UPT - Cristian PETRUS - Analytical and Numerical Investigations

Candidate: Cristian PETRUŞCoordinators: Conf. Dr. Ing. Adrian CIUTINA

Prof. Dr. Ing. Hamid BOUCHAIR

Scope The main purpose of this research is to investigate the

behavior of a T-stub connection, having various bolt layouts, bolt materials for different plate thicknesses in order to establish the most suitable choice for such a connection;

Analytic calculations are to be carried out according to the current design norms, EC3-1-8.

A connection between an IPE240 beam and a HE160A column is to be analyzed via numerical and analytic calculations.

For this study it is relevant to observe the behaviour of the tension part of the connection since plastic deformations and yielding occurs in that part.

T-stubs in connections According to EC3-1-8 an equivalent T-stub in tension

may be used to model the design resistance of some of the basic components of the connection.

T-stubs in connections The T-stub in tension method of

calculation can be applied for various connection types.

Vulnerability of T-stubs There are 3 modes of failure recognized

by the current design code, which are1. complete yielding of the flange;2. bolt failure with yielding of the flange;3. bolt failure.

Analytic calculation The rotational capacity of a connection

is obtained in function of the moment resistance Mj,Rd, rotational stiffness Sj and rotational capacity ϕ.

Analytic calculation In order to calculate the elements which

compose the design moment-rotation characteristic of the connection, it is important to identify and calculate the basic joint components using the component method.

The equivalent T-stub in tension is a versatile tool which helps in the calculation of these components.

Analytic calculation A connection may be regarded as a set of components

which together make up the load paths by which internal forces are transmitted;

Mainly, the strength of the connection is that of its weakest component, and the flexibility of the connection is the sum of the flexibilities of the components.

Analytic calculationBasic joint components Column web panel in shear Column web in transverse compression Column web in transverse tension Column flange in bending End plate in bending Flange cleat in bending Beam or column flange and web in compression Beam web in tension Plate in tension or compression Bolts in tension Bolts in shear Bolts in bearing

Analytic calculationDesign resistance of components Column web panel in shear Column web in transverse compression Column web in transverse tension Column flange in bending End plate in bending Flange cleat in bending Beam or column flange and web in compression Beam web in tension Plate in tension or compression Bolts in tension Bolts in shear Bolts in bearing

0

,, 3

**9.0

M

wcwcyRdwp

AfV

0

,,,,,

M

wcywcwcceffwcRdwcc

ftbkF

0

,,,,,

M

wcywcwcteffRdwct

ftbF

mM

F RdplRdT

,1,,1,

4

nmFnM

F RdtRdplRdT

,,2,

,2,

2

RdtRdT FF ,,3,

)(,

,,fb

RdcRdfbc th

MF

0,,

*

M

ydRdpt

fAF

0

,,,,,

M

wbywbwbteffRdwbt

ftbF

2

2,

**

M

subRdt

AfkF

2

,

**

M

ubvRdv

AfF

2

1,

****

M

ubRdb

tdfkF

Analytic calculationStiffness coefficients of components Column web panel in shear Column web in transverse compression Column web in transverse tension Column flange in bending End plate in bending Flange cleat in bending Beam or column flange and web in compression Beam web in tension Plate in tension or compression Bolts in tension Bolts in shear Bolts in bearing

zAk vc

**38.0

1

c

wcwcceff

dtb

k ,,2

*7.0

c

wcwcteff

dtb

k ,,3

*7.0

3

3

4

*9.0m

tlk

fceff

3

3

5

*9.0m

tlk

peff

3

3

6

*9.0m

tlk

aeff

b

s

LAk *6.1

10

16

2

11*16

M

ubb

Edfdnk

Edfkknk utbb*24

12

Analytic calculation Tension resistance of bolts

Shear resistance of bolts

Bearing resistance of bolts

Design moment resistance r

RdtrrRdj FhM ,, *

2

2,

**

M

subRdt

AfkF

2,

**

M

ubvRdv

AfF

2

1,

****

M

ubRdb

tdfkF

Analytic calculationThe design moment-rotation characteristic

Analytic VS numeric The behaviour of the T-stub element

was analyzed and compared with numerical results, for high strength bolts and mild steel bolts.

State of the art Studies carried out by Bursi &

Jaspart focused on studying the semi-rigid behaviour of bolted steel connections.

State of the art A quarter of the T-stub was modeled, with correct

boundary conditions; The “spin” model was introduced for the bolt with a

shank of 20mm calculated with Agerskov’s formula; Contact elements were introduced in order to

simulate the contact between the bottom of the T-stub flange and the other T-profile in tension;

The evolution of d was measured with respect to the applied force F.

State of the art T-stub models can be modeled in 2D

and 3D space; The positioning of the bolt and the

bolt length influences the behaviour of the T-stub in a 3D manner.

Bolt length calculated with the help of the Agerskov’s formula:

)2( 41 KKAA

Lb

seff

nts lllK 71.043.11

24 2.01.0 llK n

Numeric calculation Numerical investigations were

performed in 2D with the help of Cast3M software;

3D investigations were carried out with the help of Abaqus finite element software.

Numeric calculation Analysis of the T-stub was facilitated by the

symmetry, modeling only a quarter of the element, with appropriate boundary conditions.

Numeric calculation A calibration of the 2D model was

performed in comparison with the results obtained in state of the art research.

Numeric calculationParametric study: Positioning of the bolt with respect to the

edge of the T-stub flange

Numeric calculation Accuracy of 2D model versus analytic

calculation. 25% difference acceptable?

=> 3D investigation

Numeric calculation Calibration of the 3D model, according

to state of the art research.

2/3 Mj,Rd [kNm] Φj,ini [rad] Sj,ini [kNm] Difference Experimental 43.5 0.00433 10046 8.62%Numeric - Abaqus 39.8 0.00362 10994

Numeric calculationParametric study – 48 test models: Positioning of the bolt (e=30mm, 35mm, 40mm); Bolt dimension (M14, M16, M20); Bolt grade (gr. 5.8, gr. 10.9); Thickness of T-stub flange (10mm, 12.5mm, 15mm).

Investigated parameters: Force-displacement curve; Evolution of prying force; Bolt reaction.

Bolts M14 M16 M20Thickness of plate

15 mm

T15H1-14 T15H1-16 T15H1-20T15M1-14 T15M1-16 T15M1-20T15H2-14 T15H2-16 T15H2-20T15M2-14 T15M2-16 T15M2-20T15H3-14 T15H3-16 -T15M3-14 T15M3-16 -

12.5 mm

T12H1-14 T12H1-16 T12H1-20T12M1-14 T12M1-16 T12M1-20T12H2-14 T12H2-16 T12H2-20T12M2-14 T12M2-16 T12M2-20T12H3-14 T12H3-16 -T12M3-14 T12M3-16 -

10 mm

T10H1-14 T10H1-16 T10H1-20T10M1-14 T10M1-16 T10M1-20T10H2-14 T10H2-16 T10H2-20T10M2-14 T10M2-16 T10M2-20T10H3-14 T10H3-16 -T10M3-14 T10M3-16 -

Numeric calculation Position of the bolt Bolt dimension

Bolt grade Thickness of plate10mm / 12.5mm / 15mm

M14 M16 M20

Numeric calculation Investigations on M16

high strength bolts:Thickness of plate:- 15mm- 12.5mm- 10mm

Numeric calculationM16 gr.10.9Evolution of Von mises stresses; Prying force; Effective plastic strain

Numeric calculation Investigation on M16 mild

steel boltsThickness of plate:- 15mm- 12.5mm- 10mm

Numeric calculationM16 gr.5.8Evolution of Von mises stresses; Prying force; Effective plastic strain

Numeric calculation Evolution of prying force M16 High strength bolts Mild steel bolts

Thickness of plate:

-15mm-

-12.5mm-

-10mm-

Numeric calculation Evolution of bolt reaction M16 High strength bolts Mild steel bolts

Thickness of plate:

-15mm-

-12.5mm-

-10mm-

Numeric calculation Investigations on M14

high strength bolts:Thickness of plate:- 15mm- 12.5mm- 10mm

Numeric calculationM14 gr.10.9Evolution of Von mises stresses; Prying force; Effective plastic strain

Numeric calculation Investigation on M14 mild

steel boltsThickness of plate:- 15mm- 12.5mm- 10mm

Numeric calculationM14 gr.5.8Evolution of Von mises stresses; Prying force; Effective plastic strain

Numeric calculation Evolution of prying force M14 High strength bolts Mild steel bolts

Thickness of plate:

-15mm-

-12.5mm-

-10mm-

Numeric calculation Evolution of bolt reaction M14 High strength bolts Mild steel bolts

Thickness of plate:

-15mm-

-12.5mm-

-10mm-

Numeric calculation Investigations on M20

high strength bolts:Thickness of plate:- 15mm- 12.5mm- 10mm

Numeric calculationM20 gr.10.9Evolution of Von mises stresses; Prying force; Effective plastic strain

Numeric calculation Investigations on M20

mild steel bolts:Thickness of plate:- 15mm- 12.5mm- 10mm

Numeric calculationM20 gr.5.8Evolution of Von mises stresses; Prying force; Effective plastic strain

Numeric calculation Evolution of prying force M20 High strength bolts Mild steel bolts

Thickness of plate:

-15mm-

-12.5mm-

-10mm-

Numeric calculation Evolution of bolt reaction M20 High strength bolts Mild steel bolts

Thickness of plate:

-15mm-

-12.5mm-

-10mm-

Numeric calculation Comparison for high strength bolts

Numeric calculation Comparison for mild steel bolts

Conclusions High strength bolts boost the performance in terms of

ultimate force, in comparison with mild steel bolts. Using high strength bolts, the value of the prying force is

increased. Placing the bolts closer to the T-stub web increases the

chance of developing plastic hinges in the bolt. In order to achieve proper ductility of a connection, placing

the bolts at a reasonable distance from the edge of the T-stub flange, could represent an ideal solution.

A higher value of stiffness can be obtained by increasing the thickness of the T-stub flange and by placing the bolts further from the edge of the T-stub flange.

AcknowledgementsThe research work leading to the findings

in this paper were performed under the coordination of:

Prof. Dr. Ing. Hamid BOUCHAIR Conf. Dr. Ing. Adrian CIUTINASpecial thanks to Dr. Sébastien DURIF for

his help in developing this research paper.

References Eurocode 3: Design of steel structures – Part 1-8: Design of joints, European Committee for

Standardization, December 1993; Abaqus – Analysis User’s Manual, Volume I: Introduction, Spatial Modeling, Execution & Output, version

6.10 Cast3M finite element software, www-cast3m.cea.fr Bursi OS & Jaspart JP Calibration of a Finite Element Model for Isolated Bolted End-Plate Steel

Connections, J. Construct. Steel Res. Vol. 44, No. 3, pp. 225-262, 1997 Agerskov H, High strength bolted connections subjected to prying, J Struct Div 1976; 102(1), pp. 161-

175. Charis J. Gantes & Minas E. Lemonis, Influence of equivalent bolt length in finite element modeling of T-

stub steel connections, Computers and Structures 81, pp. 595-604, 2003 Gioncu V, Mateescu D, Petcu D, Anastasiadis A, Prediction of available ductility by means of local plastic

mechanism method: DUCTROT computer programme, “Moment resistant connections of steel frames in seismic areas: Design and reliability, Ed. F.M. Mazzolani, E&FN Spon, London, pp. 95-146, 2000

Ana M. Girão Coelho, Luís Simões da Silva and Frans S. K. Bijlaard, Finite-Element Modeling of the Nonlinear Behavior of Bolted T-stub Connections, Journal of Structural engineering, ASCE, pp. 918-928, 2006

Arcelor Sections Commercial Catalogue, Beams, Channels and Merchant Bars, 2005 Eurocode 1: Actions on structures – Part 1-2: General actions – Densities, self-weight, imposed loads for

buildings, European Committee for Standardization, 2002 Design of Structural Connections to Eurocode 3 – Frequenvtly Asked Questions, Watford, September

2003, Building Research Establishment, Ltd.

Thank you for your attention!