Steel Code Check - SCIA Help

Steel Code CheckTheoretical background

Chapter 0

Contacts 10EC3 - EN 1993 12

EC3 – EN Code check 12

Consulted articles 12

Convention and axis switch 14

Material properties 14

Imperfections 14

PlasticHinges 14

InitialShape 15

Classification 17

Method 1: ElasticStresses 18

Method 2: Yield Surface Intersection 19

Method 3: Iterative Approach 20

Section properties 21

SectionChecks 21

Circular Hollow Sections 27

StabilityChecks 27

Linear Moment 32

Point Loading 33

Line Loading 33

Determination of distance zg 35

Determination of distance zj 36

LTBCurves - General case 36

LTBCurves - Alternative case 36

Modified design rule for Channel sections 37

Sheeting 37

SEMI-COMP+ 42

Battened compressionmembers 45

Plate girderswith sinusoidal corrugatedwebs 47

Yielding 49

Local buckling 49

Global buckling 49

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Momentson columns in simple construction 51

Scaffolding 53

EC3 – EN Fire Resistance 59



Classification 61

VerificationDomains 61

Temperature analysis - Thermal actions 63

SectionChecks 70

StabilityChecks 71

EC3 – EN Cold-Formed 73



InitialShape 76

GeometricalProportions 78

Effective Shape 79

SectionChecks 85

StabilityChecks 94

Alternative interaction according to EN 1993-1-3The interaction is executed according to EN 1993-1-3 art.6.2.5(2). 97

Use of sheetings 98

Special considerations for Purlins 101

References 106

AISC / AISI / ANSI 112AISC – ASD:1989 112

AISC –ASD:1989 112

Supported sections 115

References 116

AISC – LRFD:2001 117

AISC - LRFDCode check 117


References 120

ANSI/AISC 360-05:2005 121

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Chapter 0

ANSI/AISC 360-05Code check 121


References 123

ANSI/AISC 360-10:2010 124

ANSI/AISC 360-10Code check 124


References 127

AISI NAS S100-2007 128

AISI NASS100-2007Code check 128

Doubly symmetric sections 132

Point symmetric sections 133

Singly symmetric sections 134

Other section types 134

Built-Up Sections 137

Single Web Channel and C-Sections 137

Single Web Z-Sections 138

Single Hat Sections 138

Other Sections 138

Determination of Ncr,T 140

Determination of Ncr,TF 141

Sheeting on the compression flange 143

Sheeting on the tension flange 143

Sheeting on one flange 144

Sheeting on both flanges 144

Sheeting on any flange 144

References 147

ABNT NBR 8800 149Consulted articles 149

References 151

ABNT NBR 14762 152Consulted articles NBR 14762 152

References 153

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SIA263:2013 154SIA263 Code check 154



Section classification 155

Slender cross-section 155

Sectionsproperties 156

Lateral torsional buckling 156

Use of diaphragms 157

Shear buckling 157

Stability check 157

Torsion check 157

Built-in beams 157

SIA263 - Fire Resistance 158

Fire actionseffect Efi 158


Temperature analysis - Thermal actions 158

Nominal temperature-time curve 158

Net heat flux 158

SteelTemperature 158

Calculationmodel 160

CodeCheck 160


References 161

Annex A: Profile Library Formcodes 163Formcode 1: I-Section 163

Formcode 2: Rectangular Hollow Section 164

Formcode 3: Circular Hollow Section 164

Formcode 4: L-Section 165

Formcode 5: Channel Section 165

Formcode 6: T-Section 166

Formcode 7: Full Rectangular Section 166

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Chapter 0

Formcode 11: Full Circular Section 167

Formcode 101: Asymmetric I-Section 167

Formcode 102: Rolled Z-Section 168

Formcode 111: Cold-Formed Angle Section 168

Formcode 112: Cold-Formed Channel Section 169

Formcode 113: Cold-Formed Z-Section 169

Formcode 114: Cold-Formed C-Section 170

Formcode 115: Cold-Formed Omega Section 170

Formcode 116: Cold-Formed C-Section Eaves Beam 171

Formcode 117: Cold-Formed C-Plus Section 171

Formcode 118: Cold-Formed ZED-Section 172

Formcode 119: Cold-Formed ZED-Section Asymmetric Lips 173

Formcode 120: Cold-Formed ZED-Section Inclined Lip 173

Formcode 121: Cold-Formed Sigma Section 174

Formcode 122: Cold-Formed Sigma Section Stiffened 175

Formcode 123: Cold-Formed Sigma-Plus Section 175

Formcode 124: Cold-Formed Sigma Section Eaves Beam 176

Formcode 125: Cold-Formed Sigma-Plus Section Eaves Beam 177

Formcode 126: Cold-Formed ZED-Section Both Lips Inclined 177

Formcode 127: Cold-Formed I-Plus Section 178

Formcode 128: Cold-Formed IS-Plus Section 179

Formcode 129: Cold-Formed Sigma Section Asymmetric 179

Formcode 130: Cold-Formed 2C-Section 180

Formcode 150: Rail Type KA 181

Formcode 151: Rail Type KF 182

Formcode 160: Virtual Joist 182

Annex B: Calculation of buckling ratio 184Introduction to the calculation of buckling ratio 184

Calculation buckling ratio – general formula 184

Calculation buckling ratios for crossing diagonals 185

Continuouscompression diagonal, supported bycontinuous tension diagonal 186

Continuouscompression diagonal, supported bypinned tension diagonal 186

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Pinned compression diagonal, supported bycontinuous tension diagonal 187

Continuouscompression diagonal, supported bycontinuouscompression diagonal 187

Continuouscompression diagonal, supported bypinned compression diagonal 188

Pinned compression diagonal, supported bycontinuouscompression diagonal 188

Calculation of critical Euler force for VARH elements 189

Calculation of criticalEuler force 189

Calculation buckling ratio for lattice tower members 190

Default slenderness limits 191

Legwith symmetrical bracing 192

Legwith intermediate transverse support 192

Legwith staggered bracing 193

Single Bracing 193

Single Bracingwith SBS (SecondaryBracing System) 194

Crossbracing 194

Crossbracingwith SBS 196

KBracing 196

HorizontalBracing 197

HorizontalBracingwith SBS 197

DiscontinuousCrossbracingwith horizontalmember 198

Calculation of buckling ratio – From Stability Analysis 198

References 199

Annex C: Calculation of moment factors for LTB 201Introduction to the calculation of moment factors 201

Calculation moment factors 201

Moment distribution generated byq load 201

Moment distribution generated byF load 202

Moment linewithmaximumat the start or at the end of the beam 203

References 203

Annex D: Use of sheeting 205Adaptation of torsional constant 205

References 206

Annex E: Lateral Torsional Buckling 2nd Order Analysis 208

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Chapter 0

Introduction to LTBII 208

Eigenvalue solution Mcr 208

2nd Order analysis 209

Supported National Codes 210

Supported Sections 210

Loadings 212

Imperfections 212

Initial bow imperfection v0 for DIN andONORM 212

Initial bow imperfection v0 for EC-EN andEAE 213

Initial bow imperfectionsv0 andw0 for other supported codes 214

LTB Restraints 214

Sheetings 214

Linked Beams 215

Limitations and Warnings 216

References 216

Annex F: Warping check 218Stress check 218

Calculation of the direct stressdue towarping 219

Calculation of the shear stressdue towarping 221

Plastic Check 222

Standard diagrams for warping torque, bimoment and the St.Venant torsion 225

Torsion fixed ends, warping free ends, local torsional loadingMt 226

Torsion fixed ends, warping fixed ends, local torsional loadingMt 227

Torsion fixed ends, warping free ends, distributed torsional loadingmt 228

Torsion fixed ends, warping fixed ends, distributed torsional loadingmt 229

One end free, other end torsion andwarping fixed, local torsional loadingMt 230

One end free, other end torsion andwarping fixed, distributed torsional loadingmt 230

Decomposition of arbitrary torsion line 231

Decomposition for situation 1 and situation 3 232

Decomposition for situation 2 232

References 232

Annex G: Check of numerical sections 234

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Stress check 234

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Chapter 1

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Contacts


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Document created: 06 / 05 / 2018

SCIAEngineer 15.3

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Chapter 2

EC3 - EN 1993

EC3 – EN Code checkThe beamelementsare checked according to the regulationsgiven in:

Eurocode 3Design of steel structures

Part 1 - 1: General rulesand rules for buildings

EN 1993-1-1:2005

CorrigendumEN 1993-1-1:2005/AC:2006

CorrigendumEN 1993-1-1:2005/AC:2009

AddendumEN 1993-1-1:2005/A1:2014

Consulted articlesAn overview for the used articles is given in the following table. The articles marked with “X” are consulted. The articlesmarkedwith (*) have a supplementaryexplanation in the following paragraphs.

EN 1993-1-1Article Title

1. General

1.7 Conventions for member axes X(*)

2. Basis of design

3. Materials X(*)

5. Structural analysis

5.2 Global analysis X

5.3 Imperfections

5.3.1 Basis

5.3.2 Imperfections for global analysis of frames

5.3.3 Imperfections for analysis of bracing systems

XX(*)

X

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EC3 - EN 1993

Article Title

5.3.4 Member imperfections

5.4 Methods of analysis considering material non-linearities X(*)

5.5 Classification of cross-sections X(*)

6. Ultimate limit states

6.1 General X

6.2 Resistance of cross-sections

6.2.1 General

6.2.2 Section properties

6.2.3 Tension

6.2.4 Compression

6.2.5 Bending moment

6.2.6 Shear

6.2.7 Torsion

6.2.8 Bending and shear

6.2.9 Bending and axial force

6.2.10 Bending, shear and axial force

X(*)

X(*)

X(*)

X(*)

X(*)

X(*)

X(*)

X(*)

X(*)

6.3 Buckling resistance ofmembers

6.3.1 Uniformmembers in compression

6.3.2 Uniformmembers in bending

6.3.3 Uniformmembers in bending and axial compression

X(*)

X(*)

X(*)

6.4 Uniform built-up compression members

6.4.1 General

6.4.3 Battened compression members

X(*)

X(*)

Annex A Method 1:Interaction factors kij for interaction formula in 6.3.3.(4) X

Annex B Method 2:Interaction factors kij for interaction formula in 6.3.3.(4) X


4.4 Plate elements without longitudinal stiffeners X

5. Resistance to shear X

5.1 Basis

5.2 Design resistance X

5.3 Contribution fromwebs X

5.4 Contribution from flanges X

5.5 Verification X

7.1 Interaction between shear force, bending moment and axial force X

AnnexD Plate girders with corrugated webs X(*)

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Chapter 2

Convention and axis switchAs indicated in EN 1993-1-1 art. 1.7(4) NOTE, all checks given in this Eurocode relate to principal axis properties. WithinSCIA Engineer, the principal axis system is denoted by the 'y-axis' and 'z-axis'. For background information, reference ismade to the TheoreticalBackground for Cross-SectionCharacteristics.

The Eurocode rules are written out in such a way that the y-axis is seen as the strong (major) principal axis. Therefore, incase the cross-section has Iz > Iywithin the check the axiswill be switched.

For the following sectionsno switch of axis isdone:

l I-Section (FC 1)l RHS (FC 2)l L-Section (FC 4)l Channel-Section (FC 5)l T-Section (FC 6)l Asymmetric I-Section (FC 101)l Cold-Formed I-PlusSection (FC 127)l Cold-Formed IS-PlusSection (FC 128)l IFBA (FC 154)l IFBB (FC 155)l SFB (FC 153)l THQ (FC 156)l Virtual Joist (FC 160)l VARH element (seeDefinitions in "Calculation of criticalEuler force for VARH elements" on page 189)l Battened compressionmembers (seeDefinitions in "Battened compressionmembers.htm")

Material propertiesFor standard steel grades, the yield strength fy and tensile strength fu are defined according to the thickness of the elementaccording to EN 1993-1-1Table 3.1.

Within the material properties the rules for reduction of the yield strength in function of the thickness can be edited. Thisallows the definition of anycustommaterialwith custom thickness reduction.

For cold formed sections, the reductionsof the yield strength in function of the thicknessarenot applied.

ImperfectionsGlobal initial sway imperfectionsare determined according to EN 1993-1-1 art. 5.3.2(3)a.

Local bow imperfectionsare determined according to EN 1993-1-1 art. 5.3.2(3)b.

Plastic HingesFor material non-linearity using plastic hinges according to EN 1993-1-1 art. 5.4.3 reference is made to the manual forNon-linear analysis.

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EC3 - EN 1993

Initial ShapeFor thin-walled cross-sectionswithmaterialSteel the InitialShape isgenerated automatically.

For aGeneral cross-section the ‘Thin-walled representation’ has to be used to be able to define the InitialShape.

The InitialShape 'translates' the cross-section shape to partsdefined by the code.

The Initial Shape is used for calculating the effective section properties aswell as determining the Classification of the cross-section.

The thin-walled cross-section parts can have the following types:

F Fixed Part – No reduction is needed

I Internal cross-section part

SO Symmetrical Outstand

UO Unsymmetrical Outstand

Parts can also be specified as reinforcement:

None Not considered as reinforcement

RUO Reinforced Unsymmetrical Outstand (edge stiffener)

RI Reinforced Intermediate (intermediate stiffener)

DEF Double Edge Fold (edge stiffener)

ROU andDEF reinforcement typescan be set only to elementsof typeSO or UO.

RI typescan be set only to elementsof type I or UO or SO.

For general cross-sections neighbouring elements of type RI are seen as one stiffener for the calculation of the stiffenerarea and inertia.

For standard profile library cross-sections, the flat parts are taken between the roundings. The roundings are set as fixedparts.

For predefined sectionswithout roundings, the initial shape isbased on the centreline dimensions i.e. the flat partsare takenbetween the intersection pointsof the centrelines.

For standard profile librarycross-sectionsand pair sections the stiffenersare handled as follows:

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Chapter 2

For the following form codesedge stiffenersare automatically set asRUO

FC 114Cold formedC-section

FC 115Cold formedOmega section

FC 116Cold formedC-Section eavesbeam

FC 118Cold formedZED section

FC 119Cold formedZED section asymmetric lips

FC 120Cold formedZED section inclined lip

FC 121Cold formedSigma section

FC 124Cold formedSigma section eavesbeam

FC 126Cold formedZED section both lips inclined

FC 129Cold formedSigma section asymmetric

FC 130Cold formed 2C-section

For the following form codesedge stiffenersare automatically set asDEF

FC 117Cold formedC-Plussection

FC 122Cold formedSigma section stiffened

FC 123Cold formedSigma-Plussection

FC 125Cold formedSigma-Plussection eavesbeam

FC 127Cold formed I-Plussection

FC 128Cold formed IS-Plussection

For the following form codes internal stiffenersare automatically set asRI








Initial Shapes for specific sectionsWithin thisparagraph special cases for the InitialShape generation are listed.

Sheet welded Iw & IwnFor these sections theweldsize isaccounted for in the generation of the InitialShape:

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EC3 - EN 1993

The length of theweb element for example is thuscalculated as:

WithHw the height of theweb and a the throat thicknessof theweld.

The sameapproach isused for the flanges.

RHSFor Rectangular Hollow Sections (FC 2) the initial shape isgenerated using a notionalwidth ofh-3t andb-3t.

The usage of this width ensures consistency between EN 1993-1-1 and EN 1993-1-5. For further information reference ismade toRef.[40].

As specified in EN 1993-1-3 art. 1.1(3) CHS & RHS members are checked according toEN 1993-1-1.

ClassificationThe classification of cross-sections isexecuted according to EN 1993-1-1 art. 5.5.2 andTable 5.2.

For standard sections, theClassification isdone according to the partsof the InitialShape.

Internal compression elements (I) are classified according toTable 5.2 Sheet 1.

Outstand compression elements (SO &UO) are classified according toTable 5.2 Sheet 2.

CHSsections (FC 3) are classified according toTable 5.2 Sheet 3.

Angle sections (FC 4) are classified according toTable 5.2 Sheet 2 and in case of uniform compression alsoSheet 3.

Cross-sectionswithout InitialShape are classified aselasticClass3.

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Chapter 2

Stress distributionElastic Stress distributionThe elastic stressesare calculated in the endpointsof the partsRef.[40].

The elastic stressdistributionψ for each part can then be determined as follows:

With f1 and f2 the elastic stressesat the endsof the part.

TheEN 1993-1-1 sign convention isusedwhich impliescompression stressesare positive

Plastic Stress distributionTo determine the plastic stressdistributionα three algorithmsare provided:

- ElasticStresses

- Yield Surface Intersection

- Iterative Approach

Method 1: Elastic StressesIn thismethod the plastic stressdistribution isbased on the elastic stresses f1 and f2 at the endsof the parts.

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EC3 - EN 1993

Uniform Compression

In case and the section is assumed to be in uniform com-pression. This implies thatα is taken as1,00 for all parts.

Standard calculation of αIn case one stress ispositive (compression) and the other negative (tension) the following calculation isused:

In all other casesα is taken as1,00 for the given part.

Doubly-symmetric I-sectionSpecifically for a doubly-symmetric I-section (Formcode 1) the α value of the web element is overruled by the following for-mulaRef.[40]:

Within this formula theNEd is taken aspositive for compression and negative for tension.

For large compressive forces this formula can lead to anα >1,00 inwhichα is limited to 1,00.

For large tensile forces this formula can lead to an α <= 0,00. In this case the element is seen as in full tension and thus noclassification is required.

In caseψ >0 for the web element this indicates that the entire web is in compression thusα=1,00.

Method 2: Yield Surface IntersectionFor this method a full plastic analysis is run as described in Ref.[41]. This plastic analysis is based on the Initial Shape andusesa stress-strain diagramwith yielding plateau.

The yield surface is generated for the given section (using a predefined set of points) and the intersection of the actualforces isdeterminedwith this surface.

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Chapter 2

The actual intersection point does not always collide exactly with a predetermined point of the surface, so small deviationscan occur.

From the location of the plastic neutral axis(PNA), which results of this analysis, the α value for the different parts can bedeterminedRef.[40].

Method 3: Iterative ApproachFor this method a full plastic analysis is run as described in Ref.[41]. This plastic analysis is based on the Initial Shape andusesa stress-strain diagramwith yielding plateau.

The actual plane of deformation for the given internal forces isdetermined iterativelywhich providesan exact solution.

From the location of the plastic neutral axis(PNA), which results of this analysis, the α value for the different parts can bedeterminedRef.[40].

Modified Classification limits according to Semi-Comp+In case the setting for using Semi-Comp+ isactivated, the classification limitsaremodified according toRef.[40].

This modification is required in order to reach the specified safety level in accordance with the ESDEP (European SteelDesignEducation Programme) background of theClassification criterion.

The following givesan overview of themodificationsdefined inRef.[40].

The c/t-limits in Table 5.2 of EN 1993-1-1 for internal parts in compression should be modified to 38 (instead of 42) at thelimit 3/4 and to 34 (instead of 38) at the limit 2/3.

The limit 1/2 indicates the same discrepancy for internal parts in compression and should also be revised to 28 (instead of33) accordingly

Classification for Cross-section design and Member buckling designFor each intermediary section, the classification for cross-section design is determined and the proper section check is per-formed. The classification can change for each intermediarypoint.

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EC3 - EN 1993

For each load case/combination, the classification for member buckling design is determined as themaximal classalong themember. This class is used to perform the stability check since stability effects are related to the whole member and not to asingle cross-section.

To determine this critical classification, all sections in the Ly and Lz system lengths of the buckling system are checked andthe worst classification is used as the critical. Note that only sections on the actual member are used so in case the systemlength spansmultiplemembers, only the sectionsof the actualmember are used to determine the critical classification.

For non-prismatic sections, the stability section classification isdetermined for each intermediarysection.

The alternative regulationsgiven in EN 1993-1-1 art. 5.5.2(9) - (12) are not supported.

Section properties

Net AreaThe net area according to EN 1993-1-1 art. 6.2.2.2 is not supported.

For anglesconnected through one leg see theChapter on "Tension" below.

Shear lag effectsShear lag effectsaccording to EN 1993-1-1 art. 6.2.2.3 is not supported.

Effective Section propertiesThe effective cross-section properties for Class4 sectionsare determined according to EN 1993-1-5 art. 4.3& 4.4.

For a detailed overview of the effective section calculation reference ismade to "Effective Shape" on page 79.

The Cross-section requires an Initial Shape in order to calculate the Effective Shape andEffective Properties.

Aeff is the effective area of the crosssectionwhen subject to uniform compression.

Weff is the effective sectionmodulusof the cross-sectionwhen subject only to amoment about the relevant axis.

eN is the shift of the relevant centroidal axiswhen the crosssection is subject to uniform compression.

Additional moments ΔMEd due to the possible shift eN of the centroid of the effective area Aeff are accounted for accordingto EN 1993-1-1 art. 6.2.2.5(4). These additionalmomentsare neglected in case theywould have a favourable effect on thecheck result.

CHSmemberswith Class4 cross-sectionsare checked aselastic, Class3.

Section Checks

TensionTheTensionCheck isexecuted according to EN 1993-1-1 art. 6.2.3.

The net areaAnet is taken equal to the grossareaAg.

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Chapter 2

For angles connected through one leg by means of bolted diagonal connections the netarea is calculated according to EN 1993-1-8 art 3.10.3. For more information see the The-oreticalBackgroud for bolted diagonal connections.

CompressionTheCompressionCheck isexecuted according to EN 1993-1-1 art. 6.2.4.

Bending MomentTheBendingCheck isexecuted according to EN 1993-1-1 art. 6.2.5.

Fastener holesare not accounted for.

ShearTheShear Check isexecuted according to EN 1993-1-1 art. 6.2.6.

By default the plastic shear resistance according to art. 6.2.6(2) will be determined for those cross-sections which have ashear areaAv defined. The following table givesan overview of the shear areas:

Cross-section type Shear Area Source

Rolled I-section (FC 1)EN 1993-1-1

ECCS 85

Rolled Asym. I- section (FC101)

EN 1993- 1- 1(mod)

ECCS 85 (mod)

Welded I-section (FC 1)EN 1993-1-1

EN 1993-1-1

Rolled U-section (FC 5)

EN 1993-1-1

EN 1993- 1- 1(mod)

Welded U-section (FC 5)

EN 1993- 1- 1(mod)

EN 1993-1-1

Rolled T-section (FC 6)

EN 1993-1-1

EN 1993- 1- 1(mod)

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EC3 - EN 1993


Welded T-section (FC 6)

EN 1993-1-1

EN 1993- 1- 1(mod)

Rolled RHS (FC 2)

EN 1993-1-1

EN 1993-1-1

Cold-Formed RHS (FC 2)

EN 1993-1-1

EN 1993-1-1

Welded RHS (FC 2)EN 1993-1-1

EN 1993-1-1

CHS (FC 3)

EN 1993-1-1

EN 1993-1-1

Full Rectangular Section (FC7)

ECCS 85

ECCS 85

Full Circular Section (FC 11)ECCS 85

ECCS 85

IFBA (FC 154) With h the height of the rolled section

ECCS 83

ECCS 83 (mod)

IFBB (FC 155) With h the height of the rolled section

ECCS 83

ECCS 83 (mod)

SFB (FC 153)ECCS 83

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Chapter 2


With h the height of the rolled section

ECCS 83 (mod)

THQ (FC 156) With h the web height

ECCS 83

ECCS 83 (mod)

Numerical(Taken from the cross-section)

(Taken from the cross-section)

The first column in this table indicates the type of the cross-section including the formcode (for background information see"AnnexA: Profile LibraryFormcodes" on page 163.)

The last column indicates the source from which this shear area was taken. The reference list contains their full denom-ination, see Ref.[1], [11], [37] and [38]. The suffix (mod) indicates that the formula has been modified based on the cross-section type. A typical example of this is themodification of the shear area formula given for a symmetric I-section in order toaccount for the different flange geometriesof an asymmetric I-section.

For anycross-sectionwhich doesnot have a shear area Av defined in the above table the elastic shear resistance accordingto art. 6.2.6(4) is determined.

The reduction factor ρ for shear, as defined in art. 6.2.8 and 6.2.10, is based on the plasticshear resistance. As a result, in case an elastic shear verification is done, ρ cannot bedetermined and thusan elastic combined section checkwill be done for this section.

Through the Steel Setup it is possible to indicate that, instead of an elastic shear check, theplastic shear checkcan be done using the shear areasAy andAz from the cross-section.

When using the Elastic verification setting in the Steel Setup, the elastic shear verificationwill be done for all sections, even thosewhichwould normallybe checked plastically.

For Shear Buckling reference ismade to "CombinedBending andAxial Tension" on page 40.

TorsionTheTorsionCheck isexecuted according to EN 1993-1-1 art. 6.2.7.

Formula (6.23) is checked as follows:

With

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EC3 - EN 1993

τEd Maximal total torsion stress in the cross-section fibres

τRd

Torsion and ShearTheCombinedShear and TorsionCheck isexecuted according to EN 1993-1-1 art. 6.2.7(9).

The following table givesan overview for which cross-section typewhich formula from art. 6.2.7(9) is used.

Cross-section type Formula

Symmetric I-section (FC 1) (6.26)

Asymmetric I-section (FC 101) (6.26)

IFBA (FC 154) (6.26)

IFBB (FC 155) (6.26)

SFB (FC 153) (6.26)

U-section (FC 5) (6.27)

RHS (FC 2) (6.28)

CHS (FC 3) (6.28)

THQ (FC 156) (6.28)

The first column in this table indicates the type of the cross-section including the formcode (for background information see"AnnexA: Profile LibraryFormcodes" on page 163.)

In case the Warping Check is activated (see "Warping" on the next page) the primary and secondary torsional shearstresses are calculated from their respective torsionalmoments. In this case, the reduction of the Shear Resistance (due toTorsion) is calculated in each fibre and the fibre resulting in the highest reduction is considered as the critical fibre. This fibrewith its respective stresseswill be shown on the output.

In case of one of the following, theCombined Torsion andShear checkcannot be executed:

l Noplastic shear resistance isavailable i.e. an elastic shear checkwasdonewhichmeans torsion cannot be accounted forin a plastic interaction check.

l Aplastic shear resistance isavailable but the cross-section doesnotmatch anyof those listed in the above table. Thisimplies that the code doesnot give a formula to account for torsion in a plastic interaction check.

l Aplastic shear resistance isavailable and the cross-sectionmatchesone of those listed in the above table, but due toextreme torsion the reduction is so big that it would cause a negative resulting shear resistanceVpl,T,Rd.

In each of those casesan elastic verification using the yield criterion according to art. 6.2.1(5) will be done instead.

The combined plastic interaction checks according to art. 6.2.9.1 account for the presenceof torsion by reducing the plastic shear resistance (which in turn reduces the plastic bend-ing resistance). Thus in case there is no shear, the torsion cannot be accounted for in aplastic verification. In such a case an elastic verification using the yield criterion according toart. 6.2.1(5) will be done instead.

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Chapter 2

WarpingIn case the warping check has been activated within the buckling data of a member, the torsional moment will be decom-posed into an internal Saint-Venant torsionalmoment and an internalwarping torsionalmoment as indicated in EN 1993-1-1 art. 6.2.7(2).

Two distinct combined checksare supported, depending on the type of section and type of analysis:

l Bydefault the elastic verification using theVonMisesyield criterion is verified.l For doublysymmetric I-sectionsof class1 or 2 a plastic interaction is verified.

Reference ismade to "AnnexF:Warping check" on page 218

Bending, Shear (and Axial force)The influence of the Shear force on theBending resistance isaccounted for according to EN 1993-1-1 art. 6.2.8&6.2.10.

In case of one of the following, the influence of the Shear force on the Bending resistance cannot be accounted for using thespecified article:

l Noplastic shear resistance isavailable i.e. an elastic shear checkwasdonewhichmeans the reduction factor ρ cannot bedetermined.

l Due to extreme shear the reduction factor ρ >1whichwould lead to a negative reduction.l In case there isno corresponding bendingmoment the reduction for shear cannot be applied (for example Vzcombined

withMzand thusno correspondingMy).

In each of those casesan elastic verification using the yield criterion according to art. 6.2.1(5) will be done instead.

Bending and Axial forceTheCombinedBending andAxial forceCheck isexecuted according to EN 1993-1-1 art. 6.2.9.

In case the elastic verification has been activated within the Steel Setup, for any cross-sec-tion class the elastic verification using the yield criterion according to art. 6.2.1(5) is verifiedinstead.

Asspecified in the code, the type of the checkdependson the classification.

Class 1 & 2 cross-sectionsClass1&2 cross-sectionsare bydefault verified byart. 6.2.9.1

Thisarticle gives formulas for the following cross-section types:

l FullRectangular Sections (Formcode 7)l DoublySymmetric I-sections (Formcode 1)l Rectangular Hollow Sections (Formcode 2)l Circular Hollow Sections (Formcode 3)

For these sections themoment resistance is reduced due to the presence of an axial force.

In case of an extreme axial forcewhichwould lead to a negative reduction the formulas from thisarticle cannot be applied. Inthis case the plastic linear summation according to art. 6.2.1(7) is applied.

For any other class 1 or 2 cross-sectionswhich do not have a reducedmoment resistance defined within this article also theplastic linear summation according to art. 6.2.1(7) is applied.

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EC3 - EN 1993

Circular Hollow SectionsFor Circular Hollow Sections (FC 3) the reducedmoment resistance due to axial force is calculated according to the formulagiven in the 2009 correction sheet Ref.[11].

In addition, the resultant shear force and resultant moment is determined. The resultant shear force is used to calculate thereduction for shear according to "Bending, Shear (andAxial force)" on the previouspage.

The unity check is then executed as follows:

Class 3 cross-sectionsClass3 cross-sectionsare bydefault verified byart. 6.2.9.2.

For shear, reference ismade to "Bending, Shear (and Axial force)" on the previouspage. The reduction factor ρ to be usedin formula (6.42) is taken as themaximumof ρy and ρz seeRef.[38].

Class 4 cross-sectionsClass4 cross-sectionsare bydefault verified byart. 6.2.9.3 formula (6.44).

Stability Checks

Flexural BucklingTheFlexuralBucklingCheck isexecuted according to EN 1993-1-1 art. 6.3.1.

Buckling CurveTable 6.3 regarding the buckling curves is revised as follows:

- I-section (formcode 1) with fabricationRolled:

Condition Other fy fy = 460 N/mm^2

if h/b >1,2

and tf <= 40 mm

and 40 < tf <= 100 mm

Curve yy

Curve zz

Curve yy

Curve zz

a

b

b

c

a0

a0

a

a

if h/b <= 1,2

and tf <= 100 mmCurve yy

Curve zz

b

c

a

a

for any h/b

and tf > 100 mmCurve yy

Curve zz

d

d

c

c

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Chapter 2

Anyother casesnot covered by the above:

Curve yy=d

Curve zz=d

- I-section (formcode 1) with fabricationWelded:

tf <= 40 mm

tf > 40 mm

Curve yy

Curve zz

Curve yy

Curve zz

b

c

c

d

- RHS (formcode 2) or CHS (formcode 3) with fabricationRolled:

Curve yy=a

Curve zz=a

In case fy=460N/mm^2 thisbecomes:

Curve yy=a0

Curve zz=a0

- RHS (formcode 2) or CHS (formcode 3) with fabricationCold-Formed:

Curve yy=c

Curve zz=c

- RHS (formcode 2) with fabricationWelded:

Curve yy=b

Curve zz=b

- RHS (formcode 2) or CHS (formcode 3) with anyother fabrication:

Curve yy=d

Curve zz=d

- Anysection of the group:

Curve yy=b

Curve zz=b

- Channel section (formcode 5) or T-section (formcode 6) or full-rectangular (formcode 7) or fullcircular (formcode 11) with any fabrication:

Curve yy=c

Curve zz=c

- L-section (formcode 4) with any fabrication:

Curve yy=b

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EC3 - EN 1993

Curve zz=b

- Asymmetric I-section (formcode 101): This follows the same rules as a symmetric I-section. For the con-ditionsb is taken as themaxof Bt andBb and tf is taken as themaxof tt and tb.

- From the group the SFB, IFBA, IFBB sections follow the same rules as a welded I-sec-tion (independent of fabrication). For the condition tf is taken as themaxof to and tu.

- From the group the THQ sectionwith any fabrication:

Curve yy=b

Curve zz=b

- Any section from the group follows the same rules as a welded I-section (independent of fab-rication). For the condition tf is taken as themax thicknessof anyof the flanges.

- Any section of the or or groups (which do not meet any of theother rules):

Curve yy=c

Curve zz=c

- Anyother section i.e. not covered byanyof the above:

Curve yy=d

Curve zz=d

The user canmanuallyoverrule the buckling curvewithin theCross-section.

For non-prismatic members with cross-sections that are not listed in Table 6.2 all generated sections will receive the userinputted valuesof the buckling curvesof the first section in the span.

Buckling LengthFor the calculation of the buckling length, reference is made to chapter " "Annex B: Calculation of buckling ratio" onpage 184".

The buckling properties for a VARH element are calculated by using the critical Euler force for this member (see chapter“"Calculation of criticalEuler force" on page 189”).

Torsional (-Flexural) BucklingTheTorsional (-Flexural) BucklingCheck isexecuted according to EN 1993-1-1 art. 6.3.1.4.

In case of an RHS section (Formcode 2) or CHS section (Formcode 3) the check will not be executed and a note will beshown instead.

In case of an I-section (Formcode 1), when the check is not limiting it will not be printed and a note is shown instead. Not lim-iting is defined here as a unity check lower than the unity check for Flexural Buckling. In case however Flexural buckling canbe ignored (due to low compression force or low slenderness) the comparison is done with the unity check of the com-pression check.

The buckling curve for torsional (-flexural) buckling is taken as the z-zbuckling curve according to the table given in "FlexuralBuckling" on page 94.

The value of the elastic critical loadNcr is taken as the smallest of Ncr,T (Torsional buckling) andNcr,TF (Torsional-Flexuralbuckling).

For doublysymmetric sections the elastic critical loadNcris taken equal to Ncr,T.A section is considered doublysymmetric if the cross-section propertydy=dz=0mmor if the following sectionsare used:- I-section (Formcode 1)

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Chapter 2

- FullRectangular Section (Formcode 7)- FullCircular Section (Formcode 11)- Cold Formed I-PlusSection (Formcode 127)- Cold-Formed IS-PlusSection (Formcode 128)- Cold-Formed 2C-Section (Formcode 130)- Virtual Joists (Formcode 160)

Calculation of Ncr,TThe elastic critical loadNcr,T for torsional buckling is calculated according toRef.[17].

With:

E Modulusof Young

G Shear modulus

It Torsion constant

Iw Warping constant

lT Buckling length for the torsional bucklingmode

y0 and z0 Coordinatesof the shear center with respect to the centroid

iy radiusof gyration about the strong axis

iz radiusof gyration about theweakaxis

Calculation of Ncr,TFThe elastic critical loadNcr,TF for torsional flexural buckling is calculated according toRef.[17].

Ncr,TF is taken as the smallest root of the following cubicequation inN:

0

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EC3 - EN 1993

With:

Ncr,y Critical axial load for flexural buckling about the y-yaxis

Ncr,z Critical axial load for flexural buckling about the z-zaxis

Ncr,T Critical axial load for torsional buckling

SheetingIn case a sheeting isused, independent onwhich side, the augmented It will be used also in TorsionalBuckling.

For more information on sheetingssee "AnnexD: Use of sheeting " on page 205.

Lateral Torsional BucklingThe Lateral TorsionalBucklingCheck isexecuted according to EN 1993-1-1 art. 6.3.2.1.

CHSsections (Formcode 3) are taken asnon-susceptible to Lateral TorsionalBuckling.

RHSsections (Formcode 2) sectionsare classified asnon-susceptible to Lateral Torsional Buckling if the following conditionis fulfilled (Ref.[9] pp.119).

With:

h Height of RHSsection

b Width of RHSsection

Relative slenderness for weakaxis flexural buckling

For all other sections the Lateral Torsional Buckling check is executed in which the elastic critical moment for Lateral-Tor-sionalBucklingMcr isdetermined by the following formulaRef.[9]:

With:

E Modulus of elasticity

G Shear modulus

L Length of the beam between points which have lateral restraint (=lLTB)

Iw Warping constant

It Torsional constant

Iz Moment of inertia about the weak axis

kLT

LTB-length factor

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Chapter 2

k Factor related to end fixity

kw Factor to account for warping endconditions

zg Distance between point of load application and shear center

zj Asymmetry factor

C1 Factor for taking into account the shape of the moment diagram

C2 Factor for taking into account the position of the loading

C3 Factor for taking into account the asymmetry of the cross-section

Haunched sections (I+Ivar, Iw+Plvar, Iw+Iwvar, Iw+Ivar, I+Iwvar) and composed rail sec-tions (Iw+rail, Iwn+rail, I+rail, I+2PL+rail, I+PL+rail, I+2L+rail, I+Ud+rail) are considered asequivalent asymmetric I sections.

For advanced Lateral Torsional buckling analysis, see "Annex D: Use of sheeting " onpage 205.

Determination of the factors C1, C2 and C3The coefficientsC1, C2 andC3 can be calculated according to three differentmethods:

ENV1993-1-1 AnnexF

ECCS119/Galea

Lopez, Yong, Serna

Bydefault themethod according to ECCS119/Galea isapplied.

The following paragraphsgive information on thesemethods.

ENV 1993-1-1 Annex FWhen this setting is chosen, themoment factorsare determined according to ENV1993-1-1 AnnexF Ref.[10].

Detailed information can be found in chapter "AnnexC: Calculation ofmoment factors for LTB" on page 201.

ECCS 119/GaleaWhen this setting is chosen, themoment factorsare determined according to ECCS119AnnexBRef.[9].

The figuresgiven in this reference for C1 andC2 in case of combined loading originate fromRef.[28] which in fact also givesthe tabulated valuesof those figuresaswell asan extended range.

The actual moment distribution is compared with several standard moment distributions. These standard moment dis-tributions are moment lines generated by a distributed q load, a nodal F load, or where the moment line ismaximum at thestart or at the end of the beam.

The standardmoment distributionwhich is closest to the actualmoment distribution, is taken for the calculation of the factorsC1 andC2.

Linear MomentIn case of a linear moment diagram theC1 coefficient isdetermined using formula (301) of ECCS119AnnexBRef.[9].

The coefficient C2 is taken aszero in this case.

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EC3 - EN 1993

Point LoadingIn case of Point loading the coefficientsC1 andC2 are calculated using tables5-8 of GaleaRef.[28].

Adouble interpolation isused for intermediate values.

Line LoadingIn case of Line loading the coefficientsC1 andC2 are calculated using tables1-4 of GaleaRef.[28].

Adouble interpolation isused for intermediate values.

In case k differs from 1.00 the C1 and C2 values determined from Galea Ref.[28] are overruled by the values from ECCS119AnnexBRef.[9] tables63 and 64

For all cases the factor C3 is taken fromECCS119 AnnexBRef.[9] tables 63 and 64. The C3 value is determined based onthe case of which theC1 valuemost closelymatches the table value.

The table for C3 uses the valueψf which is taken as0 bydefault.

For asymmetrical I-sections (Form code 101) ψf is calculated as follows:

Ifc and Ift concern themomentsof inertia of the compression ( c ) and tension ( t ) flange about theminor axis.

For thismethodψf should bewithin the following range:

When this isnot the caseψf is set to the respective limit and awarning isgiven.

I-section CantileversECCS119AnnexBRef.[9] tables65 to 68 give values for C1, C2 andC3 for I-section cantilevers.

These coefficientsare used only in case the following conditionsaremet:

l Themember concernsa cantilever.

A cantilever is defined as a member at the end of a buckling system which has free ends for both buckling aboutthe y-yand z-zaxis. In addition, the LTB length should correspond to the full system length of the buckling system.

l The cross-section isan I-section (Form code 1) or Asymmetric I-section (Form code 101).

This method differentiates between ‘warping prevented’ and ‘warping free’ at the fixed end. This setting is taken from thebuckling system.

Thismethod uses the valueψf which is calculated asspecified above.

For thismethodψf should bewithin the following range:

When this isnot the caseψf is set to the respective limit and awarning isgiven.

Thismethod uses the coefficient which isdefined as follows:

- 33 -

Chapter 2

with:

L System length for LTB

E Modulusof Young

G Shear modulus

Iz Inertia about theweakaxis

It Torsion constant

hs

Distance defined as follows:

FormCode 1: H - t

FormCode 101: H – 0,5 * tt – 0,5 * tb

should bewithin the following range:

When this isnot the case isset to the respective limit and awarning isgiven.

In addition thismethod should be used in combinationwith kequal to 2,00 and kw equal to 1,00

When this isnot the case an additionalwarning isgiven.

Lopez, Yong, SernaWhen this setting is chosen, themoment factorsare determined according to Lopez, Yong, SernaRef.[29].

When using thismethod the coefficientsC2 andC3 are set to zero.

The coefficient C1 iscalculated as follows:

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EC3 - EN 1993

With:

k1 Taken equal to kw

k2 Taken equal to kw

M1, M2,M3, M4, M5

The moments My determined on the buckling system in the given sec-tionsasshown on the above figure.

These moments are determined by dividing the beam into 10 parts (11sections) and interpolating between these sections.

Mmax ThemaximalmomentMyalong the LTBsystem.

Thismethod isonly supported in case both kand kw equal 0.50 or 1.00

Determination of distance zgThe distance zg is defined as the distance between the point of load application and the shear center. The point of loadapplication is taken as both the top (+z) and bottom (-z) of the cross-section. Depending on the sign of the moment eitherthe top or the bottom zg is used.

The sign isdetermined as follows: zg is taken aspositive for aDestabilizing load.

For a standard beam, the determination of Stabilizing/Destabilizing isdone depending on themoment:

If My>0 and loadingOn top =>Destabilizing

If My>0 and loadingOn bottom=>Stabilizing

If My<0 and loadingOn top =>Stabilizing

If My<0 and loadingOn bottom=>Detabilizing

For a cantilever, the determination of Stabilizing/Destabilizingwill be done depending on the sign of the equivalent lineload:

If q downward and loadingOn top =>Stabilizing

If q downward and loadingOn bottom=>Destabilizing

If q upward and loadingOn top =>Destabilizing

If q upward and loadingOn bottom=>Stabilizing

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Chapter 2

By setting the point of load application to Always destabilising or Always stabilising theabove dependencyon the bendingmoment or loading direction can be overruled.

In case themoment diagram concernsa linear diagram zg =0.

Determination of distance zjThe distance zj is determined from the βy asymmetryparameter of the cross-section.

If My<0 => zj =0,5 * βyIf My>0 => zj= - 0,5 * βy

In case of an axis switch (Iz > Iy) also βy and βz are switched.

LTB Curves - General caseTheGeneral case asdefined in EN 1993-1-1 art. 6.3.2.2 usesa limit slendernessof 0,2.

For deciding if the LTB check should or should not be executed art. 6.3.2.2(4) refers to the Alternative case which uses alimit slendernessof 0,4.

It is clear that this is an inconsistency within the code. In case for example the slenderness has a value just below 0,4 thiswould erroneously lead to the conclusion that no LTBcheckshould be done. In this case however theChi reduction value forcurve d for example is0,85which indicatesa 15% reduction of the bending capacity.

Therefore, conform the theory, for theGeneral case the limit slendernessused in art. 6.3.2.2(4) is set to 0,2.

LTB Curves - Alternative caseFor the 'Rolled & Equivalent welded case' given in art. 6.3.2.3 the theory in Ref.[9] clearly specifies that it is valid only for I-sectionsor sectionswith comparable shape.

Therefore thisarticle isapplied only in case of the following form-codes:

- Symmetric I-sections (Formcode 1)

- Asymmetric I-sections (Formcode 101)

A specific National Annex can overrule this condition and use this article also for other sec-tions. For more information reference is made to the Theoretical Background of NationalAnnexes to EN 1993.

Correction factor kcIn case Lateral-Torsional Buckling curves for the ‘Rolled and equivalent welded’ case are used according to EN 1993-1-1art. 6.3.2.3 the correction factor kc can be determined in twoways:

- Bydefault, kc is determined fromC1as followsRef.[30]:

- Alternatively kc can be taken fromTable 6.6

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EC3 - EN 1993

The default approach givesamore accurate value for kccompared to the simplifiedTable 6.6.

Modified design rule for Channel sectionsThe reduction factor for Lateral-TorsionalBuckling of Channel sections isdetermined according toRef.[22].

More specifically the calculation isdone as follows:

ThisModified design rule isapplied only in case the following conditionsaremet:

l The section concernsaChannel section (FormCode 5)l TheGeneralCase isused for LTB (Not theRolled andEquivalentWeldedCase)l 15 <=Lltb/h <=40 (with Lltb the LTB length and h the cross-section height)

SheetingIn case the sheeting is positioned on the compression flange and provides a fully braced support, no LTB check needs to beexecuted and a note isprinted instead.

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Chapter 2

For more information on sheetingssee "AnnexD: Use of sheeting " on page 205.

For more information on the calculation of the lateral stiffnesssee "Use of sheetings" on page 98.

Combined Bending and Axial CompressionThe Check for Combined bending and Axial Compression is executed according to EN 1993-1-1 art. 6.3.3 and AnnexesA&B.

Bending moments My,Ed and Mz,Ed

For prismatic members the value My,Ed is the maximum value of the bending moment around the strong axis in the mem-ber. The valueMz,Ed is themaximumvalue of the bendingmoment around theweakaxis in themember.

For non-prismatic sections, the values My,Ed and Mz,Ed are the concurrent bending moments for each intermediary sec-tion.

For non-prismaticmembers themaximalmoments are still used in the determination of themoment factorsCmi,0when using theGeneral formula.

Torsional(-Flexural) BucklingFor both InteractionMethods, in case Torsional Buckling is limiting (χTF <χz) the value for χz is replaced by the value of χTFand used in all formulas.

Interaction Method 1 – Annex AFor InteractionMethod 1 there isa discrepancy in the use of Ncr,T or Ncr,TF:

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EC3 - EN 1993

Within ECCS 119 Ref[9] as well as the ECCSDesign manual for EN 1993-1-1 all formulas are written using Ncr,T. There-fore alsowithin SCIAEngineer Ncr,T is used.

InteractionMethod 1 usesseveral 2nd order termswhich relate toNcr,y ; Ncr,z ; Ncr,T.

For example:

In case NEd exceeds any of those critical forces this would lead to an undetermined result (more specifically the memberalready fails in buckling so technically there isno use in verifying the combined check.)

In such a case, thuswhen NEd exceeds any of the critical forces, the combined check itself is not executed. Instead the limitforcesare printed to indicatewhich one isexceeded and the check is set to 999.

Interaction Method 2 – Annex BInteraction Method 2 makes a distinction between members susceptible and not-susceptible to torsional deformations.Within SCIAEngineer thisdistinction isdone as follows:

Doubly symmetric I sections which have a reduction factor for Lateral Torsional Buckling χLT equal to 1,00 are classified asnon-susceptible to torsional deformations.

Circular hollow sectionsare classified asnon-susceptible to torsional deformations.

Rectangular hollow sections are classified as non-susceptible to torsional deformations if the following condition is fulfilled(Ref.[9] pp.119).

h Height of RHSsection

b Width of RHSsection

Relative slenderness for weakaxis flexural buckling

InteractionMethod 2 usesspecific formulaswhich subtract a constant value from the relative slenderness:

- 39 -

Chapter 2

In these formulas, in case <0 or <0 thispart is set to 0.

Combined Bending and Axial TensionEN 1993-1-1 doesnot provide an interaction check for the Combined stability effect of Bending and Axial Tension. The pur-pose of the interaction check for Bending and Tension is to check the stressesat the compression fiber.

In general the normal force provides a beneficial effect on the instability behaviour (the compressed flange under a strongaxismoment) however the combination of aweakaxismoment can lead to an increase of the instability effect.

Therefore a specific interaction check isexecuted according to EN 1993-1-3 art. 6.3.

Even that article however does not fully provide the required interaction check and thus the interaction is based on the fol-lowing formula given in article C5: of the AISI NAS2007Ref.[18] code:

This formula is rewritten using EC-EN notationsas follows:

With:

Mb,y,Rd The Lateral TorsionalBuckling resistance

Mc,z,Rd,com Themoment resistance for the compression fiber in case ofMz

Nt,Rd TheTensionResistance

This check is only executed in case all three components (NEd ; My,Ed ; Mz,Ed) are present.In case only two componentsare present the effectsare alreadycovered byother checks.

This check isnot run for memberswhich have a reduction factor for Lateral TorsionalBuck-lingχLT equal to 1,00 since all relevant checks are in that case already covered by the Sec-tionCheck.

In case of aNumerical cross-sectionMc,z,Rd,com is calculated usingWel,z since such a sec-tion hasno fibres.

Shear BucklingTheShear BucklingCheck isexecuted according to EN 1993-1-5Chapter 5 and art. 7.1.

ConditionThe shear buckling check is verified for the following cross-sections:

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EC3 - EN 1993

l DoublySymmetric I-sections (Formcode 1)l Asymmetric I-sections (Formcode 101)

Composed rail sections (Iw+rail, Iwn+rail, I+rail, I+2PL+rail, I+PL+rail, I+2L+rail, I+Ud+rail)are considered asequivalent asymmetric I-sections.

The check is executed only in case those sections are loaded by a shear force Vz,Ed and in case the web slenderness hw/texceeds the limitsgiven in art. 5.1(2).

End post conditionThe condition for the end post used inTable 5.1 is defined through the input of Stiffenerson themember. Bydefault the endpost condition is taken asnon-rigid.

Plate slendernessThePlate slenderness isdetermined depending on the definition of stiffeners:

l In case no stiffenersare inputted on themember or stiffenersare inputted onlyat themember endsFormula (5.5) isused.

l For anyother input of stiffeners (at intermediate positions, at the endsand intermediate positions…) Formula (5.6) isused.

The shear buckling coefficient isdetermined according to AnnexA formula (A.5).

Contribution of the flangesThe capacityof the section considering only the flangesMf,Rd is determined according toRef.[16] pp70:

Thisvalue is reduced for the effect of NEd according to Formula (5.9).

InteractionWhen required according to art. 7.1(1) the interaction between bending, axial force and shear buckling is verified accordingto Formula (7.1).

The value ofMf,Rd including the effectsof NEd is determined asspecified above.

The value of Mpl,Rd concerns the plastic moment resistance of the cross-section, this includes a possible reduction due toNEd (i.e. MNRd).

l For doublysymmetric I-sections this isdetermined according to EN 1993-1-1 art. 6.2.9.1(5).l For asymmetric I-sections thisarticle doesnot provide anymethod to account for NEd, therefore the following reduction is

used:

MNRd = (1 - n)*Mpl,Rdwith n =NEd/NplRd

In case of a Class 3 or Class 4 section the following additional condition is checked before the interaction formula can beapplied:

withMR,eff the actual (effective) moment resistance of the cross-section

- 41 -

Chapter 2

Thisconditionwasdetermined fromRef.[16] pp96 and negates the definitionsofMf,Rd andMpl,Rd given in art. 7.1(1).

Articles7.1(2),(3),(5) are not supported.

SEMI-COMP+The full SEMI-COMP+publication (Ref.[40]), to have amore economical design of Class3 sections (as semi-plastic), will besupported for I-sections (Formcode 1) andRHS-sections (Formcode 2).

It providesaway to checkClass3 sectionsassemi plastic sections. Instead of the strict jump from to it providesa gradual flow between the two valuesascan be found also in AISC:

Thismethod isbydefault activated but it can bemodified in the steel setup .

In the case that a cross-section is classified asClass3, it will instead be checked asa Class2 but the value is replacedbya value:

For an I andH sections (Formcode 1) the following table applies in order to calculate the interpolation:

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EC3 - EN 1993

In addition notice under step 2 that the formula for bending & axial force (form. 6.36 - 6.38 of EN1993-1-1) has been mod-ifiedwhen using theSEMI-COMP+approach.

For anRHSsection (Formcode 2) the following table applies in order to calculate the interpolation:

In addition notice under step 2 that the formula for bending & axial force (form. 6.39 & 6.40 of EN1993-1-1) has beenmod-ifiedwhen using theSEMI-COMP+approach.

- 43 -

Chapter 2

In all placeswhere normally would be used now isused, for example:

The combined stability checksare alsomodified accordingly:

The SEMI-COMP+publication hasalso found a discrepancy in the Eurocode related to the classification limits. More inform-ation can be found in "Classification" on page 17

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EC3 - EN 1993

Battened compression membersThe following section pairsare supported asbattened compressionmember:

1. 2I2. 2Uo3. 2Uc

This specifically concerns hot rolled sections i.e. cold- formed pair sections are not sup-ported.

Battened compressionmembersare evaluated according to EN 1993-1-1 article 6.4.1 and 6.4.3.

Two links (battens) are used.

The following additional checksare performed:

l "Section checkof chord asbeam in field between battens" belowl "Buckling checkof chord" on the next pagel "Section checkof single batten" on the next page

Section check of chord as beam in field between battensThischeck isexecuted according to articles6.4.3.1 &6.2.9.1 using the following internal forces:

With:

Nch,Ed Chord force according to formula (6.69)

VEd Shear force in the built-upmember according to formula (6.70)

a Distance between battens

Note:

- For I-sections a classification is made which thus supports both an elastic or plastic interaction. For U-sections always anelastic interaction ismade.

- 45 -

Chapter 2

- is taken as the absolute value of

Buckling check of chordThisconcernsaweakaxisbuckling checkof a single chord according to articles6.4.3.1 &6.3.1.1 using chord forceNch,Ed.

Section check of single battenAn elastic section checkof a single batten isexecuted according to articles6.4.3.1, 6.2.9.2 &6.2.6 using the following forces:

With:

VEd Shear force in the built-upmember according to formula (6.70)

a Distance between battens

h0 Distance between centroidsof chords

- 46 -

EC3 - EN 1993

Plate girders with sinusoidal corrugated websPlate girders with sinusoidal corrugated webs (“SIN beams”) are covered in EN 1993-1-5 Annex D. The method given inthis chapter is specified inRef.[33]. Background information can be found inRef.[16].

The check is executed for sheet welded cross-sections of type Iw c and Iwn c. The corrugations are taken to be per-pendicular to the upper flange.

The dimensioning of corrugatedweb girders isexecuted for the in plane effectsNEd, Vz,Ed andMy,Ed.

Transformation of internal forcesFor every point of the plate girder the chord forcesN,og and N,ug are found by transformation. These chord forces are stillparallel to themember axiswhile the shear force isorthogonal to the axis.

The following anglesare defined:

l α = the slope of the lower chord against the upper chordl β= the angle between the centre line and chords.

The shear force Vz isdecomposed into a corrugation-parallel component V* and an axis-parallel component N(V)*.

N(V)* can be added directly to the calculated normal forceN. The chord forcescan now be determined as follows:

- 47 -

Chapter 2

With:

A,og Area of the upper flange

A,ug Area of the lower flange

H,steg Webheight

t,og Thicknessof the upper flange

t,ug Thicknessof the lower flange

From the chord forces the chord-parallel componentsand the corrugation-parallel componentsare

determined. For the upper chord thisbecomes:

For the lower chord the following intermediate step isused:

The actual force in the lower chord is then:

The actual component of the shear force can then bewritten as:

- 48 -

EC3 - EN 1993

The chord forces Nog* and Nug* are now known. By summation of the V* and V(Nog)* and V(Nug)* components the totalshear force isobtained.

Resistance of sinusoidal corrugated web girdersThe normal force and bendingmoment are taken by the flangeswhile the shear force is taken by the corrugatedweb.

FlangesFor the flanges the following limitsare checked:

l Yieldingl Local bucklingl Global buckling

YieldingNRd,yield =bf * tf * fy / γM0

With:

bf Flangewidth

tf Flange thickness

fy Yield strength

γM0 Partial safety factor

Local bucklingLocal buckling of the compression flange ischecked according to EN 1993-1-5 article 4.4.

To avoid local buckling the slenderness is limited to 0,748. By substituting this into the formula for the slenderness thefollowing limit isobtained for thewidth:

For a sinusoidal corrugatedwebmember the total flangewidth thusbecomes:

The resistance for local buckling can then bewritten out as:

NRd,local =b * tf * fy / γM0

Global bucklingGlobal buckling of the compression flange (Lateral-TorsionalBuckling) is checked according to EN 1993-1-1 article 6.3.2.4:

- 49 -

Chapter 2

This iswritten out to the following resistance for the compression flange:

With:

b Flangewidth

t Flange thickness

fy Yield strength

E Modulusof Young

Lc Length between lateral restraints (LTB length)

kc Correction factor according to EN 1993-1-1Table 6.6

The design value can then bewritten out as:

NRd,global =NRk / γM1

With:

γM1 Partial safety factor

WebFor theweb the shear resistance isdetermined according to EN 1993-1-5 AnnexD article D2.2:

Where χc is taken as the lesser of the reduction factors for local buckling χc,l and global buckling χc,g.

According to Ref.[34] it was found by testing and FEM that no local buckling occurs for all actually produced beams withsinusoidal corrugatedwebs. Therefore only the reduction factor for global buckling χc,g needs to be accounted for.

With:

- 50 -

EC3 - EN 1993

fy Yield strength

E Modulusof Young

ν Poisson ratio

tw Web thickness

hw Webdepth

Iz

Secondmoment of area of one corrugation of lengthw, calculated as:

a3

Height of a sinuswave

Taken as40mm for tw <3mm

Taken as43mm for tw ≥3mm

w Length of the projection of a half wave

s

Unfolded length of a half wave

Taken as178mm for tw <3mm

Taken as182mm for tw ≥3mm

Moments on columns in simple constructionThisNCCI presents a method for determining the moments on columns in simple construction due to the eccentricity of thebeam-to-column joints. This method is intended for braced frames with nominally pinned joints. The method is detailed inRef.[31] and [32].

ConditionsIn case the setting is activated in the Steel Setup the additionalmomentswill be calculated on columns in which the followingconditionsare satisfied:

l The column cross-section concernsan I-section (Form code 1) or RHSsection (Form code 2)l The column hasstructural typeColumn,Gable column or Secondarycolumnl The column isuniform i.e. doesnot have arbitrarysectionsor haunchesl Onlyconnected beamswith structural typeBeamor Rafter or PlateRib are accounted for. In addition these beams

should have a hinge at the sidewhere theyare connected to the column.l There canmaximallybe two connected beams in the sameplane in the samenode. These two connected beamsmust

have the sameX-axisdirection of their LCS.

Additional momentsWhen the above conditionsare satisfied the additionalmomentsare calculated in the followingway:

- 51 -

Chapter 2

With:

Rb1,Ed

Shear force in the considered plane in the connected beamat the specified dis-tance

hProfile height for an I-section

Profile height or width for anRHS-section

tw Web thickness for an I-section

The distribution of the additional moments to the upper and lower column sections is carried out in proportion to their stiffness, except where the ratio of the stiffnesses (I/L) does not exceed 1.5, when the momentsmay be shared equally.This is illustrated on the following picture:

With:

MU Distributedmoment to the upper column section

ML Distributedmoment to the lower column section

IU Inertia in the considered plane of the upper column section

IL Inertia in the considered plane of the lower column section

- 52 -

EC3 - EN 1993

LU System length in the considered plane of the upper column section

LL System length in the considered plane of the lower column section

These additionalmomentsare then added to the sections in the column just above and just below the connected beam.

The simplified procedure given in this chapter allows to account for eccentricities withoutspecifically adding these eccentricities in the calculation model. In case however an actualmember eccentricity is defined on the column member the above procedure will not beused since additionalmomentswill alreadybe generated during the analysis.

ScaffoldingThe scaffoldingmember and coupler checkare implemented according to EN 12811-1Ref.[23].

The following paragraphsgive detailed information on these checks.

Scaffolding member check for tubular membersThe check is executed specifically for circular hollow sections (Form code 3) and Numerical sections in case the proper set-ting isactivated in theSteelSetup.

The check is executed according to Equation 9 given in EN 12811-1 article 10.3.3.2. However, the EN 12811-1 only givesan interaction equation in case of a low shear force.

Since the EN 12811-1 is based entirely on DIN 4420-1 Teil 1 Ref.[26] the interaction formulas according to Tabelle 7 of DIN4420-1 Teil 1 are applied in case of a large shear force.

The interaction equationsare summarised as follows:

Conditions Interaction for tubularmember

and

and

and

and

- 53 -

Chapter 2

Conditions Interaction for tubularmember

M

V

Npld

Vpld

Mpld

A Area of the cross-section

Wel Elastic sectionmodulus

Wpl Plastic sectionmodulus

N Normal force

Vy Shear force in ydirection

Vz Shear force in zdirection

My Bendingmoment about the yaxis

Mz Bendingmoment about the zaxis

fy Yield strength of thematerial

Safety factor taken asγM0 of EN 1993-1-1

Asspecified in EN 12810Ref.[25] &12811Ref.[23] the scaffolding check for tubular mem-bersassumes the use of a 2nd order analysis including imperfections.In case these conditionsare not set the default EN 1993-1-1 checkshould be appliedinstead.

Scaffolding coupler checkThe scaffolding couplersaccording to EN 12811-1 AnnexCRef.[23] are provided bydefault within SCIAEngineer.

The interaction checkof the couplers isexecuted according to EN 12811-1 article 10.3.3.5.

- 54 -

EC3 - EN 1993


Coupler type Interaction equation

Right angle coupler

Friction sleeve

Fsk

CharacteristicSlipping force

Taken asNxkandVzkof the coupler properties

2Fsk=Nxk+Vzk

FpkCharacteristicPull-apart force

Taken asVykof the coupler properties

MBkCharacteristicBendingmoment

Taken asMykof the coupler properties

N Normal force




Safety factor taken asγM0 of EN 1993-1-1 for steel couplers

Safety factor taken asγM1 of EN 1999-1-1 for aluminium couplers

Manufacturer couplersIn addition to the scaffolding couplers listed above, specificmanufacturer couplersare providedwithin SCIAEngineer.

The interaction checksof these couplersare executed according to the respective validation reports.

CuplockThe cuplockcoupler which connectsa ledger and a standard isdescribed in ZulassungNr. Z-8.22-208Ref.[35].


Cuplock Coupler Interaction equation

Interaction 1

- 55 -

Chapter 2

Cuplock Coupler Interaction equation

Interaction 2

With:

Nxk Taken from the coupler properties

Myk Taken from the coupler properties

Mxk Taken from the coupler properties

N Normal force in the ledger


Mx Torsionalmoment about the xaxis

Nv Normal force in a connecting vertical diagonal

α Angle between connecting vertical diagonal and standard

Safety factor taken asγM0 of EN 1993-1-1 for steel couplers


Layher Variante II & K2000+ & HSThe Layher coupler which connectsa ledger and a standard isdescribed in ZulassungNr. Z-8.22-64Ref.[36] for Variante IIandVariante K2000+. In the sameway the details for the VarianteHSare provided in ZulassungNr. Z-8.22-939Ref.[39]

Layher Coupler Interaction equation

Interaction 1

Variante II:

Variante K2000+:

Variante HS:

- 56 -

EC3 - EN 1993

Layher Coupler Interaction equation

Note: An additional check for welds is not supported

Interaction 2

With:

NR,d=Nxk / γMWithNxk taken from the coupler properties

My,R,d=Myk / γMWithMyk taken from the coupler properties

Mz,R,d=Mzk / γMWithMzk taken from the coupler properties

MT,R,d=Mxk / γMWithMxk taken from the coupler properties

Vy,R,d=Vyk / γMWith Vyk taken from the coupler properties

Vz,R,d=Vzk / γMWith Vzk taken from the coupler properties

N Normal force in the ledger

(+) This index indicatesa tensile force




- 57 -

Chapter 2

Mx Torsionalmoment about the xaxis

Nv Normal force in a connecting vertical diagonal

α Angle between connecting vertical diagonal and standard

e

=2,75 cm for Variante II

=3,30 cm for Variante K2000+

=3,30 cm for VarianteHS

eD =5,7 cm for Variante II, Variante K2000+andVarianteHS

ξ

=1,26 cm for Variante II

=1,41 cm for Variante K2000+

=1,15 cm for VarianteHS

γMSafety factor taken asγM0 of EN 1993-1-1 for steel couplers


- 58 -

EC3 – EN Fire ResistanceThe beamelementsare checked according to the regulationsgiven in

Eurocode 3

Design of steel structures

Part 1 - 2 : General rules–Structural fire design

EN 1993-1-2:2005

Corrigendum

EN 1993-1-2:2005/AC:2005

Corrigendum

EN 1993-1-2:2005/AC:2009



1. General

1.1 Scope X

2. Basis of Design

2.1 Requirements X

2.2 Actions X

2.3 Design values ofmaterial properties X

2.4 Verification methods

2.4.1 General X

2.4.2 Member analysis X

3. Material properties X(*)

4. Structural fire design

4.2 Simple calculation models

4.2.1 General

4.2.2 Classification of cross-sections

4.2.3 Resistance

4.2.4 Critical temperature

X

X

X(*)

X(*)

- 59 -

Chapter 3

Article Title

4.2.5 Steel temperature development

4.2.5.1 Unprotected internal steelwork

4.2.5.2 Internal steelwork insulated by fire protection material

X(*)

X(*)

X(*)

Annex E Class 4 cross-sections X


3. Thermal actions for temperature analysis

3.1 General rulesX(*)

3.2 Nominal temperature-time curves

3.2.1 Standard temperature-time curve

3.2.2 External fire curve

3.2.3 Hydrocarbon curve

X(*)

X(*)

X(*)

4. Mechanical actions for structural analysis

4.3 Combination rules for actions

4.3.1 General ruleX(*)

Annex A Parametric temperature-time curves X

Material propertiesThematerial propertiesare depending on the steel temperature.

Strength and deformation properties :

The variation in function of the steel temperature of the value for yield strength ky,θ, proportional limit kp,θ and modulus ofelasticity kE,θ is given by tables in ref.[6],Table 3.1andTable E.1.

For cold formedmembersky,θ is taken fromRef.[7];Table III.2.5.

- 60 -

θa[°C] ky,θ20 1.00

100 1.00

200 1.00

300 1.00

400 0.87

500 0.59

600 0.39

700 0.12

800 0.09

900 0.06

1000 0.04

1100 0.02

1200 0

In the simplified calculationmethod, the following default propertiesare considered to be constant during the analysis :

unit mass ρa 7850 kg/m³

thermal elongation Δl/l 14 x 10-6 (θa-20)

thermal conductivity λa 45 W/mK

ClassificationThe classification of cross-sections isexecuted according to EN 1993-1-2 art. 4.2.2

For the purpose of these simplified rules the cross-sectionsmaybe classified as for normal

temperature designwith a reduced value for ε asgiven below:

where:

fy is the yield strength at 20 °C

Verification DomainsThe verification can be performed in 3 domains :

l Resistance domainl Time domainl Temperature domain

- 61 -

Chapter 3

In theResistance domain the verification isdone according to EN 1993-1-2 art. 4.2.3.. This can be summarized using the fol-lowing steps:

l The required fire resistance time isdefinedl The gas temperature θg is calculated for the requested time

l Thematerial temperature θa,t is determined using thisgas temperature and the defined fire protectionmaterial

l Thematerial temperature leads to a reduction of thematerial propertiesl The different unity checksare executed using these reduced propertiesl The overall unity checkconcerns the biggest unity checkof all resistance checks

In the Time domain the verification is done according to EN 1993-1-2 art. 4.2.4.. This can be summarized using the fol-lowing steps:



l The unity checksare executed at time t =0which gives the result at ambient temperaturel The resultingmaximal unity checkat time t =0 is taken as the degree of utilisationµ0

l The criticalmaterial temperature θa,cr is determined using the degree of utilisationµ0

l The overall unity checkconcerns the ratio of thematerial temperature θa,tat the requested time to the criticalmaterial tem-perature θa,cr

The critical material temperature θa,cr is determined using EN 1993-1-2 art. 4.2.4 formula(4.22). This formula does not account for instability phenomena in which case the Tem-perature domain should be used.

The Temperature domain concerns an extension of the Time domain in which the critical temperature is determined iter-atively. This can be summarized using the following steps:



l The criticalmaterial temperature θa,cris determined iteratively:n Thematerial temperature is increased stepwisen The increasedmaterial temperature leads to a reduction of thematerial properties

n The different unity checksare executed using these reduced propertiesn Thisprocedure continuesuntil themaximal unity checkbecomes1,00n The finalmaterial temperaturewhich leads to thisunity checkof 1,00 is taken as the criticalmaterial temperature θa,cr

l The overall unity checkconcerns the ratio of thematerial temperature θa,tat the requested time to the criticalmaterial tem-perature θa,cr.

The Temperature domain accounts for all effects including instability phenomena and thusnegates the disadvantage of the simplified formula used in the Time domain.

- 62 -

Temperature analysis - Thermal actionsIn this part, the fire action effects as well as the nominal temperature- time curves, section factors and net heat flux aredescribed in order to obtain the steel temperature. See Ref.[8], Section 3, andRef.[7], II.2.2.

Fire actions effect EfiThe design effects of actions for the fire situation Efi,d,t are taken from the results of the analysis. It is recommended to usethe accidental combination rules, for calculating the internal forcesused in the fire resistance check.

The accidental combination isgiven by (seeEN 1990 –Ref[5])

Eq. 6.11b ΣGk,j +P+Ad+ (ψ1,l or ψ2,l)Qk,l+Σψ2,iQk,i

The choice betweenψ1,l or ψ2,l is done by the user. Default isψ1,l.With:

Gk,j characteristic value of permanent action j

P relevant representative value of prestressing action

Qk,l characteristic value of leading variable action l

Qk,i characteristic value of accompanying variable action i

Ad design value of the accidental action

ψ1,l ψ2,l combination coefficients

Nominal temperature-time curveThe following temperature-time curvescan be selected :

With:

t time in [min]

θg gas temperature in [°C]

αc the coefficient of heat transfer byconvection

ISO 834 curve

external fire curve

hydrocarbon curve

- 63 -

Chapter 3

smoldering fire curve

during 21minutes, followed by the standard ISO 834 curve

user defined temperature-time curve

Section FactorSection factor Am/V for unprotected steel membersThe section factor Am/V for unprotected steel members can be determined for two situations in SCIA Engineer. Either thesteelmember is:

- Exposed to fire on all sides

Am/V= (perimeter) / (cross-section area)

- Exposed to fire on three sides

- 64 -

Am/V= (perimeter - width of the covered flange) / (cross-section area)

Section factor Ap/V for protected steel membersThe section factor Ap/V for protected steel members can be determined for four situations in SCIA Engineer. Either thesteelmember is:

- Exposed to fire on all sides with hollow encasement

Ap/V= (2b +2h) / (cross-section area)

- Exposed to fire on all sides with contour encasement

- 65 -

Chapter 3

Ap/V= (perimeter) / (cross-section area)

- Exposed to fire on three sides with hollow encasement

Ap/V= (2h +b) / (cross-section area)

- Exposed to fire on three sides with contour encasement

- 66 -

Ap/V= (perimeter - width of the covered flange) / (cross-section area)

Supported cross-sections for three sided fire exposureThe following cross-section typesare supported for fire exposure on three sides:

l Doublysymmetric I-sections (formcode 1)l Rectangular Hollow Sections (formcode 2)l Channel sections (formcode 5)l Asymmetric I-sections (formcode 101)l Slimfloor beams (formcode 153)l Integrated floor beams (formcode 154+155)l Top hat beams (formcode 156)

Net heat flux

With:

hnet,d the net heat flux

hnet,c the convective heat flux

hnet,r the radiative heat flux

With:

- 67 -

Chapter 3

Φ configuration factor [1.0]

εresresultant emissivity

= εf εm

εfemissivity related to fire compartment

= [1.00]

εmemissivity related to surfacematerial

= [0.70]

θr=θggas temperature in [°C]

θm surface temperature ofmember in [°C]

αc coefficient of heat transfer byconvection

Steel TemperatureThe increase of temperature Δθa,t in an unprotected steelmember during a time intervalΔt

With:

Am the exposed surface area per unit length [m²/m]

Vthe volume of themember per unit length [m³/m]

The factor Am/V should not be taken as less than 10m-1

ca the specificheat of steel [J/kgK]

hnet,d the net heat fluxper unit area [W/m²]

Δtthe time interval [seconds]

The value should not be taken asmore than 5 seconds

ρa the unit massof steel [kg/m³]

kshcorrection factor for the shadow effect [1.0]

The correction factor is calculated for I sectionsonly

The increase of temperature Δθa,t in an insulated steelmember during a time intervalΔt

With:

- 68 -

Ap the area of fire protectionmaterial per unit length [m²/m]

V the volume of themember per unit length [m³/m]


cp the specificheat of fire protectionmaterial [J/kgK]

dp the thicknessof the fire protectionmaterial [m]




ρp the unit massof fire protection [kg/m³]

θa,t the steel temperature at time t

θg,t the ambient gas temperature at time t

Δθg,t the increase of the ambient gas temperature during the time interval

λp the thermal conductivityof the fire protectionmaterial [W/mK]

The valueΔθa,t ≥0.0

For the increase of temperature Δθa in an insulated steel member with intumescent coating, reference is made to NEN6072.

With:

Ap the area of fire protectionmaterial per unit length [m²/m]V the volume of themember per unit length [m³/m]Pi Ap/Vca the specificheat of steel [J/kgK]Kd;ef coefficient of heat transfer of the intumescent coating

∆tthe time interval [seconds]

The value should not be taken asmore than 30 secondsρa the unit massof steel [kg/m³]θa the steel temperature at time tθt the ambient gas temperature at time t

- 69 -

Chapter 3

Section ChecksThe section checks (buckling, lateral torsional buckling) are performed according to the regulations given in EN 1993-1-2.The checksare performed in the resistance domain or in the temperature/time domain.

For eachmember, the classification of the crosssection, the section checkand the stability checkare performed.

The different section checksaccording to EN1993-1-1 ("Section Checks" on page 21)are executed andmodified accordingto the fire regulations. For the following checksadditional information isgiven:

TensionThe design tension resistance isdetermined according to art. 4.2.3.1(1) of EN 1993-1-2.

CompressionMembers with Class 1, Class 2 or Class 3 cross-sectionsThe design compression resistance for memberswith Class 1, Class 2 or Class 3 cross-sections is determined according toart. 4.2.3.2.of EN 1993-1-2

Members with Class 4The design compression resistance for memberswith Class4 isdetermined according toAnnex Eof EN 1993-1-2

The resistance of members with a class 4 cross-section should be verified with the equations given in art.4.2.3.2 of EN1993-1-2 for compressionmembers, in which the area is replaced by the effective area and the sectionmodulus is replacedby the effective sectionmodulus.

The effective cross section area and the effective section modulus should be determined in accordance with EN 1993-1-3andEN 1993-1-5, i.e. based on thematerial propertiesat 20°C.

Bending MomentMembers with Class 1, Class 2 or Class 3 cross-sectionsThe design moment resistance Mfi,θ,Rd for Class 1, Class 2 or Class 3 cross-sections with a uniform temperature θa isdetermined according to EN 1993-1-2 art. 4.2.3.3(1)

The design moment resistance Mfi,t,Rd at time t of a Class 1, Class 2 or Class 3 cross-section with a non-uniform tem-perature distribution across the cross-section isdetermined according to EN 1993-1-2 art. 4.2.3.3(3)

Members with Class 4 cross-sectionsThe designmoment resistance for Class4 cross-sections isdetermined according toAnnex Eof EN 1993-1-2.

The resistance of members with a class 4 cross-section should be verified with the equations given in art. 4.2.3.4 of EN1993-1-2 for members in bending, in which the area is replaced by the effective area and the sectionmodulus is replaced bythe effective sectionmodulus.


- 70 -

ShearMembers with Class 1, Class 2 or Class 3 cross-sectionsThe design shear resistance Vfi,t,Rd at time t of a Class 1, Class 2 and Class 3 cross-section is determined according to EN1993-1-2 art. 4.2.3.3(6).

Stability ChecksThe stability checks (buckling, lateral torsional buckling) are performed according to the regulations given in EN 1993-1-2.The checksare performed in the resistance domain or in the temperature/time domain.


The different stability checks according to EN1993-1-1 ("Stability Checks" on page 27) are executed and modified accord-ing to the fire regulations. For the following checksadditional information isgiven:

Flexural BucklingCompression members with Class 1, Class 2 or Class 3 cross-sectionsThe design buckling resistanceNb,fi,t,Rd at time t of a compressionmember with aClass1, Class2 or Class3 cross-sectionwith a uniform temperature θa isdetermined according to EN 1993-1-2 art. 4.2.3.2

For the calculation of the buckling length, we refer to chapter ""AnnexB: Calculation of buckling ratio" on page 184"

Compression members with Class 4 cross-sectionsThe design buckling resistance for memberswith Class4 isdetermined according toAnnex Eof EN 1993-1-2



Lateral Torsional BucklingMembers with Class 1 or Class 2 cross-sectionsThe design lateral torsional buckling resistance moment Mb,fi,t,Rd at time t of a laterally unrestrained member with a Class1 or Class2 cross-section isdetermined according to art. 4.2.3.3.(4)of EN 1993-1-2

Members with Class 3 cross-sectionsThe design lateral torsional buckling resistance moment Mb,fi,t,Rd at time t of a laterally unrestrained member with a Class3 cross-section isdetermined according to art. 4.2.3.4.(3)of EN 1993-1-2

Members with Class 4 cross-sectionsThe design compression resistance for memberswith Class4 isdetermined according toAnnex Eof EN 1993-1-2

The resistance of members with a class 4 cross-section should be verified with the equations given in art.4.2.3.4 of EN1993-1-2 for members in bending, in which the area is replaced by the effective area and the sectionmodulus is replaced bythe effective sectionmodulus.


- 71 -

Chapter 3

Combined Bending and Axial CompressionMembers with Class 1, Class 2 or Class 3 cross-sectionsThe design buckling resistanceRfi,t,d at time t of amember subject to combined bending and axial compression is verifiedaccording EN 1993-1-2 art. 4.2.3.5

In case TorsionalBuckling is limiting (χTF <χz) the value for χz is replaced by the value of χTF in the combined stability checkaccording to art. 4.2.3.5.

Members with Class 4 cross-sectionsThe design buckling resistance for memberswith Class4 isdetermined according toAnnex Eof EN 1993-1-2



Shear BucklingFor Shear Buckling reference ismade to chapter "Shear Buckling" on page 40. The followingmodificationsare done in caseof fire:

l The calculation of the ε coefficient isdone according to EN 1993-1-2 Formula 4.2.l The plate slendernessunder fire conditions is calculated as follows:

The abovemodification accounts for the fact that is calculated based onEN 1993-1-5 Formula (5.5) or (5.6).

- 72 -

EC3 – EN Cold-FormedThemembersare checked according to the regulationsgiven in:

Eurocode 3


Part 1 - 3: Supplementary rules for cold-formedmembersand sheeting

EN 1993-1-3:2006

Corrigendum

EN 1993-1-3:2006/AC:2009

Eurocode 3


Part 1 - 5: PlatedStructural elements

EN 1993-1-5:2006

Corrigendum

EN 1993-1-5:2006/AC:2009

Addendum

EN 1993-1-5:2006/A1:2017


Article Title

1 Introduction X

2 Basis of design X

3 Materials

3.1 General X

3.2 Structural Steel X(*)

5 Structural Analysis

5.1 Influence of rounded corners X(*)

- 73 -

Chapter 4

Article Title

5.2 Geometrical proportions X(*)

5.3 Structural modelling for analysis X

5.5 Local and distortional buckling

5.5.1 General

5.5.2 Plane elements without stiffeners

5.5.3 Plane elements with edge or intermediate stiffeners

5.5.3.1 General

5.5.3.2 Plane elements with edge stiffeners

5.5.3.3 Plane elements with intermediate stiffeners

X

X(*)

X(*)

X(*)

X(*)

6 Ultimate Limit States

6.1 Resistance of cross-sections

6.1.1 General

6.1.2 Axial Tension

6.1.3 Axial Compression

6.1.4 Bending moment

6.1.4.1 Elastic and elastic-plastic resistance with yielding at the compressed flange

6.1.5 Shear Force

6.1.6 Torsional Moment

6.1.7 Local Transverse Forces

6.1.8 Combined Tension and Bending

6.1.9 Combined Compression and Bending

6.1.10 Combined shear force, axial force and bending moment

6.1.11 Combined Bending moment and local load or support reaction

X

X(*)

X(*)

X(*)

X(*)

X(*)

X(*)

X(*)

X(*)

X(*)

X(*)

6.2 Buckling Resistance

6.2.1 General

6.2.2 Flexural buckling

6.2.3 Torsional buckling and torsional-flexural buckling

6.2.4 Lateral Torsional buckling ofmembers subject to bending

6.2.5 Bending and axial compression

X

X(*)

X(*)

X(*)

X(*)

6.3 Bending and axial tension X(*)

10 Special considerations for purlins, liner trays and sheetings

10.1 Beams restrained by sheeting

10.1.1 General X(*)

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Article Title

10.1.2 Calculation methods

10.1.3 Design criteria

10.1.4 Design resistance

10.1.5 Rotational restraint given by sheeting

10.1.5.1 Lateral spring stiffness

X

X

X(*)

X(*)

As specified in EN 1993-1-3: 1.1(3) the code does not apply to cold -formed CHS (FC 3)andRHS (FC 2) sections. For these form codes the default EN 1993-1-1 provisionsapply.

Haunches, arbitrary members and cross-sections without initial shapes are not supportedfor the EN 1993-1-3 code check. In this case the default EN 1993-1-1 code check isexecuted.

The checks are executed according to the principal axis in accordance with EN 1993-1-3art. 1.5.1(4) NOTEexcept where stated otherwise.

Material propertiesThe steel gradesgivenwithin EN 1993-1-3Table 3.1b are available in the default Material Libraryof SCIAEngineer.

Average Yield StrengthThe average yield strength is supported according to EN 1993-1-3 art. 3.2.2.

The average yield strength isapplied in the following resistance calculations:

l Axial Tensionl AxialCompressionl BendingMomentl Torsionalmomentl FlexuralBucklingl Torsional (-Flexural) Bucklingl Purlin design –Cross-section resistance

The average yield strength is calculated usingAg of the Initial shape

Steel Core ThicknessThe steel core thickness is supported according to EN 1993-1-3 art. 3.2.4.

The steel core thickness isonlyavailable for the following sections:

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Chapter 4

l Cross-sectionwhich have form code FC 111 – FC 126&FC 129l Cold-formed pair sections (2CFUo, 2CFUc, 2CFCo, 2CFCc, 2CFLT)

The ranges for the core thicknessare set ‘for sheeting andmembers’.

Form codes172&128 are not supported for the SteelCore Thickness.

Initial ShapeFor thin-walled cross-sectionswithmaterialSteel the InitialShape isgenerated automatically.


The InitialShape 'translates' the cross-section shape to partsdefined by the code.

The Initial Shape is used for calculating the effective section properties aswell as determining the Classification of the cross-section.









RI Reinforced Intermediate (intermediate stiffener)

DEF Double Edge Fold (edge stiffener)

ROU andDEF reinforcement typescan be set only to elementsof typeSO or UO.

RI typescan be set only to elementsof type I or UO or SO.

For general cross-sections neighbouring elements of type RI are seen as one stiffener for the calculation of the stiffenerarea and inertia.

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For standard profile librarycross-sectionsand pair sections the stiffenersare handled as follows:

For the following form codesedge stiffenersare automatically set asRUO

FC 114Cold formedC-section

FC 115Cold formedOmega section

FC 116Cold formedC-Section eavesbeam

FC 118Cold formedZED section

FC 119Cold formedZED section asymmetric lips

FC 120Cold formedZED section inclined lip



FC 126Cold formedZED section both lips inclined


FC 130Cold formed 2C-section

For the following form codesedge stiffenersare automatically set asDEF

FC 117Cold formedC-Plussection




FC 127Cold formed I-Plussection


For the following form codes internal stiffenersare automatically set asRI







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Chapter 4


Initial Shapes for specific sectionsWithin thisparagraph special cases for the InitialShape generation are listed.

Sheet welded Iw & IwnFor these sections theweldsize isaccounted for in the generation of the InitialShape:

The length of theweb element for example is thuscalculated as:

WithHw the height of theweb and a the throat thicknessof theweld.

The sameapproach isused for the flanges.

RHSFor Rectangular Hollow Sections (FC 2) the initial shape isgenerated using a notionalwidth ofh-3t andb-3t.

The usage of this width ensures consistency between EN 1993-1-1 and EN 1993-1-5. For further information reference ismade toRef.[40].

As specified in EN 1993-1-3 art. 1.1(3) CHS & RHS members are checked according toEN 1993-1-1.

Geometrical ProportionsTheGeometrical proportionsare checked according to EN 1993-1-3 art. 5.2(1) Table 5.1.

The limits for edge stiffeners (c) and double edge folds (d) are checked in case the correct stiffener type (RUO or DEF) hasbeen set in the initial shape.

The limit ratio’s given in EN 1993-1-3 art. 5.2(2) are checked. Lip dimensions c and d are however always accounted forandwill not be ignored.

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In addition the limit for the internal radiusgiven in EN 1993-1-3 art. 5.1(6) is checked.

For general sections, the geometrical proportions are checked for elements I, UO and SOusing their respective part lengths. Flanges includingRI stiffenersare thus considered partbypart and not asonewhole flange.

Effective Shape

Influence of rounded cornersWithin SCIA Engineer the exact method is applied i.e. all properties and dimensions are determined including the influenceof rounded corners.

The approximate procedure given in EN 1993-1-3 art. 5.1(3) and following is thusnot supported.

Notional widths

For non cold-formed sections the notional width used for the calculation of the effective shape is specified in EN 1993-1-5art.4.4(2).

For cold-formed sections the notionalwidthsare specified in EN 1993-1-3 art. 5.1 and Figure 5.1.

The initial shape elementsare taken between the roundings (i.e. internal dimensionsw).

The notionalwidthsbp are then calculated as follows:

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Chapter 4

l For an internal element (I)

bp =w + rm * sin ( φleft / 2) + rm * sin ( φright / 2)

l For an outstand element (UO, SO)

bp =w + rm * sin ( φ / 2)

In addition to the notionalwith bp, for each element the centerline length lc is determined as follows:

l For an internal element (I)

lc =bp +gr,left +gr,right

With

gr,left = rm * [tan ( φleft / 2) - sin ( φleft / 2)]

gr,right = rm * [tan ( φright / 2) - sin ( φright / 2) ]

l For an outstand element (UO, SO)

lc =bp +gr

With

gr = rm * [tan ( φ / 2) - sin ( φ / 2)]

General procedure for one elementBy default, EN 1993-1-3 specifies that the stress f (σcom,Ed) to be used for the effective section calculation should be takenas fyb/γM0

The reduction of an element is in general given by:

beff =p * b

With:

beff Effectivewidth

p Reduction factor

b Fullwidth

Step 1:For the given stress f the normal stress over the rectangular plate element of the initial geometrical shape is calculated.These stressesare calculated based on the notionalwidth bp.

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σ beg : normal stressat start point of rectangular shape – compression stress ispositive

σ end : normal stressat end point of rectangular shape – compression stress ispositive

If the rectangular shape is completely under tension, i.e. σ beg and σ end are both tensile stresses, no reduction is needed, p=1.0

In case of thin walled rectangular cross-sections (formcode 7) which consistsof only1 element, it is considered asaninternal element. The appliedmoment perpendicular to the element axis (=notionalwidth axis) isapplied based on half of the element thick-ness:M= fyx (Iyor Iz) x1/(t/2).Therefore the stresseswill be the same (you can onlydisplay1 stresson a node of the element axis)-->σbeg=σend=(M x(t/2)) / (Iyor Iz)The consequence due to the fact that both stressesare the same is that the stressgradient will be 1 (pure compression).

Step 2: Determine f1 and f2:

in case

f1 =σ beg

f2 =σ end

in case

f1 =σ end

f2 =σ beg

Step 3: Calculate the stress gradient ψ:

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Chapter 4

Step 4: If ψ = 1 the element is under uniform compression, else the element is under stressgradient.Depending on the stress gradient and the element type, the effective width can be calculated as specified in the followingparagraphs.

EN 1993-1-3 art. 6.1.4.2 concerning the plastic reserve of the tension flange is not sup-ported i.e. alwaysan elastic stressdistribution isused.

Internal Compression ElementsThe effectivewidth of internal compression elements is calculated according to EN 1993-1-5 art. 4.4 andTable 4.1.

Thisapplies to elementsof type I.

The notionalwidth bp is used as

Outstand Compression ElementsThe effectivewidth of outstand compression elements is calculated according to EN 1993-1-5 art. 4.4 andTable 4.2.

Thisapplies to elementsof typeUO andSO

The notionalwidthbp is used asc.

kσ is calculated according to EN 1993-1-5Table 4.2which, in case the biggest stress isat the toe, gives formulas forΨ up to-3.

ThereforeΨ is limited to -3when calculating kσ.

When activating the checkbox “Use Annex E E.1(1)” the formulas given in Annex E areused to determine the reduction factor ρ.

Plane Elements with Edge StiffenersThe procedure for determining the effective width/thickness of elements with edge stiffeners is given in EN 1993-1-3 art.5.5.3.2 and art. 5.5.3.1.

Thisapplies to elementsof typeRUO andDEF

General remarks regarding the stiffnessKof the edge stiffener given in formula (5.10b) .

hw is taken as lc (centreline length) of the biggest adjacent element. Adjacent elements are those elements con-nected to the flange. For typical cross-sections, there isonlyone adjacent element, theweb.

For Sigma sections, hw is taken as the sumof the centreline lengthsof theweb elements.

This concerns the following form codes:







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GeneralCross-section: hw for stiffener:

l Elementsconnected to the stiffener are not accounted for since theyare considered as flangesl Elementsconnected to those flangesare all accounted for in case theyare of type I and the summation is

made of the lengthsof these elementsl Roundingsare not accounted for

GeneralCross-section: In case there isonlyone edge stiffener

kf is taken aszero. (i.e. no interaction between two flangessince there isonlyone flange).

GeneralCross-section: In case there are two edge stiffeners

kf is determined bydefault. (i.e. interaction between the two flanges isaccounted for).

GeneralCross-section: In case there aremore than two edge stiffeners

The same logic is followed as for a single stiffener. The factor kf is thus taken aszero.

The formula for K given in the EN 1993-1-3 is based purely on simple sections with twoflanges. In case of more complex cross-sections, the only exact procedure is to perform anumerical analysis (finite strip method) to determine the critical stresses for local and dis-tortional buckling. This is referenced as the ‘AdvancedProcedure’ given in art. 5.5.1(7).

Critical stresses for local and distortional buckling obtained from a numerical analysis canbe inputted in the cross-sectionmanager.

The reduced effective area of the stiffener As,red according to art 5.5.3.2(11) is calculatedusing σcom,Ed = fyb/γM0.

Plane Elements with Intermediate StiffenersThe procedure for determining the effective width/thicknessof elementswith intermediate stiffeners isgiven in EN 1993-1-3art. 5.5.3.3 and art. 5.5.3.1.

Thisapplies to elementsof typeRI

The stiffnessKof the internal stiffener isdetermined from formula (5.11):

The reduced effective area of the stiffener As,red according to art 5.5.3.3(10) is calculatedusing σcom,Ed = fyb/γM0.

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Chapter 4

General procedure of Effective Shape calculationThe general procedure which combines the effective section calculation of plane elementswithout and plane elementswithstiffeners isgiven in EN 1993-1-3 art. 5.5.2(3) and art. 5.5.3.

Thisprocedure can bewritten out as follows:

Step 1: The effective width of the flanges and edge/intermediate stiffeners within the flanges are calculatedbased on grosssection properties.

This includes the optional iterative procedure for the edge/intermediate stiffeners as specified in art. 5.5.3.2(10)and art. 5.5.3.3(9).

Step 2: This partially effective shape of the previous step is used to determine the stress gradient and effectivewidth of theweb.

This includes the optional iterative procedure for the intermediate stiffenersasspecified in art. 5.5.3.3(9).

Step 3: The end result of the previous two steps is the effective cross-section and itspropertiescan be calculated.

Step 4: This process can now be optionally iterated using the stress ratio based on the effective cross-section inplace of the grosscross-section.

Both iteration procedures (iteration of stiffenersand iteration of the full cross-section) can be set in the SteelSetup.

The iteration of the full cross-section is not run in case Iz > Iy in order to avoid incon-sistencies in the axisbetween the initial and the effective shape.

Advanced Procedure for Effective Shape CalculationIn addition to the standard procedure described in the previous paragraphs for the calculation of the Effective Shape, alsotheAdvancedProcedure described in EN 1993-1-3 art. 5.5.1(7) is supported.

This procedure does not use analytical formulas for calculating the critical local- and distortional buckling stresses of the dif-ferent elements, but instead uses the valuesobtained bya numerical (stability) analysis.

When this setting is activated within the Cross- section, the user can input the minimal local- and distortional bucklingstresses obtained from numerical analysis for the different effective shapes. These stresses are then used for the cal-culation of the effectivewidthsand thicknesses.

The following providesan overview of the different steps:

1)Calculate the elasticbuckling stressesand identify the corresponding bucklingmodes

2) Calculate the effective width(s) according to 5.5.2 for locally buckled cross-section parts based on the minimum localbuckling stress

3) Calculate the reduced thickness (see 5.5.3.1(7)) of edge and intermediate stiffeners based on theminimum distortionalbuckling stress

4) Calculate overall buckling resistance according to 6.2 based on the effective cross-section from steps2) and 3).

This method provides an alternative for cross-sections which have more complex shapes.It should however be noted that, due to the use of the minimal stresses, this procedure isquite conservative.

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Manufacturer provided effective section propertiesIn case in the Steel Setup the option ‘Use manufacturer provided effective section properties’is activated, effective sectionproperties from themanufacturer are taken from theEffective Section Library instead of calculated byEN 1993-1-3.

The following propertiescan be defined in theEffective Section Library:

Property Description

fy [MPa] Steel grade for which the effective properties have been derived

Aeff [mm^2] Effective Area for compression

eN,y [mm] Shift of the centroidal y-y axis for compression

eN,z [mm] Shift of the centroidal z-z axis for compression

Ieff,y My+ [mm^4] Effective moment of inertia about the y-y axis for a positive momentMy

Weff,y My+ [mm^3] Effective section modulus to the extreme fiber about the y-y axis for a positive momentMy

eM,y My+ [mm] Shift of the centroidal y-y axis for a positive momentMy

Ieff,y My- [mm^4] Effective moment of inertia about the y-y axis for a negative momentMy

Weff,y My- [mm^3] Effective section modulus to the extreme fiber about the y-y axis for a negative momentMy

eM,y My- [mm] Shift of the centroidal y-y axis for a negative momentMy

Ieff,z Mz+ [mm^4] Effective moment of inertia about the z-z axis for a positive momentMz

Weff,z Mz+ [mm^3] Effective section modulus to the extreme fiber about the z-z axis for a positive momentMz

eM,z Mz+ [mm] Shift of the centroidal z-z axis for a positive momentMz

Ieff,z Mz- [mm^4] Effective moment of inertia about the z-z axis for a negative momentMz

Weff,z Mz- [mm^3] Effective section modulus to the extreme fiber about the z-z axis for a negative momentMz

eM,z Mz- [mm] Shift of the centroidal z-z axis for a negative momentMz

In case the yield strength used for the cross- section does not match any of the yieldstrengthsdefined in theEffective Section Library the default EN 1993-1-3 calculationwill beused.

Section Checks

Axial TensionTheAxial TensionCheck isexecuted according to EN 1993-1-3 art. 6.1.2.

The net section resistance Fn,Rd is taken as:

With Anet taken equal to Ag since bolt holesare not accounted for.

Axial CompressionTheAxialCompressionCheck isexecuted according to EN 1993-1-3 art. 6.1.3.

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Chapter 4

The choice between formula (6.2) and (6.3) ismade bycomparing the grossarea Ag from the initial shapewith the effectiveareaAeff of the effective shape for compression.

The grossareaAg used in the formulas is taken from the cross-sectionmanager.

This comparison using the initial shape property isof importance for the following reasons:

- Profile Librarysectionscan have different grosspropertiescompared to the initial shapesince the grosspropertiescome from certain sources (books, tables,…) and aremostlyrounded off.

- For general cross-sections the grossshape can differ from the initial shape since the initialshape concernsa thinwalled representation.

Each element onwhich a distortional buckling reduction factor χd is applied is seen as ‘stiffened’.

All other elementsare seen as ‘plane’.

Bending MomentTheBendingMoment Check isexecuted according to EN 1993-1-3 art. 6.1.4.1.

The choice between formula (6.4) and (6.5) is made by comparing the elastic section modulus Wel from the initial shapewith the effective sectionmodulusWeff of the effective shape for bending.

The elastic sectionmodulusWelused in the formulas is taken from the cross-sectionmanager.

Note: This comparison using the initial shape property isof importance for the followingreasons:

- Profile Librarysectionscan have different grosspropertiescompared to the initial shapesince the grosspropertiescome from certain sources (books, tables,…) and aremostlyrounded off.

- For general cross-sections the grossshape can differ from the initial shape since the initialshape concernsa thinwalled representation.

An element of type I is seen as ‘plane’.

An element of typeUO or SO isseen as ‘outstand’.

As indicated in EN 1993-1-3 art. 6.1.4.1(2) formula (6.5) isonlyapplied in case:

l There isonly single bending i.e. MyORMzl There isno torsion i.e. Mx=0l There isno Torsional (-Flexural) buckling i.e. χTF =1,00

l There isno Lateral Torsional buckling i.e. χLTB =1,00

l There isnoDistortional buckling i.e. all reinforcement typesof the cross-section elementsshould be ‘none’ or, in casethere are stiffeners, theyshould not be in compression.

l The angle φ between theweb and flange exceeds60°.

In case formula (6.5) should be applied but the above conditionsare not fulfilled, formula (6.6) isapplied.

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EN 1993-1-3 art. 6.1.4.2 concerning the plastic reserve of the tension flange isnot supported i.e. alwaysan elastic stressdis-tribution isused.

EN 1993-1-3 art. 6.1.4.3 concerning the effectsof shear lag isnot supported.

Shear ForceTheShear ForceCheck isexecuted according to EN 1993-1-3 art. 6.1.5.

GeneralThe shear resistance is calculated for each ‘web’ element separately and the cross-section resistance is taken as the sum ofthese element resistances.

Onlyelementswith element types I, UO andSO are accounted for.

In addition, elementswith stiffener typeRUO or DEF are not accounted for.

Formula (6.8) is rewritten as follows for both directions:

With:

αi =Angle of element i related to the principal y-yaxis

lc,i =Centreline length of element i

By default the Shear Check is executed ‘without stiffening at the support’ In case LocalTransverse Forces data are inputted which have the checkbox ‘No Local TransverseForces Check’ activated, the Shear Check in those sections is executed ‘with stiffening atthe support’.

Elements without Internal stiffenersThe centreline length lc,i for each element i is taken from the Initial shape.

The angle αi for each element i isdetermined as the angle related to the principal y-yaxis.

The relativeweb slenderness for each element i isdetermined according to formula (6.10a).

The slant height sw,i is taken as the notional width bp,i of the element under consideration as indicated on the following pic-ture.

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Chapter 4

Sections with Internal stiffenersSpecial considerationsare required for cross-sectionswith internal stiffeners (TypeRI).

The following picture illustratesawebwith internal stiffener:

The internal stiffener and connected elements are seen as ‘one web’. This ‘composed’ web is seen as ‘one’ element i in theshear calculation.

For such a ‘composed’web, the different distancesare determined as follows:

l The slant height sw is taken as the distance between- The starting point of the nominalwidth bp,i of the first element in theweb.- The end point of the nominalwidth bp,i of the last element in theweb.

l The total developed slant height sd is taken as the sumof the nominalwidthsbp,i of all the elements in theweb.

l The slant height sp concerns the notionalwidth bp,i of the largest planeweb element.

The relativeweb slenderness isdetermined according to formula (6.10b).

The inertia of the stiffener(s) Is is taken from the Initial shape

The centreline length lc of this composedweb iscalculated as follows:

l In case the first or last element of the composedweb haselement typeSO or UO:

lc =sw +grWith

gr = rm * [tan ( φ / 2) - sin ( φ / 2)]

If the first element isan outstand, gr is taken asgr at the end point of the last element.

If the last element isan outstand, gr is taken asgr at the starting point of the first element.Reference ismade to "Notionalwidths" on page 79.

l In case both the first and last element of the composedweb haselement type I:

lc =sw +gr,first +gr,endWith

gr,first taken asgr at the starting point of the first element.

gr,end taken asgr at the end point of the last element.

The angle α of the ‘composed’web concerns the angle of the centreline length lc relative to the principal y-yaxis.

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Neighbouring connected elements are seen as one ‘web’. A typical example of this is asigma section: the web has two internal stiffeners which both are connected to the sameinternal element. Assuch theyare recognized as forming oneweb.

Torsional MomentTheCombinedStressCheck including Torsion andWarping isexecuted according to EN 1993-1-3 art. 6.1.6.

Regardingwarping reference ismade to "AnnexF:Warping check" on page 218.

The average yield strength fya in all three formulas (6.11a), (6.11b), (6.11c) will only be used in case for all three force com-ponentsseparately (N,My,Mz) the average yield strengthmaybe used (Aeff =Ag ;Weff,y=Wel,y ;Weff,z=Wel,z).

Local Transverse ForcesThe local transverse forcescheck isexecuted according to EN 1993-1-3 art 6.1.7 and following.

The check isexecuted on the positionswhere there isa jump in theVzshear force diagram.

Remarks:

l The shear force diagramof both the actualmember aswell asadjacentmembers isevaluated. Adjacentmembersaredefined asmemberswhich are in the same buckling system.

l TheFlangeCondition dependson the definition of the initial shape. In case there isan element with reinforcement typeROU or DEF the setting is taken as ‘Stiffened ’.

l The distances for One-flange/Two-flange andEnd/Interior are evaluated taking into account adjacentmembers. Adja-centmembersare defined asmemberswhich are in the same buckling system.

l In case the cross-section hasmultiple webs, for determining the load condition themaximalweb height isused.l Asopposed to EN 1993-1-3 art. .1.7.2(4), the exact inputted bearing length ss will be used at all times i.e. the sim-

plification of using theminimal length for both opposing loads isnot supported.l As indicated onEN 1993-1-3 Figure 6.6, the local transverse force resistance is taken relative to the support, not accord-

ing to the principal z-axis. Therefore FEd, is determined according to the LCSaxissystemand not according to the prin-cipal axis system!

General ProcedureThis paragraph specifies the general procedure to determine the local transverse web resistance which is applied for anytype of cross-section except for FC 115 (Cold formedOmega).

In case the cross-section hasanyelement with stiffener typeRI, the procedure for stiffenedwebs isapplied first.

In a first step theweb height hw is determined for each ‘web’ element:

l Onlyelementsof type I are accounted for.In addition elementswith stiffener typesRUO andDEF are not accounted for.

l For each of those elements i the centreline length lc,i is read from the Initial shape

l For each of those elements i the angle φi is determined as the angle of the element relative to the horizontal axis (basedon Figure 6.6).In addition, onlyelementswith an angle φi≥45°are accounted for.

l Theweb height for each element i is calculated as:

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Chapter 4

l In case none of the cross-section elements fulfil the above conditions, the local transverse forcescheck isnot supportedfor the cross-section.

When hw,i is determined, the local transverse resistance Rw,Rd,i for each of those elements is determined based on EN1993-1-3 art. .1.7.2

The final cross-section resistance is taken as the sumof the individual element resistances.

Bydefault, the local transverse resistanceRw,Rd,i is determined usingEN 1993-1-3 Figure 6.7a&6.7b.

The following table shows the relation between the loading conditionsand the casesdefined in the tables.

LoadingCondition Table Case

End One Flange (EOF) 6.7a a) i)

Interior One Flange (IOF) 6.7a a) ii)

End Two Flange (ETF) 6.7b b) i)

Interior Two Flange (ITF) 6.7b b) ii)

In caseWeb rotation preventedwasset using Local Transverse Forcesdata instead of EN 1993-1-3 Figure 6.7a &6.7b theformulasgiven in EN 1993-1-3 art. 6.1.7.2(4) are used.

The following table shows the relation between the loading conditionsand the casesdefined in thisarticle.

LoadingCondition Article Case

End One Flange (EOF) art. 6.1.7.2(4) a) i)

Interior One Flange (IOF) art. 6.1.7.2(4) a) ii)

End Two Flange (ETF) art. 6.1.7.2(4) b) i)

Interior Two Flange (ITF) art. 6.1.7.2(4) b) ii)

Omega SectionsSpecifically for FC 115 (Cold formed Omega) cross- sections the special procedure for sections with two or moreunstiffened webs is applied. The local transverse resistance Rw,Rd,i for each of those webs is determined according to EN1993-1-3 art. 6.1.7.3.

Other cross-sections with two or more unstiffened webs will always be calculated accord-ing to theGeneralProcedure, not this special procedure.

The value of α in EN 1993-1-3 art. 6.1.7.3(5) is taken for ‘liner traysand hat sections’.

The following table shows the relation between the loading conditions and the categories defined in EN 1993-1-3 Figure6.9.

LoadingCondition Category

End One Flange (EOF) 1

Interior One Flange (IOF) 1

End Two Flange (ETF) 1

Interior Two Flange (ITF) 2

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Figure 6.9 does not directly specify ETF. However since two flange loading is specified ascategory 1 and End loading is also specified as category 1, the combined condition of ETFisconsidered ascategory1.

According to [27] to use la =10mm for the end support reaction force (category1) resultsin a veryconservative resistance. Amodification isgiven for case 2 and 3 of Figure 6.9: la =c+Ss.Byactivating the setting “Use la correction in (6.18)” thismodification isapplied.

StiffenedWebsThisparagraph outlines the special procedure in case of stiffenedwebsaccording to EN 1993-1-3 art. 6.1.7.4.

Thismethod isused only in case there are one or more elementswith stiffener typeRI

The procedure consistsof four steps.

Step 1: Creating ‘composed’ websIn a first step, ‘composed’ webs are created using the same procedure as outlined in "Sections with Internal stiffeners" onpage 88.

This includes the determination of the centreline length lc,i of those ‘composed’webs.

Step 2: Evaluation of ‘composed’ websThe special procedure outlined in EN 1993-1-3 art. 6.1.7.4 is only valid under certain conditions.

Therefore, each ‘composed’web isevaluated to see if it meets the following requirements:

l There isone or more elementswith stiffener typeRIl EachRI element should have element type I (i.e. it is at both sidesconnected to other elementssignifying it’sa fold instead

of a stiffener).l Elementsconnected to thisRI element should not have stiffener typeRI. This implies that the procedure isnot applied in

case of neighbouring stiffener elements i.e. elements forming ‘one’ big stiffener.

Composedwebswhich do notmeet these requirementsare further evaluated in step 3.

Composedwebswhichmeet all requirementsare further evaluated in step 4.

Example:

All four sectionshave ‘composed’webs.

Section Acontains twoRI stiffenerswhich are connected. Theweb thusdoesnotmeet the requirements.

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Chapter 4

Section Bcontainsa single RI stiffener whichmeetsall the requirements. This stiffener is thusa ‘true’ two fold stiffener so thespecial article applies.

Section C contains several RI stiffeners however not all match the requirements (one is an outstand, others are connectedetc). Theweb thusdoesnotmeet the requirements.

Section D hasa composed web which contains two RI stiffeners. Both meet all the requirements and are thus ‘true’ two foldstiffeners. The special article applies.

Step 3: Composed webs which do NOT meet the requirementsFor composed webs which do not meet the requirements, the special article is not valid. The local transverse force res-istance of thesewebswill be determined according to the "GeneralProcedure" on page 89

In this case, the centre line length lc,i of the composedweb isused in the determination of hw.

The angle φi is determined as the angle of the centre line length relative to the horizontal axis.

Step 4: Composed webs which meet all requirementsFor composedwebswhichmeet all requirements, the special procedure outlined in EN 1993-1-3 art. 6.1.7.4 is applied.

The ‘system line’ of thisweb is taken as the centre line length lc,i.

The eccentricity e is determined at each end of an RI within the ‘composed’ web. Eccentricity emin and emax are then takenas themin andmaxvalue for the considered composedweb.

In case the limit specified in formula (6.21) is not fulfilled, the special article is not applied and the composed web is con-sidered asawebwhich doesnotmeet all requirements. For such aweb the procedure outlined in step 3 isapplied.

For the developed width of the loaded flange bd any RI stiffeners of element Type I are always included, independent oftheir angle. RI stiffenersof element TypeUO or SO are always ignored.

Connected flange elements which have a relative angle > 135° are accounted for as „one‟flange for the determination ofbd.

In case there is no connected flange, for example when using a general section, then bd is considered as zero. Practicallythis implies that there isno limit for κa,s.

The data is then used to determine κa,s according to formula (6.22).

TheRw,Rd,i value of the composedweb is then calculated as:

Rw,Rd,i =κa,s *Rw,Rd,i,generalWithRw,Rd,i,general calculated according to the "GeneralProcedure" on page 89

The value of hw,i for this composedweb iscalculated using the centre line lc,i of the composedweb asoutlined in step 3.

Combined Tension and BendingTheCombined Tension andBendingCheck isexecuted according to EN 1993-1-3 art. 6.1.8.

The bending resistancesare determined using the sectionmoduliWeff of the effective shapes for bending.

Combined Compression and BendingTheCombinedCompression andBendingCheck isexecuted according to EN 1993-1-3 art. 6.1.9.

- 92 -

Additional moments due to the shift in neutral axis are calculated at the beginning of the check and added to the internalforces.

This ensures specific bending checks are executed also in case there is no initial momentbut onlyan additionalmoment.

The shifts in neutral axiseNy and eNz are read directly from the effective shape for compression.

As specified in EN 1993-1-3 art. 6.1.3(3) additional moments are only accounted for in case they lead to an unfavourablecheck result.

The bending resistancesare determined using the sectionmoduliWeff of the effective shapes for bending.

Combined Shear Force, Axial Force and Bending MomentTheCombinedShear Force, Axial Force andBendingMoment Check isexecuted according to EN 1993-1-3 art. 6.1.10.

In the following paragraphs formula (6.27) iswritten out for both directions.

Shear VyIn case of shear Vy formula (6.27) iswritten out as follows:

Remarks:

l Mf,Rd is taken aszero in case of Vy

(In case of weak axis bending, the ‘web’ becomes a ‘flange’. Since there is only a single ‘flange’ in that case, themoment resistance of this flange is negligible. In addition, in case of more webs like in a box section EN 1993-1-5art. 7.1 (5) specifiesMf,Rd = 0. Therefore, as a general conservative approach for Vy the value of Mf,Rd is takenas0.)

Shear VzIn case of shear Vz formula (6.27) iswritten out as follows:

Remarks:

l According to [Ref.16] pp70 Mf,Rd is calculated as follows:

- 93 -

Chapter 4

This isgeneralised in the followingway:

a. Onlyelementswith element types I, UO andSO are accounted forb. Onlyelementswhich have an angle α with the principal y-yaxiswhich is≤45°are considered

In case there isonlyone or none of such element, Mf,Rd =0.c. Of these elements, the onewith the lowest beff is considered. Thewidth beff concerns the effectivewith of thiselement,

read from the effective shape for bending.d. Af =beff * t with t the thicknessof the considered element.

e. Next onlyelementswhich have an angle α with the principal y-yaxiswhich is>45°are considered.

In case there are no such elements, setMf,Rd =0.f. Of these elements, the onewith the highest value of lc * sin(α) is considered, with lc the centreline length of the element.

g. hf = lc * sin(α)

h. Mf,Rd is now be calculated as:

l According to [Ref.16] pp70 Mpl,Rd is calculated as follows:

withWpl read from the grosssection properties.

Combined Bending Moment and local Load/Support ReactionThe Combined Bending Moment and local Load/Support Reaction Check is executed according to EN 1993-1-3 art.6.1.11.

In formula (6.28c) the internal force MEd is taken as the actual moment in the section considered, not the moment at theedge of the support.

Stability Checks

Flexural BucklingTheFlexuralBucklingCheck isexecuted according to EN 1993-1-3 art. 6.2.2 andEN 1993-1-1 art. 6.3.1.

Table 6.3 regarding the buckling curves is revised as follows:

Description about axis Curve

1 I sectiony-y

z-z

a

b

101 Asymmetric I sectiony-y

z-z

a

b

114 Cold formed C section any b

- 94 -

Description about axis Curve

116 Cold formed C-Section eaves beam any b

117 Cold formed C-Plus section any b

118 Cold formed ZED section any b

119 Cold formed ZED section asymmetric lips any b

120 Cold formed ZED section inclined lip any b

121 Cold formed Sigma section any b

122 Cold formed Sigma section stiffened any b

123 Cold formed Sigma-Plus section any b

124 Cold formed Sigma section eaves beam any b

125 Cold formed Sigma-Plus section eaves beam any b

126 Cold formed ZED section both lips inclined any b

127 Cold formed I-Plus sectiony-y

z-z

a

b

128 Cold formed IS-Plus sectiony-y

z-z

a

b

129 Cold formed Sigma section asymmetric any b

130 Cold formed 2C sectiony-y

z-z

a

b

2CFCo with a = 0y-y

z-z

a

b

2CFCcwith a = 0 Closed section rule 6.2.2(3)

2CFUo with a = 0y-y

z-z

a

b

2CFUcwith a = 0 Closed section rule 6.2.2(3)

2CFLTwith a = 0 any c

Any other section any c

All other sections fall in the ‘other cross-section’ case of curve c for anyaxis.

For the calculation of the buckling length, we refer to chapter ""AnnexB: Calculation of buckling ratio" on page 184"

Torsional (-Flexural) BucklingTheTorsional (-Flexural) BucklingCheck isexecuted according to EN 1993-1-3 art. 6.2.3 andEN 1993-1-1 art. 6.3.1.4.

The buckling curve for torsional (-flexural) buckling is taken as the z-zbuckling curve according to the table given in "FlexuralBuckling" on the previouspage.

The value of the elastic critical load Ncr is taken as the smallest of Ncr,T (Torsional buckling) and Ncr,TF (Torsional-Flexuralbuckling).

Calculation of Ncr,TThe elastic critical loadNcr,T for torsional buckling is calculated according toRef.[17].

- 95 -

Chapter 4

With

E Modulusof Young

G Shear modulus

It Torsion constant

Iw Warping constant


y0 and z0 Coordinatesof the shear center with respect to the centroid

iy radiusof gyration about the strong axis

iz radiusof gyration about theweakaxis

Calculation of Ncr,TFThe elastic critical loadNcr,TF for torsional flexural buckling is calculated according toRef.[17].


0

With


Ncr,z Critical axial load for flexural buckling about the z-zaxis


SheetingIn case a sheeting isused, independent onwhich side, the augmented It will be used also in TorsionalBuckling.

For more information on sheeting see "AnnexD: Use of sheeting " on page 205.

Lateral Torsional BucklingThe Lateral TorsionalBucklingCheck isexecuted according to EN 1993-1-3 art. 6.2.4 andEN 1993-1-1 art. 6.3.2.2.

- 96 -

For additional information reference ismade to "Sheeting" on the previouspage.

For information regarding the influence of diaphragms on the Lateral Torsional Buckling Check reference is made to "Useof sheetings" on the next page.

Bending and Axial CompressionFor determining the Combined Bending and Axial Compression check according to EN 1993-1-3 art. 6.2.5 EN 1993-1-3allows two possibilities:

l Use theEN 1993-1-1 interaction according to article 6.3.3l Use the alternative according to EN 1993-1-3 article 6.2.5(2)

The choice between these twomethods is set in the SteelSetup.

Interaction according to EN 1993-1-1The interaction isexecuted according to EN 1993-1-1 art. 6.3.3 using interaction factors fromAnnexA&B.

In bothMethod 1 (AnnexA) andMethod 2 (AnnexB) the cold - formed sectionsare seen as ‘class3 or 4’.

Alternative interaction according to EN 1993-1-3The interaction is executedaccording to EN 1993-1-3 art. 6.2.5(2).Nb,Rd is taken as the lowest value of

l the flexural buckling resistance about the y-yaxisl the flexural buckling resistance about the z-zaxisl the torsional (-flexural) buckling resistance

Formula (6.36) includes the strong axis bending resistance Mb,Rd. There is however noindication for a weak axis bending moment. Therefore, in case a weak axis bendingmoment is present, this interaction cannot be applied and the general interaction accordingto EN 1993-1-1 isapplied.

Bending and Axial TensionTheCombinedBending and TensionCheck isexecuted according to EN 1993-1-3 art. 6.3.

The code specifies that the same equations as for compression should be used. These interaction equations are howevernot fully valid in case of tension.

The purpose of the interaction check for bending and tension is to check the stresses at the compression fiber. In the AISINAS2007Ref.[18] code the following formula isgiven in article C5:

This formula is rewritten using EC-EN notationsas follows:

With:

- 97 -

Chapter 4

Mb,y,Rd The Lateral TorsionalBuckling resistance

Mc,z,Rd,com Themoment resistance for the compression fiber in case ofMz

Nt,Rd TheTensionResistance

Use of sheetingsThe influence of a sheeting isoutlined in the following diagram.

First of all the lateral stiffnessSof the sheeting isdetermined and compared to the required stiffnessSerf.

The lateral stiffnessS iscalculated according toRef.[19],3.5 andRef.[20],3.3.4.

a The frame distance

Ls The length of sheeting

K1 Sheeting factor K1

K2 Sheeting factor K2

The required stiffnessSerf isdetermined according to EN 1993-1-3 art. 10.1.1

- 98 -

In case S <Serf the member is seen as Inadequately braced. In this case, when the sheeting is located on the compressionside, the Lateral Torsional Buckling check is executed using the augmented torsional stiffness It. Reference is made to"Adaptation of torsional constant " on page 205.

l The LTB length

G The shear modulus

vorhCθ The actual rotational stiffnessof sheeting

As specified in art. 10.1.1 the shear stiffness S is replaced by 0,2 S in case the sheeting isconnected everysecond rib only.

In case S ≥ Serf the member is seen as Fully braced. In this case, a first test is executed to evaluate if the special purlinchecksaccording to EN 1993-1-3Chapter 10 can be applied.

More specifically, this chapter isapplied only in case the cross-section concernsa Z, C, Σ or U section:

Form code Description

5 Channel section

102 Rolled Z section

112 Cold formed channel

113 Cold formed Z

114 Cold formed C section

116 Cold formed C-Section eaves beam

117 Cold formed C-Plus section

118 Cold formed ZED section

119 Cold formed ZED section asymmetric lips

120 Cold formed ZED section inclined lip

121 Cold formed Sigma section

122 Cold formed Sigma section stiffened

123 Cold formed Sigma-Plus section

124 Cold formed Sigma section eaves beam

125 Cold formed Sigma-Plus section eaves beam

126 Cold formed ZED section both lips inclined

129 Cold formed Sigma section asymmetric

The code specifies that the chapter is also valid for hat (Omega) sectionshowever in all fur-ther paragraphs; no specific formulas are given for Omega sections. For example the freeflange geometry is described only for Z, C and Σ sections, not for Omega sections. There-fore, Omega sectionsare not supported for this special chapter.

In case the cross-section does not match any of the above, the default checks are executed. Since the member is seen asfully braced, no Lateral Torsional Buckling check needs to be executed in case the sheeting is located on the compressionside.

- 99 -

Chapter 4

In case the cross-section doesmatch the list of set form codes, a second test is executed. More specifically, the special purlinchecksaccording to EN 1993-1-3Chapter 10 can be applied only in case:

l The dimensional limitsof article 10.1.1(1) are satisfiedl The section isonly loaded byN, Vz,My

Chapter 10 specifies only checks related to in plane effects N, Vz and My. In case of otherloading components, the special articlesare still applied but an additionalwarningmessageisprinted.

For a sectionwhichmeetsall requirements, the following isdone:

l Reduced default Checksare executed i.e. not all default checkswill be executed.l Special purlin checksaccording toChapter 10

More specifically, the following ‘default’ checkswill be executed:

SectionCheck Article

Axial tension 6.1.2

Axial compression 6.1.3

Bending moment 6.1.4

Shear force 6.1.5

Torsional moment NOT

Local Transverse Forces 6.1.7

Combined tension and bending NOT

Combined compression and bending NOT

Combined shear, axial force and bending moment 6.1.10

Combined Bending and Local Transverse Force 6.1.11

Stability Check Article

Flexural buckling only for y-y 6.2.2

Torsional and Torsional-Flexural buckling NOT

Lateral-Torsional buckling NOT

Bending and axial compression NOT

Bending and axial tension NOT

TheTorsionalmoment checkwill never occur in this case since the prerequisite is to have onlyN, Vz,My.

The combined axial and bending checksare not executed since theyare replaced by the special purlin checks.

The flexural buckling check isexecuted for y-ybuckling in accordancewith EN 1993-1-3 art. 10.1.4.2(2).

Torsional buckling and Lateral-torsional buckling are prohibited by the fully braced sheeting. The compression in the freeflange is included in the special purlin checks.

The combined stability checksare not executed since theyare replaced by the special purlin checks.

In contrast to art. 10.1.3.3(2) the Local Transverse Load Checkand its interaction with thebendingmoment isexecuted even if the support reaction isa tensile force.

- 100 -

Special considerations for PurlinsAs outlined in "Use of sheetings" on page 98 for a section which meets all requirements, special purlin checks according toEN 1993-1-3Chapter 10will be executed:

Sheeting on the compression sidel Cross-section resistance according to EN 1993-1-3 art. 10.1.4.1l In case of compression in the free flange also Stability of the free flange according to EN 1993-1-3 art. 10.1.4.2

Sheeting on the tension sidel Cross-section resistance according to EN 1993-1-3 art. 10.1.4.1l Stabilityof the free flange according to EN 1993-1-3 art. 10.1.4.2

Resistance of Cross-SectionTheResistance of theCross-Section isdetermined according to EN 1993-1-3 art. 10.1.4.1.

Since this check concerns a separate formula for each flange (10.3a) and (10.3b) the effective section modulus Weff,y isdetermined for each flange separately.

The average yield strength will only be used in case for both force components separately (N, My) the average yieldstrengthmaybe used (Aeff =Ag ;Weff,y=Wel,y).

Definition of the free flange geometryThe dimension h is taken as the full crosssection height.

The propertiesof the free flange are calculated according to the z-zaxisof the full cross-section.

The following table shows the supported cross-sections including the contributingweb height.

Form code Description Contributingweb

5 Channel section 1/5 h

102 Rolled Z section 1/5 h

112 Cold formed channel 1/5 h

113 Cold formed Z 1/5 h

114 Cold formed C section 1/5 h

116 Cold formed C-Section eaves beam 1/5 h

117 Cold formed C-Plus section 1/5 h

118 Cold formed ZED section 1/5 h

119 Cold formed ZED section asymmetric lips 1/5 h

120 Cold formed ZED section inclined lip 1/5 h

121 Cold formed Sigma section 1/6 h

122 Cold formed Sigma section stiffened 1/6 h

123 Cold formed Sigma-Plus section 1/6 h

124 Cold formed Sigma section eaves beam 1/6 h

125 Cold formed Sigma-Plus section eaves beam 1/6 h

126 Cold formed ZED section both lips inclined 1/5 h

129 Cold formed Sigma section asymmetric 1/6 h

- 101 -

Chapter 4

As the code indicates in Figure 10.2, for sigma sections the rounding which leads to theweb depression is also accounted for in the height of the free flange. Therefore, to gen-eralize this principle, within SCIAEngineer the rounding between the flange and the web isalwaysaccounted for in the free flange height (for all section types).

Determination of the equivalent lateral loadThe equivalent lateral load on the free flange qh,Ed is determined from the vertical load qEd on the purlin using formula(10.4).

For any given moment diagram, the equivalent vertical line load qEd is determined as the line load which results in approx-imately the same bendingmoment diagram..

The factor kh is determined according to EN 1993-1-3 Figure 10.3.

For kh0, the general formula for Z,C or Σ sections is applied. The formula for a simple Z-section is not supported.

For Gravity loading, the vertical loading is assumed to be positioned at the outside of the web. For Uplift loading the verticalloading isassumed to be positioned exactly in themiddle of the flangewidth.

For Gravity loading the general formula including the shear center distance e isused.

For Uplift loading the general formula including the shear center distance f isused. In case of a symmetrical Z section thisdis-tancewill become a.

The load qh,Ed is given a positive sign in case it follows the same convention as shown in the code. The load is given a neg-ative sign in case it points in the other direction.

Determination of the lateral bending momentTable 10.1 provides the formulas to determineMfz,Ed for specific positionswithin the beams: at the ends (e) and at the pos-ition of themaximalmoment (m).

Within SCIA Engineer however, the check is executed in different sections. Therefore, the values of Mfz,Ed need to beknown in each section.

To thisend, as indicated in the code in EN 1993-1-3 art. 10.1.4.1(7), the general equationshave been derived using the the-oryof beamson an elasticWinkler foundation.

The differential equation for the displacement of a beam on elastic foundation loaded by a line load is written out as followsRef.[21]:

With

E Sectionmodulus

I Bending stiffness

L Member length, taken asLa

q Line load, taken asqh,Ed

- 102 -

K Foundation stiffness, taken as lateral spring stiffnessK

λ

A,B,C,D Integration constants

The integration constantsare determined depending on the boundaryconditions for the casesgiven inTable 10.1.

Using the beam equation with the second derivative of the displacement the equation for the bending moment Mfz,Ed isobtained and leads to the following solutions:

Solution for a beam on elastic Winkler foundation with Hinged end conditions

Solution for a beam on elastic Winkler foundation with Hinged-Fixed end conditions

Solution for a beam on elastic Winkler foundation with Fixed end conditions

The determination of a hinged or fixed end for Mfz,Ed is done as follows:

l Asingle spanmember isalwaysconsidered to have hinged ends.A single spanmember isdefined asamember with onlyone part in the buckling system for Ly.

l An LTB restraint isalwaysconsidered asa fixed end.l For multi-spanmembers, the endsof the buckling system for Lyare considered ashinged. The internal pointsof the buck-

ling system for Lyare considered as fixed.

As specified in EN 1993- 1- 3 art. 10.1.4.1 (5) in case the free flange is in tension M fz,Ed is taken equal to zero.

To determine if the free flange is in tension or compression the following stress is calculated:

(My,Ed /Weff,y,free flange) + (Ned / Aeff)

In case this stress results in tension, the free flange isconsidered to be in tension.

In case this stress results in compression, the free flange isconsidered to be in compression.

The sign of Mfz,Ed determines the tension/compression side of the free flange and thusdetermineswhichWfz is used in thecheck.

- 103 -

Chapter 4

The limit of R ≤40 given in art. 10.1.4.1(6) doesnot apply since the generalWinkler theoryisused instead ofTable 10.1.

Determination of the distance between anti-sag barsThe code defines anti-sag bars as bars which provide lateral rigid support to the free flange. Within SCIA Engineer, LTBrestraintsare thusseen asanti-sag bars.

In case LTB restraints are defined at the free flange, the length La is taken as the length between these restraints. In casethere are no LTB restraintsdefined at the free flange, La is read from the buckling system.

Determination of the lateral spring stiffnessThe lateral spring stiffnessK isdetermined according to EN 1993-1-3 art. 10.1.5.1(4).

The developed height of the purlin web hd is taken as the total developed slant height sd used in the Shear Check, asdescribed in "Shear Force" on page 87.

The rotational restraint CD is taken as vorhC, the rotational stiffness of the sheeting, as described in "Annex D: Use ofsheeting " on page 205.

The dimension bmod depends on the direction of the equivalent horizontal load qh,Ed and the type of cross-section. Accord-ing to the code this depends if the load brings the purlin into contact with the sheeting at the purlin web or at the tip of thepurlin flange.

This is clarified in the following picture:

The distance a i.e. position of the fastener is taken as 0,5 b. The fastener is thus assumed to be positioned in the middle ofthe flange.

Buckling Resistance of the Free FlangeTheBucklingResistance of the Free Flange isdetermined according to EN 1993-1-3 art. 10.1.4.2.

To determine if the free flange is in tension or compression the following stress is calculated:

(My,Ed /Weff,y,free flange) + (Ned / Aeff)

- 104 -

In case this stress results in tension, the free flange isconsidered to be in tension.

In case this stress results in compression, the free flange isconsidered to be in compression.

For a free flange in tension the buckling resistance doesnot need to be checked.

For determining the buckling length lfz of the free flange a difference ismade between gravity loading (downward –z load-ing) and uplift loading (upward +z loading).

Gravity LoadingIn case of downward –z loading the buckling length of the free flange isdetermined according to formula (10.9).

The ηi factorsare determined according to EN 1993-1-3Table 10.2a.

art. 10.1.4.2(4) is not supported.

Uplift LoadingIn case of upward +z loading the buckling length of the free flange isdetermined according to formula (10.9).

The ηi factorsare determined according to EN 1993-1-3Table 10.2b.

Themethod according to art. 10.1.4.2(6) & (7) isnot supported.

General NotesFor both loading types, Tables 10.2a & b differentiate between ‘simple span’, ‘end span’ and ‘intermediate span’. This isbased on the Lysystem length.

In case themember under consideration hasonlyone part for Ly then it is considered as ‘simple span’.

When the member hasmore parts for Ly it is considered asmulti-span. For a multi-span, sections located in the first or lastpart of the system length are considered as ‘end span’. Sections located in the other parts are considered as ‘intermediatespan’.

Table 10.2a does not specify ‘simple span’. The values for a ‘simple span’ are taken equalasan ‘end span’.

The ‘number of anti-sag’ bars used in Tables 10.2a & b concerns the number of LTB restraints defined on the actualmem-ber. OnlyLTB restraintsat the side of the free flange are accounted for in this ‘number’.

EN 1993-1-3 art. 10.1.4.2(5) specifies amethod for the buckling length in case of a ‘relatively large axial force’. Within SCIAEngineer this isquantified using a limit value, which is set in the SteelSetup.

In case the axial load is considered as large, themethod described in EN 1993-1-3 art. 10.1.4.2(5) is applied.

- 105 -

Chapter 4

Thisprocedure applies to both gravityand uplift loading usingTable 10.2a and 10.2b respectively.

References

[1]

Eurocode 3


Part 1 - 1 : General rulesand rules for buildings

EN 1993-1-1:2005

[2]

Eurocode 3


Part 1-3: General rules

Supplementary rules for cold-formedmembersand sheeting

EN 1993-1-3:2006

[3]

Eurocode 3


Part 1.5 : Plated structural elements

EN 1993-1-5 : 2006

[4]

R.Maquoi

ELEMENTSDECONSTRUCTIONSMETALLIQUE

Ulg , Faculté desSciencesAppliquées, 1988

[5]

EN 1990

Eurocode –Basisof structural design

EN 1990:2002E

[6]

Eurocode 3


Part 1 - 2 : General rules - Structural fire design

EN 1993-1-2:2005

[7]

ModelCode on Fire Engineering

ECCS - N°111

May2001

- 106 -

[8]

Eurocode 1

Actionson structures

Part 1-2 : GeneralActions - Actionson structuresexposed to fire

prEN 1991-1-2:2002

[9]

Rules for Member Stability in EN 1993-1-1

Background documentation and design guidelines

ECCS - N°119

2006

[10]

Eurocode 3


Part 1 - 1/ A1 : General rulesand rules for buildings

ENV1993-1-1:1992/A1, 1994

[11]

Eurocode 3



EN 1993-1-1:2005/AC:2009Corrigendum

[12]

Eurocode 3


Part 1 - 2 : General rules - Structural fire design


[13]

Eurocode 3


Part 1-3: General rules

Supplementary rules for cold-formedmembersand sheeting


[14]

Eurocode 3


Part 1.5 : Plated structural elements

- 107 -

Chapter 4

EN 1993-1-5 : 2006/AC:2009Corrigendum

[15]

Essentialsof Eurocode 3

DesignManual for SteelStructures in Building

ECCS - N°65, 1991

[16]

Commentary and Worked Examples to EN 1993-1-5 “Plated Structural Ele-ments”

JohanssonB., MaquoiR., SedlacekG.,Müller C., BegD.,

JRC - ECCS, 2007.

[17]

SN001a-EN-EU

NCCI: Critical axial load for torsional and flexural torsional bucklingmodes

AccessSteel, 2006

www.access-steel.com

[18]

AISI S100-2007

North American Specification for the Design of Cold-Formed Steel StructuralMembers

2007 edition

[19]

E. Kahlmeyer

Stahlbau nachDIN 18 800 (11.90)

Werner-Verlag, Düsseldorf

[20]

Beuth-Kommentare

Stahlbauten

Erläuterungen zuDIN 18 800 Teil 1 bisTeil 4, 1.Auflage

Beuth Verlag, Berlin-Köln 1993

[21]

D. Vandepitte

Berekening vanConstructies

Boekdeel 1 pp522

www.berekeningvanconstructies.be

[22] Design rule for Lateral TorsionalBuckling of ChannelSections

- 108 -

http://www.access-steel.com/

http://www.berekeningvanconstructies.be/

A-2007.9O-2007.21

Karin de Louw

2007

[23]

EN 12811-1

Temporaryworksequipment

Part 1: Scaffolds– performance requirementsand general design

2004

[24]

EN 12810-1

Façade scaffoldsmade of prefabricated components

Part 1: Productsspecifications

2004

[25]

EN 12810-2

Façade scaffoldsmade of prefabricated components

Part 2: Particular methodsof structural design

2004

[26]

DIN 4420 Teil 1

Arbeits- undSchutzgerüste

AllgemeineRegelungen, SicherheitstechnischeAnforderungen, Prüfungen

Dezember 1990

[27]

Correctionsand amendments to EN 1993-1-3

Meeting of ECCS-TWG 7.5

T. Höglund

2010

[28]

Déversement élastique d’une poutre à section bi- symétrique soumise à desmomentsd’extrémité et une charge répartie ou concentrée.

Y. Galéa

CTICM,ConstructionMétallique, n°2-2002.

- 109 -

Chapter 4

[29]

Lateral-Torsional buckling of steel beams:

Ageneral expression for themoment gradient factor.

A. López, D. J. Yong,M. A. Serna

Stability andDuctility of SteelStructures, 2006.

[30]

SC001a-EN-EU

Code commentary: CollectionNo. 1

Access-Steel, 2007.

[31]

SN005a-EN-EU

Determination ofmomentson columns in simple construction

Access-Steel, 2005.

[32]

SteelBuildingDesign

MediumRiseBraced Frames

SCI PUBLICATIONP365.

[33]

Target specificationDimensioning Profiles

ZEMAN&CO.GmbH

Wien, 2006.

[34]

New proposals for EN 1993-1-5, AnnexD:

Plate girderswith corrugatedwebs.

H. Pasternak, J. Robra, G. Kubieniec

IABSE-FIBConference, Dubrovnik, 2010.

[35]

ZulassungNr. Z-8.22-208

Modulsystem "CUPLOK"

Deutsches Institut für Bautechnik, 2006.

[36]


Modulsystem "Layher-Allround"


[37] Multi-StoreyBuildings in Steel

- 110 -

DesignGuide for SlimFloorswith Built-in Beams

ECCSN°83 - 1995

[38]

DesignHandbook for Braced or Non-Sway

SteelBuildingsAccording to Eurocode 3

ECCSN°85 - 1996

[39]


Modulsystem "Layher-Allround LW"


[40]

Valorisation Project Semi-Comp+

N°RFS2-CT-2010-00023

Background Information

22march 2012

[41]

NumericalMethods inNonlinear ConcreteDesign

R. Vondráček

Czech TechnicalUniversity, Prague, 2000

- 111 -

Chapter 5

AISC / AISI / ANSI

AISC – ASD:1989AISC – ASD:1989The beamelementsare checked according to the regulationsgiven in

Manual of SteelConstruction

Allowable StressDesign

Part 5 : Specification andCodes

AISC, Ninth Edition, 1989

The crosssection is classified according to Table B5.1. (compact, non compact, or slender section).

Themember is checked on following criteria:

l tension : D1l compression : E2, E3l flexuralmembers : F1,F2,F3,F4l plate girders : G2l combined forces : H1,H2

Amore detailed overview for the used articles of the relevant parts is given in the following table. The chaptersmarked with“x” are consulted. The chaptersmarkedwith (*) have a supplementaryexplanation the following chapters.

B.Design requirements

B1.Gross Area x

B2. Net Area (*)

B3. Effective Area

B4. Stability

B5. Local Buckling

1.Classification of Steel Sections

2.Slender Compression Elements

(*)

x

x

B6. Rotational Restraint at Points of Support

B7. Limiting Slenderness Ratios x

B8. Simple Spans

B9. End Restraint

B10. Proportions of Beams and Girders

B11. Proportioning of Crane Girders

D. TENSIONMEMBERS

D1. Allowable Stress x (*)

D2. Built-up members

D3. Pin-Connected Members

- 112 -

AISC / AISI / ANSI

E. COLUMNANDOTHERCOMPRESSIONMEMBERS

E1. Effective Length and Slenderness Ratio x (*)

E2. Allowable Stress x

E3. Flexural-torsional Buckling x (*)

E4. Built-up Members

E5. Pin-Connected Compression Members

E6. Column Web Shear

F. BEAMS ANDOTHERFLEXURALMEMBERS (*)

F1. Allowable Stress : Strong Axis Bending of I-Shaped Members and Channels

1.Members with Compact Sections

2.Members with Non-Compact Sections

3.Members with Compact or Non-Compact Sections with Unbraded Length Greater then Lc

x

x

x

x

F2. Allowable Stress :Weak Axis Bending of I-Shaped Members, Solid Bars and Rectangular Plates



x

x

x

F3. Allowable Stress : Bending of BoxMembers, Rectangular Tubes and Circular Tubes



x

x

x

F4. Allowable Shear Stress x

F5. Transverse Stiffeners

F6. Built-up Members

F7.Web-tapered Members

G.PLATE GIRDERS

G1.Web Slenderness Limitations

G2. Allowable Bending Stress x

G3. Allowable Shear Stress with Tension Field Action

G4. Transverse Stiffeners

G5. Combined Shear and Tension Stress

H.COMBINEDSTRESSES

H1. Axial Compression and Bending x

H2. Axial Tension and Bending x

APPENDIX B. Design requirements

B5. Local Buckling x

Classification of sectionsFor each intermediarysection, the classification isdetermined..

For each load case / combination, the critical section classification over the member is used to perform the code check. However, for non-prismatic sections, the section classification isdetermined for each intermediarysection.

- 113 -

Chapter 5

Section propertiesThe influence of the bore hole isneglected, i.e. only the grossarea isused.

Buckling lengthFor the calculation of the buckling length, we refer to ""AnnexB: Calculation of buckling ratio" on page 184".

The buckling properties for a VARH element are calculated by using the critical Euler force for this member (see “"Cal-culation of criticalEuler force for VARH elements" on page 189”).

Flexural Torsional BucklingThe slenderness ratio for flexural torsional buckling (KL/r)e is given by

SeeRef. [1], CommentaryChapter E1.

The calculation of Fe is given inRef. [2], AppendixE.

Lateral-torsional bucklingFor I sectionsand channel sections, the allowable LTBstress isgiven in F1.

For RHS (Rectangular Hollow Section) sections and CHS (Circular Hollow Section) , the allowable LTB stress is given inF3.

For angle sections with symmetrical legs, the allowable LTB stress is given in Ref. [1], pp.309-314, “Specification for allow-able stress - Design of single-anglemembers”.

For the other supported sections, the elastic criticalmoment for LTBMcr isgiven by

with

E themodulusof elasticity

G the shear modulus

L the length of the beambetween pointswhich have lateral restraint (= lLTB)

Iw thewarping constant

It the torsional constant

Iz themoment of inertia about theminor axis

See alsoRef. [4], part 7.

With thismomentMcr, the critical LTBstressσLTB is calculated :

with

- 114 -

AISC / AISI / ANSI

Wy the sectionmodulusabout themajor axis

The slenderness ratio for LTBλLTB, is given by

The allowable LTBstress is calculated using the slendernessλLTB with the formulasgiven inRef.[1], E2.

See alsoRef. [5], BijlageE.

Haunched sections (I+Ivar, Iw+Plvar, Iw+Iwvar, Iw+Ivar, I+Iwvar) and composed rail sections (Iw+rail, Iwn+rail, I+rail,I+2PL+rail, I+PL+rail, I+2L+rail, I+Ud+rail) are considered asequivalent asymmetric I sections.

Shear buckling checkComposed rail sections (Iw+rail, Iwn+rail, I+rail, I+2PL+rail, I+PL+rail, I+2L+rail, I+Ud+rail) are considered as equivalentasymmetric I sections.

Supported sectionsI Symmetric I shapes (IPE, HEA, HEB,….)

RHS Rectangular Hollow Section (RHS)

CHS Circular Hollow Section (CHS)

L Angle section

U Channel section

T T section

PPL Asymmetric I shapes

RS Rectangular section

Σ Cold formed section

COM Composed section in PRIMAWIN

O Solid tube

NUM Numerical section

The necessarydata conditions for these sectionsare described in "AnnexA: Profile LibraryFormcodes" on page 163.

TheCOMandNUMsectionsare not read out of the profile library.

I RHS CHS L U T PPL RS Σ O COM NUM

Classification x x x x x x x x x (1) (1) (1)

Compact section x x x x x

Non-compact section x x x x x x x x x x x x

Slender section x x x x x x

Shear buckling check x x x

(1) sectionsare classified asnon-compact section bydefault.

- 115 -

Chapter 5

References

[1]


Allowable StressDesign

AISC, Ninth Edition, 1989

[2]


Load&Resistance Factor Design

AISC, First Edition, 1986

[3]


Load&Resistance Factor Design

AISC, Volume I, SecondEdition, 1995

[4]

R.Maquoi



[5]

NBNB51-001

Stalen Bouwconstructies

BIN, 5e uitg. April 1977

- 116 -

AISC – LRFD:2001AISC - LRFD Code checkThe beamelementsare checked according to the regulationsgiven in

AISC –Manual of steel construction

Load andResistance Factor Design

Part 16SpecificationsandCodes

Third Edition

2001


Themember is checked on following criteria :

l tension : D1l compression : E2, E3, AppendixE3l flexuralmembers : F1,AppendixF1, AppendixF2l plate girders : AppendixG2, AppendixG3, AppendixG5l combined forces :H1,H2



B1.Gross Area x

B2. Net Area (*)

B3. Effective Area for Tension Members

B4. Stability

B5. Local Buckling

1.Classification of Steel Sections

2.Slender Compression Elements

3.Slender-Element Compression Sections

(*)

x

x

x

B6. Bracing at Support

B7. Limiting Slenderness Ratios x

B8. Simple Spans

B9. End Restraint

B10. Proportions of Beams and Girders

D. TENSIONMEMBERS

D1. Design Tensile Strength x (*)

D2. Built-up members

D3. Pin-Connected Members and Eyebars

- 117 -

Chapter 6

E. COLUMNANDOTHERCOMPRESSIONMEMBERS

E1. Effective Length and Slenderness Limitations

1.Effective Length

2.Design by Plastic Analysis

x

x (*)

E2. Design Compressive Strength for Flexural Buckling x

E3. Design Compressive Strength for Flexural-Torsional Buckling x

E4. Built-up Members

E5. Pin-Connected Compression Members

F. BEAMS ANDOTHERFLEXURALMEMBERS (*)

F1. Design for Flexure

1.Yielding

2.Lateral-Torsional Buckling

x

x

x

F2. Design for Shear x


F4. Beams and Girders with Web Openings

G.PLATE GIRDERS x

H.MEMBERS UNDERCOMBINEDFORCES ANDTORSION

H1. SymmetricMembers Subject to Bending and Axial Force x

H2. UnsymmetricMembers and Members under Torsion and Combined Torsion, Flexure, Shear and/or Axial Force x

H3. Alternative Interaction Equation for Members under Combined Stress

APPENDIX B. Design requirements

B5. Local Buckling x

APPENDIX E. COLUMNANDOTHERCOMPRESSIONMEMBERS

E3. Design Compressive Strength for Flexural-Torsional Buckling x

APPENDIX F. BEAMS ANDOTHERFLEXURALMEMBERS

F1. Design for Flexure x

F2. Design for Shear x


APPENDIX G. PLATE GIRDERS

G1. Limitations

G2. Design Flexural Strength x(*)

G3. Design Shear Strength with Tension Field Action x(*)

G4. Transverse Stiffeners

G5. Flexure-Shear Interaction x(*)

- 118 -


For each load case/combination, the critical section classification over the member is used to perform the code check. However, for non-prismatic sections, the section classification isdetermined for each intermediarysection.



The buckling properties for a VARH element are calculated by using the critical Euler force for this member (see “"Cal-culation of the criticalEuler force"”).

Lateral-torsional bucklingFor I sections, channel sections, RHS (Rectangular Hollow Section) sections, T sections, rectangular sections, and asym-metric I sections, the critical LTBmoment isgiven in F1 andAppendixF1.

For angle sections with symmetrical legs, the critical LTB moment is given in Ref. [1], pp.281-288, “Specification for LoadandResistance Factor Design of Single-Anglemembers”.

For the other supported sections, the elastic criticalmoment for LTBMcr isgiven by

with


G the shear modulus

L the length of the beambetween pointswhich have lateral restraint (= lLTB)

Iw thewarping constant


Iz themoment of inertia about theminor axis

See alsoRef. [2], part 7.


Use of sheeting SeeChapter '"AnnexD: Use of sheeting " on page 205'.


- 119 -

Chapter 6




L Angle section

U Channel section

T T section





O Solid tube










(1) sectionsare classified asnon-compact section bydefault.

References

[1]

AISC – Manual of steel construction

Load and Resistance Factor Design

Third Edition

2001

[2]

R.Maquoi



- 120 -

ANSI/AISC 360-05:2005ANSI/AISC 360-05 Code checkThe beamelementsare checked according to the regulationsgiven in

ANSI/AISC 360-05

Specifications for StructuralSteelBuildings

2005

The steel code checkcan be executed according to either ASD or LRFD provisions.



l tension : Chapter Dl compression : Chapter El flexuralmembers :Chapter Fl shear : Chapter Gl combined forces :Chapter H



B2. Loads and Load Combination x

B3. Design Basis

1.Required Strength

2.Limit States

3.Design for Strength using LRFD

4.Design for Strength using ASD

x

x

B4. Classification of Sections for Local Buckling x

D.DESIGNOFMEMBERS FORTENSION

D1. Slenderness Limitation x

D2. Tensile Strength x

D3. Area Determination x(*)

E. DESIGNOFMEMBERS FORCOMPRESSION

E1. General Provisions x

E2. Slenderness Limitations and Effective Length x(*)

E3. Compressive Strength for Flexural Buckling ofmembers without Slender Elements x

E4. Compressive Strength for Torsional and Flexural-Torsional Buckling ofmembers without Slender Elements x

E7. Members with Slender Elements x

- 121 -

Chapter 7

F. DESIGN FORMEMBERS FOR FLEXURE

F1.General Provisions x

F2. Doubly Symmetric Compact I-Shaped Members and Channels Bent about their Major Axis x

F3. Doubly Symmetric I-Shaped Members with CompactWebs and Noncompact or Slender Flanges Bent about Their Major Axis x

F4. Other I-Shaped Members with Compact or NoncompactWebs Bent about Their Major Axis x

F5. Doubly Symmetric and Singly Symmetric I-Shaped Members with Slender Webs Bent about Their Major Axis x

F6. I-Shaped Members and Channels Bent about Their Minor Axis x

F7. Square and Rectangular HSS and Box-Shaped Members x

F8. Round HSS x

F9. Tees and Double Angle Loaded in Plane of Symmetry x

F10. Single Angle x

F11. Reactangular Bars and Rounds x

F12. Unsymmetrical Shapes

G.DESIGNOFMEMBERS FORSHEAR

G1.General Provisions x

G2.Members with Unstiffened or Stiffened Webs x

G4. Single Angles x

G5. Rectangular HSS and BoxMembers x

G6. Round HSS x

G7.Weak Axis Shear in Singly and Doubly Symmetric Shapes x

H.DESIGNOFMEMBERS FORCOMBINEDFORCES ANDTORSION

H1. Doubly and Singly SymmetricMembers Subject to Flexure and Axial Force x

H2. Unsymmetric and Other Members Subject to Flexure and Axial Force x

H3.Members Under Torsion and Combined Torsion and Combined Stress x





The buckling properties for a VARH element are calculated by using the critical Euler force for this member (see “"Cal-culation of the criticalEuler force"”).

Lateral-torsional bucklingHaunched sections (I+Ivar, Iw+Plvar, Iw+Iwvar, Iw+Ivar, I+Iwvar) and composed rail sections (Iw+rail, Iwn+rail, I+rail,I+2PL+rail, I+PL+rail, I+2L+rail, I+Ud+rail) are considered asequivalent asymmetric I sections.

- 122 -

Use of sheeting SeeChapter "AnnexD: Use of sheeting " on page 205.


Supported sectionsI Symmetric I shapes (IPE, HEA, HEB,….)RHS Rectangular Hollow Section (RHS)CHS Circular Hollow Section (CHS)L Angle sectionU Channel sectionT T sectionPPL Asymmetric I shapesRS Rectangular sectionΣ Cold formed sectionCOM Composed section in PRIMAWINO Solid tubeNUM Numerical section








Shear buckling check x x x x x x

(1) Sectionsare classified asnon-compact section bydefault.

References

[1]

ANSI/AISC 360-05


2005

- 123 -

Chapter 8

ANSI/AISC 360-10:2010ANSI/AISC 360-10 Code checkThe beamelementsare checked according to the regulationsgiven in

ANSI/AISC 360-00


2010, Second printing 2012.

The steel code checkcan be executed according to either ASD or LRFD provisions.

The crosssection is classified according to Table B4.1a. for axial compression and Table B4.1b. for flexure.


l Tension : Chapter Dl Compression : Chapter El Flexuralmembers :Chapter Fl Shear : Chapter Gl Combined forces :Chapter H



B2. Loads and Load Combination x

B3. Design Basis

1.Required Strength

2.Limit States

3.Design for Strength using LRFD

4.Design for Strength using ASD

x

x

B4.Member Properties

1. Classification of Sections for Local Buckling

2. Design Wall Thickness for HSS

3.Gross and Net Area Determination

x

D.DESIGNOFMEMBERS FORTENSION

D1. Slenderness Limitation x

D2. Tensile Strength x

D3. Effective Net Area x(*)

E. DESIGNOFMEMBERS FORCOMPRESSION

E1. General Provisions x

E2. Effective Length x(*)

E3. Flexural Buckling ofMembers without Slender Elements x

E4. Torsional and Flexural-Torsional Buckling ofMembers without Slender x

- 124 -

Elements

E7. Members with Slender Elements x

F. DESIGN FORMEMBERS FOR FLEXURE

F1.General Provisions x

F2. Doubly Symmetric Compact I-Shaped Members and Channels Bent About Their Major Axis x

F3. Doubly Symmetric I-Shaped Members with CompactWebs and Noncompact or Slender Flanges Bent about Their Major Axis x

F4. Other I-Shaped Members with Compact or NoncompactWebs Bent about Their Major Axis x

F5. Doubly Symmetric and Singly Symmetric I-Shaped Members with Slender Webs Bent about Their Major Axis x

F6. I-Shaped Members and Channels Bent about Their Minor Axis x

F7. Square and Rectangular HSS and Box-Shaped Members x

F8. Round HSS x

F9. Tees and Double Angle Loaded in Plane of Symmetry x

F10. Single Angle x

F11. Rectangular Bars and Rounds x

F12. Unsymmetrical Shapes

G.DESIGNOFMEMBERS FORSHEAR

G1.General Provisions x

G2.Members with Unstiffened or Stiffened Webs x

G4. Single Angles x

G5. Rectangular HSS and BoxMembers x

G6. Round HSS x

G7.Weak Axis Shear in Singly and Doubly Symmetric Shapes x

H.DESIGNOFMEMBERS FORCOMBINEDFORCES ANDTORSION

H1. Doubly and Singly SymmetricMembers Subject to Flexure and Axial Force x

H2. Unsymmetric and Other Members Subject to Flexure and Axial Force x

H3.Members Subject to Torsion and Combined Torsion, Flexure, Shear and/or Axial Force x

Classification of sectionsFor each intermediarysection, the classification isdetermined.




The buckling properties for a VARH element are calculated by using the critical Euler force for this member (see “"Cal-culation of criticalEuler force for VARH elements" on page 189”).

- 125 -

Chapter 8

Lateral-torsional bucklingHaunched sections (I+Ivar, Iw+Plvar, Iw+Iwvar, Iw+Ivar, I+Iwvar) and composed rail sections (Iw+rail, Iwn+rail, I+rail,I+2PL+rail, I+PL+rail, I+2L+rail, I+Ud+rail) are considered asequivalent asymmetric I sections.

Use of sheeting SeeChapter "AnnexD: Use of sheeting " on page 205.





L Angle section

U Channel section

T T section





O Solid tube




I RHS CHS L U T PPL S Σ O COM NUM





Shear buckling check x x x x x x

(1) Sectionsare classified asnon-compact / non-slender section bydefault.

- 126 -

References

[1]

ANSI/AISC 360-10


2005 , 2ndPrinting February2012

[2]

ComparisonOf ANSI/AISC 360-10 ToANSI/AISC 360-05

E. Bolin and T. Dehlin

www.aisc.org

[3]

DesignExamplesversion 14.1

www.aisc.org

2011

- 127 -

Chapter 9

AISI NAS S100-2007AISI NAS S100-2007 Code checkThe beamelementsare checked according to the regulationsgiven in:

AISI S100-2007North AmericanSpecification for theDesign of Cold-FormedSteelStructuralMembers

2007 edition

AISI S100-07-E1Errata toNorth AmericanSpecification for theDesign of Cold-FormedSteelStructuralMembers

2007 edition

February20, 2008

AmendedSeptember 25, 2008

Amended June 4, 2009

AISI S100-07/S1-09Supplement No. 1 to the North American Specification for the Design of Cold-Formed SteelStructuralMembers, 2007 edi-tion

August, 2009

AISI S100-07/S2-10Supplement No. 2 to the North American Specification for the Design of Cold-Formed SteelStructuralMembers, 2007 edi-tion

February, 2010

The steel code check is supported for the United States provisions and can be executed according to either ASD or LRFDprinciples. TheCanadian LSDmethod isnot supported.

Consulted articlesAn overview for the used articles is given in the following table. The articles marked with “x” are consulted. The articlesmarkedwith (*) have a supplementaryexplanation in the following paragraphs.

Article Title

A General Provisions

A4 Allowable Strength Design X

A5 Load and resistance Factor Design X

B Elements

- 128 -

Article Title

B1 Dimensional Limits and Considerations X(*)

B2 Effective Widths of Stiffened Elements

B2.1 Uniformly Compressed Stiffened Elements

B2.3 Webs and Other Stiffened Elements under StressGradient

X(*)

X(*)

B3

Effective Widths of Unstiffened Elements

B3.1 uniformly Compressed Unstiffened Elements

B3.2 Unstiffened Elements and Edge Stiffeners with StressGradient

X(*)

X(*)

B4 Effective Width of Uniformly Compressed Elements with a Simple Lip Edge StiffenerX(*)

C Members

C1 Properties of Sections X(*)

C2 Tension Members X(*)

C3 Flexural members

C3.1 Bending

C3.1.1 Nominal Section Strength

C3.1.2 Lateral-Torsional Buckling Strength

C3.1.3 Flexural Strength of Closed Cylindrical Tubular Members

C3.1.4 Distortional Buckling Strength

X(*)

X(*)

X(*)

X(*)

C3.2 Shear

C3.2.1 Shear Strength ofWebswithout Holes

C3.3 Combined Bending and Shear

X(*)

X(*)

C3.4 Web Crippling

C3.4.1 Web Crippling Strength ofWebswithout Holes

C3.5 Combined Bending and Web Crippling

X(*)

X(*)

C3.6 Combined Bending and Torsional Loading X(*)

C4 Concentrically Loaded Compression Members

C4.1 Nominal Strength for Yielding, Flexural, Flexural-Torsional and Torsional Buckling

C4.2 Distortional Buckling Strength

X(*)

X(*)

C5

Combined Axial Load and Bending

C5.1 Combined Tensile Axial Load and Bending

C5.2 Combined Compressive Axial Load and Bending

X

X(*)

D Structural Assemblies and Systems

D6 Metal Roof and Wall Systems

- 129 -

Chapter 9

Article Title

D6.1 Purlins, Girts and Other Members

D6.1.1 Flexural Members Having One Flange Through-Fastened to Deck of Sheeting

D6.1.3 Compression Members Having One Flange Through-Fastened to Deck of Sheeting

X(*)

X(*)

Appendix 2Second-Order Analysis

2.1 General requirements X(*)

Haunches, arbitrary members and cross-sections without initial shapes are not supportedfor the AISI NAS S100-2007 code check. In this case the default AISC 2005 code check isexecuted.

Initial ShapeFor a cross-sectionwithmaterialSteel and fabrication set to Cold-Formed, the InitialShape can be defined.










RUO reinforcement typescan be set only to elementsof typeSO or UO.

The initial shape issupported for the following cross-section types:

l Standard profile librarycross-sectionsl Cold formedPair cross-sectionsof profile librarysectionsl General thin-walled sectionsl General sectionswith thin-walled representationl Thin-walled geometric sectionsl All other sectionswhich support the centerline and do not have roundings



- 130 -

Dimensional limitsDimensional limitsare supported according to article B1.1 andB1.2.

Article B1.1 (a) (1) for a simple lip is checked for an internal element (I) connected to a stiffener (RUO).

Article B1.1 (a) (2) is checked for an internal element (I).

Article B1.1 (a) (3) is checked for an outstand element (UO or SO).

Articles B1.1 (b) concerning flange curling and (c) concerning shear lag effectsare not supported.

Article B1.2 (a) is checked for web elements under stress gradient. Webs are defined as elements perpendicular (tol-erance +/-45°) to the axisof bending.

Effective WidthsUniformly Compressed Stiffened elementsThe effective width of Uniformly Compressed Stiffened elements is calculated according to article B2.1 (a) StrengthDetermination.

More specifically, this concernselementsof type I with stressgradient ψ =1

ServiceabilityDetermination isnot supported.

Webs and Other Stiffened Elements under Stress GradientThe effective width of Webs and Other Stiffened elements under stress gradient is calculated according to article B2.3 (a)StrengthDetermination.

More specifically, this concernselementsof type I with stressgradient ψ ≠1


Uniformly Compressed Unstiffened elementsThe effective width of Uniformly Compressed Unstiffened elements is calculated according to article B3.1 (a) StrengthDetermination.

More specifically, this concernselementsof type SO or UO (with or without reinforcement typeRUO) with stressgradient ψ=1


Unstiffened elements and Edge Stiffeners with Stress GradientThe effective width of Unstiffened elements and Edge Stiffenerswith StressGradient is calculated according to article B3.2(a) StrengthDetermination.

More specifically, this concernselementsof type SO or UO (with or without reinforcement typeRUO) with stressgradient ψ≠1

The alternativemethods for unstiffenedC-sectionsare not supported.


Effective width of Uniformly Compressed elements with a Simple Lip Edge StiffenerThe effective width of UniformlyCompressed elementswith a Simple Lip Edge Stiffener is calculated according to article B4(a) StrengthDetermination.

More specifically, this concerns elements of type I with stress gradient ψ = 1 which are connected to a fixed element (round-ing) which in turn is connected to an element of typeUO or SO with reinforcement typeRUO.


- 131 -

Chapter 9

Effective section properties can never be bigger than grosssection properties (for examplein case ofmanually inputted grosssection propertieswhich have been rounded down).

Properties of SectionsDeductions for holes, openingsand cut-outsare not supported.

Tension MembersThe tensile strength isdetermined according to article C2.

For yielding in the grosssection:

For rupture in the net section:

with

Fy Yield strength

Fu Tensile strength

Ag Grossarea of cross-section

An Net area of cross-section

Since deductions for holes, openings…are not supported An =Ag.

Flexural MembersNominal Section StrengthThe nominal section strength is determined according to article C3.1.1. More specificallyProcedure I - Based on Initiation ofYielding isapplied.

Lateral Torsional Buckling Open SectionThe Lateral TorsionalBuckling strength for open sections isdetermined according to article C3.1.2.1 (a).

For sheetings reference ismade to "Sheeting on the compression flange" on page 143.

The simplified formulasof article C3.1.2.1 (b) are not supported.

Doubly symmetric sectionsFor Doublysymmetric sections formula (C3.1.2.1-4) isused for either axis.

Thisapplies to the following form codes:

- 132 -

1 (Symmetric I shape)

7 (Rectangular section)

11 (Solid tube)

In addition thisapplies to the cold formed pair sections2CFUo, 2CFUc, 2CFCo, 2CFCc

Formula (C3.1.2.1-4) is rewritten as follows:

Remarks:

l For x-xbending the LTB length isused instead of the effective length KyLy.l For y-ybendingKx is taken as the buckling ratio about the x-axisand Lx the system length for buckling about the x-axis.l The equation for r0 isexpanded to allow any type of cross-section:

l Cb for x-xbending is calculated according to formula (C3.1.2.1-6) l Cb for y-ybending is taken asunity.

Point symmetric sectionsFor Point symmetric sections formula (C3.1.2.1-5) isused for either axis.


102 (Z section)

113 (Cold formedZ section)

118 (Cold formedZED section)

119 (Cold formedZED section asymmetrical lips)

120 (Cold formedZED section inclined lip)

126 (Cold formedZED section both lips inclined)

Formula (C3.1.2.1-5) is rewritten as follows:

- 133 -

Chapter 9

The same remarksare valid as for doublysymmetric sections.

Singly symmetric sectionsFor Singly symmetric sections formula (C3.1.2.1-4) is used for bending about the x-x axis and formula (C3.1.2.1-10) forbending about the y-yaxis.


5 (Channel section)

112 (Cold formedChannel section)

114 (Cold formedC section)

117 (Cold formedC-Plussection)

121 (Cold formedSigma section)

122 (Cold formedSigma section stiffened)

123 (Cold formedSigma-Plussection)

Formulas (C3.1.2.1-4) and (C3.1.2.1-10) arewritten as follows:

The same remarksare valid as for doublysymmetric sections.

The parameter j is calculated using the formula for C-sectionsgiven inRef. [4].

Other section typesAll other cross-sections which are not covered by the previous paragraphs are considered to be doubly symmetric, exceptfor the following form codes:

2 (Rectangular Hollow Section)

3 (Circular Hollow Section)

Lateral Torsional Buckling Box SectionThe Lateral TorsionalBuckling strength for boxsections isdetermined according to article C3.1.2.2.

- 134 -

Thisapplies to the following form code:


In addition thisapplies to the cold formed pair sections2CFUcand 2CFCcwith distance a =0mm

Formulas (C3.1.2.2-1) and (C3.1.2.2-2) are rewritten as follows:

The same remarksare valid as for open doublysymmetric sections.

Flexural Strength Closed Cylindrical Tubular membersTheFlexuralStrength of ClosedCylindrical Tubular members isdetermined according to article C3.1.3.



In case the diameter to thickness ratio D/t exceeds the limit 0,441 E/Fy the check is notexecuted and awarning is issued on the output.

Distortional Buckling StrengthFor both bending axis the distortional buckling strength is determined according to article C3.1.4. More specifically the gen-eralProcedure (a) is followed using formula (C3.1.4-6).

The check isexecuted in case the following conditionsaremet:

l The cross-section hasat least one element with reinforcement typeRUOl For the given bendingmoment in the section, at least one of these elements is in compression

More specifically this implies that, if the stiffener is in compression distortional buckling can occur (even if the flange itself ispartially in tension). This is in accordance with the distortional buckling shapes for weak axis bending of typical C-sectionsobtained using numerical analysisRef. [9].

Remarks:

l The unbraced length Lm is taken as the LTB length and this for both bending axis.l In case a diaphragm ispositioned on the compression side and the diaphragmprovides full bracing, themember is

regarded ascontinuously restrained and Lm=Lcr.

l The rotational stiffness of the restraining element isbydefault taken aszero.

In case a diaphragm is located on the compression side, is taken as the rotational stiffness vorhCθ of the dia-phragm.

For diaphragms reference ismade to "Sheeting on the compression flange" on page 143.

- 135 -

Chapter 9

l For calculating the compression flange properties, the default SCIAEngineer axis convention isused (x-yaxis system loc-ated at the centroid of the flange, with the x-axismeasured positive to the right from the centroid and the y-axispositive upfrom the centroid)

l The elastic sectionmodulusof the full unreduced section relative to the extreme fiber in first yield Sfy is taken asSfy,x forx-xbending andSfy,y for y-ybending.

l In determining the stressgradient in theweb, pure symmetrical bending isassumed. This implies that for x-xbend-ing thisparameter equals2 and for y-ybending thisparameter equalszero.

l The distance b0 for a standard profile librarysection is taken as thewidth property. For a general section this is taken asthe summation of the Internal (I) partsof the flange.

l The distance h0 for a standard profile librarysection is taken as the height property. For a Sigma section (FormCode 121– 125) this is taken as the (full) height property. For a general section this is taken as themaximal height of the ‘web’ ele-ments.Web elementsare defined aselementswith an angle >45° to the horizontal axis.

l When there isno ‘web’ element (i.e. CHSsection ), distortional buckling isnot checked.l Flangesare defined aselementswith angle <45° to the horizontal axis.l Connected flange elementswhich have a relative angle >135°are accounted for as ‘one’ flange for distortional buckling.l For cross-sectionswith roundings, the flange/web junction is taken to be at the intersection between the flange/web

rounding and the flat part of the flange.l The thickness t is taken as the smallest thicknessof the cross-section elements.l For Omega sections (FormCode 115) the top flange isnot seen as flange for distortional buckling.

ShearThe shear strength isdetermined according to article C3.2.1.

In the calculation of Aw only elements with element types I, UO and SO are accounted for. In addition, elements with rein-forcement typeROU are not accounted for.

For each element i the shear areaAw,i is calculated as follows:

With:

i The number (ID) of the element.

xend End position of element i .

xbeg Begin position of element i.

t Thicknessof element i.

α Angle of element i to the horizontal x-xaxis

In addition, for each element i the nominal shear stressFv,i is calculated.

The shear strength of the element then becomesVn,i =Aw,i * Fv,i

The nominal shear strength Vn for the crosssection is taken as the sumof theVn,i of the related elements.

Transverse stiffenersare not supported, therefore the shear buckling coefficient kv is taken as5,34.

- 136 -

AISI NASS100-2007 does not give provisions to calculate the shear resistance for circularhollow sections (Form Code 3). Therefore the default AISC 2005 provisions are used inthis case.

Combined Bending and ShearThe combined bending and shear check isdetermined according to articlesC3.3.1 andC3.3.2.

Transverse stiffenersare not supported; therefore the equations for unreinforcedwebsare used.

Web Crippling StrengthTheweb crippling strength isdetermined according to article C3.4.1.

More specifically the general equation (C3.4.1-1) isapplied.

The alternative given in equation (C3.4.1-2) isnot supported.

Theweb crippling check isexecuted on the positionswhere there isa jump in theVyshear force diagram.

Remarks:

l The shear force diagramof both the actualmember aswell asadjacentmembers isevaluated. Adjacentmembersaredefined asmemberswhich are in the same buckling system.

l The angle θ between the plane of theweb and the plane of the bearing surface is taken as90°.l TheFlangeConditionsdepend on the definition of the initial shape. In case there isan element with reinforcement type

ROU the setting is taken as ‘Stiffened or PartiallyStiffened Flanges’.l The distances for One-flange/Two-flange andEnd/Interior are evaluated taking into account adjacentmembers. Adja-

centmembersare defined asmemberswhich are in the same buckling system.

The following paragraphsspecify the supported cross-section types.

Built-Up SectionsFor built-up sections tableC3.4.1-1 isused.

Thisapplies to cold formed pair sections2CFUo and 2CFCowith distance a =0mmand the following form codes:

127 (Cold formed I-Plussection)

128 (Cold formed IS-Plussection)

130 (Cold formed 2C section)

Since these pair sectionsconsist of twowebs the resistance of the full section isobtained byadding the valuesof eachweb.

Single Web Channel and C-SectionsFor singleweb channel andC-sections tableC3.4.1-2 isused.


5 (Channel section)



116 (Cold formedC section eavesbeam)

- 137 -

Chapter 9


In addition thisapplies to the following pair sections:

2CFUcand 2CFCc

2CFUo and 2CFCowith distance a >0mm

Since the pair sectionsconsist of twowebs the resistance of the full section isobtained byadding the valuesof eachweb.

Single Web Z-SectionsFor singlewebZ-sections tableC3.4.1-3 isused.


102 (Z section)






Single Hat SectionsFor single hat sections tableC3.4.1-4 isused.


115 (Cold formedOmega section)

Since these sectionsconsist of twowebs the resistance of the full section isobtained byadding the valuesof eachweb.

Other SectionsFor anyother cross-section typesas those listed in the previousparagraphsnoweb crippling check isexecuted.

In addition tableC3.4.1-5 isnot supported.

Combined Bending andWeb CripplingThe combined bending andweb crippling check isdetermined according to articlesC3.5.1 andC3.5.2.

Requirement (a) isapplied to the following form codes/sections:

5 (Channel section)



116 (Cold formedC section eavesbeam)


102 (Z section)

- 138 -






115 (Cold formedOmega section)

2CFUcand 2CFCc

2CFUo and 2CFCowith distance a >0mm

Requirement (b) isapplied to the following form codes/sections:

2CFUo and 2CFCowith distance a =0mm

Requirement (c) isapplied to the following form codes/sections in case the check isexecutedwithin a lapped zone:

102 (Z section)






Remarks:

l The exception given for requirement (a) isnot supported.l In case a lapped Z section doesnotmeet the limits for requirement (c) the provisionsof requirement (a) are applied

instead.l For requirement (c) it is assumed that conditions (1), (2), (3) & (4) are fulfilled.

Combined Bending and TorsionCombined bending and torsion loading isevaluated according to article C3.6.

In each fiber of the cross-section the bending stresses Sigma Mx and Sigma My are calculated. These stresses are basedon the effective cross-sectional propertiesand calculated in the fibersof the grosscross-section.

In addition, in each fiber the shear stressdue to torsion Tau t is calculated based on grosssection properties.

Using these stresses, theR factor is calculated according to equation (C3.6-1) using the following expressions:

f bending =SigmaMx+SigmaMy

f torsion =Tau t

f bending + f torsion = (composed stress)

The critical fiber is taken as the fiber with the biggest composed stress.

The increase of theR factor in case of C-sections isnot supported.

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Chapter 9

For sheeting reference ismade to “"Sheeting on the compression flange" on page 143”.

Compression MembersNominal axial strengthThe nominal axial strength isdetermined according to article C4.1 using Fn =Fy.

Flexural BucklingThe stressFe for flexural buckling isdetermined according to article C4.1.1.

For the calculation of the effective length factor, reference is made to “"Calculation buckling ratio – general formula" onpage 184”.

In case an LTB restraint of type ‘Both’ is inputted, it specifies that both the top and bottomflange are held into position. Assuch, thispoint is seen asa fixed point for weakaxisbuck-ling.This implies that the system length Ly is taken between the LTB restraintsof type ‘Both’ andthemember ends. In addition the effective length factor ky is set to 1,00.


Torsional (-Flexural) BucklingThe stressFe for torsional (-flexural) buckling isdetermined according to the generalmethod given inRef. [7].

Doublysymmetricand hollow sectionsare taken asnot subject to torsional (-flexural) buckling.


1 (Symmetric I shape)



For anyother section the stressFe is taken as the smallest of Sigma,t andSigma,TF

Sigma,t =Ncr,T / Ag

Sigma,TF =Ncr,TF / Ag

With:


Ncr,TF Critical axial load for torsional-flexural buckling

Ag Grosssection area

Determination of Ncr,TThe elastic critical loadNcr,T for torsional buckling is calculated according toRef.[7].

- 140 -

With:

E Modulusof Young

G Shear modulus

J Torsion constant

Cw Warping constant


x0 and y0 Coordinatesof the shear center with respect to the centroid

rx radiusof gyration about the x-xaxis

ry radiusof gyration about the y-yaxis

Determination of Ncr,TFThe elastic critical loadNcr,TF for torsional flexural buckling is calculated according toRef.[7].


0

With:

Ncr,x Critical axial load for flexural buckling about the x-xaxis



The smallest value of Fe (flexural, torsional and torsional-flexural buckling) is used for calculating Fn according to articleC4.1.


Closed Cylindrical Tubular sectionsThe axial strength for closed cylindrical tubular sections isdetermined according to article C4.1.5.



In case the diameter to thickness ratio D/t exceeds the limit 0,441 E/Fy the check is notexecuted and awarning is issued on the output.

Distortional Buckling StrengthThe distortional buckling strength is determined according to article C4.2. More specifically the general Procedure (a) is fol-lowed using formula (C4.2-6).

The check isexecuted in case the cross-section hasat least one element with reinforcement typeRUO.

Remarks:

- 141 -

Chapter 9

l The same remarksare valid as for distortional buckling of flexuralmembers.l The elasticdistortional buckling stressFd isdetermined for each flange separately. TheminimalFd is taken as the limiting

value of the cross-section.

Because of this separate determination, a sheeting on onlyone flange isaccounted for in the Fd calculation ofthat specific flange.In addition, thisprocedure allowsstiffened flangesof unequal dimensions.

For sheetings reference ismade to “"Sheeting on the compression flange" on the facing page”.

Combined Compression and BendingThe combined compression and bending check isexecuted according to article C5.2.

The shifts exand eyof the neutral axis are determined for the required compressive axial strength. The additionalmomentsdue to these shiftsare then calculated bymultiplying the required compressive axial strengthwith these respective shifts.

The special provisions for angle sectionsapply for the following form codes:

4 (Angle section)

111 (Cold formedAngle section)

In case of 2nd order analysis, reference ismade to “"2ndOrder using Appendix2" on page 145”.

Use of sheetingSheetingsare used specifically in conjunctionwith article D6.1 concerning purlin and girt design.

The lateral stiffness S for a sheeting is calculated as follows in case the bolt pitch of the sheeting is set as ‘br’: (Ref.[11],3.5andRef.[12],3.3.4.):

With:

a Frame distance

Ls Sheeting length

K1 Sheeting stiffness factor K1K2 Sheeting stiffness factor K2

For a bolt pitch of ‘2br’ the shear stiffnessS is replaced by0,2 S (Ref.[11] p22).

For the rotational stiffnessvorhCθ of a sheeting reference ismade to “"AnnexD: Use of sheeting " on page 205”.

The available lateral strength S iscompared to the required lateral strength Serf Ref.[8]:

With:

- 142 -

E Modulusof Young

CW Warping constant of the purlin

L LTB length of the purlin

G Shear modulus

J Torsion constant of the purlin

Iy Secondmoment or area about the y-yaxisof the purlin

h Height of the purlin

In case the available lateral strength S is higher than or equal to the required strength Serf , the sheeting is providing suf-ficient stiffnessand the purlin is seen as fullybraced.

In case the available lateral strength S is lower than the required strength Serf, the sheeting is not providing sufficient stiff-nessand the purlin is seen as inadequatelybraced.

The influence of a sheeting on different checks (bending, compression and torsion) isoutlined in the following overview.

Bending

Sheeting on the compression flangeThe lateral stiffnessS iscalculated and compared to the required stiffnessSerf.

In caseS≥Serf themember is taken as fullybraced.

Asa result no LTBcheck is required for bending about the x-xaxis.

Distortional buckling still needs to be checked. For distortional buckling is taken asvorhCθ.

See Ref. [2] pp 47 “Since the distortional buckling has an intermediate buckling halfwavelength; the distortional buckling still needs to be considered even for braced mem-bers.”

In caseS<Serf themember is seen as inadequatelybraced.

As a result the LTB check for bending about the x- x axis is executed using the augmented torsional stiffness J.Reference ismade to “"AnnexD: Use of sheeting " on page 205”.

Distortional buckling still needs to be checked. For distortional buckling is taken asvorhCθ.

Sheeting on the tension flangeThe lateral stiffnessS iscalculated and compared to the required stiffnessSerf.

In caseS≥Serf themember is taken as fullybraced on the tension flange.

In this case article D6.1.1 isapplied.

Asa result no LTBcheck is required for bending about the x-xaxis.

In addition, no distortional buckling check is required.

In caseS<Serf or in case the limitsof article D6.1.1 are notmet, themember is seen as inadequatelybraced.

- 143 -

Chapter 9

Asa result the LTBcheck for bending about the x-xaxis isexecuted bydefault, without an increased torsional stiffnessJ.

In addition distortional buckling is checked taking aszero.

Compression

Sheeting on one flangeThe lateral stiffnessS iscalculated and compared to the required stiffnessSerf.

In caseS≥Serf themember is taken as fullybraced.

In this case article D6.1.3 isapplied.

Asa result no distortional buckling check is required.

In caseS<Serf or in case the limitsof article D6.1.3 are notmet, themember is seen as inadequatelybraced .

Asa result the default compression checksare executed.

In addition distortional bucklingwill be checked taking aszero.

Sheeting on both flangesIn this case the specificationsof the previousstep applyusing the largest lateral stiffnessSof both sheetings.

Torsion

Sheeting on any flangeThe lateral stiffnessS iscalculated and compared to the required stiffnessSerf.

In caseS≥Serf themember is taken as fullybraced against torsion.

In this case the reduction due to torsion isnot applied.

In caseS<Serf, themember is taken as inadequatelybraced.

Asa result the reduction for torsion isdetermined bydefault.

Flexural members having one flange through-fastened to sheetingThe nominal flexural strength isdetermined according to article D6.1.1.

Thisarticle isonlyapplied in case the following conditionsaremet:

l Themember is in bending about the x-xaxisl The sheeting is located on the tension flangel The diagram is through fastenedl The lateral stiffnessS≥Serfl The conditions for article D6.1.1 aremet

Remarks:

l The article isonly valid for C and Z sectionswith edge stiffeners (i.e. elementswith reinforcement typeROU).Thisapplies to the following form codes:114 (Cold formedC-section)116 (Cold formedC-section eavesbeam)117 (Cold formedC-Plussection)

- 144 -

118 (Cold formedZED section)119 (Cold formedZED section asymmetric lips)120 (Cold formedZED section inclined lip)126 (Cold formedZED section both lips inclined)

l For determining theR factor a difference ismade between simple span and continuousspans. Thisdifference isbasedon the system length Lx.When themember under consideration hasonlyone part for Lx it is taken assimple span.When themember hasmoreparts for Lx it is taken ascontinuousspan.

l The article isnot applied for cantilevers. A cantilever isdefined asamember at the end of a buckling systemwhich hasfree ends for both buckling about the x-xand y-yaxis.

l In addition, the article isnot applied for continuousbeams in the region between inflection pointsadjacent to a support.l It is assumed that conditions (8), (9), (10), (11), (12) & (13) are fulfilled.l The correction factor r for compressed insulation isnot supported.

Compression members with one flange through-fastened to sheetingThe compressive strength isdetermined according to article D6.1.3.

Thisarticle isonlyapplied in case the following conditionsaremet:

l Themember is in compressionl The sheeting is located on one or both flangesl The diagram is through fastenedl The lateral stiffnessS≥Serfl The conditions for article D6.1.3 aremet

Remarks:

l The article isonly valid for C and Z sectionswith edge stiffeners (i.e. elementswith reinforcement typeROU).Thisapplies to the following form codes:114 (Cold formedC-section)116 (Cold formedC-section eavesbeam)117 (Cold formedC-Plussection)118 (Cold formedZED section)119 (Cold formedZED section asymmetric lips)120 (Cold formedZED section inclined lip)126 (Cold formedZED section both lips inclined)

l The fastener distance x is taken as0,5.l It is assumed that conditions (7) & (8) are fulfilled.

2nd Order using Appendix 2

In case the proper setting isactivated in the steel setup, the provisionsaccording to article 2.1 of Appendix2 are applied.

More specifically, when the check isexecuted for a non-linear combination the following changesare applied:

l Effective length factor Kx is set to 1,00l Effective length factor Ky is set to 1,00l αx for article C5.2 is taken as1,00

l αy for article C5.2 is taken as1,00

l Cmx for article C5.2 is taken as1,00

l Cmy for article C5.2 is taken as1,00

- 145 -

Chapter 9

Article 2.2 of Appendix2 isnot supported.

Lapped Purlin DesignFor the analysis, the purlin line is considered prismatic i.e. the increased stiffnessdue to the doubled cross-section within thelap is ignoredRef.[5].

Since the lap length is defined along the member axis, it is important to specify a suf-ficient ‘number of sectionson averagemember’ in the Solver Setupwhen using overlaps.

Combined StrengthThe strengthwithin the lapped zones is taken as the sumof the strengthsof the individualmembersRef.[4].

The use of the combined strength of the individualmembers isapplied for the following checks:

l NominalBendingCheckl Shear Checkl CombinedBending andShear Checkl Web cripplingCheckl CombinedBending andWebCripplingCheckl Bending –DistortionalBucklingCheck

For distortional buckling, the distortional buckling stress Fd is calculated for the critical flange i.e. the flange resulting in thelowest Fd value.

The following equationsare then used:

Mcrd = (Sfsection 1 +Sfsection 2) * Fd

My= (Sfysection 1 +Sfysection 2) * Fy

Special considerations for Lateral Torsional BucklingWithin a lapped zone, at the bottom flange the LTBcheckdependson the Bottom flange fully braced settingwithin theOver-lap data.

In case this setting isactivated it implies the bottom flangewithin the lapped zone is fully fixed and thusno LTBoccurs.

Thishas the following implications:

l Within the lapped zone, in case the bottom flange is in compression, no LTBcheck isexecuted.l Outside of the lapped zone the LTB length is taken to the end of the lap.

Sheeting on the tension flangeIn case the following conditionsaremet:

l Sheeting on the top flangewhich provides full bracingl Setting Bottom flange fullybraced activated in the overlap datal The top flange is in tension

By default it would imply article D6.1.1 should be applied however this article is only valid in case the compression flange isfree. Since in this case the compression flange is fully braced this article is not applied and the nominal bending strength isused.

- 146 -

References

[1]

AISI S100-2007

North American Specification for the Design of Cold-Formed Steel StructuralMembers

2007 edition

[2]

AISI S100-2007-C

Commentary on North American Specification for the Design of Cold-FormedSteelStructuralMembers

2007 edition

[3]

AISI S100-07-E1

Errata to North American Specification for the Design of Cold-Formed SteelStructuralMembers

2007 edition

February20, 2008

AmendedSeptember 25, 2008

Amended June 4, 2009

[4]

AISI SG03-2

Cold-FormedSteelDesignManual

2002 edition

[5]

G. J. Hancock, T.M.Murray, D. S. Ellifritt

Cold-FormedSteelStructures to theAISI Specification

MarcelDekker, Inc., 2001

[6]

AGerhsi, R. Landolfo, F.M.Mazzolani

Design ofMetallic cold formed thin-walledmembers

SponPress, London, UK, 2002

[7]

SN001a-EN-EU

NCCI: Critical axial load for torsional and flexural torsional bucklingmodes

AccessSteel, 2006

www.access-steel.com

[8]

EN 1993-1-3:2006

Eurocode 3 - Design of steel structures

Part 1-3: General rules - Supplementary rules for cold- formed members andsheeting

CEN, 2006

[9]Schafer, B.W., Ádány, S.

Buckling analysisof cold-formed steelmembersusingCUFSM: conventional and

- 147 -

http://www.access-steel.com/

Chapter 9

constrained finite stripmethods.

Eighteenth International Specialty Conference on Cold- Formed Steel Struc-tures,

Orlando, FL. October 2006.

[10]

J. Schikowski

Stabilisierung von Hallenbauten unter besonderer Berücksichtigung derScheibenwirkung von Trapez- undSandwichelementdeckungen, 1999

http://www.jschik.de/

[11]

E. Kahlmeyer



[12]

Beuth-Kommentare

Stahlbauten



[13]

AISI S100-07/S1-09

Supplement No. 1 to the North American Specification for the Design of Cold-FormedSteelStructuralMembers, 2007 edition

August, 2009

[14]

AISI S100-07/S2-10

Supplement No. 2 to the North American Specification for the Design of Cold-FormedSteelStructuralMembers, 2007 edition

February, 2010

- 148 -


ABNT NBR 8800

ABNT NBR 8800

The beamelementsare checked according to the regulationsgiven in :

ABNT NBR 8800

Design of Steel andComposite structures for buildings

2008

Consulted articlesThe following list indicates the supported articles for this code check:

Item 5.1.2.1 cross section classificationIncluded sections I, H, U, Box, T, Circular hollow sections, I_monosymetric for both cases of fabrication: welded and hotrolled.

The routine is doing the classification for Compression and bending. The classification is done according to tables F.1 andG.1

Double anglesand other built-up sectionsare not supported.

Item 5.2 – Members subjected to tensionFully covered for sections I, H, U, Box, T, Circular hollow sections, I_monossymetric for both cases of fabrication: weldedand hot rolled.

Item5.2.4 ->calculation consideringNet area (reduction byholes) is considered using a% of reduction.

Item5.2.5 - >Ct factor must be enteredmanually.

Item5.2.8 Slendernesscheck fully covered

Double anglesand other built-up sectionsare not supported.

Item 5.3 – Members subjected to compressionItem5.3.2 - >Fully covered

Item 5.3.3 - Fully covered for sections I, H, U, Box, T, Circular hollow sections for both cases of fabrication: welded and hotrolled.

Item5.3.4 - >Slendernesscheck - Fully covered

Annex E – Elastic buckling Load

Section E.1.1 – Doubly symmetric sections and point symmetric sections.Fully covered for sections I, H, U, Box, T, Circular hollow sections for both casesof fabrication: welded and hot rolled.

Section E.1.2 – Monosymmetric sectionsFully covered for sections I, H, U, Box, T, Circular hollow sections for both casesof fabrication: welded and hot rolled.

- 149 -

Chapter 10

Section E.1.3 – Not covered

Section E.1.4 – Angles

Section E.1.4.1 - Fully covered

Section E.1.4.2 - covered considering that the angles will be always connected through thelarger leg and that they work in plane truss.

Section E.1.4.3 – not covered

Section E.1.4.4 – not coveredAnnex F – Local buckling factor

Sections F2 a) to F2 d) fully covered – Local buckling of unstiffened elements

Section F.3.1 – Fully covered

Section F.3.2 – Fully covered

Section F.4 – Fully covered

Section F.4.2 – Fully coveredItem 5.4.1 & 2 – BendingItem5.4.1.1

The FollowingCrossSectionsare supported:

- I, H doublysymmetric sectionsbent aboutmajor andminor axis

- I, H single Symmetric sectionsbent aboutmajor axis

- U Sectionsbent aboutmajor andminor axis

- T-Sectionsbent about axisperpendicular toWeb

- Boxand rectangular hollow sectionsdoublysymmetricbent about one of the symmetryaxis

- Solid circular and rectangular sectionsbent about anycentral axis

- Circular tubesbent about anyaxis that passes through the centroid

Item5.4.2.1 – Fully covered


Item5.4.2.3 –Cb factor must be enteredmanually

Item5.4.2.4 – sameas5.4.2.3

Item5.4.2.5 – not covered

AnnexG – Fully covered for section types listed above

AnnexH – (web slender) - Fully covered

- 150 -

ABNT NBR 8800

Item 5.4.3 – ShearTheFollowingCrossSectionsare supported:











Item5.4.3.4 –Not covered



Item 5.5 – Members subjected to combined forcesItem5.5.1 –Bendingmoment, normal and shear forces

The FollowingCrossSectionsare supported:








Item5.5.1.2 a) and b) – Fully covered

Item5.5.2 Torsion, normal, bending and shear forces

- 5.5.2.1Circular and rectangular hollow sectionssubjected to torsion only– fully covered

- 5.5.2.2Circular and rectangular hollow sectionssubjected to torsion, normal, bending, and shear

forces– fully covered

- 5.5.2.3 - not covered

References

[1]

ABNTNBR 8800

Design of Steel and Composite structures for buildings

2008

- 151 -

Chapter 10

ABNT NBR 14762

The beamelementsare checked according to the regulationsgiven in :

ABNT NBR 14762

Design of cold-formed steel structures

2010

Consulted articles NBR 14762The following list indicates the supported articles for this code check:

9.1.2 - maximum W/t ratios

9.2 Local buckling ( for validated crosssectionsonly, U, C, UE, ZE, HAT, L)

9.2.2 Effectivewidth of AAandAL elements

9.2.2.1Resistance

9.2.3 Effectivewidth of elementsunder uniform compressionwith edge stiffener

9.2.3.1Resistance

9.6 Design for tension ( for validated crosssectionsonly, U, C, UE, ZE, HAT, L)

9.7 Design for compression ( for validated crosssectionsonly, U, C, UE, ZE, HAT, L)

9.7.2Global buckling for flexure, torsion or flexural-torsional

9.7.2.1 Sectionwith double symmetryand point symmetrical

9.7.2.2 Single symmetric sections

9.7.2.3Non-symmetric sections

9.7.3Distortional buckling

9.8 Section under flexure ( for validated crosssectionsonly, U, C, UE, ZE, HAT, L)

9.8.2 Bendingmoment

9.8.2.1 Yielding of effective area

9.8.2.2 Lateral torsional buckling

9.8.2.3Distortional buckling

9.8.3 Shear ( for validated crosssectionsonly, U, C, UE, ZE, HAT, L)

9.8.4 Combined bending and shear forces

9.9 Combined bending and axial forces

ANNEX E - Elastic LTB Moment, for single symmetric sections bent about axis perpendicular to symmetryaxis

Design of built-up sections ( double angle, double channel, double I)

- 152 -

ABNT NBR 14762

References

[1]

ABNTNBR 14762

Design of cold-formed steel structures

2010

- 153 -

Chapter 11

SIA263:2013

SIA263 Code checkThe beamelementsare checked according to the regulationsgiven in

SIA263

Construction en acier

SIA263:2013

Material propertiesThe most common steel grades are used in SIA263. Their mechanical properties are described in table 1 SIA263. The fol-lowing table gives the yield strength for each type of grade commonlyused in function of the nominalweb thickness:

t<=40 t<=40 40<t<=100 40<t<=100

fy fu fy fu

S235

S 235235 360 215 340

S275

S 275275 430 255 410

S355

S 355355 510 335 490

S460

S 460460 550 430 530

Consulted articlesThe classification described in SIA263 is based on the calculation method. The calculation method in SIA263 distinguishesthemethod used respectively to determine the internal forcesand to perform the section and the stability check.

Aparallel can bemade between the calculationmethod of SIA263 and the section classification proposed in EN 1993.

According to SIA263 Table 5a-5b , crosssectionsare classified in 4 types:

l PP (plastic-plastic) or class1l EP (elastic-plastic) or class2l EE (elastic-elastic) or class3l EER (elastic-elastic reduced) or class4

The first letter of the classification denomination is related to the method used to calculate internal forces in the structure.The second letter indicates if we perform the section and the stability check with a elastic or a plastic approach. Finally, wemust note that the steel code SIA263 is essentially oriented for symmetrical and bisymmetrical profile like I profiles. In thepresentmodulus, other profilesare calculated byusing a classicelasticapproach (EEclassification).

The section is checked for tension, compression, shear, combination of bending and axial forces. For the stability check, thebeam element is checked for lateral torsional buckling, shear buckling, compression and bending with axial compression. Amore detailed overview for the used articles isgiven in the following table:

- 154 -

SIA263:2013

4 Analyse structurale et dimensionnement

4.1 Généralités x

4.2 Bases de l'analyse structurale et du dimensionnement x

4.3 Modélisation

4.3.1 Classification des sections

4.3.5 Résistance ultime élastique des sections

x

x

4.4 Méthode de vérification x

4.5 Stabilité

4.5.1 Flambage x

4.5.2 Déversement des poutres fléchies x

4.5.3 Voilement d' éléments plans comprimés x

4.5.4 Voilement des éléments plans cisaillés x

4.8 Situation de projet incendie

4.8.1 Principes x

4.8.2 Propriétés de l'acier en cas d'incendie x

4.8.5 Méthode de calcul simplifiée x

5 Eléments de construction

5.1 Poutres et poteaux des classes de section 1 et 2 x

5.2 Poutres et poteaux des classes de section 3 x

5.3 Poutres et poteaux des classes de section 4 x

5.5 Eléments comprimés à section composée

5.5.1 Barres étrésillonnées ( à travers de liaison) x

5.6 Poutres composées à âme pleine x

Annexe BMoment critique de déversement élastique Mcr x

Annexe CEchauffement des éléments de construction en cas d'incendie x

Annexe F Voilement par cisaillement avec raidisseurs spéciaux aux extrémités

F1 Résistance à l'effort tranchant des panneaux de l'âme x

Section classificationFor each intermediary section, the classification is determined and the proper section check is performed. The classificationcan change for each intermediary point. For each load case/combination, the critical section classification over the memberisused to perform the stability check.

So, the stability section classification can change for each load case/combination. However, for non-prismatic sections, thestability section classification isdetermined for each intermediarysection.

Slender cross-sectionThe design of a section that not satisfies the table 5 of SIA263 is always performed by using a reduced area. This clas-sification corresponds to theEERmethod. The determination of a reduced area isbased on the effectivewidth of each com-pression element in the current section (Art. 4.5.3). The using of a reduced area implies the recalculation of the shear centreposition, the inertia and the elasticmodulus.

- 155 -

Chapter 11

Sections propertiesThe holesdue to fastener are neglected in the area of a section

Lateral torsional bucklingFor double symmetric I profile, we don't have to perform any lateral torsional buckling check if NEd/Npl,Rd ≤ 0.15 and theconditionsprovided in Table 6SIA263 are satisfied. For anyother case, a LTBcheckmust be perform.

Calculationsdescribed in AnnexB for I,U andPPL can be applied to T sectionsonly if the flange is subjected to compression.Otherwise, as for section not supported by SIA263 in the LTB check, we use prescriptions given in EC3-ENV Annex F.Those rules allow us to determine an elastic critical moment for lateral torsional buckling for symmetrical (formula F.2 EC3)and non symmetrical (formula F.1. EC3) sectionsaround theminor axis.

In the case of I, U, PPL and, T onlywith compression in flange, characterised by a reduced area or not, we have to determ-ine before anycalculation irc, defined as the radiusof gyration of a section comprising the compression flange plus1/3 of thecompressionweb area, taken about an axis in the plane of theweb.


h-factorTheSIA 263 code onlydescribesone case for calculatinghwhich isused in the formula for obtainingscr,D. The onlyusecase that is covered is the onewith endmomentswhile in reality you could also have amoment diagram coming fromapoint load or line load. Below a summaryof the different use casesand their corresponding formulas for h

Moment diagram caused by endmoments

h=1,75 - 1,05 xy +0,3 xy²buty≥ -0,5

Moment diagram caused by point loads

If MEd,max ≥0 :h=1,35 xA+Bx (1,75 - 1,05 xy +0,3 xy²) buty≥ -0,5

- 156 -

SIA263:2013

If MEd,max <0 :h=Ax ( 2,75 xB+1 ) x1,35 +Bx (-1,62 xA+ 1 ) x (1,75 - 1,05 xy +0,3 xy²) buty≥ -0,5

with:

A= ( FxL ) / ( 4 xMEd,max+F xL )

B= ( 4 xMEd,max) / ( 4 xMEd,max+F xL )

Moment diagram caused by line loads

If MEd,max ≥0 :h=1,13 xA+Bx (1,75 - 1,05 xy +0,3 xy²) buty≥ -0,5

If MEd,max<0 :h=Ax (1,45 xB+1) x1,13 +Bx (-0,71 xA+ 1) x (1,75 - 1,05 xy +0,3 xy²) buty≥ -0,5

with:

A= ( q xL² ) / ( 8 xMEd,max+q xL² )

B= ( 8 xMEd,max) / ( 8 xMEd,max+q xL² )

For advanced Lateral-torsional buckling analysis, see "AnnexD: Use of sheeting " on page 205.

Use of diaphragms SeeChapter '"AnnexD: Use of sheeting " on page 205'.

Shear bucklingComposed rail sections (Iw+rail, Iwn+rail, I+rail, I+2PL+rail, I+PL+rail, I+2L+rail, I+Ud+rail) are considered as equivalentasymmetric I sections.

Stability checkFor double symmetric I profile PP or EP, SIA263 provides specific formula to perform the stability check of member sub-mitted to biaxial moment. For other sections, non symmetric or from EE and EER classification, a general formula isprovided to designmember under mono-axial solicitations.

Torsion checkFor the crosssection check inclusive torsion andwarping, we refer to Chapter "AnnexF:Warping check" on page 218.

Built-in beamsFor built- in beam sections (IFB, SFB, THQ sections), proper section checks are performed, taking into account the localplate bending. SeeChapter "AnnexH: Section check for built-in beams (IFB, SFB, THQ sections)".

- 157 -

Chapter 12

SIA263 - Fire ResistanceFire actions effect EfiThe design effects of actions for the fire situation Efi,d,t are taken from the results of the analysis. It is recommended to usethe accidental combination rules, for calculating the internal forcesused in the fire resistance check.

The accidental combination isgiven by

ΣGk +Pk +Ad+Σψ2,iQk,i

With:

Gk characteristic valuesof permanent actions

Qk,i characteristic value of the variable action i

Ad design valuesof accidental action from fire exposure

ψ2,j combination coefficients

Pk characteristic value of prestressing action

Material propertiesThematerial propertiesare depending on the steel temperature.

Strength and deformation properties:

The variation in function of the steel temperature of the value for yield strength ky,θ andmodulusof elasticity kE,θ is given bytables in ref.[1], Figure 15.

In the simplified calculationmethod, the following default propertiesare considered to be constant during the analysis :

thermal elongation Δl/l 14 x 10-6 (θa-20)

thermal conductivity λa 45 W/mK

Temperature analysis - Thermal actionsIn this part, the nominal temperature-time curves and the related net heat flux are described. For more info, EC3 Chapter"Temperature analysis - Thermal actions" on page 63

Nominal temperature-time curveSeeEC3Chapter "Nominal temperature-time curve" on page 63.

Net heat fluxSeeEC3Chapter "Net heat flux" on page 67

Steel TemperatureSeeRef.[1], AnnexeC.

- 158 -

The increase of temperature Δθa,t in an unprotected steelmember during a time intervalΔt

With:

Am the exposed surface area per unit length [m²/m]

Vthe volume of themember per unit length [m³/m]

The factor Am/V should not be taken as less than 10m-1


hnet,d the net heat fluxper unit area [W/m²]




The increase of temperature Δθa,t in an insulated steelmember during a time intervalΔt

With:




cp the specificheat of fire protectionmaterial [J/kgK]

dp the thicknessof the fire protectionmaterial [m]




ρp the unit massof fire protection [kg/m³]

θa,t the steel temperature at time t

θg,t the ambient gas temperature at time t


λp the thermal conductivityof the fire protectionmaterial [W/mK]

The valueΔθa,t ≥0.0

- 159 -

Chapter 12

The increase of temperature Δθa,t in an insulated steelmember with intumescent coating during a time intervalΔt



Pi =Ap/V


kd;ef coefficient of heat transfer of the intumescent coating




θa the steel temperature at time t

θt the ambient gas temperature at time t


λi;d;ef the thermal conductivityof the fire protectionmaterial [W/mK]

Calculation modelThe calculation can be performed in 2 domains :

n strength domainn temperature/time domain

In the strength domain, the strength Rfi,d,t(unity check) is calculated after a given time t (e.g. strength after 45 min). In thetemperature/time domain, the critical steel temperature θcr,d is computed. From this critical temperature, the fire resistancetime tfi,d is calculated (the time domain).

Code CheckThe section and stability checks (buckling, lateral torsional buckling) are performed according to the regulationsgiven inRef.[1], 4.8.5.


The following checksare executed :

l Classification of crosssection : art. 4.8.5.2.l Resistance for tensionmembers : art. 4.8.5.4.l Resistance for compressionmembers (class1,2 or 3) : art. 4.8.5.5.l Resistance for membersof class1,2,3: art. 4.8.5.6., art. 4.8.5.7., art. 4.8.5.8.l Resistance for membersof class4: art. 4.8.5.9.

- 160 -


RHS Rectangular Hollow Section

CHS Circular Hollow Section

L Angle section

U Channel section

T T section


Z Z section



COM Composed section

O Solid tube




I RHS CHS L U T PPL RS Z Σ O COM NUM

Classification x x x x x x x x (1) x (1) (1) (1)

Section check PP x x x

Section check EP x x x

Section check EE x x x x x x x x x x x x x

Section check EER x x x x x x

Stability check PP x x x x x x x x x x x x x

Stability check EP x x x x x x x x x x x x x

Stability check EE x x x x x x x x x x x x x

Stability check EER x x x x x x


LTB x x(2) x(2) x(2) x(2) x(2) x x(2) x(2) x(2) x(2) x(2) x(2)

(1) sectionsare classified asclass3 crosssection bydefault.

(2) general formula for Mcr

References[1]

SIA263

Construction en acier

- 161 -

Chapter 13

SIA263:2013

[2]

SIA263/1

Construction en acier / Spécification complémentaires

SIA263/1:2013

- 162 -

AnnexA: Profile LibraryFormcodes

Annex A: Profile Library Formcodes

Within SCIA Engineer, each shape within the Profile Library is uniquely identified by a so called Formcode. The Formcodedefines the shape, the parameters which describe the shape and in some cases also additional parameters like distancebetween bolt holes, unit warping ordinatesetc.

In thisAnnex the different Formcodesand their parametersare described.

Formcode 1: I-Section

Parameters Description

h Height

b Flange width

t Flange thickness

s Web thickness

r Radius at flange root

r1 Radius at flange toe

a Flange slope

W Internal bolt distance

wm Unit warping at flange toe

- 163 -

Chapter 14

Formcode 2: Rectangular Hollow Section


h Height

b Width

s Thickness

r Outer radius

r1 Inner radius

Formcode 3: Circular Hollow Section


d Diameter

w Thickness

- 164 -


Formcode 4: L-Section


h Height

b Width

t Thickness



W1 Bolt distance

W2 Bolt distance

W3 Bolt distance

Formcode 5: Channel Section


h Height

b Flange width

- 165 -

Chapter 14


t Flange thickness

s Web thickness



a Flange slope

wm1 Unit warping at flange root

wm2 Unit warping at flange toe

Formcode 6: T-Section


h Height

b Flange width

t Flange thickness

s Web thickness



r2 Radius at web root

a1 Flange slope

a2 Web slope

Formcode 7: Full Rectangular Section

- 166 -



h Height

b Width

Formcode 11: Full Circular Section


d Diameter

Formcode 101: Asymmetric I-Section


h Height

s Web thickness

bt Flange width top

bb Flange width bottom

- 167 -

Chapter 14


tt Flange thickness top

tb Flange thickness bottom


Formcode 102: Rolled Z-Section


h Height

b Flange width

t Flange thickness

s Web thickness



Formcode 111: Cold-Formed Angle Section

- 168 -



s Thickness

r Inner radius

b Width

h Height

Formcode 112: Cold-Formed Channel Section


s Thickness

r Inner radius

b Flange width

h Height

Formcode 113: Cold-Formed Z-Section

- 169 -

Chapter 14


s Thickness

r Inner radius

b Total width

h Height

Formcode 114: Cold-Formed C-Section


s Thickness

r Inner radius

b Flange width

h Height

c Lip

Formcode 115: Cold-Formed Omega Section

- 170 -



s Thickness

r Inner radius

b Total width

h Height

c Inner length

Formcode 116: Cold-Formed C-Section Eaves Beam


s Thickness

r Inner radius

b Flange width

h Height

c Lip

a Flange angle

Formcode 117: Cold-Formed C-Plus Section

- 171 -

Chapter 14


s Thickness

r Inner radius

b Flange width

h Height

c Lip

c2 Pluslip

a Pluslip angle

Formcode 118: Cold-Formed ZED-Section


s Thickness

r Inner radius

bt Flange width top


h Height

c Lip

- 172 -


Formcode 119: Cold-Formed ZED-Section AsymmetricLips


s Thickness

r Inner radius

bt Flange width top


h Height

ct Lip top

cb Lip bottom

Formcode 120: Cold-Formed ZED-Section Inclined Lip


s Thickness

r Inner radius

- 173 -

Chapter 14


bt Flange width top


h Height

ct Lip top

cb Lip bottom

a Lip angle

Formcode 121: Cold-Formed Sigma Section


s Thickness

r Inner radius

b Flange width

h Height

h1 Web height near flange

h2 Inner web height

c Lip

b1 Web depression

- 174 -


Formcode 122: Cold-Formed Sigma Section Stiffened


s Thickness

r Inner radius

b Flange width

h Height


h2 Inner web height

c Lip

c2 Pluslip

b1 Web depression

Formcode 123: Cold-Formed Sigma-Plus Section


s Thickness

- 175 -

Chapter 14


r Inner radius

b Flange width

h Height


h2 Inner web height

c Lip

c2 Pluslip

b1 Web depression

a Pluslip angle

Formcode 124: Cold-Formed Sigma Section EavesBeam


s Thickness

r Inner radius

b Flange width

h Height


h2 Inner web height

c Lip

b1 Web depression

a Flange angle

- 176 -


Formcode 125: Cold-Formed Sigma-Plus SectionEaves Beam


s Thickness

r Inner radius

b Flange width

h Height


h2 Inner web height

c Lip

c2 Pluslip

b1 Web depression

a Flange angle

a2 Pluslip angle

Formcode 126: Cold-Formed ZED-Section Both LipsInclined

- 177 -

Chapter 14


s Thickness

r Inner radius

bt Flange width top


h Height

ct Lip top

cb Lip bottom

a Lip angle

Formcode 127: Cold-Formed I-Plus Section


s Thickness

r Inner radius

b Flange width

h Height

c Lip

c2 Pluslip

a Pluslip angle

- 178 -


Formcode 128: Cold-Formed IS-Plus Section


s Thickness

r Inner radius

b Flange width

h Height


h2 Inner web height

c Lip

c2 Pluslip

b1 Web depression

a Pluslip angle

Formcode 129: Cold-Formed Sigma Section Asym-metric

- 179 -

Chapter 14


s Thickness

r Inner radius

bt Flange width top


h Height


h2 Inner web height

ct Lip top

cb Lip bottom

b1 Web depression

Formcode 130: Cold-Formed 2C-Section


s Thickness

r Inner radius

b Flange width

h Height

c Lip

- 180 -


Formcode 150: Rail Type KA


h1 Height

h2 Intermediate top height


b1 Width bottom

b2 Intermediate width


k Width top

f1 Intermediate bottom height



r1 Radius

r2 Radius

r3 Radius

r4 Radius

r5 Radius

a Wear

- 181 -

Chapter 14

Formcode 151: Rail Type KF


h1 Height



b1 Width bottom


k Width top



r1 Radius

r2 Radius

r3 Radius

Formcode 160: Virtual Joist

- 182 -



D Depth

B Width

TB Flange thickness

TD Web thickness

DEE Depth ofWeb

BSD MinimumBearing Seat Depth

- 183 -

Chapter 15

Annex B: Calculation of buckling ratio

Introduction to the calculation of buckling ratioFor the calculation of buckling ratio, severalmethodscan be applied.

The generalmethod isdescribed in chapter ""Calculation buckling ratio – general formula" below".

For crossing diagonals, the buckling ratio is explained in chapter ""Calculation buckling ratios for crossing diagonals" on thefacing page".

For VARH elements, the critical Euler force is calculated according to the method given in chapter ""Calculation of criticalEuler force for VARH elements" on page 189".

For lattice tower members, see the chapter ""Calculation buckling ratio for lattice tower members" on page 190".

When using member buckling data the buckling ratio can be calculated from a stability analysis. See chapter Calculation ofbuckling ratio – FromStabilityAnalysis."Buckling factors from stabilityanalysis"

Calculation buckling ratio – general formulaFor the calculation of the buckling ratios, some approximate formulas are used. These formulas are treated in reference[1], [2] and [3].

The following formulasare used for the buckling ratios (Ref[1],pp.21) :

l for a non swaystructure :

l for a swaystructure :

with:

L the system length

E themodulusof Young

I themoment of inertia

Ci the stiffness in node i

Mi themoment in node i

Fi the rotation in node i

- 184 -

AnnexB: Calculation of buckling ratio

The values for Mi andφi are approximatelydetermined by the internal forcesand the deformations, calculated by load caseswhich generate deformation forms, having an affinitywith the buckling form. (See alsoRef.[5], pp.113 andRef.[6],pp.112).

The following load casesare considered:

l load case 1 : on the beams, the local distributed loadsqy=1N/mand qz=-100N/mare used, on the columns the global dis-tributed loadsQx=10000N/mandQy=10000N/mare used.

l load case 2 : on the beams, the local distributed loadsqy=-1N/mand qz=-100N/mare used, on the columns the globaldistributed loadsQx= -10000N/mandQy= -10000N/mare used.

In addition, the following limitationsapply (Ref[1],pp.21):

l The valuesof ρi are limited to aminimumof 0.0001

l The valuesof ρi are limited to amaximumof 1000

l The indicesare determined such that ρ1≥ρ2l Specifically for the non-swaycase, if ρ1≥1000 and ρ2≤0,34 the ratio l/L is set to 0,7

The used approach gives good results for frame structures with perpendicular rigid or semi-rigid beam connections. Forother cases, the user has to evaluate the presented bucking ratios. In such cases a more refined approach (from stabilityanalysis) can be applied.

Calculation buckling ratios for crossing diagonalsFor crossing diagonal elements, the buckling length perpendicular to the diagonal plane, is calculated according to Ref.[9]EN 1993-2, TableD.2 andRef.[4], DIN18800 Teil 2, table 15.

According to thismethod the buckling length factor β isno longer purelygeometricdata but isalso dependent on the load dis-tribution in the element.

In the following chapters, the buckling length factor β isdefined,

with

β Buckling length factor

l Length of the diagonal

l1 Length of the supporting diagonal

I Moment of inertia (in the buckling plane) of the diagonal

I1 Moment of inertia (in the buckling plane) of the supporting diagonal

N Compression force in the diagonal

N1 Compression force in the supporting diagonal

Z Tension force in the supporting diagonal

E Elasticitymodulusof Young

- 185 -

Chapter 15

Continuous compression diagonal, supported by continuous tension diagonal

SeeRef.[9], TableD.2, Case 1.

Continuous compression diagonal, supported by pinned tension diagonal


- 186 -


Pinned compression diagonal, supported by continuous tension diagonal


Continuous compression diagonal, supported by continuous compressiondiagonal

- 187 -

Chapter 15


Continuous compression diagonal, supported by pinned compression diag-onal

SeeRef.[9], TableD.2, Case 3 (2).

Pinned compression diagonal, supported by continuous compression diag-onal

SeeRef.[9], TableD.2, Case 3 (3).

- 188 -


Calculation of critical Euler force for VARH elementsCalculation of critical Euler force

DefinitionAVARH element isdefined as follows :

The member has the properties of a symmetric I section (Formcode=1), where only the height is linear variable along themember. The system length for buckling around the local yy-axis (strong axis), isequal tomember length.

For thisnon-prismatic section, the criticalEuler force isgiven in the next section.

Calculation of critical Euler forceFor aVARH element we can define:

ky buckling coefficient aroundthe yy-axis

Ly system length around the yy-axis

Iy, maxmaximum moment of inertiaaround the y-axis

Iy, minminimummoment of inertiaaround the y-axis

Iy,eqequivalent moment of inertiaaround the y-axis

E modulusof Young

Ncr,ycritical Euler force around they-axis

- 189 -

Chapter 15

Hirt and Crisinel (Ref[10],pp. 291) present expressions for the elastic critical load of axially loaded non-prismatic membersof double symmetric cross-sections (i.e. I-sections formcode 1). Flexural buckling about the strong axis of the cross-sectionoccurs for:

where:

And C is a coefficient that depends on the parameter r, defined as the ratio between the minimum and the maximummomentsof inertia.

For a taperedmember:

Calculation buckling ratio for lattice tower membersWhen the national code EC-EN is selected, the buckling configurations given in the following paragraphs can be selected.These systemsare onlyused in case of L-sections (Formcode 4).

- 190 -


The following propertiesare defined:

iyy radiusof gyration around yyaxis

izz radiusof gyration around zzaxis

ivv radiusof gyration around vvaxis

When the option 'Bracing members are sufficiently supported' is activated in the buckling data, the effective slenderness isreduced as follows:

l for vv-axis :

l for yy-axis :

l for zz-axis :

Reference ismade to EN 1993-1-1 AnnexBBArticle BB.1.2 and formula (BB.1).

Default slenderness limitsFor each configuration, the limit slenderness is defined in the Setup and an additional check on this limit slenderness isexecuted. The default limit valuesare taken fromRef.[8].

Type Default Slenderness limit

Leg with symmetrical bracing 120

Leg with intermediate transverse support 120

Leg with staggered bracing 120

Secondary Bracing System 240

Single bracing 200

Single bracing with SBS 200

Cross bracing 200

Cross bracing with SBS 200 and 350 (L3)

- 191 -

Chapter 15

Type Default Slenderness limit

K bracing 200

Horizontal bracing 250

Horizontal bracing with SBS 250

DiscontinuousCross bracing with horizontal member 250

Leg with symmetrical bracing

Leg with intermediate transverse support

- 192 -


Leg with staggered bracing

Single Bracing

- 193 -

Chapter 15

Single Bracing with SBS (Secondary Bracing System)

Cross bracing

- 194 -


with

Lcom Length of compressedmember (L2 from figure)

Fcom Force in compressedmember (L2 from figure)

Fsup Force in supportingmember (member crossingmember L2)

E Modulusof Young

fy Yield strength

- 195 -

Chapter 15

Cross bracing with SBS

with

Lcom Length of compressedmember (L3 from figure)

Fcom Force in compressedmember (L3 from figure)

Fsup Force in supportingmember (member crossingmember L3)

Kb SeeChapter '"Crossbracing" on page 194'

K Bracing

- 196 -


Horizontal Bracing

with

P1 Compression load

P2 Tensile load

Horizontal Bracing with SBS

with

P1 Compression load

P2 Tensile load

- 197 -

Chapter 15

Discontinuous Cross bracing with horizontal member

with

F normal force to check

FSd actual compression force in horizontalmember

N1 tensile force in diagonal

N2 compression force in diagonal

Calculation of buckling ratio – From Stability AnalysisWhenmember buckling data from stability are defined, the critical buckling load Ncr for a prismaticmember is calculated asfollows:

UsingEuler’s formula, the buckling ratio kcan then be determined:

With:

- 198 -


λ Critical load factor for the selected stability combination

NEd Design loading in themember

E Modulusof Young

I Moment of inertia

s Member length

In case of a non-prismatic member, the moment of inertia is taken in the middle of the ele-ment.

References

[1]

HandleidingmoduulSTACO VGI

StaalbouwkundigGenootschap

StaalcentrumNederland

5684/82

[2]

Newmark N.M. A simple approximate formula for effective end- fixity ofcolumns

J.Aero.Sc. Vol.16 Feb.1949 pp.116

[3]

Stabiliteit voor de staalconstructeur

uitgaveStaalbouwkundigGenootschap

[4]

DIN18800 Teil 2

Stahlbauten : Stabilitätsfälle, Knicken vonStäben undStabwerken

November 1990

[5]

Rapportnr. BI-87-20/63.4.3360

Controleregels voor lijnvormige constructie-elementen

IBBCMaart 1987

[6]

StaalconstructiesTGB1990

Basiseisen en basisrekenregels voor overwegend statisch belaste con-structies

NEN 6770, december 1991

[7] Y.Galéa

- 199 -

Chapter 15

Flambement despoteauxà inertie variable

ConstructionMétallique 1-1981

[8]

NEN-EN 50341-3-15

Overhead electrical linesexceedingAC 45 kV - Part 3: Set of NationalNorm-ative Aspects

Number 15: NationalNormative Aspects (NNA) for TheNetherlands

[9]

Eurocode 3


Part 2: SteelBridges

EN 1993-2: 2006

[10]

ECCSEurocodeDesignManuals

Eurocode 3: Design of steel structures

Part 1-1: General rulesand rules for buildings

1st edition, 2010

- 200 -

AnnexC: Calculation ofmoment factors for LTB

Annex C: Calculation of moment factors for LTB

Introduction to the calculation of moment factorsFor determining the moment factors C1 and C2 for lateral torsional buckling (LTB), we use the standard tables which aredefined inRef.[1] Art.12.25.3 table 9.1.,10 and 11.

The current moment distribution is compared with several standard moment distributions. These standard moment dis-tributions are moment lines generated by a distributed q load, a nodal F load, or where the moment line ismaximum at thestart or at the end of the beam.

The standard moment distribution which is closest to the current moment distribution, is taken for the calculation of thefactorsC1 andC2.

The factor C3 is taken out of the tablesF.1.1. and F.1.2. fromRef.[2] - AnnexF.

Calculation moment factorsMoment distribution generated by q load

For ENV 1993, IS800 and CM66if M2 <0

C1=A* (1.45 B* +1) 1.13 +B* (-0.71 A* +1) E*

C2=0.45A* [1 +C* eD* (½ β+½)]

if M2 >0

C1=1.13A* +B* E*

C2=0.45A*

For DIN18800 and ONORM4300if M2 <0

C1=A* (1.45 B* +1) 1.12 +B* (-0.71 A* +1) E*

C2=0.45A* [1 +C* eD* (½ β+½)]

if M2 >0

C1=1.12A* +B* E*

- 201 -

Chapter 16

C2 =0.45A*

with :

For DIN18800 / ONORM 4300

For ENV 1993 and IS800

For NEN6770/6771, SIA263E*=1.75-1.05*β+0.30*β² andE*<2.3

For CM66

Moment distribution generated by F load

M2<0

C1=A** (2.75 B** +1) 1.35 +B** (-1.62 A** +1) E**

C2=0.55A** [1 +C** eD** (½ β+½)]

M2 >0

C1=1.35A** +B** E**

C2=0.55A**

with :

- 202 -

AnnexC: Calculation ofmoment factors for LTB

The values for E** can be taken asE* from chapter "Moment distribution generated byq load" on page 201.

Moment line with maximum at the start or at the end of the beam

C2=0.0

For DIN18800 / ONORM 4300

For ENV 1993 / IS800

For CM66

For NEN6770/6771, SIA263 CodeE*=1.75-1.05*β+0.30*β² andE*<2.3

References

[1]

StaalconstructiesTGB1990

Stabiliteit

NEN 6771 - 1991

[2]Eurocode 3 : Design of steel structures

Part 1-1 : General rulesand rules for buildings

- 203 -

Chapter 16

ENV1993-1-1:1992

- 204 -

AnnexD: Use of sheeting

Annex D: Use of sheeting

Adaptation of torsional constant SeeRef.[1], Chapter 10.1.5., Ref.[2],3.5 andRef.[3],3.3.4..

When steel sheeting is used, the torsional constant It is adapted for symmetric/asymmetric I sections, channel sections, Zsections, cold formedU, C , Z sections.

The torsional constant It isadaptedwith the stiffnessof the sheeting:

with

l the LTB length

G the shear modulus

vorhCθ the actual rotational stiffnessof sheeting

CθM,k the rotational stiffnessof the sheeting

CθA,k the rotational stiffnessof the connection between the sheeting and the beam

CθP,k the rotational stiffnessdue to the distortion of the beam

k

numerical coefficient

=2 for single or two spansof the sheeting

=4 for 3 or more spansof the sheeting

EIeff bending stiffnessof per unit width of the sheeting

- 205 -

Chapter 17

s spacing of the beam

ba thewidth of the beam flange (inmm)

C100 rotation coefficient - see table

h beamheight

t thicknessbeam flange

s thicknessbeamweb

References

[1]

ENV1993-1-3:1996

Eurocode 3 : Design of steel structures

Part 1-3 : General rules

Supplementary rules for cold formed thin gaugemembersand sheeting

CEN 1996

- 206 -

AnnexD: Use of sheeting

[2]

E. Kahlmeyer



[3]

Beuth-Kommentare

Stahlbauten



- 207 -

Chapter 18

Annex E: Lateral Torsional Buckling 2nd Order Ana-lysis

Introduction to LTBIIFor a detailed Lateral TorsionalBuckling analysis, a linkwasmade to the Friedrich +Lochner LTBII applicationRef.[1].

The FriLo LTBII solver can be used in 2 separateways:

1. Calculation ofMcr through eigenvalue solution2. 2ndOrder calculation including torsional andwarping effects

For both methods, the member under consideration is sent to the FriLo LTBII solver and the respective results are sentback to SCIAEngineer.

Adetailed overview of bothmethods isgiven in the following chapters.

Eigenvalue solution McrThe single element is taken out of the structure and considered asa single beam,with:

l Appropriate end conditions for torsion andwarpingl End and begin forcesl Loadingsl Intermediate restraints (sheetings, LTB restraints)

The end conditions for warping and torsion are defined as follows:

Cw_i Warping condition at end i (beginning of themember)

Cw_j Warping condition at end j (end of themember)

Ct_i Torsion condition at end i (beginning of themember)

Ct_j Torsion condition at end j (end of themember)

To take into account loading and stiffnessof linked beams, see chapter "LinkedBeams" on page 215”.

For this system, the elastic criticalmoment Mcr for lateral torsional buckling can be analyzed as the solution of an eigenvalueproblem:

with

η Critical load factor

Ke Elastic linear stiffnessmatrix

Kg Geometrical stiffnessmatrix

- 208 -

AnnexE: Lateral TorsionalBuckling 2ndOrder Analysis

For memberswith arbitrarysections, the criticalmoment can be obtained in each section, with: (SeeRef.[3],pp.176)

with

η Critical load factor

Myy Bendingmoment around the strong axis

Myy(x) Bendingmoment around the strong axisat position x

Mcr(x) Criticalmoment at position x

The calculatedMcr is then used in the Lateral TorsionalBuckling checkof SCIAEngineer.

For more background information, reference ismade toRef[2].

2nd Order analysisThe single element is taken out of the structure and considered asa single beam,with:

l Appropriate end conditions for torsion andwarpingl End and begin forcesl Loadingsl Intermediate restraints (sheetings, LTB restraints)l Imperfections

To take into account loading and stiffnessof linked beams, see chapter "LinkedBeams" on page 215.

For this system, the internal forcesare calculated using a 2ndOrder 7 degreesof freedomcalculation.

- 209 -

Chapter 18

The calculated torsional and warping moments (St Venant torque Mxp, Warping torque Mxs and Bimoment Mw) are thenused in theStresscheckof SCIAEngineer (See chapter "AnnexF:Warping check" on page 218).

Specifically for this stresscheck, the following internal forcesare used:

o Normal force fromSCIAEngineero Maximal shear forces fromSCIAEngineer / FriLo LTBIIo Maximal bendingmoments fromSCIAEngineer / FriLo LTBII

Since Lateral TorsionalBuckling hasbeen taken into account in this2ndOrder stresscheck, it is nomore required to executea Lateral TorsionalBucklingCheck.

For more background information, reference ismade toRef[2].

Supported National CodesThe following codesare supported for the analysisofMcr.

l EC3 - ENVl EC3 - ENl DIN18800l ONORMl NENl SIAl ISl EAE

For the following national codes, the 2ndOrder analysisapproach issupported.

l EC3 - ENVl EC3 - ENl DIN18800l ONORMl NENl SIAl EAE

Supported SectionsThe following table showswhich cross-section typesare supported for which type of analysis:

FRILO LTBII CSS SCIA Engineer CSSEigenvalue

analysis

2ndOrder

analysis

Double T I section from library x x

Thin walled geometric I x x

Sheet welded Iw x x

Double T unequal IPY from library x x

- 210 -


FRILO LTBII CSS SCIA Engineer CSSEigenvalue

analysis

2ndOrder

analysis

Thin walled geometric asymmetric I x x

Haunched sections x x

Welded I+Tl x x

Sheet welded Iwn x x

HATSection IFBA, IFBB x x

U cross section U section from library x x

Thin walled geometric U x x

Thin walled Cold formed from library x x

Cold formed from graphical input x x

Double T with top flange angle Welded I+2L x

Sheet welded Iw+2L x

Rectangle Full rectangular from library x

Full rectangular from thin walled geometric x

Static values double symmetric all other double symmetric CSS x

Static values single symmetric all other single symmetric CSS x

Remark: Haunched sectionsare replaced byequivalent asymmetric I sections, by ignoring themiddle flanges.

The following picture illustrates the relation between the local coordinate system of SCIAEngineer and FriLo LTBII. Specialattention is required for U sectionsdue to the inversion of the yand z-axis.

For more information, reference ismade toRef[2]

- 211 -

Chapter 18

LoadingsThe following load impulsesare supported:

l Point force in node (if the node ispart of the exported beam)l Point force on beaml Line force in beaml Moment in node (if the node ispart of the exported beam)l Moment on beaml Linemoment in beam (only for Mx in LCS)

The supported load impulsesand their eccentricitiesare transformed into the local LCSof the exportedmember.

The dead load is replaced byan equivalent line force on the beam.

Load eccentricitiesare replaced by torsionalmoments.

The forces in local x-direction are ignored, except for the torsionalmoments.

In Frilo LTBII a distinction is made between the centroid and the shear center of a cross-section. Load impulseswhich do not pass through the shear center will cause additional tor-sionalmoments.

ImperfectionsIn the 2nd Order LTB analysis the bow imperfections v0 (in local y direction) and w0 (in local z direction) can be taken intoaccount.

For DIN, ONORM, EC-EN and EAE the imperfections can be calculated according to the code. The codes indicate that fora 2ndOrder calculationwhich takes into account LTB, only the imperfection v0 needs to be considered.

The sign of the imperfection according to code dependson the sign ofMz in SCIAEngineer.

Initial bow imperfection v0 for DIN and ONORMThe imperfection is calculated according toRef.[6] article 2.2

For prismaticuniformmembers:

- 212 -


Resistance check Section Bucking curve v0

EE

(Elastic)any a0 L/1050

any a L/900

any b L/750

any c L/600

any d L/450

EP

PP

(Plastic)

I section a0 L/700

I section a L/600

I section b L/500

I section c L/400

I section d L/300

For non-uniformmembers, the bow imperfection is considered at the centre of the buckling system length L.

Initial bow imperfection v0 for EC-EN and EAEThe imperfection is calculated according toRef.[4] article 5.3.4(3)

with:

kFactor taken from theNationalAnnexof EC-EN

Factor taken as0,5 for EAE

e0 Bow imperfection of theweakaxis

The value of e0 is taken from following table:

Buckling curve eo /L – elastic analysiseo/L – plastic analysis

a0 1/350 1/300

a 1/300 1/250

b 1/250 1/200

c 1/200 1/150

d 1/150 1/100

with

L Member system length

- 213 -

Chapter 18

Initial bow imperfections v0 and w0 for other supported codesFor all other supported codes (EC-ENV, NEN and SIA) as well as DIN, ONORM, EC-EN and EAE the user can manuallyinput the imperfectionsv0 andw0.

LTB RestraintsLTB restraintsare transformed into 'Supports' (Ref.[2] p22), with horizontal elastic restraint Cy:

Cy=1e15 kN/m

The position of the restraint z(Cy) isdepending on the position of the LTB restraint (top/bottom).

The use of an elastic restraint allows the positioning of the restraint since this isnot possible for a fixed restraint. (Ref.[2] p23)

Specifically for U-sections, an elastic restraint Cz is used with position y(Cz) due to the rotation of U-sections in the FriLoLTBII solver. (seeChapter "Supported Sections" on page 210)

SheetingsSheetings are transformed into 'Elastic Foundations' of type ‘elastic restraint’ (Ref.[2] p25). Both a horizontal restraint Cyand a rotational restraint Cθ are used.

The elastic restraint Cy [kN/m^2] is calculated as follows (Ref.[2] p52 andRef.[5] p40):

with

S Shear stiffnessof the sheeting

L Sheeting length along themember

The above formula for Cy is valid in case the bolt pitch of the sheeting is set as ‘br’. For a bolt pitch of ‘2br’ the shear stiffnessS is replaced by0,2 S (Ref.[5] p22).

The shear stiffnessS for a sheeting is calculated as follows (Ref.[7],3.5 andRef.[8],3.3.4.):

- 214 -


with

a Frame distance

Ls Length of the sheeting

K1 Factor K1 of the sheeting

K2 Factor K2 of the sheeting

The position of the restraint z(Cy) isdepending on the position of the sheeting.

Specifically for U-sections, an elastic restraint Cz is used with position y(Cz) due to the rotation of U-sections in the FriLoLTBII solver. (seeChapter "Supported Sections" on page 210)

The rotational restraint Cθ [kNm/m] is taken asvorhCθ (seeChapter "Adaptation of torsional constant " on page 205)

Linked BeamsLinked beamsare transformed into 'Supports' (Ref.[2] p22), with elastic restraint.

The direction of the restraint isdependent on the direction of the linked beam:

If the linked beam hasan angle less then 45°with the local y-axis of the beam under consideration, the restraint is set asCy.In all other cases the restraint is set asCz.

The position of the restraint z(Cy) or y(Cz) isdepending on the application point of the linked beam (top/bottom).

The position isonly taken into account in case of a flexible restraint (Ref.[2] p23).

The end forcesof the linked beamare transformed to point loadson the considered 1Dmember,

l in z -direction for linked beamsconsidered asy-restraintl in y- direction for linked beamsconsidered asz-restraint

- 215 -

Chapter 18

Specifically for U-sections, if the linked beam has an angle less then 45° with the local y-axis of the beam under con-sideration, the restraint is set asCz. In all other cases the restraint is set asCy. This is due to the rotation of U-sections in theFriLo LTBII solver. (seeChapter "Supported Sections" on page 210)

Limitations and WarningsTheFRILO LTBsolver isusedwith following limitations

l Onlystraightmembersare supportedl LTBII analysis isdone for thewhole 1Dmember, not for a part of themember, not for moremembers togetherl When a LTBsystem length is inputtedwhich differs from themember length, awarningwill be given.

Intermediate lateral restraints should be defined through LTB restraints, sheetingsand linked beams.

During the analysis, the FriLo LTBII solver may return a warningmessage. Themost important causesof the warningmes-sage are listed here.

Eigenvalue solution McrLateral TorsionalBuckling isnot governing – relative slenderness<0,4

Due to the low relative slenderness, no LTBcheckneeds to be performed. In this case it is not required to use theFriLo LTBII solver.

Design Torsion! Simplified analysisof lateral torsional buckling isnot possible.

Due to the torsion in themember it isadvised to execute a 2nd order analysis instead of an eigenvalue calculation.

Bending of U-section about y-axis!

The programcalculates theminimumbifurcation load only.

2nd Order Analysis

Load isgreater thenminimumbifurcation load (Error at elastic calculation – system is instable in II.Order )

The loading on themember is too big, a 2nd order calculation cannot be executed.

You want to calculate the structural safety with Elastic-Plasticmethod. This analytical procedure cannot be usedfor this cross-section. It is recommended to use theElastic-Elasticmethod.

Plastic calculation isnot possible, use imperfection according to code elastic instead of plastic.

For more information, reference ismade toRef[1] and [2].

References

[1]

FriLo LTBII softwareFriedrich + Lochner Lateral Torsional Buckling 2 nd Order AnalysisBiegetorsionstheorie II.Ordnung (BTII)

http://www.frilo.de

[2]Friedrich + Lochner LTBII ManualBTII HandbuchRevision 1/2006

- 216 -

http://www.frilo.de/


[3]

J.Meister

NachweispraxisBiegeknicken undBiegedrillknicken

Ernst &Sohn, 2002

[4]

Eurocode 3



EN 1993-1-1:2005

[5]

J. Schikowski

Stabilisierung vonHallenbauten unter besonderer Berücksichtigung der Scheiben-wirkung von Trapez- und Sandwichelementdeckungen, 1999http://www.jschik.de/

[6]

DIN 18800 Teil 2

Stahlbauten

Stabilitätsfälle, Knicken vonStäben undStabwerken

November 1990

[7]

E. Kahlmeyer



[8]

Beuth-Kommentare

Stahlbauten



- 217 -


Chapter 19

Annex F: Warping check

Stress checkIn crosssectionssubject to torsion, the following is checked:

with

fy the yield strength

σtot,Ed

the total direct stress

τtot,Ed

the total shear stress

γM=γM0 (class1,2 and 3 section)

=γM1 (class4 section)

γM0the partial safety factor for resistance of cross-sectionswhere failure is causedbyyielding

γM1the partial safety factor for resistance of cross-sectionswhere failure is causedbybuckling

σN,Ed

the direct stressdue to the axial force on the relevant effective cross-section

σMy,Ed

the direct stress due to the bending moment around y axis on the relevanteffective cross-section

σMz,Ed

the direct stress due to the bending moment around z axis on the relevanteffective cross-section

σ the direct stressdue towarping on the grosscross-section

- 218 -

AnnexF:Warping check

w,Ed

τVy,Ed

the shear stressdue to shear force in ydirection on the grosscross-section

τVz,Ed

the shear stressdue to shear force in zdirection on the grosscross-section

τt,Ed the shear stressdue to uniform (St. Venant) torsion on the grosscross-section

τw,Ed the shear stressdue towarping on the grosscross-section

The warping effect is considered for standard I sections and U sections, and for Σ (= “cold formed sections”) sections. Thedefinition of I sectionsandU sections, and Σ sectionsare described in "AnnexA: Profile LibraryFormcodes" on page 163.

The other standard sections ( RHS, CHS, Angle section, T section and rectangular sections) are considered as warpingfree. See alsoRef.[2], Bild 7.4.40.

Calculation of the direct stress due to warpingThe direct stressdue towarping isgiven by (Ref.[2] 7.4.3.2.3, Ref.[3])

with

Mw the bimoment

wM the unit warping

Cm thewarping constant

I sectionsFor I sections, the value of wM is given in the tables (Ref. [2], Tafel 7.87, 7.88). This value is added to the profile library. Thediagramof wM is given in the following figure:

- 219 -

Chapter 19

The direct stressdue towarping is calculated in the critical points (see circles in figure).

The value for wMcan be calculated by (Ref.[5] pp.135) :

b the sectionwidth

hm the section height (see figure)

U sectionsFor U sections, the value of wM is given in the tables aswM1 and wM2 (Ref. [2], Tafel 7.89). These values are added to theprofile library. The diagramof wM is given in the following figure :

The direct stressdue towarping is calculated in the critical points (see circles in figure).

Σ sectionsThe values for wM are calculated for the critical points according to the general approach given in Ref.[2] 7.4.3.2.3 and Ref.[8] Part 27.

The critical points for each part are shown ascircles in the figure.

- 220 -


Calculation of the shear stress due to warpingThe shear stressdue towarping isgiven by (Ref.[2] 7.4.3.2.3, Ref.[3])

Mxs

the warping torque (see "Standard diagrams for warping torque, bimoment andtheSt.Venant torsion" on page 225)

wM

the unit warping

Cm

thewarping constant

t the element thickness

I sectionsThe shear stressdue towarping is calculated in the critical points (see circles in figure)

For I sections, we have the following :

U sections, Σ sectionsStarting from thewM diagram, we calculate the value

for the critical points.

- 221 -

Chapter 19

The shear stressdue towarping is calculated in these critical points (see circles in figures)

Plastic CheckFor doublysymmetric I sectionsof class1 and class2 (plastic check), the interaction formula given inRef.[10] isused.

Used variables

Section Properties

A sectional area

b width

H heigth of section

tf flange thickness

- 222 -


Section Properties

tw web thickness

h = H - tfAw = 1.05 (h+tf) tw for rolled section

Aw = h tw for welded sections

Wz,pl plastic section modulus around z axis

Wy,pl plastic section modulus around y axis

Material Properties

fy,d yield strength

τy,d shear strength

Internal forces

NSd normal force

My,Sd bending moment around y axis

Mz,Sd bending moment around z axis

Mw,Sd bimoment

Vy,Sd shear force in y direction

Vz,Sd shear force in z direction

Mxp,Sd torque due to St. Venant

Mxs,Sd warping torque

Plastic capacities

Npl,Rd = A fy,dMz,pl,Rd =Wz,pl fy,dVz,pl,Rd = Aw τy,d

My,pl,Rd =Wy,pl fy,d

Vy,pl,Rd = Af τy,d

- 223 -

Chapter 19

Section Properties

Shear force reduction

- 224 -


Section Properties

Sign

p=sign ( Mz,Sd xMw,Sd)

Unity checks:

Remark: the valuesbetween {} must be >0.

Standard diagrams for warping torque, bimoment andthe St.Venant torsionThe following 6 standard situationsare given in the literature (Ref.[2], Ref.[3]).

The value λ isdefined as follows :

- 225 -

Chapter 19

Mxthe total torque

=Mxp +Mxs

Mxp the torque due to St. Venant

Mxs thewarping torque

Mw the bimoment


Cm thewarping constant


G the shear modulus

Torsion fixed ends, warping free ends, local torsional loading Mt

Mx

Mxp for a side

Mxp for b side

- 226 -


Mxs for a side

Mxs for b side

Mw for a side

Mw for b side

Torsion fixed ends, warping fixed ends, local torsional loading Mt

Mx

Mxp for a side

Mxp for b side

Mxs for a side

Mxs for b side

Mw for a side

- 227 -

Chapter 19

Mw for b side

Torsion fixed ends, warping free ends, distributed torsional loading mt

Mx

Mxp

- 228 -


Mxs

Mw

Torsion fixed ends, warping fixed ends, distributed torsional loading mt

Mx

Mxp

Mxs

Mw

- 229 -

Chapter 19

One end free, other end torsion and warping fixed, local torsional loading Mt

Mx

Mxp

Mxs

Mw

One end free, other end torsion and warping fixed, distributed torsional load-ing mt

Mx

- 230 -


Mxp

Mxs

Mw

Decomposition of arbitrary torsion lineSince the SCIA Engineer solver does not take into account the extra DOF for warping, the determination of the warpingtorque and the related bimoment, isbased on some standard situations.

The following end conditionsare considered:

l warping free

l warping fixed

This results in the following 3 beamsituations :

l situation 1 : warping free / warping free

l situation 2 : warping free / warping fixed

l situation 3 : warping fixed / warping fixed

- 231 -

Chapter 19

Decomposition for situation 1 and situation 3The arbitrary total torque line isdecomposed into the following standard situations:

l n number of torsion linesgenerated bya local torsional loadingMtnl one torsion line generated bya distributed torsional loadingmtl one torsion linewith constant torqueMt0

The values for Mxp, Mxs and Mw are taken from the previous tables for the local torsional loadingsMtn and the distributedloadingmt. The valueMt0 is added to theMxp value.

Decomposition for situation 2The arbitrary total torque line isdecomposed into the following standard situations:

l n number of torsion linesgenerated bya local torsional loadingMtnl one torsion line generated bya distributed torsional loadingmt

The values for Mxp, Mxs and Mw are taken from the previous tables for the local torsional loadingsMtn and the distributedloadingmt.

References

[1]

ENV1993-1-3:1996

Eurocode 3 : Design of steel structures

Part 1-3 : General rules– Supplementary rules for cold formed thin gaugemem-bersand sheeting

CEN 1996

[2]

Stahl imHochbau

14. AuglageBand I/ Teil 2

Verlag StahleisenmbH, Düsseldorf 1986

[3]

Kaltprofile

3. Auflage

Verlag StahleisenmbH, Düsseldorf 1982

[4]Roik, Carl, Lindner

Biegetorsionsprobleme gerader dünnwandiger Stäbe

- 232 -


Verlag vonWilhemernst &Sohn, Berlin 1972

[5]

Dietrich vonBerg

Krane undKranbahnen –BerechnungKonstruktion Ausführung

B.G. Teubner, Stuttgart 1988

[6]

DASt-Richtlinie 016

Bemessung und konstruktive Gestaltung von Tragwerken aus dünnwandigenkaltgeformtenBauteilen

Stahlbau-Verlagsgesellschaft, Köln 1992

[7]

EsaPrimaWin

SteelCodeCheckManual

SCIA

EPW3.10

[8]

C. Petersen

Stahlbau : Grundlagen der Berechnung und baulichen Ausbildung von Stahl-bauten

Friedr. Vieweg&Sohn, Braunschweig 1988

[9]

Eurocode 3



ENV1993-1-1:1992, 1992

[10]

I. Vayas,

Interaktion der plastischen Grenzschnittgrössen doppelsymmetrischer I-Quer-schnitte

Stahlbau 69 (2000), Heft 9

- 233 -

Chapter 20

Annex G: Check of numerical sections

Stress checkThe stresscalculation for a numerical section isas follows:

with

σvm the VonMisesstress, the composed stress

σtot the total normal stress

τtot the total shear stress

σN the normal stressdue to the normal forceN

σMy the normal stress due to the bendingmomentMyyaround yaxis

σMz the normal stressdue to the bendingmomentMzzaround zaxis

τVy the shear stressdue to shear force Vy in ydirection

τVz the shear stressdue to shear force Vz in zdirection

Ax the sectional area

Ay the shear area in ydirection

Az the shear area in zdirection

Wy the elastic sectionmodulusaround yaxis

Wz the elastic sectionmodulusaround zaxis

- 234 -

Steel Code Check - SCIA Help

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