92311182 steel code check theory enu

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TheorySteel Code Check


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TABLE OF CONTENTS

EC 3 ENV 1993.............................................................................................................2

EC3 code check ...................................................................................................................................................2

Material properties...........................................................................................................................................2

Consulted articles............................................................................................................................................3

Classification of sections ..........................................................................................................................4

Effective cross-section properties for class 4 cross-section ...................................................................5

Section properties.....................................................................................................................................5

Bending moment.......................................................................................................................................5

Bending, shear and axial force.................................................................................................................5Torsion check............................................................................................................................................5

Built-in beams .............. ................ ................. ................ ................. ................. ................ ................. .........6

Compression members ............................................................................................................................6

Lateral-torsional buckling .........................................................................................................................6

Use of diaphragms....................................................................................................................................6

Shear buckling check ...............................................................................................................................7

Shear buckling check for cold formed sections .......................................................................................7

Stability check for torsional buckling and torsional-flexural buckling ......................................................8

Bending and axial compression .............................................................................................................11

Battened compression members ...........................................................................................................11

EC3 - Fire Resistance ................ ................. ................ ................. ................ ................. ............... ................. .....12

Fire actions effect Efi .....................................................................................................................................12

Material properties.........................................................................................................................................13Temperature analysis - Thermal actions ......................................................................................................13

Nominal temperature-time curve ..................................................................................................................13

Net heat flux...................................................................................................................................................14

Steel Temperature.........................................................................................................................................15

Calculation model..........................................................................................................................................16

Code Check ................ ................. ................ ................. ................ ................. ................ ................ ................16

Supported sections ...........................................................................................................................................17

References..........................................................................................................................................................18

EC 3 EN 1993 .............................................................................................................20

EC3 code check .................................................................................................................................................20

Material properties.........................................................................................................................................20Consulted articles ............... ................ ................. ................. ................ ................. ................ ................. .......22

Classification of sections ........................................................................................................................23

Effective cross-section properties for class 4 cross-section .................................................................24

Section properties...................................................................................................................................24

Torsion check..........................................................................................................................................24

Built-in beams .............. ................ ................. ................ ................. ................. ................ ................. .......24

Compression members ..........................................................................................................................24

Lateral-torsional buckling .......................................................................................................................24

Use of diaphragms..................................................................................................................................25

Combined bending and axial compression............................................................................................25

Shear buckling check .............................................................................................................................26

EC3 EN Fire Resistance ............... ............... ................. ................ ................. ................. ................ ................26


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Fire actions effect Efi .....................................................................................................................................26

Material properties.........................................................................................................................................27

Temperature analysis - Thermal actions ......................................................................................................27

Nominal temperature-time curve............................................................................................................27Net heat flux............................................................................................................................................28



Code Check ................ ................. ................ ................. ................ ................. ................ ................ ................31


References..........................................................................................................................................................32

DIN18800.......................................................................................................................34

DIN18800 Code check .......................................................................................................................................34


Consulted articles ............... ................ ................. ................. ................ ................. ................ ................. .......35


Net area properties ............... ............... ................. ................ ................. ................. ................ ................37Plastic interaction formula for RHS section ...........................................................................................38

Plastic interaction formula for CHS section ...........................................................................................40

Torsion check..........................................................................................................................................42

Built-in beams .............. ................ ................. ................ ................. ................. ................ ................. .......42

Calculation of the buckling length ..........................................................................................................42

Torsional buckling...................................................................................................................................42


LTB Check .............. ................ ................. ................ ................. ............... ................. ................. .............44

Combined flexion for check method 2....................................................................................................48


Effective area properties.........................................................................................................................49


Shear buckling check with buckling influence .......................................................................................50Cold formed thin gauge members ................................................................................................................50


References..........................................................................................................................................................52

ONORM B 4300.............................................................................................................54

ONORM B 4300 Code check.............................................................................................................................54




References..........................................................................................................................................................56

NEN...............................................................................................................................58

NEN6770/6771 Code check...............................................................................................................................58





Effective cross-section properties for class 4 cross-section .................................................................62

Torsion check..........................................................................................................................................62

Built-in beams .............. ................ ................. ................ ................. ................. ................ ................. .......62

Buckling length........................................................................................................................................62





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Shear buckling check with buckling influence .......................................................................................65

NEN6072 - Fire Resistance ...............................................................................................................................65

Fire actions effect ............... ................ ................. ................. ................ ................. ................ ................. .......66Material properties.........................................................................................................................................66

Nominal temperature-time curve ..................................................................................................................67



Code Check ................ ................. ................ ................. ................ ................. ................ ................ ................70


References..........................................................................................................................................................72

AISC ASD : 1989........................................................................................................73

AISC - ASD Code check ............... ................ ................. ................. ............... ................. ................ ................. ..73

Classification of sections...............................................................................................................................75

Section properties .........................................................................................................................................75

Buckling length .............. ................ ................. ................ ................. ............... ................. ................. .............75

Flexural Torsional Buckling ...........................................................................................................................75

Lateral-torsional buckling ..............................................................................................................................75

Shear buckling check ............... ................ ................. ................. ............... ................. ................ ................. ..76


References..........................................................................................................................................................77

AISC LRFD : 2001......................................................................................................79

AISC - LRFD Code check ................ ............... ................. ................. ................ ................. ................ ................79



Buckling length .............. ................ ................. ................ ................. ............... ................. ................. .............81

Lateral-torsional buckling ..............................................................................................................................81Use of diaphragms ................ ................. ................ ................. ................ ................. ............... ................. .....82



References..........................................................................................................................................................83

ANSI/AISC 360-05:2005 ................................................................................................84

ANSI/AISC 360-05 Code check.........................................................................................................................84



Buckling length .............. ................ ................. ................ ................. ............... ................. ................. .............86

Lateral-torsional buckling ..............................................................................................................................86

Use of diaphragms ................ ................. ................ ................. ................ ................. ............... ................. .....86



References..........................................................................................................................................................87

CM66.............................................................................................................................88

CM66 Code check .............. ................ ................. ................ ................. ............... ................. ................. .............88



Plastic coefficient ............... ................ ................. ................. ............... ................. ................ ................. ..90


Factor kf ............... ................ ................. ................. ................ ................. ................ ................. ...............90

LTB Check .............. ................ ................. ................ ................. ............... ................. ................. .............90


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Combined flexion ............... ................ ................. ................. ............... ................. ................ ................. ..90



References..........................................................................................................................................................91

CM66 - Additif 80..........................................................................................................93

CM66 - Additif 80 Code check ................ ................. ................ ................. ............... ................. ................ ........93



Section check..........................................................................................................................................94





References..........................................................................................................................................................95

BS5950-1:1990..............................................................................................................96

BS5950-1:1990 Code Check .............................................................................................................................96




Slender cross-section .............................................................................................................................99


Bending moment.....................................................................................................................................99

Bending, shear, axial force.....................................................................................................................99

Lateral torsional buckling..................................................................................................................... 100

Use of diaphragms............................................................................................................................... 101

Compression member ......................................................................................................................... 101

Shear buckling check .......................................................................................................................... 101Supported sections ........................................................................................................................................ 101

References....................................................................................................................................................... 102

BS5950-1:2000............................................................................................................103

BS5950-1:2000 Code Check .......................................................................................................................... 103

Material properties...................................................................................................................................... 103

Governing code clauses............................................................................................................................ 104

Classification of sections ..................................................................................................................... 106

Slender cross-sections ........................................................................................................................ 106

Section properties................................................................................................................................ 106

Moment capacity.................................................................................................................................. 106

Bending, shear, axial force/capacity interaction ................................................................................. 106

Lateral torsional buckling due to major axis moments ....................................................................... 107Torsional buckling about an eccentric axis (Annex G) ....................................................................... 107

Lateral buckling due axial compression.............................................................................................. 107

Combined axial and bending buckling unity check/utilisation ............................................................ 107

Torsion effects ..................................................................................................................................... 108

Supported sections ........................................................................................................................................ 108

SIA263.........................................................................................................................109

SIA263 Code check......................................................................................................................................... 109


Consulted articles ....................................................................................................................................... 109

Section classification ........................................................................................................................... 110

Slender cross-section .......................................................................................................................... 111


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Sections properties .............................................................................................................................. 111



Shear buckling ..................................................................................................................................... 111Stability check ...................................................................................................................................... 112

Torsion check....................................................................................................................................... 112

Built-in beams ...................................................................................................................................... 112

SIA263 - Fire Resistance................................................................................................................................ 112

Fire actions effect Efi ................ ................. ................ ................. ............... ................. ................ ................ 112


Temperature analysis - Thermal actions ................................................................................................... 113

Nominal temperature-time curve ............................................................................................................... 113

Net heat flux................... ................. ................ ................. ............... ................. ................ ................. .......... 113

Steel Temperature...................................................................................................................................... 113

Calculation model....................................................................................................................................... 114

Code Check ................................................................................................................................................ 115


References....................................................................................................................................................... 116

GBJ 17-88 ...................................................................................................................117

The GBJ 17-88 code check ............... ................ ................. ................. ................ ................. ................ .......... 117




Shear buckling check .......................................................................................................................... 119

Buckling curves.................................................................................................................................... 119

Buckling length..................................................................................................................................... 120


Local stability of compressed members.............................................................................................. 120



References....................................................................................................................................................... 121

Korean steel code check ...........................................................................................122

The Korean steel code check........................................................................................................................ 122



Section classification ........................................................................................................................... 123


Buckling length..................................................................................................................................... 124


Combined stresses .............................................................................................................................. 125



References....................................................................................................................................................... 127

BSK 99........................................................................................................................128

BSK 99 Code check .............. ................ ................. ............... ................. ................ ................. ................. ....... 128



Effective cross-section properties for class 3 cross-section .............................................................. 131


Section check....................................................................................................................................... 131

Compression members ....................................................................................................................... 131


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Stability check for torsional buckling and torsional-flexural buckling ................................................. 132

Lateral-torsional buckling .................................................................................................................... 133


Shear force ( shear buckling) .............................................................................................................. 134Supported sections ........................................................................................................................................ 135

References....................................................................................................................................................... 136

IS 800..........................................................................................................................137

IS:800 Code check ................ ............... ................. ................. ................ ................. ................ ................. ....... 137





Section check....................................................................................................................................... 139

Compression members ....................................................................................................................... 139

Stability check for torsional buckling and torsional-flexural buckling ................................................. 139

Lateral-torsional buckling .................................................................................................................... 140Use of diaphragms............................................................................................................................... 141


References....................................................................................................................................................... 142

EAE code check .........................................................................................................143




Effective cross-section properties for class 4 cross-section .............................................................. 146


Torsion check....................................................................................................................................... 147

Built-in beams ...................................................................................................................................... 147

Compression members ....................................................................................................................... 147Lateral-torsional buckling .................................................................................................................... 147


Combined bending and axial compression......................................................................................... 148



References....................................................................................................................................................... 149

Calculation of buckling ratio......................................................................................151

Introduction to the calculation of buckling ratio ........................................................................................ 151

Calculation buckling ratio general formula.............................................................................................. 151

Calculation buckling ratios for crossing diagonals................................................................................... 153

Continuous compression diagonal, supported by continuous tension diagonal ...................................... 154

Continuous compression diagonal, supported by pinned tension diagonal............................................. 155Pinned compression diagonal, supported by continuous tension diagonal ............................................. 156

Continuous compression diagonal, supported by continuous compression diagonal ............................. 157

Continuous compression diagonal, supported by pinned compression diagonal.................................... 158

Pinned compression diagonal, supported by continuous compression diagonal .................................... 159

Calculation of critical Euler force for VARH elements .............................................................................. 159

Definitions................................................................................................................................................... 159

Calculation of the critical Euler force ......................................................................................................... 159

Calculation buckling ratio for lattice tower members................................................................................ 162

Leg with symmetrical bracing..................................................................................................................... 163

Leg with intermediate transverse support ................................................................................................. 163


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Leg with staggered bracing........................................................................................................................ 164

Single Bracing ............................................................................................................................................ 164

Single Bracing with SBS (Secondary Bracing System) ............................................................................ 165

Cross bracing ............................................................................................................................................. 165Cross bracing with SBS ............................................................................................................................. 167

K Bracing .................................................................................................................................................... 167

Horizontal Bracing ...................................................................................................................................... 168

Horizontal Bracing with SBS ...................................................................................................................... 168

Discontinuous Cross bracing with horizontal member.............................................................................. 170

References....................................................................................................................................................... 170

Calculation of moment factors for LTB.....................................................................172

Introduction to the calculation of moment factors .................................................................................... 172

Calculation moment factors .......................................................................................................................... 172

Moment distribution generated by q load .................................................................................................. 172

Moment distribution generated by F load .................................................................................................. 174

Moment line with maximum at the start or at the end of the beam........................................................... 175

References....................................................................................................................................................... 175

LTBII: Lateral Torsional Buckling 2nd Order Analysis.............................................176

Introduction to LTBII ...................................................................................................................................... 176

Eigenvalue solution Mcr ................................................................................................................................ 176

2nd

Order analysis .............. ................ ................. ................ ................. ............... ................. ................. .......... 177

Supported National Codes ............................................................................................................................ 178

Supported Sections........................................................................................................................................ 179

Loadings .......................................................................................................................................................... 181

Imperfections................................................................................................................................................... 181

Initial bow imperfection v0 for DIN and ONORM....................................................................................... 182

Initial bow imperfection v0 for EC-EN and EAE ........................................................................................ 182

Initial bow imperfections v0 and w0 for other supported codes................................................................ 183

LTB Restraints................................................................................................................................................. 184

Diaphragms ..................................................................................................................................................... 185

Linked Beams.................................................................................................................................................. 186

Limitations and Warnings.............................................................................................................................. 186

References....................................................................................................................................................... 187

Profile conditions for code check .............................................................................189

Introduction to profile characteristics ......................................................................................................... 189

Data for general section stability check ...................................................................................................... 189

I section............... ................ ................. ................. ................ ................. ............... ................. ................ ..... 190

RHS.......... ................ ................. ................ ................. ................ ................. ............... ................. ................ 190

CHS.......... ................ ................. ................ ................. ................ ................. ............... ................. ................ 191

Angle section .............................................................................................................................................. 192

Channel section.......................................................................................................................................... 193

T section ..................................................................................................................................................... 194

Full rectangular section .............................................................................................................................. 195

Full circular section..................................................................................................................................... 196

Asymmetric I section .................................................................................................................................. 197

Z section ..................................................................................................................................................... 198

General cold formed section ...................................................................................................................... 199

Cold formed angle section ......................................................................................................................... 202


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Cold formed channel section ..................................................................................................................... 203

Cold formed Z section ................................................................................................................................ 204

Cold formed C section................................................................................................................................ 204

Cold formed Omega section ...................................................................................................................... 205Rail type KA ................................................................................................................................................ 206

Rail type KF ................................................................................................................................................ 207

Rail type KQ................................................................................................................................................ 209

Warping check............................................................................................................210

Stress check ............... ................ ................. ............... ................. ................. ................ ................. ................ .. 210

Calculation of the direct stress due to warping ......................................................................................... 211

I sections..................................................................................................................................................... 211

U sections ................................................................................................................................................... 212

sections....................................................................................................................................................... 212

Calculation of the shear stress due to warping.......................................................................................... 213

I sections..................................................................................................................................................... 213

U sections, sections ............................................................................................................................... 214

Plastic Check................................................................................................................................................... 215

Standard diagrams for warping torque, bimoment and the St.Venant torsion ...................................... 219

Torsion fixed ends, warping free ends, local torsional loading Mt............................................................ 219

Torsion fixed ends, warping fixed ends, local torsional loading Mt .......................................................... 221

Torsion fixed ends, warping free ends, distributed torsional loading mt .................................................. 223

Torsion fixed ends, warping fixed ends, distributed torsional loading mt................................................. 224

One end free, other end torsion and warping fixed, local torsional loading Mt ........................................ 225

One end free, other end torsion and warping fixed, distributed torsional loading mt............................... 226

Decomposition of arbitrary torsion line....................................................................................................... 227

Decomposition for situation 1 and situation 3 ........................................................................................... 227

Decomposition for situation 2..................................................................................................................... 228References....................................................................................................................................................... 228

Check of numerical sections .....................................................................................230

Stress check ............... ................ ................. ............... ................. ................. ................ ................. ................ .. 230

Use of diaphragms.....................................................................................................231

Adaptation of torsional constant.................................................................................................................. 231

References....................................................................................................................................................... 232

Section check for built-in beams (IFB, SFB, THQ sections).....................................234

Introduction ..................................................................................................................................................... 234

Reduction of plastic moment capacity due to plate bending ................................................................... 234

Plastic interaction formula for single bending and shear force............................................................... 236

Plastic check for plate in bending................................................................................................................ 237

Stress check for slim floor beams................................................................................................................ 238

Normal stress check................................................................................................................................... 238

Shear stress check in plate........................................................................................................................ 239

Torsion check due to unbalanced loading................................................................................................. 239

References....................................................................................................................................................... 241

Effective cross-section properties for lattice tower angle members.......................242

Effective cross-section properties for compressed lattice tower angle members................................ 242

References....................................................................................................................................................... 243


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SCIA.ESA PT Steel Code Check Theoretical Background

SCIA 1


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EC 3 ENV 1993

EC3 code check

The beam elements are checked according to the regulations given in

Eurocode 3

Design of steel structures

Part 1 - 1 : General rules and rules for buildings

ENV 1993-1-1:1992

Material properties

For standard steel grades, the yield strength fy and tensile strength fu are defined according to the thickness ofthe element (see Ref. 1, art.3.2.2.1.)

(fy, fu in N/mm, t in mm)

t


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fu the tensile ultimate strength

t the material thickness

Ag the gross cross-sectional area

k is a coefficient depending on the type of forming :

k = 0.7 for cold rolling

k = 0.5 for other methods of forming

n the number of 90 bends in the section

Consulted articles

The cross-section is classified according to Table 5.3.1. (class 1,2,3 or 4). The section is checked for tension (art.5.4.3.), compression (art. 5.4.4.), shear (art. 5.4.6.) and the combination of bending, shear and axial force (art.5.4.9.).

For the stability check, the beam element is checked according to art.5.5.. The following criteria are considered :

for compression : art. 5.5.1.

for lateral torsional buckling : art. 5.5.2.

for bending and axial compression : art. 5.5.4.

The shear buckling resistance is checked using the simple post-critical method from art. 5.6.3.

A more detailed overview for the used articles is given for part 5.3., 5.4., 5.5. and 5.6. in the following table. Thechapters marked with x are consulted. The chapters marked with (*) have a supplementary explanation thefollowing chapters.

5.3. Classification of cross sections

5.3.1. Basis x

5.3.2. Classification x

5.3.3. Cross-section requirements for plastic global analysis

5.3.4. Cross-section requirements when elastic global analysis is used5.3.5. Effective cross-section properties for class 4 cross-section x (*)

5.3.6. Effects of transverse forces on webs

5.4. Resistance of cross-sections

5.4.1. General x

5.4.2. Section properties (*)

5.4.3. Tension x

5.4.4. Compression x

5.4.5. Bending moment x (*)


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Effective cross-section properties for class 4 cross-section

The calculation of the effective area is performed with the direct method (sigma_d = fy,k).

For each intermediary section, the classification (and if necessary, the effective area ) is determined and theproper section check is performed. The classification (and effective area) can change for each intermediarypoint. The most critical check is displayed on the screen.

For each load case and combination, the most critical effective area properties are saved :

Aeff is the effective area of the cross section when subject to uniform compression. Weff is the effective sectionmodulus of the cross-section when subject only to moment about the relevant axis. eN is the shift of the relevantcentroidal axis when the cross section is subject to uniform compression.

With these critical properties, the stability check is performed.

For non-prismatic elements, the effective area properties are calculated on each intermediary section, also forthe stability check.

For angle sections, see chapter 'Effective cross-section properties for compressed lattice tower angle members'.

Section properties

5.4.2.2 : The net area properties are only taken into account in the Tension Check in case of lattice tower anglesections with bolted diagonal connections if the LTA functionality has been activated. For more information,reference is made to the Theoretical Background Bolted Diagonal Connections. In all other cases the net areaproperties are not taken into account.

5.4.2.3 : The shear lag effects are neglected .

Bending moment

5.4.5.3 : The holes for fasteners are neglected.

Bending, shear and axial force

The reduced design plastic resistance moment for the interaction of bending, shear and axial force, is taken fromTable 5.17. Ref. 2

Torsion check

For the cross section check inclusive torsion and warping, we refer to Chapter 'Warping check'.


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Built-in beams

For built-in beam sections (IFB, SFB, THQ sections), proper section checks are performed, taking into accountthe local plate bending. See Chapter Section check for built-in beams (IFB, SFB, THQ sections)

Compression members

5.5.1.5 For the calculation of the buckling length, we refer to chapter "Calculation of buckling ratio"

The buckling properties for a VARH element are calculated by using the critical Euler force for this member (seechapter Calculation of critical Euler force for VARH elements).

The buckling curves for steel grade S420 and S460 are taken from Ref.[5], Annex D.

Lateral-torsional buckling

For I sections (symmetric and asymmetric), RHS (Rectangular Hollow Section) sections and CHS (CircularHollow Section) sections, the elastic critical moment for LTB Mcr is given by the general formula F.2. Annex FRef. 1. For the calculation of the moment factors C1, C2 and C3 we refer to "Calculation of moment factors forLTB".

For the other supported sections, the elastic critical moment for LTB Mcr is given by

z

2t

z

2z

2

EI

LGI

I

Iw

L

EIMcr

with E the modulus of elasticity

G the shear modulus

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

Iw the warping constant

It the torsional constant

Iz the moment of inertia about the minor axis

See also Ref. 3, part 7 and in particular part 7.7. for channel sections.

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 as equivalent asymmetric I sections.

For advanced Lateral-torsional buckling analysis, see chapter LTBII: Lateral Torsional Buckling 2nd OrderAnalysis.

Use of diaphragms


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See Chapter 'Adaptation of torsional constant'.

Shear buckling check

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 check for cold formed sections

See Ref.[4] 5.8 :

The shear resistance of the web Vw,Rd shall be taken as the lesser of the shear buckling resistance V b,Rd and theplastic shear resistance Vpl,Rd.

The shear resistance of the web should be checked if:

E

f

t

s346.0

f

f83.0

ybww

_

1M

0M

y

ybw

_

The shear buckling resistance Vb,Rd is given by

1M

bvwRd,b

ftsV

The plastic shear resistance Vpl,Rd is given by

3

ftsV

0M

yw

Rd,pl

withw the relative web slenderness

fyb the basic yield strength

fy the average yield strength

sw the web length

t the web thickness

E the modulus of elasticity

fbv the shear buckling strength


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i

y1

i

l

E

42

1

yiii

l

ECGI

iA

1

),min(

f

0

0

y

y

y,cr

T,cry,crT,cry,crT,cry,crTF,cr

20

2z

2y

20

2T

mt2

0g

T,cr

TF,crT,crcr

A

cr

yb

with A the ratio Aeff/A (see Ref.[1] 5.5)

fyb the basic yield strength

cr the critical stresscr,T the elastic critical stress for torsional buckling

cr,TF the elastic critical stress for torsional-flexural buckling

G the shear modulus

E the modulus of elasticity

IT the torsion constant of the gross section

CM the warping constant

iy the radius of gyration about yy-axis

iz the radius of gyration about zz-axis

lT the buckling length of the member for torsional buckling

y0 the position of the shear center

ly the buckling length for flexural buckling about the yy-axis


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Bending and axial compression

When the torsional buckling and/or the torsional-flexural buckling is governing, the formula (6.12) from Ref.[4],article 6.5.2. is applied.

Battened compression members

The following section pairs are supported as battened compression member :

(1) 2I

(2) 2Uo(3) 2Uc

Two links (battens) are used.

The following additional checks are performed :

- buckling resistance check around weak axis of single chord with N f,Sd

- section check of single chord, using internal forces :

4

aVM

2

VV

NN

s

G

sG

SDf,G

- section check of single batten, using the internal forces :

4

aVM

2h

aVT

s

0

s


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For the calculation of Vs, the value of Ms is increased with the value of the internal force M zz.

l

a

ho

EC3 - Fire Resistance

Fire actions effect Efi

The design effects of actions for the fire situation Efi,d,t are taken from the results of the analysis. It isrecommended to use the accidental combination rules, for calculating the internal forces used in the fireresistance check.

The accidental combination is given by

)f(AQQGdj,kj,21,k1,1kGA

with Gk characteristic values of permanent actions

Qk,1 characteristic value of the (main) variable action


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Qk,j characteristic values of the other variable actions

Af(d) design values of actions from fire exposure

GA partial safety factor for permanent actions in the accidental situation

=[1.0]

1,1 2,j combination coefficients

Material properties

The material properties are depending on the steel temperature.

Strength and deformation properties :

a

,a,E

y

,p,p

y

,y,y

EE

k

f

fk

f

fk

The variation in function of the steel temperature of the value for yield strength ky,, proportional limit kp, andmodulus of elasticity kE, is given by tables in Ref.[6], table 3.1.

For cold formed members ky, is taken from Ref.[7], table III.2.5.

In the simplified calculation method, the following default properties are considered to be constant during theanalysis :

unit mass a 7850 kg/m

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

thermal conductivity a 45 W/mK

Temperature analysis - Thermal actions

In this part, the nominal temperature-time curves and the related net heat flux are described. See Ref.[8],Section 4, and Ref.[7], II.2.2.

Nominal temperature-time curve

The following temperature-time curves can be selected :


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with t time in [min]

g gas temperature in [C]

c the coefficient of heat transfer by convection

ISO 834 curve

Km/W25

)1t8(log34520

c

10g

external fire curve

Km/W25

20e313.0e687.01660

c

t8.3t32.0

g

hydrocarbon curve

Km/W5020e675.0e325.011080

c

t5.2t167.0

g

smoldering fire curve

20t1544g

during 20 minutes, followed by the standard ISO 834 curve

Net heat flux

r,netr,nc,netc,nd,net hhh

with hnet,d the net heat flux

hnet,c the convective heat flux

hnet,r the radiative heat flux


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n,c factor depending on NAD [1.0]

n,r factor depending on NAD [1.0]

mgcc,neth

4m4

r

8

resr,net 2732731067.5h

with configuration factor [1.0]

res resultant emissivity

= fm

f emissivity related to fire compartment

= [0.800]m emissivity related to surface material

= [0.625]

r = ggas temperature in [C]

m surface temperature of member in [C]

c coefficient of heat transfer by convection

Steel Temperature

The increase of temperature a,t in an unprotected steel member during a time interval t

thc

V/Ad,net

aa

mt,a

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

V the volume of the member per unit length [m/m]

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

ca the specific heat of steel [J/kgK]

hnet,d the net heat flux per unit area [W/m]

t the time interval [seconds]The value should not be taken as more than 5 seconds

a the unit mass of steel [kg/m]

The increase of temperature a,t in an insulated steel member during a time interval t


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V/Adc

c

1et

31

cd

V/A

pp

aa

pp

t,g

10/t,at,g

aap

pp

t,a

with Ap the area of fire protection material per unit length [m/m]

V the volume of the member per unit length [m/m]

ca the specific heat of steel [J/kgK]

cp the specific heat of fire protection material [J/kgK]

dp the thickness of the fire protection material [m]

t the time interval [seconds]The value should not be taken as more than 30 seconds

a the unit mass of steel [kg/m]

p the unit mass of fire protection [kg/m]

a,t the steel temperature at time t

g,t the ambient gas temperature at time t

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

p the thermal conductivity of the fire protection material [W/mK]

The value a,t 0.0

For the increase of temperature a,t in an insulated steel member with intumescent coating, we refer to the NENspecifications, Chapter 'Steel Temperature'.

Calculation model

The calculation can be performed in 2 domains :

- strength domain

- temperature/time domain

In the strength domain, the strength R fi,d,t(unity check) is calculated after a given time t (e.g. strength after 45min). In the temperature/time domain, the critical steel temperature cr,d is computed. From this criticaltemperature, the fire resistance time t fi,d is calculated (the time domain).

Code Check

The section and stability checks (buckling, lateral torsional buckling) are performed according to the regulationsgiven in 'ENV 1993-1-2:1995' and/or 'Model Code on Fire Engineering - ECCS N 111'. The checks areperformed in the resistance domain or in the temperature/time domain..

Torsional buckling and shear buckling are not considered.


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For each member, the classification of the cross section, the section check and the stability check are performed.

The following checks are executed :

EC3-1-2 :

- classification of cross section : art. 4.2.2.

- resistance for tension members : art. 4.2.3.1

- resistance for compression members (class 1,2 or 3) : art. 4.2.3.2.

- resistance for beams (class 1,2) : art. 4.2.3.3.

- resistance for beams (class 3) : art.4.2.3.4.

- resistance for members (class 1,2,3) subject to bending and compression : art. 4.2.3.5.

- critical temperature : art. 4.2.4.

ECCS Model Code on Fire Engineering

- resistance for tension members : art. III.5.2.- resistance for compression members (class 1,2 or 3) : art. III.5.3.

- resistance for beams (class 1,2) : art. III.5.4.

- resistance for beams (class 3) : art. III.5.5.

- resistance for members (class 1,2,3) subject to bending and compression : art. III.5.6.

- resistance for members (class 4) : art. III.5.7.

- critical temperature : art. III.5.8.

Supported sections

I Symmetric I shapes (IPE, HEA, HEB, .)

RHS Rectangular Hollow Section

CHS Circular Hollow Section

L Angle section

U Channel section

T T section

PPL Asymmetric I shapes

Z Z section

RS Rectangular section

Cold formed sectionCOM Composed section in PRIMAW IN

O Solid tube

NUM Numerical section

The necessary data conditions for these sections are described in chapter "Profile conditions for code check

".

The COM and NUM sections are not read out of the profile library.

I RHS CHS L U T PPL RS Z O COM NUM


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Classification x x x x x x x x (1) x (1) (1) (1)

Section check class 1 x x x

Section check class 2 x x xSection check class 3 x x x x x x x x x x x x x

Section check class 4 x x x x x x

Stability check class1

x x x


x x x


x x x x x x x x x x x x x


x x x x x x

Shear buckling check x x x x

(1) sections are classified as class 3 cross section by default.

References

1 Eurocode 3Design of steel structures


ENV 1993-1-1:1992, 1992

2 Essentials of Eurocode 3Design Manual for Steel Structures in Building

ECCS - N 65, 1991

3 R. MaquoiELEMENTS DE CONSTRUCTIONS METALLIQUE

Ulg , Facult des Sciences Appliques, 1988

[4] ENV 1993-1-3:1996

Eurocode 3 : Design of steel structures

Part 1-3 : General rules

Supplementary rules for cold formed thin gauge members and sheeting

CEN 1996

[5] Eurocode 3


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

ENV 1993-1-1:1992/A1, 1994

[6] Eurocode 3


Part 1 - 2 : General rules - Structural fire design

ENV 1993-1-2:1995, 1995

[7] Model Code on Fire Engineering


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ECCS - N 111

May 2001

[8] Eurocode 1Basis of design and actions on structures

Part 2-2 : Actions on structures - Actions on structures exposed to fire

ENV 1991-2-2:1995


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EC 3 EN 1993

EC3 code check

The beam elements are checked according to the regulations given in

Eurocode 3



EN 1993-1-1:2005

Material properties

For standard steel grades, the yield strength fy and tensile strength fu are defined according to the thickness ofthe element (see Ref. 1, table 3.1.)

Steel Grade fy(N/mm)

fu(N/mm)

S 235 235 360

S 275 275 430

S 355 355 510

S 275 N/NL 275 390

S 355 N/NL 355 490

S 420 N/NL 420 540

S 460 N/NL 460 570

S 275 M/ML 275 380

S 355 M/ML 355 470

S 420 M/ML 420 520

S 460 M/ML 460 550

S 460 Q/QL/QL1 460 570

S 235 W 235 360

S 355 W 355 510S 235 H 235 360

S 275 H 275 430

S 355 H 355 510

S 275 NH/NLH 275 370

S 355 NH/NLH 355 470

S 460 NH/NLH 460 550

S 275 MH/MLH 275 360

S 355 MH/MLH 355 470

S 420 MH/MLH 420 500


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S 460 MH/MLH 460 530Table 1

The name of the steel grade (e.g. 'S 355 W') is used to identify the steel grade.

Remark : For cold formed section, the values for fy and fu are not influenced by the previous table

Remark : For cold formed sections, the average yield strength fya can be used (by setting the proper data flag inthe Cross Section input dialog).

The average yield strength is determined as follows :

ybuybug

ybya f2.1,fminffA

kntff

with f yb the tensile yield strength = fy

fu the tensile ultimate strength

t the material thickness

Ag the gross cross-sectional area

k is a coefficient depending on the type of forming :

k = 0.7 for cold rolling

k = 0.5 for other methods of forming

n the number of 90 bends in the section


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Consulted articles

The beam elements are checked according to the regulations given in "Eurocode 3: Design of steel structures -Part 1-1: General rules and rules for buildings - EN 1993-1-1:2005".

The cross-sections are classified according to Table 5.2. All classes of cross-sections are included. For class 4sections (slender sections) the effective section is calculated in each intermediary point, according to prEN 1993-1-5:2003, Chapter 4.4 .

The stress check is taken from art. 6.2.: the section is checked for tension (art. 6.2.3.), compression (art. 6.2.4.),bending (art. 6.2.5.), shear (art. 6.2.6.), torsion (art.6.2.7.) and combined bending, shear and axial force (art.6.2.8., art.6.2.9. and art.6.2.10.).

The stability check is taken from art. 6.3.: the beam element is checked for buckling (art. 6.3.1.), lateral torsionalbuckling (art. 6.3.2.), and combined bending and axial compression (art. 6.3.3.).

The shear buckling is checked according to prEN 1993-1-5:2003, Chapter 5.

For I sections, U sections and cold formed sections warping can be considered.

A check for critical slenderness and torsion moment is also included.

For integrated beams, the local plate bending is taken into account for the plastic moment capacity and thebending stresses in the section. The out-of-balance loading is checked.

A more detailed overview for the used articles is given in the following table. The chapters marked with x areconsulted. The chapters marked with (*) have a supplementary explanation the following chapters.

EN 1993-1-1

5.5 Classification of cross section (

*)

5.5.1. Basis x

5.5.2. Classification x

6. Ultimate limit states

6.1. General x

6.2. Resistance of cross-sections

6.2.1 General x

6.2.2 Section properties x(*)

6.2.3 Tension x

6.2.4 Compression x

6.2.5 Bending moment x

6.2.6 Shear x

6.2.7 Torsion x(*)

6.2.8 Bending and shear x

6.2.9 Bending and axial force x


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6.2.10 Bending, shear and axial force x

6.3. Buckling resistance of members

6.3.1 Uniform members in compression

x(*)

6.3.2 Uniform members in bending x

6.3.3 Uniform members in bending and axial compression 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

prEN 1993-1-3

6.1.2. Axial tension

6.1.3. Axial compression

6.1.5. Shear force

6.1.6. Torsional moment

prEN 1993-1-5

4.4. Plate elements without longitudinal stiffeners

5. Resistance to shear

5.1. Basis

5.2. Design resistance

5.3. Contribution from webs

5.4. Contribution from flanges

5.5. Verification

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

Classification of sections

For each intermediary section, the classification is determined and the proper section check is performed. Theclassification can change for each intermediary point.

For each load case/combination, the critical section classification over the member is used to perform thestability check. So, the stability section classification can change for each load case/combination.

However, for non-prismatic sections, the stability section classification is determined for each intermediarysection.


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Effective cross-section properties for class 4 cross-section

The calculation of the effective area is performed with the direct method (sigma_d = fy,k).

For each intermediary section, the classification (and if necessary, the effective area ) is determined and theproper section check is performed. The classification (and effective area) can change for each intermediarypoint. The most critical check is displayed on the screen.

For each load case and combination, the most critical effective area properties are saved :

Aeff is the effective area of the cross section when subject to uniform compression. Weff is the effective sectionmodulus of the cross-section when subject only to moment about the relevant axis. e

92311182 steel code check theory enu

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