Structural Calculations FOR Sample Project Demonstrating ... · DESIGN PHILOSOPHY Design is purely to demonstrate some the range of designs available in the Modern Engineered Software

Structural Calculations

FOR

Sample Project Demonstrating

MESS Light Gauge Steel Add in for Tedds

Modern Engineered Software Solutions Ltd

Suite 4

Tilcon House

Low Moor Lane

Lingerfield

Knaresborough

North Yorkshire

HG5 9JB

UK

+441423 855938

[email protected]

www.mess.uk.com

16057 - October 2016 (Rev A – V2.2 and instructions added)

Contents

DESIGN PHILOSOPHY .......................................................................................................................................... 3

Standards and Codes of Practice ........................................................................................................................ 3

BREVe .................................................................................................................................................................... 5

Wind loading (EN1991) ........................................................................................................................................... 6

wind loading (EN1991-1-4) .................................................................................................................................. 6

Roof Joist - C section ............................................................................................................................................ 12

Floor Truss - Lattice .............................................................................................................................................. 17

External load bearing stud design (Green) ............................................................................................................ 23

Lintel ..................................................................................................................................................................... 31

Factored Stud Check ............................................................................................................................................ 38

Facade (Infill) Stud design .................................................................................................................................... 43

Racking, Sliding and Bracing ................................................................................................................................ 48

Building Dimensions ...................................................................................................................................... 49

Loads applied ................................................................................................................................................. 49

Profile selected applied .................................................................................................................................. 49

Bracing Forces ............................................................................................................................................... 50

Braced bays required to resist wind load applied to face ‘L’ .......................................................................... 50

Braced bays required to resist wind load applied to face ‘W’ ......................................................................... 50

Overturning Check ......................................................................................................................................... 51

Sliding Check ................................................................................................................................................. 51

Alpha-Crit Checks .......................................................................................................................................... 52

DESIGN PHILOSOPHY

Design is purely to demonstrate some the range of designs available in the Modern Engineered Software

Solutions Ltd Add in for Tedds and Breve and to show users how to enter the required data properly. The

building is a sample 10m square, three storey building with a C section roof joist and lattice truss floor

joists. Wall studs are at 600mm c/c under load bearing and ‘façade’ or infill face.

Infill and ‘Façade’ is stud designed, detailed and installed so carry ONLY own self weight of studs and

cladding with wind load ONLY. Façade studs do NOT carry floor or roof loads OR contribute to ‘racking’

faces.

Load Bearing stud design is checking studs under floor and roof loading, as well as self weight

and wind load. Loads are entered as per metre run (taken from reactions of joists) and the calculation

separates out per stud based on ‘centres’

Racking and sliding checks are in accordance with latest industry guidance, including 4.5kN per pair of

studs at 600mm c/c, Alpha Crit checks and lack of member capacity checks in bracing as deemed to not

be required as deflection limits design.

Wind loading calculation, roof joist, wall stud design’s (load bearing and infill / façade), floor joist, lintel and

sliding, racking and overturning checks are to Euro Codes, BS EN 1993-1-3 for material and EN 1991-1-4

for wind loading. Calculations are in line with industry guidance such as SCI guide ED005. The software

also produces trimmer designs around openings, similar to the roof and floor designs to both EN 1993-1-3

and BS 5950-5, as are all the other designs.

Loads as table below noted in calculations and repeated here for clarity

Description Load in kN/m2

Roof Dead Load 0.9kN/m2

Roof Imposed Load 0.6kN/m2

Wind load on roof -0.88kN/m2

Wind load on walls 1.06kN/m2

Wall Dead Load 0.5kN/m2

Profile used is 150 x 1.6 and 100 x 1.2, but many more are available.

Standards and Codes of Practice

All imposed loadings are in accordance with assumed loads.

Structure is designed in accordance with SCI Guide P402 as Industry Guidance in terms of stability

ethos, etc. It is assumed that the erection, construction and generic details such as holding down

not specifically detailed in these calculations are based on this guide for the calculations’ to be

valid.

Material has been designed to BS EN 1993-1-3 and BS 5950-5

Please note that this design is a sample desk top study and not intended to be built from. In the case that it was to be built from

the erector is responsible for checking site details are as per design. Any and all queries to be directed to the engineer. Practice

do not take design responsibility for the use of the calculations without signing off any manufacturing or construction drawings to

ensure that design intent has been fully translated. The production of this report and calculations is subject to our standard terms

and conditions, available upon request and posted on the practice web site. Site inspection is categorically not allowed for and is

not the responsibility of the engineer or practice.

Drawings and 3D images kindly supplied by Vertex(UK) Ltd

MMCEngineer Ltd

Suite 3, Tilcon House, Low Moor Lane

Lingerfield, Knareasborough

North Yorkshire, HG5 9JB

Project

Sample design showing output of LGS add in for Tedds

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BREVE

Above is created using the MESS Breve Add in for Excel.

Site ID is EITHER

selected from map by

using Browse Site OR

directly entering into the

SiteID box.

Click on “Run

BREVe3.1”

Click on the

“BVe32X2” button

and follow the

prompts. At nd, click

on “Return To Excel”

button

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WIND LOADING (EN1991)

This section is produced using the built in Tedds Wind Module from the “Engineering Library” -

WIND LOADING (EN1991-1-4)

TEDDS calculation version 3.0.16

Building data

Type of roof Flat

Length of building L = 10000 mm

Width of building W = 10000 mm

Height to eaves H = 8550 mm

Eaves type Sharp

Total height h = 8550 mm

Basic values

Location ST139963

Wind speed velocity (FigureNA.1) vb,map = 22.6 m/s

Distance to shore Lshore = 34.00 km

10

00

0

85

50

Due to limitations in Tedds it’s

currently NOT possible to ‘pre

load’ the figures from Breve, so

we suggest keeping Breve /

Excel open for ease of

accessing the required figures

from Breve

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Altitude above sea level Aalt = 181.0m

Altitude factor calt = Aalt 0.001m-1 + 1 = 1.2

Fundamental basic wind velocity vb,0 = vb,map calt = 26.7 m/s

Direction factor cdir = 1.00

Season factor cseason = 1.00

Shape parameter K K = 0.2

Exponent n n = 0.5

Probability factor cprob = [(1 - K ln(-ln(1-p)))/(1 - K ln(-ln(0.98)))]n = 1.00

Basic wind velocity (Exp. 4.1) vb = cdir cseason vb,0 cprob = 26.7 m/s

Reference mean velocity pressure qb = 0.5 vb2 = 0.436 kN/m2

Orography

Orography factor not significant co = 1.0

Terrain category Country

Displacement height (sheltering effect excluded) hdis = 0mm

The velocity pressure for the windward face of the building with a 0 degree wind is to be considered as 1 part as

the height h is less than b (cl.7.2.2)

The velocity pressure for the windward face of the building with a 90 degree wind is to be considered as 1 part as

the height h is less than b (cl.7.2.2)

Peak velocity pressure - windward wall - Wind 0 deg and roof

Reference height (at which q is sought) z = 8550mm

Displacement height (sheltering effects excluded) hdis = 0 mm

Exposure factor (Figure NA.7) ce = 2.30

Peak velocity pressure qp = ce qb = 1.00 kN/m2

Structural factor

Structural damping s = 0.050

Height of element hpart = 8550 mm

Size factor (Table NA.3) cs = 0.921

Dynamic factor (Figure NA.9) cd = 1.049

Structural factor csCd = cs cd = 0.966

Peak velocity pressure - windward wall - Wind 90 deg and roof

Reference height (at which q is sought) z = 8550mm

Displacement height (sheltering effects excluded) hdis = 0 mm

Exposure factor (Figure NA.7) ce = 2.30

Peak velocity pressure qp = ce qb = 1.00 kN/m2

Structural factor

Structural damping s = 0.050

Height of element hpart = 8550 mm

Size factor (Table NA.3) cs = 0.921

Dynamic factor (Figure NA.9) cd = 1.049

Structural factor csCd = cs cd = 0.966

Peak velocity pressure for internal pressure

Peak velocity pressure – internal (as roof press.) qp,i = 1.00 kN/m2

Pressures and forces

Net pressure p = csCd qp cpe - qp,i cpi

Net force Fw = pw Aref

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Roof load case 1 - Wind 0, cpi 0.20, -cpe

Zone Ext pressure

coefficient cpe

Peak velocity pressure

qp, (kN/m2)

Net pressure p (kN/m2)

Area Aref (m2)

Net force Fw (kN)

F (-ve) -2.00 1.00 -2.13 5.00 -10.67

G (-ve) -1.40 1.00 -1.55 5.00 -7.77

H (-ve) -0.70 1.00 -0.88 40.00 -35.10

I (-ve) -0.20 1.00 -0.39 50.00 -19.69

Total vertical net force Fw,v = -73.23 kN

Total horizontal net force Fw,h = 0.00 kN

Walls load case 1 - Wind 0, cpi 0.20, -cpe

Zone Ext pressure

coefficient cpe


qp, (kN/m2)


Area Aref (m2)

Net force Fw (kN)

A -1.20 1.00 -1.36 17.10 -23.27

B -0.80 1.00 -0.97 68.40 -66.63

D 0.78 1.00 0.55 85.50 47.44

E -0.46 1.00 -0.65 85.50 -55.28

Overall loading

Equiv leeward net force for overall section Fl = Fw,wE = -55.3 kN

Net windward force for overall section Fw = Fw,wD = 47.4 kN

Lack of correlation (cl.7.2.2(3) – Note) fcorr = 0.85 as h/W is 0.855

Overall loading overall section Fw,D = fcorr (Fw - Fl + Fw,h) = 87.3 kN

Roof load case 2 - Wind 0, cpi -0.3, +cpe

Zone Ext pressure

coefficient cpe


qp, (kN/m2)


Area Aref (m2)

Net force Fw (kN)

F (+ve) -2.00 1.00 -1.63 5.00 -8.17

G (+ve) -1.40 1.00 -1.05 5.00 -5.27

H (+ve) -0.70 1.00 -0.38 40.00 -15.07

I (+ve) 0.20 1.00 0.49 50.00 24.69



Walls load case 2 - Wind 0, cpi -0.3, +cpe

Zone Ext pressure

coefficient cpe


qp, (kN/m2)


Area Aref (m2)

Net force Fw (kN)

A -1.20 1.00 -0.86 17.10 -14.71

B -0.80 1.00 -0.47 68.40 -32.38

D 0.78 1.00 1.06 85.50 90.25

E -0.46 1.00 -0.15 85.50 -12.47

Overall loading



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Lack of correlation (cl.7.2.2(3) – Note) fcorr = 0.85 as h/W is 0.855


Roof load case 3 - Wind 90, cpi 0.20, -cpe

Zone Ext pressure

coefficient cpe


qp, (kN/m2)


Area Aref (m2)

Net force Fw (kN)

F (-ve) -2.00 1.00 -2.13 5.00 -10.67

G (-ve) -1.40 1.00 -1.55 5.00 -7.77

H (-ve) -0.70 1.00 -0.88 40.00 -35.10

I (-ve) -0.20 1.00 -0.39 50.00 -19.69



Walls load case 3 - Wind 90, cpi 0.20, -cpe

Zone Ext pressure

coefficient cpe


qp, (kN/m2)


Area Aref (m2)

Net force Fw (kN)

A -1.20 1.00 -1.36 17.10 -23.27

B -0.80 1.00 -0.97 68.40 -66.63

D 0.78 1.00 0.55 85.50 47.44

E -0.46 1.00 -0.65 85.50 -55.28

Overall loading



Lack of correlation (cl.7.2.2(3) – Note) fcorr = 0.85 as h/L is 0.855


Roof load case 4 - Wind 90, cpi -0.3, +cpe

Zone Ext pressure

coefficient cpe


qp, (kN/m2)


Area Aref (m2)

Net force Fw (kN)

F (+ve) -2.00 1.00 -1.63 5.00 -8.17

G (+ve) -1.40 1.00 -1.05 5.00 -5.27

H (+ve) -0.70 1.00 -0.38 40.00 -15.07

I (+ve) 0.20 1.00 0.49 50.00 24.69



Walls load case 4 - Wind 90, cpi -0.3, +cpe

Zone Ext pressure

coefficient cpe


qp, (kN/m2)


Area Aref (m2)

Net force Fw (kN)

A -1.20 1.00 -0.86 17.10 -14.71

B -0.80 1.00 -0.47 68.40 -32.38

D 0.78 1.00 1.06 85.50 90.25

E -0.46 1.00 -0.15 85.50 -12.47

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Overall loading



Lack of correlation (cl.7.2.2(3) – Note) fcorr = 0.85 as h/L is 0.855


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ROOF JOIST - C SECTION

Select Standard to be used

Member as Roof OR

Floor (Roof defaults to

‘Flat Roof’ type in output)

Distance between

supports for member

Form of joist – Solid

C or Lattice Truss

Distance, centre to

centre, between joists

Loads to apply:

Permanent (Dead)

Variable (Imposed)

Wind Uplift (Roof ONLY)

Select section from list

Roof Joist

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Results Page:

Moment Capacity

Single Deflection Check for ROOF

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Dimensions

Member span L = 5000mm

Joist spacing Sjoists = 600 mm

BoardType = "Flat Roof"

Loads

Permanent load (unfactored) gk = 0.90 kN/m2

Variable load (unfactored) qk = 0.6 kN/m2

Wind Uplift (Unfactored) qkW = 0.9 kN/m2

Load factors

Permanent G = 1.35

Variable Q = 1.5

Section dimensions and material properties for a joist to EN 1993-1-3

The floor joist is a lipped C section from Generic 150x45x1.6, manufactured from 390 N/mm2 steel with a Z275 coating to

BS EN 10346.

Section depth h = 150.0 mm

Flange width b = 45.0 mm

Stiffener depth c = 12.0 mm

Corner radius r = 2.4mm

Nominal thickness t = 1.6 mm

Core thickness tn = t – 0.04mm = 1.6mm

Basic yield strength fyb = 390.0 N/mm2

Modulus of elasticity E = ESEC3 = 210.0 kN/mm2

Shear modulus G = 80769 N/mm2

Partial factor M0 = 1.0


Section Properties

Gross Properties

Second moment of area about y axis Iy = 129.1 cm4

Effective Section Properties

Second moment of area about y axis Iy.eff = 121.5 cm4

Elastic section modulus for bending about y axis Weff.y = 15.8 cm3

Serviceability Deflections

For cross-section stiffness properties the influence of rounded corners should always be taken into account. For this

example it is assumed that the maximum stress at serviceability is the design yield strength divided by 1.5. BS EN 1993-1-

3, 5.1(3)

Iy = 129.1cm4

Iy.eff = 121.5cm4

Ific = Iy – (1/1.5) (Iy – Iy.eff) = 124cm4

BS EN 1993-1-3, 7.1(3)

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The influence of rounded corners has been taken account in the calculation of the Igr and Ieff values used to calculate Ific.

Therefore, the second moment of area for serviceability is given by

Ific = 124cm4

Support Reaction’s

Reaction under gk ultimate loads is,

RA,ULSgk = (G gk Sjoists L ) / 2 = 1.8kN

Reaction under qkV ultimate loads is,

RA,ULSqk = (Q qk Sjoists L ) / 2 = 1.4kN

Reaction under qkW ultimate loads is,

RA,ULSqkW = (Q qkW Sjoists L ) / 2 = 2.0kN

Reaction under ultimate loads is,

RA,ULS = Max((RA,ULSgk + RA,ULSqk), (RA,ULSgk - RA,ULSqkW)) = 3.2kN

Reaction under gk un factored loads is,

RA,SLSgk = (gk L ) / 2 = 2.3kN/m

Reaction under qk un factored loads is,

Variable, RA,SLSqk = (qk L ) / 2 = 1.5kN/m

Wind, RA,SLSqkW = (qkW L ) / 2 = 2.3kN/m

Reaction under un factored loads is,

RA,SLS = Max ((RA,SLSgk + RA,SLSqk) , (RA,SLSgk - RA,SLSqkW)) = 3.8kN/m

Design Moment

Applied design moment is given by,

BM = Max((((G gk + Q × qk) Sjoists L2 ) / 8), (((G gk - Q × qkW) Sjoists L2 ) / 8)) = 4.0kNm

Resistance of Cross-Section

Bending Moment – BS EN 1993-1-3, 6.1.4

Design moment resistance for bending about y axis is given by, Mcy,Rd = (Weff.y fyb ) / M0 = 6.1kNm

Ratio 0.65

Moment Capacity - PASS

Buckling Resistance of Member

Lateral Torsional Buckling

The member is assumed to be restrained along the length of the inner and outer faces by the connection to the diagonals

and boarding. Therefore, the member is not required to be checked for lateral torsional buckling.

Roof Deflection Check

For light weight steel roofs assuming fall to roof to prevent ponding there is only one serviceability criteria that should be

checked to ensure acceptable performance of the roof in service.

Imposed load deflection less than span/360.

Total load is, W = Max(L Sjoists qk, L Sjoists (qkW – gk)) = 1.8 kN

Deflection due to load is given by = (5/384) (W L3)/ (E Ific)) = 11.2mm

Reactions used in

stud calculation

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Deflection limit is

limit = L / 360 = 13.9mm

Ratio 0.81

Deflection Criteria - PASS

Roof Deflection Check

For light weight steel roofs assuming fall to roof to prevent ponding there is only one serviceability criteria that should be

checked to ensure acceptable performance of the roof in service.


Total load is, W = Max(L Sjoists qk, L Sjoists (qkW – gk)) = 1.9 kN


Deflection limit is

limit = L / 360 = 14.6mm

Ratio 0.98

Deflection Criteria - PASS

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FLOOR TRUSS - LATTICE

Member as Roof OR Floor (Floor

offers differing ‘Board types’

which affect deflection

Distance between

supports for member


C or Lattice Truss

Distance, centre to

centre, between joists


– Note: Section to be re

selected when changing

Standard

Loads to apply:

Permanent (Dead)

Variable (Imposed)

Wind Uplift (Roof ONLY)


Partial Factors – Auto Complete and

NOT applicable to British Standards so

removed when standard selected

Floor Truss

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When it comes to selecting the floor type don’t forget to look at the Notes!

SCI Guide P402 discusses various floor types in Table 2.7 but as an Engineer doesn’t tell us weights OR floor types for the four

deflection checks. Working with the SCI we have ‘enhanced’ the tables and included them in the Notes – sample below:

Output Screen

Moment Checks

Deflection Checks

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Dimensions

Member span L = 5000mm

Joist spacing Sjoists = 600 mm

BoardType = "Flat Roof"

Loads

Permanent load (unfactored) gk = 0.50 kN/m2

Variable load (unfactored) qk = 2.20 kN/m2

Number of effective joists carrying 1kN point load Neff = 2.75

Load factors

Permanent G = 1.35

Variable Q = 1.5

For a lattice joist, using C section’s from Generic 150x45x1.6, manufactured from 390 N/mm2 steel with a Z275 coating to:

Effective cross sectional area of section Aeff = 2.3 cm2

Gross cross sectional area of section Agr = 4.0cm2

Depth of C section b = 45.0mm

Depth of lattice truss D = 245.0mm

Position of cenroid in relation to the web yc,eff =b / 2 = 22.5mm

Diameter of screw d = 4.2mm

Gross Second moment of area of section Iz = 9.8cm4

Effective Second moment of area of section Iz.eff = 8.2cm4

Effective Second moment of area of section IficC = Iz – (1/1.5) (Iz – Iz.eff) = 8.70cm4

Gross Second moment of area of section Iy = 129.1cm4

Effective Second moment of area of section Iy.eff = 121.5cm4

Effective Second moment of area of section Ificy = Iy – (1/1.5) (Iy – Iy.eff) = 124.06cm4

Material gauge t = 1.6mm

Material gaug, effective tcor = t – 0.04mm = 1.6mm

Yield strength of section fyb = 390N/mm2

Ultimate Yield strength of section fu = 440N/mm2

Average yield strength fya= MIN((fyb + (fu - fyb) ((7 4 tcor2) / Agr)), ((fu +fyb) /2)) = 399N/mm2

Modulus of elasticity E = ESEC3 = 210 kN/mm2

Effective depth of lattice deff = D – (2 yc,eff) = 20cm



Second moment of area of lattice Ific = 2(IficC +( Aeff (deff/2)2)) = 479cm4

Maximum member length for lattice Lm = deff /cos(45) = 28cm

Compressive resistance Nc,Rd = (Aeff fyb / M0 = 90.1kN

Tensile resistance Nt,Rd = (Agr fya / M0 = 157.5kN

Members restrained at either end by 2No. 5.5 diameter screws:

Member as Roof OR Floor (Floor

offers differing ‘Board types’

which affect deflection


C or Lattice Truss

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= MIN((3.2 ( tcor / d)),2.1) = 2.0

Fb,Rd = ( fu d tcor) / M2 = 4.5kN


Reaction under gk ultimate loads is, RA,ULSgk = (G gk Sjoists L ) / 2 = 1.0kN

Reaction under qk ultimate loads is, RA,ULSqk = (Q qk Sjoists L ) / 2 = 5.0kN

Reaction under ultimate loads is, RA,ULS = RA,ULSgk + RA,ULSqk = 6.0kN

Reaction under gk un factored loads is, RA,SLSgk = (gk L ) / 2 = 1.3kN/m

Reaction under qk un factored loads is, RA,SLSqk = (qk L ) / 2 = 5.5kN/m

Reaction under un factored loads is, RA,SLS = RA,SLSgk + RA,SLSqk = 6.8kN/m

Design Moment

Applied design moment is given by, BM = ((G gk + Q × qk) Sjoists L2 ) / 8 = 7.5kNm

Strength:

Tensile force in truss Pt,truss = BM/ deff = 37.3kN

Tensile capacity of member Nt,Rd = 157.5kN

Ratio 0.24

Bending Check - PASS

Maximum shear Fv = RA,ULS = 6.0kN

Maximum compressive load in member Pc = (Fv Lm) / deff = 8.4kN

Nc,Rd =90.1kN

Ratio 0.09

Shear Check - PASS

Fixings required, based up on applied load and fixing capacity, No. = ceiling(MAX((Pc / Fb,Rd),2),1) = 2 fixings per end.





Criteria 1

Dead load plus imposed load deflection less than span/350 or 15 mm whichever is smaller.

Total load is, W = L Sjoists (gk + qk) = 8.1 kN

Deflection due to load is given by = (5/384)W L3)/ (E Ific)) = 13.1mm

Deflection limit is limit1 = MIN((L / 350),15mm) = 14.3mm

Ratio 0.92

Deflection Criteria 1 - PASS

Reactions used in stud designs

Note Number of

fixings required

MMCEngineer Ltd




Project


Job Ref.

16057

Section


Sheet no./rev.

22 A

Calc. by

SDN

Date

30/08/2017

Chk'd by

SLN

Date

30/08/2017

App'd by

Date

Criteria 2


Total load is, W = L Sjoists qk = 6.6 kN


Deflection limit is limit2 = L / 450 = 11.1mm

Ratio 0.96


Criteria 3

Natural frequency of the floor not less than 8 Hz.

Total load for this criteria is, W = L Sjoists (gk + 0.2 qk) = 2.8 kN


Deflection limit for 8 Hz is limit3 = 5mm

Ratio 0.91


Criteria 4

Deflection of floor system less than critical value subject to 1 kN point load.

Total load for this criteria is, W = 1.0 kN

Deflection due to load is given by = (1/48) (W L3)/ (E Ific Neff)) = 0.94mm

The deflection limit for this criteria is dependent on the span of the joist.

limit4 = 1mm 3.7554 (L/1m)-0.627 = 1.37 mm

Ratio 0.69


Deflection Checks –

ratio included.

MMCEngineer Ltd




Project


Job Ref.

16057

Section


Sheet no./rev.

23 A

Calc. by

SDN

Date

30/08/2017

Chk'd by

SLN

Date

30/08/2017

App'd by

Date

EXTERNAL LOAD BEARING STUD DESIGN (GREEN)




Standard

Loads to apply:

Roof & Floor Loads taken from relevant calculations

Number of floors (Don’t include Ground Floor)

Wall self weight (0.5kN/m2 x Storey height =

1.4kN/m)

Wind Load – taken from original wind analysis.

Element load to be used.

Note Loads entered as per metre run


Clear Stud height Stud centres – drop down box

Number of noggins

(horizontal members

preventing twist on plan) –

drop down box

Wall stud

MMCEngineer Ltd




Project


Job Ref.

16057

Section


Sheet no./rev.

24 A

Calc. by

SDN

Date

30/08/2017

Chk'd by

SLN

Date

30/08/2017

App'd by

Date

When it comes to wall self-weight don’t forget to look at the Notes!

SCI Guide P402 discusses various floor types in Table 2.5 but as an Engineer doesn’t tell us weights. We have ‘enhanced’ the

tables, with SCI’s knowledge, and included them in the Notes – sample below:

Output Screen

Capacity Checks

EC on Left, BS on Right

EC shown, BS hidden

MMCEngineer Ltd




Project


Job Ref.

16057

Section


Sheet no./rev.

25 A

Calc. by

SDN

Date

30/08/2017

Chk'd by

SLN

Date

30/08/2017

App'd by

Date

MMCEngineer Ltd




Project


Job Ref.

16057

Section


Sheet no./rev.

26 A

Calc. by

SDN

Date

30/08/2017

Chk'd by

SLN

Date

30/08/2017

App'd by

Date

Dimensions

Stud height L = 2.85m

Stud spacing s = 600.0mm

Number of noggins N = 3.0

Number of floors NFloor = 3.0

Section dimensions and material properties

The wall stud is a C section’s from Generic 100 x 50 x 1.6, manufactured from 390 N/mm2 steel with a Z275 coating to BS

EN 10346.

Section depth h = 100.0mm

Flange width b = 50.0mm

Stiffener depth c = 12.5mm


Nominal thickness t = 1.6mm

Core thickness tn = t – 0.04mm =1.6mm

Basic yield strength fyb = 390.0N/mm2

Modulus of elasticity ESEC3 =210000.0N/mm2


Partial factor M0 =1.0


Section Properties

The calculation of section properties is not included in this calculation.

Gross Properties

Area Agr = 3.4cm2

Radius of gyration about y axis iy = 40.2mm

Radius of gyration about z axis iz = 18.4mm

Position of y axis from flange yflange = 49.2mm

Position of z axis from web zweb = 15.9mm

Position of shear centre with respect to the z axis yo = 39.3mm

Position of shear centre with respect to the y axis zo = 0mm

Torsion constant It = 276.6mm4

Warping constant Iw = 229.3cm6

Second moment of area about y axis Iy =54.5cm4

Second moment of area about z axis Iz = 11.4cm4


Effective area subject to compression Aeff = 2.4cm2

Elastic section modulus for bending about y axis Weff.y = 10.0cm3

Elastic section modulus for bending about z axis Weff.zlips = 2.9cm3

Position of y axis from flange(due to compression) yeff.flange = 49.2mm

Position of z axis from web (due to compression) zeff.web = 16.7mm

Second moment of area about y axis (due to bending) Iy.eff = 51.2cm4

Loads

Roof Load (Permanent) Ned,RoofP = 2.3kN/m

Roof Load (Variable) Ned,RoofV = 1.5kN/m

Floor Load (Permanent) Ned,FloorP = 1.3kN/m

Floor Load (Variable) Ned,FloorV = 5.5kN/m

MMCEngineer Ltd




Project


Job Ref.

16057

Section


Sheet no./rev.

27 A

Calc. by

SDN

Date

30/08/2017

Chk'd by

SLN

Date

30/08/2017

App'd by

Date

Number of floors, NFloor = 3.0

Wall Load Ned,wall = 1.4kN/m

Unfactored wind load qk = 1.0 kN/m2

Load factors

Permanent G = 1.35

Variable Q = 1.5

Unfactored axial load’s

Unfactored Permanent axial load, NedPSLS =(Ned,RoofP + (Ned,FloorP NFloor )+ (Ned,wall NFloor + 1))) = 11.8kN/m

Unfactored Variable axial load, NedQSLS = (Ned,RoofV + (Ned,FloorV NFloor )) = 18.0kN/m

Unfactored Total axial load, NedSLS = (NedPSLS + NedQSLS ) s = 17.9kN

Unfactored wind load qkSLS = qk =1.0kN/m2

Factored axial load’s

Factored Permanent axial load, NedP =(Ned,RoofP + (Ned,FloorP NFloor )+ (Ned,wall NFloor + 1))) G = 15.9kN/m

Factored Variable axial load, NedQ = (Ned,RoofV + (Ned,FloorV NFloor )) Q = 27.0kN/m

Factored Total axial load, Ned = (NedP + NedQ ) s = 25.8kN

Factored wind load qkuls = qk Q =1.5kN/m2

Maximum applied moment in strong axis

My,Ed =MAX((((Ned,FloorP G) + (Ned,FloorV Q)) s) ((h/2)+25mm) + ((L2 s qk 0.75) / 8 ), (((Ned,FloorP G) + (Ned,FloorV

1.05)) s) ((h/2)+25mm) +((L2 s qk Q) / 8 )) = 1.3kNm

Maximum applied moment in strong axis, My,Ed = 1.3kNm

Maximum applied moment in weaker axis, Mz,Ed = 0kNm

Bending Moment factors from SCI P362, based on Table C1, Partial,

combination and reduction factors for the STR and GEO ultimate limit

states for buildings


Axial Compression

Design resistance of cross section for compression is given by, Nc,Rd = (Aeff × fyb )/ M0 = 94.0kN

Bending Moment

Design moment resistance for bending about y axis is given by, Mcy,Rd = (Weff.y × fyb) / M0 = 3.9kNm

Design moment resistance for bending about z axis Mcz,Rd = (Weff.zlips × fyb) / M0 = 1.1kNm


Flexural Buckling about major axis (y axis)

From Table 6.3 of BS EN 1993-1-3, the buckling curve for a lipped C section buckling about any axis is buckling curve b.

The buckling length for buckling about the y axis is taken as equal to the member length.

Lcr,y = L = 2850.0mm

1 = (ESEC3 / fyb) = 72.9

Non dimensional slenderness factor is, = Lcr,y / iy) (((Aeff / Agr))/1) = 0.8

For buckling curve b, the imperfection factor, = 0.34

Factored Axial Load

used in Racking Design

MMCEngineer Ltd




Project


Job Ref.

16057

Section


Sheet no./rev.

28 A

Calc. by

SDN

Date

30/08/2017

Chk'd by

SLN

Date

30/08/2017

App'd by

Date

= 0.5 ( 1+ (– 0.2) + 2) = 0.9

2)) = 0.7

Flexural buckling resistance is, Nb,Rd = (Aeff fyb) / M1 = 66.8kN

Ratio 0.4

Unity Check - PASS

Combined Compression and Bending

The shift in the position of the effective section neutral axis relative to gross section neutral axis causes an additional

moment due to axial load which is assumed to be applied at the gross section neutral axis.

The shift in y axis due to axial compression is given by, eNy = yeff.flange - yflange = 0.0 mm

The shift in z axis due to axial compression is given by, eNz = zeff.web - zweb = 0.7 mm

Additional y axis moment due to shift in axis is, My,Ed = eNy Ned = 0.0 kNm

Additional z axis moment due to shift in axis is, Mz,Ed = eNz Ned = 0.0 kNm

Unity Check

U1 = (Ned / Nc,Rd) + ((My,Ed + My,Ed)/ Mcy,Rd) + ((Mz,Ed + Mz,Ed)/ Mcz,Rd) = 0.6

Ratio 0.6

Unity Check - Pass

Flexural Buckling about minor axis (z axis)

The buckling length for buckling about the z axis is based on the number of noggins reducing the effective height, i.e. 1

noggin gives half height, and introduce lateral restraint in the wall.

Lcr,z = L / (N+1) = 712.5mm

1 = 72.9

Non dimensional slenderness factor is = ( Lcr,z / iz) (((Aeff / Agr)) /1) = 0.4

For buckling curve b, the imperfection factor = 0.34

= 0.5 ( 1+ ( – 0.2) + 2) = 0.6

= 1/ (+2)) = 0.9


Ratio 0.3

Unity Check - PASS

Torsional Buckling

The torsional buckling lengths are

LT,y = L = 2850.0 mm

LT,z = Lcr,z =712.5 mm

The polar radius of gyration is calculated as below, io =( iy2 + iz2 + yo2 + zo

2 ) = 59mm

The elastic critical force for torsional buckling of a simply supported member is given by,

Ncr,T = (1/ io2) ((G It ) + ((2 ESEC3 Iw) / LT,z2)) = 274.0kN

MMCEngineer Ltd




Project


Job Ref.

16057

Section


Sheet no./rev.

29 A

Calc. by

SDN

Date

30/08/2017

Chk'd by

SLN

Date

30/08/2017

App'd by

Date

Non dimensional slenderness factor is T= ((Aeff fyb) / Ncr,T) = 0.6


= 0.5 ( 1+ (T – 0.2) + T2) = 0.7

T

2)) = 0.8

Torsional buckling resistance is, Nb,Rd = (Aeff fyb) / M1 = 79.3kN

Ratio 0.3

Unity Check Pass

Torsional-Flexural Buckling

Ncr,y = (2 ESEC3 Iy) / LT,y2 = 139.0kN

= 1 –(yo / io)2 = 0.6

The elastic critical force for torsional-flexural buckling is given by,

Ncr,TF = (Ncr,y / (2 Ncr,T / Ncr,y) - ((1-( Ncr,T / Ncr,y))2+ 4(yo / io)2 (Ncr,T / Ncr,y))) = 108.1kN

Non dimensional slenderness factor is

TF = ((Aeff fyb )/ Ncr,TF) = 0.9


TF = 0.5 ( 1+ (TF – 0.2) + TF 2) = 1.1

TFTFTFTF

2)) = 0.6

Torsional buckling resistance is, Nb,Rd = (TFAeff fyb) / M1 = 60.2kN

Ratio 0.4

Unity Check - PASS


The maximum length of member between points of minor axis lateral restraint is determined by noggin centres.

LT,z = 712.5mm

Coefficients dependent on loading and end restraint C1 = 1.127

C2 = 0.454

Effective length factor for end rotation on plan k = 1.00

Effective length factor for end warping kw = 1.00

The distance from the point of load application to the shear centre is taken as half the stud depth.

zg = h / 2 = 50.0 mm

The factor g is used in the calculation of Mcr, it may conservatively be taken as 1.0 or may be calculated as below.

g = (1-(Iz / Iy)) = 0.889

The elastic critical moment for lateral torsional buckling is given by

Mcr = C1 ((2 ESEC3 Iz) / ((k LT,z)2 g)) (((k/ kw)2 (Iw / Iz) + (((k LT,z)2 (G It))/ (2 ESEC3 Iz)) + (C2 zg)2) – (C2

zg)) = 16.6kNm

For lateral torsional buckling curve b should be used.

Non dimensional slenderness factor is LT = ((Weff.y fyb )/ Mcr) = 0.5


LT = 0.5 ( 1+ ( LT – 0.2) + LT 2) = 0.7

MMCEngineer Ltd




Project


Job Ref.

16057

Section


Sheet no./rev.

30 A

Calc. by

SDN

Date

30/08/2017

Chk'd by

SLN

Date

30/08/2017

App'd by

Date

LT= 1 /LTLT2LT

2)) = 0.9

Lateral torsional buckling resistance is,

Mb,Rd = ( LT Weff.y × fyb) / M1 = 3.5kNm

Combined Bending and Axial Compression

The interaction of bending moment and axial force may be obtained from a second order analysis or by using the formula

below:

(Ned / Nb,Rd)0.8 + (My,Ed / Mb,Rd)0.8

Ratio 0.9

Unity Check - PASS

Nb,Rd is the minimum value from flexural, torsional and torsional-flexural buckling.

My,Ed includes any additional moments due to the shift in the neutral axis.

Serviceability Deflections

For cross-section stiffness properties the influence of rounded corners should always be taken into account. For this

example it is assumed that the maximum stress at serviceability is the design yield strength divided by 1.5.

Iy = 54.5cm4

Iy.eff = 51.2cm4

Ific = Iy – (1/1.5) (Iy - Iy.eff) = 52cm4

BS EN 1993-1-3, 7.1(3) Total wind load is W = L s qk = 1.7kN

Deflection due to wind is given by d= (5/384) ((W L3)/ (ESEC3 Ific)) = 4.7mm

Deflection limit is taken as length divided by 360, dlimit = L / 360 = 7.9 mm

Ratio 0.6

Deflection Check - Pass

MMCEngineer Ltd




Project


Job Ref.

16057

Section


Sheet no./rev.

31 A

Calc. by

SDN

Date

30/08/2017

Chk'd by

SLN

Date

30/08/2017

App'd by

Date

LINTEL




Standard


Depth ONLY available

IF ‘Truss’ type selected

– NOT calculated to

allow user to drive.

Pre-determined and ONLY

shown if Eurocodes.

Defaults to Span / 360 but

other values can be used.

C section or Lattice Truss?

Lintel

MMCEngineer Ltd




Project


Job Ref.

16057

Section


Sheet no./rev.

32 A

Calc. by

SDN

Date

30/08/2017

Chk'd by

SLN

Date

30/08/2017

App'd by

Date

Dimensions as the diagram

Loads to apply:

Wind Load – taken from original wind analysis.

Element load to be used.

Roof & Floor Loads taken from relevant calculations

Number of floors (Don’t include Ground Floor)

Wall self weight (0.5kN/m2 x Storey height =

1.4kN/m)

MMCEngineer Ltd




Project


Job Ref.

16057

Section


Sheet no./rev.

33 A

Calc. by

SDN

Date

30/08/2017

Chk'd by

SLN

Date

30/08/2017

App'd by

Date

Wind Loads and Dimensions

Wind Pressure, p = 1.0kN/m2

Stud height, H =2.9m

Floor to window head, Wh = 2.5m

Window width, L = 1.5m

Floor to window cill, Wc = 1.2m

Window height, hwin = Wh - Wc = 1.3m

Window head height, Hh = H – Wh = 0.4m

Window height, hwin = Wh - Wc = 130.0cm

Deflection limit specified, DefLimit = 360

Allowable deflection, based on plasterboard finish, dfln = H / DefLimit = 7.9mm

Loads

Roof Load (Permanent) Ned,RoofP = 2.3kN/m

Roof Load (Variable) Ned,RoofV = 1.5kN/m

Floor Load (Permanent) Ned,FloorP = 1.3kN/m

Floor Load (Variable) Ned,FloorV = 5.5kN/m

Wall Load Ned,wall = 1.4kN/m

Number of floors NFloor = 3.0

Unfactored wind load p = 1.0 kN/m2

Uniform Permanent load (unfactored) gk = Ned,RoofP + (Ned,FloorP NFloor )+ (Ned,wall NFloor + 1)) = 11.9kN/m

Uniform Variable load (unfactored) qk = Ned,RoofV + (Ned,FloorV NFloor ) = 18.00 kN/m

Concentrated Permanent load (unfactored) gkPL = 0kN

Concentrated Variable load (unfactored) qk PL = 0kN

Position along span, from left support, of PL, X = 0mm

For a lattice joist, using C section’s from Generic 100 x 50 x 1.6, manufactured from 390 N/mm2 steel with a Z275 coating

to:

MMCEngineer Ltd




Project


Job Ref.

16057

Section


Sheet no./rev.

34 A

Calc. by

SDN

Date

30/08/2017

Chk'd by

SLN

Date

30/08/2017

App'd by

Date

Effective cross sectional area of section Aeff = 2.4 cm2

Gross cross sectional area of section Agr = 3.4cm2

Depth of C section b = 50.0mm

Depth of lattice truss D = 350.0mm

Position of cenroid in relation to the web yc,eff =b / 2 = 25.0mm

Diameter of screw d = 4.2mm

Gross Second moment of area of section Iz = 11.4cm4

Effective Second moment of area of section Iz.eff = 9.9cm4

Effective Second moment of area of section IficC = Iz – (1/1.5) (Iz – Iz.eff) = 10.39cm4

Gross Second moment of area of section Iy = 54.5cm4


Effective Second moment of area of section Ificy = Iy – (1/1.5) (Iy – Iy.eff) = 52.32cm4






Modulus of elasticity E = ESEC3 = 210 kN/mm2

Effective depth of lattice deff = D – (2 yc,eff) = 30cm



Second moment of area of lattice Ific = 2(IficC +( Aeff (deff/2)2)) = 1105cm4

Maximum member length for lattice Lm = deff /cos(45) = 42cm

Compressive resistance Nc,Rd = (Aeff fyb / M0 = 94.0kN

Tensile resistance Nt,Rd = (Agr fya / M0 = 134.8kN

Members restrained at either end by 2No. 5.5 diameter screws:

= MIN((3.2 ( tcor / d)),2.1) = 2.0

Fb,Rd = ( fu d tcor) / M2 = 4.5kN

Horizontal Section Properties

Gross Second moment of area of section resisting lateral load Iy = 54.5cm4


Effective Second moment of area of section IficH = Iy – (1/1.5) (Iy – Iy.eff) = 52.32cm4

UDL Live load on joist,SLS WLL = L qk = 27.0kN

UDL Dead load on joist,SLS WDL = L gk = 17.9kN

Total UDL load on beam,SLS WT = WLL+ WDL = 44.9kN

MMCEngineer Ltd




Project


Job Ref.

16057

Section


Sheet no./rev.

35 A

Calc. by

SDN

Date

30/08/2017

Chk'd by

SLN

Date

30/08/2017

App'd by

Date

Total UDL load on joist,ULS WULS = (WLL Q)+ (WDL G) = 64.6kN

Total Point Load load on beam,SLS WTPL = gkPL + qkPL = 0.0kN

Total Point Load load on joist,ULS WULSPL = (qkPL Q)+ (gkPL G) = 0.0kN

Horizontal Design

Wind load deflection less than span/360.

Area C AC = (L / 2) ((Wh – Wc) / 4) = 0.2m2

Area D AD= (L / 2) ((H – Wh) / 2) = 0.1m2

Wind load on lintel, SLS, WLSLS = p (AC + AD) 2 = 0.8kN

Design Moment from horizontal loads

Applied design moment is given by, Mc = (Q × WLSLS L ) / 8 = 0.2kNm

Deflection due to load is given by h= (5/384) ( WLSLS L 3)/ (E IficH)) = 0.3mm

Deflection limit is limith = L / 360 = 4.2mm

Horizontal Deflection Criteria - PASS

Horizontal Checks


Bending Moment – BS EN 1993-1-3, 6.1.4

Design moment resistance for bending about y axis is given by,Mcy,Rd = (Weff.y fyb ) / M0 = 3.9kNm

Moment Capacity - PASS



MMCEngineer Ltd




Project


Job Ref.

16057

Section


Sheet no./rev.

36 A

Calc. by

SDN

Date

30/08/2017

Chk'd by

SLN

Date

30/08/2017

App'd by

Date




Reaction under gk ultimate loads is,

RA,ULSgk = ((G gk L ) / 2 ) + (((gkPL G) X) / L) = 12.0kN

RB,ULSgk = ((G gk L ) / 2 ) + (((gkPL G) (L - X)) / L) = 12.0kN

Reaction under qk ultimate loads is,

RA,ULSqk = ((Q qk L ) / 2) + (((qkPL Q) X) / L) = 20.3kN

RB,ULSqk = ((Q qk L ) / 2) + (((qkPL Q) (L - X)) / L) = 20.3kN

Reaction under ultimate loads is,

RA,ULS = RA,ULSgk + RA,ULSqk = 32.3kN

RB,ULS = RB,ULSgk + RB,ULSqk = 32.3kN

Reaction under gk un factored loads is,

RA,SLSgk = ((gk L ) / 2) + ((gkPL X) / L)= 8.9kN

RB,SLSgk = ((gk L ) / 2) + ((gkPL (L - X)) / L)= 8.9kN

Reaction under qk un factored loads is,

RA,SLSqk = ((qk L ) / 2) + ((qkPL X) / L) = 13.5kN

RB,SLSqk = ((qk L ) / 2) + ((qkPL (L - X)) / L) = 13.5kN

Reaction under un factored loads is,

RA,SLS = RA,SLSgk + RA,SLSqk = 22.4kN

RB,SLS = RB,SLSgk + RB,SLSqk = 22.4kN

Bending Capacity Checks

Max momentMx = ((WULSL)/8) + ((WULSPL X (L-X)) / L) = 12.1kNm

Tensile force in truss Pt,truss = Mx / deff = 40.4kN

Tensile capacity of member Nt,Rd = 134.8kN

Ratio 0.30

Bending Check - PASS

Shear Capacity Checks

Maximum shear Fv = (WULS / 2) + (RA,ULS) = 64.6kN

Maximum compressive load in member Pc = (Fv Lm) / deff = 91.4kN

Nc,Rd =94.0kN

Ratio 0.97

Shear Check - PASS

This is the reaction used

in the factored stud

design, supporting the

lintel

MMCEngineer Ltd




Project


Job Ref.

16057

Section


Sheet no./rev.

37 A

Calc. by

SDN

Date

30/08/2017

Chk'd by

SLN

Date

30/08/2017

App'd by

Date

Fixings required, based up on applied load and fixing capacity, No. = ceiling(MAX((Pc / Fb,Rd),2),1) = 21 fixings per end.





Criteria 1

Dead load plus imposed load deflection less than span/360.

Deflection due to load is given by

= Max(((5/384) WT L3)/ (E Ific))), (WT X L – X) ) / (24 E Ific L ) (L2 + X ( L – X)) + ((WTPL X ( L – X)

(L + X)) / (27 E Ific L ) (3 (L – X) (L + X )))) =0.8mm

Deflection limit is

limit = L / 360 = 4.2mm

Ratio 0.20


Criteria 2


Deflection due to load is given by

= Max((5/384) ( WLL L 3)/ (E Ific)), (WLL X L – X) ) / (24 E Ific L ) (L2 + X ( L – X)) + ((WTPL X ( L – X)

(L + X)) / (27 E Ific L ) (3 (L – X) (L + X )))) =0.5mm

Deflection limit is limit = L / 450 = 3.3mm

Ratio 0.15


Fixing requirements – This many WILL require ‘plating’!

MMCEngineer Ltd




Project


Job Ref.

16057

Section


Sheet no./rev.

38 A

Calc. by

SDN

Date

30/08/2017

Chk'd by

SLN

Date

30/08/2017

App'd by

Date

FACTORED STUD CHECK




Standard


Factored load – found in

reaction section of ALL

calculations relating to

Horizontal Members (Lintels,

Trimmers and Joists) – Note in

this case load used is HALF

reaction from Lintel as

checking DOUBLE STUDS,

back to back. This also means

Noggins at ¼ points as FULLY

restrained.

Moment and Shear calculated by user.

My,Ed is calculated as Ned x eccentricity

(100mm), and in this case halved as

based on double studs. Shear is taken

as 7.5kN based on tie forces in

progressive collapse.

Stud under Lintel

MMCEngineer Ltd




Project


Job Ref.

16057

Section


Sheet no./rev.

39 A

Calc. by

SDN

Date

30/08/2017

Chk'd by

SLN

Date

30/08/2017

App'd by

Date

Stud height L = 2.9m

Number of noggins N = 3.0

Compound fixing spacing

SC1= L/3 = 1.0m

SC2 = 50 iz = 0.9m

Fixing centres, SC = MIN(SC1, SC2) = 0.92m

Section dimensions and material properties

The wall stud is a C section’s from Generic 100 x 50 x 1.6, manufactured from 390 N/mm2 steel with a Z275 coating to BS

EN 10346.

Section depth h = 100.0mm

Flange width b = 50.0mm

Stiffener depth c = 12.5mm


Nominal thickness t = 1.6mm

Core thickness tn = t – 0.04mm =1.6mm

Basic yield strength fyb = 390.0N/mm2

Modulus of elasticity ESEC3 =210000.0N/mm2


Partial factor M0 =1.0


Section Properties

The calculation of section properties is not included in this calculation.

Gross Properties

Area Agr = 3.4cm2

Radius of gyration about y axis iy = 40.2mm

Radius of gyration about z axis iz = 18.4mm

Position of y axis from flange yflange = 49.2mm

Position of z axis from web zweb = 15.9mm

Position of shear centre with respect to the z axis yo = 39.3mm

Position of shear centre with respect to the y axis zo = 0mm

Torsion constant It = 276.6mm4

Warping constant Iw = 229.3cm6

Second moment of area about y axis Iy =54.5cm4

Second moment of area about z axis Iz = 11.4cm4


Effective area subject to compression Aeff = 2.4cm2

Elastic section modulus for bending about y axis Weff.y = 10.0cm3

Elastic section modulus for bending about z axis Weff.zlips = 2.9cm3

Position of y axis from flange(due to compression) yeff.flange = 49.2mm

Position of z axis from web (due to compression) zeff.web = 16.7mm

Second moment of area about y axis (due to bending) Iy.eff = 51.2cm4

Loads

Factored Total axial load, Ned = 16.2kN

Maximum applied moment in strong axis, My,Ed = 1.6kNm

MMCEngineer Ltd




Project


Job Ref.

16057

Section


Sheet no./rev.

40 A

Calc. by

SDN

Date

30/08/2017

Chk'd by

SLN

Date

30/08/2017

App'd by

Date

Maximum applied moment in weak axis, Mz,Ed = 0.0kNm

Maximum Shear load, Fv = 7.5 kN


Axial Compression

Design resistance of cross section for compression is given by, Nc,Rd = (Aeff × fyb )/ M0 = 94.0kN

Bending Moment

Design moment resistance for bending about y axis is given by, Mcy,Rd = (Weff.y × fyb) / M0 = 3.9kNm

Design moment resistance for bending about z axis Mcz,Rd = (Weff.zlips × fyb) / M0 = 1.1kNm


Flexural Buckling about major axis (y axis)

From Table 6.3 of BS EN 1993-1-3, the buckling curve for a lipped C section buckling about any axis is buckling curve b.

The buckling length for buckling about the y axis is taken as equal to the member length.

Lcr,y = L = 2850.0mm

1 = (ESEC3 / fyb) = 72.9

Non dimensional slenderness factor is, = Lcr,y / iy) (((Aeff / Agr))/1) = 0.8


= 0.5 ( 1+ (– 0.2) + 2) = 0.9

2)) = 0.7


Ratio 0.2

Unity Check - PASS

Combined Compression and Bending

The shift in the position of the effective section neutral axis relative to gross section neutral axis causes an additional

moment due to axial load which is assumed to be applied at the gross section neutral axis.

The shift in y axis due to axial compression is given by, eNy = yeff.flange - yflange = 0.0 mm

The shift in z axis due to axial compression is given by, eNz = zeff.web - zweb = 0.7 mm

Additional y axis moment due to shift in axis is, My,Ed = eNy Ned = 0.0 kNm

Additional z axis moment due to shift in axis is, Mz,Ed = eNz Ned = 0.0 kNm

Unity Check

U1 = (Ned / Nc,Rd) + ((My,Ed + My,Ed)/ Mcy,Rd) + ((Mz,Ed + Mz,Ed)/ Mcz,Rd) = 0.6

Ratio 0.6

Unity Check - Pass

Flexural Buckling about minor axis (z axis)

NOTE: Large difference in

moment capacities in BOTH axis.

MMCEngineer Ltd




Project


Job Ref.

16057

Section


Sheet no./rev.

41 A

Calc. by

SDN

Date

30/08/2017

Chk'd by

SLN

Date

30/08/2017

App'd by

Date

The buckling length for buckling about the z axis is based on the number of noggins reducing the effective height, i.e. 1

noggin gives half height, and introduce lateral restraint in the wall.

Lcr,z = L / (N+1) = 712.5mm

1 = 72.9

Non dimensional slenderness factor is = ( Lcr,z / iz) (((Aeff / Agr)) /1) = 0.4


= 0.5 ( 1+ ( – 0.2) + 2) = 0.6

= 1/ (+2)) = 0.9


Ratio 0.2

Unity Check - PASS

Torsional Buckling

The torsional buckling lengths are

LT,y = L = 2850.0 mm

LT,z = Lcr,z =712.5 mm

The polar radius of gyration is calculated as below, io =( iy2 + iz2 + yo2 + zo

2 ) = 59mm

The elastic critical force for torsional buckling of a simply supported member is given by,

Ncr,T = (1/ io2) ((G It ) + ((2 ESEC3 Iw) / LT,z2)) = 274.0kN

Non dimensional slenderness factor is T= ((Aeff fyb) / Ncr,T) = 0.6


= 0.5 ( 1+ (T – 0.2) + T2) = 0.7

T

2)) = 0.8

Torsional buckling resistance is, Nb,Rd = (Aeff fyb) / M1 = 79.3kN

Ratio 0.2

Unity Check Pass

Torsional-Flexural Buckling

Ncr,y = (2 ESEC3 Iy) / LT,y2 = 139.0kN

= 1 –(yo / io)2 = 0.6

The elastic critical force for torsional-flexural buckling is given by,

Ncr,TF = (Ncr,y / (2 Ncr,T / Ncr,y) - ((1-( Ncr,T / Ncr,y))2+ 4(yo / io)2 (Ncr,T / Ncr,y))) = 108.1kN

Non dimensional slenderness factor is

TF = ((Aeff fyb )/ Ncr,TF) = 0.9


TF = 0.5 ( 1+ (TF – 0.2) + TF 2) = 1.1

TFTFTFTF

2)) = 0.6

Torsional buckling resistance is, Nb,Rd = (TFAeff fyb) / M1 = 60.2kN

Ratio 0.3

MMCEngineer Ltd




Project


Job Ref.

16057

Section


Sheet no./rev.

42 A

Calc. by

SDN

Date

30/08/2017

Chk'd by

SLN

Date

30/08/2017

App'd by

Date

Unity Check - PASS


The maximum length of member between points of minor axis lateral restraint is determined by noggin centres.

LT,z = 712.5mm

Coefficients dependent on loading and end restraint C1 = 1.127

C2 = 0.454

Effective length factor for end rotation on plan k = 1.00

Effective length factor for end warping kw = 1.00

The distance from the point of load application to the shear centre is taken as half the stud depth.

zg = h / 2 = 50.0 mm

The factor g is used in the calculation of Mcr, it may conservatively be taken as 1.0 or may be calculated as below.

g = (1-(Iz / Iy)) = 0.889

The elastic critical moment for lateral torsional buckling is given by

Mcr = C1 ((2 ESEC3 Iz) / ((k LT,z)2 g)) (((k/ kw)2 (Iw / Iz) + (((k LT,z)2 (G It))/ (2 ESEC3 Iz)) + (C2 zg)2) – (C2

zg)) = 16.6kNm

For lateral torsional buckling curve b should be used.

Non dimensional slenderness factor is LT = ((Weff.y fyb )/ Mcr) = 0.5


LT = 0.5 ( 1+ ( LT – 0.2) + LT 2) = 0.7

LT= 1 /LTLT2LT

2)) = 0.9

Lateral torsional buckling resistance is,

Mb,Rd = ( LT Weff.y × fyb) / M1 = 3.5kNm

Combined Bending and Axial Compression

The interaction of bending moment and axial force may be obtained from a second order analysis or by using the formula

below:

(Ned / Nb,Rd)0.8 + (My,Ed / Mb,Rd)0.8

Ratio 0.9

Unity Check - PASS

Nb,Rd is the minimum value from flexural, torsional and torsional-flexural buckling.

My,Ed includes any additional moments due to the shift in the neutral axis.

MMCEngineer Ltd




Project


Job Ref.

16057

Section


Sheet no./rev.

43 A

Calc. by

SDN

Date

30/08/2017

Chk'd by

SLN

Date

30/08/2017

App'd by

Date

FACADE (INFILL) STUD DESIGN




Standard

Dimensions as the diagram Loads to apply:

Wind Load – taken from original wind

analysis. Element load to be used.

Balcony ONLY used IF balcony on the project

(default to zero)

Deflection limit:

Rainscreen = H / 250

Brittle = H / 360

Masonry = H / 500

All as SCI guide ED017. Note: If

masonry loads CAN be halved, but

deflection limit is strict.

Façade studs

MMCEngineer Ltd




Project


Job Ref.

16057

Section


Sheet no./rev.

44 A

Calc. by

SDN

Date

30/08/2017

Chk'd by

SLN

Date

30/08/2017

App'd by

Date

Select section from list for EACH element

Don’t forget to select the NUMBER of each profile

to be used – single, double (back to back C’s OR 4

way compound -

MMCEngineer Ltd




Project


Job Ref.

16057

Section


Sheet no./rev.

45 A

Calc. by

SDN

Date

30/08/2017

Chk'd by

SLN

Date

30/08/2017

App'd by

Date

Wind Loads and Dimensions

Wind Pressure, p = 1.1kN/m2

Stud height, H =2.9m

Floor to window head, Wh = 2.5m

Window width, L = 1.8m

Floor to window cill, Wc = 1.2m

Window height, hwin = Wh - Wc = 1.3m

Window head height, Hh = H – Wh = 0.4m

Typical stud spacing, c = 600.0mm

Window height, hwin = Wh - Wc = 125.0cm

Juliet Balcony height from bottom of stud WJ = 0.0m

Deflection limit specified, DefLimit = 360

Allowable deflection, based on plasterboard finish, dfln = H / DefLimit = 7.9mm

Area’s Calculated

Area for ‘typical’ stud, ATyp = H c = 1.7m2

Area A, AA = H (c /2) = 0.9m2

Area B, AB = (hwin L) / 4 = 0.6m2

Area C, AC = AB / 2 = 0.3m2

Area D for Cill, ADCill = (Wc / 2) (L /2) = 0.5m2

Area D for Head, ADHead = (Hh / 2) (L /2) = 0.2m2

Loads Applied

Load from Typical Area, Typ = ATyp p = 1.8kN

Load from Area A, A = AA p = 0.9kN

Load from Area B, B = AB p = 0.6kN

Load from Area C, C = AC p = 0.3kN

Load from Area D at Head, DHead = ADHead p = 0.2kN

Load from Area D at Cill, DCill = ADCill p = 0.6kN

Load from Juliet Balcony, PBal = 0.0kN

I values required by loads applied

I required to carry UDL from A, IA = (5 A (H 0.85)3) / (384 ESEC3 dfln) = 10.1cm4

MMCEngineer Ltd




Project


Job Ref.

16057

Section


Sheet no./rev.

46 A

Calc. by

SDN

Date

30/08/2017

Chk'd by

SLN

Date

30/08/2017

App'd by

Date

I required to carry UDL from B, IB = (B / (384 ESEC3 dfln)) ((8 (H 0.85)3 ) + (4 (H 0.85) Hh2) – Hh

3) = 10.8cm4

I required to carry PL from C & D at Head, IDHead = (((C + DHead) (Wh Hh) ( H + Hh)) / (27 ESEC3 dfln H)) (3 Wh

(H + Hh)) = 5.9cm4

I required to carry PL from C & D at Cill, IDCill = (((C + DCill) (Wc (H Wc)) (H + (H – Wc))) / (27 ESEC3 dfln H)) (3

Wc(H + (H – Wc))) = 24.4cm4

I required to carry UDL applied to ‘typical stud’, ITyp = (5 Typ (H 0.85)3) / (384 ESEC3 dfln) = 20.2cm4

I required to carry PL from Juliet Balcony, IJuliet = ((PBal (WJ (H WJ)) ( H + (H – WJ))) / (27 ESEC3 dfln H)) (3

WJ (H WJ)) = 0.0cm4

Typical Stud Details

Typical stud is designed using C section from Generic 100 x 45 x 1.2, manufactured from 390 N/mm2 steel with a Z275

coating.

Depth of section hStud = 100.0mm

Thickness of web tStud = 1.2mm

Thickness allowing for galv tcor = tStud-0.04mm = 1.2mm

Gross area of section AgrStud = 2.3cm2

Second moment of area about strong axis Iy.effStud = 33.2cm4

Gross Second moment of area about strong axis IyStud = 37.3 cm4

Yield strength fybStud = 390.0N/mm2

Effective Second moment of area of section IficStud = IyStud – (1/1.5) (IyStud – Iy.effStud)= 35cm4

Number of studs NoStud = 1

I required for typical stud ITyp = 20.2cm4

Combined I of stud’s IficStudTot = NoStud IficStud = 34.5cm4

Typical Stud Ratio 0.58

Typical Stud Deflection - Pass

Jamb Stud Details

Sum of I’s required to carry Jamb stud loads, IxJamb = IA + IB + IDHead + IDCill + IJuliet = 51.2cm4

Jamb stud is designed using C section(s) from Generic 100 x 45 x 1.2, manufactured from 390 N/mm2 steel with a Z275

coating.

Depth of section hJamb = 100.0mm

Thickness of web tJamb = 1.2mm

Thickness allowing for galv tcor = tJamb-0.04mm = 1.2mm

Gross area of section AgrJamb = 2.3cm2

Second moment of area about strong axis Iy.effJamb = 33.2cm4

Gross Second moment of area about strong axis IyJamb = 37.3 cm4

Yield strength fybJamb = 390.0N/mm2

Effective Second moment of area of section IficJamb = IyJamb – (1/1.5) (IyJamb – Iy.effJamb)= 35cm4

Number of studs NoJamb = 2

I required for typical stud IxJamb = 51.2cm4

Combined I of stud’s IficJambTot = NoJamb IficJamb = 69.1cm4

MMCEngineer Ltd




Project


Job Ref.

16057

Section


Sheet no./rev.

47 A

Calc. by

SDN

Date

30/08/2017

Chk'd by

SLN

Date

30/08/2017

App'd by

Date

Jamb Deflection Ratio 0.74

Jamb Stud Deflection - Pass

Head and Cill Member

Window head member’s carry double load from C and D and requires an IHead = max( ((5/384)((DHead 2) (L 0.8) 3)/

(ES5950 (L / 360)))) + ((C 2 L3) / (60 ES5950 dfln)), ((5/384)((DCill 2) (L 0.8) 3)/ (ES5950 (L / 360)))) + ((C 2

L3) / (60 ES5950 (L / 360))))= 10.0cm4 (Calculation is based on worst case Head or Cill)

Head and Cill members are designed using C section(s) from Generic 100 x 45 x 1.2, manufactured from 390 N/mm2 steel

with a Z275 coating.

Depth of section hCill = 100.0mm

Thickness of web tCill = 1.2mm

Thickness allowing for galv tcorCill= tCill-0.04mm = 1.2mm

Gross area of section AgrCill = 2.3cm2

Second moment of area about strong axis Iy.effCill = 33.2cm4

Yield strength fybCill = 390.0N/mm2

Effective Second moment of area of section IficCill = IyCill – (1/1.5) (IyCill – Iy.effCill)= 35cm4

Ultimate Yield strength of section fuCill = 440N/mm2

Number of members NoCill = 1

I required for Head or Cill IHead = 10.0cm4

Combined I of members spec’d IficCillTot = NoCill IficCill = 34.5cm4

Cill and Head Ratio 0.29

Head and Cill Deflection Check - Pass

Connection Checks

Based on reaction and screw dia, dCill = 5.0mm, screw capacity in bearing, and Partial factor M2 = 1.25

= MIN((3.2 ( tCill / dCill)),2.1) = 1.6

Fb,Rd = ( fuCill dCill tCill) / M2 = 3.3kN

Reaction / connection capacity required from Head or Cill to Jamb studs, RHead = Max((B / 2) + C + DHead, (B / 2) + C +

DCill)= 1.2kN

Fixings required, based upon applied load and fixing capacity, No. = ceiling(MAX((RHead / Fb,Rd),2),1) = 2 fixings per end.

Reaction to supporting structure from typical stud, RStud = (Typ / c) / 2 = 1.5kN/m

MMCEngineer Ltd




Project


Job Ref.

16057

Section


Sheet no./rev.

48 A

Calc. by

SDN

Date

30/08/2017

Chk'd by

SLN

Date

30/08/2017

App'd by

Date

RACKING, SLIDING AND BRACING




Standard

Dimensions as the diagram

Stud height is also known as

‘Storey Height’ and Bay

Width is spacing of the studs

Number of stories

is a drop down box

How many walls are

used in racking?

Wind load taken from

Tedds Wind Analysis

Loads used in roof,

floor and wall

designs previously –

need to re enter

here.

MMCEngineer Ltd




Project


Job Ref.

16057

Section


Sheet no./rev.

49 A

Calc. by

SDN

Date

30/08/2017

Chk'd by

SLN

Date

30/08/2017

App'd by

Date

Building Dimensions

Building height, H = 8.6m

Stud Height, Hstud = 2450mm

Bay width, bw = 600mm

Length of building, L = 10.0m

Width of building, W = 10.0 m

Loads applied

Vertical loads:

Permanent Roof Load, PRp = 0.9kN/m2

Variable Roof Load, PRv = 0.6 kN/m2

Wall Self Weight, PRw = 0.5 kN/m2

Floor self weight, PRf = 0.5kN/m2

Floor Imposed Load, QkFlr = 2.2kN/m2

Profile selected applied

Profile used is a Generic 150x45x1.6, manufactured from 390 N/mm2 steel with a gross area of 3.95cm2. Yield






Diameter of screw d = 5mm



Horizontal loads:

Bracing load limited to, Hmax = 4.5kN (bw / 600mm) = 4.5kN

SCI ED002 states that for a riveted (or screwed) panel with integral k bracing and studs at 600mm centres the serviceability

load limit may be taken as 4.5 kN for a 2.4m wide panel with one bay containing integral bracing. This is for a deflection

limit of storey height / 500, and includes the stiffening contribution from one layer of plasterboard on one side of the panel.

The load limit of 4.5 kN should be reduced proportionally for closer stud spacings. The load limit does not need to be

reduced for changes in storey height as the allowable deflection is also proportional to storey height. The amount of sway

deflection which is due to the tensile extension of the bracing member is of minor significance to the overall sway deflection

(see ED002 page 26). Therefore, changes to the bracing cross sectional area may be neglected as influencing the

serviceability load limit. However, the bracing member section size must be at least equal to the vertical stud section size.

Serviceability allowable load = 4.5 kN x stud spacing in mm / 600 mm.

Wind load applied to Length Face, Fw,DL = 87.3kN

Wind load applied to Width Face, Fw,DW = 87.3kN

MMCEngineer Ltd




Project


Job Ref.

16057

Section


Sheet no./rev.

50 A

Calc. by

SDN

Date

30/08/2017

Chk'd by

SLN

Date

30/08/2017

App'd by

Date

Bracing Forces

Horizontal Bay Force is limited to , Hmax = 4.5kN by above.

Worst case is only the self weight of wall act’s against uplift, Vwall = Hstud bw PRw = 0.7kN

Taking moments about Compressive Reaction gives Tensile force in braced bay as,

VBrace = (Hmax Hstud) / bw = 18.4kN

Thus fixing Capacity Required at ground floor per braced bay based on ground floor level,

FCapReq = VBrace – (H PRw bw) = 15.8kN

NOTE: Stud at either end of ‘run of braced bays’ needs to have this capacity ‘spare’ as system

will also apply an equal and opposite compressive force as shown. Adjacent bays will ‘cancel

out’ till the ‘end of the run’ of braced bays when the loads must be accounted for.

Braced bays required to resist wind load applied to face ‘L’

Wind load applied in direction, PL = (Fw,DL / (L H)) =

1.0kN/m2

Equivalent Horizontal Force, EHF= ((L W) (PRf + QkFlr) 0.005) = 1.4kN

Horizontal Force bracing can carry, Hmax = 4.5kN

Storey Height, Hstud = 2.5m


Width of building, W = 10.0m

Surface area of wall per floor, AWallFloorL = L Hstud = 24.5m2

Braced bays required for 3rd Floor, NBSTop1 = Ceiling((((L (Hstud / 2) PL) + EHF) / Hmax ),1) = 4No

Number of floors carrying bracing in next line, NFloors = 2

Braced bays required for 2nd Floor, NBS2nd= Ceiling(((AWallFloorL PL + EHF NFloors – 0.5)) / Hmax),1) = 6No


Braced bays required for Ground Floor, NBSGroundL = Ceiling(((AWallFloorL PL+ EHF NFloors – 0.5)) / Hmax),1) = 7No

Braced bays required to resist wind load applied to face ‘W’

Wind load applied in direction, PW = (Fw,DL / (W H)) =

1.0kN/m2

Equivalent Horizontal Force, EHF= ((L W) (PRf + QkFlr) 0.005) = 1.4kN

Horizontal Force bracing can carry, Hmax = 4.5kN

Storey Height, Hstud = 2.5m


Width of building, W = 10.0m

This is the force the fixing

used to hold down the

braced bay has to resist

MMCEngineer Ltd




Project


Job Ref.

16057

Section


Sheet no./rev.

51 A

Calc. by

SDN

Date

30/08/2017

Chk'd by

SLN

Date

30/08/2017

App'd by

Date

Surface area of wall per floor, AWallFloorW = W Hstud = 24.5m2

Braced bays required for 3rd Floor, NBSTop1 = Ceiling((((L (Hstud / 2) PL) + EHF) / Hmax ),1) = 4No


Braced bays required for 2nd Floor, NBS2nd= Ceiling((((AWallFloorW PL) + EHF NFloors – 0.5)) / Hmax),1) = 6No


Braced bays required for Ground Floor, NBSGroundW = Ceiling((((AWallFloorW PL) + EHF NFloors – 0.5)) / Hmax),1) = 7No

Overturning Check

Wind blowing on Face ‘L’ (Worst Case)

Resistance to Overturning Moment

Vertical load from roof, Vroof = (LW/2) PRp) = 45.0kN

Vertical load from walls, Vwalls = (L + W)H PRw = 86.0kN

Vertical load from floor, Vfloor = (LW/2) PRp) (H / Hstud) = 158.0kN

Contribution from braced bays and ground floor fixings, VBracing = (VBrace – (H PRw bw)) NBSGroundL = 110.6kN

Suggest minimum base fixity of soleplate to foundations is additional fixings at bay centers in the noted walls.

Pullout capacity of Holding down bolt VFixing = 13.5kN

Number of cross walls, NoWalls = 2.0

Additional resistance moment RTMADD = VFixing ((L + (NoWalls (W/2))) / bw) W = 4500kNm

Total Vertical Load, VTotal = Vroof + Vwalls + Vfloor + VBracing = 399.5kN

Resistance to Overturning Moment, RTM = (VTotal W 0.9) + RTMADD = 8095.7kNm

Designed to Euro Codes so load factor of Fct = 1.5 to be used.

Overturning Moment, OTM = Fw,DL H Fct= 1126.2kNm

RTM / OTM = 7.2

Building will not overturn, PASS

Sliding Check

Standards Designed to require a load factor of, Fct = 1.5

Co-efficient of friction for steel shims, CFRIC = 0.30

Resisting Load, RL = VTotal CFRIC = 119.9kN

Horizontal Load, SL = (Fw,DL / 2) Fct = 65.5 kN

RL / SL = 1.8

SL / RL <1, Building will not slide, no additional fixings required

Note how the required

number of bays

increases toward lower

floors as these floor are

carrying more load.

MMCEngineer Ltd




Project


Job Ref.

16057

Section


Sheet no./rev.

52 A

Calc. by

SDN

Date

30/08/2017

Chk'd by

SLN

Date

30/08/2017

App'd by

Date

IF sliding resistance is not adequate, difference between applied and capacity from self weigh friction,

Fres = (L Hstud (Fw,DL / (L W))) – RL = -98.5kN

Suggest Tapcons are used. Tapcons are self drill, self tap screws for connection LGS to concrete. 5mm dia screw with

44mm embedment has a shear capacity, Fcap = 1.66kN in ‘Grade 25’ concrete.

Thus fixings required, Freq = Fres / Fcap = -59.3. In this case is a negative number as fixings are NOT required

Alpha-Crit Checks

Sway delta for a floor calculated in accordance with Cl 5.2.1 of BS EN 1993-1-1.

Profile used is a Generic 150x45x1.6, manufactured from 390 N/mm2 steel with a gross area of 3.95cm2.

Maximum, factored, axial load applied from member checks, Ned = 26.7kN

Force in system / bay, HF = Hmax + (Ned 0.005) 1.5 = 4.7kN

Height of stud, Hstud = 2450mm

Width of bay, bw = 600mm

Length of K forming Diagonal, LD = ( bw2 + (Hstud/2)2) = 1364mm

Area of C section, Agr =4.0 cm2

Force in Diagonal FD = HF LD / bw = 10.7kN

L = ((FD / Agr) / ESEC3) LD = 0.18mm

Deflection of ‘system’ (K - Bracing), = (((LD + L)2 – (Hstud/2)2) – bw) = 0.40mm

Alpha Crit (Eurocode), cr = (Hmax / Ned) (Hstud ) = 1033.94

As cr is > 10 therefore sway frame is non-sway sensitive

MMCEngineer Ltd




Project


Job Ref.

16057

Section


Sheet no./rev.

53 A

Calc. by

SDN

Date

30/08/2017

Chk'd by

SLN

Date

30/08/2017

App'd by

Date

Further capacity and connection checks are NOT required based on SCI / DTi and Trada report ED002, page 93, show that

there is sufficient margin of safety between the SLS load limit and the ULS load reistance that the ULS checks do not

govern the design. This applies to K bracing design ONLY.

Documents

Structural Calculations FOR Sample Project Demonstrating ... · DESIGN PHILOSOPHY Design is purely to demonstrate some the range of designs available in the Modern Engineered Software