance. For other controls following BS5950, we refer to the corresponding benchmarks. Each beam checked is not laterally fully restrained so that a lateral torsional buckling control must be performed. The condition to be satisfied in all the cases is that:
bxbA pSMMmM ⋅=≤⋅=
where pb is the bending strength and is related to the equivalent slenderness given by
λ⋅⋅⋅=λ vunLT in which n is the equivalent slenderness
For beam without loading between points of lateral restraint, n=1 and m depends on the ratio of the end moments at the point of restraint. Similarly, for beam loaded between points of lateral restraint, m=1 and n depend both on the ratio of the end moment at the point of restraint and on the ratio of the larger moment to the mid-span free moment. There are thus two method to work with lateral buckling: - ‘m approach’ with m calculated and n=1
- ‘n approach’ with m=1 and n calculated Both method are used in the following examples and compare with result found in the second reference Steelwork Design Guide to BS5950: Part 1: 1990 Volume 2 Worked examples (Revised edition). In any given situation, only one method is admissible and it’s always conservative to use m=n=1. Steelwork Design Guide to BS5950: Part 1: 1990 Volume 2 Worked examples (Revised edition) gives two notes appield in EPW: 1. if the loading is destabilising both m and n factors must be taken as unity 2. Since the publication of BS5950 Part 1:1990, doubt has been cast on the correctness of using n-factors less than 1
in combination with an effective length LE less than L in the calculation of λ=λ nuvLT . In the future it may be
possible, some correction may occur. However, as a interim measure, pending clarification from BS, it is recommended that λLT is taken as the smaller of λLT1 and λLT2:
y
E1LT r
Lvu ⋅⋅=λ and
y2LT r
Lvun ⋅⋅⋅=λ
Calculation note - Example 2 : PST060902a.epw BS 5950 Check
Macro 1 Member 2 UB457/191/82 Grade 43 Loadcase 1 0.95
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Material data
Design strength 275.00 MPa
fabrication rolled
SECTION CHECK
Width to thickness ratio for webs
ratio 41.17 on position 0.00 m
ratio
Maximum ratio 1 79.00
Maximum ratio 2 98.00
Maximum ratio 3 120.00
==> Class cross-section Plastic
Width to thickness ratio for outstand flanges
ratio 5.97 on position 0.00 m
ratio
Maximum ratio 1 8.50
Maximum ratio 2 9.50
Maximum ratio 3 15.00
==> Class cross-section Plastic
The critical check is on position 0.00 m
Axis definition :
- local x- axis in this code check is referring to the local y axis in EPW
- local y- axis in this code check is referring to the local z axis in EPW
Internal forces
F 0.00 kN
Fvx 0.00 kN
Fvy -19.03 kN
Mt 0.00 kNm
Mx 417.80 kNm
My 0.00 kNm
Shear check (Fvy)
according to article 4.2.3.
Table of values
Avy 4554.00 mm^2
Pvy 751.41 kN
Unity check 0.03
Combined bending, axial force and shear force check
according to article 4.8.2.
Table of values
Mcx 504.35 kNm
Mcy 64.68 kNm
Unity check 0.83
Element satisfies the section check !
STABILITY CHECK
LTB
L ltb 3.00 m
k 1.00
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LTB
m 0.91
n 1.00
Stabilizing load according to Art. 4.3.4. and Table 13.
LTB check
according to article 4.3.7. & Appendix B
Table of values
N factor 0.50
Slenderness 71.09
Torsional index x 30.96
Buckling parameter u 0.88
Slender. factor v 0.94
Equivalent slender. 58.71
Limiting equiv. slender. 34.31
Perry factor 0.17
Mcr elastic 1076.60 kNm
Red. LTB factor 882.41 kNm
Mb 396.96 kNm
Max. MA 417.80 kNm
Equiv. uniform M 378.90 kNm
Unity check 0.95
Compression and bending check
according to article 4.8.3.2.
Table of values
Max 396.96 kNm
May 83.32 kNm
Unity check 0.95
0.95 +0.00=0.95
NO shear buckling check
Element satisfies the stability check !
Calculation note - Example 3 - PST060902b.epw
BS 5950 Check
Macro 1 Member 2 UB610/229/140 Grade 43 Loadcase 1 0.93
Material data
Design strength 265.00 MPa
fabrication rolled
SECTION CHECK
Width to thickness ratio for webs
ratio 41.80 on position 0.00 m
ratio
Maximum ratio 1 80.48
Maximum ratio 2 99.83
Maximum ratio 3 122.24
==> Class cross-section Plastic
Width to thickness ratio for outstand flanges
ratio 5.21 on position 0.00 m
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ratio
Maximum ratio 1 8.66
Maximum ratio 2 9.68
Maximum ratio 3 15.28
==> Class cross-section Plastic
The critical check is on position 0.00 m
Axis definition :
- local x- axis in this code check is referring to the local y axis in EPW
- local y- axis in this code check is referring to the local z axis in EPW
Internal forces
F 0.00 kN
Fvx 0.00 kN
Fvy -19.03 kN
Mt 0.00 kNm
Mx 417.80 kNm
My 0.00 kNm
Shear check (Fvy)
according to article 4.2.3.
Table of values
Avy 8085.32 mm^2
Pvy 1285.57 kN
Unity check 0.01
Combined bending, axial force and shear force check
according to article 4.8.2.
Table of values
Mcx 1097.65 kNm
Mcy 124.34 kNm
Unity check 0.38
Element satisfies the section check !
STABILITY CHECK
LTB
L ltb 7.65 m
k 1.00
m 1.00
n 0.94
Stabilizing load according to Art. 4.3.4. and Table 13.
LTB check
according to article 4.3.7. & Appendix B
Table of values
N factor 0.50
Slenderness 152.06
Torsional index x 30.58
Buckling parameter u 0.88
Slender. factor v 0.82
Equivalent slender. 108.84
Limiting equiv. slender. 34.95
Perry factor 0.52
Mcr elastic 707.51 kNm
Red. LTB factor 1085.54 kNm
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Table of values
Mb 451.67 kNm
Max. MA 417.80 kNm
Equiv. uniform M 417.80 kNm
Unity check 0.93
Compression and bending check
according to article 4.8.3.2.
Table of values
Max 451.67 kNm
May 162.03 kNm
Unity check 0.93
0.93 +0.00=0.93
NO shear buckling check
Element satisfies the stability check !
Calculation note - Example 4 : PST060902c.epw BS 5950 Check
Macro 1 Member 2 UB457/152/52 Grade 43 Loadcase 1 0.67
Material data
Design strength 275.00 MPa
fabrication rolled
SECTION CHECK
Width to thickness ratio for webs
ratio 53.66 on position 0.00 m
ratio
Maximum ratio 1 79.00
Maximum ratio 2 98.00
Maximum ratio 3 120.00
==> Class cross-section Plastic
Width to thickness ratio for outstand flanges
ratio 6.97 on position 0.00 m
ratio
Maximum ratio 1 8.50
Maximum ratio 2 9.50
Maximum ratio 3 15.00
==> Class cross-section Plastic
The critical check is on position 0.00 m
Axis definition :
- local x- axis in this code check is referring to the local y axis in EPW
- local y- axis in this code check is referring to the local z axis in EPW
Internal forces
F 0.00 kN
Fvx 0.00 kN
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Internal forces
Fvy -13.37 kN
Mt 0.00 kNm
Mx 152.80 kNm
My 0.00 kNm
Shear check (Fvy)
according to article 4.2.3.
Table of values
Avy 3420.00 mm^2
Pvy 564.30 kN
Unity check 0.02
Combined bending, axial force and shear force check
according to article 4.8.2.
Table of values
Mcx 301.40 kNm
Mcy 27.92 kNm
Unity check 0.51
Element satisfies the section check !
STABILITY CHECK
LTB
L ltb 3.00 m
k 1.00
m 0.81
n 1.00
Stabilizing load according to Art. 4.3.4. and Table 13.
LTB check
according to article 4.3.7. & Appendix B
Table of values
N factor 0.50
Slenderness 96.47
Torsional index x 43.98
Buckling parameter u 0.86
Slender. factor v 0.95
Equivalent slender. 78.48
Limiting equiv. slender. 34.31
Perry factor 0.31
Mcr elastic 360.05 kNm
Red. LTB factor 386.39 kNm
Mb 184.46 kNm
Max. MA 152.80 kNm
Equiv. uniform M 123.81 kNm
Unity check 0.67
Compression and bending check
according to article 4.8.3.2.
Table of values
Max 184.46 kNm
May 36.48 kNm
Unity check 0.67
0.67 +0.00=0.67
NO shear buckling check
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Element satisfies the stability check !
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1.21 PST.06.10 – 01 : GBJ 17-88 Steel Code Check Tutorial Frame Description The unity check according to GBJ 17-88 of members 4, 7 and macro 18 of the Tutorial Frame project are calculated manually. The result is compared with the result of ESA-Prima Win. Project data See input file. Reference Ref.[1] National standard of the People’s Republic of China
Code for design of steel structures GBJ 17-88 Beijing 1995
See the chapter "Manual calculation" for the manual calculation according to this reference. Result Member/Macro EPW Manually % Diff. member 7 0.12
0.72 0.12 0.72
0 % 0 %
member 19 0.66 0.06 0.47 0.68
0.66 0.06 0.47 0.68
0 % 0 % 0 % 0 %
macro 18 0.09 0.44 0.04
0.09 0.44 0.04
0 % 0 % 0 %
See the chapter "Calculation note" for the detailed output of ESA-Prima Win. Version ESA-Prima Win 3.20.03 Input file + calculation note PST061001.epw Modules 3D Frame (PRS.11) GBJ-17 Code Check (PST.06.10) Author CVL Manual calculation - Member 7.
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Buckling data First we will discuss the buckling data of this member.
5. System length L: Since there are no intermediate restraints on this member the system length L = the full
member length for all buckling modes. (L=6m)
6. The member is loaded through the shear centre.
7. Sway modes: Y-Y: non-sway Z-Z: non-sway. Buckling factor kx=ky=1.0.
8. The load application is on the top flange.
Check of IPE270 section. Section data E 210000 N/mm² A 4590 mm² fy 235 N/mm² Wx 429000 mm³ Wy 62200 mm³ ix 112 mm iy 30.2 mm Sx 242000 mm³ height h 270 mm width b 135 mm flange tf 10.2 mm web tw 6.6 mm radius r 15 mm
Now, we will discuss the different steps :
Classification of the section c) Width-to-thickness ratio for webs. (Using art.5.4.2.) b/tw = 219.6 / 6.6 = 33.27 The web is subjected to compression at 0.0 m. The slenderness λ in the web plane = 53.4. The maximal ratio for a slender section is 25 + 0.5 λ = 51.70
Since 33.27 < 51.7, the web is no slender element. d) Width-to-thickness ratio for outstand flanges (Using art.5.4.1.)
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b/tf = 67.5/10.2 = 6.61
Max. ratio for flange subject to compression is 20. Since 6.62 < 15 , the flanges are no slender elements. � Section IPE270 is no slender section. Since 6.61 < 13 (art.4.1.1.) we can use the plasticity factors : γx =1.05 γy =1.20
Stability check Since this check is the most critical check, we will only perform this check. Critical check = Ultimate combination 7 on position x=3m. Combination 7, member 7 on x =3.0 m: X = 1.57 kN Mx = 11.58 kNm Z = 1.79 kN (Shear) Stability check for Bending + Compression Using article 5.2.5., and formula (5.2.5.-1) and (5.2.5.-2) :
fW
M
N
N8.01W
M
A
N
yby
yty
EXxx
xmx
x
≤ϕ
β+
−γ
β+
ϕ
f
N
N8.01W
M
W
M
A
N
EYyy
ymy
xbx
xtx
y
≤
−γ
β+
ϕ
β+
ϕ
E 210000 N/mm² A 4590 mm² f 215 N/mm² N 1.57 kN Mx 11.58 kNm Wx 429000 mm³ γx 1.05 γy 1.20 βtx No end moments
� 1.0
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βmx Sway system � 1.0
ϕx b/h < 0.8 � buckling curve a λx=6000/112 slenderness λx = 53.40 using Table A3.1 � 0.906
ϕy buckling curve b λy = 6000/30.2 slenderness λy = 198 using Table A3.2 � 0.19
ϕbx Appendix A1.5, formula A1.3 =1.07 - λy²/44000 λy= 6000 / 30.2 = 198 � 0.18
NEX = π²EA/λx² � 3333 kN
NEY = π²EA/λy² � 242 kN
formula 5.2.5-1 : 0.4 + 25.7 + 0.0 = 26.1 N/mm² unity check = 26.1 / 215 = 0.12 formula 5.2.5-2 : 1.8 + 153.5 + 0.0 = 155.3 N/mm² unity check = 155.3 / 215 = 0.72 Manual calculation - Member 19 Buckling data
First we will discuss the buckling data of this macro.
5. System length L: The beams on a height of 3m provide restraint to the column. Therefore the system lengths for member 19: Ly = Lz = 5 m.
6. The member is loaded through the shear centre.
7. Sway modes: Y-Y: non-sway (bracing in roof-plane) Z-Z: non-sway
8. K factors : Kx = 0.85 / Ky = 0.90
Check of HEB160 section The critical check is performed on section 0.0 m for combination number 6. The internal forces are : N 63.31 kN
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Vy 8.276 kN Mx 41.33 kNm My 0.61 kNm Section data E 210000 N/mm² A 5430 mm² fy 235 N/mm² Wx 311000 mm³ Wy 111000 mm³ ix 67.8 mm iy 40.5 mm Sx 177000 mm³ height h 160 mm width b 160 mm flange tf 13 mm web tw 8 mm radius r 15 mm Classification of the section a) Width-to-thickness ratio for webs. (Using Art.5.4.2)
b/tw = 104 / 8 = 13 For this case, we calculate α0.
max
maxmax0 σ
σ−σ=α
σN = N/A = 63310/5425 = 11.6 N/mm² σM = Mx h / Ix = 41320000 52 /24920000 = 86.22 N/mm² σmax = 11.67 + 86.22 = 98 N/mm² σmin = 11.6 – 86.22 = -74 N/mm² α0 = (98+74)/98 = 1.76 The slenderness λ in the web plane = 62.8. The maximal ratio for a slender section is 48 α0 + 0.5 λ - 26.2 = 89.44
Since 13 < 89.4 , the web is no slender section element.
c) Width-to-thickness ratio for outstand flanges (Using Art.5.4.1.) b/tf = (80-4)/13 = 5.85
Max. ratio for flange subject to compression/bending is 15. Since 5.85 < 15 , the flanges are no slender elements.
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� Section HEB160 is no slender section. Since 5.85 < 13 (art.4.1.1.) we can use the plasticity factors : γx =1.05 γy =1.20
Section check This check is executed at member 19 on position x = 0 m. (start of member 19) Combination 6 : Normal stress check
Using article 5.2.1., formula 5.2.1.
fW
M
W
M
A
N
yy
y
xx
x <γ
+γ
+
N 63.31 kN A 5425 mm² Mx 41.3 kNm γx 1.05 Wx 311500 mm³ My 0.61 kNm γy 1.20 Wy 111200 mm³ f 215 N/mm² 11.67 + 126 + 4.6 = 142 N/mm² < 215 N/mm² Unity check = 142/215 = 0.66 Shear check
Using article 4.1.2., formula 4.1.2.
vw
fIt
VS<=τ
V 8.27 kN S 177000 mm³ I 24920000 mm4 tw 8 mm fv 125 N/mm² τ = 7.4 N/mm² < 125 N/mm² Unity check = 7.4/125 = 0.06 Stability check for Bending + Compression Since this check is the most critical check, we will only perform this check.
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Critical check = Ultimate combination 6 on position x=0m of member 19. Combination 6, member 19 on x =0.0 m: Using article 5.2.5., and formula (5.2.5.-1) and (5.2.5.-2) :
fW
M
N
N8.01W
M
A
N
yby
yty
EXxx
xmx
x
≤ϕ
β+
−γ
β+
ϕ
f
N
N8.01W
M
W
M
A
N
EYyy
ymy
xbx
xtx
y
≤
−γ
β+
ϕ
β+
ϕ
N 63.31 kN Mx 41.33 kNm My 0.61 kNm Wx 311500 mm³ Wy 111200 mm³ γx 1.05 γy 1.20 βty
βtx Non sway system, no transverse loading, = 0.65 + 0.35 M2/M1 ; M2 = 0.0 � 0.65
βmy
βmx Non sway system, no transverse loading, = 0.65 + 0.35 M2/M1 ; M2 = 0.0 � 0.65
ϕx b/h > 0.8 � buckling curve b λx = 4260/67.8 λx = 62.86 slenderness λx = 62.86 using Table A3.2 � 0.795
ϕy buckling curve b slenderness λy = 4510/40.5 slenderness λy = 111 using Table A3.2 � 0..487
ϕby 1.0 ϕbx Appendix A1.5, formula A1.3
=1.07 - λy²/44000 λy= 5000 / 40.5 = 123,46 � 0.72
NEX = π²EA/λx² � 2833 kN
NEY = π²EA/λy²
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� 902 kN
formula 5.2.5-1 : 14.6 + 84 + 3.5 = 102 N/mm² unity check = 102 / 215 = 0.47 formula 5.2.5-2 : 24 + 120 + 3.1 = 147 N/mm² unity check = 147 / 215 = 0.68 Manual calculation - Macro 18 Buckling data
First we will discuss the buckling data of this macro.
5. System length L: 6. For each member: Ly = memberlength = 1m. Lz = Macrolength / 2 = 6 m. (Lateral restraint by middle-rafter) Lltb = Macrolength / 2 = 6 m. (Lateral restraint by middle-rafter)
7. The member is loaded through the shear center.
8. Sway modes: Y-Y: non-sway Z-Z: non-sway (bracing in roof-plane)
9. K factors : Kx=1.00; Ky=0.94
Check of T120/120/13 section Section data E 210000 N/mm² A 2960 mm² fy 235 N/mm² Wx 42000 mm³ Wy 29700 mm³ ix 35.1 mm iy 24.5 mm Ix 3660000 mm4 Iy 1780000 mm4 ex 32.8 mm height h 120 mm width b 120 mm flange tf 13 mm web tw 13 mm radius r 13 mm
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Classification of the section
Width-to-thickness ratio for outstand flanges (Using Art.5.4.1.) b/tf = (60-13/2)/13 = 4.12
Max. ratio for flange subject to compression/bending is 15. Since 4.12 < 15 , the flanges are no slender elements. � Section is no slender section. Since 4.12 < 13 (art.4.1.1.) we can use the plasticity factors : γx1 =1.05 γx2 =1.20 γy =1.20
Stability check: Compression critical buckling check Since this check is the most critical check, we will only perform this check. Critical check = Ultimate combination 1 on position x=0m. of member 47. Combination 5, member 47 on x =0.0 m: N = -34.26 kN (compression) Mx = 0.51 kNm My = 0.00941 kNm Using article 5.2.5., and formula (5.2.5.-1) and (5.2.5.-2) :
fW
M
N
N8.01W
M
A
N
yby
yty
EXxx
xmx
x
≤ϕ
β+
−γ
β+
ϕ
f
N
N8.01W
M
W
M
A
N
EYyy
ymy
xbx
xtx
y
≤
−γ
β+
ϕ
β+
ϕ
N 34.27 kN Mx 0.51 kNm My 0.00941 kNm Ix 3660000 mm4 Wx1 at top , at compression side
= Ix/hx = 3660000/87.2 = 41972 mm³
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Wy 29700 mm³ At top side (compression side) the influence of the moment My is 0.0.
γx 1.20 (top side) γy 1.20 βtx No linear moment distribution along the LTB part (6 m) of
this element. � 1.0
βmx Non sway system, no transverse loading, = 0.65 + 0.35 M2/M1 ; M2 = -0.05 kNm M1 = 0.57 kNm � 0.62
ϕx � buckling curve b λx = 1000/35.1 slenderness λx = 28.44 using Table A3.2 � 0.94
ϕy buckling curve c λy = 5640/24.5 slenderness λy = 230 using Table A3.3 � 0.138
ϕby 1.0 ϕbx Appendix A1.5, formula A1.7
Flange in tension � 1.00
NEX = π²EA/λx² � 7585 kN
NEY = π²EA/λy² � 115 kN
formula 5.2.5-1 : 12.3 + 6.1 + 0.0 = 18.4 N/mm² unity check = 18.4 / 215 = 0.09 formula 5.2.5-2 : 83.7 + 11.8 + 0.0 = 95.5 N/mm² unity check = 95.5 / 215 = 0.44 Stability check: Tension critical buckling check Since this check is the most critical check, we will only perform this check. Critical check = Ultimate combination 1 on position x=0m. of member 47. Combination 5, member 47 on x =0.0 m: N = -34.27 kN (compression) Mx = 0.51 kNm My = 0.01 kNm Using article 5.2.2., and (extended) formula (5.2.2.-2)
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f
N
N25.11W
M
N
N25.11W
M
A
N
EYyy
ymy
EXxx
xmx ≤
−γ
β+
−γ
β−
N 34.26 kN Mx 0.41 kNm My 0.01 kNm Ix 3660000 mm4 Wx1 at bottom , at tension side
= Ix/hx = 3660000/32.8 = 111585 mm³ Wy 29700 mm³
γx 1.05 (bottom side) γy 1.20 βmx Non sway system, no transverse loading,
= 0.65 + 0.35 M2/M1 ; M2 = -0.05 kNm M1 = 0.57 kNm � 0.62
βmy Non sway system, no transverse loading, = 0.65 + 0.35 M2/M1 ; M2 = 0.0 kNm � 0.65
NEX = π²EA/λx² � 7585 kN
NEY = π²EA/λy² � 115 kN
formula 5.2.2-2 : 11.6 – 2.8 – 0.2 = 8.6 N/mm² unity check = 8.6 / 215 = 0.04 Calculation note - Member 7 GBJ-17 Code Check
Macro 4 Member 7 IPE270 Grade3 Ult. comb 8 0.72
Material data
yield strength fy 235.00 MPa
f 215.00 MPa
fv 125.00 MPa
fabrication rolled
SECTION CHECK
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Section classification
Cfr. Chapter 5.4. ratio limit ratio Position
Webs 33.27 51.71 0.00 m
Outstanding flanges 6.29 20.00 0.00 m
The critical check is on position 3.00 m
Axis definition :
- local x- axis in this code check is referring to the local y axis in EPW
- local y- axis in this code check is referring to the local z axis in EPW
Internal forces
N -1.57 kN
Vx 0.00 kN
Vy 1.79 kN
Mt 0.00 kNm
Mx 11.58 kNm
My -0.00 kNm
Normal stress check
according to article 4.1.1./5.2.1. and formula (4.1.1.)(5.2.1.)
Table of values
normal stress 26.07 MPa
f 215.00 MPa
Gamma x 1.05
Gamma y 1.20
unity check 0.12
Shear stress check
according to article 4.1.2. and formula (4.1.2.)
Table of values
shear stress 1.13 MPa
fv 125.00 MPa
unity check 0.01
Element satisfies the section check !
STABILITY CHECK
Buckling parameters xx yy
type sway non-sway
Slenderness 53.42 198.35
Reduced slenderness 0.57 2.13
Buckling curve a b
Alfa 1 0.41 0.65
Alfa 2 0.99 0.96
Alfa 3 0.15 0.30
Fi 0.91 0.19
Length 6.00 6.00 m
Buckling factor 1.00 1.00
Buckling length 6.00 6.00 m
Critical Euler load 3269.96 237.21 kN
LTB
l1 6.00 m
negative influence of load position
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Distributed loading
No lateral support
Buckling check
according to article 5.1.2. and formula (5.1.2.)
Table of values
Fi 0.19
unity check 0.01
1.82 < 215.00 MPa
Compression and bending check
according to article 5.2.5 and formula (5.2.5-1)
Table of values
Fi x 0.91
Gamma x 1.05
Beta m x 1.00
Beta t y 1.00
Fi b y 1.00
unity check 0.12
0.38 +25.73 +0.00=26.11 < 215.00 MPa
Compression, bending and LTB check
according to article 5.2.5 and formula (5.2.5-2)
Table of values
Fi y 0.19
Beta t x 1.00
Fi b x 0.18
Beta m y 1.00
Gamma y 1.20
unity check 0.72
1.82 +153.61 +0.00=155.42 < 215.00 MPa
Shear buckling check
in buckling field 1
according to article A2.1 and formula (A2.1)
Table of values
a 6000.00 mm
ho 219.60 mm
tw 6.60 mm
C1 166.00
l1 6000.00 mm
l2 219.60 mm
Sigma cr 6458.46 MPa
Sigma c cr 1499.45 MPa
Tau cr 1112.16 MPa
Sigma 22.31 MPa
Sigma c 0.00 MPa
Tau 1.23 MPa
unity check 0.00
Calculation note - Member 19
Macro 11 Member 19 HEB160 Grade3 Ult. comb 7 0.69
Material data
yield strength fy 235.00 MPa
f 215.00 MPa
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Material data
fv 125.00 MPa
fabrication rolled
SECTION CHECK Section classification
Cfr. Chapter 5.4. ratio limit ratio Position
Webs 13.00 89.67 0.00 m
Outstanding flanges 5.85 15.00 0.00 m
The critical check is on position 0.00 m
Axis definition :
- local x- axis in this code check is referring to the local y axis in EPW
- local y- axis in this code check is referring to the local z axis in EPW
Internal forces
N -63.31 kN
Vx 0.12 kN
Vy -8.27 kN
Mt -0.00 kNm
Mx 41.33 kNm
My -0.61 kNm
Normal stress check
according to article 4.1.1./5.2.1. and formula (4.1.1.)(5.2.1.)
Table of values
normal stress 142.67 MPa
f 215.00 MPa
Gamma x 1.05
Gamma y 1.20
unity check 0.66
Shear stress check
according to article 4.1.2. and formula (4.1.2.)
Table of values
shear stress 7.38 MPa
fv 125.00 MPa
unity check 0.06
Element satisfies the section check !
STABILITY CHECK
Buckling parameters xx yy
type non-sway non-sway
Slenderness 62.58 115.97
Reduced slenderness 0.67 1.25
Buckling curve b b
Alfa 1 0.65 0.65
Alfa 2 0.96 0.96
Alfa 3 0.30 0.30
Fi 0.79 0.46
Length 5.00 5.00 m
Buckling factor 0.85 0.94
Buckling length 4.24 4.69 m
Critical Euler load 2818.96 820.91 kN
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LTB
l1 5.00 m
load in center of gravity
Linear moment distribution
No lateral support
Buckling check
according to article 5.1.2. and formula (5.1.2.)
Table of values
Fi 0.46
unity check 0.12
25.42 < 215.00 MPa
Compression and bending check
according to article 5.2.5 and formula (5.2.5-1)
Table of values
Fi x 0.79
Gamma x 1.05
Beta m x 0.65
Beta t y 0.65
Fi b y 1.00
unity check 0.47
14.69 +83.70 +3.55=101.95 < 215.00 MPa
Compression, bending and LTB check
according to article 5.2.5 and formula (5.2.5-2)
Table of values
Fi y 0.46
Beta t x 0.65
Fi b x 0.72
Beta m y 0.65
Gamma y 1.20
unity check 0.69
25.42 +119.39 +3.15=147.96 < 215.00 MPa
Shear buckling check
in buckling field 1
according to article A2.1 and formula (A2.1)
Table of values
a 5000.00 mm
ho 104.00 mm
tw 8.00 mm
C1 166.00
l1 5000.00 mm
l2 104.00 mm
Sigma cr 42307.70 MPa
Sigma c cr 9822.49 MPa
Tau cr 7280.49 MPa
Sigma 97.97 MPa
Sigma c 0.00 MPa
Tau 9.93 MPa
unity check 0.00
Calculation note - Macro 18
GBJ-17 Code Check
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Macro 18 Member 47 T120/120/13 Grade3 Ult. comb 6 0.44
Material data
yield strength fy 235.00 MPa
f 215.00 MPa
fv 125.00 MPa
fabrication rolled
SECTION CHECK Section classification
Cfr. Chapter 5.4. ratio limit ratio Position
Outstanding flanges 4.12 15.00 0.00 m
The critical check is on position 0.00 m
Axis definition :
- local x- axis in this code check is referring to the local y axis in EPW
- local y- axis in this code check is referring to the local z axis in EPW
Internal forces
N -34.26 kN
Vx -0.00 kN
Vy -0.41 kN
Mt -0.00 kNm
Mx 0.51 kNm
My 0.01 kNm
Normal stress check
according to article 4.1.1./5.2.1. and formula (4.1.1.)(5.2.1.)
Table of values
normal stress 21.46 MPa
f 215.00 MPa
Gamma x 1.20
Gamma y 1.20
unity check 0.10
Shear stress check
according to article 4.1.2. and formula (4.1.2.)
Table of values
shear stress 0.68 MPa
fv 125.00 MPa
unity check 0.01
Element satisfies the section check !
STABILITY CHECK
Buckling parameters xx yy
type non-sway non-sway
Slenderness 28.44 229.99
Reduced slenderness 0.31 2.47
Buckling curve b c
Alfa 1 0.65 0.73
Alfa 2 0.96 1.22
Alfa 3 0.30 0.30
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Buckling parameters xx yy
Fi 0.94 0.14
Length 1.00 6.00 m
Buckling factor 1.00 0.94
Buckling length 1.00 5.64 m
Critical Euler load 7441.29 113.77 kN
Warning: slenderness 229.99 is larger then 200.00 !
LTB
l1 6.00 m
load in center of gravity
Linear moment distribution
No lateral support
Buckling check
according to article 5.1.2. and formula (5.1.2.)
Table of values
Fi 0.14
unity check 0.39
83.69 < 215.00 MPa
Compression and bending check
according to article 5.2.5 and formula (5.2.5-1)
Table of values
Fi x 0.94
Gamma x 1.20
Beta m x 0.85
Beta t y 0.65
Fi b y 1.00
unity check 0.10
12.29 +8.42 +0.01=20.72 < 215.00 MPa
Compression and bending (tension side)
according to article 5.2.2 and formula (5.2.2-2)
Table of values
Gamma x 1.05
Beta m x 0.85
Gamma y 1.20
Beta m y 0.65
unity check 0.03
11.57 +-3.87 +-0.23=7.48 < 215.00 MPa
Compression, bending and LTB check
according to article 5.2.5 and formula (5.2.5-2)
Table of values
Fi y 0.14
Beta t x 0.85
Fi b x 1.00
Beta m y 0.65
Gamma y 1.20
unity check 0.44
83.69 +10.07 +0.01=93.77 < 215.00 MPa
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1.22 PST.06.11 – 01 : Korean Steel Code Check Tutorial Frame Description The unity check according to KS of members 4, 7 and macro 18 of the Tutorial Frame project are calculated manually. The result is compared with the result of ESA-Prima Win. Project data See input file. Reference Ref.[1] Korean Standard
See the chapter "Manual calculation" for the manual calculation according to this reference. Result Member/Macro EPW Manually % Diff. member 7 0.30
0.14 0.30 0.14
0 % 0 %
member 19 0.50 0.38
0.50 0.38
0 % 0 %
macro 18 0.53 0.53 0 % See the chapter "Calculation note" for detailed output of ESA-Prima Win. Version ESA-Prima Win 3.20.03 Input file + calculation note PST061101.epw Modules 3D Frame (PRS.11) Korean Steel Code Check (PST.06.11) Author CVL Manual calculation - Member 7 Buckling data First we will discuss the buckling data of this member.
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9. System length L: Since there are no intermediate restraints on this member the system length L = the full member length for all buckling modes. (L=6m)
10. The member is loaded through the shear centre.
11. Sway modes: Y-Y: non-sway Z-Z: non-sway. Buckling factor kx=ky=1.0.
12. The load application is on the top flange.
Check of IPE270 section. Section data E 210000 N/mm² A 4590 mm² fy 240 N/mm² Fy 2.4 t/cm² Wx 429000 mm³ Wy 62200 mm³ ix 112 mm iy 30.2 mm Sx 242000 mm³ height h 270 mm width b 135 mm flange tf 10.2 mm web tw 6.6 mm radius r 15 mm
Now, we will discuss the different steps :
Classification of the section e) Width-to-thickness ratio for webs. (Using art.4.1.) b/tw = 219.6 / 6.6 = 33.27 Actually, the web is subjected to bending and tension. But because of the small value of this tensile force (0.15 kN), we consider bending only. For this case, the maximal ratio for a non-slender section is 110/√Fy = 71.0
Since 33.27 < 71 , the web is no slender element. f) Width-to-thickness ratio for outstand flanges (Using art.4.1.) b/tf = 67.5/10.2 = 6.61
Max. ratio for outstanding element is 24/√Fy = 15.5.
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Since 6.62 < 15.5 , the flanges are no slender elements. � Section IPE270 is no slender section.
Stability check Since this check is the most critical check, we will only perform this check. Critical check = Ultimate combination 6 on position x=3m. Combination 6, member 7 on x =3.0 m: X = 0.15 kN (tension) Mx = 9.72 kNm Stability check for Bending + Tension Using article 3.3.2. and formula (3.3.) and (3.4.) :
1f
tt
1f
c
f
c
f
t
bybxt
by
by
bx
bx
bx
t
≤σ+σ+σ
≤σ
+σ
+σ
−
E 210000 N/mm² A 4590 mm² N 0.15 kN Mx 9.72 kNm ft 160 N/mm² fby 160 N/mm² fbx lb = 6000 mm
Cm = 1.0 Af = 270 x 10.2 = 1377 mm² h = 270 mm 1/6 of beam heigth = (270-10.2)/6 = 43.3 mm Ar = 270 x 10.2 + 43.3 x 6.6 = 1663 mm² Ir = 10.2 135³ / 12 + 43.3 6.6³ / 12 = 2092355 mm4 ib = sqrt(Ir/Ar) = 35.5 mm λp = 120 formula (2.7) fbx = 33 N/mm² formula (2.8) fbx = 77 N/mm² � 77 N/mm²
σt 150/4590 = 0.03 N/mm² cσbx 9720000/429000 = 22.66 N/mm² tσbx 9720000/429000 = 22.66 N/mm² cσby 0 N/mm² tσby 0 N/mm²
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formula (3.4) compression side : -0.03/77 + 22.6/77 = 0.29 formula (3.3) tension side : +0.03/160 + 22.6/160 = 0.14 Manual calculation - Member 19 Buckling data
First we will discuss the buckling data of this macro.
9. System length L: The beams on a height of 3m provide restraint to the column. Therefore the system lengths for member 19: Ly = Lz = 5 m.
10. The member is loaded through the shear centre.
11. Sway modes: Y-Y: non-sway (bracing in roof-plane) Z-Z: non-sway
12. K factors : Kx = 0.85 / Ky = 0.90
Check of HEB160 section The critial check is performed on section 0.0 m for combination number 3. The internal forces are : N -33.14 kN Vy 3.96 kN Mx 19.79 kNm My 0.32 kNm Section data E 210000 N/mm² A 5430 mm² fy 240 N/mm² Fy 2.4 t/cm² Wx 311000 mm³ Wy 111000 mm³ ix 67.8 mm iy 40.5 mm Sx 177000 mm³ height h 160 mm width b 160 mm flange tf 13 mm web tw 8 mm radius r 15 mm
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Classification of the section a) Width-to-thickness ratio for webs. (Using Art.4.1)
b/tw = 104 / 8 = 13 For this case, the limit is
fyP
P100
F
110−
P = 33.14 kN Pf = 240 N/mm² x A = 1303 kN � limit = 68.46.
Since 13 < 68.46, the web is no slender section element.
d) Width-to-thickness ratio for outstand flanges (Using Art.4.1.) b/tf = 80/13 = 6.15
Max. ratio for flange subject to compression/bending is 15.5. Since 6.15 < 15.5 , the flanges are no slender elements. � Section HEB160 is no slender section.
Section check This check is executed at member 19 on position x = 0 m. (start of member 19) Combination 3 :
sw
fIt
VS<=τ
V 3.96 kN S 177000 mm³ I 24920000 mm4 tw 8 mm fs 92.4 N/mm² τ = 3.54 N/mm² < 92.4 N/mm² Unity check = 3.54/92.4 = 0.04 Stability check for Bending + Compression Critical check = Ultimate combination 3 on position x=0m of member 19. Combination 3, member 19 on x =0.0 m:
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Using article 3.3.1.., and formula (E3.2) and (E3.3.) :
1f
tt
1f
c
f
c
f
t
cbybx
by
by
bx
bx
c
c
≤σ−σ+σ
≤σ
+σ
+σ
N 33.14 kN Mx 19.779 kNm My 0.32 kNm Wx 311500 mm³ Wy 111200 mm³ fc slenderness λx = 4260/67.8
slenderness λx = 62.86 using Table pp.270 � fcx = 127 N/mm² slenderness λy = 4510/40.5 slenderness λy = 111 using Table pp.270 � fcy = 76 N/mm² � fc = 76 N/mm²
ft 160 N/mm² fby 160 N/mm² fbx lb = 5000 mm
M1=0.0 � Cm = 1.75 Af = 160 x 13 = 2080 mm² h = 160 mm 1/6 of beam heigth = (160-13)/6 = 24.5 mm Ar = 160 x 13 + 24.5 x 8 = 2276 mm² Ir = 13 160³ / 12 + 24.5 8³ / 12 = 4438379 mm4 ib = sqrt(Ir/Ar) = 44.16 mm λp = 120 formula (2.7) fbx = 127.44 N/mm² formula (2.8) fbx = 234 N/mm² � 160 N/mm²
σc 33140/5430 = 6.10 N/mm² cσbx 19790000/311000 = 63.6 N/mm² tσbx 19790000/311000 = 63.6 N/mm² cσby 320000/111000 = 2.8 N/mm² tσby 320000/111000 = 2.8 N/mm²
formula (E3.2.): 6.1/76.00 + 63.6/160 + 2.8/160 = 0.08 + 0.40 + 0.02 = 0.50 > 1
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formula (E3.3.): -6.1/160.00 + 63.6/160 + 2.8/160 = -0.04 + 0.40 + 0.02 = 0.38 > 1 Manual calculation - Macro 18 Buckling data
First we will discuss the buckling data of this macro.
10. System length L: For each member: Ly = memberlength = 1m. Lz = Macrolength / 2 = 6 m. (Lateral restraint by middle-rafter) Lltb = Macrolength / 2 = 6 m. (Lateral restraint by middle-rafter)
11. The member is loaded through the shear center.
12. Sway modes: Y-Y: non-sway Z-Z: non-sway (bracing in roof-plane)
13. K factors : Kx =1.0 ; Ky = 0.94
Check of T120/120/13 section Section data E 210000 N/mm² A 2960 mm² fy 240 N/mm² Fy 2.4 t/cm² Wx 42000 mm³ Wy 29700 mm³ ix 35.1 mm iy 24.5 mm Ix 3660000 mm4 Iy 1780000 mm4 ex 32.8 mm height h 120 mm width b 120 mm flange tf 13 mm web tw 13 mm radius r 13 mm Classification of the section a) Width-to-thickness ratio for webs of T section. (Using Art.4.1)
b/tw = (120-13) / 13 = 8.23
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Since 8.23 < 15.5 , the web is no slender section element. b) Width-to-thickness ratio for outstand flanges (Using Art.4.1.) b/tf = 60/13 = 4.62
Max. ratio for flange subject to compression/bending is 15.5. Since 4.62 < 15.5 , the flanges are no slender elements. � Section is no slender section.
Stability check Since this check is the most critical check, we will only perform this check. Combination 6, member 47 on x =0.0 m: Using article 3.3.1.., and formula (E3.2) and (E3.3.) :
1f
tt
1f
c
f
c
f
t
cbybx
by
by
bx
bx
c
c
≤σ−σ+σ
≤σ
+σ
+σ
N 25.35 kN Mx 0.39 kNm My 0.02 kNm fc slenderness λx = 1000/35.1
slenderness λx = 28.44 using Table pp.270 � fcx = 153 N/mm² slenderness λy = 5640/24.5 slenderness λy = 230 using Table pp.270 � fcy = 18.1 N/mm² � fc = 18.1 N/mm²
ft 160 N/mm² fby 160 N/mm² fbx The flange is in tension
� 160 N/mm² σc 25350/2960 = 8.56 N/mm² cσbx 390000/42000 = 9.3 N/mm² tσbx 390000*32.8/3660000 = 3.5 N/mm² cσby 0.00 N/mm² tσby 20000/29700 = 0.67 N/mm²
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formula (E3.2.): 8.56/18.10 + 9.3/160 + 0 = 0.47 + 0.06 + 0 = 0.53 < 1 formula (E3.3.): -8.56/160.00 + 3.5/160 + 0.67/160 = -0.05 + 0.02 + 0 = 0.03 < 1 Calculation note - Member 7 KS Check
Macro 4 Member 7 IPE270 SS41 Ult. comb 7 0.30
Material data
Yield stress Fy 240.00 MPa
fabrication rolled
Section classification
Cfr. Chapter 4. ratio limit ratio
Webs 33.27 71.00
Outstanding flanges 6.62 15.49
The critical check is on position 3.00 m
Axis definition :
- local x- axis in this code check is referring to the local y axis in EPW
- local y- axis in this code check is referring to the local z axis in EPW
Internal forces
N 0.15 kN
Vx 0.00 kN
Vy 1.50 kN
Mt 0.00 kNm
Mx 9.72 kNm
My -0.00 kNm
LTB data
Unsupported length lb 6.00 m
cm 1.00
Shear check
according to article 2.1.2. and formula (2.2)
Table of values
tau 0.95 MPa
Allow. shear stress fs 92.38 MPa
unity check 0.01
Combined stresses (tension and bending)
Compression side: according to article 3.3.2. and formula (3.4)
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Tension side: according to article 3.3.2. and formula (3.3)
Table of values Article Formula
ft 2.1.1. (2.1)
fbx 2.1.4.a (2.7 / 2.8)
fby 2.1.4.b (2.1)
Table of values
sigma t 0.03 MPa
t sigma b x -22.67 MPa
t sigma b y -0.00 MPa
c sigma b x 22.67 MPa
c sigma b y 0.00 MPa
ft 160.00 MPa
fbx 76.50 MPa
fby 160.00 MPa
Af 1377.00 mm^2
lb/ib 169.14
-0.00+0.30+0.00=0.30 < 1 ((3.4))
0.00+0.14+0.00=0.14 < 1 ((3.3))
Shear buckling check
according to article 7.5.2. and formula (7.3)
Table of values
a 6.00 m
d 0.22 m
t 6.60 mm
alfa 2.00
k1 32.00
C1 0.27
sigma 0 160.00 MPa
sigma 18.47 MPa
k2 5.35
C2 0.67
v0 92.38 MPa
v 1.03 MPa
0.01+0.00=0.01 < 1 ((7.3))
Element satisfies the stability check !
Calculation note - Member 19
Macro 11 Member 19 HEB160 SS41 Ult. comb 4 0.50
Material data
Yield stress Fy 240.00 MPa
fabrication rolled
Section classification
Cfr. Chapter 4. ratio limit ratio
Webs 13.00 68.46
Outstanding flanges 6.15 15.49
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The critical check is on position 0.00 m
Axis definition :
- local x- axis in this code check is referring to the local y axis in EPW
- local y- axis in this code check is referring to the local z axis in EPW
Internal forces
N -33.14 kN
Vx 0.06 kN
Vy -3.96 kN
Mt -0.00 kNm
Mx 19.79 kNm
My -0.32 kNm
Buckling parameters xx yy
type non-sway non-sway
Slenderness 62.58 115.97
Length 5.00 5.00 m
Buckling factor 0.85 0.94
Buckling length 4.24 4.69 m
Euler stress fe 529.23 154.12 MPa
Allow. compr. stress fc 127.22 70.82 MPa
LTB data
Unsupported length lb 5.00 m
cm 1.75
Shear check
according to article 2.1.2. and formula (2.2)
Table of values
tau 3.53 MPa
Allow. shear stress fs 92.38 MPa
unity check 0.04
Combined stresses (compression and bending)
Compression side: according to article 3.3.1. and formula (3.1) (E3.2.)
Tension side: according to article 3.3.1. and formula (3.2) (E3.3.)
Table of values Article Formula
fc 2.1.3. (2.3)(2.4)
ft 2.1.1. (2.1)
fbx 2.1.4.a (2.7 / 2.8)
fby 2.1.4.b (2.1)
Table of values
sigma c 6.10 MPa
t sigma b x -63.57 MPa
t sigma b y -2.85 MPa
c sigma b x 63.57 MPa
c sigma b y 2.85 MPa
fc 70.82 MPa
ft 160.00 MPa
fbx 160.00 MPa
fby 160.00 MPa
Af 2080.00 mm^2
lb/ib 113.23
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0.09+0.40+0.02=0.50 < 1 ((3.1) (E3.2.))
-0.04+0.40+0.02=0.38 < 1 ((3.2) (E3.3.))
Shear buckling check
according to article 7.5.2. and formula (7.3)
Table of values
a 5.00 m
d 0.10 m
t 8.00 mm
alfa 1.74
k1 23.75
C1 0.32
sigma 0 160.00 MPa
sigma 47.42 MPa
k2 5.34
C2 0.67
v0 92.38 MPa
v 4.76 MPa
0.09+0.00=0.09 < 1 ((7.3))
Element satisfies the stability check !
Calculation note - Macro 18
KS Check
Macro 18 Member 47 T120/120/13 SS41 Ult. comb 7 0.53
Material data
Yield stress Fy 240.00 MPa
fabrication rolled
Section classification
Cfr. Chapter 4. ratio limit ratio
Outstanding flanges 4.62 15.49
The critical check is on position 0.00 m
Axis definition :
- local x- axis in this code check is referring to the local y axis in EPW
- local y- axis in this code check is referring to the local z axis in EPW
Internal forces
N -25.35 kN
Vx -0.00 kN
Vy -0.31 kN
Mt -0.00 kNm
Mx 0.39 kNm
My 0.02 kNm
Buckling parameters xx yy
type non-sway non-sway
Slenderness 28.44 229.99
Length 1.00 6.00 m
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Buckling parameters xx yy
Buckling factor 1.00 0.94
Buckling length 1.00 5.64 m
Euler stress fe 2562.76 39.18 MPa
Allow. compr. stress fc 152.60 18.09 MPa
Warning: slenderness 229.99 is larger then 200.00 !
LTB data
Unsupported length lb 6.00 m
Shear check
according to article 2.1.2. and formula (2.2)
Table of values
tau 0.59 MPa
Allow. shear stress fs 92.38 MPa
unity check 0.01
Combined stresses (compression and bending)
Compression side: according to article 3.3.1. and formula (3.1) (E3.2.)
Tension side: according to article 3.3.1. and formula (3.2) (E3.3.)
Table of values Article Formula
fc 2.1.3. (2.3)(2.4)
ft 2.1.1. (2.1)
fbx 2.1.4.a (2.7 / 2.8)
fby 2.1.4.b (2.1)
Table of values
sigma c 8.56 MPa
t sigma b x -3.70 MPa
t sigma b y -0.52 MPa
c sigma b x 9.22 MPa
c sigma b y -0.03 MPa
fc 18.09 MPa
ft 160.00 MPa
fbx 160.00 MPa
fby 160.00 MPa
0.47+0.06+0.00=0.53 < 1 ((3.1) (E3.2.))
-0.05+0.02+0.00=-0.03 < 1 ((3.2) (E3.3.))
Element satisfies the stability check !
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2. CONNECTIONS 2.1 PST.07.01 – 01 : Calculation of a base plate Description Calculation of a bolted base plate connection. The moment resistance MRd, the normal force resistance NRd and the shear resistance VRd are calculated manually for node 10 and compared with the result from ESA-Prima Win. Project data See input file. Reference [2] Eurocode 3
Design of steel structures Part 1 - 1 : General rules and rules for buildings ENV 1993-1-1:1992, 1992
[3] Eurocode 3 : Part 1.1. Revised annex J : Joints in building frames ENV 1993-1-1/pr A2
See the chapter "Manual calculation" for the manual calculation of the connection according to Eurocode 3. Result Manual calculation EPW % Diff. MRd 44.99 kNm 44.76 kNm 0.51 % NRd,t 406 kN 406 kN 0 % NRd,c 1633 kN 1644 kN 0.67 % VRd 64.5 kN 64.5 kN 0 % See the chapter "Calculation note" for the detailed output of ESA-Prima Win. Version ESA-Prima Win 3.20.03 Input file + calculation note PST070101.epw Modules 2D Frame (PRS.01) Connect Frame - Rigid (PST.07.01) Author CVL
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Manual calculation
CD
HEB280
Section CD
15
15
2.1.1 The design compression resistance NRd,c (Ref.[2]-Annex L)
jc,Rd AfN =
with A the resulting bearing area (The area in compression
under the base plate) fj the bearing strength of the joint cdjjj fkf ⋅⋅β= = 22 N/mm²
βj 0.66 kj 2.00 fcd 25 N/mm² For the determination of the resulting bearing area the additional bearing width c is introduced.
0Mj
y
γf3
ftc
⋅⋅⋅=
with t the thickness of the steel base plate
= 40 mm fy the yield strength of the steel base plate material
= 235 N/mm²
In this case we have :
mm9.711.1223
23540c =
⋅⋅⋅=
For the resulting bearing area we have :
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= 74233 mm² NRd,c = 74233 x 22 = 1633 kN
2.1.2 The design moment resistance The design compression resistance for concrete under the flange.
jflRd,base,c fAF ⋅=
with fj the bearing strength of the joint Afl the bearing area under the compression flange.
= 29392
kN6472229392F Rd,base,c =⋅=
Column flange in compression Fc,fb,Rd (Ref.[3]-J.3.5.4) The plastic moment of HEB280 = 360 kNm.
Mc,Rd = 360/1.1 = 327 kN Fc,fb,Rd = Mc,Rd/h = 1249 kN
( ) ( ) ( )297.712182805.1097.712280297.711815A ⋅−⋅−⋅+⋅+⋅⋅++=
( ) 28097.711815Afl ⋅++=
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Design tension resistance of anchor row
e 60 mm m 79.85-10.5/2-0.8x6x√2 = 67.8 mm m2 277-228-0.8x9x√2=38.8 mm λ1 67.8/(67.8+60)= 0.531 λ2 38.8/(67.8+60)= 0.304
α 6.00 p 144 mm leff,cp,i 2πm = 426 mm leff,nc,i αm = 406 mm leff,cp,g πm+p = 357 mm leff,nc,g 0.5p+αm-(2m+0.625e) = 305 mm For individual bolt row : leff,1 406 mm leff,2 406 mm Mpl,1,Rd (elastic moment is taken Mpl = lefft²fy/ 6)
23129696 Nmm
Mpl,2,Rd 23129696 Nmm
Ft,Rd,1 1364 kN Ft,Rd,2 457 kN Ft,Rd,3 203 kN For bolt group : leff,1 610 mm leff,2 610 mm Mpl,1,Rd (elastic moment is taken Mpl = lefft²fy/ 6)
34466666 Nmm
Mpl,2,Rd 34466666 Nmm
Ft,Rd,1 2033 kN Ft,Rd,2 729 kN Ft,Rd,3 406 kN
kN6.10125.1
4003539.0
γ
fA9.0Rd,Bt
mb
ubs =⋅⋅
==
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At the first anchor row, we have Ft,1=203 kN (<327<647 kN). Since 203 kN > 1.9 Bt,Rd , the following bolt row is linear determined in relation to the compression point. Ft,2=60x203/204=59 kN
MRd = 203 x 0.204 + 59 x 0.06 = 44.99 kN
2.1.3 The design tension resistance NRd,t It is the design tension resistance for the group of all bolt-rows (no compression limits). NRd,t is the resistance against tension due to uplift. NRd,t = 406 kN
2.1.4 The design shear resistance VRd.
For anchors, this value need to be corrected with 0.85 (Ref.[3] – 6.5.5.(6)) Since all bolts are under tension, the VRd is given by VRd = 0.28 x 67.7 x 0.85 x 4 = 64.5 kN
kN7.6725.1
4003536.0
γ
fA6.0F
Mb
ubsRd,v =
⋅⋅==
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Calculation note
Node 10 : bolted baseplate connection
According to EC3, Annex L & Revised Annex J
1. Input data
Column HEB280
h 280.00 mm
b 280.00 mm
tf 18.00 mm
tw 10.50 mm
r 24.00 mm
fy 235.00 MPa
fu 360.00 MPa
Partial safety factors
Gamma M0 1.10
Gamma M1 1.10
Gamma Mb 1.25
Gamma Mw 1.25
Gamma c 1.50
Gamma fr 2.00
Concrete block
fck_c 25.00 MPa
bond condition poor
Beta_j 0.66
kj 2.00
kfr 0.25
Baseplate
h 311.00 mm
b 281.00 mm
t 40.00 mm
fy 235.00 MPa
fu 360.00 MPa
Anchors M-24 (DIN601)
type straight
bar type high bond
grade 4.6
fu 400.00 MPa
As 353.00 mm^2
do 26.00 mm
S 36.00 mm
e 39.60 mm
h head 15.00 mm
h nut 19.00 mm
Anchor position
row y[mm] spacing[mm]
1 228.00 159.70
2 84.00 159.70
Internal forces
Loadcase number 1
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Loadcase number 1
N -293.31 kN
Vz 1.90 kN
My -3.71 kNm
Tension on left side.
WARNING: NSd > 0.1*Npl,Rd,Column
Projected forces (Reactions)
N' = -293.31 kN
T' = 1.90 kN
2. Design compression resistance NRd,c
According to EC3, Annex L
NRd,c data
fcd 16.67 MPa
fj 22.00 MPa
c 71.97 mm
Resulting bearing area 74725.46 mm^2
NRd,c 1643.96 kN
3. Design moment resistance MRd
According to EC3, Revised Annex J
3.1 Design resistance of basic components
3.1.1. Concrete in compression.
Fc,base,Rd data
Fc,base,Rd 655.08 kN
Area under compression flange. 29776.36 mm^2
h eq 193.48 mm
3.1.2 Column flange and web in compression (J.3.5.4)
Fc,fb,Rd data
Fc,fb,Rd 1250.83 kN
section class 1
Mc,Rd 327.72 kNm
hb-tfb 262.00 mm
3.1.3. Design tension resistance of anchor row
(effective lengths in mm, resistance in kN)
Bt,Rd = 101.66 kN
row p (p1+p2) alfa e m n
1 0.0+72.0 5.99 60.65 67.81 60.65
2 72.0+ 0.0 5.99 60.65 67.81 60.65
row leff,cp,i leff,nc,i
1 426.07 406.52
2 426.07 406.52
row leff,cp,g leff,nc,g leff,cp,ge1 leff,nc,ge1 leff,cp,ge2 leff,nc,ge2
1 - - - - 357.04 305.00
2 - - 357.04 305.00 - -
For individual anchor row:
row leff,1 leff,2 leff Ft,ep,Rd Ft,wb,Rd
1 406.52 406.52 406.52 203.33 911.91
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row leff,1 leff,2 leff Ft,ep,Rd Ft,wb,Rd
2 406.52 406.52 406.52 203.33 911.91
For anchor group:
group leff,1 leff,2 leff Ft,ep,Rd Ft,wb,Rd
1- 1 406.52 406.52 406.52 203.33 911.91
1- 2 609.99 609.99 609.99 406.66 1368.32
3.2 Determination of Mj,Rd
row h[mm] Ft[kN]
1 203.00 203.33
2 59.00 59.10
Mj,Rd = 44.76 kNm Mj,Rd = 44.76 kNm(inclusive normal force)
4. Design tension resistance NRd,t
According to EC3, Revised Annex J
NRd,t = 406.66 kN
5. Design shear resistance VRd
VRd data
VRd 64.52 kN
Fv,Rd 57.61 kN
e1,ep 83.00 mm
p1 144.00 mm
alfa,ep 1.00
Fb,ep,Rd 691.20 kN
6. Stiffness calculation 6.1 Design rotational stiffness
row k5[mm] k7[mm] keff[mm]
1 53.21 2.29 2.19
2 53.21 2.29 2.19
Sj data
Sj 17.88 MNm/rad
Sj,ini 17.88 MNm/rad
z 170.57 mm
mu 1.00
kc 22.33 mm
keq 3.37 mm
6.2 Stiffness classification
Not applicable.
6.3 Check of stiffness requirement
Not applicable.
6.4 Ductility classification
In the endplate we have the following :
t > 0.53 sqrt(fub/fy) d
This results in a non-ductile classification for ductility : class 3.
7. Unity checks
Unity checks
NSd/NRd,c 0.18
MSd/MjRd 0.08
VSd/VRd 0.03
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The connection satisfies.
8. Design Calculations.
8.1 Anchorage length.
Designed for Loadcase number 1
Anchorage data
Ft,anchor,max 101.66 kN
As,req 353.00 mm^2
As,prov 353.00 mm^2
lb 916.59 mm
a 1.00
lb,net 916.59 mm
lb,min 274.98 mm
l,anchor 916.59 mm
8.2. Calculation weldsize
8.2.1. Calculation af
data
MRd 44.76 kNm
Gamma 1.40
h 262.00 mm
FRd 239.19 kN
NT,Rd 1076.73 kN
N 821.98 kN
fu 360.00 MPa
BetaW 0.80
minimum af 5.77 mm
af 9.00 mm
8.2.2. Calculation aw
data
Ft 203.33 kN
Fv 0.95 kN
lw 406.52 mm
fu 360.00 MPa
BetaW 0.80
minimum aw (a2) 1.00 mm
aw 6.00 mm
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2.2 PST.07.01 – 02 : Calculation of a bolted connection Description Five bolted connections are calculated with ESA-Prima Win. The moment resistance MRd and the stiffness Sj of node 3, 5, 6, 10 and 9 are compared with results from the literature. Project data See input file. Reference [2] Eurocode 3
Design of steel structures Part 1 - 1 : General rules and rules for buildings ENV 1993-1-1:1992, 1992
[3] Eurocode 3 : Part 1.1. Revised annex J : Joints in building frames ENV 1993-1-1/pr A2
[4] Frame Design Including Joint Behaviour Volume 2 ECSC Contracts n° 7210-SA/212 and 7210-SA/320 january 1997
Result Results for MRd (kNm) Description Node
number Source result Ref[4]
ESA-Prima Win results
% Diff.
Worked example Chapter 2 3 30.60 32.75 6.6 % Worked example Chapter 3a 5 20.25 21.37 5.53 % Worked example Chapter 3b 6 20.25 21.37 5.53 % Worked example Chapter 4a 10 24.10 29.52 22.49 % Worked example Chapter 4b 9 24.10 29.52 22.49 % Result for Sj,ini (kNm) Description Node
number Source result Ref[4]
ESA-Prima Win results
% Diff.
Worked example Chapter 2 3 10617 11103 4.58 % Worked example Chapter 3a 5 5906 5220 11.62 % Worked example Chapter 3b 6 5977 5313 11.11 % Worked example Chapter 4a 10 15433 15040 2.55 % Worked example Chapter 4b 9 15433 15040 2.55 % Remark : The source results are calculated with a simplified version of the revised ANNEX J. See the chapter "Calculation note" for the detailed output of ESA-Prima Win.
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Version ESA-Prima Win 3.20.03 Input file + calculation note PST070102.epw Modules 2D Frame (PRS.01) Connect Frame - Rigid (PST.07.01) Author CVL Calculation note
CD
IPE220
Section CD
HEB140
10
75
15 15
Figure 35 : node 3
Node 3 : bolted beam-to-column connection side CD
According to EC3, Revised Annex J
1. Input data
Column HEB140
h 140.00 mm
b 140.00 mm
tf 12.00 mm
tw 7.00 mm
r 12.00 mm
fy 235.00 MPa
fu 360.00 MPa
Connected beam IPE220
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Connected beam IPE220
h 220.00 mm
b 110.00 mm
tf 9.20 mm
tw 5.90 mm
r 12.00 mm
fy 235.00 MPa
fu 360.00 MPa
Partial safety factors
Gamma M0 1.10
Gamma M1 1.10
Gamma Mb 1.25
Gamma Ms 1.25
Gamma Mw 1.25
End plate
h 305.00 mm
b 140.00 mm
t 15.00 mm
fy 235.00 MPa
fu 360.00 MPa
Bolts M-16 (DIN960)
type normal
grade 8.8
fu 800.00 MPa
As 157.00 mm^2
do 18.00 mm
S 24.00 mm
e 26.75 mm
h head 10.00 mm
h nut 13.00 mm
Bolt position
row y[mm] spacing[mm]
1 271.00 89.50
2 180.00 89.50
3 60.00 89.50
Internal forces
Loadcase number 1
N 1.12 kN
Vz 12.15 kN
My -7.51 kNm
Tension top
2. Design moment resistance MRd
2.1. Design resistance of basic components 2.1.1. Column web panel in shear (J.3.5.2.)
Vwp,Rd data
Vwp,Rd 145.64 kN
Beta 1.00
Avc 1312.00 mm^2
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2.1.2. Column web in compression (J.3.5.3.)
Fc,wc,Rd data
Fc,wc,Rd 172.16 kN
beff 161.27 mm
twc 7.00 mm
ro1 0.71
ro2 0.45
ro 0.71
kwc 1.00
lambda_rel 0.54
dc 92.00 mm
2.1.3. Beam flange and web in compression (J.3.5.4.)
Fc,fb,Rd data
Fc,fb,Rd 289.85 kN
section class 1
Mc,Rd 61.10 kNm
hb-tfb 210.80 mm
2.1.4. Design tension resistance of bolt row
(effective lengths in mm, resistance in kN)
Bt,Rd = 90.43 kN
2.1.4.1. Column flange
kfc = 1.00
row p (p1+p2) alfa e m n e1
1 0.0+45.5 - 25.25 31.65 25.25 -
2 45.5+60.0 - 25.25 31.65 25.25 -
3 60.0+ 0.0 - 25.25 31.65 25.25 -
row leff,cp,i leff,nc,i
1 198.86 158.16
2 198.86 158.16
3 198.86 158.16
row leff,cp,g leff,nc,g leff,cp,ge1 leff,nc,ge1 leff,cp,ge2 leff,nc,ge2
1 - - - - 190.43 124.58
2 211.00 105.50 190.43 124.58 219.43 139.08
3 - - 219.43 139.08 - -
For individual bolt row:
row leff,1 leff,2 leff Ft,fc,Rd Ft,wc,Rd ro
1 158.16 158.16 158.16 123.02 170.44 0.72
2 158.16 158.16 158.16 123.02 170.44 0.72
3 158.16 158.16 158.16 123.02 170.44 0.72
For bolt group:
group leff,1 leff,2 leff Ft,fc,Rd Ft,wc,Rd ro
1- 1 158.16 158.16 158.16 123.02 170.44 0.72
1- 2 249.16 249.16 249.16 227.88 205.20 0.55
1- 3 369.16 369.16 369.16 340.58 224.57 0.41
2.1.4.2. Endplate
row p (p1+p2) alfa e m n
1 0.0+45.5 - 34.00 35.34 34.00
2 45.5+60.0 5.11 25.25 38.41 25.25
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row p (p1+p2) alfa e m n
3 60.0+ 0.0 5.11 25.25 38.41 25.25
row leff,cp,i leff,nc,i
1 161.53 70.00
2 241.31 196.28
3 241.31 196.28
row leff,cp,g leff,nc,g leff,cp,ge1 leff,nc,ge1 leff,cp,ge2 leff,nc,ge2
1 161.53 70.00 - - - -
2 - - - - 240.66 163.69
3 - - 240.66 163.69 - -
For individual bolt row:
row leff,1 leff,2 leff Ft,ep,Rd Ft,wb,Rd
1 70.00 70.00 70.00 95.20 -
2 196.28 196.28 196.28 145.85 247.40
3 196.28 196.28 196.28 145.85 247.40
For bolt group:
group leff,1 leff,2 leff Ft,ep,Rd Ft,wb,Rd
1- 1 70.00 70.00 70.00 95.20 -
2- 2 196.28 196.28 196.28 145.85 247.40
2- 3 327.37 327.37 327.37 267.09 412.64
2.2. Determination of Mj,Rd
row h[mm] Ft[kN]
1 256.40 95.20
2 165.40 50.44
3 45.40 0.00
Mj,Rd = 32.75 kNm Mj,Rd = 32.75 kNm(inclusive normal force)
3. Design shear resistance VRd
VRd data
VRd 188.10 kN
Fv,Rd 60.29 kN
e1,ep 34.00 mm
p1 91.00 mm
alfa,ep 0.63
alfa,fc 1.00
Fb,ep,Rd 108.80 kN
VRd beam 138.24 kN
VRd beam 196.25 kN
4. Stiffness calculation
4.1. Design rotational stiffness
row k3[mm] k4[mm] k5[mm] k7[mm] keff[mm]
1 5.77 6.64 4.55 6.52 1.43
2 4.89 5.62 8.29 6.52 1.52
Sj data
Sj 11.10 MNm/rad
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Sj data
Sj,ini 11.10 MNm/rad
z 219.41 mm
mu 1.00
k1 2.27 mm
k2 8.59 mm
keq 2.82 mm
4.2. Stiffness classification
Stiffness data
E 210000.00 MPa
Ib 27699999.92 mm^4
Lb 2500.00 mm
frame type braced
S1 18.61 MNm/rad
S2 1.16 MNm/rad
System SEMI RIGID
4.3 Check of stiffness requirement
Stiffness data
Fi y infinity MNm/rad
Stiffness modification coef. 2.00
Sj,app infinity MNm/rad
Sj,lower boundary 18.61 MNm/rad
Sj,upper boundary infinity MNm/rad
Sj,ini is not inside the boundaries.
The actual joint stiffness is not conform with the joint stiffness of the analysis model.
4.4 Ductility classification
The failure mode is situated in the column shear zone.
This results in a ductile classification for ductility : class 1.
5. Unity checks
Unity checks
MSd/MjRd 0.23
VSd/VRd 0.06
The connection satisfies.
6. Design calculations 6.1. Calculation weldsize af / Minimum thickness th for stiffener in column
data
MRd 32.75 kNm
Gamma 1.40
h 210.80 mm
FRd 217.52 kN
NT,Rd 216.20 kN
N 216.20 kN
fu 360.00 MPa
BetaW 0.80
minimum af 3.86 mm
af 5.00 mm
Minimum th 9.20 mm
6.2. Calculation aw
data
Ft 50.44 kN
Fv 4.05 kN
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data
lw 196.28 mm
fu 360.00 MPa
BetaW 0.80
minimum aw (a2) 1.00 mm
aw 3.00 mm
CD
IPE220
Section CD
HEB140
77
15 15
Figure 36 : node 5
Node 5 : bolted beam-to-column connection side CD According to EC3, Revised Annex J
1. Input data
Column HEB140
h 140.00 mm
b 140.00 mm
tf 12.00 mm
tw 7.00 mm
r 12.00 mm
fy 235.00 MPa
fu 360.00 MPa
Connected beam IPE220
h 220.00 mm
b 110.00 mm
tf 9.20 mm
tw 5.90 mm
r 12.00 mm
fy 235.00 MPa
fu 360.00 MPa
Partial safety factors
Gamma M0 1.10
Gamma M1 1.10
Gamma Mb 1.25
Gamma Ms 1.25
Gamma Mw 1.25
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End plate
h 206.00 mm
b 140.00 mm
t 15.00 mm
fy 235.00 MPa
fu 360.00 MPa
Bolts M-16 (DIN960)
type normal
grade 8.8
fu 800.00 MPa
As 157.00 mm^2
do 18.00 mm
S 24.00 mm
e 26.75 mm
h head 10.00 mm
h nut 13.00 mm
Bolt position
row y[mm] spacing[mm]
1 163.00 89.50
2 43.00 89.50
Internal forces
Loadcase number 1
N 1.12 kN
Vz 12.15 kN
My -8.27 kNm
Tension top
2. Design moment resistance MRd
2.1. Design resistance of basic components 2.1.1. Column web panel in shear (J.3.5.2.)
Vwp,Rd data
Vwp,Rd 145.64 kN
Beta 1.00
Avc 1312.00 mm^2
2.1.2. Column web in compression (J.3.5.3.)
Fc,wc,Rd data
Fc,wc,Rd 162.16 kN
beff 144.27 mm
twc 7.00 mm
ro1 0.75
ro2 0.50
ro 0.75
kwc 1.00
lambda_rel 0.51
dc 92.00 mm
2.1.3. Beam flange and web in compression (J.3.5.4.)
Fc,fb,Rd data
Fc,fb,Rd 289.85 kN
section class 1
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Fc,fb,Rd data
Mc,Rd 61.10 kNm
hb-tfb 210.80 mm
2.1.4. Design tension resistance of bolt row
(effective lengths in mm, resistance in kN)
Bt,Rd = 90.43 kN
2.1.4.1. Column flange
kfc = 1.00
row p (p1+p2) alfa e m n e1
1 0.0+60.0 - 25.25 31.65 25.25 -
2 60.0+ 0.0 - 25.25 31.65 25.25 -
row leff,cp,i leff,nc,i
1 198.86 158.16
2 198.86 158.16
row leff,cp,g leff,nc,g leff,cp,ge1 leff,nc,ge1 leff,cp,ge2 leff,nc,ge2
1 - - - - 219.43 139.08
2 - - 219.43 139.08 - -
For individual bolt row:
row leff,1 leff,2 leff Ft,fc,Rd Ft,wc,Rd ro
1 158.16 158.16 158.16 123.02 170.44 0.72
2 158.16 158.16 158.16 123.02 170.44 0.72
For bolt group:
group leff,1 leff,2 leff Ft,fc,Rd Ft,wc,Rd ro
1- 1 158.16 158.16 158.16 123.02 170.44 0.72
1- 2 278.16 278.16 278.16 235.72 211.64 0.51
2.1.4.2. Endplate
row p (p1+p2) alfa e m n
1 0.0+60.0 5.11 25.25 38.41 25.25
2 60.0+ 0.0 5.11 25.25 38.41 25.25
row leff,cp,i leff,nc,i
1 241.31 196.28
2 241.31 196.28
row leff,cp,g leff,nc,g leff,cp,ge1 leff,nc,ge1 leff,cp,ge2 leff,nc,ge2
1 - - - - 240.66 163.69
2 - - 240.66 163.69 - -
For individual bolt row:
row leff,1 leff,2 leff Ft,ep,Rd Ft,wb,Rd
1 196.28 196.28 196.28 145.85 247.40
2 196.28 196.28 196.28 145.85 247.40
For bolt group:
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group leff,1 leff,2 leff Ft,ep,Rd Ft,wb,Rd
1- 1 196.28 196.28 196.28 145.85 247.40
1- 2 327.37 327.37 327.37 267.09 412.64
2.2. Determination of Mj,Rd
row h[mm] Ft[kN]
1 165.40 123.02
2 45.40 22.63
Mj,Rd = 21.37 kNm Mj,Rd = 21.37 kNm(inclusive normal force)
3. Design shear resistance VRd
VRd data
VRd 67.52 kN
Fv,Rd 60.29 kN
e1,ep 43.00 mm
p1 120.00 mm
alfa,ep 0.80
alfa,fc 1.00
Fb,ep,Rd 137.60 kN
VRd beam 138.24 kN
VRd beam 196.25 kN
4. Stiffness calculation
4.1. Design rotational stiffness
row k3[mm] k4[mm] k5[mm] k7[mm] keff[mm]
1 6.44 7.41 8.29 6.52 1.77
2 6.44 7.41 8.29 6.52 1.77
Sj data
Sj 5.22 MNm/rad
Sj,ini 5.22 MNm/rad
z 139.56 mm
mu 1.00
k1 3.57 mm
k2 7.68 mm
keq 2.68 mm
4.2. Stiffness classification
Stiffness data
E 210000.00 MPa
Ib 27699999.92 mm^4
Lb 2500.00 mm
frame type braced
S1 18.61 MNm/rad
S2 1.16 MNm/rad
System SEMI RIGID
4.3 Check of stiffness requirement
Stiffness data
Fi y infinity MNm/rad
Stiffness modification coef. 2.00
Sj,app infinity MNm/rad
Sj,lower boundary 18.61 MNm/rad
Sj,upper boundary infinity MNm/rad
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Sj,ini is not inside the boundaries.
The actual joint stiffness is not conform with the joint stiffness of the analysis model.
4.4 Ductility classification
The failure mode is situated in the column shear zone.
This results in a ductile classification for ductility : class 1.
5. Unity checks
Unity checks
MSd/MjRd 0.39
VSd/VRd 0.18
The connection satisfies.
6. Design calculations 6.1. Calculation weldsize af / Minimum thickness th for stiffener in column
data
MRd 21.37 kNm
Gamma 1.40
h 210.80 mm
FRd 141.95 kN
NT,Rd 216.20 kN
N 141.95 kN
fu 360.00 MPa
BetaW 0.80
minimum af 2.53 mm
af 5.00 mm
Minimum th 6.04 mm
6.2. Calculation aw
data
Ft 123.02 kN
Fv 6.08 kN
lw 196.28 mm
fu 360.00 MPa
BetaW 0.80
minimum aw (a2) 2.00 mm
aw 3.00 mm
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AB
IPE220
Section AB
HEB140
10
10
15 15
Figure 37 : node 6
Node 6 : bolted beam-to-column connection side AB According to EC3, Revised Annex J
1. Input data
Column HEB140
h 140.00 mm
b 140.00 mm
tf 12.00 mm
tw 7.00 mm
r 12.00 mm
fy 235.00 MPa
fu 360.00 MPa
Connected beam IPE220
h 220.00 mm
b 110.00 mm
tf 9.20 mm
tw 5.90 mm
r 12.00 mm
fy 235.00 MPa
fu 360.00 MPa
Partial safety factors
Gamma M0 1.10
Gamma M1 1.10
Gamma Mb 1.25
Gamma Ms 1.25
Gamma Mw 1.25
End plate
h 240.00 mm
b 140.00 mm
t 15.00 mm
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End plate
fy 235.00 MPa
fu 360.00 MPa
Bolts M-16 (DIN960)
type normal
grade 8.8
fu 800.00 MPa
As 157.00 mm^2
do 18.00 mm
S 24.00 mm
e 26.75 mm
h head 10.00 mm
h nut 13.00 mm
Bolt position
row y[mm] spacing[mm]
1 180.00 89.50
2 60.00 89.50
Internal forces
Loadcase number 1
N 1.12 kN
Vz 12.15 kN
My -8.27 kNm
Tension top
2. Design moment resistance MRd 2.1. Design resistance of basic components
2.1.1. Column web panel in shear (J.3.5.2.)
Vwp,Rd data
Vwp,Rd 145.64 kN
Beta 1.00
Avc 1312.00 mm^2
2.1.2. Column web in compression (J.3.5.3.)
Fc,wc,Rd data
Fc,wc,Rd 172.16 kN
beff 161.27 mm
twc 7.00 mm
ro1 0.71
ro2 0.45
ro 0.71
kwc 1.00
lambda_rel 0.54
dc 92.00 mm
2.1.3. Beam flange and web in compression (J.3.5.4.)
Fc,fb,Rd data
Fc,fb,Rd 289.85 kN
section class 1
Mc,Rd 61.10 kNm
hb-tfb 210.80 mm
2.1.4. Design tension resistance of bolt row
(effective lengths in mm, resistance in kN)
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Bt,Rd = 90.43 kN
2.1.4.1. Column flange
kfc = 1.00
row p (p1+p2) alfa e m n e1
1 0.0+60.0 - 25.25 31.65 25.25 -
2 60.0+ 0.0 - 25.25 31.65 25.25 -
row leff,cp,i leff,nc,i
1 198.86 158.16
2 198.86 158.16
row leff,cp,g leff,nc,g leff,cp,ge1 leff,nc,ge1 leff,cp,ge2 leff,nc,ge2
1 - - - - 219.43 139.08
2 - - 219.43 139.08 - -
For individual bolt row:
row leff,1 leff,2 leff Ft,fc,Rd Ft,wc,Rd ro
1 158.16 158.16 158.16 123.02 170.44 0.72
2 158.16 158.16 158.16 123.02 170.44 0.72
For bolt group:
group leff,1 leff,2 leff Ft,fc,Rd Ft,wc,Rd ro
1- 1 158.16 158.16 158.16 123.02 170.44 0.72
1- 2 278.16 278.16 278.16 235.72 211.64 0.51
2.1.4.2. Endplate
row p (p1+p2) alfa e m n
1 0.0+60.0 5.11 25.25 38.41 25.25
2 60.0+ 0.0 5.11 25.25 38.41 25.25
row leff,cp,i leff,nc,i
1 241.31 196.28
2 241.31 196.28
row leff,cp,g leff,nc,g leff,cp,ge1 leff,nc,ge1 leff,cp,ge2 leff,nc,ge2
1 - - - - 240.66 163.69
2 - - 240.66 163.69 - -
For individual bolt row:
row leff,1 leff,2 leff Ft,ep,Rd Ft,wb,Rd
1 196.28 196.28 196.28 145.85 247.40
2 196.28 196.28 196.28 145.85 247.40
For bolt group:
group leff,1 leff,2 leff Ft,ep,Rd Ft,wb,Rd
1- 1 196.28 196.28 196.28 145.85 247.40
1- 2 327.37 327.37 327.37 267.09 412.64
2.2. Determination of Mj,Rd
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row h[mm] Ft[kN]
1 165.40 123.02
2 45.40 22.63
Mj,Rd = 21.37 kNm Mj,Rd = 21.37 kNm(inclusive normal force)
3. Design shear resistance VRd
VRd data
VRd 67.52 kN
Fv,Rd 60.29 kN
e1,ep 60.00 mm
p1 120.00 mm
alfa,ep 1.00
alfa,fc 1.00
Fb,ep,Rd 172.80 kN
VRd beam 138.24 kN
VRd beam 196.25 kN
4. Stiffness calculation
4.1. Design rotational stiffness
row k3[mm] k4[mm] k5[mm] k7[mm] keff[mm]
1 6.44 7.41 8.29 6.52 1.77
2 6.44 7.41 8.29 6.52 1.77
Sj data
Sj 5.31 MNm/rad
Sj,ini 5.31 MNm/rad
z 139.56 mm
mu 1.00
k1 3.57 mm
k2 8.59 mm
keq 2.68 mm
4.2. Stiffness classification
Stiffness data
E 210000.00 MPa
Ib 27699999.92 mm^4
Lb 2500.00 mm
frame type braced
S1 18.61 MNm/rad
S2 1.16 MNm/rad
System SEMI RIGID
4.3 Check of stiffness requirement
Stiffness data
Fi y infinity MNm/rad
Stiffness modification coef. 2.00
Sj,app infinity MNm/rad
Sj,lower boundary 18.61 MNm/rad
Sj,upper boundary infinity MNm/rad
Sj,ini is not inside the boundaries.
The actual joint stiffness is not conform with the joint stiffness of the analysis model.
4.4 Ductility classification
The failure mode is situated in the column shear zone.
This results in a ductile classification for ductility : class 1.
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5. Unity checks
Unity checks
MSd/MjRd 0.39
VSd/VRd 0.18
The connection satisfies.
6. Design calculations
6.1. Calculation weldsize af / Minimum thickness th for stiffener in column
data
MRd 21.37 kNm
Gamma 1.40
h 210.80 mm
FRd 141.95 kN
NT,Rd 216.20 kN
N 141.95 kN
fu 360.00 MPa
BetaW 0.80
minimum af 2.53 mm
af 5.00 mm
Minimum th 6.04 mm
6.2. Calculation aw
data
Ft 123.02 kN
Fv 6.07 kN
lw 196.28 mm
fu 360.00 MPa
BetaW 0.80
minimum aw (a2) 2.00 mm
aw 3.00 mm
AB
IPE220
Section AB CD
IPE220
Section CD
77
15 15
77
15 15
Figure 38 : node 10
Node 10 : bolted plate-to-plate connection
According to EC3, Revised Annex J
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1. Input data
Right side
Connected beam IPE220
h 220.00 mm
b 110.00 mm
tf 9.20 mm
tw 5.90 mm
r 12.00 mm
fy 235.00 MPa
fu 360.00 MPa
End plate
h 206.00 mm
b 140.00 mm
t 15.00 mm
fy 235.00 MPa
fu 360.00 MPa
Bolts M-16 (DIN960)
type normal
grade 8.8
fu 800.00 MPa
As 157.00 mm^2
do 18.00 mm
S 24.00 mm
e 26.75 mm
h head 10.00 mm
h nut 13.00 mm
Bolt position
row y[mm]
1 163.00 90.00
2 43.00 90.00
Left side
Connected beam IPE220
h 220.00 mm
b 110.00 mm
tf 9.20 mm
tw 5.90 mm
r 12.00 mm
fy 235.00 MPa
fu 360.00 MPa
End plate
h 206.00 mm
b 140.00 mm
t 15.00 mm
fy 235.00 MPa
fu 360.00 MPa
Partial safety factors
Gamma M0 1.10
Gamma M1 1.10
Gamma Mb 1.25
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Partial safety factors
Gamma Ms 1.25
Gamma Mw 1.25
Internal forces
Loadcase number 1
N 1.12 kN
Vz -0.00 kN
My 6.53 kNm
Tension bottom
2. Design moment resistance MRd
2.1. Design resistance of basic components 2.1.1.Beam flange and web in compression (J.3.5.4.) - Right side
Fc,fb,Rd data
Fc,fb,Rd 289.85 kN
section class 1
Mc,Rd 61.10 kNm
hb-tfb 210.80 mm
2.1.2. Beam flange and web in compression (J.3.5.4.) - Left side
Fc,fb,Rd data
Fc,fb,Rd 289.85 kN
section class 1
Mc,Rd 61.10 kNm
hb-tfb 210.80 mm
2.1.3. Design tension resistance of bolt row
(effective lengths in mm, resistance in kN)
Bt,Rd = 90.43 kN
2.1.3.1. Endplate - right side
row p (p1+p2) alfa e m
2 0.0+60.0 5.09 25.00 38.66 25.00
1 60.0+ 0.0 5.09 25.00 38.66 25.00
row leff,cp,i
2 242.88 196.94
1 242.88 196.94
row leff,cp,g leff,nc,g leff,cp,ge1 leff,nc,ge1 leff,cp,ge2
2 - - - - 241.44 164.01
1 - - 241.44 164.01 - -
For individual bolt row:
row leff,1 leff,2 leff Ft,ep,Rd
2 196.94 196.94 196.94 145.39 248.24
1 196.94 196.94 196.94 145.39 248.24
For bolt group:
group leff,1 leff,2 leff Ft,ep,Rd
2- 2 196.94 196.94 196.94 145.39 248.24
2- 1 328.01 328.01 328.01 265.91 413.44
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2.1.3.2. Endplate - left side
row p (p1+p2) alfa e m
2 0.0+60.0 5.09 25.00 38.66 25.00
1 60.0+ 0.0 5.09 25.00 38.66 25.00
row leff,cp,i
2 242.88 196.94
1 242.88 196.94
row leff,cp,g leff,nc,g leff,cp,ge1 leff,nc,ge1 leff,cp,ge2
2 - - - - 241.44 164.01
1 - - 241.44 164.01 - -
For individual bolt row:
row leff,1 leff,2 leff Ft,ep,Rd
2 196.94 196.94 196.94 145.39 248.24
1 196.94 196.94 196.94 145.39 248.24
For bolt group:
group leff,1 leff,2 leff Ft,ep,Rd
2- 2 196.94 196.94 196.94 145.39 248.24
2- 1 328.01 328.01 328.01 265.91 413.44
2.2. Determination of Mj,Rd
row h[mm] Ft[kN]
2 165.40 145.39
1 45.40 120.52
Mj,Rd = 29.52 kNm Mj,Rd = 29.52 kNm(inclusive normal force)
3. Design shear resistance VRd
VRd data
VRd 67.52 kN
Fv,Rd 60.29 kN
data right
e1 43.00 mm
p1 120.00 mm
alfa,ep 0.80
Fb,ep,Rd 137.60 kN
data left
e1 43.00 mm
p1 120.00 mm
alfa,ep 0.80
Fb,ep,Rd 137.60 kN
4. Stiffness calculation 4.1. Design rotational stiffness
row k5[mm] k5[mm] k7[mm]
2 8.15 8.15 6.05 2.43
1 8.15 8.15 6.05 2.43
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Sj data
Sj 15.04 MNm/rad
Sj,ini 15.04 MNm/rad
z 139.56 mm
mu 1.00
keq 3.68 mm
4.2. Stiffness classification Right side
Stiffness data
E 210000.00 MPa
Ib 27699999.92 mm^4
Lb 2500.00 mm
frame type braced
S1 18.61 MNm/rad
S2 1.16 MNm/rad
System SEMI RIGID
Left side
Stiffness data
E 210000.00 MPa
Ib 27699999.92 mm^4
Lb 2500.00 mm
frame type braced
S1 18.61 MNm/rad
S2 1.16 MNm/rad
System SEMI RIGID
4.3 Check of stiffness requirement Right side
Stiffness data
Fi y infinity MNm/rad
Stiffness modification coef. 3.00
Sj,app infinity MNm/rad
Sj,lower boundary 18.61 MNm/rad
Sj,upper boundary infinity MNm/rad
Sj,ini is not inside the boundaries.
The actual joint stiffness is not conform with the joint stiffness of the analysis model.
Left side
Stiffness data
Fi y infinity MNm/rad
Stiffness modification coef. 3.00
Sj,app infinity MNm/rad
Sj,lower boundary 18.61 MNm/rad
Sj,upper boundary infinity MNm/rad
Sj is not inside the boundaries.
The actual joint stiffness is not conform with the joint stiffness of the analysis model.
4.4 Ductility classification
In the endplate we have the following :
0.36 sqrt(fub/fy) d < t <= 0.53 sqrt(fub/fy) d
This results in an intermediate classification for ductility : class 2.
5. Unity checks
Unity checks
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Unity checks
MSd/MjRd 0.22
VSd/VRd 0.00
The connection satisfies.
6. Design calculations 6.1. Calculation af - Right side
data
MRd 29.52 kNm
Gamma 1.40
h 210.80 mm
FRd 196.05 kN
NT,Rd 216.20 kN
N 196.05 kN
fu 360.00 MPa
BetaW 0.80
minimum af 3.50 mm
af 5.00 mm
6.2. Calculation aw - Right side
data
Ft 265.91 kN
Fv 0.00 kN
lw 328.01 mm
fu 360.00 MPa
BetaW 0.80
minimum aw (a2) 2.00 mm
aw 3.00 mm
6.3. Calculation af - Left side
data
MRd 29.52 kNm
Gamma 1.40
h 210.80 mm
FRd 196.05 kN
NT,Rd 216.20 kN
N 196.05 kN
fu 360.00 MPa
BetaW 0.80
minimum af 3.50 mm
af 5.00 mm
6.4. Calculation aw - Left side
data
Ft 265.91 kN
Fv 0.00 kN
lw 328.01 mm
fu 360.00 MPa
BetaW 0.80
minimum aw (a2) 2.00 mm
aw 3.00 mm
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AB
IPE220
Section AB CD
IPE220
Section CD
10
10
15 15
10
10
15 15
Figure 39 : node 9
Node 9 : bolted plate-to-plate connection According to EC3, Revised Annex J
1. Input data
Right side
Connected beam IPE220
h 220.00 mm
b 110.00 mm
tf 9.20 mm
tw 5.90 mm
r 12.00 mm
fy 235.00 MPa
fu 360.00 MPa
End plate
h 240.00 mm
b 140.00 mm
t 15.00 mm
fy 235.00 MPa
fu 360.00 MPa
Bolts M-16 (DIN960)
type normal
grade 8.8
fu 800.00 MPa
As 157.00 mm^2
do 18.00 mm
S 24.00 mm
e 26.75 mm
h head 10.00 mm
h nut 13.00 mm
Bolt position
row y[mm]
1 180.00 90.00
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row y[mm]
2 60.00 90.00
Left side
Connected beam IPE220
h 220.00 mm
b 110.00 mm
tf 9.20 mm
tw 5.90 mm
r 12.00 mm
fy 235.00 MPa
fu 360.00 MPa
End plate
h 240.00 mm
b 140.00 mm
t 15.00 mm
fy 235.00 MPa
fu 360.00 MPa
Partial safety factors
Gamma M0 1.10
Gamma M1 1.10
Gamma Mb 1.25
Gamma Ms 1.25
Gamma Mw 1.25
Internal forces
Loadcase number 1
N -4.03 kN
Vz 0.00 kN
My 8.63 kNm
Tension bottom
2. Design moment resistance MRd
2.1. Design resistance of basic components
2.1.1.Beam flange and web in compression (J.3.5.4.) - Right side
Fc,fb,Rd data
Fc,fb,Rd 289.85 kN
section class 1
Mc,Rd 61.10 kNm
hb-tfb 210.80 mm
2.1.2. Beam flange and web in compression (J.3.5.4.) - Left side
Fc,fb,Rd data
Fc,fb,Rd 289.85 kN
section class 1
Mc,Rd 61.10 kNm
hb-tfb 210.80 mm
2.1.3. Design tension resistance of bolt row
(effective lengths in mm, resistance in kN)
Bt,Rd = 90.43 kN
2.1.3.1. Endplate - right side
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row p (p1+p2) alfa e m
2 0.0+60.0 5.09 25.00 38.66 25.00
1 60.0+ 0.0 5.09 25.00 38.66 25.00
row leff,cp,i
2 242.88 196.94
1 242.88 196.94
row leff,cp,g leff,nc,g leff,cp,ge1 leff,nc,ge1 leff,cp,ge2
2 - - - - 241.44 164.01
1 - - 241.44 164.01 - -
For individual bolt row:
row leff,1 leff,2 leff Ft,ep,Rd
2 196.94 196.94 196.94 145.39 248.24
1 196.94 196.94 196.94 145.39 248.24
For bolt group:
group leff,1 leff,2 leff Ft,ep,Rd
2- 2 196.94 196.94 196.94 145.39 248.24
2- 1 328.01 328.01 328.01 265.91 413.44
2.1.3.2. Endplate - left side
row p (p1+p2) alfa e m
2 0.0+60.0 5.09 25.00 38.66 25.00
1 60.0+ 0.0 5.09 25.00 38.66 25.00
row leff,cp,i
2 242.88 196.94
1 242.88 196.94
row leff,cp,g leff,nc,g leff,cp,ge1 leff,nc,ge1 leff,cp,ge2
2 - - - - 241.44 164.01
1 - - 241.44 164.01 - -
For individual bolt row:
row leff,1 leff,2 leff Ft,ep,Rd
2 196.94 196.94 196.94 145.39 248.24
1 196.94 196.94 196.94 145.39 248.24
For bolt group:
group leff,1 leff,2 leff Ft,ep,Rd
2- 2 196.94 196.94 196.94 145.39 248.24
2- 1 328.01 328.01 328.01 265.91 413.44
2.2. Determination of Mj,Rd
row h[mm] Ft[kN]
2 165.40 145.39
1 45.40 120.52
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Mj,Rd = 29.52 kNm
Mj,Rd = 29.52 kNm(inclusive normal force)
3. Design shear resistance VRd
VRd data
VRd 67.52 kN
Fv,Rd 60.29 kN
data right
e1 60.00 mm
p1 120.00 mm
alfa,ep 1.00
Fb,ep,Rd 172.80 kN
data left
e1 60.00 mm
p1 120.00 mm
alfa,ep 1.00
Fb,ep,Rd 172.80 kN
4. Stiffness calculation
4.1. Design rotational stiffness
row k5[mm] k5[mm] k7[mm]
2 8.15 8.15 6.05 2.43
1 8.15 8.15 6.05 2.43
Sj data
Sj 15.04 MNm/rad
Sj,ini 15.04 MNm/rad
z 139.56 mm
mu 1.00
keq 3.68 mm
4.2. Stiffness classification Right side
Stiffness data
E 210000.00 MPa
Ib 27699999.92 mm^4
Lb 2500.00 mm
frame type braced
S1 18.61 MNm/rad
S2 1.16 MNm/rad
System SEMI RIGID
Left side
Stiffness data
E 210000.00 MPa
Ib 27699999.92 mm^4
Lb 2500.00 mm
frame type braced
S1 18.61 MNm/rad
S2 1.16 MNm/rad
System SEMI RIGID
4.3 Check of stiffness requirement Right side
Stiffness data
Fi y infinity MNm/rad
Stiffness modification coef. 3.00
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Stiffness data
Sj,app infinity MNm/rad
Sj,lower boundary 18.61 MNm/rad
Sj,upper boundary infinity MNm/rad
Sj,ini is not inside the boundaries.
The actual joint stiffness is not conform with the joint stiffness of the analysis model.
Left side
Stiffness data
Fi y infinity MNm/rad
Stiffness modification coef. 3.00
Sj,app infinity MNm/rad
Sj,lower boundary 18.61 MNm/rad
Sj,upper boundary infinity MNm/rad
Sj is not inside the boundaries.
The actual joint stiffness is not conform with the joint stiffness of the analysis model.
4.4 Ductility classification
In the endplate we have the following :
0.36 sqrt(fub/fy) d < t <= 0.53 sqrt(fub/fy) d
This results in an intermediate classification for ductility : class 2.
5. Unity checks
Unity checks
MSd/MjRd 0.29
VSd/VRd 0.00
The connection satisfies.
6. Design calculations 6.1. Calculation af - Right side
data
MRd 29.52 kNm
Gamma 1.40
h 210.80 mm
FRd 196.05 kN
NT,Rd 216.20 kN
N 196.05 kN
fu 360.00 MPa
BetaW 0.80
minimum af 3.50 mm
af 5.00 mm
6.2. Calculation aw - Right side
data
Ft 265.91 kN
Fv 0.00 kN
lw 328.01 mm
fu 360.00 MPa
BetaW 0.80
minimum aw (a2) 2.00 mm
aw 3.00 mm
6.3. Calculation af - Left side
data
MRd 29.52 kNm
Gamma 1.40
h 210.80 mm
FRd 196.05 kN
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data
NT,Rd 216.20 kN
N 196.05 kN
fu 360.00 MPa
BetaW 0.80
minimum af 3.50 mm
af 5.00 mm
6.4. Calculation aw - Left side
data
Ft 265.91 kN
Fv 0.00 kN
lw 328.01 mm
fu 360.00 MPa
BetaW 0.80
minimum aw (a2) 2.00 mm
aw 3.00 mm
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2.3 PST.07.01 – 03 : Calculation of a bolted connection Description Calculation of a bolted connection : the moment resistance MRd and the stiffness Sj of node 1 are calculated with ESA-Prima Win and compared with results from the literature. Project data See input file. Reference [2] Eurocode 3
Design of steel structures Part 1 - 1 : General rules and rules for buildings ENV 1993-1-1:1992, 1992
[3] Eurocode 3 : Part 1.1. Revised annex J : Joints in building frames ENV 1993-1-1/pr A2
[4] Joints in Building Frames (Revised Annex J) CEN / TC250/SC3-PT9 September 1993
Result Source
result Ref.[4]
ESA-Prima Win result
% Diff.
MRd 31.75 31.78 0 % Sj,ini 11760 11592 1.43 % See the chapter "Calculation note" for detailed output of ESA-Prima Win. Version ESA-Prima Win 3.20.03 Input file + calculation note PST070103.epw Modules 2D Frame (PRS.01) Connect Frame - Rigid (PST.07.01) Author CVL
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Calculation note
CD
IPE220
Section CD
HEB140
15
70
15 15
Node 1 : bolted beam-to-column connection side CD
According to EC3, Revised Annex J
1. Input data
Column HEB140
h 140.00 mm
b 140.00 mm
tf 12.00 mm
tw 7.00 mm
r 12.00 mm
fy 235.00 MPa
fu 360.00 MPa
Connected beam IPE220
h 220.00 mm
b 110.00 mm
tf 9.20 mm
tw 5.90 mm
r 12.00 mm
fy 235.00 MPa
fu 360.00 MPa
Partial safety factors
Gamma M0 1.10
Gamma M1 1.10
Gamma Mb 1.25
Gamma Ms 1.25
Gamma Mw 1.25
End plate
h 305.00 mm
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End plate
b 140.00 mm
t 12.00 mm
fy 235.00 MPa
fu 360.00 MPa
Bolts M-16 (DIN960)
type normal
grade 8.8
fu 800.00 MPa
As 157.00 mm^2
do 18.00 mm
S 24.00 mm
e 26.75 mm
h head 10.00 mm
h nut 13.00 mm
Bolt position
row y[mm] spacing[mm]
1 265.00 80.00
2 195.00 80.00
3 55.00 80.00
Internal forces
Loadcase number 1
N 0.00 kN
Vz 9.65 kN
My -9.34 kNm
Tension top
2. Design moment resistance MRd 2.1. Design resistance of basic components
2.1.1. Column web panel in shear (J.3.5.2.)
Vwp,Rd data
Vwp,Rd 145.64 kN
Beta 1.00
Avc 1312.00 mm^2
2.1.2. Column web in compression (J.3.5.3.)
Fc,wc,Rd data
Fc,wc,Rd 173.24 kN
beff 163.27 mm
twc 7.00 mm
ro1 0.71
ro2 0.45
ro 0.71
kwc 1.00
lambda_rel 0.54
dc 92.00 mm
2.1.3. Beam flange and web in compression (J.3.5.4.)
Fc,fb,Rd data
Fc,fb,Rd 289.85 kN
section class 1
Mc,Rd 61.10 kNm
hb-tfb 210.80 mm
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2.1.4. Design tension resistance of bolt row
(effective lengths in mm, resistance in kN)
Bt,Rd = 90.43 kN
2.1.4.1. Column flange
kfc = 1.00
row p (p1+p2) alfa e m n e1
1 0.0+35.0 - 30.00 26.90 30.00 -
2 35.0+70.0 - 30.00 26.90 30.00 -
3 70.0+ 0.0 - 30.00 26.90 30.00 -
row leff,cp,i leff,nc,i
1 169.02 145.10
2 169.02 145.10
3 169.02 145.10
row leff,cp,g leff,nc,g leff,cp,ge1 leff,nc,ge1 leff,cp,ge2 leff,nc,ge2
1 - - - - 154.51 107.55
2 210.00 105.00 154.51 107.55 224.51 142.55
3 - - 224.51 142.55 - -
For individual bolt row:
row leff,1 leff,2 leff Ft,fc,Rd Ft,wc,Rd ro
1 145.10 145.10 145.10 134.58 162.68 0.75
2 145.10 145.10 145.10 134.58 162.68 0.75
3 145.10 145.10 145.10 134.58 162.68 0.75
For bolt group:
group leff,1 leff,2 leff Ft,fc,Rd Ft,wc,Rd ro
1- 1 145.10 145.10 145.10 134.58 162.68 0.75
1- 2 215.10 215.10 215.10 245.99 195.32 0.61
1- 3 355.10 355.10 355.10 382.07 223.09 0.42
2.1.4.2. Endplate
row p (p1+p2) alfa e m n
1 0.0+35.0 - 40.00 24.34 30.43
2 35.0+70.0 5.99 30.00 33.66 30.00
3 70.0+ 0.0 5.99 30.00 33.66 30.00
row leff,cp,i leff,nc,i
1 136.48 70.00
2 211.47 201.57
3 211.47 201.57
row leff,cp,g leff,nc,g leff,cp,ge1 leff,nc,ge1 leff,cp,ge2 leff,nc,ge2
1 136.48 70.00 - - - -
2 - - - - 245.73 185.51
3 - - 245.73 185.51 - -
For individual bolt row:
row leff,1 leff,2 leff Ft,ep,Rd Ft,wb,Rd
1 70.00 70.00 70.00 88.46 -
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row leff,1 leff,2 leff Ft,ep,Rd Ft,wb,Rd
2 201.57 201.57 201.57 133.95 254.07
3 201.57 201.57 201.57 133.95 254.07
For bolt group:
group leff,1 leff,2 leff Ft,ep,Rd Ft,wb,Rd
1- 1 70.00 70.00 70.00 88.46 -
2- 2 201.57 201.57 201.57 133.95 254.07
2- 3 371.01 371.01 371.01 260.13 467.64
2.2. Determination of Mj,Rd
row h[mm] Ft[kN]
1 245.40 88.46
2 175.40 57.18
3 35.40 0.00
Mj,Rd = 31.74 kNm
Mj,Rd = 31.74 kNm(inclusive normal force)
3. Design shear resistance VRd
VRd data
VRd 188.10 kN
Fv,Rd 60.29 kN
e1,ep 40.00 mm
p1 70.00 mm
alfa,ep 0.74
alfa,fc 1.00
Fb,ep,Rd 102.40 kN
VRd beam 138.24 kN
VRd beam 196.25 kN
4. Stiffness calculation 4.1. Design rotational stiffness
row k3[mm] k4[mm] k5[mm] k7[mm] keff[mm]
1 8.12 5.73 7.13 7.08 1.73
2 7.92 5.59 7.15 7.08 1.71
Sj data
Sj 11.59 MNm/rad
Sj,ini 11.59 MNm/rad
z 216.42 mm
mu 1.00
k1 2.30 mm
k2 8.70 mm
keq 3.34 mm
4.2. Stiffness classification
Stiffness data
E 210000.00 MPa
Ib 27699999.92 mm^4
Lb 2000.00 mm
frame type braced
S1 23.27 MNm/rad
S2 1.45 MNm/rad
System SEMI RIGID
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4.3 Check of stiffness requirement
Stiffness data
Fi y infinity MNm/rad
Stiffness modification coef. 2.00
Sj,app infinity MNm/rad
Sj,lower boundary 23.27 MNm/rad
Sj,upper boundary infinity MNm/rad
Sj,ini is not inside the boundaries.
The actual joint stiffness is not conform with the joint stiffness of the analysis model.
4.4 Ductility classification
The failure mode is situated in the column shear zone.
This results in a ductile classification for ductility : class 1.
5. Unity checks
Unity checks
MSd/MjRd 0.29
VSd/VRd 0.05
The connection satisfies.
6. Design calculations 6.1. Calculation weldsize af / Minimum thickness th for stiffener in column
data
MRd 31.74 kNm
Gamma 1.40
h 210.80 mm
FRd 210.79 kN
NT,Rd 216.20 kN
N 210.79 kN
fu 360.00 MPa
BetaW 0.80
minimum af 3.76 mm
af 5.00 mm
Minimum th 8.97 mm
6.2. Calculation aw
data
Ft 57.18 kN
Fv 3.22 kN
lw 201.57 mm
fu 360.00 MPa
BetaW 0.80
minimum aw (a2) 1.00 mm
aw 3.00 mm
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2.4 PST.07.01 – 04 : Calculation of a bolted connection Description Calculation of a bolted connection : a manual calculation for the moment resistance MRd and the stiffness Sj are performed for node 3 and compared with the EPW results. Project data See input file. Reference [2] Eurocode 3
Design of steel structures Part 1 – 1 : General rules and rules for buildings ENV 1993-1-1:1992, 1992
[3] Eurocode 3 : Part 1.1. Revised annex J : Joints in building frames ENV 1993-1-1/pr A2
See the chapter "Manual calculation" for the manual calculation according to this reference. Result Manual calc. ESA-Prima
Win result % Diff.
MRd 30.9 30.2 2.27 % VRd 231 231 0 % Sj,ini 7882 7795 1.10 % See the chapter "Calculation note" for the detailed output of ESA-Prima Win. Version ESA-Prima Win 3.20.03 Input file + calculation note PST070104.epw Modules 2D Frame (PRS.01) Connect Frame - Rigid (PST.07.01) Author CVL Manual calculation • Beam to column.
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• Bolted flush end-plate. The references are default made to Ref[3], if not the reference is mentioned. 1. Input data. Beam & Column : Column HEA 160 Beam IPE 270 For the properties of the beam and the column, see input file. Bolts: M-16, grade 10.9 For the position of the bolts, see the chapter Calculation note. End-plate: Flush end-plate with a thickness of 12.0 mm.
CD
IPE270
Section CD
HEA160
15
5
2. Design moment resistance MRd. 2.1 Design resistance of the basic components. 2.1.1 Column web panel in shear. (J.3.5.2) Vwp,Rd Formula (J.16)
• Avc (Ref[2], 5.4.6) = 1324 mm² � Vwp,Rd = 146.98 kN • Transformation parameter β: Ref[3].Table J.4 β = 1
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2.1.2 Column web in compression. (J.3.5.3) Fc,wc,Rd Formula (J.18) + Annexed page J39’ • beff,c : The effective width of the column web in compression Formula (J.19) = 166.08 • ρ : Reduction factor for possible effects of shear in the column web panel. Table J.5 = ρ1 = 0.76
• λ : Relative slenderness of the column web. • dc = the clear depth of the column web.
dc = 152 - 2(9 + 15) = 104 mm
⇒ λ = 0.68 > 0.67, so reduction factor for local buckling is necessary. Reduction factor: = 0.995 • kwc : Reduction factor for longitudinal compressive stress in the column. σcom,Ed = 42.4 N/mm² < 0.5fy,wc kwc = 1.0 � Fc,wc,Rd = 160.54 kN 2.1.3. Beam flange and part of web in compression. (J.3.5.4) Fc,fb,Rd Formula (J.23)
• Mc,Rd The design moment resistance of the beam cross-section (EC3 5.4.5 & 5.4.7)
The beam is a class-1 section (Wpl is used) ⇒ Mc,Rd= 103.4 kNm • hb - tfb = 259.8 mm � Fc,fb,Rd = 398.0 kN 2.1.4 Design tension resistance of the bolt rows. Bt,Rd The design tension resistance of a bolt assembly. = Ft,,Rd (Ref[3] J.3.2 (6) & Ref[2] Table 6.5.3) � Bt,Rd = 113.04 kN 2.1.4.1 The column flange in bending. (J.3.5.5) The column flange is stiffened. (J.3.5.5.3) Method of the equivalent T-stub flange. (J.3.2) Dimensions: (Figure J.25) • m = 30 mm • e = 35 mm • emin = 22 mm 2.1.4.1.1. Determination of Fti,fc,Rd : Fti,fc,Rd =The design resistance of the column flange in bending for the individual bolt-row i. Determination of Ft1,fc,Rd: Determination of leff: effective lengths for a stiffened column flange Using Table J.7.
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Bolt row 1 is adjacent to a stiffener. (use of α) leff,cp1 = 2 π m = 188.5 mm leff,nc1 = α m = 182.64 mm Determination of α : figure J.27 e = 35 mm m = (bcol - tweb,col)/2 - e - 0.8rcol = 30 mm m2 = (distance from centre-line of bolt-row 1 till edge stiffener) - 0.8 √2aweld Note: The top of the stiffener == top of the beam ⇒ m2 = (45+5-12) - 0.8 √2x6 = 31.21 mm λ1 = 0.4615 λ2 = 0.4802
• α = 6.09
leff for failure mode 1 = leff,1 = leff,nc but ≤ leff,cp • leff,1 = 182.64 mm
leff for failure mode 2 = leff,2 = leff,nc • leff,2 = 182.64 mm Ft1,fc,Rd,1 : The design tension resistance of the column flange for bolt-row 1 individually, for mode 1: Complete yielding of the flange. Formula (J.4)
• Mpl1,Rd = 790 kNmm Formula ( J.7a) ⇒ Ft1,fc,Rd,1 = 105.35 kN Ft1,fc,Rd,2 : The design tension resistance of the column flange for bolt-row 1 individually, for mode 2: Bolt failure + yielding of the flange. Formula (J.5) • Mpl,2,Rd = 790 kNmm Formula ( J.7b) • n = 22 mm Formula (J.8) ⇒ Ft1,fc,Rd,2 = 126.04 kN Ft1,fc,Rd,3 : The design tension resistance of the column flange for bolt-row 1 individually, for mode 3: Bolt Failure. Formula (J.6)
• ∑ Bt,Rd = 226.08 kN (2 bolts in bolt-row 1)
⇒ Ft1,fc,Rd,3 = 226.08 kN Ft1,fc,Rd = Minimum of ( Ft1,fc,Rd,1 , Ft1,fc,Rd,2 , Ft1,fc,Rd,3 ) � Ft1,fc,Rd = 105.35 kN � Failure mode is mode 1: Complete yielding of the flange. Determination of Ft2,fc,Rd:
Determination of leff: Using Table J.7. Bolt row 2 is NOT adjacent to a stiffener. leff,1 = 163.75 mm leff,2 = 163.75 mm
The determination of the other Fti,fc,Rd is analogue to that of Ft1,fc,Rd , so we’ll just mention the results: • Mpl,1,Rd = 708 kNmm • Ft2,fc,Rd,1 = 94.45 kN
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• Mpl,2,Rd = 708 kNmm • Ft2,fc,Rd,2 = 122.90 kNmm • Ft2,fc,Rd,3 = 226.08 kN � Ft2,fc,Rd = 94.45 kN � Failure mode is mode 1: Complete yielding of the flange. Determination of Ft3,fc,Rd: • Mpl,1,Rd = 708 kNmm • Ft3,fc,Rd,1 = 94.45 kN • Mpl,2,Rd = 708 kNmm • Ft3,fc,Rd,2 = 122.9 kNmm • Ft3,fc,Rd,3 = 226.08 kN � Ft3,fc,Rd = 94.45 kN � Failure mode is mode 1: Complete yielding of the flange. Determination of Ft4,fc,Rd: • Mpl,1,Rd = 708 kNmm • Ft4,fc,Rd,1 = 94.45 kN • Mpl,2,Rd = 708 kNmm • Ft4,fc,Rd,2 = 122.9 kNmm • Ft4,fc,Rd,3 = 226.08 kN � Ft4,fc,Rd = 94.45 kN � Failure mode is mode 1: Complete yielding of the flange. 2.1.4.1.2. Determination of Ft(i+j+…),fc,Rd : F(ti+j+…),fc,Rd = The design resistance of the column flange in bending for the group of bolts (i + j + …) Determination of Ft(1+2),fc,Rd: Determination of leff: effective lengths for a stiffened column flange Using Table J.7. Bolt-row 1 is adjacent to a stiffener. leff1,cp,ge = π m + p = 144.25 mm leff1,nc,ge = 0.5p + α m - (2m + 0.625e) = 125.76 mm Bolt-row 2 is an end bolt-row for the group (1+2) leff2,cp,ge = π m + p = 144.25 mm leff2,nc,ge = 2m + 0.625e + 0.5 p = 106.88 mm
Note: p is taken as the pitch for the concerned bolt group, therefore in the output tables the distinction between leff,..,ge1
& leff,..,ge2 is made.
E.g. for the bolt-group (1+2), the pitch for bolt row 2 is taken as p1, the pitch between bolt-row 1 and bolt-row 2; this
results in the use of leff,..,ge1.
(Analogue: for the group of bolt-rows (2+3), leff,..,ge2 is used for bolt-row 2, and leff,..,ge1 for bolt-row 3)
Mode 1:
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leff(1+2),1 = ∑ leff,nc,g but ≤ ∑ leff,cp
• leff(1+2),1 = 125.76 + 106.88 = 232.64 mm • Mpl,Rd,1 = 1006 kNmm => Ft(1+2),fc,Rd,1 = 134.19 kN Mode 2:
leff(1+2),2 = ∑ leff,nc,g
• leff(1+2),2 = 232.64 • Mpl,Rd,2 = 1006 kNmm => Ft(1+2),fc,Rd,2 = 230.0 kN Mode 3:
=> Ft(1+2),fc,Rd,3 = 452.2 kN Result: �Ft(1+2),fc,Rd = 134.19 kN �Failure mode is mode 1 The determination of Ft(i+j+…),fc,Rd for the other bolt groups is completely analogue to that of Ft(1+2),fc,Rd. Determination of Ft(1+2+3),fc,Rd : Bolt-row 1 is adjacent to a stiffner. Bolt-row 2 is an inner bolt-row for this group. Bolt-row 3 is an end bolt-row for this group. Result: �Ft(1+2+3),fc,Rd = 163.03 kN Determination of Ft(1+2+3+4),fc,Rd : Bolt-row 1 is adjacent to a stiffner. Bolt-row 2 is an inner bolt-row for this group. Bolt-row 3 is an inner bolt-row for this group. Bolt-row 4 is an end bolt-row for this group. Result: �Ft(1+2+3+4),fc,Rd = 217.83 kN According to Annex J of EC3, we also have to consider extra groups of bolt-rows. A group of bolt-rows is an extra group within a bolt-group.
Determination of Ft(2+3): Bolt-row 2 is an end bolt-row for this group. Bolt-row 3 is an end bolt-row for this group. Result: �Ft(2+3),fc,Rd = 123.3 kN Other Results: �Ft(3+4),fc,Rd = 149.25 kN �Ft(2+3+4),fc,Rd = 178.1 kN 2.1.4.2 The column web in tension. (J.3.5.6) Ft,wc,Rd Formula (J.26)
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• beff : For a bolted connection, the effective width beff of the column web, is always taken as the non-circular effective length of the equivalent T-stub, representing the column flange.
• ρ : Reduction factor for the possible effects of shear in the column web-panel is determined from Table J.5.
But, in this particular case, none of the above is used, because the column web is stiffened.
• For stiffened column webs:
Ft,wc,Rd is taken as equal to Fc,fb,Rd : the design resistance of the beam flange in compression. � Ft,wc,Rd = 398.0 kN
This is only allowed, if the stiffeners are designed to resist the applied forces: Annex J, J.3.3(2) gives us an easy and quick check for this requirement:
1. The steel grade of the stiffeners is not lower than the that of the beam flanges. => O.K.
2. The thickness of the stiffeners is not smaller than the flange thickness of the beam. => O.K.
3. The outstand of the stiffeners is not less than (bb - twc) / 2 where: bb = the breadth of the beam flange. twc = the thickness of the column web => O.K.
Note: These 3 checks are executed by the program at the moment of input of the stiffeners.
2.1.4.3 Endplate in bending: (J.3.5.7) Analogue to the analysis of the column flange, we get the following results: Note: The flanges of the beam act as stiffeners to the endplate. Effective lengths: According to Table J.8.
Results: Ft1,ep,Rd = 132.49 kN Ft2,ep,Rd = 129.85 kN Ft3,ep,Rd = 129.85 kN Ft4,ep,Rd = 136.15 kN Ft(1+2),ep,Rd = 195.58 kN Ft(1+2+3),ep,Rd = 236.96 kN Ft(1+2+3+4),ep,Rd = 335.61 kN Ft(2+3),ep,Rd = 187.2 kN Ft(3+4),ep,Rd = 244.47 kN Ft(2+3+4),ep,Rd = 285.84kN 2.1.4.4 The beam web in tension. (J.3.5.8) Ft,wb,Rd Formula (J.31) • beff : The effective width beff of the beam web, is always taken as the non-circular effective length of the equivalent T-
stub, representing the end-plate. (= leff in the output tables) Results: Ft1,wb,Rd = 262.7 kN Ft2,wb,Rd = 248.4 kN Ft3,wb,Rd = 248.4 kN Ft4,wb,Rd = 282.6 kN Ft(1+2),wb,Rd = 333.2 kN
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Ft(1+2+3),wb,Rd = 403.7 kN Ft(1+2+3+4),wb,Rd = 571.8 kN Ft(2+3),wb,Rd = 318.9 kN / beff(2+3) = leff(2+3),nc = 113.1 + 113.1 = 226.2 mm Ft(3+4),wb,Rd = 416.5 kN / beff(3+4) = leff(3+4),nc = 135.6 + 159.8 = 295.4 mm Ft(2+3+4),wb,Rd = 487.0 kN / beff(2+3+4) = leff(2+3+4),nc = 113.1 + 72.5 + 159.8 = 345.4 mm 2.1.4.5 Determination of the effective design tension resistance Ftr,Rd for each bolt-row r : According to the procedure of J.3.6.2 Ft1,Rd is the smallest value of: • Vwp,Rd/ β = 147.0 kN • Fc,wc,Rd = 160.5 kN • Fc,fb,Rd = 398.0 kN • Ft1,fc,Rd = 105.4 kN • Ft1,wc,Rd = 398.0 kN • Ft1,ep,Rd = 132.5 kN • Ft1,wb,Rd = 262.7 kN � Ft1,Rd = 105.4 kN Ft2,Rd is the smallest value of: • Vwp,Rd/ β - Ft1,Rd = 41.6 kN • Fc,wc,Rd - Ft1,Rd = 55.1 kN • Fc,fb,Rd - Ft1,Rd = 292.6 kN • Ft2,fc,Rd = 94.5 kN • Ft2,wc,Rd = 398.0 kN • Ft2,ep,Rd = 129.9 kN • Ft2,wb,Rd = 248.4 kN • Ft(1+2),fc,Rd - Ft1,Rd = 134.19 - 105.4 = 28.8 kN • Ft(1+2),wc,Rd - Ft1,Rd = 398.0 - 105.4 = 292.6 kN • Ft(1+2),ep,Rd - Ft1,Rd = 195.6 - 105.4 = 90.2 kN • Ft(1+2),wb,Rd - Ft1,Rd = 333.2 - 105.4 = 227.8 kN � Ft2,Rd = 28.8 kN Ft3,Rd is the smallest value of: • Vwp,Rd/ β - Ft1,Rd - Ft2,Rd = 12.8 kN • Fc,wc,Rd - Ft1,Rd - Ft2,Rd = 26.3 kN • Fc,fb,Rd - Ft1,Rd - Ft2,Rd = 263.8 kN • Ft3,fc,Rd = 94.5 kN • Ft3,wc,Rd = 398.0 kN • Ft3,ep,Rd = 129.9 kN • Ft3,wb,Rd = 248.4 kN • Ft(1+2+3),fc,Rd - Ft1,Rd - Ft2,Rd = 163.03 - 105.4 - 28.8 = 28.8 kN • Ft(1+2+3),wc,Rd - Ft1,Rd - Ft2,Rd = 398.0 - 105.4 - 28.8 = 263.8 kN • Ft(1+2+3),ep,Rd - Ft1,Rd - Ft2,Rd = 237.0 - 105.4 - 28.8 = 102.8 kN • Ft(1+2+3),wb,Rd - Ft1,Rd - Ft2,Rd = 335.61 - 105.4 - 28.8 = 201.4 kN • Ft(2+3),fc,Rd - Ft2,Rd = 123.3 - 28.8 = 94.5 kN • Ft(2+3),wc,Rd - Ft2,Rd = 398.0 - 28.8 = 369.2 kN • Ft(2+3),ep,Rd - Ft2,Rd = 187.2 - 28.8 = 158.4 kN • Ft(2+3),wb,Rd -Ft2,Rd = 318.9 - 28.8 = 290.1 kN
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� Ft3,Rd = 12.8 kN Ft4,Rd is the smallest value of: • Vwp,Rd/ β - Ft1,Rd - Ft2,Rd -Ft3,Rd = 0.0 KN �Bolt-row 4 is in the compression zone! � Ft4,Rd = 0.0 kN For the sake of completeness, the other possible limitations are mentioned: • Fc,wc,Rd - Ft1,Rd - Ft2,Rd -Ft3,Rd • Fc,fb,Rd - Ft1,Rd - Ft2,Rd -Ft3,Rd • Ft4,fc,Rd • Ft4,wc,Rd • Ft4,ep,Rd • Ft4,wb,Rd • Ft(1+2+3+4),fc,Rd - Ft1,Rd - Ft2,Rd - Ft3,Rd • Ft(1+2+3+4),wc,Rd - Ft1,Rd - Ft2,Rd - Ft3,Rd • Ft(1+2+3+4),ep,Rd - Ft1,Rd - Ft2,Rd - Ft3,Rd • Ft(1+2+3+4),wb,Rd - Ft1,Rd - Ft2,Rd - Ft3,Rd • Ft(3+4),fc,Rd - Ft3,Rd • Ft(2+3+4),fc,Rd - Ft2,Rd - Ft3,Rd • Ft(3+4),wc,Rd - Ft3,Rd • Ft(2+3+4),wc,Rd - Ft2,Rd - Ft3,Rd • Ft(3+4),ep,Rd - Ft3,Rd • Ft(2+3+4),ep,Rd - Ft2,Rd - Ft3,Rd • Ft(3+4),wb,Rd -Ft3,Rd • Ft(2+3+4),wb,Rd - Ft2,Rd - Ft3,Rd
2.2 Determination of Mj,Rd. (J.3.6.2) Mj,Rd : The design moment resistance of the joint: Formula (J.32)
None of the bolt-rows has an effective design tension resistance greater than 1.9Bt,Rd, so there is no need to reduce any of the bolt-row effective tension resistance’s. (J.3.6.2 (8)) � Mj,Rd = 30.97 kNm We can also make allowance for the normal force acting in the beam. This is done as follows: N = 13.15 kN (compression) MjRd = 30.97 kNm –13.15/2 x (lever-arm = (hb-tfb) = 0.2598 m) �Mj,Rd(N) = 29.22 kNm
Check: Msd = 13.7 kNm => Joint is O.K. for Moment & Normal force. 3. Determination of the design shear resistance of the joint. According to EC3 6.5.5 & J.3.1.2
Fv,Rd : The design shear resistance of 1 bolt. (EC3 Table 6.5.3) • grade: 10.9 • fub = 1000 N/mm²
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• As = 157 mm² • γMb = 1.25 (Most negative case is considered: shear plane passes through the threaded portion of the bolt.) �Fv,Rd = 62.8 kN Bearing resistance for the column-flange: Fb,fc,Rd • αfc is the smallest of: • e1,fc / 3d0 = 38/17x3 = 0.745
e1 = end-distance between the first bolt-row and the top of the column. • p1/ 3d0 -0.25 = 50/17x3 -0.25 = 0.73
p1 = pitch between first bolt-rows = 50 mm • fub/fu = 1000/360 = 2.78 • 1.0 ⇒ αfc = 0.73 �Fb,fc,Rd = 75.73 kN Bearing resistance for the end-plate: Fb,ep,Rd Analogue to Fb,fc,Rd
⇒ αep =0.73 �Fb,ep,Rd = 100.97 kN
Vrd: The design shear resistance of the joint. • For bolts who are already subject to tension, the shear design resistance is reduced to 0.286 Fv,Rd . (J.3.1.2 (2b)) ⇒ Vrd1 = 62.8(2+6x0.28) = 231.1 kN ⇒ Vrd2 = 8 x 75.73 = 605.84 kN ⇒ Vrd3 = 8 x 100.97 = 807.76 kN � Vrd = min(Vrd1, Vrd2, Vrd3) = 231.1 kN
Check: Vsd = 8.65 kN => Joint is O.K. for shear.
4. Stiffness calculation.
4.1 Design rotational stiffness. (J.4.1) Since, the joint exists of an end-plate connection with more than one bolt row in tension , the general method of J.4.2.2 is used. Determination of keq: Formula (J.36) Since this example is a beam-to-column joint with an end-plate connection, keq should be based upon the following stiffness coefficients: • k3: The column flange in bending. • k4: The column web in tension. • k5: The end-plate in bending. • k7: The bolts in tension.
I. Determination of keff,r: the effective stiffness coefficient for bolt row r: Formula (J.37) 1. keff,r for bolt-row 1: (keff,1) A. Determination of ki1: ki1: The stiffness coefficient representing component i, relative to bolt row 1
• k31: Formula (J.41)
• leff,1: The smallest of the effective lengths given for bolt-row 1. (considered as an individual bolt-group, or as part of a bolt group.)
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� leff,1 = 117.48 mm � k31 = 2.70 mm
• k41: Formula (J.42) • beff,1 is taken as the smallest non-circular effective length for bolt-row 1. (considered as an individual bolt-group, or as part of a group of bolt rows.)
� beff,1 = 117.48 mm
• dc = the clear depth of the column web. � dc = 152 - 2(9 + 15) = 104 mm � k41 = 4.74 mm
• k51: Formula (J.43) • leff,1: The smallest of the effective lengths given for bolt-row 1 for the endplate.
(considered as an individual bolt-group, or as part of a group of bolt-rows.) � leff,1 = 123.24 mm
• tp = the thickness of the end-plate. � tp = 12.0 mm
• m = 37.17 mm �k51 = 3.52 mm
• k71: Formula (J.45) • As = 157 mm² • Lb: The elongation length of the bolt. Lb = tfc + tep + 0.5(hbolt,head + hbolt,nut)
� Lb = 32.5 mm �k71 = 7.73 mm
B. Determination of keff,1: keff,1: The effective stiffness coefficient for bolt-row 1.
Formula (J.37) �keff,1 = 1.01 mm
2. keff,r for the other Bolt-rows:
This is analogue to the determination of keff,1 keff,2 = 0.46 keff,3 = 0.64 Bolt-row 4 is not in tension. II. Determination of z: the lever arm. (J.4.3) Formula (J.38)
�z = 197.86 mm According to Formula (J.36): �keq = 2.01 mm Determination of k1: For an unstiffened column web-panel in shear. Formula (J.39):
• Avc = 1324 mm² • z = 197.86 mm • β = 1.0
� k1 = 2.54 mm Determination of k2: For an Unstiffened column web in compression. Formula (J.40):
• beff,c = 166.1 mm (See 2.1.2 or J.3.5.3) � k2 = 6.71 mm
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Determination of Sj,ini: The initial rotational stiffness of the joint. Sj,ini = Sj x µ (Formula (J.34)) �Sj,ini = 7882 x 106 Nmm/rad Determination of µµµµ: The stiffness ratio. Formula (J.35)
• Mj,Rd = 32.26 kNm (inclusive normal force N = 13.15 kN (compression)) • Msd = 13.7 kNm (Tension in the top of the joint) • ψ = 2.7
� µ = 1.0 Determination of Sj: The rotational stiffness of the joint. Formula (J.34)
� Sj = 7882 x 106 Nmm/rad 4.2. Stiffness classification. (J.2.5.1) Figure J.8
• Frame type: braced. • Lb = 6325 mm • Ib =5790 cm4 Determination of the classification boundaries: • Rigid: Sj,ini ≥ 8EIb/Lb = 15380 x 106 Nmm/rad • Semi-rigid • Nominally pinned: Sj,ini ≤ 0.5EIb/Lb = 961 x 106 Nmm/rad
�Joint-system is SEMI-RIGID Calculation note
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Sj,ini = 7794.80 kNm/radSj,MRd = 2608.31 kNm/rad
5.786e-003 1.157e-002 1.736e-002 2.314e-002
rad
10.0
20.0
30.0 kNm
Figure 40 : Moment-rotation diagram
Node 3 : bolted beam-to-column connection side CD
According to EC3, Revised Annex J
1. Input data
Column HEA160
h 152.00 mm
b 160.00 mm
tf 9.00 mm
tw 6.00 mm
r 15.00 mm
fy 235.00 MPa
fu 360.00 MPa
Connected beam IPE270
h 270.00 mm
b 135.00 mm
tf 10.20 mm
tw 6.60 mm
r 15.00 mm
fy 235.00 MPa
fu 360.00 MPa
Partial safety factors
Gamma M0 1.10
Gamma M1 1.10
Gamma Mb 1.25
Gamma Ms 1.25
Gamma Mw 1.25
Stiffener
Stiffener in tension zone
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No. pos.[mm] fy[MPa]
1 276.23 235.00
End plate
h 295.00 mm
b 135.00 mm
t 12.00 mm
fy 235.00 MPa
fu 360.00 MPa
Bolts M-16 (DIN6914)
type normal
grade 10.9
fu 1000.00 MPa
As 157.00 mm^2
do 18.00 mm
S 27.00 mm
e 29.60 mm
h head 10.00 mm
h nut 13.00 mm
Bolt position
row y[mm] spacing[mm]
1 250.00 90.00
2 200.00 90.00
3 150.00 90.00
4 55.00 90.00
Internal forces
ULS Combination number 6
N -13.76 kN
Vz 8.42 kN
My -14.24 kNm
Tension top
2. Design moment resistance MRd
2.1. Design resistance of basic components 2.1.1. Column web panel in shear (J.3.5.2.)
Vwp,Rd data
Vwp,Rd 146.98 kN
Beta 1.00
Avc 1324.00 mm^2
2.1.2. Column web in compression (J.3.5.3.)
Fc,wc,Rd data
Fc,wc,Rd 160.66 kN
beff 166.48 mm
twc 6.00 mm
ro1 0.76
ro2 0.50
ro 0.76
kwc 1.00
lambda_rel 0.68
dc 104.00 mm
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2.1.3. Beam flange and web in compression (J.3.5.4.)
Fc,fb,Rd data
Fc,fb,Rd 398.00 kN
section class 1
Mc,Rd 103.40 kNm
hb-tfb 259.80 mm
2.1.4. Design tension resistance of bolt row
(effective lengths in mm, resistance in kN)
Bt,Rd = 113.04 kN
2.1.4.1. Column flange
kfc = 1.00
row p (p1+p2) alfa e m n e1
1 0.0+25.0 5.67 35.00 30.00 22.50 44.40
2 25.0+25.0 - 35.00 30.00 22.50 -
3 25.0+47.5 - 35.00 30.00 22.50 -
4 47.5+ 0.0 - 35.00 30.00 22.50 -
row leff,cp,i leff,nc,i
1 188.50 169.97
2 188.50 163.75
3 188.50 163.75
4 188.50 163.75
row leff,cp,g leff,nc,g leff,cp,ge1 leff,nc,ge1 leff,cp,ge2 leff,nc,ge2
1 - - - - 144.25 113.10
2 100.00 50.00 144.25 106.87 144.25 106.87
3 145.00 72.50 144.25 106.87 189.25 129.37
4 - - 189.25 129.37 - -
For individual bolt row:
row leff,1 leff,2 leff Ft,fc,Rd Ft,wc,Rd ro
1 169.97 169.97 169.97 98.04 398.00 1.00
2 163.75 163.75 163.75 94.45 398.00 1.00
3 163.75 163.75 163.75 94.45 398.00 1.00
4 163.75 163.75 163.75 94.45 398.00 1.00
For bolt group:
group leff,1 leff,2 leff Ft,fc,Rd Ft,wc,Rd ro
1- 1 169.97 169.97 169.97 98.04 398.00 1.00
1- 2 219.97 219.97 219.97 126.88 398.00 1.00
1- 3 269.97 269.97 269.97 155.72 398.00 1.00
1- 4 364.97 364.97 364.97 210.52 398.00 1.00
2.1.4.2. Endplate
row p (p1+p2) alfa e m n
1 0.0+25.0 5.03 22.50 37.17 22.50
2 25.0+25.0 - 22.50 37.17 22.50
3 25.0+47.5 - 22.50 37.17 22.50
4 47.5+ 0.0 5.42 22.50 37.17 22.50
row leff,cp,i leff,nc,i
1 233.57 187.09
2 233.57 176.82
3 233.57 176.82
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row leff,cp,i leff,nc,i
4 233.57 201.44
row leff,cp,g leff,nc,g leff,cp,ge1 leff,nc,ge1 leff,cp,ge2 leff,nc,ge2
1 - - - - 166.79 123.68
2 100.00 50.00 166.79 113.41 166.79 113.41
3 145.00 72.50 166.79 113.41 211.79 135.91
4 - - 211.79 160.53 - -
For individual bolt row:
row leff,1 leff,2 leff Ft,ep,Rd Ft,wb,Rd
1 187.09 187.09 187.09 133.47 263.80
2 176.82 176.82 176.82 130.82 249.32
3 176.82 176.82 176.82 130.82 249.32
4 201.44 201.44 201.44 137.17 284.04
For bolt group:
group leff,1 leff,2 leff Ft,ep,Rd Ft,wb,Rd
1- 1 187.09 187.09 187.09 133.47 263.80
1- 2 237.09 237.09 237.09 196.20 334.30
1- 3 287.09 287.09 287.09 237.58 404.80
1- 4 406.71 406.71 406.71 336.57 573.46
2.2. Determination of Mj,Rd
row h[mm] Ft[kN]
1 228.83 98.04
2 178.83 28.84
3 128.83 20.09
4 33.83 0.00
Mj,Rd = 30.18 kNm
Mj,Rd = 30.18 kNm(inclusive normal force)
3. Design shear resistance VRd
VRd data
VRd 231.10 kN
Fv,Rd 62.80 kN
e1,ep 45.00 mm
e1,cf 44.40 mm
p1 50.00 mm
alfa,ep 0.68
alfa,fc 0.68
Fb,ep,Rd 93.44 kN
VRd beam 70.08 kN
VRd beam 272.50 kN
4. Stiffness calculation
4.1. Design rotational stiffness
row k3[mm] k4[mm] k5[mm] k7[mm] keff[mm]
1 2.60 4.57 3.54 7.73 0.98
2 1.15 2.02 1.43 7.73 0.46
3 1.66 2.93 2.07 7.73 0.64
Sj data
Sj 7.79 MNm/rad
Sj,ini 7.79 MNm/rad
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Sj data
z 197.09 mm
mu 1.00
k1 2.55 mm
k2 6.72 mm
keq 1.98 mm
4.2. Stiffness classification
Stiffness data
E 210000.00 MPa
Ib 57900000.68 mm^4
Lb 6324.56 mm
frame type braced
S1 15.38 MNm/rad
S2 0.96 MNm/rad
System SEMI RIGID
4.3 Check of stiffness requirement
Stiffness data
Fi y infinity MNm/rad
Stiffness modification coef. 2.00
Sj,app infinity MNm/rad
Sj,lower boundary 15.38 MNm/rad
Sj,upper boundary infinity MNm/rad
Sj,ini is not inside the boundaries.
The actual joint stiffness is not conform with the joint stiffness of the analysis model.
4.4 Ductility classification
The failure mode is situated in the column shear zone.
This results in a ductile classification for ductility : class 1.
5. Unity checks
Unity checks
MSd/MjRd 0.47
VSd/VRd 0.04
The connection satisfies.
6. Design calculations 6.1. Calculation weldsize af / Minimum thickness th for stiffener in column
data
MRd 30.18 kNm
Gamma 1.40
h 274.13 mm
FRd 154.14 kN
NT,Rd 294.18 kN
N 154.14 kN
fu 360.00 MPa
BetaW 0.80
minimum af 2.24 mm
af 6.00 mm
Minimum th 5.34 mm
6.2. Calculation aw
data
Ft 126.88 kN
Fv 2.11 kN
lw 237.09 mm
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data
fu 360.00 MPa
BetaW 0.80
minimum aw (a2) 2.00 mm
aw 4.00 mm
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2.5 PST.07.01 – 05 : Calculation of welded connections Description Calculation of welded simple T connection : the moment resistance MRd and its components, and the weld sizes are calculated for node 10. Project data See input file. Reference [2] Eurocode 3 : Part 1.1.
Revised annex J : Joints in building frames ENV 1993-1-1/pr A2
[3] Eurocode 3 Design of steel structures Part 1 - 1 : General rules and rules for buildings ENV 1993-1-1:1992, 1992
See the chapter "Manual calculation" for the manual calculation according to Eurocode 3. Result Manual
calculation EPW % Diff.
Vwp,Rd 652 kN 652 kN 0 % Fc,wc,Rd 668 kN (*) 643 kN 3.74 % Fc,fb,Rd 1116 kN 1114 kN 0 % Ft,fc,Rd 677 kN 677 kN 0 % Ft,wc,Rd 635 kN (*) 614 kN 3.31 % Mj,Rd 338 kN 327 kNm 3.25 % af 7.2 mm 7.2 mm 0 % aw 3 mm 3 mm 0 % (*) Remark : the differences between the EPW and the hand calculation, are due to the fact the program starts its calculation with the minimal weld size. The calculation of af and aw is performed after the calculation of the moment resistance. It means that the values of EPW are on the safe side. The program can use some default values for the weld sizes (see Ref.1). In this case, the program starts its calculation with these default values for the weld sizes. See the chapter "Calculation note" for the detailed output of ESA-Prima Win. Version ESA-Prima Win 3.20.03 Input file + calculation note PST070105.epw Modules
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2D Frame (PRS.01) Connect Frame - Rigid (PST.07.01) Author CVL Manual calculation
CD
IPE550
8
8
3
Section CD
HEB280
9
1. Calculation Vwp,Rd : Column web panel in shear (Ref.[2] – J.3.5.2)
When a web doubler is used :
2. Calculation Fc,wc,Rd : Column web in compression (Ref.[2] – J.3.5.3)
0M
vcyRd,wp
γ3
'Af9.0V =
kN6521.13
58792350.9RdVwp,
²mm58795.101724073'A
²mm4073A
18)2425.10(18280213100A
t)r2t(bt2AA
tbA'A
vc
vc
vc
fwfvc
ssvcvc
=⋅
⋅⋅=
=⋅+=
=
⋅++⋅⋅−=
++−=
+=
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3. Calculation Fc,fb,Rd : Beam flange in compression (Ref.[2] – J.3.5.4)
4. Calculation Ft,fc,Rd : Column flange in bending (Ref.[2] – J.3.5.5.1)
Ft fc, Bd,
twc
2 rc
7 ktfc
twc
fy
γM0
.
k =
tfc
tfb
fy fc,
fy fb,
1
Ft fc, Rd,
10.5 2 24. 7 1. 18.( )17.20 235.
1.1. 677 kN.
5. Calculation Ft,wc,Rd : Column web in tension (Ref.[2] – J.3.5.6)
( )
kN6681.1
23575.1525079.0F
79.0
'A
tb3.11
1ρ
ρρ
(*)mm250)2418(58222.17b
rt5a22tb
mm75.155.105.1t5.1t
γ
ftbρF
Rd,wc,c
2
vc
wceff
1
1
eff
fcfbeff
wwc
0M
ywceffRd,wc,c
=⋅⋅⋅
=
=
+
=
=
=++⋅+=
+++=
=⋅==
=
kN11162.17550
595F
kNm5951.1
655
γ
MM
th
MF
Rd,fb,c
0M
Rd,plRd,c
fbb
Rd,cRd,fb,c
=−
=
===
−=
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6. Calculation MRd : Design moment resistance
7. Calculation af The weld size af is designed according to the resistance of the joint. The design force in the beam flange can be estimated as:
kN635532.0
338F
h
MF
Rd
RdRd
==
=
The design resistance of the weld Fw shall be greater than the flange force FRd, multiplied by a factor γ. The value of the factor γ is (ref[2], J.3.1.3.) :
γ = 1.7 for sway frames γ = 1.4 for non sway frames
However, in no case shall the weld design resistance be required to exceed the design plastic resistance of the beam flange Nt.Rd :
kN7711.1
2352.17210N
γ
ftbN
Rd,t
M
ybfbfRd,t
0
=⋅⋅
=
⋅⋅=
kNm338635532.0M
FzM
Rd
RdRd
=⋅=
⋅=
Ft wc, Rd,
ρbeff twc
fy
γM0
twc
1.4 tw
1.4 10.5. 14.7 mm
beff
tfb
2 2 a. 5 tfc
r
beff
17.2 2 2 8. 5 18 24( ) 250 mm
ρ ρ1
ρ1
1
1 1.3beff
twc
Avc
2
0.81
Ft wc, Rd,
0.81 250. 14.7. 235.
1.1635 kN
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Fw = min ( Nt.Rd, γ FRd) = min (771, 1.4 x 635)= 771 kN
The weld size design for af, using Annex M of EC3 (Ref.[3])
mm23.72210360
8.025.1771000a
2bf
βγFa
f
fu
WMwwf
=⋅⋅
⋅⋅≥
⋅⋅
⋅⋅≥
We take af=8 mm.
Calculation of aw
The section is sollicitated by the moment M, the normal force N and the shear force D.
The moment M is defined by the critical design moment resistance of the connection. The normal force
N is taken as the maximum internal normal force on the node, the shear force D is taken as the
maximum internal shear force on the node.
M = 338 kNm
N = 148 kN
D = 84 kN
To determine the weldsize a2 in a connection, we use a iterative process with a2 as parameter until the Von Mises rules is respected (Ref[3],Annex M/EC3). We start with the minimal weld size a2=3 mm.
We can define the following properties :
a1 = 8 mm
a3 = 8 mm
a2 = 3 mm
l1 = 210 mm
l2 = h –3 tfb –2r = 550 – 3*17.2-2*24= 450 mm
l3 = (bf – twb – 2r) /2.0 = (210-11.1-2*24)/2.0=75.45 mm
43
fb33
32211
mm08e601.4)²2.17.2550(45.7586
4503
2
²5502108I
)²t.2h(la6
la
2
²hlaI
+=−⋅+⋅
+⋅⋅
=
−⋅+⋅
+⋅⋅
=
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²mm/N1292
1
08e601.42
450338000000
8474
148000τσ
2
1
I2
lM
A
Nτσ
21
221
=
⋅
⋅+==
⋅
⋅+==
²mm/N3.3145032
84000τ
la2
Dτ
1
221
=⋅⋅
=
⋅⋅=
( ) ( )
²mm/N28825.1
360
γ
f129σ
N/mm² 360 25.18.0
360
γβ
f²mm/N263²1293.313129ττ3σ
w
w
211
M
u1
Mw
u22222
==≤=
=⋅
=⋅
≤=+⋅+=+⋅+
Calculation note
Sj,ini = 151019.98 kNm/radSj,MRd = 50534.50 kNm/rad
3.239e-003 6.477e-003 9.716e-003 1.295e-002
rad
100.0
200.0
300.0
kNm
Node 3 : welded beam-to-column connection side CD
According to EC3, Revised Annex J
1. Input data
Column HEB280
h 280.00 mm
b 280.00 mm
tf 18.00 mm
tw 10.50 mm
r 24.00 mm
fy 235.00 MPa
fu 360.00 MPa
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Connected beam IPE550
h 550.00 mm
b 210.00 mm
tf 17.20 mm
tw 11.10 mm
r 24.00 mm
fy 235.00 MPa
fu 360.00 MPa
Partial safety factors
Gamma M0 1.10
Gamma M1 1.10
Gamma Mb 1.25
Gamma Ms 1.25
Gamma Mw 1.25
Webdoubler
ls 768.49 mm
bs 172.00 mm
ts 12.00 mm
as 9.00 mm
fy 235.00 MPa
Internal forces
Loadcase number 1
N 142.93 kN
Vz 79.99 kN
My -104.61 kNm
Tension top
2. Design moment resistance MRd
2.1. Design resistance of basic components 2.1.1. Column web panel in shear (J.3.5.2.)
Vwp,Rd data
Vwp,Rd 652.62 kN
Beta 1.00
Avc 5879.00 mm^2
2.1.2. Column web in compression (J.3.5.3.)
Fc,wc,Rd data
Fc,wc,Rd 643.59 kN
beff 235.69 mm
twc 15.75 mm
ro1 0.81
ro2 0.57
ro 0.81
kwc 1.00
lambda_rel 0.42
dc 196.00 mm
2.1.3. Beam flange and web in compression (J.3.5.4.)
Fc,fb,Rd data
Fc,fb,Rd 1114.69 kN
section class 1
Mc,Rd 593.91 kNm
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Fc,fb,Rd data
hb-tfb 532.80 mm
2.1.4. Column flange in bending (J.3.5.5.)
Ft,fc,Rd data
Ft,fc,Rd 677.95 kN
k 1.00
2.1.5. Column web in tension (J.3.5.6.)
Ft,wc,Rd data
Ft,wc,Rd 614.36 kN
beff 235.69 mm
twc 14.70 mm
ro1 0.83
ro2 0.60
ro 0.83
2.2. Determination of Mj,Rd
Mj,Rd data
F 614.36 kN
h 532.80 mm
Mj,Rd 327.33 kNm
Mj,Rd 327.33 kNm
(inclusive normal force)
3. Design shear resistance VRd
VRd =887.15 kN
4. Stiffness calculation
4.1. Design rotational stiffness
Sj data
Sj 151.02 MNm/rad
Sj,ini 151.02 MNm/rad
z 532.80 mm
mu 1.00
k1 4.19 mm
k2 13.26 mm
k4 12.37 mm
4.2. Stiffness classification
Stiffness data
E 210000.00 MPa
Ib 670999987.05 mm^4
Lb 6000.00 mm
frame type braced
S1 187.88 MNm/rad
S2 11.74 MNm/rad
System SEMI RIGID
4.3 Check of stiffness requirement
Stiffness data
Fi y infinity MNm/rad
Stiffness modification coef. 2.00
Sj,app infinity MNm/rad
Sj,lower boundary 187.88 MNm/rad
Sj,upper boundary infinity MNm/rad
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Sj,ini is not inside the boundaries.
The actual joint stiffness is not conform with the joint stiffness of the analysis model.
4.4 Ductility classification
The failure mode is not situated in the column shear zone.
This results in an intermediate classification for ductility : class 2.
5. Unity checks
Unity checks
MSd/MjRd 0.32
VSd/VRd 0.09
The connection satisfies.
6. Design calculations 6.1. Calculation weldsize af / Minimum thickness th for stiffener in column
data
MRd 327.33 kNm
Gamma 1.40
h 532.80 mm
FRd 860.10 kN
NT,Rd 771.65 kN
N 771.65 kN
fu 360.00 MPa
BetaW 0.80
minimum af 7.22 mm
af 8.00 mm
Minimum th 17.20 mm
6.2. Calculation aw
data
M 327.33 kNm
N 142.93 kN
V 79.99 kN
fu 360.00 MPa
BetaW 0.80
a1 8.00 mm
a3 8.00 mm
l1 210.00 mm
l2 450.40 mm
l3 75.45 mm
A 6675.20 mm^2
I 429791090.71 mm^4
minimum aw (a2) 1.00 mm
aw 3.00 mm
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2.6 PST.07.01 – 06 : Calculation of required stiffness Description Calculation of a bolted knee connection : the moment resistance MRd, the rotational stiffness and the stiffness boundaries are calculated and compared with literature results. Project data See input file. Reference [1] Eurocode 3 : Part 1.1.
Revised annex J : Joints in building frames ENV 1993-1-1/pr A2
[2] Eurocode 3 Design of steel structures Part 1 - 1 : General rules and rules for buildings ENV 1993-1-1:1992, 1992
[3] Frame Design Including Joint Behaviour Volume 1 ECSC Contracts n° 7210-SA/212 and 7210-SA/320 January 1997
Result The comparison is performed for node nr.7. The approximate joint stiffness is introduced in the model as Sj,app/2 = 13000 kNm/rad. Ref.[3],
Chapter 10 Worked example 1
EPW % Diff.
Mj,Rd 128 kNm 129 kNm 0.78 % Sj,ini 58000 kNm/rad 60369 kNm/rad 4.08 % Sj,upper 68000 kNm/rad 62786 kNm/rad 7.67 % S,app 26000 kNm/rad 26000 kNm/rad 0 % See the chapter "Calculation note" for the detailed output of ESA-Prima Win. Version ESA-Prima Win 3.20.03 Input file + calculation note PST070106.epw Modules 2D Frame (PRS.01)
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Connect Frame - Rigid (PST.07.01) Author CVL Calculation note
1 2 3
4 5 6
7 8 9
IPE500 IPE500
IPE400 IPE400
HEA200
HEA200
HEA300
HEA300
HEA200
HEA200
Figure 41 : Frame geometry
CD
IPE400
7
7
5
Section CD
HEA200
11
14
5
15
15
Figure 42 : Connection geometry
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Sj,ini
Sj,ini = 60369.63 kNm/rad
Sj,low
Sj,low = 15008.30 kNm/rad
Sj,upper
Sj,upper = 62786.74 kNm/rad
1.070e-003 2.141e-003 3.211e-003 4.282e-003
rad
50.0
100.0
kNm
Figure 43 : Check required stiffness
Sj,ini = 60369.63 kNm/radSj,MRd = 20200.97 kNm/rad
3.199e-003 6.398e-003 9.597e-003 1.280e-002
rad
50.0
100.0
kNm
Figure 44 : Moment rotation diagramma
Node 7 : bolted beam-to-column connection side CD
According to EC3, Revised Annex J
1. Input data
Column HEA200
h 190.00 mm
b 200.00 mm
tf 10.00 mm
tw 6.50 mm
r 18.00 mm
fy 235.00 MPa
fu 360.00 MPa
Connected beam IPE400
h 400.00 mm
b 180.00 mm
tf 13.50 mm
tw 8.60 mm
r 21.00 mm
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Connected beam IPE400
fy 235.00 MPa
fu 360.00 MPa
Haunch under IPE400
hc 360.00 mm
lc 623.25 mm
b 180.00 mm
tf 13.50 mm
tw 8.60 mm
weld ab 14.00 mm
weld ac 11.00 mm
Partial safety factors
Gamma M0 1.10
Gamma M1 1.10
Gamma Mb 1.25
Gamma Ms 1.25
Gamma Mw 1.25
End plate
h 790.00 mm
b 180.00 mm
t 20.00 mm
fy 235.00 MPa
fu 360.00 MPa
Bolts M-20 (DIN960)
type normal
grade 8.8
fu 800.00 MPa
As 245.00 mm^2
do 22.00 mm
S 30.00 mm
e 33.53 mm
h head 13.00 mm
h nut 16.00 mm
Bolt position
row y[mm] spacing[mm]
1 721.00 90.00
2 640.00 90.00
3 429.00 90.00
4 71.00 90.00
Internal forces
ULS Combination number 1
N -22.53 kN
Vz 151.08 kN
My -31.72 kNm
Tension top
2. Design moment resistance MRd
2.1. Design resistance of basic components 2.1.1. Column web panel in shear (J.3.5.2.)
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Vwp,Rd data
Vwp,Rd 200.37 kN
Beta 1.00
Avc 1805.00 mm^2
2.1.2. Column web in compression (J.3.5.3.)
Fc,wc,Rd data
Fc,wc,Rd 196.55 kN
beff 198.40 mm
twc 6.50 mm
ro1 0.78
ro2 0.52
ro 0.78
kwc 1.00
lambda_rel 0.78
dc 134.00 mm
2.1.3. Beam flange and web in compression (J.3.5.4.)
Fc,fb,Rd data
Fc,fb,Rd 722.99 kN
section class 1
Mc,Rd 279.44 kNm
hb-tfb 386.50 mm
2.1.4. Design tension resistance of bolt row
(effective lengths in mm, resistance in kN)
Bt,Rd = 141.12 kN
2.1.4.1. Column flange
kfc = 1.00
row p (p1+p2) alfa e m n e1
1 0.0+40.5 - 55.00 27.35 34.19 69.00
2 40.5+105.5 - 55.00 27.35 34.19 -
3 105.5+179.0 - 55.00 27.35 34.19 -
4 179.0+ 0.0 - 55.00 27.35 34.19 -
row leff,cp,i leff,nc,i
1 171.85 158.08
2 171.85 178.15
3 171.85 178.15
4 171.85 178.15
row leff,cp,g leff,nc,g leff,cp,ge1 leff,nc,ge1 leff,cp,ge2 leff,nc,ge2
1 - - - - 166.92 129.58
2 292.00 146.00 166.92 129.58 296.92 194.58
3 569.00 284.50 296.92 194.58 443.92 268.08
4 - - 443.92 268.08 - -
For individual bolt row:
row leff,1 leff,2 leff Ft,fc,Rd Ft,wc,Rd ro
1 158.08 158.08 158.08 123.48 184.13 0.84
2 171.85 178.15 178.15 134.23 199.67 0.81
3 171.85 178.15 178.15 134.23 199.67 0.81
4 171.85 178.15 178.15 134.23 199.67 0.81
For bolt group:
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group leff,1 leff,2 leff Ft,fc,Rd Ft,wc,Rd ro
1- 1 158.08 158.08 158.08 123.48 184.13 0.84
1- 2 239.08 239.08 239.08 186.75 236.92 0.71
1- 3 450.08 450.08 450.08 351.56 297.45 0.48
1- 4 808.08 808.08 808.08 631.20 323.82 0.29
2.1.4.2. Endplate
row p (p1+p2) alfa e m n
1 0.0+40.5 6.26 45.00 35.04 43.80
2 40.5+105.5 - 45.00 35.04 43.80
3 105.5+179.0 6.26 45.00 35.04 43.80
4 179.0+ 0.0 6.26 45.00 35.04 43.80
row leff,cp,i leff,nc,i
1 220.18 219.51
2 220.18 196.42
3 220.18 219.51
4 220.18 219.51
row leff,cp,g leff,nc,g leff,cp,ge1 leff,nc,ge1 leff,cp,ge2 leff,nc,ge2
1 - - - - 191.09 161.80
2 292.00 146.00 191.09 138.71 321.09 203.71
3 - - 321.09 226.80 - -
4 - - 468.09 300.30 - -
For individual bolt row:
row leff,1 leff,2 leff Ft,ep,Rd Ft,wb,Rd
1 219.51 219.51 219.51 275.75 403.30
2 196.42 196.42 196.42 263.24 360.88
3 219.51 219.51 219.51 275.75 403.30
4 219.51 219.51 219.51 275.75 403.30
For bolt group:
group leff,1 leff,2 leff Ft,ep,Rd Ft,wb,Rd
1- 1 219.51 219.51 219.51 275.75 403.30
1- 2 300.51 300.51 300.51 476.45 552.12
1- 3 534.60 534.60 534.60 760.10 982.21
4- 4 219.51 219.51 219.51 275.75 403.30
2.2. Determination of Mj,Rd
row h[mm] Ft[kN]
1 698.20 123.48
2 617.20 63.27
3 406.20 9.80
4 48.20 0.00
Mj,Rd = 129.24 kNm
Mj,Rd = 129.24 kNm(inclusive normal force)
3. Design shear resistance VRd
VRd data
VRd 346.21 kN
Fv,Rd 94.08 kN
e1,ep 69.00 mm
e1,cf 69.00 mm
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VRd data
p1 81.00 mm
alfa,ep 0.98
alfa,fc 0.98
Fb,ep,Rd 281.45 kN
VRd beam 140.73 kN
VRd beam 1147.19 kN
4. Stiffness calculation
4.1. Design rotational stiffness
row k3[mm] k4[mm] k5[mm] k7[mm] keff[mm]
1 4.55 3.72 25.57 8.81 1.56
2 5.38 4.96 21.92 8.81 1.83
3 7.14 6.05 34.69 8.81 2.23
Sj data
Sj 60.37 MNm/rad
Sj,ini 60.37 MNm/rad
z 584.16 mm
mu 1.00
k1 1.17 mm
k2 6.74 mm
keq 5.35 mm
4.2. Stiffness classification
Stiffness data
E 210000.00 MPa
Ib 230999998.17 mm^4
Lb 7200.00 mm
frame type braced
S1 53.90 MNm/rad
S2 3.37 MNm/rad
System RIGID
4.3 Check of stiffness requirement
Stiffness data
Fi y 13.00 MNm/rad
Stiffness modification coef. 2.00
Sj,app 26.00 MNm/rad
Sj,lower boundary 15.01 MNm/rad
Sj,upper boundary 62.79 MNm/rad
Sj,ini is inside the boundaries.
The actual joint stiffness is conform with the joint stiffness of the analysis model.
4.4 Ductility classification
The failure mode is not situated in the column shear zone.
In the column flange we have the following :
t <= 0.36 sqrt(fub/fy) d
This results in a ductile classification for ductility : class 1.
5. Unity checks
Unity checks
MSd/MjRd 0.25
VSd/VRd 0.44
The connection satisfies.
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6. Design calculations 6.1. Calculation weldsize af / Minimum thickness th for stiffener in column
data
MRd 129.24 kNm
Gamma 1.40
h 745.45 mm
FRd 242.73 kN
NT,Rd 519.14 kN
N 242.73 kN
fu 360.00 MPa
BetaW 0.80
minimum af 2.65 mm
af 7.00 mm
Minimum th 6.31 mm
6.2. Calculation aw
data
Ft 186.75 kN
Fv 37.77 kN
lw 300.51 mm
fu 360.00 MPa
BetaW 0.80
minimum aw (a2) 2.00 mm
aw 5.00 mm
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2.7 PST.07.01 - 07: Bolted connection with column minor axis Description This benchmark consists in a manual verification of a connection by using the minor axis theory combined with Annex J Revised EC3. Those results are compared with the design calculation of EPW 3.20 Project data See input file Reference [1] Eurocode 3
Design of steel structures Part 1 - 1 : General rules and rules for buildings ENV 1993-1-1:1992, 1992
[2] Eurocode 3 : Part 1.1. Revised annex J : Joints in building frames ENV 1993-1-1/pr A2
[3] COST C1 Control of the semi-rigid behaviour of civil engineering structural connections Edited by René Maquoi, Université de Liège, Belgium Application of the component method to steel joints
See the chapter "Manual calculation" for the manual calculation according to this reference. Result Manual calculation EPW % Diff. FPunching,Rd,l1,tension 247.1 kN 247.05 kN 0.02 % FPunching,Rd,l1,compression 192.1kN 192.12 kN 0.01 % FPunching,Rd,l2 185.5 kN 185.53 kN 0.02 % FComb,Rd,tension 65.4 kN 65.44 kN 0.06 % FComb,Rd,compression 110.0 kN 110.01 kN 0 % FGlobal,Rd,tension 57.6 kN 56.59 kN 1.75 % FGlobal,Rd,compression 156.2 kN 156.19 kN 0 % See the chapter "Calculation note" for the detailed output of ESA-Prima Win. Version ESA-Prima Win 3.20.03 Input file + Calculation note PST070107.epw Modules 2D Frame (PRS.01)
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Connect Frame - Rigid (PST.07.01) Author NEM/CVL Manual calculation The following connection is composed with a endplate, 1 bolt row above the beam flange, 2 bolt rows between the beam flange and 1 bolt row under the beam flange. The plate is made of steel with following properties: S235 and is characterised by properties described in the EPW results document. The present document assumes that all the tensions, the stresses and the most dangerous combination computed by EPW are right. The node use for the check is the minor axis column-beam connection number 4 in PST070107.epw. This connection is composed with a HEA180 column and a IPE240 beam. We assume that the most dangerous combination is the 4th. The verification concerns only the weak axis part. For other controls from Annex J Revised EC3, other benchmarks are available.
AB
IPE240
5
5
4
Section AB
HEA180
80
80
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End plate
120
400
Plate 15
30 61
50
70
160
70
8 x M-12 (DIN601)
Local failure: Punching Punching Loading case 1
Tension zone
mm95.192
199.20
2
dmed m =
+=
+=
mm70c0 = and mm955.87d9.0cc m0 =⋅+=
mm61pitch x boltb0 == and mm955.78d9.0bb m0 =⋅+=
( )kN05.247
3
ftcb2F
0M
ywc
1LRd,Punching =γ⋅
⋅⋅+⋅=
Compression zone:
mm8.9tc fbeam ==
mm120bb beam ==
( )kN11.192
3
ftcb2F
0M
ywcRd,Punching 1L
=γ⋅
⋅⋅+⋅=
Punching Loading case 2
n=4 bolt rows
kN5.1853
ftdnF
0M
ywcmRd,Punching =
γ⋅
⋅⋅⋅π⋅=
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Combined punching and bending
Tension zone
mm152thd fcc =−=
mm5.1294
r32dL =⋅−=
mm5.50bLa =−=
1k5.0L
cb=⇒>
+
0109.4mm Lt
c8.211
c
t82.01Lb
2
wc
2
2
2wc
m >=
⋅++⋅−⋅=
mm3.36bL
bb
L
t
L
c23.0
L
tLx
m
m3
1
wc3
2
wc0 −=
−
−⋅
⋅⋅+
⋅=
bb 0x m≤=
( )( )
kN44.651
xat3
xxc5.1
xa
c2xaLftkF
0Mwc
2
y2wcRd,Comb =
γ⋅
+⋅⋅
+⋅⋅+
+
⋅++⋅⋅π⋅⋅⋅=
Compression zone
mm152thd fcc =−=
mm5.1294
r32dL =⋅−=
mm5.9bLa =−=
1k5.0L
cb=⇒>
+
0.00 Lt
c8.211
c
t82.01Lb
2
wc
2
2
2wc
m =<
⋅++⋅−⋅=
mm23.16bL
bb
L
t
L
c23.0
L
tLx
m
m3
1
wc3
2
wc0 =
−
−⋅
⋅⋅+
⋅=
( )[ ] bb if mm6.23c4xaL2
t3ca5..1aax m0
wc2 >=⋅++⋅⋅π⋅⋅
+⋅⋅−+−=
( )( )
kN1101
xat3
xxc5.1
xa
c2xaLftkF
0Mwc
2
y2wcRd,Comb =
γ⋅
+⋅⋅
+⋅⋅+
+
⋅++⋅⋅π⋅⋅⋅=
Global failure Tension zone
4.55 bL
z=
−=ρ with z=230.1mm
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kN92.1ft25.0
m0M
y2w
pl =γ
⋅⋅=
kN59.571
2z
b2m
2
FF
0Mpl
tension,Rd,ComRd,Global =
γ⋅
ρ⋅+π+
⋅⋅+=
Compression zone
4.55 bL
z=
−=ρ with z=230.1mm
kN19.1561
2z
b2m
2
FF
0Mpl
ncompressio,Rd,ComRd,Global =
γ⋅
ρ⋅+π+
⋅⋅+=
Calculation note Node 4 : bolted beam-to-column connection side AB
According to COST C1 September 1998 & Revised Annex J EC3
1. Input data
Column HEA180
h 171.00 mm
b 180.00 mm
tf 9.50 mm
tw 6.00 mm
r 15.00 mm
fy 235.00 MPa
fu 360.00 MPa
Connected beam IPE240
h 240.00 mm
b 120.00 mm
tf 9.80 mm
tw 6.20 mm
r 15.00 mm
fy 235.00 MPa
fu 360.00 MPa
Partial safety factors
Gamma M0 1.10
Gamma M1 1.25
Gamma Mb 1.25
Gamma Ms 1.25
Gamma Mw 1.25
End plate
h 400.00 mm
b 120.00 mm
t 15.00 mm
fy 235.00 MPa
fu 360.00 MPa
Bolts M-12 (DIN601)
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Bolts M-12 (DIN601)
type normal
grade 4.6
fu 400.00 MPa
As 84.50 mm^2
do 14.00 mm
S 19.00 mm
e 20.90 mm
h head 8.00 mm
h nut 10.00 mm
Bolt position
row y[mm] spacing[mm]
1 350.00 61.00
2 280.00 61.00
3 120.00 61.00
4 50.00 61.00
Internal forces
ULS Combination number 9
N 0.29 kN
Vz 21.49 kN
My -0.00 kNm
Tension top
2. Design moment resistance MRd
2.1. Design resistance of basic components 2.1.1. Column web in bending and punching: Local mechanism
2.1.1.1. Punching Loadcase 1
Tension Zone
dm 19.95 mm
b0 61.00 mm
b 78.95 mm
c0 70.00 mm
c 87.95 mm
FRd,punch,LC1,tens 247.05 kN
Compression zone
b0 0.00 mm
b 120.00 mm
c0 0.00 mm
c 9.80 mm
FRd,punch,LC1,comp 192.12 kN
2.1.1.2. Punching Loadcase 2
Tension Zone
dm 19.95 mm
n 4
FRdpunch,LC2,tens 185.53 kN
Compression zone
n 4
FRd,punch,LC2,comp 185.53 kN
2.1.1.3. Combined flexural and punching shear local
Tension Zone
L 129.50 mm
bm 109.42 mm
x0 -36.38 mm
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Tension Zone
x 0.00 mm
a 50.55 mm
k 1.00
FComb,Rd,tens 65.44 kN
Compression zone
L 129.50 mm
bm 0.00 mm
x0 16.23 mm
x 23.61 mm
a 9.50 mm
k 1.00
FComb,Rd,comp 110.01 kN
FLocal,Rd= 65.44kN
2.1.2. Column in bending and punching: Global mechanism
Tension Zone
mpl 1.92 kN
z 230.10 mm
ro 4.55
FGlobal,Rd,tens 57.59 kN
Compression zone
z 230.10 mm
ro 24.22
FGlobal,Rd,comp 156.19 kN
FGlobal,Rd= 57.59kN
2.1.3. Beam flange and web in compression (J.3.5.4.)
Fc,fb,Rd data
Fc,fb,Rd 339.67 kN
section clas 1
Mc,Rd 78.19 kNm
hb-tfb 230.20 mm
2.1.4. Design tension resistance of bolt row
(effective lengths in mm, resistance in kN)
Bt,Rd = 24.34 kN
2.1.4.2. Endplate
row p (p1+p2) alfa e m n
1 0.0+35.0 - 50.00 24.34 30.43
2 35.0+80.0 6.27 29.50 22.87 28.59
3 80.0+35.0 6.27 29.50 22.87 28.59
4 35.0+ 0.0 - 50.00 24.34 30.43
row leff,cp,i leff,nc,i
1 135.48 60.00
2 143.72 143.47
3 143.72 143.47
4 135.48 60.00
row leff,cp,g leff,nc,g leff,cp,ge1 leff,nc,ge1 leff,cp,ge2 leff,nc,ge2
1 135.48 60.00 - - - -
2 - - - - 231.86 159.29
3 - - 231.86 159.29 - -
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row leff,cp,g leff,nc,g leff,cp,ge1 leff,nc,ge1 leff,cp,ge2 leff,nc,ge2
4 135.48 60.00 - - - -
For individual bolt row :
row leff,1 leff,2 leff Ft,ep,Rd Ft,wb,Rd
1 60.00 60.00 60.00 48.67 -
2 143.47 143.47 143.47 48.67 190.04
3 143.47 143.47 143.47 48.67 190.04
4 60.00 60.00 60.00 48.67 -
For bolt group :
group leff,1 leff,2 leff Ft,ep,Rd Ft,wb,Rd
1- 1 60.00 60.00 60.00 48.67 -
2- 2 143.47 143.47 143.47 48.67 190.04
2- 3 318.57 318.57 318.57 97.34 421.97
4- 4 60.00 60.00 60.00 48.67 -
2.2. Determination of Mj,Rd
row h[mm] Ft[kN]
1 265.10 32.72
2 195.10 24.87
3 35.10 0.00
4 -34.90 0.00
Mj,Rd = 13.53 kNm
Mj,Rd = 13.53 kNm(inclusive normal force)
3. Design shear resistance VRd
VRd data
VRd 83.07 kN
Fv,Rd 16.22 kN
e1,ep 50.00 mm
p1 70.00 mm
alfa,ep 1.00
alfa,fc 1.00
Fb,ep,Rd 129.60 kN
Fb,wc,Rd 51.84 kN
VRd beam 235.93 kN
4. Stiffness calculation 4.1. Design rotational stiffness
row k5[mm] k7[mm]
1 11.93 4.04
2 34.39 4.04
Sj data
Sj 1.52 MNm/rad
Sj,ini 7.58 MNm/rad
z 232.31 mm
mu 5.00
k1 1.94 mm
k2 1.21 mm
keq 6.47 mm
4.2. Stiffness classification
Stiffness data
E 210000.00 MPa
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Stiffness data
Ib 38900001.53 mm^4
Lb 6000.00 mm
frame type braced
S1 10.89 MNm/rad
S2 0.68 MNm/rad
System SEMI RIGID
4.3 Check of stiffness requirement
Stiffness data
Fi y 0.00 MNm/rad
Stiffness modification coef. 2.00
Sj,app 0.00 MNm/rad
Sj,lower boundary 0.00 MNm/rad
Sj,upper boundary 0.68 MNm/rad
Sj,ini is not inside the boundaries.
The actual joint stiffness is not conform with the joint stiffness of the analysis model.
5. Unity checks
Unity checks
MSd/MjRd 0.00
VSd/VRd 0.26
The connection satisfies.
6. Design calculations
6.1. Calculation weldsize af / Minium thickness th for stiffener in column
data
MRd 13.53 kNm
Gamma 1.40
h 230.20 mm
FRd 82.26 kN
NT,Rd 251.24 kN
N 82.26 kN
fu 360.00 MPa
BetaW 0.80
minimum af 1.35 mm
af 5.00 mm
Minimum th 3.21 mm
6.2. Calculation aw
data
Ft 24.87 kN
Fv 5.37 kN
lw 143.47 mm
fu 360.00 MPa
BetaW 0.80
minimum aw (a2) 1.00 mm
aw 4.00 mm
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2.8 PST.07.01 - 08: Welded connection with column minor axis Description This benchmark consists in a manual verification of a connection by using the minor axis theory combined with Annex J Revised EC3. Those results are compared with the design calculation of EPW 3.20 Project data See input file. Reference [1] Eurocode 3
Design of steel structures Part 1 - 1 : General rules and rules for buildings ENV 1993-1-1:1992, 1992
[2] Eurocode 3 : Part 1.1. Revised annex J : Joints in building frames ENV 1993-1-1/pr A2
[3] COST C1 Control of the semi-rigid behaviour of civil engineering structural connections Edited by René Maquoi, Université de Liège, Belgium Application of the component method to steel joints
See the chapter "Manual calculation" for the manual calculation according to this reference. Result Manual calculation EPW % Diff. FPunching,Rd, 192.1 kN 192.12 kN 0 % FComb,Rd 72.5 kN 72.55 kN 0 % FGlobal,Rd 112.4 kN 112.39 kN 0 % See the chapter "Calculation note" for the detailed output of ESA-Prima Win. Version ESA-Prima Win 3.20.03 Input file + calculation note PST070108.epw Modules 2D Frame (PRS.01) Connect Frame - Rigid (PST.07.01) Author NEM -CVL
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Manual calculation The following connection is composed only with a column and a beam welded on the web column around the flange beam. The present document assumes that all the tensions, the stresses and the most dangerous combination computed by EPW are right. The node use for the check is the minor axis column-beam connection number 4 in PST070108.epw. This connection is composed with a HEA180 column and a IPE240 beam. We assume that the most dangerous combination is the 4th. The verification concerns only the weak axis part. For other controls from Annex J Revised EC3, other benchmarks are available. Local failure: Punching Punching Loading case 1
Tension & compression zone
mm8.9tc fbeam ==
mm120bb beam ==
( )kN11.192
3
ftcb2F
0M
ywc
1LRd,Punching =γ⋅
⋅⋅+⋅=
Combined punching and bending
Tension & compression zone
mm152thd fcc =−=
mm5.1294
r32dL =⋅−=
mm5.9bLa =−=
1k5.00023.1L
cb=⇒>=
+
002.56- Lt
c8.211
c
t82.01Lb
2
wc
2
2
2wc
m =<=
⋅++⋅−⋅=
mm2.16bL
bb
L
t
L
c23.0
L
tLx
m
m3
1
wc3
2
wc0 =
−
−⋅
⋅⋅+
⋅=
( )[ ] bb if mm6.23c4xaL2
t3ca5..1aax m0
wc2 >=⋅++⋅⋅π⋅⋅
+⋅⋅−+−=
( )( )
kN55.721
xat3
xxc5.1
xa
c2xaLftkF
0Mwc
2
y2wcRd,Comb =
γ⋅
+⋅⋅
+⋅⋅+
+
⋅++⋅⋅π⋅⋅⋅=
Compression zone
mm152thd fcc =−=
mm5.1294
r32dL =⋅−=
mm5.9bLa =−=
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1k5.0L
cb=⇒>
+
0.00 Lt
c8.211
c
t82.01Lb
2
wc
2
2
2wc
m =<
⋅++⋅−⋅=
mm23.16bL
bb
L
t
L
c23.0
L
tLx
m
m3
1
wc3
2
wc0 =
−
−⋅
⋅⋅+
⋅=
( )[ ] bb if mm6.23c4xaL2
t3ca5..1aax m0
wc2 >=⋅++⋅⋅π⋅⋅
+⋅⋅−+−=
( )( )
kNxat
xxc
xa
cxaLftkF
Mwc
ywcRdComb 5.721
3
5.12
0
22
, =⋅
+⋅⋅
+⋅⋅+
+
⋅++⋅⋅⋅⋅⋅=
γπ
Global failure Tension zone
mm5.71 bL
z=
−=ρ with z=166.2mm
kN92.1ft25.0
m0M
y2w
pl =γ
⋅⋅=
kN38.1121
2z
b2m
2
FF
0Mpl
tension,Rd,ComRd,Global =
γ⋅
ρ⋅+π+
⋅⋅+=
Compression zone
mm5.71 bL
z=
−=ρ with z=166.2mm
kN92.1ft25.0
m0M
y2w
pl =γ
⋅⋅=
kNz
bm
FF
M
pl
ncompressioRdCom
RdGlobal 38.1121
22
2 0
,,, =⋅
⋅++⋅
⋅+=γ
ρπ
Calculation note Node 4 : bolted beam-to-column connection side AB
According to COST C1 September 1998 & Revised Annex J EC3
1. Input data
Column HEA180
h 171.00 mm
b 180.00 mm
tf 9.50 mm
tw 6.00 mm
r 15.00 mm
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Column HEA180
fy 235.00 MPa
fu 360.00 MPa
Connected beam IPE240
h 240.00 mm
b 120.00 mm
tf 9.80 mm
tw 6.20 mm
r 15.00 mm
fy 235.00 MPa
fu 360.00 MPa
Partial safety factors
Gamma M0 1.10
Gamma M1 1.25
Gamma Mb 1.25
Gamma Ms 1.25
Gamma Mw 1.25
Internal forces
ULS Combination number 4
N 0.18 kN
Vz 0.92 kN
My 0.00 kNm
Tension bottom
2. Design moment resistance MRd
2.1. Design resistance of basic components 2.1.1. Column web in bending and punching: Local mechanism
2.1.1.1. Punching Loadcase 1
Tension Zone
dm 0.00 mm
b0 0.00 mm
b 120.00 mm
c0 0.00 mm
c 9.80 mm
FRd,punch,LC1,tens 192.12 kN
Compression zone
b0 0.00 mm
b 120.00 mm
c0 0.00 mm
c 9.80 mm
FRd,punch,LC1,comp 192.12 kN
2.1.1.3. Combined flexural and punching shear local
Tension Zone
L 129.50 mm
bm 0.00 mm
x0 16.23 mm
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Tension Zone
x 23.61 mm
a 9.50 mm
k 1.00
FComb,Rd,tens 72.55 kN
Compression zone
L 129.50 mm
bm 0.00 mm
x0 16.23 mm
x 23.61 mm
a 9.50 mm
k 1.00
FComb,Rd,comp 72.55 kN
FLocal,Rd= 72.55kN
2.1.2. Column in bending and punching: Global mechanism
Tension Zone
mpl 1.92 kN
z 166.25 mm
ro 17.50
FGlobal,Rd,tens 112.39 kN
Compression zone
z 166.25 mm
ro 17.50
FGlobal,Rd,comp 112.39 kN
FGlobal,Rd= 112.39kN
2.1.3. Beam flange and web in compression (J.3.5.4.)
Fc,fb,Rd data
Fc,fb,Rd 339.67 kN
section clas 1
Mc,Rd 78.19 kNm
hb-tfb 230.20 mm
2.2. Determination of Mj,Rd
Mj,Rd data
F 72.55 kN
h 230.20 mm
Mj,Rd 16.70 kNm
Mj,Rd 16.70 kNm
(inclusive normal force)
3. Design shear resistance VRd
VRd =235.93 kN
4. Stiffness calculation
4.1. Design rotational stiffness
Sj data
Sj 2163.15 kNm/rad
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Sj data
Sj,ini 10815.74 kNm/rad
z 230.20 mm
mu 5.00
k1 1.94 mm
k2 1.94 mm
4.2. Stiffness classification
Stiffness data
E 210000.00 MPa
Ib 38900001.53 mm^4
Lb 6000.00 mm
frame type braced
S1 10892.00 kNm/rad
S2 680.75 kNm/rad
System SEMI RIGID
4.3 Check of stiffness requirement
Stiffness data
Fi y 0.00 kNm/rad
Stiffness modification coef. 2.00
Sj,app 0.00 kNm/rad
Sj,lower boundary 0.00 kNm/rad
Sj,upper boundary 680.75 kNm/rad
Sj,ini is not inside the boundaries.
The actual joint stiffness is not conform with the joint stiffness of the analysis model.
5. Unity checks
Unity checks
MSd/MjRd 0.00
VSd/VRd 0.00
The connection satisfies.
6. Design calculations 6.1. Calculation weldsize af / Minium thickness th for stiffener in column
data
MRd 16.70 kNm
Gamma 1.40
h 230.20 mm
FRd 101.57 kN
NT,Rd 251.24 kN
N 101.57 kN
fu 360.00 MPa
BetaW 0.80
minimum af 1.66 mm
af 5.00 mm
Minimum th 3.96 mm
6.2. Calculation aw
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data
M 16.70 kNm
N 0.18 kN
V 0.92 kN
fu 360.00 MPa
BetaW 0.80
a1 5.00 mm
a3 5.00 mm
l1 120.00 mm
l2 180.60 mm
l3 41.90 mm
A 2399.20 mm^2
I 28438455.99 mm^4
minimum aw (a2) 1.00 mm
aw 4.00 mm
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2.9 PST.07.01 - 09: Bolted connection Description This benchmark consists in a verification of bolted beam-to-column connections compared with the table values given in reference [1], Chapter 5 : "Bemessungshilfen für nachgiebige Stahlknoten mit Stirnplattenanschlüssen", Table 5-25 and 5-26. Project data Column data : HEB280 (S235) Beam data : IPE240, IPE270, IPE300, IPE330, IPE360, IPE400, all made of S235 Bolt grade : 10.9 Reference [1] Stahlbau Kalender 1999
1. Jahrgang DSTV -1999
Result Connection EPW SBK 99 %
MRd [kNm] 58 57 1.7 VRd [kN] 236 236
HEB280/IPE240/M24/20 node 3
Sj,ini [kNm/rad] 10566 12060 MRd [kNm] 74 71 4.1 VRd [kN] 237 273
HEB280/IPE270/M24/25 node 5
Sj,ini [kNm/rad] 15038 16699 MRd [kNm] 74 80 8.1 VRd [kN] 237 273
HEB280/IPE270/M24/35 node 6
Sj,ini [kNm/rad] 15328 16898 MRd [kNm] 92 87 5.4 VRd [kN] 237 317
HEB280/IPE300/M24/25 node 7
Sj,ini [kNm/rad] 19428 21159 MRd [kNm] 92 92 0.0 VRd [kN] 237 317
HEB280/IPE300/M24/35 node 8
Sj,ini [kNm/rad] 19733 21393 MRd [kNm] 99 98 1.0 VRd [kN] 308 317
HEB280/IPE300/M27/25 (1) node 9
Sj,ini [kNm/rad] 17104 19555 MRd [kNm] 99 98 1.0 VRd [kN] 308 317
HEB280/IPE300/M27/25 (2) node 10
Sj,ini [kNm/rad] 17104 19572 MRd [kNm] 107 103 3.7 VRd [kN] 237 363
HEB280/IPE330/M24/25 node 11
Sj,ini [kNm/rad] 24275 25963 MRd [kNm] 107 103 3.7 VRd [kN] 237 363
HEB280/IPE330/M24/35 node 12
Sj,ini [kNm/rad] 24581 26229 HEB280/IPE330/M27/25 (1) MRd [kNm] 112 110 1.8
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VRd [kN] 308 380 node 13 Sj,ini [kNm/rad] 21661 24231 MRd [kNm] 112 111 0.9 VRd [kN] 308 380
HEB280/IPE330/M27/25 (2) node 14
Sj,ini [kNm/rad] 21661 24252 MRd [kNm] 117 113 3.4 VRd [kN] 237 363
HEB280/IPE360/M24/25 node 15
Sj,ini [kNm/rad] 28483 30200 MRd [kNm] 123 121 1.6 VRd [kN] 308 433
HEB280/IPE360/M27/25 (1) node 16
Sj,ini [kNm/rad] 25723 28369 MRd [kNm] 123 122 0.8 VRd [kN] 308 433
HEB280/IPE360/M27/25 (2) node 17
Sj,ini [kNm/rad] 25723 28392 MRd [kNm] 123 121 1.6 VRd [kN] 377 433
HEB280/IPE360/M30/20 node 18
Sj,ini [kNm/rad] 24556 27258 MRd [kNm] 127 127 0.0 VRd [kN] 377 433
HEB280/IPE360/M30/25 (1) node 19
Sj,ini [kNm/rad] 28610 29199 MRd [kNm] 150 141 6.0 VRd [kN] 377 433
HEB280/IPE360/M30/25 (2) node 20
Sj,ini [kNm/rad] 33905 36971 MRd [kNm] 132 129 2.3 VRd [kN] 237 363
HEB280/IPE400/M24/25 node 21
Sj,ini [kNm/rad] 35720 37770 MRd [kNm] 140 138 1.4 VRd [kN] 308 472
HEB280/IPE400/M27/25 (1) node 22
Sj,ini [kNm/rad] 33369 35806 MRd [kNm] 140 139 0.7 VRd [kN] 308 472
HEB280/IPE400/M27/25 (2) node 23
Sj,ini [kNm/rad] 33369 35835 MRd [kNm] 145 145 0.0 VRd [kN] 376 527
HEB280/IPE400/M30/25 (1) node 24
Sj,ini [kNm/rad] 37234 36816 MRd [kNm] 177 168 5.1 VRd [kN] 376 527
HEB280/IPE400/M30/25 (1) node 25
Sj,ini [kNm/rad] 44240 46882 Version ESA-Prima Win 3.20.03 Input file + calculation note PST070109.epw Modules 2D Frame (PRS.01) Connect Frame - Rigid (PST.07.01) Author CVL
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2.10 PST.07.02 – 01 : Frame pinned connection (plate welded on the web) Description A pinned connection with a plate welded on the beam web and the column flange is calculated manually in node 2 of the Tutorial Frame project. The results are compared with the results of ESA-Prima Win. Project data The following connection will be calculated : h=0.163 m b=0.164 m t=0.012 m Play=0.01m The connection is composed of two plates welded symmetrically on each side of the beam’s web and to the column’s flange. The plates are made of Fe 360. The node use for the check is the column-beam connection number 2 in the Tutorial Frame project. This connection is composed with a HEA160 column and an IPE 240 Beam. We assume that the most dangerous load combination is the 4th. Considering that the moment approaches 0 precision, we can say that we have a pinned connection. Forces in the connection :
N=262.4939 N Tz=7990 N M≅0 Reference Eurocode 3 : Design of steel structures
Part 1-1 : General rules and rules for buildings ENV 1993-1-1:1992 Revised Annex J ENV 19+93-1-1/pr A2
See the chapter "Manual calculation" for the manual calculation according to this reference. Result See the chapter "Calculation note" for the detailed output of ESA-Prima Win.
0.038m
Weld Part
0.164m
0.01m
0.163m
Play
Weldsize
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Version ESA-Prima Win 3.20.03 Input file + calculation note PST070201.epw Modules 3D Frame (PRS.11) Connect Frame – Pinned (PST.07.02) Author NEM/CVL Manual calculation 1. Calculation of VRd and NRd 1.1. Calculation Design Shear Resistance VRd for Connection Element
Transversal section of the plate : 2plplpl m003912.0th2A =⋅⋅= (2 plates)
Normal stress : 2pl
N mN667.67099
003912.0
4939.262
A
N===σ
Flexion module : 32
plpl m000106276.0
6
ht2W
pl
=⋅
⋅=
Design Shear Resistance : a= 0.082 m is the bolt center
N66.240087
A
3
W
a2
f
N
a4
W
a2
W
a2
V
2pl
2
2
2M
2y2
N2
22
pl
N
pl
N
Rd
pl
0=
+⋅
γ−σ⋅
⋅−
⋅σ⋅+
⋅σ⋅−
=
1.2 Calculation Design Shear Resistance VRd for Beam
Shear Area : ( ) 2fwfv m00191276.0tr2ttb2AA =⋅⋅++⋅⋅−=
Shear Resistance : N57.2359253
fAVRd
0M
yv =γ⋅
⋅=
1.3 Calculation Design Tension Resistance NRd for Connection Element
Area of the element : 2plplpl m003912.0th2A =⋅⋅=
Tension Resistance : N45.835745fA
N0M
yplRd =
γ
⋅=
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1.4 Calculation Design Tension Resistance NRd for Beam
Area of the Beam : 2m003910.0A =
Tension Resistance : N18.835318fA
N0M
yRd =
γ
⋅=
1.5 Unity Check The most critical design shear resistance and design tension resistance is used to calculate the unity check :
Shear Unity Check : 11038.357.235925
7990
V
V 2
Rd
Sd ≤⋅== − ⇒ Connection OK for Shear
Tension Unity Check : 11014.345.835745
4939.262
N
N 4
Rd
Sd ≤⋅== − ⇒ Connection OK for Tension
2. Weldsize Calculation for Plate, Beam and Column To determine the weldsize a for the plate on the beam and on the column, we must use a iterative process with a as parameter until the Von Mises rules is respected (Annexe M/EC3) :
( )ww
211M
u1
Mw
u222 f and
f3
γ≤σ
γ⋅β≤τ+τ⋅+σ
We’ll only check the weldsize for the final value of a. For the weld between plate and beam we find a=4mm and for weld between plate and column, the weldsize is a=10mm. 2.1 Weldsize Plate/Beam We define the play as the effective distance between the end of the beam and the flange of the column. In this case, the play is 10mm. By using EC3 and the Chapter 11 of the manual, we compute the following parameters : Weldsize : a=0.004 Weld Length : m139.012.02163.0t2hl plpl1 =⋅−=⋅−=
m13.0t2Playbl plpl2 =⋅−−=
m154.001.0164.0Playll pl =−=−=
By EC3 : fuw=360000000N/m2 and βw=0.8 The order parameters are :
( )10.104
la414.1la577.0
lla577.0la707.0g
21
11 =⋅⋅+⋅⋅
⋅⋅⋅+⋅⋅=
30377.0la414.1la577.0
la577.0
21
1 =⋅⋅+⋅⋅
⋅⋅=δ
15603.0hla577.0la117.0
la117.0
pl221
21 =
⋅⋅⋅+⋅⋅
⋅⋅=µ
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3987.0la14.1la707.0
la707.0
21
1 =⋅⋅+⋅⋅
⋅⋅=Γ
g10L +=
Shear force on one plate : N789.1179622
VD Rd == (for one plate)
Normal force on one plate : N24.1312
NN ==
Moment on the plate : Nm781.13459LDM =⋅=
Weld Check 1: 21
211 mN74.115363040
la2
N
la2
M6
1
==⋅⋅
⋅Γ+
⋅⋅
⋅µ⋅=σ=τ
21
2 mN72.64449431
la
D=
⋅⋅δ
=τ
Unity Check : ( )
14.0f
and 1316.0f
3
ww
211
M
u
1
Mw
u
222
≤=
γ
σ≤=
γ⋅β
τ+τ⋅+σ
Weld Check 2 : ( )
22
11 mN8731.55840293
la22
D1=
⋅⋅⋅
⋅δ−=τ=σ
( ) ( )2
222 m
N161.134095932la2
N1
lah
M1=
⋅⋅⋅Γ−
+⋅⋅⋅µ−
=τ
Unity Check : ( )
1193.0f
and 1715.0f
3
ww
211
M
u
1
Mw
u
222
≤=
γ
σ≤=
γ⋅β
τ+τ⋅+σ
2.2 Weldsize Plate/Column Weldsize : a=0.01 m Normal Force : N=262.4939N Moment : Nm89674.19345082.057.235925LDM =⋅=⋅= Stress Calculation :
22pl
11 mN96.154518316
6
ha22
LD
la22
N
W
M
la22
N=
⋅⋅⋅
⋅+
⋅⋅⋅=+
⋅⋅⋅=τ−=σ
22 mN7485.72369806
la2
D=
⋅⋅=τ
Unity Check : ( )
192.0f
3
w
211
Mw
u
222
≤=
γ⋅β
τ+τ⋅+σ
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153.0f
wM
u
1 ≤=
γ
σ
Calculation note Node 2 : frame pinned beam-to-column connection side CD 1. Input data
Column HEA160
h 152.00 mm
b 160.00 mm
tf 9.00 mm
tw 6.00 mm
r 15.00 mm
fy 235.00 MPa
fu 360.00 MPa
Connected beam IPE240
h 240.00 mm
b 120.00 mm
tf 9.80 mm
tw 6.20 mm
r 15.00 mm
fy 235.00 MPa
fu 360.00 MPa
Welded plate
number 2
h 163.00 mm
b 164.00 mm
t 12.00 mm
position (to top of beam) 38.00 mm
play beam/column 10.00 mm
fy 235.00 MPa
fu 360.00 MPa
Partial safety factors
Gamma M0 1.10
Gamma M1 1.10
Gamma Mb 1.25
Gamma Ms 1.25
Gamma Mw 1.25
Internal forces
ULS Combination number 5
N 0.26 kN
Vz 7.99 kN
My -0.00 kNm
2. Design shear resistance
2.1.Design shear resistance VRd for connection element
data
sigmaN 0.07 MPa
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data
A 3912.00 mm^2
W 106276.00 mm^3
a 82.00 mm
VRd 240.09 kN
2.2.Design shear resistance VRd for beam
data
Av 1912.76 mm^2
VRd 235.93 kN
2.3.Critical design shear resistance VRd = 235.93 kN
3, Design tension/compression resistance NRd
3.1.Design compression/tension resistance NRd for connection element
data
A 3912.00 mm^2
NRd 835.75 kN
3.2.Design compression/tension resistance NRd for beam
data
A 3910.00 mm^2
NRd 835.32 kN
3.3.Critical design tension/compression NRd = 835.32 kN
4. Unity checks
Unity checks
VSd/VRd 0.03
NSd/NRd 0.00
The connection satisfies.
5. Weldsize calculation 5.1. Weldsize plate/beam
data
fu 360.00 MPa
beta 0.80
a 3.00 mm
l1 139.00 mm
l2 130.00 mm
L 114.10 mm
g 104.10 mm
delta 0.30
mu 0.16
tau 0.40
D 117.96 kN
N 0.13 kN
M 13.46 kNm
for weld check 1:
sigma,1 154.28 MPa
tau,1 154.28 MPa
tau,2 85.93 MPa
for weld check 2:
sigma,1 74.68 MPa
tau,1 74.68 MPa
tau,2 178.79 MPa
5.2. Weldsize pate/column
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data
fu 360.00 MPa
beta 0.80
a 10.00 mm
L 82.00 mm
D 235.93 kN
N 0.26 kN
M 19.35 kNm
sigma,1 154.98 MPa
tau,1 154.98 MPa
tau,2 72.37 MPa
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2.11 PST.07.02 – 02 : Frame pinned connection (plate bolted to the web) Description A pinned connection with a plate bolted on the beam web and welded on the column flange is calculated manually in node 2 of the Tutorial Frame project. The results are compared with the results of ESA-Prima Win. In the first part normal bolts are used. In the second part, we replace these bolts by PRESTRESSED BOLTS and develop the calculation note only for points that change by using this type of bolts. Project data The following connection is calculated :
The connection is composed of two plates bolted symmetrically on each side of the beam’s web and welded to column. The plates are made of Fe 360. The node used for the check is the column-beam connection number 2 in the Tutorial Frame project. This connection is composed with a HEA160 column and an IPE 240 Beam. We assume that the most dangerous load combination is the 4th. Considering that the moment approaches 0 precision, we can say that we have a pinned connection.
The forces in the connection :
N=262.4939 N Tz=7990 N M≅0 Reference Eurocode 3 : Design of steel structures
Part 1-1 : General rules and rules for buildings ENV 1993-1-1:1992 Revised Annex J ENV 19+93-1-1/pr A2
See the chapter "Manual calculation" for the manual calculation according to this reference.
Weld Part
M-16(DIN601) Normal Bolt
0.189m
0.034m
0.01m
0.024m
0.188m
Play
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Result See the chapter "Calculation note" for the detailed output of ESA-Prima Win. Version ESA-Prima Win 3.20.03 Input file + calculation note PST070202.epw Modules 3D Frame (PRS.11) Connect Frame – Pinned (PST.07.02) Author NEM/CVL Manual calculation 1. Dimensions of the Plate and Position according to EC3 The plate is bolted to the web’s beam on each side with M-16(DIN601) normal bolts. The position of the bolts and of the plate on the web’s beam and its dimensions are represented in the figure. First, we must verify, according to EC3, the positioning of holes for bolts in the plate. The EC3 prescribes a minimum and maximum end distance, a minimum and maximum edge distance and a minimum and maximum spacing.
• the end distance e1 from the center of a fastener hole to the adjacent end of any part, measured in the direction of the load transfer must be not be less than 1,5d0, where d0 is the diameter of the hole. We impose e1=24≤1.5d0.
• the edge distance e2 from the center of a fastener hole to the adjacent edge of any part, measured at right angles to the direction of the load transfer must be not less than 1,5d0. We impose e2=24≤1.5d0. 2. Calculation of VRd and NRd 2.1. Calculation Design Shear Resistance VRd for Connection Element
Transversal section of the plate : 2m004512.0012.0188.02th2A =⋅⋅=⋅⋅= (2 plates)
Normal Stress : 2N mN8395.58176
004512.0
4939.262
A
N===σ
Flexion Module : 32
m000141376.06
ht2W =
⋅⋅=
Bolt Center : a=0.0995m Design Shear Resistance :
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N015.266422
A
3
W
a2
f
N
a4
W
a2
W
a2
V
22
2
2M
2y2
N2
22NN
Rd0
=
+⋅
γ−σ⋅
⋅−
⋅σ⋅+
⋅σ⋅−
=
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2.2. Calculation Design Shear Resistance VRd for Beam
Shear Area : ( ) 2fwfv m00191276.0tr2ttb2AA =⋅⋅++⋅⋅−=
Net Area : m56.001689.0dt2AA 0wvnet =⋅⋅−=
For the calculation of VRd in the beam, we use Av because 2v
u
ynet m00124860.0A
f
fA =⋅≥
Shear Resistance: N57.2359253
fAVRd
0M
yv =γ⋅
⋅=
2.3. Calculation Design Tension Resistance NRd for Connection Element
Area : 2m004512.0ht2A =⋅⋅=
Net Area : 20net m003648.0d2t2AA =⋅⋅⋅−=
Tension Resistance :
γ
⋅⋅
γ
⋅=
1
net
0 M
u
M
yRd
fA9.0,
fAminN ( ) N27.96392781.1074501,27.963927min ==
2.4. Calculation Design Tension Resistance NRd for Beam
Area : 2m003910.0A =
Net Area : 20net m0036868.0dt2AA =⋅⋅−=
Tension Resistance :
γ
⋅⋅
γ
⋅=
1
net
0 M
u
M
yRd
fA9.0,
fAminN ( ) N18.83531818.1085930,18.835318min ==
2.5. Calculation Design Shear Resistance VRd for Bolt in Beam The calculation of the shear resistance for bolt in beam is based on the following equation to be solve :
0Qn
N
nI
dNa2V
I
da
I
ca
n
1V 2
2
2
pRd2
p
22
2p
22
22Rd
=−+
⋅⋅⋅⋅
⋅+
⋅+
⋅+⋅
m
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Where : 0.0995ma = 0.094mb = 0.0655mc = 0.07md =
24
1i
22ip m036761.066.95rI ∑ ∑ ===
=
( )( )beam,Rd,bplate,Rd,bRd,v F;Fmin,F2minQ ⋅= =31740.8256N for two plates, where
• N30144Af6.0
FMb
subV dR
=γ
⋅⋅=
• N8256.31740tdf5.2
FMb
upBeam,Rd,b =
γ
⋅⋅⋅α⋅=
444.01;f
f;
4
1
d3
p;
d3
eminwith
u
ub
0
1
0
1p =
−=α
• N712.122867tdf5.2
FMb
plupplate,Rd,b =
γ
⋅⋅⋅α⋅=
444.01;f
f;
4
1
d3
p;
d3
eminwith
u
ub
0
1
0
1p =
−=α
By solving the second-degree equation, we find N89.67907VRd = 2.6. Calculation Design Block Shear Resistance The design value of the effective resistance to block shear is determined by the following expression :
eff,veffv,M
eff,vyRd,eff LtA with
3
AfV
0
⋅=γ⋅
⋅=
We determined the effective shear area Av,eff as follows :
m049.0a1 = m155.0a 2 = m051.0a 3 =
m14.0aahL 21v =−−=
( )
( ) m24.02849.0;24.0min
f
fdnaaL;aaLminL
y
u031v31v3
==
⋅⋅−++++=
( ) m049.0d5;aminL 011 =⋅=
( )
bolt rows 2for 2.5k with
m1685.0f
fdkaL
y
u022
=
=⋅⋅−=
( ) m24.0L;LLLminL 321veff,v =++=
2
eff,v m001488.0A =
a1
Lv
a3
a2
d
c
b
a
ri
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N40.1835343
AfV
0M
eff,vyRd,eff =
γ⋅
⋅=
2.7. Unity Check The most critical design shear resistance and design tension resistance is used to calculate the unity check :
Shear Unity Check: 11176.089.67907
7990
V
V
Rd
Sd ≤== ⇒ Connection OK for Shear
Tension Unity Check: 11014.345.835745
4939.262
N
N 4
Rd
Sd ≤⋅== − ⇒ Connection OK for Tension
3. Weldsize Calculation between Plate and Column As before, to determine the weldsize a for the plate on the column, we must use a iterative process with a as parameter until the Von Mises rules is respected:
( )w
211Mw
u222 f3
γ⋅β≤τ+τ⋅+σ and 1
f
wM
u
1 ≤
γ
σ
We’ll only check the weldsize for the final value of a. For weld between plate and column, the weldsize is a=0.004m. The data are : Weldsize : a=0.004 m Normal force : D=67907.89N Moment : Nm835.67560995.089.67907LDM =⋅=⋅=
Flexion module : 352
m106645.66
ha22W pl −⋅=⋅⋅⋅=
l : length of the weld l=0.188m Stress calculation :
22pl
11 mN087.10151858
6
ha22
LD
la22
N
W
M
la22
N=
⋅⋅⋅
⋅+
⋅⋅⋅=+
⋅⋅⋅=τ−=σ
22 mN25.4515604
la2
D=
⋅⋅=τ
Unity Check : ( )
10352.0f
and 10604.0f
3
ww
211
M
u
1
Mw
u
222
≤=
γ
σ≤=
γ⋅β
τ+τ⋅+σ
4.Plate Bolted to Beam, Weld to Column with Prestressed Bolt The following calculation is also based on a connection composed with a plate bolt to beam and weld to column. The difference between this connection and the precedent is that we use prestressed bolt. The settings, meaning the type and the dimension of the plate, the position of the bolt and of the plate in the web’s beam, are exactly the same. Prestressed
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d
c
b
a
ri
bolts use in this connection are M-16(DIN6914) grade 10.9. The results and the calculation of the shear resistance for connection element, the block shear resistance, the tension/compression resistance for the connection element and for the beam, and the unity check for tension are identical. This connection involves only the calculation of the design shear resistance for bolts in beam and the weld size calculation. 4.1. Calculation Design Shear Resistance VRd for Bolts in Beam The calculation of the shear resistance for bolt in beam is based on the following equation to be solve:
0Qn
N
nI
dNa2V
I
da
In
ca2
I
ca
n
1V 2
2
2
pRd2
p
22
p2p
22
22Rd
=−+
⋅
⋅⋅⋅⋅+
⋅+
⋅
⋅⋅+
⋅+⋅
Where: 0.0995ma = 0.094mb = 0.0655mc = 0.07md =
24
1i
22ip m036761.066.95rI ∑ ∑ ===
=
Rd,bFQ = =26376N for two plates, where
• ( ) NN26376F8.0Fnk
F tSdCd,pMs
sRd,b =⋅−⋅
γ
µ⋅⋅=
traction)(no 0F
hole) theof clearance nominal(standart 1k
tion)classifica surface (C 0.3
N109900Af7.0Fwith
Sdt,
s
subCdp,
=
=
=µ
=⋅⋅=
Assuming that there is no traction in the bolt (N=0), the resolution of the second-degree equation give
N126.56430VRd = . This value is the most critical value of the design shear resistance and involves a new calculation of the unity check and of the weldsize between the plate and the column. 4.2. Unity Check The most critical design shear resistance and design tension resistance is used to calculate the unity check:
Shear Unity Check: 1141.0126.56430
7990
V
V
Rd
Sd ≤== ⇒ Connection OK for Shear
Tension Unity Check: 11014.345.835745
4939.262
N
N 4
Rd
Sd ≤⋅== − ⇒ Connection OK for Tension
3.3. Weldsize between Plate and Column
As before, to determine the weldsize a for the plate on the beam and on the column, we must use a iterative process with a as parameter until the Von Mises rules is respected:
( )1
f and 1
f
3
ww
211
M
u
1
Mw
u
222
≤
γ
σ≤
γ⋅β
τ+τ⋅+σ
We’ll only check the weldsize for the final value of a. For weld between plate and column, the weldsize is a=0.004m. The data are :
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Weldsize : a=0.004 m Normal force : D=56430.126N Moment : Nm79.56140995.0126.56430LDM =⋅=⋅=
Flexion module : 352
m106645.66
ha22W pl −⋅=⋅⋅⋅=
l: length of the weld l=0.188m Stress calculation :
22pl
11 mN46.84624528
6
ha22
LD
la22
N
W
M
la22
N=
⋅⋅⋅
⋅+
⋅⋅⋅=+
⋅⋅⋅=τ−=σ
22 mN59.37520030
la2
D=
⋅⋅=τ
Unity Check : ( )
1293.0f
and 1503.0f
3
ww
211
M
u
1
Mw
u
222
≤=
γ
σ≤=
γ⋅β
τ+τ⋅+σ
Calculation note Normal bolts Node 2 : frame pinned beam-to-column connection side CD
1. Input data
Column HEA160
h 152.00 mm
b 160.00 mm
tf 9.00 mm
tw 6.00 mm
r 15.00 mm
fy 235.00 MPa
fu 360.00 MPa
Connected beam IPE240
h 240.00 mm
b 120.00 mm
tf 9.80 mm
tw 6.20 mm
r 15.00 mm
fy 235.00 MPa
fu 360.00 MPa
Bolted plate
number 2
h 188.00 mm
b 189.00 mm
t 12.00 mm
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Bolted plate
position (to top of beam) 25.00 mm
play beam/column 10.00 mm
fy 235.00 MPa
fu 360.00 MPa
Bolts M-16 (DIN601)
type normal
grade 4.6
fu 400.00 MPa
As 157.00 mm^2
do 18.00 mm
S 24.00 mm
e 26.20 mm
h head 10.00 mm
h nut 13.00 mm
Bolt position
number of rows 2
number of columns 2
x1 34.00 mm
x2 24.00 mm
y1 24.00 mm
y2 24.00 mm
Partial safety factors
Gamma M0 1.10
Gamma M1 1.10
Gamma Mb 1.25
Gamma Ms 1.25
Gamma Mw 1.25
Internal forces
ULS Combination number 5
N 0.26 kN
Vz 7.99 kN
My -0.00 kNm
2. Design shear resistance 2.1.Design shear resistance VRd for connection element
data
sigmaN 0.06 MPa
A 4512.00 mm^2
W 141376.00 mm^3
a 99.50 mm
VRd 266.42 kN
2.2.Design shear resistance VRd for beam
data
Av 1912.76 mm^2
Av,net 1689.56 mm^2
VRd 235.93 kN
2.3.Design shear resistance VRd for bolts in beam
Bolt resistance
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Bolt resistance
e1 24.00 mm
p1 140.00 mm
alfa,el 0.44
alfa,bw 0.44
Fb,el,Rd 122.88 kN
Fb,bw,Rd 31.74 kN
Fv,Rd 30.14 kN
data
a 99.50 mm
b 94.00 mm
d 70.00 mm
c 65.50 mm
Ip 36761.00 mm^2
VRd 67.91 kN
2.4.Design block shear resistance VRd
data
k 1.50
a1 49.00 mm
a2 155.00 mm
a3 51.00 mm
L1 49.00 mm
L2 196.09 mm
L3 240.00 mm
Lv 140.00 mm
Lv,eff 240.00 mm
Av,eff 1488.00 mm^2
VRd 183.53 kN
2.5.Critical design shear resistance VRd = 67.91 kN
3, Design tension/compression resistance NRd 3.1.Design compression/tension resistance NRd for connection element
data
A 4512.00 mm^2
A,net 3648.00 mm^2
NRd 963.93 kN
3.2.Design compression/tension resistance NRd for beam
data
A 3910.00 mm^2
A,net 3686.80 mm^2
NRd 835.32 kN
3.3.Critical design tension/compression NRd = 835.32 kN
4. Unity checks
Unity checks
VSd/VRd 0.12
NSd/NRd 0.00
The connection satisfies.
5. Weldsize calculation 5.1. Weldsize plate/column
data
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data
fu 360.00 MPa
beta 0.80
a 4.00 mm
L 99.50 mm
D 67.91 kN
N 0.26 kN
M 6.76 kNm
sigma,1 101.82 MPa
tau,1 101.82 MPa
tau,2 45.16 MPa
Prestressed bolts Node 2 : frame pinned beam-to-column connection side CD
1. Input data
Column HEA160
h 152.00 mm
b 160.00 mm
tf 9.00 mm
tw 6.00 mm
r 15.00 mm
fy 235.00 MPa
fu 360.00 MPa
Connected beam IPE240
h 240.00 mm
b 120.00 mm
tf 9.80 mm
tw 6.20 mm
r 15.00 mm
fy 235.00 MPa
fu 360.00 MPa
Bolted plate
number 2
h 188.00 mm
b 189.00 mm
t 12.00 mm
position (to top of beam) 25.00 mm
play beam/column 10.00 mm
fy 235.00 MPa
fu 360.00 MPa
Bolts M16-10.9 (DIN6914)
type prestressed
grade 10.9
fu 1000.00 MPa
As 157.00 mm^2
do 18.00 mm
S 27.00 mm
e 29.60 mm
h head 10.00 mm
h nut 13.00 mm
Bolt position
number of rows 2
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Bolt position
number of columns 2
x1 34.00 mm
x2 24.00 mm
y1 24.00 mm
y2 24.00 mm
Partial safety factors
Gamma M0 1.10
Gamma M1 1.10
Gamma Mb 1.25
Gamma Ms 1.25
Gamma Mw 1.25
Internal forces
ULS Combination number 5
N 0.26 kN
Vz 7.99 kN
My -0.00 kNm
2. Design shear resistance
2.1.Design shear resistance VRd for connection element
data
sigmaN 0.06 MPa
A 4512.00 mm^2
W 141376.00 mm^3
a 99.50 mm
VRd 266.42 kN
2.2.Design shear resistance VRd for beam
data
Av 1912.76 mm^2
Av,net 1689.56 mm^2
VRd 235.93 kN
2.3.Design shear resistance VRd for bolts in beam
Data for high strength bolts
ks 1.00
n 1.00
slip factor 0.30
Fp,Cd 109.90 kN
Ft,Sd 0.00 kN
Fs,Rd 26.38 kN
data
a 99.50 mm
b 94.00 mm
d 70.00 mm
c 65.50 mm
Ip 36761.00 mm^2
VRd 56.43 kN
2.4.Design block shear resistance VRd
data
k 1.50
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data
a1 49.00 mm
a2 155.00 mm
a3 51.00 mm
L1 49.00 mm
L2 196.09 mm
L3 240.00 mm
Lv 140.00 mm
Lv,eff 240.00 mm
Av,eff 1488.00 mm^2
VRd 183.53 kN
2.5.Critical design shear resistance VRd = 56.43 kN
3, Design tension/compression resistance NRd 3.1.Design compression/tension resistance NRd for connection element
data
A 4512.00 mm^2
A,net 3648.00 mm^2
NRd 963.93 kN
3.2.Design compression/tension resistance NRd for beam
data
A 3910.00 mm^2
A,net 3686.80 mm^2
NRd 835.32 kN
3.3.Critical design tension/compression NRd = 835.32 kN
4. Unity checks
Unity checks
VSd/VRd 0.14
NSd/NRd 0.00
The connection satisfies.
5. Weldsize calculation 5.1. Weldsize plate/column
data
fu 360.00 MPa
beta 0.80
a 4.00 mm
L 99.50 mm
D 56.43 kN
N 0.26 kN
M 5.61 kNm
sigma,1 84.62 MPa
tau,1 84.62 MPa
tau,2 37.52 MPa
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2.12 PST.07.02 – 03 : Frame pinned connection (Angles) Description A pinned connection with two angles is calculated manually in node 2 of the Tutorial Frame project. The results are compared with the results of ESA-Prima Win. Project data The following connection is calculated : The connection is composed of two angle profiles bolted symmetrically on each side of the beam’s web and to the column’s flange. The angles are made of Fe 360. The angle used to build this connection is an H60/60/6 profile bolted to the beam on each side and to the column by using normal bolts M-12(DIN601). The settings necessary to verify this connection according to EC3 are represented in the figure. The node use for the check is the column-beam connection number 2 in the Tutorial frame project. This connection is composed with a HEA160 column and an IPE 240 Beam. We assume that the most dangerous load combination is the 4th. Considering that the moment approaches 0 precision, we can say that we have a pinned connection. The forces in the connection :
N=262.4939 N Tz=7990 N M≅0 Reference Eurocode 3 : Design of steel structures
Part 1-1 : General rules and rules for buildings ENV 1993-1-1:1992 Revised Annex J ENV 19+93-1-1/pr A2
See the chapter "Manual calculation" for the manual calculation according to this reference.
0.03m
0.018
Colum
View A-A
Beam
0.01
Play
M-12(DIN601)
H60/60/6
0.03m
0.059m
0.018m
0.188m
0.025m
Column A
A
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Result See the chapter "Calculation note" for the detailed output of ESA-Prima Win. Version ESA-Prima Win 3.20.03 Input file + calculation note PST070203.epw Modules 3D Frame (PRS.11) Connect Frame – Pinned (PST.07.02) Author NEM Manual calculation 1. Bolted Angle in Beam and Column As we can see, the dimension of the column and the beam allowed only one column of two bolts on the beam and the column, conforming to the rules in the EC3 concerning the position of holes in the connected members. 2. Calculation of VRd and NRd 2.1 Calculation Design Shear Resistance VRd for Connection Element
Transversal section of the corner : 2corcorcor m002256.0th2A =⋅⋅= (2 corners)
Normal Stress : 2cor
N mN67.116353
002256.0
4939.262
A
N===σ
Flexion Module : MOMENT NO m000706.06
ht2 0W 3
2cor
pl
cor
⇔
=
⋅⋅=
Design Shear Resistance :
N7939.278261V0f
A
3V Rd2
M
2y2
N22
Rd
0
=⇔=γ
−σ+⋅
2.2 Calculation Design Shear Resistance VRd for Beam
Shear Area : ( ) 2fwfv m00191276.0tr2ttb2AA =⋅⋅++⋅⋅−=
Net Area : m00173916.0dt2AA 0wvnet =⋅⋅−=
For the calculation of VRd in the beam, we use Av because 2v
u
ynet m00124860.0A
f
fA =⋅≥
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Shear Resistance : N57.2359253
fAVRd
0M
yv =γ⋅
⋅=
2.3. Calculation Design Shear Resistance VRd for Bolt in Beam The calculation of the shear resistance for bolt in beam is based on the following equation to be solve:
0Qn
N
nI
dNa2V
I
da
In
ca2
I
ca
n
1V 2
2
2
pRd2
p
22
p2p
22
22Rd
=−+
⋅
⋅⋅⋅⋅+
⋅+
⋅
⋅⋅+
⋅+⋅
m
Where : 0.03ma = 0.094mb = 0mc = 0.076md =
22ip m011552.0rI ∑ == m018.0e1 = m152.0p1 =
( )( )beam,Rd,bcor,Rd,bRd,v F;Fmin,F2minQ ⋅= =22957.71N for two corners, where
• N16224Af6.0
FMb
subV dR
=γ
⋅⋅=
• N71.22957tdf5.2
FMb
upBeam,Rd,b =
γ
⋅⋅⋅α⋅=
428.01;f
f;
4
1
d3
p;
d3
eminwith
u
ub
0
1
0
1p =
−=α
• N28.44434tdf5.2
FMb
corupcor,Rd,b =
γ
⋅⋅⋅α⋅=
428.01;f
f;
4
1
d3
p;
d3
eminwith
u
ub
0
1
0
1p =
−=α
By solving the second-degree equation, we find N41.42718VRd = 2.4. Calculation Design Block Shear Resistance The design value of the effective resistance to block shear is determined by the following expression :
eff,veffv,M
eff,vyRd,eff LtA with
3
AfV
0
⋅=γ⋅
⋅=
We determined the effective shear area Av,eff as follows :
m043.0a1 = m045.0a 2 = m02.0a 3 =
m152.0aahL 21v =−−=
( )
( ) m24.0324.0;24.0min
f
fdnaaL;aaLminL
y
u031v31v3
==
⋅⋅−++++=
d
b
a
ri
a1
Lv
a3
a2
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( ) m043.0d5;aminL 011 =⋅=
( )
5.0k with
m019914.0f
fdkaL
y
u022
=
=⋅⋅−=
( ) m2149.0L;LLLminL 321veff,v =++=
2
eff,v m001332.0A =
N14.1643513
AfV
0M
eff,vyRd,eff =
γ⋅
⋅=
2.5. Calculation Design Shear Resistance for Bolts in Column The profile use in the present connection is a H60/60/6. To determine the design shear resistance for bolts in the flange of the column, we use a iterative process with hD as parameter until we reach a equilibrium :
γγ=σ
00 M
cor,y
M
beam,yD
f,
fmin
We’ll only consider the check for the final value of hD. As represented in the figure, we have the following data :
m008.0r = m03.0a = m006.0s =
m0128436.0s577.1r4227.0b =⋅+⋅= m0028436.0Playbbs =−=
m011.0h D = 22ipD m029194.0rID
==∑
We compute : 0951.1anI
aK
2pD
=⋅−
=
Corne
Beam
Column
Play
α
s b
r
bs
σD
View A-A
hD
σD
d
Web Beam
Corner A A
a
e
p1
Flange Column
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We define xj=0.03m and zj=0.165m respectively as the maximum horizontal distance between bolts and d and the maximum vertical distance between the bolts and d. Its corresponds to the further bolts how is submitted to the higher force.
( ) 5.0xaKn
1A j =−⋅+= 18069.0zKB j =⋅=
N16224Fn4.1
N1F,FminQ
Rd,tRd,vRd,b =
⋅⋅−⋅= where:
• N16224Af6.0
FMb
subcor,V dR
=γ
⋅⋅= and N24336
Af9.0F
Mb
subRd,t =
γ
⋅⋅=
• N2.22187tdf5.2
FMb
corupcor,Rd,b =
γ
⋅⋅⋅α⋅=
• N28.33281tdf5.2
FMb
flangeupflange,Rd,b =
γ
⋅⋅⋅α⋅=
428.01;f
f;
4
1
d3
p;
d3
eminwith
u
ub
0
1
0
1p =
−=α
With this values, we have :
N94.61032BA
Q2V
22ColFlange,Rd =
+
⋅= ∑ ∑ =⋅⋅= N64.5948zKVQ jRdh
2DD
hD m
N89.209194259bh
Q=
⋅=σ∑
2.6. Calculation Design Tension Resistance NRd for Connection Element
Area : 2m002256.0ht2A =⋅⋅=
Net Area : 20net m001920.0d2t2AA =⋅⋅⋅−=
Tension Resistance:
γ
⋅⋅
γ
⋅=
1
net
0 M
u
M
yRd
fA9.0,
fAminN ( ) N63.481963277.565527,63.481963min ==
2.7. Calculation Design Tension Resistance NRd for Beam
Area : 2m003910.0A =
Net Area : 20net m0037364.0dt2AA =⋅⋅−=
Tension Resistance :
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γ
⋅⋅
γ
⋅=
1
net
0 M
u
M
yRd
fA9.0,
fAminN ( ) N175.83531863.1100539,18.835318min ==
2.8. Calculation Design Tension Resistance NRd As prescribed in EC3 Annexe J, we can substituted a bolt joint by a equivalent T-stub to model the resistance of the column flange. The length of the considered T-stub is note leff. 2.8.1. T-Stub Model: Calculation of the equivalent length First, we have to calculate the length leff in the corner for the equivalent T-Stub model by considering the bolts individually (note I) or as part of a group of bolt-rows (note g). Each of this case we’ll be calculate for a circular pattern (note cp) and a non-circular pattern (note nc). We define in the following table p as the pitch of the holes and the parameters m and e as represented in the figures.
Bolt for Element
Start Bolt for Element End Bolt for Element
2tam cor−=
0.027m
( )1i,cp,eff e2m;m2minl ⋅+⋅π⋅π⋅= leff,cp,i,e1=0.1208 leff,cp,i,e2=0.1208
( )1i,nc,eff ee625.0m2;e25.1m4minl +⋅+⋅⋅+⋅= leff,nc,i,e1=0.09075 leff,nc,i,e2=0.09075
( )11g,cp,eff pe2;pmminl +⋅+⋅π= leff,cp,g,e1=0.188 leff,cp,g,e2=0.188
( )p5.0e625.0m2;p5.0eminl 1g,nc,eff ⋅+⋅+⋅⋅+= leff,nc,g,e1=0.094 leff,nc,g,e2=0.094
Bolt for Column-Flange
Start Bolt for Column End Bolt for Column
r8.02t
2t
am col,wbeam,w ⋅−−+= 0.0181m
( )m;m2minl i,cp,eff ⋅π⋅π⋅= leff,cp,i,col1=0.0.1137 leff,cp,i,col2=0.1137
P=0.152
e1=0.018
mCor
eColumn=0.022625
mCol a=0.03m
eelement=0.03
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( )e625.0m2;e25.1m4minl i,nc,eff ⋅+⋅⋅+⋅= leff,nc,i,col1=0.14976 leff,nc,i,col2=0.1497
( )1g,cp,eff p;pmminl +⋅π= leff,cp,g,col1=0.20886 leff,cp,g,col2=0.20886
( )p5.0e625.0m2;p5.0minl g,nc,eff ⋅+⋅+⋅⋅= leff,cp,g,col1=0.15088 leff,cp,g,col2=0.15088
ELEMENT COLUMN
Bolt Consider Individually Start Bolt End Bolt Start Bolt End Bolt
MODE1 ( )i,nc,effi,cp,eff1,eff l,lminl =
0.0907 0.0907 0.1137 0.1137
MODE 2
i,nc,eff2,eff ll = 0.0907 0.0907 0.14977 0.14977
Bolt considered as a part of a group bolt-rows
MODE 1
( ∑∑∑ = g,nc,effg,cp,eff1,eff l,lminl
Min(0.376, 0.188)=0.188
Min(0.4177,0.30177)=
0.30177
MODE 2
∑∑ = g,nc,eff2,eff ll
0.188
0.30177
2.8.2. Failure Mode According to EC3, to obtain the design tension resistance of a connection represented by an equivalent T-Stub flange model, it is necessary to determine the maximum resistance of each bolt-group (element and column) and for each bolt-row. Bolt-Group:
ELEMENT
COLUMN
0
r
M
y2
1,effRd,1,pl
ftl25.0M
γ
⋅⋅⋅=
∑
361.4727Nm
1305.5196Nm
0M
y2
2,effRd,2,pl
ftl25.0M
γ
⋅⋅⋅=
∑
361.4727Nm
1305.5196Nm
Mb
sbolt,uRd,tRd,t
Af9.0FB
γ
⋅⋅==
24336N
24336N
Rd,tboltRd,t BnB ⋅=∑ 97344N
97344N
FAILURE MODE 1
m
M4F
Rd,1,plRd,T
⋅=
53551.51N
288512.634N
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FAILURE MODE 2
nm
BnM2F
Rd,tRd,2,plRd,T +
⋅+⋅=
∑
63916.93N
118193.91N
FAILURE MODE 3
∑= Rd,tRd,T BF
97344N
97344N
Note: nElement=emin=0.03 nColumn=emin=0.022625 Each bolt-row considered individually:
ELEMENT
1ST
ROW
2ND ROW
0M
y2core,1,eff
Rd,1,pl
ftl25.0M
γ
⋅⋅⋅=
174.487Nm
174.487Nm
0M
y2core,2,eff
Rd,2,pl
ftl25.0M
γ
⋅⋅⋅=
174.487Nm
174.487Nm
FAILURE MODE 1
m
M4F
Rd,1,plRd,T
⋅=
25850N
25850N
FAILURE MODE 2
nm
BnM2F
Rd,tRd,2,plRd,T +
⋅+⋅=
∑
31739.21N
31739.21N
FAILURE MODE 3
∑= Rd,tRd,T BF
48672N
48672N
COLUMN
1ST
ROW
2ND ROW
0M
y2fcolcol,1,eff
Rd,1,pl
ftl25.0M
γ
⋅⋅⋅=
491.9926Nm
491.9926Nm
0M
y2fcolcol,2,eff
Rd,2,pl
ftl25.0M
γ
⋅⋅⋅=
647.947Nm
647.947Nm
( ) N51.53551FminF Rd,TGroup,Element,Rd,T ==
( ) N97344FminF Rd,TGroup,Column,Rd,T ==
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FAILURE MODE 1
m
M4F
Rd,1,plRd,T
⋅=
108727.65N
108727.65N
FAILURE MODE 2
nm
BnM2F
Rd,tRd,2,plRd,T +
⋅+⋅=
∑
58860.601N
58860.601N
FAILURE MODE 3
∑= Rd,tRd,T BF
48672N
48672N
The previous table lead to the determination of the design resistance tension for the column flange, the column web and the connected element:
( ) ( )
( ) ( )
( )
0)(M connection pinned ain 0 because 1 where
6826.386820ftl,lmin
N
N9734497344;97344minF,FminN
N5170051.53551;51700minF,FminN
0M
ywbColumn,2,effColumn,1,effColumnWeb,Rd
Group,Column,Rd,TBoltrow,Column,Rd,TBoltColumn,Rd
Group,Element,Rd,TBoltrow,Element,Rd,TtBoltElemen,Rd
==β=ρ
=γ
⋅⋅⋅ρ=
===
===
∑∑
2.9. Unity Check The most critical design shear resistance and design tension resistance is used to calculate the unity check:
Shear Unity Check : 1187.041.42718
7990
V
V
Rd
Sd ≤== ⇒ Connection OK for Shear
Tension Unity Check : 110077.551700
4939.262
N
N 3
Rd
Sd ≤⋅== − ⇒Connection OK for Tension
( )( )∑ =+==
∑ =+==
N973444867248672FminF
N517002585025850FminF
Rd,TBoltrow,Column,Rd,T
Rd,TBoltrow,Element,Rd,T
ESA-Prima Win Steel and timber design benchmarks
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Calculation note Node 2 : frame pinned beam-to-column connection side CD
1. Input data
Column HEA160
h 152.00 mm
b 160.00 mm
tf 9.00 mm
tw 6.00 mm
r 15.00 mm
fy 235.00 MPa
fu 360.00 MPa
Connected beam IPE240
h 240.00 mm
b 120.00 mm
tf 9.80 mm
tw 6.20 mm
r 15.00 mm
fy 235.00 MPa
fu 360.00 MPa
Angle H60/60/6
number 2
h 188.00 mm
b 59.00 mm
t 6.00 mm
position (to top of beam) 25.00 mm
play beam/column 10.00 mm
fy 235.00 MPa
fu 360.00 MPa
Bolts in beam M-12 (DIN601)
type normal
grade 4.6
fu 400.00 MPa
As 84.50 mm^2
do 14.00 mm
S 19.00 mm
e 20.90 mm
h head 8.00 mm
h nut 10.00 mm
Bolt position in beam
number of rows 2
number of columns 1
x1 30.00 mm
x2 29.00 mm
y1 18.00 mm
y2 18.00 mm
Bolts in column M-12 (DIN601)
type normal
grade 4.6
fu 400.00 MPa
ESA-Prima Win Steel and timber design benchmarks
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Bolts in column M-12 (DIN601)
As 84.50 mm^2
do 14.00 mm
S 19.00 mm
e 20.90 mm
h head 8.00 mm
h nut 10.00 mm
Bolt position in column
number of rows 2
number of columns 1
x1 30.00 mm
x2 30.00 mm
y1 18.00 mm
y2 18.00 mm
Partial safety factors
Gamma M0 1.10
Gamma M1 1.10
Gamma Mb 1.25
Gamma Ms 1.25
Gamma Mw 1.25
Internal forces
ULS Combination number 5
N 0.26 kN
Vz 7.99 kN
My -0.00 kNm
2. Design shear resistance 2.1.Design shear resistance VRd for connection element
data
sigmaN 0.12 MPa
A 2256.00 mm^2
VRd 278.26 kN
2.2.Design shear resistance VRd for beam
data
Av 1912.76 mm^2
Av,net 1739.16 mm^2
VRd 235.93 kN
2.3.Design shear resistance VRd for bolts in beam
Bolt resistance
e1 18.00 mm
p1 152.00 mm
alfa,el 0.43
alfa,bw 0.43
Fb,el,Rd 44.43 kN
Fb,bw,Rd 22.96 kN
Fv,Rd 16.22 kN
data
a 30.00 mm
b 94.00 mm
ESA-Prima Win Steel and timber design benchmarks
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data
d 76.00 mm
c 0.00 mm
Ip 11552.00 mm^2
VRd 42.71 kN
2.4.Design block shear resistance VRd
data
k 0.50
a1 43.00 mm
a2 20.00 mm
a3 45.00 mm
L1 43.00 mm
L2 19.91 mm
L3 240.00 mm
Lv 152.00 mm
Lv,eff 214.91 mm
Av,eff 1332.47 mm^2
VRd 164.35 kN
2.5.Design shear resistance VRd for bolts in column
Bolt resistance
e1 18.00 mm
p1 152.00 mm
alfa,el 0.43
alfa,cf 0.43
Fb,el,Rd 22.22 kN
Fb,cf,Rd 33.33 kN
Fv,Rd 16.22 kN
Ft,Rd 24.34 kN
data
hd 11.00 mm
bd 2.84 mm
sigma,d 209.19 MPa
a 30.00 mm
Ipd 29194.00 mm^2
zk 165.00 mm
xj 30.00 mm
K 1.10e-003 1/mm
A 5.00e-001
B 1.81e-001
VRd 61.03 kN
2.6.Critical design shear resistance VRd = 42.71 kN
3, Design tension/compression resistance NRd
3.1.Design compression/tension resistance NRd for connection element
data
A 2256.00 mm^2
A,net 1920.00 mm^2
NRd 481.96 kN
3.2.Design compression/tension resistance NRd for beam
data
A 3910.00 mm^2
A,net 3736.40 mm^2
NRd 835.32 kN
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3.3.Design tension resistance NRd
(effective lengths in mm, resistance in kN)
Bt,Rd = 24.34 kN
3.3.1.Column flange
kfc = 1.00
row p (p1+p2) e m n
1 152.00 61.90 18.10 22.63
2 152.00 61.90 18.10 22.63
row leff,cp,i leff,nc,i leff,cp,g leff,nc,g
1 113.73 149.77 208.86 150.89
2 113.73 149.77 208.86 150.89
NRd data
Som Fti,fc,Rd 97.34 kN
Ftg,fc,Rd 97.34 kN
Ft,wc,Rd 386.82 kN
3.3.2.Connection element
row p (p1+p2) e m n
1 152.00 30.00 27.00 30.00 18.00
2 152.00 30.00 27.00 30.00 18.00
row leff,cp,i leff,nc,i leff,cp,g leff,nc,g
1 120.82 90.75 188.00 94.00
2 120.82 90.75 188.00 94.00
NRd data
Som Fti,el,Rd 51.70 kN
Ftg,el,Rd 53.55 kN
3.4.Critical design tension/compression NRd = 51.70 kN
4. Unity checks
Unity checks
VSd/VRd 0.19
NSd/NRd 0.01
The connection satisfies.
ESA-Prima Win Steel and timber design benchmarks
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2.13 PST.07.02 – 04 : Frame pinned connections (Short endplate) Description A pinned connection with a short endplate is calculated manually in node 2 of the Tutorial Frame project. The results are compared with the results of ESA-Prima Win. Project data The following connection is calculated :
The connection is composed of a endplate made in Fe 360. This endplate is bolted to column’flange and welded to beam’s web. The node used for the check is the column-beam connection number 2 in the Tutorial Frame project. This connection is composed with a HEA160 column and an IPE 240 Beam. We assume that the most dangerous load combination is the 4th. Considering that the moment approaches 0 precision, we can say that we have a pinned connection. The forces in the connection :
N=262.4939 N Tz=7990 N M≅0 Reference Eurocode 3 : Design of steel structures
Part 1-1 : General rules and rules for buildings
Colum
0.03m
0.018
View A-A
M-12(DIN601)
bendplate=0.159
0.86m
Beam
Play
Column
Endplate
Weld Part
25 mm
0.188mm
A
A
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ENV 1993-1-1:1992 Revised Annex J ENV 19+93-1-1/pr A2
See the chapter "Manual calculation" for the manual calculation according to this reference. Result See the chapter "Calculation note" for the detailed output of ESA-Prima Win. Version ESA-Prima Win 3.20.03 Input file + calculation note PST070204.epw Modules 3D Frame (PRS.11) Connect Frame – Pinned (PST.07.02) Author NEM/CVL Manual calculation 1. Dimensions and Position of the Endplate This type of frame pinned connection is composed by a plate placed between the beam and the column. The plate is bolted to the flange’s column by normal bolts and weld to the web’s beam. The following figure specifies the settings. We must note that the disposition of the bolts does not satisfy the rules imposed by EC3. In spite of this, we continue the control this connection so that we can use 3 rows of bolts and the specific calculation that implies (intermediate row of bolts). The solution would be to place 2 rows of bolts in place of three. 2. Calculation of VRd and NRd 2.1. Calculation design local shear resistance VRd for beam
Transversal section of the corner : 2beamwebEndplEndpl m0011656.0thA =⋅=
Normal stress : 2Endpl
N mN669.225200
0011656.0
4939.262
A
N===σ
Flexion module : MOMENT NO 0Wpl ⇔=
Design Shear Resistance : 0f
A
3V
2M
2y2
N22
Rd
0
=γ
−σ+⋅
By solving this second degree, we obtain : 548.143768VRd =
ESA-Prima Win Steel and timber design benchmarks
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2.2. Calculation Design Shear Resistance VRd for Bolt in Column The calculation of the design shear resistance for bolt in the column is based on the following expression:
N002.97219F,F4.1n
N1FminV Rd,b
Rd,tRd,vRd =
⋅⋅−⋅= , where
Where : 0.018me1 = 0.152mp1 = 6n =
• N16224Af6.0
FMb
subV dR
=γ
⋅⋅=
• N24336Af9.0
FMb
subRd,t =
γ
⋅⋅=
• N71.33325tdf5.2
FMb
upColumn,Rd,b =
γ
⋅⋅⋅α⋅=
4285.01;f
f;
4
1
d3
p;
d3
eminwith
u
ub
0
1
0
1p =
−=α
• N285.44434tdf5.2
FMb
corupEndpl,Rd,b =
γ
⋅⋅⋅α⋅=
4285.01;f
f;
4
1
d3
p;
d3
eminwith
u
ub
0
1
0
1p =
−=α
2.3. Calculation Design Tension Resistance NRd for Beam
Area of the element: 2wBeamEndpl m0011655.0thA =⋅=
Tension Resistance: N18.24899318fA
N0M
yRd =
γ
⋅=
2.4. Calculation Design Tension Resistance NRd for Bolt and Column Flange As prescribed in EC3 Annexe J, we can substituted a bolt joint by a equivalent T-stub to model the resistance of the column flange. The length of the considered T-stub is note leff. 2.4.1. T-Stub Model: Calculation of the equivalent length The sheme follows to calculate the length leff for the equivalent T-Stub model is the same that we used in bolted angle (Chap.4). As we’ve seen, the computing of the equivalent length is quite complicate by the amount of value to determine. To simplify the presentation, we’ll only calculate leff for the intermediate bolt considered individually and as part of a group of bolt-rows. Each of this case we’ll be calculate for a circular pattern (note cp) and a non-circular pattern (note nc). We define in the following table p as the pitch of the holes and the parameters m and n as represented in the figures. The other equivalent length are calculated in the same way than in the bolted angle connection.
p1=0.076
e1=0.018
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Bolt for Element and Column Flange
Intermediate Bolt for Element Intermediate Bolt for Column Flange
m 0.03537m 0.028m
m2l i,cp,eff ⋅π⋅= leff,cp,i,e1=0.222 leff,cp,i,e2=0.1759
e25.1m4l i,nc,eff ⋅+⋅= leff,nc,i,e1=0.1871 leff,nc,i,e2=0.177
p2l g,cp,eff ⋅= leff,cp,g,e1=0.152 leff,cp,g,e2=0.152
pl g,nc,eff = leff,nc,g,e1=0.076 leff,nc,g,e2=0.076
2.4.2. Failure Mode The maximum resistance of each bolt group (element and column) and for each bolt-row are calculated in the same we that in the bolted angle. The results are: Bolt-Group: ( ) N989.114384FminF Rd,TGroup,Endpl,Rd,T ==
( ) N08.126304FminF Rd,TGroup,Column,Rd,T ==
Bolt-rows individually: ( )∑ == N576.145856FminF Rd,TBoltrow,Endplt,Rd,T
( )∑ == N146016FminF Rd,TBoltrow,Column,Rd,T
The previous results lead to the determination of the design resistance tension for the column flange, the column web and the connected element:
eelement=0.0365 eColumn0.052
m
P=0.076
e1=0.018
ESA-Prima Win Steel and timber design benchmarks
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( )
( )
( )N183.421718
ftl,lminN
N08.126304F,FminN
N989.114384F,FminN
0M
ywbColumn,2,effColumn,1,effColumnWeb,Rd
Group,Column,Rd,TBoltrow,Column,Rd,TBoltColumn,Rd
Group,Element,Rd,TBoltrow,Element,Rd,TBoltEndplt,Rd
=γ
⋅⋅⋅ρ=
==
==
∑∑
2.5. Unity Check The most critical design shear resistance and design tension resistance is used to calculate the unity check:
Shear Unity Check : 10821.0002.97219
7990
V
V
Rd
Sd ≤== ⇒ Connection OK for Shear
Tension Unity Check : 11029.2989.114384
4939.262
N
N 3
Rd
Sd ≤⋅== − ⇒Connection OK for Tension
2.6. Weldsize Endplate/Beam
Weldsize : a=0.04 m Moment: M=0 (Pinned Frame) )f;min(ff Columnu,Endplu,uw =
Normal force : N=262.4939
Shear force : 002.97219VD Rd == N
Stress calculation :
211 mN524.1237800
la22
N
W
M
la22
N=+
⋅⋅⋅=+
⋅⋅⋅=τ−=σ where l=0.188m
22 mN474.64640294
la2
D=
⋅⋅=τ
Unity Check : ( )
11029.4f
and 1311.0f
34
M
u
1
Mw
u
222
ww
211 ≤⋅=
γ
σ≤=
γ⋅β
τ+τ⋅+σ− where βw=0.8
Calculation note Node 2 : frame pinned beam-to-column connection side CD
1. Input data
Column HEA160
h 152.00 mm
b 160.00 mm
tf 9.00 mm
tw 6.00 mm
r 15.00 mm
fy 235.00 MPa
fu 360.00 MPa
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Connected beam IPE240
h 240.00 mm
b 120.00 mm
tf 9.80 mm
tw 6.20 mm
r 15.00 mm
fy 235.00 MPa
fu 360.00 MPa
Endplate
h 188.00 mm
b 159.00 mm
t 12.00 mm
position (to top of beam) 25.00 mm
fy 235.00 MPa
fu 360.00 MPa
Bolts in beam M-12 (DIN601)
type normal
grade 4.6
fu 400.00 MPa
As 84.50 mm^2
do 14.00 mm
S 19.00 mm
e 20.90 mm
h head 8.00 mm
h nut 10.00 mm
Bolt position in column
number of rows 3
spacing 86.00 mm
y1 18.00 mm
y2 18.00 mm
Partial safety factors
Gamma M0 1.10
Gamma M1 1.10
Gamma Mb 1.25
Gamma Ms 1.25
Gamma Mw 1.25
Internal forces
ULS Combination number 5
N 0.26 kN
Vz 7.99 kN
My -0.00 kNm
2. Design shear resistance 2.1.Design local shear resistance VRd for beam
data
sigmaN 0.23 MPa
A 1165.60 mm^2
VRd 143.77 kN
2.2.Design shear resistance VRd for bolts in column
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Bolt resistance
e1 18.00 mm
p1 76.00 mm
alfa,el 0.43
alfa,cf 0.43
Fb,el,Rd 44.43 kN
Fb,cf,Rd 33.33 kN
Fv,Rd 16.22 kN
Ft,Rd 24.34 kN
data
n 6
VRd 97.22 kN
2.3.Critical design shear resistance VRd = 97.22 kN
3, Design tension/compression resistance NRd 3.1.Design tension/compression resistance NRd for beam web
data
A 1165.60 mm^2
NRd 249.01 kN
3.2.Design tension resistance NRd
(effective lengths in mm, resistance in kN)
Bt,Rd = 24.34 kN
3.2.1.Column flange
kfc = 1.00
row p (p1+p2) e m n
1 76.00 52.00 28.00 35.00
2 76.00 52.00 28.00 35.00
3 76.00 52.00 28.00 35.00
row leff,cp,i leff,nc,i leff,cp,g leff,nc,g
1 175.93 177.00 163.96 126.50
2 175.93 177.00 152.00 76.00
3 175.93 177.00 163.96 126.50
NRd data
Som Fti,fc,Rd 146.02 kN
Ftg,fc,Rd 126.30 kN
Ft,wc,Rd 421.72 kN
3.2.2.Connection element
row p (p1+p2) e m n
1 76.00 36.50 35.37 36.50 18.00
2 76.00 36.50 35.37 36.50 -
3 76.00 36.50 35.37 36.50 18.00
row leff,cp,i leff,nc,i leff,cp,g leff,nc,g
1 147.13 111.56 112.00 56.00
2 222.26 187.12 152.00 76.00
3 147.13 111.56 112.00 56.00
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NRd data
Som Fti,el,Rd 145.86 kN
Ftg,el,Rd 114.38 kN
3.3.Critical design tension/compression NRd = 114.38 kN
4. Unity checks
Unity checks
VSd/VRd 0.08
NSd/NRd 0.00
The connection satisfies.
5. Weldsize calculation 5.1. Weldsize endplate/column
data
fu 360.00 MPa
beta 0.80
a 4.00 mm
L 0.00 mm
D 97.22 kN
N 0.26 kN
M 0.00 kNm
sigma,1 0.12 MPa
tau,1 0.12 MPa
tau,2 64.64 MPa
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2.14 PST.07.02 - 05 : Frame pinned connection (Angles) with column minor axis Description This benchmark consists in a manual verification of a connection by using the minor axis theory combined with Annex J Revised EC3. Those results are compared with the design calculation of EPW 3.20 Project data See input file. Reference Eurocode 3 : Design of steel structures
Part 1-1 : General rules and rules for buildings ENV 1993-1-1:1992 Revised Annex J ENV 19+93-1-1/pr A2
See the chapter "Manual calculation" for the manual calculation according to this reference. Result Manual calculation EPW FPunching,Rd,l1,ind 331.8 kN 331.87 kN FPunching,Rd,l1,group 402.8 kN 402.75 kN FPunching,Rd,l2 185.5 kN 185.53 kN FComb,Rd,ind 105.8 kN 105.81 kN FComb,Rd,group 123.6 kN 123.69 kN See the chapter "Calculation note" for the detailed output of ESA-Prima Win. Version ESA-Prima Win 3.20.03 Input file + calculation note PST070205.epw Modules 2D Frame (PRS.01) Connect Frame - Rigid (PST.07.02) Author NEM - CVL Manual calculation The following connection is composed with a angle attached respectively on the web beam and the web column through 2 bolt rows. The angle, symmetrically bind around the beam flange, is composed of the profile L70/70/5. The angle is made of steel with following properties: S235 and is characterised by properties described in the EPW results
ESA-Prima Win Steel and timber design benchmarks
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document. The present document assumes that all the tensions, the stresses and the most dangerous combination computed by EPW are right. The node use for the check is the minor axis column-beam connection number 4 in PST070205.epw. This connection is composed with a HEA180 column and a IPE240 beam. We assume that the most dangerous combination is the 4th. The verification concerns only the weak axis part. For other controls from Annex J Revised EC3, other benchmarks are available.
AB
IPE240
Section AB
HEA18025
27
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70
18
8
35
14
16
0
2 x M-12 (DIN601)
70
18
8
188
70
14 160
35
2 x M-12 (DIN601)
188
70
Local failure: Punching Punching Loading case 1 The connection is submitted to tension. The bolt will transmit the forces through the column web. Individual bolt row
mm95.192
199.20
2
dmed m =
+=
+=
mm95.17d9.0c m =⋅=
mm2.76x2tmm702b 2wbeam0 =⋅−+⋅=
mm15.94d9.0bb m0indivi =⋅+=
ESA-Prima Win Steel and timber design benchmarks
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( )kN8.331n
3
ftcb2nF boltrow
0M
ywcboltrowindividual,1LRd,Punching =⋅
γ⋅
⋅⋅+⋅=⋅
Bolt pattern group
mm2.76d9.0bb m0group =⋅+=
mm160yyhc 21angle0 =−−=
mm95.177d9.0cc m0groupe =⋅+=
( )kN75.402
3
ftcb2F
0M
ywcgroup,Rd,Punching 1L
=γ⋅
⋅⋅+⋅=
Punching Loading case 2
n=2 bolts row*nbolt row=4
kN5.1853
ftdnF
0M
ywcmindividual,Rd,Punching =
γ⋅
⋅⋅⋅π⋅=
kN5.1853
ftdnF
0M
ywcmgroup,Rd,Punching =
γ⋅
⋅⋅⋅π⋅=
Combined punching and bending
Individual bolt row
mm152thd fcc =−=
mm5.1294
r32dL =⋅−=
mm3.35bLa individualindividual =−=
1k5.0L
cbindi
indiindi =⇒>+
0mm1.75 Lt
c8.211
c
t82.01Lb
2
wc
2indi
2indi
2wc
indi,m >=
⋅++⋅−⋅=
mm3.9bL
bb
L
t
L
c23.0
L
tLx
indi,m
indi,mindi3
1
wcindi3
2
wcindi,0 =
−
−⋅
⋅⋅+
⋅=
( )[ ] bb if mm3.8c4xaL2
t3ca5..1aax mindiindi,0indi
wcindiindi
2indiindiindi >=⋅++⋅⋅π⋅
⋅+⋅⋅−+−=
( )( )
kN8.105n1
xat3
xxc5.1
xa
c2xaLftkF boltrow
0Mindiindiwc
2indiindiindi
indiindi
indiindiindiy
2wcindiRd,Comb =⋅
γ⋅
+⋅⋅
+⋅⋅+
+
⋅++⋅⋅π⋅⋅⋅=
Bolt pattern group
mm3.35bLa group =−=
1k5.0L
cb groupgroup=⇒>
+
ESA-Prima Win Steel and timber design benchmarks
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112.8mm Lt
c8.211
c
t82.01Lb
2
wc
2group
2
2wc
group,m =
⋅++⋅−⋅=
mm4.35bL
bb
L
t
L
c23.0
L
tLx
group,m
group,mgroup3
1
wcgroup3
2
wcgroup,0 −=
−
−⋅
⋅⋅+
⋅=
groupm,groupgroup bb 0x <=
( )( ) kN
xat
xxc
xa
cxaLftkF
Mgroupgroupwc
groupgroupgroup
groupgroup
groupgroupgroup
ywcgroupgroupRdComb 6.1231
3
5.12
0
22
,, =⋅
+⋅⋅
+⋅⋅+
+
⋅++⋅⋅⋅⋅⋅=
γ
π
Calculation note Node 4 : frame pinned beam-to-column connection side AB
1. Input data
Column HEA180
h 171.00 mm
b 180.00 mm
tf 9.50 mm
tw 6.00 mm
r 15.00 mm
fy 235.00 MPa
fu 360.00 MPa
Connected beam IPE240
h 240.00 mm
b 120.00 mm
tf 9.80 mm
tw 6.20 mm
r 15.00 mm
fy 235.00 MPa
fu 360.00 MPa
Angle L70/70/5
number 2
h 188.00 mm
b 70.00 mm
t 5.00 mm
position (to top of beam) 25.00 mm
play beam/column 10.00 mm
fy 235.00 MPa
fu 360.00 MPa
Bolts in beam M-12 (DIN601)
type normal
grade 4.6
fu 400.00 MPa
As 84.50 mm^2
do 14.00 mm
S 19.00 mm
e 20.90 mm
h head 8.00 mm
h nut 10.00 mm
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Bolt position in beam
number of rows 2
number of columns 1
x1 35.00 mm
x2 35.00 mm
y1 14.00 mm
y2 14.00 mm
Bolts in column M-12 (DIN601)
type normal
grade 4.6
fu 400.00 MPa
As 84.50 mm^2
do 14.00 mm
S 19.00 mm
e 20.90 mm
h head 8.00 mm
h nut 10.00 mm
Bolt position in column
number of rows 2
number of columns 1
x1 35.00 mm
x2 35.00 mm
y1 14.00 mm
y2 14.00 mm
Partial safety factors
Gamma M0 1.10
Gamma M1 1.25
Gamma Mb 1.25
Gamma Ms 1.25
Gamma Mw 1.25
Internal forces
ULS Combination number 5
N 0.38 kN
Vz 23.74 kN
My -0.00 kNm
Warning : Bending moment is present !
2. Design shear resistance 2.1.Design shear resistance VRd for connection element
data
sigmaN 0.20 MPa
A 1880.00 mm^2
VRd 231.88 kN
2.2.Design shear resistance VRd for beam
data
Av 1912.76 mm^2
Av,net 1739.16 mm^2
VRd 235.93 kN
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2.3.Design shear resistance VRd for bolts in beam
Bolt resistance
e1 14.00 mm
p1 160.00 mm
alfa,el 0.33
alfa,bw 0.33
Fb,el,Rd 28.80 kN
Fb,bw,Rd 17.86 kN
Fv,Rd 16.22 kN
data
a 35.00 mm
b 94.00 mm
d 80.00 mm
c 0.00 mm
Ip 12800.00 mm^2
VRd 32.72 kN
2.4.Design block shear resistance VRd
data
k 0.50
a1 39.00 mm
a2 25.00 mm
a3 41.00 mm
L1 39.00 mm
L2 27.57 mm
L3 240.00 mm
Lv 160.00 mm
Lv,eff 226.57 mm
Av,eff 1404.76 mm^2
VRd 173.27 kN
2.5.Design shear resistance VRd for bolts in column
Bolt resistance
e1 14.00 mm
p1 160.00 mm
alfa,el 0.33
alfa,cf 0.33
Fb,el,Rd 14.40 kN
Fb,cf,Rd 17.28 kN
Fv,Rd 16.22 kN
Ft,Rd 24.34 kN
data
hd 18.00 mm
bd 1.69 mm
sigma,d 201.63 MPa
a 35.00 mm
Ipd 29870.50 mm^2
zk 165.50 mm
xj 35.00 mm
K 1.28e-003 1/mm
A 5.00e-001
B 2.11e-001
VRd 53.06 kN
2.6.Critical design shear resistance VRd = 32.72 kN
3, Design tension/compression resistance NRd
3.1.Design compression/tension resistance NRd for connection element
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data
A 1880.00 mm^2
A,net 1600.00 mm^2
NRd 401.64 kN
3.2.Design compression/tension resistance NRd for beam
data
A 3910.00 mm^2
A,net 3736.40 mm^2
NRd 835.32 kN
3.3.Design tension resistance NRd
(effective lengths in mm, resistance in kN)
3.3.1. Column web in tension
NRd individual bolt row local punching
# bolt row 2
dm 19.95 mm
b0 76.20 mm
b ind 94.15 mm
c ind 17.95 mm
FPunch,Rd,ind, L1 331.87 kN
FPunch,Rd,ind, L2 185.53 kN
FPunch,Rd,ind 185.53 kN
NRd Bolt group local punching
# bolt row 2
b0 76.20 mm
b gr 94.15 mm
c0 gr 160.00 mm
c gr 177.95 mm
FPunch,Rd,gr,L1 402.75 kN
FPunch,Rd,gr,L2 185.53 kN
FRd,Punch 185.53kN
NRd individual bolt row local combined
L 129.50 mm
bm ind 57.14 mm
x0 ind 9.30 mm
x ind 8.38 mm
a ind 35.35 mm
k ind 1.00
FCombRd,ind 105.81 kN
NRd Bolt group local combined
L 129.50 mm
bm gr 112.89 mm
x0 gr -35.43 mm
x gr 0.00 mm
a gr 35.35 mm
k gr 1.00
FCombRd,gr 123.69 kN
FRd,Punch 105.81kN
3.3.2.Connection element
row p (p1+p2) e m n
1 160.00 35.00 32.50 35.00 14.00
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row p (p1+p2) e m n
2 160.00 35.00 32.50 35.00 14.00
row leff,cp,i leff,nc,i leff,cp,g leff,nc,g
1 130.10 100.88 188.00 94.00
2 130.10 100.88 188.00 94.00
NRd data
Som Fti,el,Rd 33.15 kN
Ftg,el,Rd 30.90 kN
3.4.Critical design tension/compression NRd = 30.90 kN
4. Unity checks
Unity checks
VSd/VRd 0.73
NSd/NRd 0.01
The connection satisfies.
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2.15 PST 07 03 01: Hollow section joint design Annex K Description Benchmark for hollow section connection design following EC3 Annex K, Revised Annex KK and CIDECT design Guide for circular hollow section (CHS) under predominantly static loading. Project data The project tested is a Warren truss consisting of circular hollow section. To limit the number of joints, a K-joint configuration is chosen. The following dimension are assumed: Span: 36m Depth: 2,4m Purlins: 6m K angle: 38.66° The load P=108kN including the weight of the truss is applied in each node and a pin-jointed analysis is performed. Reference CIDECT Design guide for circular hollow section (CHS) joints under predominantly static loading J. Wardenier, Y. Kurobane, J.A. Packer, D.Dutta, N. Yeomans Verlag TUV Rheinland Work example p.46 See the chapter "Manual calculation" for the calculation according to this reference. Result
CIDECT EPW Manual
Unity Check 1.17 1.12 1.12
Version ESA-Prima Win 3.20.03 Input file + calculation note PST070301.epw Modules 2D Frame (PRS.01) Truss connections (PST.07.03)
φ219.1/7.1
φ139.7/4.5
φ88.9/3.6
φ193.7/6.3
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Author NEM/CVL Manual calculation
Calculation following CIDECT reference
Configuration of the node: Connection combination: CC Connection type: K joint Calculation type: K joint (one bracing in compression and one bracing in tension) Profile used: Chord: 219.1/7.1 Bracings: 139.7/4.5 88.9/3.6 Partial security factor: γM1=1.1 Geometrical data:
521.0d2
dd
0
21 =⋅
+=β
429.15t2
d
0
0 =⋅
=γ
( )mm38.91
sin2
d
sin2
d
sinsin
sin
2
deg
2
2
1
1
21
210 =θ⋅
−θ⋅
−θθ
θ+θ
+= with e=0
Range of validity
1405.0d
d2.0 and 163.0
d
d2.0 :1 Criterion
0
2
0
1 ≤=≤≤=≤
2534.12t2
d and 2552.15
t2
d :2 Criterion
2
2
1
1 ≤=≤=
°≤°=θ=θ≤° 9066.3830 :3 Criterion 11
2542.15t2
d :4 Criterion
0
0 ≤==γ
25.00d
e0.55- :5 Criterion
0
≤=≤
mm1.8ttmm38.91g :6 Criterion 21 =+≥=
22y2y1 mmN355
mmN275ff :8Criterion ≤==
RANGE OF VALIDITY OK for calculation Design of the joint The function f(n’) that appear in the chord plastification failure mode incorporates the chord prestress in the joint. The prestress in the joint designs the load in the chord not necessary for the equilibrium of the bracing load components.
220
opop mm
N38.71mm4728
N337500
A
Nf −=
−== pinned joint -> no moment in the connection
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201.0
mmN355
mmN38.71
f
f'n
2
2
0y
op−=
−==
( ) 927.0'n3.0'n3.01'nf 2 =−+=
( ) 735.11e
024.01'g,f
33.1'g5.0
2.12.0 =
+
γ⋅+⋅γ=γ
−⋅ with 87.12
t
g'g
0
==
Joint strength: Chord Plastification
( ) ( ) ( ) N13.3828431.1
'nf'g,f2.108.1sin
tfN
1M1
20yo
Rd,1 =γ
⋅⋅γ⋅β⋅+⋅θ
⋅=
N13.382843sin
sinNN
2
1Rd,1Rd,2 =
θ
θ⋅=
Unity Check: 1128.113.382843
432210
N
N
Rd
maxSd >==
Punching shear
N13294591.1
sin2
sin1td
3
fN
1M201
0yRd,1 =
γ⋅
θ⋅
θ+⋅⋅⋅
⋅π=
N8460191.1
sin2
sin1td
3
fN
1M202
0yRd,2 =
γ⋅
θ⋅
θ+⋅⋅⋅
⋅π=
Weldsize calculation
Following EC3 a1=a2≥0.87t1=4mm Calculation note
Node 14: Welded truss connection
1. Input data
Chord: Member 12 13 B219.1/7.1
d 219.00 mm
t 7.10 mm
fy 355.00 MPa
fu 510.00 MPa
Bracing: Member 24 B139.7/4.5
d 140.00 mm
t 4.50 mm
teta 38.66 deg
fy 275.00 MPa
fu 430.00 MPa
Bracing: Member 25 B88.9/3.6
d 88.90 mm
t 3.60 mm
teta 38.66 deg
fy 275.00 MPa
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Bracing: Member 25 B88.9/3.6
fu 430.00 MPa
2. General node data
Node characteristics
References CIDECT Design Guide CHS Fig.8&24
Standard configuration K Joint
Standard combination CC Type
Type of calculation K type
Gamma M1 1.10
Gamma Mw 1.00
Geometrical data
beta 0.52
gamma 15.42
e 0.00 mm
gap (g) 90.54 mm
Range of Validity
0.2<di/d0<=1.0 OK
di/2ti<=25 OK
30°<=tetai<=90° OK
gamma<=25 OK
-0.55<=e/d0<0.25 OK
g>=t1+t2 OK
fyi<= 355.00 MPa OK
3. Failure mode and results
Chord plastification
Nop -337.50 kN
fop -72.11 MPa
n' -0.20
g' 12.75
f(n') 0.93
f(gamma,g') 1.74
NRd,c Bracing 24 383.32 kN
NRd,t Bracing 25 383.32 kN
NSd,c Bracing 24 -432.21 kN
NSd,t Bracing 25 259.33 kN
Unity Check bracing 24 1.13
Unity Check bracing 25 0.68
Punching shear
NSd bracing 24 -432.21 kN
NRd bracing 24 1332.32 kN
Unity Check bracing 24 0.32
NSd bracing 25 259.33 kN
NRd bracing 25 846.03 kN
Unity Check bracing 25 0.31
4. Weldsize CalculationEC3 Annex K.5
Weldsize bracing 24
alfa weld 0.80
a 4.00 mm
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Weldsize bracing 25
alfa weld 0.80
a 4.00 mm
Critical loadcase:2 Critical NRd: 383.32 kN
Unity Check 1.13 Chord plastification
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2.16 PST 07 03 02: Hollow section joint design Annex K Description Benchmark for hollow section connection design following EC3 Annex K, Revised Annex KK and CIDECT design Guide for rectangular hollow section (RHS) under predominantly static loading. Project data The project tested is a Warren truss consisting of rectangular hollow section. To limit the number of joints, a K-joint configuration is chosen. The following dimension are assumed: Span: 36m Depth: 2,4m Purlins: 6m K angle: 38.66° We must note that the chord is composed with a square profile. The load P=108kN including the weight of the truss is applied in each node between the support and the load P=54kN on each extremity. A pin-jointed analysis is performed. Reference CIDECT Design guide for rectangular hollow section (RHS) joints under predominantly static loading J. Wardenier, Y. Kurobane, J.A. Packer, D.Dutta, N. Yeomans Verlag TUV Rheinland Work example p.46 See the chapter "Manual calculation" for the calculation according to this reference. Result
CIDECT EPW Manual
Unity Check 0.74 0.73 0.73
See the chapter "Calculation note" for the detailed output of ESA-Prima Win. Version ESA-Prima Win 3.20.03 Input file PST070302.epw
180/180/8
120/120/4
80/80/3.2
150/150/6.3
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Modules 2D Frame (PRS.01) Truss connections (PST.07.03) Author NEM - CVL Manual calculation
Calculation following CIDECT reference
Configuration of the node: Connection combination: RR square Connection type: K joint Calculation type: K joint (one bracing in compression and one bracing in tension) Profile used: Chord: 180/180/8 Bracings: 120/120/4 80/80/3.2 Partial security factor: γM1=1.1 Geometrical data:
555.0b4
hhbb
0
2121 =⋅
+++=β
25.11t2
b
0
0 =⋅
=γ
( )mm92.64
sin2
h
sin2
h
sinsin
sin
2
heg
2
2
1
1
21
210 =θ⋅
−θ⋅
−θθ
θ+θ
+= with e=0
Range of validity
3252.0t
b01.01.044.0
b
b and 3252.0
t
b01.01.066.0
b
b :1 Criterion
0
0
0
2
0
0
0
1 =⋅+≥==⋅+≥=
3522.5t
b51 :2 Criterion
0
0 ≤=≤
3.1833.0b2
bb.60 :3 Criterion
1
21 ≤=⋅
+=β≤
( ) ( ) mm1.7tt 64.92mmg and 66.015.136.0b
g22.0-10.5 :4 Criterion 21
0
=+≥==β−⋅≤=≤=β⋅
25.00d
e0.55- :5 Criterion
0
≤=≤
°≤°=θ=θ≤° 9066.3830 :6 Criterion 11
8.0696.0f
f
8.0696.0f
f
mmN355
mmN355ff :7Criterion
u2
y2
u1
y1
22y2y1
≤=
≤=
≤==
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in tensionmember 3525t
b
ncompressioin member 4.30f
E25.130
t
b :8Criterion
2
2
1y1
1
≤=
=⋅≤=
RANGE OF VALIDITY OK for calculation Design of the joint The function f(n) that appear in the chord yielding face incorporates the effect of the maximum aplied axial stress in the chord or the maximum stress due to axial force and bending moment.
220
oo mm
N199.162mm5410
N877500
A
Nf −=
−== pinned joint -> no moment in the connection
456.0
mmN355
mmN199.162
f
fn
2
2
0y
o −=−
==
( ) 97.0n4.0
3.1nf =⋅β
+=
Joint strength: Chord face yielding
( ) N76.5850641.1
nfb2
bb
sin
tf9.8N
1M
21
0
21
1
20yo
Rd,1 =γ
⋅⋅γ⋅
⋅
+⋅
θ
⋅⋅=
N76.585064sin
sinNN
2
1Rd,1Rd,2 =
θ
θ⋅=
Unity Check: 1738.0585064
432210
N
N
Rd
maxSd <==
Weldsize calculation
Following EC3 a1 ≥1.01t1=5mm a2 ≥1.01t2=4mm Calculation note Node 14: Welded truss connection
1. Input data
Chord: Member 12 13 SC180/180/8
h (in plane) 180.00 mm
b (out plane) 180.00 mm
t 8.00 mm
fy 355.00 MPa
fu 510.00 MPa
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Bracing: Member 24 SC120/120/4
h (in plane) 120.00 mm
b (out plane) 120.00 mm
t 4.00 mm
teta 38.66 deg
fy 355.00 MPa
fu 510.00 MPa
Bracing: Member 25 SC80/80/3.2
h (in plane) 80.00 mm
b (out plane) 80.00 mm
t 3.20 mm
teta 38.66 deg
fy 355.00 MPa
fu 510.00 MPa
2. General node data
Node characteristics
References Cidect Design Guide RHS Table 2&2a
Standard configuration K Joint
Standard combination RR Type
Type of calculation K type
Gamma M1 1.10
Gamma Mw 1.00
Geometrical data
beta 0.56
gamma 11.25
e 0.00 mm
gap (g) 64.92 mm
Range of Validity
hi/b0&bi/b0>=0.1+0.01b0/t0 & beta>=0.35 OK
15<=b0/t0<=35 OK
0.6<=b1+b2/2b1<=1.3 OK
0.5(1-Beta)<=g/t0<=1.5(1-Beta) g>=t1+t2 OK
-0.55<=e/h0<=0.25 OK
30°<=tetai<=90° OK
fyi<= 355.00 MPa fyi(orfyj)/fui<=0.8 OK
bc/tc&hc/tc<=1.25sqrt(E/fyc) and bc/tc&hc/tc<=35 OK
bt/tt&ht/tt<=35 OK
3. Failure mode and results
Chord face plastification
fo -159.55 MPa
n -0.45
f(n) 0.98
gamma 11.25
NRd,c Bracing 24 588.94 kN
NRd,t Bracing 25 588.94 kN
NSd,c Bracing 24 -432.21 kN
NSd,t Bracing 25 259.33 kN
Unity Check bracing 24 0.73
Unity Check bracing 25 0.44
4. Weldsize CalculationEC3 Annex K.5
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Weldsize bracing 24
alfa weld 0.80
a 4.00 mm
Weldsize bracing 25
alfa weld 0.80
a 4.00 mm
Critical loadcase:1 Critical NRd: 588.94 kN
Unity Check0.73 Chord face plastification
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2.17 PST 07 03 03: Hollow section joint design Annex K Description Benchmark for hollow section connection design following EC3 Annex K, Revised Annex KK and CIDECT design Guide for rectangular hollow section (RHS) under predominantly static loading. Reference CIDECT Design guide for circular hollow section (CHS) joints under predominantly static loading J. Wardenier, Y. Kurobane, J.A. Packer, D.Dutta, N. Yeomans Verlag TUV Rheinland See the chapter "Manual calculation" for the calculation according to this reference. Result
EPW Manual
Unity Check 0.97 0.97
See the chapter "Calculation note" for the detailed output of ESA-Prima Win. Version ESA-Prima Win 3.20.03 Input file + calculation note PST070303.epw Modules 2D Frame (PRS.01) Truss connections (PST.07.03) Author NEM - CVL Manual calculation
Calculation following CIDECT reference Configuration of the node: Connection combination: RR square Connection type: X joint Calculation type: X joint Profile used: Chord: 150/75/5 Bracings: 110/70/3 110/70/3 Partial security factor: γM1=1.1 Geometrical data:
933.0b
b
0
1 ==β
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5.7t2
b
0
0 =⋅
=γ
Range of validity
25.0866.1b
h and 25.093.0
b
b :1 Criterion
0
2,1
0
2,1 ≥=≥=
22b
h.50 :2 Criterion
1,2
1,2 ≤=≤
3530t
h and 3515
t
b :3 Criterion
0
0
0
0 ≤=≤=
°≤°=θ≤° 904030 :6 Criterion 1
8.0652.0f
f
8.0652.0f
f
mmN355
mmN235ff :7Criterion
u2
y2
u1
y1
22y2y1
≤=
≤=
≤==
in tensionmember 3533,23t
b
ncompressioin member 35 35 ; 36.37f
E25.1min33,23
t
b :8Criterion
2
2
1y1
1
≤=
=
=⋅≤=
RANGE OF VALIDITY OK for calculation Design of the joint The function f(n) that appear in the chord yielding face incorporates the effect of the maximum applied axial stress in the chord or the maximum stress due to axial force and bending moment.
20
0
ooup mm
N19.120W
M
A
Nf −=+= in upper fiber and 2
0
0
oobot mm
N19.120W
M
A
Nf −=+= in bottom fiber
56.0
mmN235
mmN19.120
f
fn
2
2
0y
oupup −=
−== and 51.0
mmN235
mmN19.120
f
fn
2
2
0y
obotbot −=
−==
( ) 108.1n4.0
3.1nf up ≤=⋅β
+= and ( ) 1nf bot =
Joint strength: Chord face yielding with β=0.85 η=h1/b0=1.866
( )( ) ( ) N29.448
1.1nf14
sin
2
sin1
tfN
1M
5.0
11
20yo
Rd,2&1 =γ
⋅⋅
β−+
θη⋅
⋅θ⋅β−
⋅=
Chord Side Wall Failure (β=1)
Slenderness: 83.120sin
12
t
h46.3
5.0
10
0 =
θ⋅
−⋅=λ
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Euler slenderness: 91.93f
E
0y1 =⋅π=λ
Reduced slenderness: 286.11
red =λλ
=λ
Reduction factor: ( )
478.01
5.022=
λ−φ+φ=χ with
( )( ) =λ+−λ⋅α+⋅=φ 22.015.0
and 21.0=α
Buckling stress: 219.1021
ff1M
0ynk =γ
⋅⋅χ=
Member in compression: connection Xfor 2.565fsin8.0f nk1k =⋅θ⋅=
N55.1981.1
t10sin
h2
sin
tfN
1M0
1
1
1
0kRd,2&1 =
γ⋅
⋅+
θ
⋅⋅
θ
⋅=
Interpolation with 1933.085.0 ≤=β≤ between chord face yielding and side wall failure
N82.312N erpol,intRd =
Unity Check: 1895.055.198
280
N
N
Rd
maxSd <==
Effective width
( ) 65.2871.1
b2t4h2tfN1M
e1111yRd2,1 =γ
⋅⋅+⋅−⋅⋅⋅=
with 7077.77btf
tf
tb10
b 111y
00y
0
0e ≤=⋅
⋅
⋅⋅=
Unity Check: 1973.0280
65.287
N
N
Rd
maxSd <==
Calculation note Node 2: Welded truss connection
1. Input data
Chord: Member 1 2 AC150/75/5
h (in plane) 150.00 mm
b (out plane) 75.00 mm
t 5.00 mm
fy 235.00 MPa
fu 360.00 MPa
Bracing: Member 3 AC140/70/3
h (in plane) 140.00 mm
b (out plane) 70.00 mm
t 3.00 mm
teta 40.00 deg
fy 235.00 MPa
fu 360.00 MPa
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Bracing: Member 4 AC140/70/3
h (in plane) 140.00 mm
b (out plane) 70.00 mm
t 3.00 mm
teta 40.00 deg
fy 235.00 MPa
fu 360.00 MPa
2. General node data
Node characteristics
References Cidect Design Guide RHS Table 3&3a
Standard configuration X Joint
Standard combination RR Type
Type of calculation X type
Gamma M1 1.10
Gamma Mw 0.00
Geometrical data
beta 0.93
gamma 7.50
Range of Validity
bi/b0&hi/b0>=0.25 OK
0.5<=hi/bi<=2 OK
b0/t0&h0/t0<=35 OK
30°<=tetai<=90° OK
fyi<= 355.00 MPa fyi(orfyj)/fui<=0.8 OK
bc/tc&hc/tc<=1.25sqrt(E/fyc) and bc/tc&hc/tc<=35 Not OK
bt/tt&ht/tt<=35 OK
3. Failure mode and results
Interpol. of chord face yielding and side wall failure
eta bracing 3 1.87
fo bracing 3 -120.19 MPa
n bracing 3 -0.51
f(n) bracing 3 1.00
eta bracing 4 1.87
fo bracing 4 -120.19 MPa
n bracing 4 -0.51
f(n) bracing 4 1.00
NRd f.yield (Beta=0.85) bracing 3 448.29 kN
NRd f.yield (Beta=0.85) bracing 4 448.29 kN
slenderness 120.84
reduced slenderness 1.29
imperfection factor 0.21
reduction factor 0.48
fkn 102.09 MPa
fk 52.50 MPa
NRd SideWall bracing 3 198.30 kN
NRd SideWall bracing 4 198.30 kN
NRd interpol bracing 3 309.41 kN
NRd interpol bracing 4 309.41 kN
NSd bracing 3 -280.00 kN
NSd bracing 4 -259.00 kN
Unity Check bracing 3 0.90
Unity Check bracing 4 0.84
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Effective width
be bracing 3 70.00 mm
be bracing 4 70.00 mm
NRd bracing 3 287.64 kN
NRd bracing 4 287.64 kN
NSd bracing 3 -280.00 kN
NSd bracing 4 -259.00 kN
Unity Check bracing 3 0.97
Unity Check bracing 4 0.90
4. Weldsize CalculationEC3 Annex K.5
Weldsize bracing 3
d1 Galvanisation hole out plane 0.00 mm
d2 Galvanisation hole out plane 0.00 mm
d3 Galvanisation hole in plane 0.00 mm
d4 Galvanisation hole in plane 0.00 mm
Weld factor 1.00
Betaw 0.80
sigma1, weld 0.00 MPa
tau1, weld 0.00 MPa
tau2, weld 0.00 MPa
Unity check (Von Mises) 10.00
Unity Check (sigma1) 10.00
a 0.00 mm
Weldsize bracing 4
d1 Galvanisation hole out plane 0.00 mm
d2 Galvanisation hole out plane 0.00 mm
d3 Galvanisation hole in plane 0.00 mm
d4 Galvanisation hole in plane 0.00 mm
Weld factor 1.00
Betaw 0.80
sigma1, weld 0.00 MPa
tau1, weld 0.00 MPa
tau2, weld 0.00 MPa
Unity check (Von Mises) 10.00
Unity Check (sigma1) 10.00
a 0.00 mm
Critical loadcase:1 Critical NRd: 287.64 kN
Unity Check0.97 Effective width
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2.18 PST 07 03 04: Hollow section joint design Annex K Description Benchmark for hollow section connection design following EC3 Annex K, Revised Annex KK and CIDECT design Guide for rectangular hollow section (RHS) under predominantly static loading. Reference CIDECT Design guide for circular hollow section (CHS) joints under predominantly static loading J. Wardenier, Y. Kurobane, J.A. Packer, D.Dutta, N. Yeomans Verlag TUV Rheinland See the chapter "Manual calculation" for the calculation according to this reference. Result
EPW Manual
Unity Check 0.91 0.908
See the chapter "Calculation note" for the detailed output of ESA-Prima Win. Version ESA-Prima Win 3.20.03 Input file + calculation note PST070304.epw Modules 2D Frame (PRS.01) Truss connections (PST.07.03) Author NEM - CVL Manual calculation
Calculation following CIDECT reference
Configuration of the node: Connection combination: RR square Connection type: K joint Calculation type: K joint Profile used: Chord: 150/75/5 Bracings: 110/70/3 (40°) 110/70/3 (70°) Partial security factor: γM1=1.1 Geometrical data:
3.1b4
hhbb
0
2121 =⋅
+++=β
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5.7t2
b
0
0 =⋅
=γ
Range of validity
25.0t
b01.01.046.1/86.1
b
h 25.0
t
b01.01.093.0
b
b
35.046.1b
h and 35.086.1
b
h 35.093.0
b
b :1 Criterion
0
0
0
2,1
0
0
0
2,1
0
2
0
1
0
2,1
=⋅+≥==⋅+≥=
≥=≥=≥=
257.1b
h.50 22
b
h.50 :2 Criterion
2
2
1
1 ≤=≤≤=≤
3530t
h and 3515
t
b :3 Criterion
0
0
0
0 ≤=≤=
( ) ( ) OKNot 15.1b
g-10.5
OKNot 6tt7.3g :4 Criterion
0
21
β−⋅≤≤β⋅
=+≤=
25.023.0h
e0.55 :5 Criterion
0
≤=≤−
°≤°=θ≤°°≤°=θ≤° 907030904030 :6 Criterion 21
8.0652.0f
f
8.0652.0f
f
mmN355
mmN235ff :7Criterion
u2
y2
u1
y1
22y2y1
≤=
≤=
≤==
in tensionmember 3533,23t
b
ncompressioin member 35 35 ; 36.37f
E25.1min33,23
t
b :8Criterion
2
2
1y1
1
≤=
=
=⋅≤=
RANGE OF VALIDITY Not OK Design of the joint The function f(n) that appear in the chord yielding face incorporates the effect of the maximum applied axial stress in the chord or the maximum stress due to axial force and bending moment.
20
0
oo mm
N76.720W
M
A
Nf =+=
06.3
mmN235
mmN76.720
f
fn
2
2
0y
o ===
( ) 124.2n4.0
3.1nf ≤=⋅β
+=
Joint strength: Chord face yielding
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( )( )
kN1.198sin
sinNN
kN603.2891.1
nfb4
hhbb
sin1
tf9.8N
2
1Rd,1Rd,2
M
5.0
0
2121
1
20yo
Rd,11
=θ
θ⋅=
=γ
⋅⋅γ⋅
⋅
+++⋅
θ⋅β−
⋅=
Chord Shear
Reduced Area: ( ) 76.0
t3
g41
1th wi1785.09mm tbh2A
5.0
20
22
000v =
⋅
⋅+
=α=⋅⋅α+⋅=
Plastic Shear: kN2,2423
AfV
v0ypl =
⋅=
kN74.2571.1
sin3
AfN and kN796.376
1.1
sin3
AfN
11 M2
v0yRd2
M1
v0yRd1 =
γ⋅
θ⋅
⋅==
γ⋅
θ⋅
⋅=
( ) kN44.369V
V1fAfAAN
5.02
pl
Sd0yv0yv0)Gap In(Rd,0 =
−⋅⋅+⋅−=
Effective width
( )( )
mm70bmm77,70btf
tf
tb10
b with
kN34.245bbt4h2tfN
kN64.287bbt4h2tfN
1111y
00y
0
02&e1
e22222yRd1
e11111yRd1
=≤=⋅⋅
⋅⋅=
=++⋅−⋅⋅⋅=
=++⋅−⋅⋅⋅=
Unity Check: 1895.01.198
180
N
N
ieldingRdChordFaceY
maxSd <==
Effective width
( ) 65.2871.1
b2t4h2tfN1M
e1111yRd2,1 =γ
⋅⋅+⋅−⋅⋅⋅=
with 7077.77btf
tf
tb10
b 111y
00y
0
0e ≤=⋅
⋅
⋅⋅=
Unity Check: 1908.0280
65.287
N
N
Rd
maxSd <==
Calculation note Node 2: Welded truss connection
1. Input data
Chord: Member 1 2 AC150/75/5
h (in plane) 150.00 mm
b (out plane) 75.00 mm
t 5.00 mm
fy 235.00 MPa
fu 360.00 MPa
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Bracing: Member 3 AC140/70/3
h (in plane) 140.00 mm
b (out plane) 70.00 mm
t 3.00 mm
teta 40.00 deg
fy 235.00 MPa
fu 360.00 MPa
Bracing: Member 7 AC110/70/3
h (in plane) 110.00 mm
b (out plane) 70.00 mm
t 3.00 mm
teta 70.00 deg
fy 235.00 MPa
fu 360.00 MPa
2. General node data
Node characteristics
References Cidect Design Guide RHS Table 3&3a
Standard configuration K Joint
Standard combination RR Type
Type of calculation K type
Gamma M1 1.10
Gamma Mw 0.00
Geometrical data
beta 1.30
gamma 7.50
e 0.00 mm
gap (g) -50.75 mm
p 117.06 mm
q 50.75 mm
overlap Ov(%) 43.35
Overlapping member 7
Overlapped member 3
Range of Validity
bi/b0&hi/h0 >=0.25 OK
0.5<=hi/bi<=2 OK
b0/t0&h0/t0<=40 OK
25%<=Ov<=100% ti/tj<=1.0 & bi/bj>=0.75 OK
-0.55<=e/h0<=0.25 OK
30°<=tetai<=90° OK
fyi<= 355.00 MPa fyi(orfyj)/fui<=0.8 OK
bc/tc&hc/tc<=1.1sqrt(E/fyc) Not OK
bt/tt&ht/tt<=35 Not OK
3. Failure mode and results
Effective width
Overlap Ov(%) 43.35
be1 70.00 mm
be2 70.00 mm
be(Ov) 30.00 mm
NSd bracing 7 180.00 kN
NSd bracing 3 -140.00 kN
NRd bracing 7 197.65 kN
NRd bracing 3 234.33 kN
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Effective width
Unity Check bracing 7 0.91
Unity Check bracing 3 0.60
4. Weldsize CalculationEC3 Annex K.5
Weldsize bracing 3
d1 Galvanisation hole out plane 0.00 mm
d2 Galvanisation hole out plane 0.00 mm
d3 Galvanisation hole in plane 0.00 mm
d4 Galvanisation hole in plane 0.00 mm
Weld factor 1.00
Betaw 0.80
sigma1, weld 0.00 MPa
tau1, weld 0.00 MPa
tau2, weld 0.00 MPa
Unity check (Von Mises) 10.00
Unity Check (sigma1) 10.00
a 0.00 mm
Weldsize bracing 7
d1 Galvanisation hole out plane 0.00 mm
d2 Galvanisation hole out plane 0.00 mm
d3 Galvanisation hole in plane 0.00 mm
d4 Galvanisation hole in plane 0.00 mm
Weld factor 1.00
Betaw 0.80
sigma1, weld 0.00 MPa
tau1, weld 0.00 MPa
tau2, weld 0.00 MPa
Unity check (Von Mises) 10.00
Unity Check (sigma1) 10.00
a 0.00 mm
Critical loadcase:1 Critical NRd: 197.65 kN
Unity Check0.91 Effective width
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2.19 PST.07.03 -5: KLS Truss connection: weldsize calculation Description Control of weld size in connection composed with special Voest KLS profiles according to Voest specifications. The node controlled has the index 2. Only members 1,2 and 32 are activated to form a Y-connection. Project data See input file. Reference See the chapter "Manual calculation" for the calculation according to the Voest specifications. Result Manual calculation EPW σ1 61.6 N/mm² 61.28 N/mm² τ1 189.4 N/mm² 188.63 N/mm² unity check 0.97 0.97 kN unity check 0.22 0.21 kN See the chapter "Calculation note" for detailed output of ESA-Prima Win. Version ESA-Prima Win 3.20.03 Input file PST070305.epw Modules 2D Frame (PRS.01) Truss connections (PST.07.03) Author NEM - CVL Manual calculation The chord is composed with a K180/100/10 profile and the bracing is composed by a KLS70/70/5 profile. Properties of those profiles are listed in the results document of EPW. The frame type following CIDECT documentation is a Y-type RHS-KLS joint. The angle between the chord and the bracing is 26,57°.
kN168.19657.26sin57.438sinNT
kN57.39257.26cos57.438cosNV
=°⋅=α=
=°⋅=α=
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( ) mmvvBN
mmvB
D
mmBC
mmB
E
mmEBN
mmvBB
v
mmRABB
8.225²35.012
5.87²32
12
7.5312
31
13.692
22
4.207221
26.138*12
23.2sin
1
628701
=++=
=+=
==
==
=+=
==
==
=−=−=
α
To determine the weld size a in the connection, we use a iterative process with a as parameter until the Von Mises rules is respected (Ref[1],Annex M/EC3). This benchmark controls only the optimal value found by the iterative process. With a weldsize a=10 mm, we have:
ESA-Prima Win Steel and timber design benchmarks
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430
²/6.612
1
221 mmNaN
T=
⋅== τσ
²/4.18911 mmN
aN
V=
⋅=τ
( )122.0 and 197.0
3
w
211
M
1
222
≤=≤=
⋅
+⋅+
γ
σ
γβ
ττσ
u
Mw
u ff
w
with βw=0.8 Calculation note Node 2: Welded truss connection
1. Input data
Chord: Member 1 2 K180/100/10
h (in plane) 180.00 mm
b (out plane) 100.00 mm
t 10.00 mm
fy 355.00 MPa
fu 510.00 MPa
Bracing: Member 32 KLS70/70/5
B 70.00 mm
B1 62.00 mm
RA 8.00 mm
t 5.00 mm
teta 26.57 deg
fy 235.00 MPa
fu 360.00 MPa
2. General node data
Node characteristics
Standard configuration Y Joint
Standard combination RHS-KLS Type
Type of calculation Only weld size
Gamma M1 1.10
Gamma Mw 1.25
No range of validity and failure calculation
3. Geometry and internal forces of bracings
Bracing: Member 32 KLS70/70/5
N 438.57 kN
V 392.27 kN
T 196.13 kN
v 2.24
B2 138.64 mm
E2 69.32 mm
N1 207.95 mm
C1 53.69 mm
D2 87.68 mm
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Bracing: Member 32 KLS70/70/5
N2 226.32 mm
4. Weldsize CalculationEC3 Annex K.5 : Default weldsize and Optimisation
Weldsize bracing 32: a=0.7.t
Weld factor 1.00
Betaw 0.80
sigma1, weld 153.20 MPa
tau1, weld 471.58 MPa
tau2, weld 153.20 MPa
Unity check (Von Mises) 2.42
Unity Check (sigma1) 0.53
a 4.00 mm
Weldsize bracing 32 Optimisation
Weld factor 1.00
Betaw 0.80
sigma1, weld 61.28 MPa
tau1, weld 188.63 MPa
tau2, weld 61.28 MPa
Unity check (Von Mises) 0.97
Unity Check (sigma1) 0.21
a 10.00 mm
Critical Member32 Critical loadcase:1
Unity check2.42
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2.20 PST.07.04 – 01 : Bolted diagonal connections Description Bolted diagonal connections are calculated manually. The results are compared with the results of ESA-Prima Win. Project data Reference Eurocode 3 : Design of steel structures
Part 1-1 : General rules and rules for buildings ENV 1993-1-1:1992 Revised Annex J ENV 19+93-1-1/pr A2
See the chapter "Manual calculation" for the calculation according to this reference. Result Manually
[kN] EPW [kN]
Node 12 Npl,Rd (diagonal) 479 480 Nu,Rd (diagonal) 282 282 Fv,Rd 60.28 60.28 Fb,Rd (diagonal) 68.8 68.8 Npl,Rd (plate) 320 320 Nu,Rd (plate) 342 342 Fb,Rd (plate) 69.12 69.12 Node 10 Nu,Rd (diagonal) 238.74 239.42 Fb,Rd (diagonal) 67.52 67.52 Fb,Rd (plate) 56.44 56.53 Node 8 Fp,Cd 109.9 109.9 Fs,Rd 26.4 26.4 Node 4 Npl,Rd (diagonal) 725 725 Nu,Rd (diagonal) 629.5 629 Node 2 Nu,Rd (diagonal) 639.7 639 See the chapter "Calculation note" for the detailed output of ESA-Prima Win. Version 3.20 Input file PST070401.epw Modules 3D Frame (PRS.11) Bolted Diagonal Connection (PST.07.04)
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Author CVL Manual calculation Partial safety factors : γM0 = 1.10 γM2 = 1.25 γMb = 1.25 Node 12 Diagonal element : • H100/100/10 • fy = 275 N/mm² • fu = 430 N/mm² • A = 1915 mm²
The design plastic resistance for the angle section is kN4791.1
2751915AfN
0M
yRd,pl =
⋅=
γ=
Bolts :
• M16 - 8.8 • d = 16 mm • d0 = 18 mm • fub = 800 N/mm² • A = 157 mm² • e2 = 50 mm • e1 = 27 mm
The design ultimate resistance of the net section for angle diagonal with 1 bolt :
( ) ( )kN282
25.1
10185.0500.2tfd5.0e0.2N
2M
uo2Rd,u =
⋅−=
γ
−=
The shear resistance per shear plane and per bolt is
kN28.6025.1
1578006.00.1
Af6.0F
Mb
subLfRd.v =
⋅⋅=
γβ=
The bearing resistance (in the angle section) is
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50.0183
27)0.1,
f
f,
4
1
d3
p,
d3
emin(
kN8.6825.1
101643050.05.2dtf5.2F
u
ub
0
1
0
1
Mb
uRd.b
=⋅
=−=α
=⋅⋅⋅⋅
=γ
α=
For single lap joints with one bolt, Fb,Rd is limited by
kN56.8225.1
10164305.1dtf5.1F
Mb
uRd.b =
⋅⋅⋅=
γ=
� Fb,Rd = 68.8 kN Gusset element : • b= 150 mm • t = 10 mm • e1=40 mm
The design plastic resistance for the plate is kN3201.1
2351500AfN
0M
yRd,pl =
⋅=
γ=
The design ultimate resistance of the net section is
kN34225.1
360)10*181500(9.0fA9.0N
2M
unetRd,u =
−⋅=
γ=
The bearing resistance (in the plate) is
741.0183
40)0.1,
f
f,
4
1
d3
p,
d3
emin(
kN33.8525.1
1016360741.05.2dtf5.2F
u
ub
0
1
0
1
Mb
uRd.b
=⋅
=−=α
=⋅⋅⋅⋅
=γ
α=
For single lap joints with one bolt, Fb,Rd is limited by
kN12.6925.1
10163605.1dtf5.1F
Mb
uRd.b =
⋅⋅⋅=
γ=
� Fb,Rd = 69.12 kN Node 10 Identical characteristics as in node 12, but with 2 bolts per row, p=40 mm The design ultimate resistance of the net section for angle diagonal with 2 bolts :
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kN74.23825.1
430)10*181915(40.0fAN
2M
unet2Rd,u =
−⋅=
γ
β=
There p < 2.5 d0 ( 40 < 45 ), β2 = 0.4 The bearing resistance (in the angle section) is
49.0)49.0,5.0min()25.0183
40,
183
27min()0.1,
f
f,
4
1
d3
p,
d3
emin(
kN52.6725.1
101643049.05.2dtf5.2F
u
ub
0
1
0
1
Mb
uRd.b
==−⋅⋅
=−=α
=⋅⋅⋅⋅
=γ
α=
The bearing resistance (in the plate) is
49.0)25.0183
40,
183
40min()0.1,
f
f,
4
1
d3
p,
d3
emin(
kN448.5625.1
101636049.05.2dtf5.2F
u
ub
0
1
0
1
Mb
uRd.b
=−⋅⋅
=−=α
=⋅⋅⋅⋅
=γ
α=
Node 8 Identical characteristics as in node 12, but with prestressed bolt M16-10.9
kN9.10915710007.0Af7.0F subCd,p =⋅⋅=⋅⋅=
kN37.269.10925.1
3.011F
nkF Cd,p
Ms
sRd,s =
⋅⋅=
γ
⋅µ⋅⋅=
Node 4 Diagonal element UPE200
• fy = 275 N/mm² • fu = 430 N/mm² • A = 2900 mm²
The design plastic resistance for the channel section is kN7251.1
2752900AfN
0M
yRd,pl =
⋅=
γ=
Bolts :
• M16 - 8.8 • d = 16 mm • d0 = 18 mm • fub = 800 N/mm² • A = 157 mm² • e1 = 27 mm • 2 bolts in the web of the channel, w=100 mm
The design ultimate resistance of the net section for channel diagonal :
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644.016289843
9843
AA3
A3
²mm20331628644.0984AAA
kN5.62925.1
43020339.0fA9.0N
21
1
21n
2M
unRd,u
=+⋅
⋅=
+=ξ
=⋅+=ξ+=
=⋅⋅
=γ
=
A1 = 200 x 6 - 2 x 18 x 6 = 984 mm² A2 = 2 ( 74 x 11) = 1628 mm² Node 2 Identical characteristics as in node 12, but with 2 bolts per row (p=80 mm), staggered position (s=40 mm) The design ultimate resistance of the net section for channel diagonal :
65.0162810083
10083
AA3
A3
²mm2066162865.01008AAA
kN75.63925.1
43020339.0fA9.0N
21
1
21n
2M
unRd,u
=+⋅
⋅=
+=ξ
=⋅+=ξ+=
=⋅⋅
=γ
=
²mm10081004
²40181850100506
p4
²sddepetA
2002221 =
⋅+−−++⋅=
+−−++⋅=
A2 = 2 ( 74 x 11) = 1628 mm² Calculation note
Bolted connection
Node: 12
Diagonal item: H100/100/10
Equal legs connection
b 100mm
t 10mm
fy 275.000MPa
fu 430.000MPa
Non-Staggered bolt position
w 50mm
e1 27mm
p1 0mm
Partial safety factors
Gama M0 1.10
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Partial safety factors
Gama M2 1.25
Gama Mb 1.25
Gama Ms 1.25
Gama Mw 1.25
Gusset plate
b 150mm
t 10mm
fy 235.000MPa
fu 360.000MPa
Non-Staggered bolt position
e2 75mm
p2 0mm
e1 40mm
M16-8.8 (DIN960)
Type Normal
Grade 8.8
fu 800.000MPa
As 157mm^2
d0 18mm
S 24mm
e 27mm
h head 10mm
h nut 13mm
Total number of bolts 1
Number of bolt rows 1
Non-Staggered bolt position
Internal forces
Group of load case(s) : 1
N1 100.000kN
Member resistance
Resistance of the gross section of diagonal1
A 1920mm^2
Npl,Rd 480.000kN
Resistance of the net section of diagonal1
Anet 820mm^2
Nu,Rd 282.080kN
Resistance of the gross section of gusset
A 1500mm^2
Npl,Rd 320.455kN
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Resistance of the net section of gusset
Anet 1320mm^2
Nu,Rd 342.144kN
Connection resistance
Shear resistance
Lj 0mm
Beta Lf 1.000
Fv,Rd 60.288kN
Bearing resistance for diagonal
Alfa 0.500
Fb,Rd 68.800kN
Bearing resistance for gusset
Alfa 0.741
Fb,Rd 69.120kN
The design shear force per bolt
Fv,Sd,diagonal1 100.000kN
Unity check
Member resistance 0.35
Connection resistance 1.66
The connection satisfies !
Weld size calculation for gusset plate
a 5mm
La 58mm
NRd 60.288kN
Beta W 0.80
Fw,Rd 1039.230kN/m
Node: 10
Diagonal item: H100/100/10
Equal legs connection
b 100mm
t 10mm
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Equal legs connection
fy 275.000MPa
fu 430.000MPa
Non-Staggered bolt position
w 50mm
e1 27mm
p1 40mm
Partial safety factors
Gama M0 1.10
Gama M2 1.25
Gama Mb 1.25
Gama Ms 1.25
Gama Mw 1.25
Gusset plate
b 150mm
t 10mm
fy 235.000MPa
fu 360.000MPa
Non-Staggered bolt position
e2 75mm
p2 0mm
e1 40mm
M16-8.8 (DIN960)
Type Normal
Grade 8.8
fu 800.000MPa
As 157mm^2
d0 18mm
S 24mm
e 27mm
h head 10mm
h nut 13mm
Total number of bolts 2
Number of bolt rows 1
Non-Staggered bolt position
Internal forces
Group of load case(s) : 1
1
N1 100.000kN
Member resistance
Resistance of the gross section of diagonal1
A 1920mm^2
Npl,Rd 480.000kN
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Resistance of the net section of diagonal1
Anet 1740mm^2
Nu,Rd 239.424kN
Beta2 0.400
Resistance of the gross section of gusset
A 1500mm^2
Npl,Rd 320.455kN
Resistance of the net section of gusset
Anet 1320mm^2
Nu,Rd 342.144kN
Connection resistance
Shear resistance
Lj 40mm
Beta Lf 1.000
Fv,Rd 60.288kN
Bearing resistance for diagonal
Alfa 0.491
Fb,Rd 67.526kN
Bearing resistance for gusset
Alfa 0.491
Fb,Rd 56.533kN
The design shear force per bolt
Fv,Sd,diagonal1 50.000kN
Unity check
Member resistance 0.42
Connection resistance 0.88
The connection satisfies !
Weld size calculation for gusset plate
a 5mm
La 109mm
NRd 113.067kN
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Beta W 0.80
Fw,Rd 1039.230kN/m
Node: 8
Diagonal item: H100/100/10
Equal legs connection
b 100mm
t 10mm
fy 275.000MPa
fu 430.000MPa
Non-Staggered bolt position
w 50mm
e1 27mm
p1 0mm
Partial safety factors
Gama M0 1.10
Gama M2 1.25
Gama Mb 1.25
Gama Ms 1.25
Gama Mw 1.25
Gusset plate
b 150mm
t 10mm
fy 235.000MPa
fu 360.000MPa
Non-Staggered bolt position
e2 75mm
p2 0mm
e1 40mm
M16-10.9 (DIN6914)
Type PreStressed
Grade 10.9
fu 1000.000MPa
As 157mm^2
d0 18mm
S 27mm
e 30mm
h head 10mm
h nut 13mm
Total number of bolts 1
Number of bolt rows 1
Non-Staggered bolt position
Internal forces
Group of load case(s) : 1
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Internal forces
1
1
N1 100.000kN
Member resistance
Resistance of the gross section of diagonal1
A 1920mm^2
Npl,Rd 480.000kN
Resistance of the net section of diagonal1
Anet 820mm^2
Nu,Rd 282.080kN
Resistance of the gross section of gusset
A 1500mm^2
Npl,Rd 320.455kN
Resistance of the net section of gusset
Anet 1320mm^2
Nu,Rd 342.144kN
Connection resistance
Shear resistance
Fp,Cd 109.900kN
ks 1.00
mi 0.30
n,diagonal1 1
Fs,Rd,diagonal1 26.376kN
Bearing resistance for diagonal
Alfa 0.500
Fb,Rd 68.800kN
Bearing resistance for gusset
Alfa 0.741
Fb,Rd 69.120kN
The design shear force per bolt
Fv,Sd,diagonal1 100.000kN
Unity check
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Member resistance 0.35
Connection resistance 3.79
The connection satisfies !
Weld size calculation for gusset plate
a 5mm
La 25mm
NRd 26.376kN
Beta W 0.80
Fw,Rd 1039.230kN/m
Node: 4
Diagonal item: UPE200
Web connection
b 200mm
t 6mm
fy 275.000MPa
fu 430.000MPa
Non-Staggered bolt position
w 100mm
e1 27mm
p1 0mm
Partial safety factors
Gama M0 1.10
Gama M2 1.25
Gama Mb 1.25
Gama Ms 1.25
Gama Mw 1.25
Gusset plate
b 300mm
t 6mm
fy 235.000MPa
fu 360.000MPa
Non-Staggered bolt position
e2 100mm
p2 100mm
e1 40mm
M16-8.8 (DIN960)
Type Normal
Grade 8.8
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M16-8.8 (DIN960)
fu 800.000MPa
As 157mm^2
d0 18mm
S 24mm
e 27mm
h head 10mm
h nut 13mm
Total number of bolts 2
Number of bolt rows 2
Non-Staggered bolt position
Internal forces
Group of load case(s) : 1
1
1
1
N1 100.000kN
Member resistance
Resistance of the gross section of diagonal1
A 2900mm^2
Npl,Rd 725.000kN
Resistance of the net section of diagonal1
Anet 2033mm^2
A1 984mm^2
A2 1628mm^2
Zeta 0.645
Nu,Rd 629.514kN
Resistance of the gross section of gusset
A 1800mm^2
Npl,Rd 384.545kN
Resistance of the net section of gusset
Anet 1584mm^2
Nu,Rd 410.573kN
Connection resistance
Shear resistance
Lj 0mm
Beta Lf 1.000
Fv,Rd 60.288kN
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Bearing resistance for diagonal
Alfa 0.500
Fb,Rd 41.280kN
Bearing resistance for gusset
Alfa 0.741
Fb,Rd 51.200kN
The design shear force per bolt
Fv,Sd,diagonal1 50.000kN
Unity check
Member resistance 0.26
Connection resistance 1.21
The connection satisfies !
Weld size calculation for gusset plate
a 3mm
La 132mm
NRd 82.560kN
Beta W 0.80
Fw,Rd 623.538kN/m
Node: 2
Diagonal item: UPE200
Web connection
b 200mm
t 6mm
fy 275.000MPa
fu 430.000MPa
Staggered bolt position
s 40mm
w 100mm
e1 27mm
p1 80mm
Partial safety factors
Gama M0 1.10
Gama M2 1.25
Gama Mb 1.25
Gama Ms 1.25
Gama Mw 1.25
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Gusset plate
b 160mm
t 6mm
fy 235.000MPa
fu 360.000MPa
Staggered bolt position
e2 30mm
p2 100mm
e1 40mm
M16-8.8 (DIN960)
Type Normal
Grade 8.8
fu 800.000MPa
As 157mm^2
d0 18mm
S 24mm
e 27mm
h head 10mm
h nut 13mm
Total number of bolts 4
Number of bolt rows 2
Staggered bolt position
Internal forces
Group of load case(s) : 1
1
1
1
1
N1 100.000kN
Member resistance
Resistance of the gross section of diagonal1
A 2900mm^2
Npl,Rd 725.000kN
Resistance of the net section of diagonal1
Anet 2066mm^2
A1 1008mm^2
A2 1628mm^2
Zeta 0.650
Nu,Rd 639.717kN
Resistance of the gross section of gusset
A 960mm^2
Npl,Rd 205.091kN
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Resistance of the net section of gusset
Anet 768mm^2
Nu,Rd 199.066kN
Connection resistance
Shear resistance
Lj 120mm
Beta Lf 1.000
Fv,Rd 60.288kN
Bearing resistance for diagonal
Alfa 0.500
Fb,Rd 41.280kN
Bearing resistance for gusset
Alfa 0.741
Fb,Rd 51.200kN
The design shear force per bolt
Fv,Sd,diagonal1 25.000kN
Unity check
Member resistance 0.50
Connection resistance 0.61
The connection satisfies !
Weld size calculation for gusset plate
a 3mm
La 265mm
NRd 165.120kN
Beta W 0.80
Fw,Rd 623.538kN/m
4 x M16-8.8 (DIN960)Channel: UPE200
80 4027
50
100
50
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First Diagonal, Node 2
Gusset: th. 6mm4 x M16-8.8 (DIN960) 80 4040
30
100
30
Gusset plate Node 2
Whole connection Node 2
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3. TIMBER 3.1 PTR.06.01 – 01 : EC 5 Timber Code Check Description The unity checks in ULS and the deformation in SLS are compared with literature results. Project data See input file. Reference [1] Eurocode 5
Design of timber structures Part 1-1 : General rules and rules for buildings ENV 1995-1-1:1993 E
[2] Informationsdienst Holz Holzbau Handbuch Reihe 2 - Tragwerksplanung Eurocode 5 - Holzbauwerke Bemessungsgrundlagen und Beispiele 1995
Result Example 1.2.4. is considered. Ref.[2] EPW unet,fin - member 1 51 mm (1/207) 50.58 mm (1/209) ULS unity check member 1 1.02 1.02 See the chapter "Calculation note" for detailed output of ESA-Prima Win. Version ESA-Prima Win 3.20.03 Input file + calculation note PTR060101.epw Modules 3D Frame (PRS.11) EC5 Timber code check (PTR.06.01) Author CVL Calculation note
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450
Relative deformation on member(s) with creep. Member extreme Values of kdef
Permanent : 0.60
Long term : 0.50
Medium term : 0.25
Short term : 0.00
Group of member(s) :1/3
Group of serviceability combi :1/2
memb cr.nr combi dx
[m]
ux
[mm]
uz
[mm]
fiy
[mrad]
1 1 2 5.278 -0.04
1/265242
-50.58
1/209 0.00
1 1 2 2.111 -0.03
1/414441
-30.05
1/351
2.93
1 1 2 8.445 -0.03
1/414441
-30.05
1/351
-2.93
2 1 2 5.278 -0.04
1/265241
-50.58|
1/209 -0.00
2 1 2 2.111 -0.03
1/414440
-30.05
1/351
2.93
2 1 2 8.445 -0.03
1/414442
-30.05
1/351
-2.93
3 2 2 12.209 -0.00 0.00 0.00
EUROCODE 5 - DESIGN OF TIMBER STRUCTURES, ENV 1995-1-1.
Tension paralel to the grain (5.1.2)
Compression paralel to the grain (5.1.4)
Bending (5.1.6a and 5.1.6b)
Shear (5.1.7.1)
Torsion (5.1.8)
Combined bending and axial tension (5.1.9a and 5.1.9b)
Combined bending and axial compression (5.1.10a and 5.1.10b)
Columns and beams (5.2.1e and 5.2.1f)
Detailed output, element extremes.
Macro :1 Member :1 L=10.556m CS : 1 - REC (160,550)
Material: BS14k
Service class : 1
gamma m =1.30 k m =0.70 (rectangle)
section=5.278m ult.combi=4 k mod = 0.90
Section check
N Vy Vz Mx My Mz
Design force -162.5[kN] 0.0[kN] 0.0[kN] 0.0[kNm] 137.8[kNm] 0.0[kNm]
Design stress -1.8[MPa] 0.0[MPa] 0.0[MPa] 0.0[MPa] 17.1[MPa] 0.0[MPa]
Limit stress 19.0[MPa] 1.9[MPa] 1.9[MPa] 1.9[MPa] 19.4[MPa] 19.4[MPa]
Unity check 0.10 0.00 0.00 0.00 0.88 0.00
Bending : 0.88 (5.1.6a)
Shear : 0.00 (5.1.7.1)
Compression + bending : 0.89 (5.1.10a)
Stability check
L0
m
k L
m
lam sigma krit
MPa
lam_rel beta c k
k crit
kc
Y 10.56 1.00 10.56 66.49 22.3 1.110 0.10 1.146 0.70
Z 10.56 0.33 3.44 74.51 17.8 1.244 0.10 1.311 0.58
LTBy 10.56 0.33 3.44 106.1 0.514 1.00
LTBz 10.56 0.33 3.44 4311.3 0.081 1.00
Compression (5.2.1) : 1.02 (5.2.1f)
Bending (5.2.2) : 1.02
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Maximal unity check = 1.02 The member does NOT satisfy the check !
ESA-Prima Win Steel and timber design benchmarks
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3.2 PTR.06.01 – 02 : EC 5 Timber Code Check Description The unity checks in ULS are compared with literature results. Project data See input file. Reference [1] Eurocode 5
Design of timber structures Part 1-1 : General rules and rules for buildings ENV 1995-1-1:1993 E
[2] Informationsdienst Holz Holzbau Handbuch Reihe 2 - Tragwerksplanung Eurocode 5 - Holzbauwerke Bemessungsgrundlagen und Beispiele 1995
Result Example 1.3 is considered. Ref.[2] EPW ULS unity check member 1 0.95 0.96 ULS unity check member 2 0.95 0.92 See the chapter "Calculation note" for detailed output of ESA-Prima Win. Version ESA-Prima Win 3.20.03 Input file + calculation note PTR060102.epw Type of calculation 3D Frame (PRS.11) EC5 Timber code check (PTR.06.01) Author CVL Calculation note
EUROCODE 5 - DESIGN OF TIMBER STRUCTURES, ENV 1995-1-1.
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Tension paralel to the grain (5.1.2)
Compression paralel to the grain (5.1.4)
Bending (5.1.6a and 5.1.6b)
Shear (5.1.7.1)
Torsion (5.1.8)
Combined bending and axial tension (5.1.9a and 5.1.9b)
Combined bending and axial compression (5.1.10a and 5.1.10b)
Columns and beams (5.2.1e and 5.2.1f)
Detailed output, element extremes.
Macro :1 Member :1 L=6.430m CS : 1 - REC (260,480)
Material: BS 11
Service class : 1
gamma m =1.30 k m =0.70 (rectangle)
section=0.000m ult.combi=14 k mod = 0.90
Section check
N Vy Vz Mx My Mz
Design force -86.4[kN] 0.0[kN] 31.5[kN] 0.0[kNm] -128.4[kNm] 0.0[kNm]
Design stress -0.7[MPa] 0.0[MPa] 0.4[MPa] 0.0[MPa] -12.9[MPa] 0.0[MPa]
Limit stress 16.6[MPa] 1.9[MPa] 1.9[MPa] 1.9[MPa] 16.6[MPa] 16.6[MPa]
Unity check 0.04 0.00 0.20 0.00 0.77 0.00
Bending : 0.77 (5.1.6a)
Shear : 0.20 (5.1.7.1)
Compression + bending : 0.78 (5.1.10a)
Stability check
L0
m
k L
m
lam sigma krit
MPa
lam_rel beta c k
k crit
kc
Y 6.43 2.70 17.36 125.29 5.8 2.037 0.10 2.651 0.23
Z 6.43 1.00 6.43 85.67 12.4 1.393 0.10 1.515 0.47
LTBy 6.43 1.00 6.43 158.4 0.389 1.00
LTBz 6.43 1.00 6.43 996.7 0.155 1.00
Compression (5.2.1) : 0.96 (5.2.1f)
Bending (5.2.2) : 0.96
Maximal unity check = 0.96 - satisfies.
Macro :2 Member :2 L=5.830m CS : 2 - REC (160,260)
Material: BS 11
Service class : 1
gamma m =1.30 k m =0.70 (rectangle)
section=2.915m ult.combi=13 k mod = 0.90
Section check
N Vy Vz Mx My Mz
Design force -110.6[kN] 0.0[kN] 0.0[kN] 0.0[kNm] 9.2[kNm] 0.0[kNm]
Design stress -2.7[MPa] 0.0[MPa] 0.0[MPa] 0.0[MPa] 5.1[MPa] 0.0[MPa]
Limit stress 16.6[MPa] 1.9[MPa] 1.9[MPa] 1.9[MPa] 16.6[MPa] 16.6[MPa]
Unity check 0.16 0.00 0.00 0.00 0.31 0.00
Bending : 0.31 (5.1.6a)
Shear : 0.00 (5.1.7.1)
Compression + bending : 0.33 (5.1.10a)
Stability check
L0
m
k L
m
lam sigma krit
MPa
lam_rel beta c k
k crit
kc
Y 5.83 1.00 5.83 77.68 15.0 1.263 0.10 1.336 0.56
Z 5.83 1.00 5.83 126.22 5.7 2.052 0.10 2.683 0.23
LTBy 5.83 1.00 5.83 122.1 0.443 1.00
LTBz 5.83 1.00 5.83 524.1 0.214 1.00
Compression (5.2.1) : 0.92 (5.2.1e)
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Bending (5.2.2) : 0.92
Maximal unity check = 0.92 - satisfies.
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3.3 PTR.06.01 – 03 : EC 5 Timber Code Check Description The unity checks in ULS are compared with literature results. Project data See input file. Reference [1] Eurocode 5
Design of timber structures Part 1-1 : General rules and rules for buildings ENV 1995-1-1:1993 E
[2] Timber Engineering STEP 2 Design - Details ans structural systems First Edition, Centrum Hout, The Netherlands 1995
Result Example of a truss made from glulam is considered. Ref.[2], pp. E7/5 - E7/8 Ref.[2] EPW remarks ULS unity check macro 2 - top chord 0.70 0.66 In Ref.[2] the value for km is taken as 1.0, in EPW
km=0.7. ULS unity check macro 1 - bottom chord 0.73 0.63 In EPW the netto section is ignored for tension forces.
In EPW the moment is taken into account.
Version ESA-Prima Win 3.20.03 Input file + calculation note PTR060103.epw Modules 3D Frame (PRS.11) EC5 Timber code check (PTR.06.01) Author CVL Calculation note
EUROCODE 5 - DESIGN OF TIMBER STRUCTURES, ENV 1995-1-1.
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Tension paralel to the grain (5.1.2)
Compression paralel to the grain (5.1.4)
Bending (5.1.6a and 5.1.6b)
Shear (5.1.7.1)
Torsion (5.1.8)
Combined bending and axial tension (5.1.9a and 5.1.9b)
Combined bending and axial compression (5.1.10a and 5.1.10b)
Columns and beams (5.2.1e and 5.2.1f)
Detailed output, element extremes.
Macro :1 Member :4 L=2.250m CS : 1 - REC (160,200)
Material: GL32h
Service class : 1
gamma m =1.30 k m =0.70 (rectangle)
section=2.250m ult.combi=4 k mod = 0.90
Section check
N Vy Vz Mx My Mz
Design force 273.2[kN] 0.0[kN] -0.0[kN] 0.0[kNm] 1.7[kNm] 0.0[kNm]
Design stress 8.5[MPa] 0.0[MPa] -0.0[MPa] 0.0[MPa] 1.6[MPa] 0.0[MPa]
Limit stress 15.2[MPa] 2.0[MPa] 2.0[MPa] 2.0[MPa] 22.2[MPa] 22.2[MPa]
Unity check 0.56 0.00 0.00 0.00 0.07 0.00
Bending : 0.07 (5.1.6a)
Tension + bending : 0.63 (5.1.9a)
Stability check
L0
m
k L
m
lam sigma krit
MPa
lam_rel beta c k
k crit
kc
Y 2.25 2.54 5.73 99.17 10.6 1.693 0.10 1.993 0.33
Z 2.25 1.00 2.25 48.71 44.1 0.832 0.10 0.863 0.92
LTB 2.25 1.00 2.25 473.3 0.260 1.00
Compression (5.2.1) : 0.07 (5.2.1f)
Bending (5.2.2) : 0.07
Maximal unity check = 0.63 - satisfies.
Macro :2 Member :13 L=2.285m CS : 2 - REC (200,200)
Material: GL32h
Service class : 1
gamma m =1.30 k m =0.70 (rectangle)
section=1.143m ult.combi=4 k mod = 0.90
Section check
N Vy Vz Mx My Mz
Design force -287.6[kN] 0.0[kN] 0.0[kN] 0.0[kNm] 7.0[kNm] 0.0[kNm]
Design stress -7.2[MPa] 0.0[MPa] 0.0[MPa] 0.0[MPa] 5.2[MPa] 0.0[MPa]
Limit stress 21.1[MPa] 2.0[MPa] 2.0[MPa] 2.0[MPa] 22.2[MPa] 22.2[MPa]
Unity check 0.34 0.00 0.00 0.00 0.24 0.00
Bending : 0.24 (5.1.6a)
Shear : 0.00 (5.1.7.1)
Compression + bending : 0.35 (5.1.10a)
Stability check
L0
m
k L
m
lam sigma krit
MPa
lam_rel beta c k
k crit
kc
Y 2.29 1.00 2.29 39.58 66.8 0.676 0.10 0.737 0.97
Z 2.29 1.66 3.79 65.71 24.2 1.122 0.10 1.160 0.69
LTB 2.29 1.00 2.29 728.0 0.210 1.00
Compression (5.2.1) : 0.66 (5.2.1e)
Bending (5.2.2) : 0.24
Maximal unity check = 0.66 - satisfies.