Steel Code Check Theory Enu

TheorySteel Code Check

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TABLE OF CONTENTS

EC 3 – ENV 1993.............................................................................................................2EC3 code check ...................................................................................................................................................2

Material properties...........................................................................................................................................2Consulted articles ............................................................................................................................................3

Classification of sections ..........................................................................................................................4Effective cross-section properties for class 4 cross-section ...................................................................5Section properties.....................................................................................................................................5Bending moment.......................................................................................................................................5Bending, shear and axial force.................................................................................................................5Torsion check............................................................................................................................................5Built-in beams ...........................................................................................................................................6Compression members ............................................................................................................................6Lateral-torsional buckling .........................................................................................................................6Use of diaphragms....................................................................................................................................6Shear buckling check ...............................................................................................................................7Shear buckling check for cold formed sections .......................................................................................7Stability check for torsional buckling and torsional-flexural buckling ......................................................8Bending and axial compression .............................................................................................................11Battened compression members ...........................................................................................................11

EC3 - Fire Resistance ........................................................................................................................................12Fire actions effect Efi .....................................................................................................................................12Material properties.........................................................................................................................................13Temperature analysis - Thermal actions ......................................................................................................13Nominal temperature-time curve ..................................................................................................................13Net heat flux...................................................................................................................................................14Steel Temperature.........................................................................................................................................15Calculation model ..........................................................................................................................................16Code Check ...................................................................................................................................................16

Supported sections ...........................................................................................................................................17References..........................................................................................................................................................18

EC 3 – EN 1993 .............................................................................................................20EC3 code check .................................................................................................................................................20

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

Classification of sections ........................................................................................................................23Effective cross-section properties for class 4 cross-section .................................................................24Section properties...................................................................................................................................24Torsion check..........................................................................................................................................24Built-in beams .........................................................................................................................................24Compression members ..........................................................................................................................24Lateral-torsional buckling .......................................................................................................................24Use of diaphragms..................................................................................................................................25Combined bending and axial compression............................................................................................25Shear buckling check .............................................................................................................................26

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

Fire actions effect Efi .....................................................................................................................................26Material properties.........................................................................................................................................27Temperature analysis - Thermal actions ......................................................................................................27

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

Steel Temperature.........................................................................................................................................29Calculation model ..........................................................................................................................................31Code Check ...................................................................................................................................................31


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


Classification of sections ........................................................................................................................37Net area properties .................................................................................................................................37Plastic interaction formula for RHS section ...........................................................................................38Plastic interaction formula for CHS section ...........................................................................................40Torsion check..........................................................................................................................................42Built-in beams .........................................................................................................................................42Calculation of the buckling length ..........................................................................................................42Torsional buckling...................................................................................................................................42Use of diaphragms..................................................................................................................................43LTB Check ..............................................................................................................................................44Combined flexion for check method 2....................................................................................................48Battened compression members ...........................................................................................................48Effective area properties.........................................................................................................................49Shear buckling check .............................................................................................................................50Shear buckling check with buckling influence .......................................................................................50

Cold formed thin gauge members ................................................................................................................50


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



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


Section properties...................................................................................................................................61Classification of sections ........................................................................................................................62Effective cross-section properties for class 4 cross-section .................................................................62Torsion check..........................................................................................................................................62Built-in beams .........................................................................................................................................62Buckling length........................................................................................................................................62Lateral-torsional buckling .......................................................................................................................63Use of diaphragms..................................................................................................................................63Battened compression members ...........................................................................................................63

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

NEN6072 - Fire Resistance ...............................................................................................................................65Fire actions effect ..........................................................................................................................................66Material properties.........................................................................................................................................66Nominal temperature-time curve ..................................................................................................................67Steel Temperature.........................................................................................................................................67Calculation model ..........................................................................................................................................70Code Check ...................................................................................................................................................70


AISC – ASD : 1989........................................................................................................73AISC - ASD Code check ....................................................................................................................................73

Classification of sections...............................................................................................................................75Section properties .........................................................................................................................................75Buckling length ..............................................................................................................................................75Flexural Torsional Buckling...........................................................................................................................75Lateral-torsional buckling ..............................................................................................................................75Shear buckling check ....................................................................................................................................76


AISC – LRFD : 2001......................................................................................................79AISC - LRFD Code check ..................................................................................................................................79

Classification of sections...............................................................................................................................81Section properties .........................................................................................................................................81Buckling length ..............................................................................................................................................81Lateral-torsional buckling ..............................................................................................................................81Use of diaphragms ........................................................................................................................................82Shear buckling check ....................................................................................................................................82


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

Classification of sections...............................................................................................................................85Section properties .........................................................................................................................................86Buckling length ..............................................................................................................................................86Lateral-torsional buckling ..............................................................................................................................86Use of diaphragms ........................................................................................................................................86Shear buckling check ....................................................................................................................................86


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

Consulted articles ..........................................................................................................................................88Section properties...................................................................................................................................89Plastic coefficient ....................................................................................................................................90Compression members ..........................................................................................................................90Factor kf ..................................................................................................................................................90LTB Check ..............................................................................................................................................90

Use of diaphragms..................................................................................................................................90Combined flexion ....................................................................................................................................90Shear buckling check .............................................................................................................................91


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

Consulted articles ..........................................................................................................................................93Classification of sections ........................................................................................................................94Section check..........................................................................................................................................94Compression members ..........................................................................................................................94Lateral-torsional buckling .......................................................................................................................94Use of diaphragms..................................................................................................................................94


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


Classification of sections ........................................................................................................................99Slender cross-section .............................................................................................................................99Section properties...................................................................................................................................99Bending moment.....................................................................................................................................99Bending, shear, axial force.....................................................................................................................99Lateral torsional buckling..................................................................................................................... 100Use of diaphragms............................................................................................................................... 101Compression member ......................................................................................................................... 101Shear buckling check .......................................................................................................................... 101

Supported sections ........................................................................................................................................ 101References....................................................................................................................................................... 102

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

Material properties...................................................................................................................................... 103Governing code clauses............................................................................................................................ 104

Classification of sections ..................................................................................................................... 106Slender cross-sections ........................................................................................................................ 106Section properties................................................................................................................................ 106Moment capacity.................................................................................................................................. 106Bending, shear, axial force/capacity interaction ................................................................................. 106Lateral torsional buckling due to major axis moments ....................................................................... 107Torsional buckling about an eccentric axis (Annex G) ....................................................................... 107Lateral buckling due axial compression.............................................................................................. 107Combined axial and bending buckling unity check/utilisation ............................................................ 107Torsion effects ..................................................................................................................................... 108

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

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

Material properties...................................................................................................................................... 109Consulted articles ....................................................................................................................................... 109

Section classification ........................................................................................................................... 110Slender cross-section .......................................................................................................................... 111

Sections properties .............................................................................................................................. 111Lateral torsional buckling..................................................................................................................... 111Use of diaphragms............................................................................................................................... 111Shear buckling ..................................................................................................................................... 111Stability check ...................................................................................................................................... 112Torsion check....................................................................................................................................... 112Built-in beams ...................................................................................................................................... 112

SIA263 - Fire Resistance................................................................................................................................ 112Fire actions effect Efi .................................................................................................................................. 112Material properties...................................................................................................................................... 112Temperature analysis - Thermal actions ................................................................................................... 113Nominal temperature-time curve ............................................................................................................... 113Net heat flux................................................................................................................................................ 113Steel Temperature...................................................................................................................................... 113Calculation model ....................................................................................................................................... 114Code Check ................................................................................................................................................ 115


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


Section properties................................................................................................................................ 119Shear buckling check .......................................................................................................................... 119Buckling curves.................................................................................................................................... 119Buckling length..................................................................................................................................... 120Lateral torsional buckling..................................................................................................................... 120Local stability of compressed members.............................................................................................. 120Shear buckling check .......................................................................................................................... 120


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


Section classification ........................................................................................................................... 123Section properties................................................................................................................................ 124Buckling length..................................................................................................................................... 124Lateral torsional buckling..................................................................................................................... 124Combined stresses .............................................................................................................................. 125Shear buckling check .......................................................................................................................... 126


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

Consulted articles ....................................................................................................................................... 130Classification of sections ..................................................................................................................... 130Effective cross-section properties for class 3 cross-section .............................................................. 131Section properties................................................................................................................................ 131Section check....................................................................................................................................... 131Compression members ....................................................................................................................... 131

Stability check for torsional buckling and torsional-flexural buckling ................................................. 132Lateral-torsional buckling .................................................................................................................... 133Use of diaphragms............................................................................................................................... 134Shear force ( shear buckling) .............................................................................................................. 134


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


Classification of sections ..................................................................................................................... 138Section properties................................................................................................................................ 138Section check....................................................................................................................................... 139Compression members ....................................................................................................................... 139Stability check for torsional buckling and torsional-flexural buckling ................................................. 139Lateral-torsional buckling .................................................................................................................... 140Use of diaphragms............................................................................................................................... 141


EAE code check .........................................................................................................143Material properties...................................................................................................................................... 143Consulted articles ....................................................................................................................................... 145

Classification of sections ..................................................................................................................... 146Effective cross-section properties for class 4 cross-section .............................................................. 146Section properties................................................................................................................................ 147Torsion check....................................................................................................................................... 147Built-in beams ...................................................................................................................................... 147Compression members ....................................................................................................................... 147Lateral-torsional buckling .................................................................................................................... 147Use of diaphragms............................................................................................................................... 148Combined bending and axial compression......................................................................................... 148Shear buckling check .......................................................................................................................... 148


Calculation of buckling ratio......................................................................................151Introduction to the calculation of buckling ratio ........................................................................................ 151Calculation buckling ratio – general formula.............................................................................................. 151Calculation buckling ratios for crossing diagonals................................................................................... 153

Continuous compression diagonal, supported by continuous tension diagonal ...................................... 154Continuous compression diagonal, supported by pinned tension diagonal ............................................. 155Pinned compression diagonal, supported by continuous tension diagonal ............................................. 156Continuous compression diagonal, supported by continuous compression diagonal ............................. 157Continuous compression diagonal, supported by pinned compression diagonal .................................... 158Pinned compression diagonal, supported by continuous compression diagonal .................................... 159

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

Calculation buckling ratio for lattice tower members................................................................................ 162Leg with symmetrical bracing..................................................................................................................... 163Leg with intermediate transverse support ................................................................................................. 163

Leg with staggered bracing........................................................................................................................ 164Single Bracing ............................................................................................................................................ 164Single Bracing with SBS (Secondary Bracing System) ............................................................................ 165Cross bracing ............................................................................................................................................. 165Cross bracing with SBS ............................................................................................................................. 167K Bracing .................................................................................................................................................... 167Horizontal Bracing ...................................................................................................................................... 168Horizontal Bracing with SBS ...................................................................................................................... 168Discontinuous Cross bracing with horizontal member .............................................................................. 170

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

Calculation of moment factors for LTB.....................................................................172Introduction to the calculation of moment factors .................................................................................... 172Calculation moment factors .......................................................................................................................... 172

Moment distribution generated by q load .................................................................................................. 172Moment distribution generated by F load .................................................................................................. 174Moment line with maximum at the start or at the end of the beam........................................................... 175

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

LTBII: Lateral Torsional Buckling 2nd Order Analysis .............................................176Introduction to LTBII ...................................................................................................................................... 176Eigenvalue solution Mcr ................................................................................................................................ 1762nd Order analysis ........................................................................................................................................... 177Supported National Codes ............................................................................................................................ 178Supported Sections........................................................................................................................................ 179Loadings .......................................................................................................................................................... 181Imperfections................................................................................................................................................... 181

Initial bow imperfection v0 for DIN and ONORM....................................................................................... 182Initial bow imperfection v0 for EC-EN and EAE ........................................................................................ 182Initial bow imperfections v0 and w0 for other supported codes................................................................ 183

LTB Restraints................................................................................................................................................. 184Diaphragms ..................................................................................................................................................... 185Linked Beams.................................................................................................................................................. 186Limitations and Warnings.............................................................................................................................. 186References....................................................................................................................................................... 187

Profile conditions for code check .............................................................................189Introduction to profile characteristics ......................................................................................................... 189Data for general section stability check ...................................................................................................... 189

I section....................................................................................................................................................... 190RHS............................................................................................................................................................. 190CHS............................................................................................................................................................. 191Angle section .............................................................................................................................................. 192Channel section.......................................................................................................................................... 193T section ..................................................................................................................................................... 194Full rectangular section .............................................................................................................................. 195Full circular section..................................................................................................................................... 196Asymmetric I section .................................................................................................................................. 197Z section ..................................................................................................................................................... 198General cold formed section ...................................................................................................................... 199Cold formed angle section ......................................................................................................................... 202

Cold formed channel section ..................................................................................................................... 203Cold formed Z section ................................................................................................................................ 204Cold formed C section................................................................................................................................ 204Cold formed Omega section ...................................................................................................................... 205Rail type KA ................................................................................................................................................ 206Rail type KF ................................................................................................................................................ 207Rail type KQ................................................................................................................................................ 209

Warping check............................................................................................................210Stress check .................................................................................................................................................... 210Calculation of the direct stress due to warping ......................................................................................... 211

I sections..................................................................................................................................................... 211U sections ................................................................................................................................................... 212sections....................................................................................................................................................... 212

Calculation of the shear stress due to warping.......................................................................................... 213I sections..................................................................................................................................................... 213U sections, sections ............................................................................................................................... 214

Plastic Check................................................................................................................................................... 215Standard diagrams for warping torque, bimoment and the St.Venant torsion...................................... 219

Torsion fixed ends, warping free ends, local torsional loading Mt............................................................ 219Torsion fixed ends, warping fixed ends, local torsional loading Mt .......................................................... 221Torsion fixed ends, warping free ends, distributed torsional loading mt .................................................. 223Torsion fixed ends, warping fixed ends, distributed torsional loading mt ................................................. 224One end free, other end torsion and warping fixed, local torsional loading Mt ........................................ 225One end free, other end torsion and warping fixed, distributed torsional loading mt............................... 226

Decomposition of arbitrary torsion line....................................................................................................... 227Decomposition for situation 1 and situation 3 ........................................................................................... 227Decomposition for situation 2..................................................................................................................... 228

References....................................................................................................................................................... 228

Check of numerical sections .....................................................................................230Stress check .................................................................................................................................................... 230

Use of diaphragms.....................................................................................................231Adaptation of torsional constant .................................................................................................................. 231References....................................................................................................................................................... 232

Section check for built-in beams (IFB, SFB, THQ sections).....................................234Introduction ..................................................................................................................................................... 234Reduction of plastic moment capacity due to plate bending ................................................................... 234Plastic interaction formula for single bending and shear force............................................................... 236Plastic check for plate in bending ................................................................................................................ 237Stress check for slim floor beams................................................................................................................ 238

Normal stress check................................................................................................................................... 238Shear stress check in plate........................................................................................................................ 239Torsion check due to unbalanced loading................................................................................................. 239

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

Effective cross-section properties for lattice tower angle members.......................242Effective cross-section properties for compressed lattice tower angle members................................ 242References....................................................................................................................................................... 243

SCIA.ESA PT Steel Code Check Theoretical Background

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EC 3 – ENV 1993

EC3 code check

The beam elements are checked according to the regulations given in

Eurocode 3Design of steel structuresPart 1 - 1 : General rules and rules for buildingsENV 1993-1-1:1992

Material properties

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

(fy, fu in N/mm², t in mm)

t<=40 t<=40 40<t<=100 40<t<=100 100<t<=250 100<t<=250fy fu fy fu fy fy

S235S 235

235 360 215 340 175 320

S275S 275

275 430 255 410 205 380

S355S 355

355 510 335 490 275 450

S420S 420

420 520 390 520

S460S 460

460 550 430 550

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 in the Cross Section input dialog).The average yield strength is determined as follows :

ybuybug

ybya f2.1,fminffA

²kntff

with fyb the tensile yield strength = fy


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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 rollingk = 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. The chapters marked with “x” are consulted. The chapters marked with (*) have a supplementary explanation the following 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 used

5.3.5. 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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5.4.6. Shear x

5.4.7. Bending and shear x

5.4.8. Bending and axial force x

5.4.9. Bending, shear and axial force x (*)

5.4.10. Transverse forces on webs

5.5. Buckling resistance of members

5.5.1. Compression members x (*)

5.5.2. Lateral-torsional buckling x (*)

5.5.3. Bending and axial tension

5.5.4. Bending and axial compression x (*)

5.6. Shear buckling resistance

5.6.1. Basis x

5.6.2. Design methods

5.6.3. Simple post-critical method x

5.6.4. Tension field method

5.6.5. Intermediate transverse stiffeners

5.6.6. Welds

5.6.7. Interaction between shear force, bending moment and axial force x

5.9. Built-up compression members

5.9.3. Battened compression members

5.9.3.1. Application x(*)

5.9.3.2. Constructional details

5.9.3.3. Second moment of inertia x

5.9.3.4. Chord forces ar mid-length x

5.9.3.5. Buckling resistance of chords x

5.9.3.6. Moments and shear due to battening x

Classification of sections

For each intermediary section, the classification is determined and the proper section check is performed. The classification can change for each intermediary point. For each load case/combination, the critical section classification over the member is used to perform the stability 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 intermediary section.


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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 the proper section check is performed. The classification (and effective area) can change for each intermediary point. 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 section modulus of the cross-section when subject only to moment about the relevant axis. eN is the shift of the relevant centroidal 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 for the 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 angle sections 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 area properties 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 from Table 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 account the 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 (see chapter “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 (Circular Hollow Section) sections, the elastic critical moment for LTB Mcr is given by the general formula F.2. Annex F Ref. 1. For the calculation of the moment factors C1, C2 and C3 we refer to "Calculation of moment factors for LTB".For the other supported sections, the elastic critical moment for LTB Mcr is given by

z2

t

z2

z2

EIL²GI

IIw

LEIMcr

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 Order Analysis’.

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 as equivalent 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 Vb,Rd and the plastic shear resistance Vpl,Rd.

The shear resistance of the web should be checked if:

Ef

ts

346.0

ff

83.0

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

ywRd,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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M0 the partial safety factor for resistance of cross-sections where failure is caused by yielding (=1.1)

M1 the partial safety factor for resistance of cross-sections where failure is caused by buckling (=1.1)

The value for fbv is given by :

w_ fbv

<1.40

f48.0

1.40

f67.0

w_

yb

Remarks :

For an arbitrary composed section, the total Vb,Rd and Vpl,Rd is taken as the sum of resistance of each web, where the angle (teta) is larger than 45° (see figure)

The basic yield strength is taken equal to the average yield strength.

Stability check for torsional buckling and torsional-flexural buckling

See Ref.[4] 6.2.3.

The design buckling resistance Nb,Rd for torsional or torsional-flexural buckling shall be obtained using buckling curve b, and with relative slenderness given by :


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²iy1

²il

E²

4²21

yiii

lEC²GI

iA1

),min(

f

0

0

y

yy,cr

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

20

2z

2y

20

2T

mt2

0gT,cr

TF,crT,crcr

Acr

yb

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

fyb the basic yield strength

cr the critical stress

cr,T the elastic critical stress for torsional buckling

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

G the shear modulus


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 Nf,Sd

- section check of single chord, using internal forces :

4aV

M

2V

V

NN

sG

sG

SDf,G

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

4aV

M

2haV

T

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 Mzz.

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 is recommended to use the accidental combination rules, for calculating the internal forces used in the fire resistance check.

The accidental combination is given by

)f(AQQG dj,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

EEk

ffk

ffk

The variation in function of the steel temperature of the value for yield strength ky,, proportional limit kp, and modulus 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 the analysis :

unit mass a 7850 kg/m³

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 curveThe 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

K²m/W25)1t8(log34520

c

10g

external fire curve

K²m/W25

20e313.0e687.01660

c

t8.3t32.0g

hydrocarbon curve

K²m/W50

20e675.0e325.011080

c

t5.2t167.0g

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


SCIA 15

n,c factor depending on NAD [1.0]

n,r factor depending on NAD [1.0]

mgcc,neth

4m

4r

8resr,net 2732731067.5h

with configuration factor [1.0]

res resultant emissivity= f m

f emissivity related to fire compartment= [0.800]

m emissivity related to surface material= [0.625]

r = g

gas 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 [m²/m]

V the volume of the member per unit length [m³/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/m²]

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

a the unit mass of steel [kg/m³]

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


SCIA 16

V/Adcc

1et

31cd

V/A

ppaa

pp

t,g10/t,at,g

aap

ppt,a

with Ap the area of fire protection material per unit length [m²/m]

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


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

dp the thickness of the fire protection material [m]



p the unit mass of fire protection [kg/m³]

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 NEN specifications, Chapter 'Steel Temperature'.

Calculation model

The calculation can be performed in 2 domains :

- strength domain

- 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 the temperature/time domain, the critical steel temperature cr,d is computed. From this critical temperature, the fire resistance time tfi,d is calculated (the time domain).

Code CheckThe section and stability checks (buckling, lateral torsional buckling) are performed according to the regulations given in 'ENV 1993-1-2:1995' and/or 'Model Code on Fire Engineering - ECCS N° 111'. The checks are performed 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 sectionsI 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 section

COM Composed section in PRIMAWIN

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 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 class 1

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.

References1 Eurocode 3

Design of steel structuresPart 1 - 1 : General rules and rules for buildingsENV 1993-1-1:1992, 1992

2 Essentials of Eurocode 3Design Manual for Steel Structures in BuildingECCS - N° 65, 1991

3 R. MaquoiELEMENTS DE CONSTRUCTIONS METALLIQUEUlg , Faculté des Sciences Appliquées, 1988

[4] ENV 1993-1-3:1996Eurocode 3 : Design of steel structures Part 1-3 : General rulesSupplementary rules for cold formed thin gauge members and sheetingCEN 1996

[5] Eurocode 3Design of steel structuresPart 1 - 1/ A1 : General rules and rules for buildingsENV 1993-1-1:1992/A1, 1994

[6] Eurocode 3Design of steel structuresPart 1 - 2 : General rules - Structural fire designENV 1993-1-2:1995, 1995

[7] Model Code on Fire Engineering


SCIA 19

ECCS - N° 111May 2001

[8] Eurocode 1Basis of design and actions on structuresPart 2-2 : Actions on structures - Actions on structures exposed to fireENV 1991-2-2:1995


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EC 3 – EN 1993

EC3 code check


Eurocode 3

Design of steel structures

Part 1 - 1 : General rules and rules for buildings

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 of the element (see Ref. 1, table 3.1.)

Steel Grade fy (N/mm²)

fu (N/mm²)

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 355 510

S 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 sections, the average yield strength fya can be used (by setting the proper data flag in the Cross Section input dialog).

The average yield strength is determined as follows :

ybuybug

ybya f2.1,fminffA

²kntff








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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 4 sections (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 torsional buckling (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 the bending 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” are consulted. 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 x5.5.2. Classification x6. Ultimate limit states

6.1. General x6.2. Resistance of cross-sections6.2.1 General x6.2.2 Section properties x

(*)

6.2.3 Tension x

6.2.4 Compression x6.2.5 Bending moment x6.2.6 Shear x6.2.7 Torsion x

(*)

6.2.8 Bending and shear x6.2.9 Bending and axial force x


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6.2.10 Bending, shear and axial force x6.3. Buckling resistance of members6.3.1 Uniform members in compression x

(*)

6.3.2 Uniform members in bending x6.3.3 Uniform members in bending and axial compression x

(*)

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


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

For each load case/combination, the critical section classification over the member is used to perform the stability 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 intermediary section.


SCIA 24





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

With these critical properties, the stability check is performed.


Section properties

The net area properties are not taken into account .

The shear lag effects are neglected .

Torsion check


Built-in beams


Compression members

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



For I sections (symmetric and asymmetric), RHS (Rectangular Hollow Section) sections and CHS (Circular Hollow Section) sections, the elastic critical moment for LTB Mcr is given by the general formula F.2. Annex F


SCIA 25

Ref. 10. For the calculation of the moment factors C1, C2 and C3 we refer to "Calculation of moment factors for LTB".For the other supported sections, the elastic critical moment for LTB Mcr is given by

z2

t

z2

z2

EIL²GI

IIw

LEIMcr


G the shear modulus








Use of diaphragms


Combined bending and axial compression

For prismatic members the value My,Ed is the maximum value of the bending moment around the strong axis in the member. The value Mz,Ed is the maximum value of the bending moment around the weak axis in the member.

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

Interaction Method 1 – Annex A

By default for Czz the formula given in Ref.[1] is used:

In this formula however the position of the factor eLT is incorrect. For exact analysis the formula according to Ref.[9] can be used:


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Interaction Method 2 – Annex B

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

With: h Height of RHS section

b Width of RHS section

Relative slenderness for weak axis



EC3 – EN Fire Resistance



The accidental combination is given by (see EN 1990 – Ref[5])

Eq. 6.11b

Gk,j + P + Ad+ (1,l or 2,l)Qk,l+ 2,iQk,i

The choice between 1,l or 2,l is done by the user. Default is 1,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

1,l 2,l combination coefficients


SCIA 27

Material properties



a

,a,E

y

,p,p

y

,y,y

EEk

ffk

ffk

The variation in function of the steel temperature of the value for yield strength ky,, proportional limit kp, and modulus 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.


unit mass a

7850 kg/m³

thermal elongation l/l

14 x 10-6 (a-20)

thermal conductivity a

45 W/mK


In this part, the nominal temperature-time curves and the related net heat flux are described. See Ref.[8], Section 3, and Ref.[7], II.2.2.

Nominal temperature-time curve

The following temperature-time curves can be selected :



c the coefficient of heat transfer by convection


SCIA 28

ISO 834 curve

KmWt

c

g

²/25)18(log34520 10

external fire curve

KmW

ee

c

ttg

²/25

20313.0687.01660 8.332.0

hydrocarbon curve

KmW

ee

c

ttg

²/50

20675.0325.011080 5.2167.0

smoldering fire curve

20t1544g

during 20 minutes, followed by the standard ISO 834 curve

user defined temperature-time curve

Net heat flux

rnetcnetdnet hhh ,,,

with hnet,d the net heat flux

hnet,c the convective heat flux


SCIA 29

hnet,r the radiative heat flux

mgcc,neth

4m

4r

8resr,net 2732731067.5h

with configuration factor [1.0]

res resultant emissivity= f m

f emissivity related to fire compartment= [0.800]

m emissivity related to surface material= [0.625]

r = g

gas 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

VAk dnetaa

mshta ,,

/







ksh correction factor for the shadow effect [1.0]The correction factor is calculated for I sections only



SCIA 30

V/Adcc

1et

31cd

V/A

ppaa

pp

t,g10/t,at,g

aap

ppt,a













The value a,t 0.0



SCIA 31

Calculation model


- strength domain



Code CheckThe section and stability checks (buckling, lateral torsional buckling) are performed according to the regulations given in 'EN 1993-1-2:2005'. The checks are performed in the resistance domain or in the temperature/time domain..Torsional buckling and shear buckling are not considered.



- 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.

- check for class 4 sections : Annex E




L Angle section

U Channel section

T T section


Z Z section


Cold formed section


O Solid tube


SCIA 32



".









x x x


x x x




x x x x x x



References1 Eurocode 3

Design of steel structuresPart 1 - 1 : General rules and rules for buildingsEN 1993-1-1:2005

[2] Eurocode 3 Design of steel structuresPart 1-3: General rulesSupplementary rules for cold-formed members and sheetingEN 1993-1-3:20XX, 2003

3 Eurocode 3 Design of steel structuresPart 1.5 : Plated structural elementsprEN 1993-1-5 : 2003


[5] EN 1990Eurocode – Basis of structural designEN 1990:2002 E

[6] Eurocode 3


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Design of steel structuresPart 1 - 2 : General rules - Structural fire designEN 1993-1-2:2005

[7] Model Code on Fire EngineeringECCS - N° 111May 2001

[8] Eurocode 1Actions on structuresPart 1-2 : General Actions - Actions on structures exposed to fireprEN 1991-1-2:2002

[9] Rules for Member Stability in EN 1993-1-1Background documentation and design guidelinesECCS - N° 1192006



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DIN18800DIN18800 Code check


DIN 18800 Teil 1StahlbautenBemessung und KonstruktionDK 693.814.014.2, November 1990

DIN 18800 Teil 2StahlbautenStabilitätsfälle, Knicken von Stäben und StabwerkenDK 693.814.074.5, November 1990

DIN 18800 Teil 3StahlbautenStabilitätsfälle, PlattenbeulenDK 693.814.073.1, November 1990

Material properties

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

The standard steel grades are :


t<=40 t<=40 40<t<=80 40<t<=80

fy fu fy fu

S235S 235St 37-2

240 360 215 360

S275S 275

280 430 255 430

S355S 355St 52-3

360 510 325 510

t<=40 t<=40 40<t<=100 40<t<=100


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fy fu fy fu

S420S 420

420 520 390 520

S460S 460

460 550 430 550

Consulted articles

For the section check, the cross section is classified according to DIN18800 Teil I, Table 12,13,14,15 and 18.. Depending on this classification, the section is checked as slender section, EL/EL (elastic/elastic), as EL/PL (elastic/plastic) or as PL/PL (plastic/plastic). For the EL/EL check, DIN18800 Teil I, Element (746), (747), (748), (749), (750) are used.

The EL/PL check takes the rules from DIN18800 Teil I, Element (756), (757) and Table (16) ,(17). The PL/PL check is done according to DIN18800 Teil I, Element (758), Table (16),(17). The slender cross section is checked according to DIN18800 Teil 2, Element (715).

For the stability check, the beam element is checked according to DIN18800 Teil 2 for buckling, lateral torsional buckling and bending and compression. The following criteria are used :

compression : Element (304),(306)

lateral torsional buckling : Element (311),(309)

bending and axial compression : Element (313),(321),(322)

bending (LTB) and compression : Element (320),(323)

For slender sections, the following criteria are used :

calculation of effective area : Element (705),(706),(708),(709),(712),(713)

buckling check : Element (715),(716),(718),(719)

LTB check : Element (725),(726),(728),(729)

For the shear buckling check, the beam element is checked according to DIN18800 Teil 3. The following criteria are used : Element (113), (504), (602),(603)

A more detailed overview for the used articles is given for the relevant parts following table. The chapters marked with “x” are consulted. The chapters marked with (*) have a supplementary explanation the following chapters.

Teil 1

7.5. Verfahren beim Tragsicherheitsnachweis Nachweise (*)

7.5.1. Abgrenzungskriterien und Detailregelungen (*)

7.5.2. Nachweis nach dem Verfahren Elastisch-Elastisch(745)………………………………………………………………………………(746) ………………………………………………………………………………(747) ………………………………………………………………………………(748) ………………………………………………………………………………(749) ………………………………………………………………………………(750) ………………………………………………………………………………

xxxxxxx


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Nachweis nach dem Verfahren Elastisch-Plastisch(753) ………………………………………………………………………………(756) ………………………………………………………………………………(757) ………………………………………………………………………………

xxxx

Nachweis nach dem Verfahren Plastisch-Plastisch(758) ………………………………………………………………………………

x x

Teil 2

3.2. Planmässig mittiger Druck3.2.1. Biegeknicken(304) ………………………………………………………………………………

xxx (*)

3.2.2. Biegedrillknicken(306) ………………………………………………………………………………

x x (*)

3.3. Einachsige Biegung ohne Normalkraft3.3.1. Allgemeines(307) ………………………………………………………………………………

x x x

3.3.2. Behinderung der Verformung(309) ………………………………………………………………………………

x x (*)

3.3.3. Nachweis des Druckgurtes als Druckstab


xx (*)

3.4. Einachsige Biegung mit Normalkraft3.4.1. Stäbe mit geringer Normalkraft(312) ………………………………………………………………………………

xx x

3.4.2. Biegeknicken(314) ………………………………………………………………………………

x x


x x

3.5. Zweiachsige Biegung mit oder ohne Normalkraft3.5.1. Biegeknicken(321) ………………………………………………………………………………(322) ………………………………………………………………………………

x x xx(*)


xx

4. Mehrteilige, einfeldrige Stäbes4.1. Allgemeines4.2. Häufig verwendete Formelzeichnen(404) ………………………………………………………………………………4.3. Ausweichen rechtwinklig zur stofffreien Achse(405) ………………………………………………………………………………(406)……………………………………………………………………………….(408)……………………………………………………………………………….(409)……………………………………………………………………………….

x(*)

x

xxxx

7. Planmässig gerade Stäbe mit ebenen dünnwandigen Quenschnittsteilen7.1. Allgemeines(701) ………………………………………………………………………………(702) ………………………………………………………………………………(704) ………………………………………………………………………………

x x xxx


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7.2. Berechnungsgrundlage(705) ………………………………………………………………………………(706) ………………………………………………………………………………(707) ………………………………………………………………………………(708) ………………………………………………………………………………(709) ………………………………………………………………………………

x xxxxx

7.3. Wirksame Breite beim Verfahren Elastisch-Elastisch(711) ………………………………………………………………………………(712) ………………………………………………………………………………(713) ………………………………………………………………………………

x xx (*)x

7.4. Wirksame Breite beim Verfahren Elastisch-Plastisch

7.5. Biegeknicken7.5.1. Spannungsnachweis beim Verfahren Elastisch-Elastisch(715) ………………………………………………………………………………

x x x

7.5.2. Vereinfachte Nachweise(716) ………………………………………………………………………………(718) ………………………………………………………………………………(719) ………………………………………………………………………………(721) ………………………………………………………………………………

x xxxx

7.6. Biegedrillknicken(722) ………………………………………………………………………………(723) ………………………………………………………………………………(725) ………………………………………………………………………………(726) ………………………………………………………………………………(728) ………………………………………………………………………………(729) ………………………………………………………………………………

x xxxxxx

Teil 3

5. Nachweise(504) ………………………………………………………………………………

(*)x

6. Abminderungsfaktoren(601) ………………………………………………………………………………(602) ………………………………………………………………………………

x xx




Net area properties


The holes for fasteners are neglected.


SCIA 38

Plastic interaction formula for RHS section

b

s/2h

AG

AS/2

For RHS section, classified as Plastic-Plastic or Elastic-Plastic, the plastic interaction formula according to Ref.[13], can be selected.

Used variable :

A sectional area

AS = s h

AG = (A-AS)/2.0

Wel,y elastic section modulus around y axis

Wel,z elastic section modulus around z axis

fy,d yield strength

y,d shear strength


SCIA 39

Vz,pl,Rd = AS y,d

Vy,pl,Rd = 2AG y,d

NSd normal force

My,Sd bending moment around y axis

Mz,Sd bending moment around z axis

Vy,Sd shear force in y direction

Vz,Sd shear force in z direction

MT,Sd torsional moment

2

Rd,pl,z

Sd,TSd,z

z

zRd,pl,z

Sd,TSd,z

Vb

MV

1else

0.141

Vb

MV

if

2

Rd,pl,y

Sd,TSd,y

y

yRd,pl,y

Sd,TSd,y

Vh

MV

1else

0.141

Vh

MV

if

Ar= zAS + 2yAG

r

Sz A

A

Npl,Rd = Ar fy,d

ydy,elRd,plRd,pl,y fW25.1,hN4

2minM

ydz,elRd,plRd,pl,z fW25.1,bN4

1minM


SCIA 40

Rd,pl

Sd

NNn

Rd,pl,y

Sd,yy M

Mm

Rd,pl,z

Sd,zz M

Mm

The following interaction formula are checked :

Plastic interaction formula for CHS section

For CHS section, classified as Plastic-Plastic or Elastic-Plastic, the plastic interaction formula according to Ref.[14], Tafel 6.74, is used :


SCIA 41

selQ,plQ,pl

srQ,pl

r

2

pl

v

pl

v

pl

v

spl

2z

2yv

2z

2yv

plQ

vQ,pl

v

W25.1,NdminM

ANdtA

QQ

1:41

QQ

1:41

QQ

3dt2Q

MMM

QQQ

1

2NNcos

1MM

with Qy,Qz internal shear force

Nv internal normal force

My,Mz internal bending moments

s yield strength

d,t dimensions from CHS

Wel elastic section modulus

t

d


SCIA 42

Torsion check


The stability check (DIN 18800 T2, formula 28 & 30) for doubly symmetric I section becomes (Ref.[9], pp. 259) :

)30(0.1kM

MMk

MM

NN

)28(0.1kM

MMk

MM

NN

zd,z,pl

w,zzy

d,y,plM

y

d,plz

zd,z,pl

w,zzy

d,y,pl

y

d,pl

with Mz,w

hM2 w

Mw bimoment (see chapter 'Standard diagrams for warping torque, bimoment and the St.Venant torsion')

kz = 1.50 In case there is no compression force kz is taken as 1.00 (Ref.[9], pp. 270).

Built-in beams


Calculation of the buckling length

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 (see “Calculation of critical Euler force for VARH elements”).


Torsional buckling

The slenderness for torsional buckling vi is given by (see Ref.6 , 7.5):


SCIA 43

222

22

0

222

2

221093.04

112

M

Mz

pM

z

zzvi

ic

zic

cic

il

with l0 the torsional buckling length, refers to the input value for the system length lyz

lz the system length for buckling around zz-axis

Remark : the z-axis refers to the axis which goes through the shear force centre.

z refers to the buckling ratio around the zz-axis

Remark : the z-axis refers to the axis which goes through the shear force centre.

0 refers to end warping and is input by the value kxy

zM the shear center

iy the radius of gyration around major axis

iz the radius of gyration around minor axis

ip² = iy² + iz²

iM² = ip² + zM²


Iz the moment of inertia around minor axis


z

tzzzzw

IIlllIc

2200

22 039.0/

With this slenderness vi and the buckling curve c, the reduction factor is calculated.

Use of diaphragms

(see also Ref.7,3.5 and Ref.8,3.3.4.)

The shear stiffness S for diaphragm is calculated as follows:

LK+K

10a.=S

s

21

4


SCIA 44

with a the frame distance

Ls the length of diaphragm

K1 factor K1

K2 factor K2

The torsional constant It is adapted with the stiffness of the diaphragms:

GlvorhCII2

2

tid,t

with l the LTB length

G the shear modulus

vorhC

the actual rotational stiffness of diaphragm

LTB Check

For aysmmetric I sections, RHS (Rectangular Hollow Section) sections and CHS (Circular Hollow Section) sections, the elastic critical moment for LTB Mcr is given by the general formula F.2. Annex F Ref. 4. For the calculation of the moment factors C1, C2 and C3 we refer to "Calculation of moment factors for LTB".

Depending on the input of the basic data, Mcr for symmetric I sections is given by the general formula F.2. Annex F Ref. 4, by the DIN formula (19), or by formula according to Ref.[11] "Roik, Carl, Lindner, Biegetorsionsprobleme gerader dünnwandiger Stäbe, Verlag von Wilhelm Ernst & Sohn, 1972".

DIN formula (19) :

p

2p

2ik z5.0z25.0cNMcr

z

t2

z2

002

zw2

IIl039.0l/lIc

with l,l0 the LTB length

z refers to rotational end-restraint ‘in plan’ (about the z-z local axis).

0 refers to end warping

zp the point of load application



SCIA 45

Iz the moment of inertia around minor axis


A the sectional area


vi the slenderness for torsional buckling ( see above)

the moment factor ( equivalent for factor C1)

2z

z2

ik lEIN

Roik, Carl & Lindner

z

tw

p2

pzcry,ki

II²l039.0Ic

²z5

²c²

z5²l

²EIMM

with

moment factor according to Roik, Carl, Lindner

modulus of elasticity

moment of inertia around weak axis zz

system length for LTB

application point for loading, negative value is on top and has negative influence

warping constant

torsional constant

The factor is supported for the following cases (described in Ref.[11], tables 5.13, 5.14, 5.15, 5.18, 5.19, 5.20, 5.21, 5.22, 5.23, 5.24, 5.25, 5.26, 5.27, 5.28, 5.29, 5.30, 5.33) :

linear moment distribution :


SCIA 46

moment line according to distributed loading

moment line according to concentrated loading


SCIA 47

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

z2

t2

z2

z2

EIGIL

IIw

LEIMcr


G the shear modulus









SCIA 48

Combined flexion for check method 2

The value My is the maximum value of the bending moment around the strong axis in the member. The value Mz is the maximum value of the bending moment around the weak axis in the member. For non-prismatic sections, the values My and Mz are the concurrent bending moments for each intermediary section.



(1) 2I

(2) 2Uo

(3) 2Uc



- buckling resistance check around weak axis of single chord with NG

- section check of single chord, using internal forces (Ref.[7], pp.88-95) :

4amaxV

M

2maxV

V

WA

)lasin(Mmax

2NN

yG

yG

*z

GzG

- section check of single batten, using the internal forces (Ref.[7], pp.88-95) :

2TeM

2hamaxV

Ty

y


SCIA 49

For the calculation of maxVy, the value of Mz is increased with the value of the internal force Mzz.

l

a

hy

e

Effective area properties

The calculation of the effective area is performed with the direct method (sigma_d = fy,k) according to the El-El procedure (DIN18800 T2, 7.3.).


For each load case and combination, the most critical effective area properties are saved. The most critical effective area properties are the effective area properties on the position where the appropriate moment of inertia is the minimum.With these critical properties, the stability check is performed.



SCIA 50



Shear buckling check with buckling influence

The influence of the buckling effect into the shear buckling control, is neglected when there is a bending moment present.

It means that k=1 if <0.9. See also Ref.[3], Element 503.

Cold formed thin gauge membersThe following table includes a list of DASt-Richtlinie 016 (Ref.[12]) elements which are implemented in EPW by using the related DIN18800 T2 (Ref.[2]) element.

Supported elements fromDASt - Richtlinie 016

Covered by DIN 18800 T2 elements

Remarks

3.7.1. Grenzzustand der Tragfähigkeit

328 Tab.26

329 712

330 712

333 Tab.27

335 706

4.3.1. Biegemomententragfähigkeit

404 715

4.4. Biegedrillknicken biegebeanspruchter Bauteile4.4.3. Allgemeiner Nachweis

421 311

422 311

423 725, 726

4.5. Druckbeanspruchte einteilige Stäbe4.5.1. Allgemeines

429 708-710

430 708-710

431 708-710

432 708-710

433 708-710

434 708-710

4.5.2. Planmäig mittiger Druck


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435 716 ADef is not used

436 manual input / input in profile library for KSL

437 723

438 723

4.5.3. Einachsige Biegung mit Druck

440 707

441 718

442 728

4.5.3. Zweiachsige Biegung mit Druck

443 707

444 721 ADef is not used

445 729


RHS Rectangular Hollow Section (RHS)

CHS Circular Hollow Section (CHS)

L Angle section

U Channel section

T T section



Cold formed section


O Solid tube



".


I RHS CHS L U T PPL RS O COM NUM

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

Section check PL-PL x x

Section check EL-PL x x

Section check EL-EL x x x x x x x x x x x x

Section check slender section

x x x x x x

Stability check x x x x x x x x x x x x

Stability check slender x x x x x x


SCIA 52

section


(1) sections are classified as EL-EL cross section by default.

References1 DIN 18800 Teil 1

StahlbautenBemessung und KonstruktionDK 693.814.014.2, November 1990

2 DIN 18800 Teil 2StahlbautenStabilitätsfälle, Knicken von Stäben und StabwerkenDK 693.814.074.5, November 1990

3 DIN 18800 Teil 3StahlbautenStabilitätsfälle, PlattenbeulenDK 693.814.073.1, November 1990

[4] Eurocode 3Design of steel structuresPart 1 - 1 : General rules and rules for buildingsENV 1993-1-1:1992, 1992

[5] R. MaquoiELEMENTS DE CONSTRUCTIONS METALLIQUEUlg , Faculté des Sciences Appliquées, 1988

[6] G. Hünersen, E. FritzscheStahlbau in BeispielenBerechnungspraxis nach DIN 18 800 Teil 1 bis Teil 3 (11.90)Werner-Verlag, Düsseldorf 1991

[7] E. KahlmeyerStahlbau nach DIN 18 800 (11.90)Werner-Verlag, Düsseldorf

[8] Beuth-KommentareStahlbautenErläuterungen zu DIN 18 800 Teil 1 bis Teil 4, 1.AuflageBeuth Verlag, Berlin-Köln 1993


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[9] Stahlbau Kalender 1999DSTVErnst & Sohn, 1999


[11] Roik, Carl, LindnerBiegetorsionsprobleme gerader dünnwandiger StäbeVerlag von Wilhelm Ernst & Sohn1972

[12] DASt-Richtlinie 016Bemessung und konstruktive Gestaltung von Tragwerken aus dünnwandigen kaltgeformted BauteilenStahlbau-Verlagsgesellschaft - 1992

[13] H. Rubin,Interaktionsbeziehungen für doppeltsymmetrische I- und Kasten-Querschnitte bei zweiachsiger Biegung und NormalkraftDer Stahlbau 5/1978, 6/1978

[14] Stahl im Hochbau14. Auflage, Band I / Teil 21986, Verlag Stahleisen mbH, Düsseldorf


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ONORM B 4300ONORM B 4300 Code check


ÖNORM B 4300-1StahlbauBerechnung und Konstruktion der TragwerkeBemessung nach GrenzzuständenDK 624.014.2.046, März 1994

ÖNORM B 4300-2StahlbauKnicken von Stäben und StabwerkenBedingungen für die gemeinsame Anwendung von DIN 18 800 Teil 2 und ÖNORM B 4300-1DK 624.014.2.075.2, April 1994

ÖNORM B 4300-3PlattenbeulenBedingungen für die gemeinsame Anwendung von DIN 18 800 Teil 3 und ÖNORM B 4300-1DK 624.014.2.075.4, April 1994

DIN 18800 Teil 1StahlbautenBemessung und KonstruktionDK 693.814.014.2, November 1990

DIN 18800 Teil 2StahlbautenStabilitätsfälle, Knicken von Stäben und StabwerkenDK 693.814.074.5, November 1990

DIN 18800 Teil 3StahlbautenStabilitätsfälle, PlattenbeulenDK 693.814.073.1, November 1990

Material properties

For standard steel grades, the yield strength fy and tensile strength fu are defined according to the thickness of the element (see Ref. 1, 2.1. and Ref. 4, Tab.1)




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t<=40 t<=40 40<t<=80 40<t<=80

fy fu fy fu

St 360S235S 235

240 360 215 360

St 430S275S 275

280 430 255 430

St 510S355S 355

360 510 325 510

t<=40 t<=40 40<t<=100 40<t<=100

fy fu fy fu

S420S 420

420 520 390 520

S460S 460

460 550 430 550

Consulted articles

For the section check, the cross section is classified according to ONORM B 4300-1 Tab.3,4,5 and to DIN18800 Teil I, Table 15,18. Depending on this classification, the section is checked as slender section, EL/EL (elastic/elastic), as EL/PL (elastic/plastic) or as PL/PL (plastic/plastic). For the EL/EL check, ONORM B 4300-1 Art. 5.2. is used. (The 7% increase of the moment of inertia is taken into account for rolled I section - see Ref. 1, Art. 5.2.5.4.).

The EL/PL check takes the rules from DIN18800 Teil I, Element (756), (757) and Table (16) ,(17). The PL/PL check is done according to DIN18800 Teil I, Element (758), Table (16),(17). The slender cross section is checked according to DIN18800 Teil 2, Element (715).

For the stability check, the beam element is checked according to DIN18800 Teil 2 for buckling, lateral torsional buckling and bending and compression. The following criteria are used :

compression : Element (304),(306)

lateral torsional buckling : Element (311),(309)

bending and axial compression : Element (313),(321),(322)

bending (LTB) and compression : Element (320),(323)

For slender sections, the following criteria are used :

calculation of effective area : Element (705),(706),(708),(709),(712),(713)

buckling check : Element (715),(716),(718),(719)

LTB check : Element (725),(726),(728),(729)


SCIA 56

For the shear buckling check, the beam element is checked according to DIN18800 Teil 3. The following criteria are used : Element (113), (504), (602),(603)

A more detailed overview for the used articles is given in "DIN18800 Code check".




L Angle section

U Channel section

T T section



Cold formed section


O Solid tube

NUM Numerical sections


".




Section check PL-PL x

Section check EL-PL x

Section check EL-EL x x x x x x x x x x x x

Section check slender section

x x x x x x

Stability check x x x x x x x x x x x x

Stability check slender section

x x x x x x


(1) sections are classified as EL-EL cross section by default.

References

1 ÖNORM B 4300-1StahlbauBerechnung und Konstruktion der Tragwerke


SCIA 57

Bemessung nach GrenzzuständenDK 624.014.2.046, März 1994

2 ÖNORM B 4300-2StahlbauKnicken von Stäben und StabwerkenBedingungen für die gemeinsame Anwendung von DIN 18 800 Teil 2 und ÖNORM B 4300-1DK 624.014.2.075.2, April 1994

3 ÖNORM B 4300-3PlattenbeulenBedingungen für die gemeinsame Anwendung von DIN 18 800 Teil 3 und ÖNORM B 4300-1DK 624.014.2.075.4, April 1994

[4] DIN 18800 Teil 1StahlbautenBemessung und KonstruktionDK 693.814.014.2, November 1990

[5] DIN 18800 Teil 2StahlbautenStabilitätsfälle, Knicken von Stäben und StabwerkenDK 693.814.074.5, November 1990

[6] DIN 18800 Teil 3StahlbautenStabilitätsfälle, PlattenbeulenDK 693.814.073.1, November 1990


SCIA 58

NENNEN6770/6771 Code check


Staalconstructies TGB 1990Basiseisen en basisrekenregels voor overwegend statisch belaste constructiesNEN 6770, december 1991

Staalconstructies TGB 1990StabiliteitNEN 6771, december 1991-januari 2000

Material properties

For standard steel grades, the yield strength fy and tensile strength fu are defined according to the thickness of the element (see Ref. 1, art.9.1.2.1.1.)



t<=40 t<=40 40<t<=100 40<t<=100 100<t<=250 100<t<=250fy fu fy fu fy fy

S235S 235

235 360 215 340 175 320

S275S 275

275 430 255 410 205 380

S355S 355

355 510 335 490 275 450

S420S 420

420 520 390 520

S460S 460

460 550 430 550

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

Consulted articles


SCIA 59

The cross section is classified according to NEN 6771 Table 1. (class 1,2,3 or 4).

The section is checked on following criteria :

tension : NEN 6770 Art. 11.2.1., NEN 6771 Art. 11.2.1.

compression : NEN 6770 Art. 11.2.2., NEN 6771 Art. 11.2.2.

shear : NEN 6770 Art. 11.2.4., NEN 6771 Art. 11.2.4.

bending, shear and axial force : NEN 6770 Art. 11.3., NEN 6771 Art. 11.3.

For the stability check, the element is checked on following criteria :

compression : NEN 6771 Art.12.1.1.1/ 12.1.2./12.1.3.

lateral torsional buckling : NEN 6771 Art.12.2.

bending and axial compression: NEN 6771 Art.12.3.

shear buckling : NEN 6771 Art.13.8. / 13.9.


SCIA 60

A more detailed overview for the used articles is given for NEN6770 part 11,12 and NEN6771 part 10,11,12,13. The chapters marked with “x” are consulted. The chapters marked with (*) have a supplementary explanation the following chapters.

NEN6770

11.Toetsing van de doorsnede11.1. Algemeen

xx

11.2. Enkelvoudige krachten en momenten11.2.1. Axiale trek

xx

11.2.2. Axiale druk x

11.2.3. Buiging

11.2.4. Afschuiving x

11.2.5. Torsie x

11.3. Combinaties van krachten en momenten11.3.1. Enkele buiging met normaalkracht en afschuiving

xx

11.3.2. Dubbele buiging met normaalkracht en afschuiving x

11.4. Vloeicriterium x

11.5. De invloed van de boutgaten (*)

NEN6771

10.2.4. Doorsneden x (*)

11.Toetsing van de doorsnede11.1. Algemeen

xx

11.2. Enkelvoudige krachten en momenten11.2.1. Axiale trek

xx

11.2.2. Axiale druk x

11.2.3. Buiging

11.2.4. Afschuiving x

11.2.5. Torsie

11.3. Combinaties van krachten en momenten x

12. Toetsing van de stabiliteit12.1. Op druk belaste staven12.1.1. Knikstabiliteit

xxx (*)

12.1.2. Torsiestabiliteit x

12.1.3. Torsieknikstabiliteit x

12.1.4. Verend gesteunde staven

12.1.5. Staven in vakwerken

12.1.6. Samengestelde staven12.1.6.1 Algemeen12.1.6.2. Benodigde grootheden12.1.6.3. Toetsing van het middenveld van de samengestelde staaf12.1.6.4. Toetsing van de eindvelden van de samengestelde staaf12.1.6.4.2 Staven met raamwerkverband

x(*)xxxxx


SCIA 61

12.2. Op buiging belaste staven(kipstabiliteit)12.2.1. Toepassingsgebied

xxx

12.2.2. Toetsingsregel x

12.2.3. Ongesteunde lengte

12.2.4. Opleggingen en zijdelingse steunen

12.2.5. Het theoretisch elastische kipmoment x (*)

12.3. Op druk en buiging belaste staven12.3.1. Knikstabiliteit

xx

12.3.2. Torsiestabilteit x

12.3.3. Torsieknikstabiliteit x

12.4. Op trek en buiging belaste staven

13. Toetsing van de plooistabiliteit13.1. Algemeen

xx

13.2. Geometrie van het verstijfde en onverstijfde plaatveld x

13.3. Geometrie van de verstijvingen

13.4. Belasting in het vlak van het plaatveld13.4.1. Normaalspanning in langsrichting

xx

13.4.2. Schuifspanningen x

13.4.3. Normaalspanningen in dwarsrichting

13.4.4. Platen in en loodrecht op hun vlak belast

13.5. Belasting op verstijvingen

13.6. Ideële kritieke plooispanning van een onverstijfd plaatveld x

13.7. De plooispanning van een onverstijfd plaatveld13.7.1. Bepaling van de relatieve slankheid van het plaatveld

xx

13.7.2. De plooispanning voor een onverstijfd plaatveld met als opleggingen dwarsverstijving(en) en/of randen x

13.7.3. De plooispanning voor een onverstijfd plaatveld met ten minste een langsverstijving als oplegging

13.8. Eisen waaraan plaatvelden en verstijvingen moeten voldoen13.8.1. Onverstijfd plaatveld

xx

13.8.2. Dwarsverstijvingen

13.8.3. Langsverstijvingen

13.8.4. Stijfheidseisen te stellen aan langs- en dwarsverstijvingen

13.8.5. Doorsnedecontrole voor langs- en dwarsverstijvingen

13.9. Interactie tussen plooi en knik13.9.1. Algemeen

x (*)x

13.9.2. Constructies opgebouwd uit plaatvelden al of niet verstijfd met dwarsverstijvingenx

13.9.3. Constructies opgebouwd uit plaatvelden verstijfd met langsverstijvingen en/of niet verstijfd met dwarsverstijvingen

13.9.4. Berekeningen van de dwarsverstijvingen

Section properties

The influence of the bore hole is neglected.


SCIA 62








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

With these critical properties, the stability check is performed.


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

Torsion check


Built-in beams

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

Buckling length

For the calculation of the buckling length, we refer tochapter "Calculation of buckling ratio".




SCIA 63


For symmetric I sections and RHS (Rectangular Hollow Section) sections, the elastic critical moment for LTB Mcr is given by the formula of Ref 2, part 12.2.5.. When the factor > 5000, the elastic critical moment for LTB Mcr is given by the general formula in EC3, Annex F, F.2. Ref 3. For asymmetric I sections, the elastic critical moment for LTB Mcr is given by the general formula in EC3, Annex F, F.2. Ref 3.

For the calculation of the moment factors C1, C2 and C3 we refer to Ref.[7], tables 9 (case 1), 10 and 11.


z2

t2

z2

z2

EIGIL

IIw

LEIMcr


G the shear modulus








Use of diaphragms




(1) 2I

(2) 2Uo

(3) 2Uc


SCIA 64



- buckling resistance check around weak axis of single chord with Nf,s;d

- section check of single chord, using internal forces :

4aQ

M

2Q

V

NN

f;s;dG

f;s;dG

f;s;dG

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

4aQ

M

2haQ

V

ds;f;ds;k;

0

ds;f;ds;k;

For the calculation of Qf;s;d, the value of My;s;d is increased with the value of the internal force Mzz.


SCIA 65

l

a

ho



Shear buckling check with buckling influence

The influence of the buckling effect into the shear buckling control, is neglected when there is a bending moment present, i.e. if <0.9.

NEN6072 - Fire ResistanceFor more info, we refer to Ref.[8], Ref.[9].


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Fire actions effect

The design effects of actions for the fire situation are taken from the results of the analysis. It is recommended to use the special combination rules according to Ref.[10], NEN6702 6.2.2., for calculating the internal forces used in the fire resistance check.

This special combination is given by

rep;aa;frep;iiq;frepg;f FQG

with Grep characteristic values of permanent actions

Qi characteristic value of the variable action

Fa;rep design values of special action (from fire exposure)

f;g partial safety factor for permanent actions in the special combination=1.0

f;q partial safety factor for variable actions in the special combination=1.0

f;a partial safety factor for special actions in the special combination=1.0

I the 'momentaaan' factor for the variable action

Material properties

The yield strength is depending on the steel temperature :

d;yd;;y ff

The variation in function of the steel temperature of the value for yield strength is given by :

- =1.0 when a 400° C

- 26.01e03.1

when 400°C < a 1200° C

with

2.39482a

a steeltemperature in °C

fy;d design value for yield strength at room temperature

fy;;d design value for yield strength at increased temperature


SCIA 67

The following default properties are considered to be constant during the analysis :

unit mass a 7850 kg/m³



Nominal temperature-time curveThe standard temperature-time (ISO 834) curve is used :

)1t8(log34520 10g



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

4a

4t

at

rr

rc

ataa

a

100273

10027367.5

tPc



P = Am/V

t gas temperature in [°C]

a steel temperature [°C]


t the time interval [seconds]


r resultant emissivity= 0.5

c coefficient of heat transfer by convection = 25 W/(m²K)


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The increase of temperature a in an insulated (non intumescent coating) steel member during a time interval t

iiaa

ii

M

i

ef;d;ief

t5/

atMiaa

efa

Pdc2c

321

1d

K

1etPcK



Pi = Ap/V


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

di the thickness of the fire protection material [m]



i the unit mass of fire protection [kg/m³]

a the steel temperature at time t

t the ambient gas temperature at time t

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

i;d;ef the thermal conductivity of the fire protection material [W/mK]

The increase of temperature a in an insulated (intumescent coating) steel member during a time interval t

tPcK

atiaa

ef;da



Pi = Ap/V


Kd;ef coefficient of heat transfer of the intumescent coating



SCIA 69


a the steel temperature at time t

t the ambient gas temperature at time t

i;d;ef the thermal conductivity of the fire protection material [W/mK]


SCIA 70

Calculation model


- strength domain


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

The critical steel temperature a,cr is given by :

4821

8925.01ln2.39 846.3cr,a

with degree of utilization at time t=0

correction factor= 1.00 for tension elements= 1.00 for beams, statically determined, 4 side exposure= 0.70 for beams, statically determined, 3 side exposure= 0.85 for beams, statically undetermined, 4 side exposure= 0.60 for beams, statically undetermined, 3 side exposure= 1.20 for compression elements (inclusive the buckling check)= 1.20 for compression and bending elements (inclusive the buckling and LTB check)

Code CheckThe section and stability checks (buckling, lateral torsional buckling) are performed according to the regulations given in NEN6770/6771, adapted with the yield strength for the increased temperature and the correction factor. The checks are performed in the resistance domain or in the temperature/time domain. Shear buckling is not considered.




L Angle section


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U Channel section

T T section


Z Z section


Cold formed section


O Solid tube



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








x x x


x x x




x x x x x x




SCIA 72

References1 Staalconstructies TGB 1990

Basiseisen en basisrekenregels voor overwegend statisch belaste constructiesNEN 6770, december 1991

2 Staalconstructies TGB 1990StabiliteitNEN 6771, december 1991

3 Eurocode 3Design of steel structuresPart 1 - 1 : General rules and rules for buildingsENV 1993-1-1:1992, 1992




[7] Staalconstructies TGB 1990StabiliteitNEN 6771, januari 2000

[8] NEN 6072Rekenkundige bepaling van de brandwerendheid van bouwdelenStaalconstructiesDecember 1991

[9] NEN 6072/A2 - WijzigingsbladRekenkundige bepaling van de brandwerendheid van bouwdelenStaalconstructiesDecember 2001

[10] NEN 6702Belastingen en vervormingen TGB 1990December 1991


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AISC – ASD : 1989

AISC - ASD Code check


Manual of Steel Construction

Allowable Stress Design

Part 5 : Specification and Codes

AISC, Ninth Edition, 1989

The cross section is classified according to Table B5.1. (compact, noncompact, or slender section).

The member is checked on following criteria :

tension : D1

compression : E2, E3

flexural members : F1,F2,F3,F4

plate girders : G2

combined forces : H1,H2

A more detailed overview for the used articles of the relevant parts is given in the following table. The chapters marked with “x” are consulted. The chapters marked with (*) have a supplementary explanation the following chapters.

B. DESIGN REQUIREMENTS

B1. Gross Area x

B2. Net Area (*)

B3. Effective Area

B4. Stability

B5. Local Buckling1.Classification of Steel Sections2.Slender Compression Elements

(*)xx

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. TENSION MEMBERS

D1. Allowable Stress x (*)


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D2. Built-up members

D3. Pin-Connected Members

E. COLUMN AND OTHER COMPRESSION MEMBERS

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 AND OTHER FLEXURAL MEMBERS (*)

F1. Allowable Stress : Strong Axis Bending of I-Shaped Members and Channels1.Members with Compact Sections2.Members with Non-Compact Sections3.Members with Compact or Non-Compact Sections with Unbraded Length Greater then Lc

x

xxx

F2. Allowable Stress : Weak Axis Bending of I-Shaped Members, Solid Bars and Rectangular Plates1.Members with Compact Sections2.Members with Non-Compact Sections

x

xx

F3. Allowable Stress : Bending of Box Members, Rectangular Tubes and Circular Tubes1.Members with Compact Sections2.Members with Non-Compact Sections

x

xx

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. COMBINED STRESSES

H1. Axial Compression and Bending x

H2. Axial Tension and Bending x

APPENDIX B. DESIGN REQUIREMENTS

B5. Local Buckling x


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Classification of sectionsFor each intermediary section, the classification is determined..

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 is determined for each intermediary section.

Section properties The influence of the bore hole is neglected, i.e. only the gross area is used.

Buckling lengthFor the calculation of the buckling length, we refer to "Calculation of buckling ratio".The buckling properties for a VARH element are calculated by using the critical Euler force for this member (see “Calculation of critical Euler force for VARH elements”).

Flexural Torsional Buckling

The slenderness ratio for flexural torsional buckling (KL/r)e is given by

FeE

rKL

e

See Ref. 1, Commentary Chapter E1.

The calculation of Fe is given in Ref. 2, Appendix E.

Lateral-torsional bucklingFor I sections and channel sections, the allowable LTB stress is given in F1.For RHS (Rectangular Hollow Section) sections and CHS (Circular Hollow Section) , the allowable LTB stress is given in F3.

For angle sections with symmetrical legs, the allowable LTB stress is given in Ref. 1, pp.309-314, “Specification for allowable stress - Design of single-angle members”.


z2

t2

z2

z2

EIGIL

IIw

LEIMcr


G the shear modulus



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See also Ref. 4, part 7.

With this moment Mcr, the critical LTB stress LTB is calculated :

y

crLTB I

M

with Iy the moment of inertia about the major axis

The slenderness ratio for LTB LTB, is given by

LTBLTB

E

The allowable LTB stress is calculated using the slenderness LTB with the formulas given in Ref.1, E2.

See also Ref. 5, Bijlage E.





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L Angle section

U Channel section

T T section



Cold formed section


O Solid tube


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

O COM NUM

Classification 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

Slender section x x x x x x


x x x

(1) sections are classified as non-compact section by default.

References1 Manual of Steel Construction

Allowable Stress DesignAISC, Ninth Edition, 1989

2 Manual of Steel ConstructionLoad & Resistance Factor DesignAISC, First Edition, 1986

3 Manual of Steel ConstructionLoad & Resistance Factor DesignAISC, Volume I, Second Edition, 1995


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[5] NBN B 51-001Stalen BouwconstructiesBIN, 5e uitg. April 1977


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AISC – LRFD : 2001

AISC - LRFD Code check


AISC – Manual of steel construction

Load and Resistance Factor Design

Part 16 Specifications and Codes

Third Edition

2001



tension : D1

compression : E2, E3, Appendix E3

flexural members : F1,Appendix F1, Appendix F2

plate girders : Appendix G2, Appendix G3, Appendix G5

combined forces : H1,H2



B1. Gross Area x

B2. Net Area (*)

B3. Effective Area for Tension Members

B4. Stability

B5. Local Buckling1.Classification of Steel Sections2.Slender Compression Elements3.Slender-Element Compression Sections

(*)xxx

B6. Bracing at Support

B7. Limiting Slenderness Ratios x

B8. Simple Spans

B9. End Restraint

B10. Proportions of Beams and Girders

D. TENSION MEMBERS


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D1. Design Tensile Strength x (*)

D2. Built-up members

D3. Pin-Connected Members and Eyebars

E. COLUMN AND OTHER COMPRESSION MEMBERS

E1. Effective Length and Slenderness Limitations1.Effective Length2.Design by Plastic Analysis

xx (*)

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 AND OTHER FLEXURAL MEMBERS (*)

F1. Design for Flexure1.Yielding2.Lateral-Torsional Buckling

xxx

F2. Design for Shear x


F4. Beams and Girders with Web Openings

G. PLATE GIRDERS x

H. MEMBERS UNDER COMBINED FORCES AND TORSION

H1. Symmetric Members Subject to Bending and Axial Force x

H2. Unsymmetric Members 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. COLUMN AND OTHER COMPRESSION MEMBERS

E3. Design Compressive Strength for Flexural-Torsional Buckling x

APPENDIX F. BEAMS AND OTHER FLEXURAL MEMBERS

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


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G5. Flexure-Shear Interaction x(*)


For each intermediary section, the classification is determined..


Section properties

The influence of the bore hole is neglected, i.e. only the gross area is used.

Buckling length

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



For I sections, channel sections, RHS (Rectangular Hollow Section) sections, T sections, rectangular sections, and asymmetric I sections, the critical LTB moment is given in F1 and Appendix F1.

For angle sections with symmetrical legs, the critical LTB moment is given in Ref. 1, pp.281-288, “Specification for Load and Resistance Factor Design of Single-Angle members”.


z2

t2

z2

z2

EIGIL

IIw

LEIMcr


G the shear modulus





See also Ref. 2, part 7.


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Use of diaphragms







L Angle section

U Channel section

T T section



Cold formed section


O Solid tube




I RHS

CHS L U T PPL

RS O COM NUM



Non-compact section

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



x x x



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References

1 AISC – Manual of steel construction

Load and Resistance Factor Design

Third Edition

2001



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ANSI/AISC 360-05:2005

ANSI/AISC 360-05 Code check


ANSI/AISC 360-05

Specifications for Structural Steel Buildings

2005

The steel code check can be executed according to either ASD or LRFD provisions.



tension : Chapter D

compression : Chapter E

flexural members :Chapter F

shear : Chapter G

combined forces : Chapter H



B2. Loads and Load Combination x

B3. Design Basis1.Required Strength2.Limit States3.Design for Strength using LRFD4.Design for Strength using ASD

xx

B4. Classification of Sections for Local Buckling x

D. DESIGN OF MEMBERS FOR TENSION

D1. Slenderness Limitation x

D2. Tensile Strength x

D3. Area Determination x(*)

E. DESIGN OF MEMBERS FOR COMPRESSION

E1. General Provisions x

E2. Slenderness Limitations and Effective Length x(*)

E3. Compressive Strength for Flexural Buckling of members without Slender Elements x


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E4. Compressive Strength for Torsional and Flexural-Torsional Buckling of members without Slender Elements

x

E7. Members with Slender Elements x

F. DESIGN FOR MEMBERS 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 Compact Webs and Noncompact or Slender Flanges Bent about Their Major Axis

x

F4. Other I-Shaped Members with Compact or Noncompact Webs 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. DESIGN OF MEMBERS FOR SHEAR

G1. General Provisions x

G2. Members with Unstiffened or Stiffened Webs x

G4. Single Angles x

G5. Rectangular HSS and Box Members x

G6. Round HSS x

G7. Weak Axis Shear in Singly and Doubly Symmetric Shapes x

H. DESIGN OF MEMBERS FOR COMBINED FORCES AND TORSION

H1. Doubly and Singly Symmetric Members 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





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Section properties


Buckling length



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 as equivalent asymmetric I sections.

Use of diaphragms See Chapter 'Adaptation of torsional constant'.

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 equivalent asymmetric I sections.


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L Angle section

U Channel section

T T section



Cold formed section


O Solid tube



I RHS

CHS L U T PPL

RS O COM NUM



Non-compact section




x x x x x x


References

1 ANSI/AISC 360-05Specifications for Structural Steel Buildings2005


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CM66

CM66 Code check


Règles de calcul des constrcutions en acier

ITBTP / CTICM

Régles CM Decembre 1966

Editions Eyrolles 1982

Consulted articles

The cross-section is checked for tension (art. 3,1), bending (art. 3,2.) and shear (art. 3,3.).

For the stability check, the following criteria are considered :

for compression : art. 3,4.

for compression and bending : art. 3,5

for lateral torsional buckling : art. 3,6.

for double bending and axial compression : art. 3,7.

for shear buckling : art 5,212

A more detailed overview for the used articles is given for the relevant parts in the following table. The chapters marked with “x” are consulted. The chapters marked with (*) have a supplementary explanation the following chapters.

3 Règles générales concernant les calculs de résistance et de déformation

3,0 Données numériques x

3,1 Pièces soumises à traction simple x (*)

3,2 Pièces soumises à flexion simple ou déviée x

3,21 Flexion simple x(*)

3,22 Flexion déviée

3,3 Effet de l’effort tranchant dans les pièces fléchies x

3,4 Pièces soumises à la compression – flambement simple

3,40 Généralités x(*)

3,41 Pièces comprimées a parois pleines x


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3,42 Pièces composées a treilis

3,43 Pièces composées a traverses de liaison

3,44 Conditions spéciales imposées aux éléments comprimés a parois minces x

3,5 Pièces soumises à compression avec flexion dans le plan de flambement

3,50 Principe x

3,51 Coefficient d’amplification des contraintes de flexion x (*)

3,52 Vérfication des pièces a parois pleines x

3,53 Vérification des pièces composées à treilis

3,54 Vérification des pièces composées à traverses de liaison

3,6 Déversement en flexion simple

3,60 Généralités x

3,61 Pièces symétriquement chargées et appuyées

3,611 Poutres à äme pleine x(*)

3,612 Poutres à treilis

3,62 Cas des piéces soumises à deux moments différents au droit des appuis x(*)

3,63 Cas des poutrelles en console parfaitement encastrées

3,64 Coeffcients utilisés pour la détermination de kd

3,641 Coefficient D x

3,642 Coefficient C x(*)

3,643 Coefficient B x(*)

3,7 Flexion composée

3,70 Domaine d’application x

3,71 Notations x

3,72 Principe des vérifications x

3,73 Formules enveloppes pour les pièces à parois pleines x (*)

3,8 Flambement dans les systémes hyperstatiques

3,9 Déformations x

5 Règles spéciales à certains éléments

5,212 Poutres composées à âme pleine – âmes x

Section properties



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Plastic coefficient

The plastic coefficients are calculated according to the Ref.[1], 13,212 (Valeurs du coefficient ψ d’adaptation plastique).

Compression members



Factor kf

The factor kf is calculated using the formula given in Ref[1], 3,516

3;1lM

A172.125.0

k

2

med

M

f

If Mmed ≈ 0.0, the formula 3,513 is used : 3.125.0k f

LTB Check

The LTB check is performed for symmetric I sections. For other cross sections the factor kd=1.0.

For the calculation of the coefficient C, we refer to "Calculation of moment factors for LTB".

The coefficient B is calculated by interpolating the table for B given in Ref[1] 3,643, and using the calculated C value with table for C given in Ref[1] 3,642.


Use of diaphragms


Combined flexion

The values fx is the maximum value of the bending stress in the member for the bending around the strong axis. The value fy is the maximum value of the bending stress in the member for the bending around the weak axis.


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For non-prismatic sections the values fx and fy are the local (i.e. in each intermediary section) bending stresses.


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.




L Angle section

U Channel section

T T section



Cold formed section


O Solid tube




I RHS CHS L U T PPL RS

O COM NUM

Section check x x x x x x x x x x x x

Buckling check x x x x x x x x x x x x

Slender section buckling check

x x x x x x x x

LTB Check x


References

1 Règles de calcul des constrcutions en acierITBTP / CTICMRégles CM Decembre 1966Editions Eyrolles 1982


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CM66 - Additif 80

CM66 - Additif 80 Code check

The beam elements are checked according to the regulations given in Additif 80

Consulted articles

The cross-section is classified according to art. 5,12. (classification 'plastic' or 'elastic').

The section is checked for tension and compression (art. 4,2), bending (art 4,3), shear force (art. 4,4), the combination of bending and axial force (art. 4,5 and art 4.6).

For the stability check, the following criteria are considered :

for lateral torsional buckling : art. 5,2.

for compression : art. 5,31.

for compression and bending : art. 5,32

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

4 Resistance des sections

4,1 Règle générale (*)

4,2 Effort normale x

4,3 Moment de flexion x

4,4 Effort tranchant x

4,5 Moment de flexion et effort normal x

4,6 Momens de flexion, effort normal et effort tranchant x

5 Stabilité des éléments

5,1 Conditions de non voilement local x (*)

5,2 Résistance au déversement des poutre fléchies

5,21 Règles de contreventement latéral au voisinage des sections plastifiées

5,22 Moment ultime de déversement en flexion simple x (*)

5,23 Dimensionnement des entretoises

5,24 Résistance au déversement en flexion déviée x

5,3 Résistance au flambement

5,31 Eléments simplement comprimés x

5,32 Eléments comprimés et fléchis x

5,33 Longueur de flambement (*)


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For each intermediary section, the classification is determined and the proper section check is performed. The classification can change for each intermediary point. For each load case/combination, the critical section classification over the member is used to perform the stability 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 intermediary section.

Section check

If the sections are not according to the conditions specified in art. 5,1, the sections are checked according to the regulations given in Ref.[2].If a torsional moment is present, the sections are checked according to the regulations given in Ref.[2].

Compression members




For the calculation of the moment factors C1 and C2, we refer to "Calculation of moment factors for LTB", using the EC3 values.


Use of diaphragms





L Angle section


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U Channel section

T T section



Cold formed section


O Solid tube




Classification Add 80 x x

Plastic section check Add 80

x x

Buck:ling check Add 80 x x

LTB check Add 80 x x

Compression + bending Add 80

x x

References[1] Additif 80

2 Règles de calcul des constrcutions en acierITBTP / CTICMRégles CM Decembre 1966Editions Eyrolles 1982


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BS5950-1:1990

BS5950-1:1990 Code Check

The beam elements are checked according to the regulations given in :

British Standard BS 5950

Structural use of steelwork in building

Part1. Code of practice for design in simple

and continuous construction:hot rolled section

British Standard distribution BS5950 Part1 1990 revised in 1992

Material properties

For standard steel grades, the yield strength py is defined according to the thickness of the element (see Table 6 Art.3.1.1.). The standard steel grades are :

Grade 43 : yield strength defined between 245 and 275 N/mm²



(pY in N/mm², t in mm)

Steel grade Thickness limits PY

Grade 43

t16 mm 275 N/Mm²

t40 mm 265 N/mm²

t63 mm 255 N/mm²

t100 mm 245 N/mm²

Grade 50

t16 mm 355 N/mm²

t40 mm 345 N/mm²

t63 mm 340 N/mm²

t100 mm 325 N/mm²


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Grade 55

t16 mm 450 N/mm²

t25 mm 430 N/mm²

t40 mm 415 N/mm²

t63 mm 400 N/mm²

Remark: For cold-formed section, values for Py are not influenced by the previous table.Remark : The reduction rules from previous table are only valid when the used material is defined as material for the selected code.

Consulted articlesAccording to Art. 3.5. and table 7, cross sections are classified in 4 types:

Plastic

Compact

Semi-compact

Slender

A reduction factor is applied to the design strength of the material in use for slender sections by following the rules described in Art. 3.6 and in Table 8. Partial safety factor of design strength is included in py value.The section is checked for bending (Art.4.2.), tension (Art.4.6.), compression (Art.4.7.), shear (Art.4.2.3.), combined moment and axial force (Art. 4.8.) and biaxial moments (Art.4.9.). For the stability check, the beam element is checked for lateral torsional buckling, shear buckling, compression and bending with axial compression. Articles used for this stability check are the following:

for lateral torsional buckling : Art. 4.3.

shear buckling : Art. 4.4.5.

for compression : Art. 4.7.

for bending and axial compression : Art. 4.8.

A more detailed overview of used articles is given in the following table.

Part. 3 Section properties

3.5. Limiting proportions of cross sections Art. 3.5.1.

Art. 3.5.2.

Art. 3.5.4.

Table 7

Fig.3

3.6. Slender cross section Art. 3.6.1.


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Art. 3.6.2.-3.6.3.

Art. 3.6.4.

Table 8

Part. 4 Design of structural elements

4.2. Member in bending Art. 4.2.1.3. (a) (c)

Shear capacity Art. 4.2.3.

Moment capacity with low shear Art. 4.2.5.

Moment capacity with high shear Art. 4.2.6.

4.3. Lateral torsional buckling

Member in bending Art. 4.3.7.

LTB factor

General Art. 4.3.7.1.

Equivalent uniform moment Art. 4.3.7.2.

Buckling Resistance Art. 4.3.7.3.

Bending strength pb Art. 4.3.7.4.

Equivalent slenderness LT, , , u, v Art. 4.3.7.5.Appendix B.

Factors m, n Art. 4.3.7.6.

Equal flanged rolled section Art. 4.3.7.7.

Buckling resistance moment for single angle Art.4.3.8.

4.4. Plate Girders

General Art. 4.4.1.

Dimensions of webs and flanges Art. 4.4.2.2. Art. 4.4.2.3.

Moment capacity Art. 4.4.4.

Section with slender webs Art. 4.4.4.2. (a)

Shear buckling resistance of thin webs Art. 4.4.5.1.

Design without using tension field action Art. 4.4.5.3. and Appendix H.1.

4.6. Axially loaded tension members

Tension capacity Art. 4.6.1.

Effective Area of simple tension members Art. 4.6.3.1. Art. 4.6.3.3.

4.7. Compression member

Slenderness Art. 4.7.3.2.

Compression resistance Art. 4.7.4.

Compressive strength Art. 4.7.5. Appendix C

4.8. Axially loaded members with moments


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Tension members with moments Art. 4.8.2. + EC3 5.4.9.&Annex F

Compression members with moments Art. 4.8.3.

Local capacity check Art. 4.8.3.2.

Buckling check with exact approach Art. 4.8.3.3.2.

4.9. Members with biaxial moments See 4.8.


For each intermediary section, the classification is determined and the proper section check is performed. The classification can change for each intermediary point.For each load case/combination, the critical section classification over the member is used to perform the stability 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 intermediary section.

Slender cross-section

Slender sections are particularly sensitive to local buckling. British Standard code (Art. 3.6.) defines stress reduction factor to prevent this phenomenon. For webs subject to moments and axial load and for circular hollow sections, the design strength py should be assumed such that the limiting proportions for semi-compact section are met. For other sections, where a slender outstand is in compression, the design strength should be reduced by the factor given in Table 8.

Section properties

The net area of a section is taken as its gross section neglecting the deduction due to fastener holes: Art. 3.3. Shear area of a cross-section is calculated by using Art. 4.2.3.

Bending moment

Before any calculation of members in bending, it's necessary to determine the shear capacity. For plastic and compact section with high shear load, moment capacity is calculated with the plastic modulus only for I and PLL sections (Art. 4.2.6. and 4.8.). For other cross-section, with plastic or compact section classification, characterised or not by a low shear load, we assumed that the moment capacity is calculated by using the same approach than for semi-compact section: the elastic modulus (elastic calculation).

Bending, shear, axial force

For plastic and compact sections, BS5950 Art. 4.8.2. & 4.8.3.2. (b) prescribes a detailed approach to determine the unity check of axially loaded members with moments. The detailed relationship allows a greater economy for plastic and compact section . In this expression, we use a reduced moment capacity Mr respectively about the major and the minor axis. Those values are determined by using EC3 Art.5.4.9. (see Ref.[5]). For semi-compact and slender section, the simplified approach is applied following Art. 4.8.2.and Art. 4.8.3.2. (a).


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Lateral torsional buckling

For I sections (symmetric and asymmetric PPL), rectangular sections (solid and hollow), T sections, channel sections and angle section, the critical lateral torsional buckling moment is given by the general formula Art. 4.3.7. and Annex B2&3. For other sections, we follow conservative recommendation described in Art. 4.3.7.5. and calculation proposed in EC3 to determine the elastic critical moment Mcr EC3 Annex F1.1. Formula (F.1.) see Ref [5].

The condition to be satisfied in all the cases is that

with

Mb=Sxpb

and

(m is an equivalent uniform moment factor)

pb is the bending strength and is related to the equivalent slenderness :

in which n is an equivalent slenderness factor.

For beam without loading point between points of lateral restraint, n=1 and m depends on the ratio of the end moments at the points of restraint.For beam loaded between point of lateral restraint, m=1 and n depend on the ratio of the end moments at the points of restraint and on the ratio of the larger moment to the mid-span free moment. There are thus two methods for dealing with lateral torsional buckling namely:

'm approach' i.e. the 'equivalent uniform moment method' with n=1

'n approach' i.e. the 'equivalent slenderness method' with m=1

In any given situation, only one method will be admissible, taking into account that it is always conservative to use m=n=1. Since the publication of BS5950 Part 1 1990, doubt has been cast on the correctness of using n factors less than 1 in combination with an effective length LLTB less than the length of the member L in the calculation of LTB. However, as a interim measure, pending clarification ina future version of BS5950, it is recommended that LTB is taken as the smaller of the two following values:

By using the settings of BS5950, the user can define which method correspond to his situation or define his choice as the conservative method m=n=1.


SCIA 101


Use of diaphragms


Compression member

For member submitted to compression, we applied the recommendations given in BS 5950 and Appendix C to determine the compressive strength.






L Angle section

U Channel section

T T section



Cold formed section


O Solid tube





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

Section check class 1 x x x x x x x x



SCIA 102

Section check class 3 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 x x x




x x x x x x x x

Shear buckling check x x x

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

References

[1] British Standard BS5950 Part 1 : 1990+Revised text 1992Structural use of steel work in buildingPart1 Code of practice for design in simple and continuous construction: hot rolled sections

[2] Plastic design to BS5950J.M. Davies & B.A. BrownThe steel Construction institute

[3] Steelwork designGuide to BS5950: Part 1: 1990Volume 2 Worked examples (revised edition)

[4] Essentials of Eurocode 3Design Manual for Steel Structures in BuildingECCS - N° 65, 1991

[5] Eurocode 3Design of steel structuresPart 1 - 1 : General rules and rules for buildingsENV 1993-1-1:1992



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BS5950-1:2000BS5950-1:2000 Code Check

The steel members are checked according to the recommendations given in :

British Standard BS 5950-1:2000Structural use of steelwork in buildingPart1. Code of practice for design – Rolled and welded sections

Material properties

For standard steel grades, the design strength py is defined according to the thickness of the element (see Table 9 Cl.3.1.1.). The partial safety factor on design strength is included in the py value.


Grade S275 : yield strength defined between 225 and 275 N/mm²



(pY in N/mm², t in mm)

Steel grade Thickness limits PY

Grade S275

t16 mm 275 N/Mm²

t40 mm 265 N/mm²

t63 mm 255 N/mm²

t80 mm 245 N/mm²

t<100 mm 235 N/mm2

t< 150 mm 225 N/mm2

Grade S355

t16 mm 355 N/mm²

t40 mm 345 N/mm²

t63 mm 335 N/mm²


SCIA 104

t80 mm 325 N/mm²

t<100 mm 315 N/mm2

t< 150 mm 295 N/mm2

Grade S460

t16 mm 460 N/mm²

t40 mm 440 N/mm²

t63 mm 430 N/mm²

t80 mm 410 N/mm²

t< 100 mm 400 N/mm2

Note that the reduced yield/design stresses given in the above table are only applied when the steel material is chosen from the designated grades S275, S355 or S460

Governing code clauses

According to Cl. 3.5. and tables 11 and 12, cross sections are classified in 4 types:

Class 1 Plastic

Class 2 Compact

Class 3 Semi-compact

Class 4 Slender

The section is checked for shear (Cl 4.2.5 and 4.4.4), bending (Cl.4.2.), tension (Cl.4.6.), compression (Cl.4.7.), combined moment and axial force (Cl. 4.8.) and biaxial moments (Cl.4.9.). For the stability checks, the potential buckling length is checked for lateral torsional buckling due to moments, lateral buckling due to compression and combined bending with axial compression. Relevant clauses for this stability check are the following:

for lateral torsional buckling : Cl. 4.3.

for compression : Cl. 4.7.

for bending and axial compression : Cl. 4.8.Where appropriate, restrained or torsional buckling lengths are identified and checked to Annex G

More detailed clause references are given in the following table.

Part. 3 Section properties

3.5. Limiting proportions of cross sections Cl. 3.5.1.

Cl. 3.5.2.

Cl. 3.5.5.

Cl. 3.5.6

Tables 11 and 12


SCIA 105

Fig.5

3.6. Slender cross section Cl. 3.6.1.

Cl. 3.6.2.-3.6.4.

Cl. 3.6.5.

Fig. 8

Part. 4 Design of structural elements

4.2. Member in bending Cl. 4.2.1.1. (a) (d)

Shear capacity Cl. 4.2.3.

Moment capacity with low shear Cl. 4.2.5.2

Moment capacity with high shear Cl. 4.2.5.3

4.3. Lateral torsional buckling

Member in bending Cl. 4.3.6

Lateral-torsional buckling factors

General Cl. 4.3.6.1

Equivalent uniform moment Cl. 4.3.6.2

Buckling Resistance moment Cl. 4.3.6.4

Bending strength pb Cl. 4.3.6.5

Equivalent slenderness LT, , , u, v, βW, x Cl. 4.3.6.7-9Annex B.

Factors m Cl. 4.3.6.6.

Equal flanged rolled section Cl. 4.3.7

Buckling resistance moment for single angles Cl.4.3.8.

4.4. Plate Girders

General Cl. 4.4.1.

Dimensions of webs and flanges Cl. 4.4.3

Moment capacity Cl. 4.4.4.

Section with slender webs Cl. 4.4.4.2

Shear buckling resistance of thin webs Cl. 4.4.5.1(a).

Design without using tension field action Cl. 4.4.5.2. and Annex H.1.

4.6. Axially loaded tension members

Tension capacity Cl. 4.6.1.

Effective Area of simple tension members Cl. 4.6.3.1-3

4.7. Compression members

Segment length Cl. 4.7.1.1

Restraints Cl. 4.7.1.2

Slenderness Cl. 4.7.2

Compression resistance Cl. 4.7.4.


SCIA 106

Compressive strength Cl. 4.7.5. Annex C

4.8. Axially loaded members with moments

Tension members with moments Cl. 4.8.2.

Compression members with moments Cl. 4.8.3.

Local capacity check Cl. 4.8.3.2.

Buckling check – simplified method Cl 4.8.3.3.1

Buckling check – more exact approach Cl. 4.8.3.3.2.

4.9. Members with biaxial moments See 4.8.


For each intermediate section, the classification is determined and the proper section check is performed. The classification can change for each intermediate point.For each load case/combination, the critical section classification over the member is used to perform the stability 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 intermediate section.

Slender cross-sections

Slender sections are particularly sensitive to local buckling. BS 5950-1:2000 generally allows for the resultant reduction in strength by the method of effective section properties adapted from EC3. Refer to 3.6.2-6.

Section properties

The net area of a section is taken as its gross section neglecting the deduction due to fastener holes: Cl. 3.4. Shear area of a cross-section is calculated by using Cl. 4.2.3.

Moment capacity

Before any calculation of members in bending, it is necessary to determine the shear capacity. For plastic and compact sections with high shear, moment capacity is calculated with the plastic modulus only for symmetrical sections (Cl. 4.2.5.3. and 4.8.). For other sections, with plastic or compact section classification, and high shear, moment capacity is calculated by the same method as for semi-compact sections using the elastic modulus (elastic calculation).

Bending, shear, axial force/capacity interaction

For plastic and compact sections, BS5950 Cl. 4.8.2. & 4.8.3.2. (b) prescribes a detailed approach to determine the unity check (utilisation) of axially loaded members with moments. The detailed relationship allows a greater


SCIA 107

economy for plastic and compact sections . In this expression, reduced moment capacities Mr respectively about the major and the minor axis are calculated in accordance with Annexe I2 .

For semi-compact and slender sections, the simplified approach is applied following Cl. 4.8.2.and Cl. 4.8.3.2. (a).

Lateral torsional buckling due to major axis moments

The lateral-torsional buckling resistance moment Mb is calculated in accordance with Cl 4.3.6 for each potentialbuckling length between adjacent lateral restraintsThe lateral-torsional bending strength pb is calculated in accordance with Cl 4.3.6.5 and Annex B 2.1. This bending strength is dependent on the equivalent slenderness LT which is calculated in accordance with Cl 4.3.6.7-9.The moment gradient (shape of the moment diagram between restraints) is allowed for by means of the equivalent uniform moment factor mLT in accordance with Cl 4.3.6.6 and Table 18.

Torsional buckling about an eccentric axis (Annex G)

This form of buckling under the action of axial compression and/or major axis bending is also known as “restrained buckling” and “distortional buckling.” The term `torsional’ refers to the mode of buckling and is not related to torsion loading or torsion moment effects. Torsional buckling may occur in any member segment between compression flange restraints which has intermediate restraints to the tension flange. It is therefore load combination dependent. It is particularly important in portal frames rafters and columns. The program will detect any potential buckling length and carry out a stability check in accordance with BS 5950-1:2000 Cl. 5.3.4 and Annex G.

Lateral buckling due axial compression

The lateral buckling compression resistance Pc of any member or segment between lateral restraints is calculated in accordance with Cl 4.7.4. The compressive strength pc allowing for buckling is calculated using Cl. 4.7.5 using the strut curves appropriate to the section type, thickness and axis of buckling (Table 23) as expressed in the formulae of Annex C. This compressive strength is dependent on the slenderness per Cl 4.7.2

Combined axial and bending buckling unity check/utilisation

The interaction of axial and bending buckling effects is measured by the two simplified formulae given in Cl 4.8.3.3.1.The first equation refers to flexural buckling and is applied to the member length between major axis restraints. The second equation refers to the interaction of lateral-torsional buckling due to the moment field and lateral buckling due to axial compression and is applied to potential buckling lengths between minor axis restraints. Clause 4.8.3.3.2 provides a more exact method for symmetrical I-sections and Cl. 4.8.3.3.3 for CHS and RHS sections. It is permissible to take the more favourable result. (Lower utilisation), The moment gradient (shape of the moment diagram between restraints) is allowed for by means of the equivalent uniform moment factor mLT in accordance with Cl 4.3.6.6 and Table 18 for lateral-torsional buckling. For flexural (in plane) buckling the factors mx, my and myx are obtained from Table 26.


SCIA 108

Torsion effects

The current version of the BS 5950-1:2000 steel check does not deal with torsion moments. Any torsion moments generated by the frame analysis will be ignored.Most steel structures do not in fact rely on torsion effects to transmit loads.

Where it is found necessary for members to sustain torsion moments as part of the primary load system, alternative checks should be made. The BS 5950-1:1990 steel check does deal with torsion.

Supported sectionsI Symmetric I shapes (UB, UC, IPE, HEA, HEB, ….)

RHS Rectangular Hollow Sections (RHS) [hot rolled or cold formed]

CHS Circular Hollow Sections (CHS) [hot rolled or cold formed]

L Angle sections and double angles

U Channel sections and double channels

T T sections

PPL Asymmetric I shapes used in haunches

RS Rectangular single plate sections


SCIA 109

SIA263

SIA263 Code check


SIA263

Construction en acier

SIA263:2003

Material propertiesThe most common steel grades are used in SIA263. Their mechanical properties are described in table 1 SIA263. The following table gives the yield strength for each type of grade commonly used in function of the nominal web thickness:

t<=40 t<=40 40<t<=100 40<t<=100fy fu fy fu

S235S 235

235 360 215 340

S275S 275

275 430 255 410

S355S 355

355 510 335 490

S460S 460

460 550 430 530

Consulted articlesThe classification described in SIA263 is based on the calculation method. The calculation method in SIA263 distinguish the method used respectively to determine the internal forces and to perform the section and the stability check. By facility, we can obviously make a parallel between the calculation method of SIA263 and the section classification proposed in EC3.

According to SIA263 Table 5a-5b , cross sections are classified in 4 types:

PP (plastic-plastic) or class 1

EP (elastic-plastic) or class 2

EE (elastic-elastic) or class 3

EER (elastic-elastic reduced) or class 4


SCIA 110

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, we must note that the steel code SIA263 is essentially oriented for symmetrical and bisymmetrical profile like I profiles. In the present modulus, others profiles are calculated by using a classic elastic approach (EE classification) and EC3 prescriptions.

The section is checked for tension, compression, shear, combination of bending and axial forces. For the stability check, the beam element is checked for lateral torsional buckling, shear buckling, compression and bending with axial compression. A more detailed overview for the used articles is given in the following table :

4 Analyse structurale et dimensionnement

4.1 Généralités x

4.2 Bases de l'analyse structurale et du dimensionnement

4.3 Modélisation4.3.1 Classification des sections x

4.4 Résistance des sections4.4.1 Effort normal x

4.4.2 Flexion x

4.4.3 Effort tranchant x

4.4.4 Flexion et effort tranchant x

4.4.5 Flexion et effort normal x

4.4.6 Sollicitations multiaxiales x

4.5 Stabilité4.5.1 Flambage x

4.5.2 Déversement des poutres fléchies x

4.5.3 Flexion et compression x

4.5.4 Voilement des éléments plans comprimés x

4.5.5 Voilement des éléments plans cisaillés x

4.8 Situtation de projet incendie4.8.1 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 construction5.1 POUTRES ET POTEAUX DES CLASSES DE SECTION 1 ET 2 x

5.3 Eléments comprimés à section composée5.3.1 Barres étrésillonées ( à travers de liaison) x

5.4 Poutres composées à âme pleine5.4.1 Résistance à la flexion x

5.4.2 Résistance à l'effort tranchant x

5.4.3 Interaction entre flexion et effort tranchant x

Annexe B Moment critique de déversement élastique Mcr x

Annexe C Echauffement des éléments de construction en cas d'incendie x

Section classification

For each intermediary section, the classification is determined and the proper section check is performed. The classification can change for each intermediary point. For each load case/combination, the critical section


SCIA 111

classification over the member is used to perform the stability 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 intermediary section.

Slender cross-section

The design of a section that not satisfies the table 5 of SIA263 is always performed by using a reduced area. This classification correspond to the EER method. The determination of a reduced area is based on the effective width of each compression element in the current section (Art. 4.5.4). The using of a reduced area implies the recalculation of the shear centre position, the inertia and the elastic modulus.

Sections properties

The holes due to fastener are neglected in the area of a section


For double symmetric I profile, we don't have to perform any lateral torsional buckling check if NEd/Npl,Rd0.15 and the conditions provided in Table 6 SIA263 are satisfied. For any other case, a LTB check must be perform. Calculations described in Annex B for I,U and PPL can be applied to T sections only 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 Annex F. Those rules allow us to determine a elastic critical moment for lateral torsional buckling for symmetrical (formula F.2 EC3) and non symmetrical (formula F.1. EC3) sections around the minor axis.In the case of I, U, PPL and, T only with compression in flange, characterised by a reduced area or not, we have to determined before any calculation irc, defined as the radius of gyration of a section comprising the compression flange plus 1/3 of the compression web area, taken about an axis in the plane of the web.



Use of diaphragms


Shear buckling



SCIA 112

Stability check

For double symmetric I profile PP or EP, SIA263 provides specific formula to perform the stability check of member submitted to biaxial moment. For other sections, non symmetric or from EE and EER classification, a general formula is provided to design member under mono-axial sollicitations.

Torsion check


Built-in beams

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

SIA263 - Fire Resistance





Gk + Pk + Ad+ 2,iQk,i

with Gk characteristic values of permanent actions

Qk,i characteristic value of the variable action i

Ad design values of accidental action from fire exposure

2,j combination coefficients

Pk characteristic value of prestressing action

Material properties




SCIA 113

20,a,E,a

20,y,y,y

EkEfkf

The variation in function of the steel temperature of the value for yield strength ky, and modulus of elasticity kE,

is given by tables in ref.[1], Figure 15.





In this part, the nominal temperature-time curves and the related net heat flux are described. For more info, EC3 Chapter 'Temperature analysis - Thermal actions'

Nominal temperature-time curveSee EC3 Chapter 'Nominal temperature-time curve'.

Net heat fluxSee EC3 Chapter 'Net heat flux'

Steel Temperature See Ref.[1], Annexe C.

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

thc

V/Ad,net

aa

mt,a






SCIA 114




V/Adcc

1et

31cd

V/A

ppaa

pp

t,g10/t,at,g

aap

ppt,a













The value a,t 0.0


Calculation model


- strength domain



SCIA 115


Code CheckThe section and stability checks (buckling, lateral torsional buckling) are performed according to the regulations given in Ref.[1], 4.8.5.



- classification of cross section : art. 4.8.5.2.

- resistance for tension members : art. 4.8.5.4.

- resistance for compression members (class 1,2 or 3) : art. 4.8.5.5..

- resistance for beams (class 1,2,3) : art. 4.8.5.6., art. 4.8.5.7., art. 4.8.5.8.

- resistance for members (class 4) : art. 4.8.5.9.




L Angle section

U Channel section

T T section


Z Z section


Cold formed section

COM Composed section

O Solid tube






Section check PP x x(2) x(3)

Section check EP x x(2) x(3)

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


SCIA 116

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(4) x(4) x(4) x(4) x(4) x x(4) x(4) x(4) x(4) x(4) x(4)


(2) check according to EN 1993-1-1

(3) check according to ENV 1993-1-1

(4) general formula for Mcr

References[1] SIA263

Construction en acierSIA263:2003

[2] SIA263/1Construction en acier / Spécification complémentairesSIA263/1:2003


SCIA 117

GBJ 17-88

The GBJ 17-88 code check

The beam elements are checked according to the regulations given in :

National standard of the People’s Republic of China

Code for design of steel structures

GBJ 17-88

Beijing 1995

Material propertiesThe used steel grades are

Grade3

16Mn

16Mnq

15Mn

15Mnq

For Steel3, the following groups are defined according to the element thickness (in mm):

Group

Diameter or thickness of bars Thickness of L-, I- and U sections

Thickness of Plates

1 <=40 <=15 <=202 >40-100 >15-20 >20-403 >20 >40-80

The design values are (in N/mm²)

Steel Group Thickness f fv fce fy

Steel3 123

215200190

125115110

320320320

235235235

16Mn16Mnq

<=1617-2526-36

315300290

185175170

445425410

345345345

15Mn15Mnq

<=1617-2526-36

350335320

205195185

450435415

390390390

with f the resistance design value for tension, compression, bending (N/mm²)


SCIA 118

fv the resistance design value for shear (N/mm²)

fce the bearing resistance (N/mm²)

fy the yield strength (N/mm²)

Remark : The reduction rules from previous table are only valid when the used material is defined as material for the selected code. If they are not defined as GBJ material, the following rule is used

f = 0.91 x yield strength

fv = 0.58 x yield strength

Consulted articlesThe section and elements are checked according to part 4 and 5. When plastic design is allowed, part 9 is supported.

A more detailed overview for the used articles of the relevant parts is given in the following table. The chapters marked with “x” are consulted.

4. Calculation of flexural members

4.1.Strength

4.1.1.4.1.2.

x (*)x

4.2.Overall stability (*)

4.2.1.4.2.2.4.2.3.4.2.4.

xxxx

4.3.Local stability (*)

4.3.1.4.3.2.4.3.3.4.3.9.

xxxx

5.Calculation of axially loaded members and members subjected to combined axial load and bending

5.1.Axially loaded members

5.1.1.5.1.2.

x(*)x(*)

5.2.Members subjected ot combined axial load and bending

5.2.1.5.2.2.5.2.5.

x(*)xx

5.3.Effective length and allowable slenderness ratio (*)

5.4.Local stability of compression members

5.4.1.5.4.2.

xx


SCIA 119

5.4.3.5.4.4.5.4.5.

xxx (*)

9.Plastic design

9.1.General requirements

9.1.3.9.1.4.

xx

9.2.Calculation of members (*)

9.2.1.9.2.2.9.2.3.9.2.4.

xxxx

9.3.Allowable slenderness and detailing requirements

Appendix 1 Overall stability factor of beams

A1.1.Simply supported beam of uniform welded I section x

A1.2.Simply supported beam of rolled I section x

A1.3.Simply supported beam of rolled channel section x

A1.4.Cantilever beams of doubly symmetric I section x

A1.5.Approximate calculation of overall stability factors x

Appendix 2 Calculation of local stability of girder web

A2.1.Web plate strengthened with transverse stiffeners x(*)

A2.2.Web strengthened with transverse and longitudinal stiffeners

A2.2.Web strengthened with transverse, longitudinal and short stiffeners

Appendix 3 Stability factor of axially loaded compression members x

Section properties

The influence of the net section is neglected, i.e. only the gross area is used.


The local compressive stress c, is considered as 0.0.

Buckling curves

For welded I and PPL sections the default value for the buckling curve about the weak axis is “b”. This can be changed to “c” on users request.


SCIA 120

Buckling length


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


The LTB check is supported for the following sections : I section, U section, RHS section, T section, PPL section.

For the other section type, the factor b = 1.0.


Local stability of compressed members

For each intermediary section, the ratio’s are determined. The section classification and the effective area properties are determined for each intermediary section for performing the section check.For each load case/combination, the critical section classification and the effective area properties over the member are used to perform the stability check. However, for non-prismatic sections, the section classification and the effective area properties are determined for each intermediary section to perform the stability check.

When the web ratio ( dept /thickness) does not conform to the requirements, the web is reduced for calculating of the section check and stability check. A width of 20 tw sqrt(235/fy) on each side of the web is taken into account.

yw f

235t20d




SCIA 121

Supported sections

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



L Angle section

U Channel section

T T section



Cold formed section


O Solid tube




I RHS CHS L U T PPL RS

O COM NUM

Plastic (single bending) x x

Compact section (with ) x x x x x x

Non-compact section x x x x x x x x x x


Normal buckling x x x x x x x x x x x x

LTB x x x x x

Shear buckling x x x

Plastic stability check (single bending)

x x

References[1] Chinese Steel Code

GBJ 17-88(Chinese version)

.[2] National standard of the People’s Republic of ChinaCode for design of steel structuresGBJ 17-88Beijing 1995


SCIA 122

Korean steel code check

The Korean steel code check

Material propertiesThe following design values are used :

Steel fyt<=40 mm

fyt>40 mm

SS41SPS41SPSR41

240 220

SS50 280 260

SS55 380 380

with fy the yield strength (N/mm²)

The following steel characteristics are valid :

modulus of elasticity 210000 N/mm²

shear modulus 81000 N/mm²

coefficient of linear thermal expansion 12 x 10-6density 7850 kg/m³

Consulted articles

The section and elements are checked according to part 2 and 3. The shear buckling check is perfromed using article 7.5.2. The classiffication of sections is based on the rules of part 4.A more detailed overview for the used articles of the relevant parts is given in the following table. The chapters marked with “x” are consulted.

TEXT

2.Allowable stress

2.1.Structural material x

2.1.1.Allowable tensile stress x

2.1.2.Allowable shear stress x


SCIA 123

2.1.3.Allowable compressive stress x

2.1.4.Allowable bending stressa)b)c)

(*)xxx

2.1.5.Allowable bearing stress

3.Load and stresses

3.3.Combined stresses (*)

3.3.1.Compression force and bending moment x

3.3.2.Tensile force and bending moment x (*)

3.3.3.Shear force and tensile stress

4.Width-Thickness ratio of plates (*)

4.1.1.Cantilever plate x

4.1.2.Two side fixed plate x

4.1.3.Effective area x

4.2.CHS section and thickness ratio x

5. Tensile member

6.Compressive member

6.1.Slenderness ratio x

6.2.Buckling length x(*)

7.Beam element

7.5.Stiffener

7.5.2.Buckling verification of the weba)

x

Section classification


For each load case/combination, the critical section classification and the effective area properties over the member are used to perform the code check. However, for non-prismatic sections, the section classification and the effective area properties are determined for each intermediary section.When the element properties don’t satisfy the limiting values for the ratios, the section is classified as slender. The section have to be reduced for the calculation of the stresses. For outstand compression elements, the part that is situated on the fixed side, remains. The length of the part b’ is calculated by the equation in which the ratio b’/t is equal on the limiting ratio.


SCIA 124

For internal compression elements, the remaining parts are symmetrically divided to the end of the elements. The length of the part d’ is calculated by the equation in which the ratio d’/t is equal on the limiting ratio.

The reduced section properties are calculated for I, U, PPL, RHS and Cold formed sections-types.

The slenderness ratios (for buckling and LTB) are calculated with the full section properties.

Section properties


Buckling length

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

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


For I sections, PPL sections, U sections RHS and CHS sections, the formulas from 2.1.4 are used.


z2

t2

z2

z2

EIGIL

IIw

LEIMcr

with L LTB length

E modulus of elasticity


SCIA 125

with L LTB length

G shear modulus

Iw warping constant

It torsion constant

Iz moment of inertia about minor axis

With this moment Mcr, the critical LTB stress LTB is calculated :

y

crLTB I

M

with Iy moment of inertia about major axis

The slenderness ratio for LTB LTB, is given by

LTBLTB

E

The allowable LTB stress is calculated using the slenderness LTB with the formulas given in 2.1.3.


Combined stresses

For compression and bending, the following formulas are used :

1ftt

1f

cf

cf

t

cbybx

by

by

bx

bx

c

c


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For tension and bending, the following formulas are used :

1f

tt

1f

cf

cf

t

bybxt

by

by

bx

bx

bx

t

with c normal compression stress

t normal tension stress

cb bending compression stress

tb bending tension stress

cbx bending compression stress around x axis

tbx bending tension stress around x axis

cby bending compression stress around y axis

tby bending tension stress around y axis

ft allowable tension stress

fc allowable compression stress

fb allowable bending stress

fbx allowable bending stress around x axis

fby allowable bending stress around y axis



Supported sections




L Angle section

U Channel section

T T section



Cold formed section


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O Solid tube




I RHS

CHS L U T PPL RS O COM NUM

Slender sections x x x x x

Allowable stresses


Shear buckling x x x

References[1] Korean Standard

(Korean Version)1983

[2] Extracts Korean Standard(Internal English Version)Translated by Karam Kim - 19.03.1998

[3] Regulations of Structural Standard ofBuilding Architecture(internal english document)


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BSK 99

BSK 99 Code check


BSK 99

StalKonstruktioner

Boverket, Byggavdelningen, 2000

Material properties

For standard steel grades, the characteristic yield strength fyk and tensile strength fuk are defined according to the thickness of the element (see Ref. 1, tab.2:21a and tab.2:21b)


SteelName Type E-modulus

(N/mm2)Poisson Unit mass

(kg /m3)Extensibility (m/m K)

Ultimate tensile strength (N/mm2)

Yield strength (N/mm2)

S235S 235

Steel 210000 0.3 7850 12*10-6 340 235

S275S 275

Steel 210000 0.3 7850 12*10-6 410 275

S355S 355

Steel 210000 0.3 7850 12*10-6 490 355

S420 S 420

Steel 210000 0.3 7850 12*10-6 500 420

S460 S 460

Steel 210000 0.3 7850 12*10-6 530 460

S500 S 500

Steel 210000 0.3 7850 12*10-6 590 500

S550 S 550

Steel 210000 0.3 7850 12*10-6 640 550

S620 S 620

Steel 210000 0.3 7850 12*10-6 700 620

S690 S 690

Steel 210000 0.3 7850 12*10-6 770 690

(fyk, fuk in N/mm², t in mm)


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Steel grade

Thickness fuk fyk

S235, S 235

0 < t <= 16 340 235

16 < t <= 40 340 225

40 < t <= 63 340 215

63 < t <= 80 340 215

80 < t <=100 340 215

S275, S 275

0 < t <= 16 410 275

16 < t <= 40 410 265

40 < t <= 63 410 255

63 < t <= 80 410 245

80 < t <=100 410 235

S355, S355

0 < t <= 16 490 355

16 < t <= 40 490 345

40 < t <= 63 490 335

63 < t <= 80 490 325

80 < t <=100 490 315

S420, S 420

0 < t <= 16 500 420

16 < t <= 40 500 400

40 < t <= 63 500 390

S460, S 460

0 < t <= 16 530 460

16 < t <= 40 530 440

40 < t <= 63 530 430

S500, S 500

0 < t <= 50 550 500

50 < t <= 100 550 480

S550, S 550

0 < t <= 50 640 550

50 < t <= 100 640 550

S620, S 620

0 < t <= 50 700 620

50 < t <= 100 700 580

S690, S 690

0 < t <= 50 770 690

50 < t <= 100 760 650

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

Remark : The reduction rules from previous table are only valid when the used material is defined as material for the selected code.


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Consulted articles

The cross-section is classified according to Table 6:211a . (class 1,2 or 3).

The section is checked for tension (art. 6:22), compression (6:23), bending (6:24), shear force (art. 6:26), torsion (art. 6:27), the combination of bending and axial force (art. 6:25).

A more detailed overview for the used articles is given for part 6:2 in the following table. The chapters marked with “x” are consulted. The chapters marked with (*) have a supplementary explanation in the following chapters.

6:2.Calculation of the capacity of construction elements

6:21.Limiting values of slenderness for cross section parts x

6:211.Classes of cross sections x (*)

6:212.Design methods for the different section classes x (*)

6:22.Tensile force x

6:23.Compression force x

6:231. Initial curvature, initial inclination and load eccentricity

6:232.Loss of restraint x (*)

6:233.Reduction factor for flexural buckling x

6:24.Bending moment x

6:241.Cross section classes x (*)

6:242.Shape factors in flexure x (*)

6:243.Bending moment x

6:244.Lateral torsional buckling x (*)

6:2441.Lateral bracing of beam x

6:2442.Reduction factor for LTB x

6:25. Bending and axial force

6:251.Section check x

6:252.Flexural buckling x

6:253.Flexural-torsional buckling x

6:26.Shear force and concentrated load

6:261.Shear force x(*)

6:262.Web crippling under concentrated force

6:263.Local compression

6:27.Torsional moment x

6:271.Pure torsion x

6:272.Warping

6:273.Torsional moment, shear force and bending moment x


For each intermediary section, the classification is determined and the proper section check is performed using the actual internal forces. The classification can change for each intermediary point.


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The calculation of the effective area properties is performed according to the rules given in [5], part :23 and :24.

For each intermediary section, the classification (and if necessary, the effective area ) is determined and the proper section check is performed. The classification (and effective area) can change for each intermediary point. The most critical check is displayed on the screen.Aeff is the effective area of the cross section when subject to uniform compression. Weff is the effective section modulus of the cross-section when subject only to moment about the relevant axis. With these properties, the section and stability check is performed.

Section properties

6:22 ; 6:243 ; 6:251 ; 6:261 : The net area properties are not taken into account .

Section check

- Double symmetric I sections (I) use the formula (6:251a) and (6:251b)

- Solid sections (O, RS) and hollow sections (RHS, CHS) use the formula (6:251c)

- For single bending, the sections U, PPL, T use formula (6:251a). For double bending the biaxial state of stress is consulted.

- All other cases use the biaxial state of stress.

The (bi)axial stress check is given by formula (3:412a) and (3:412c):

yd22

x

ydx

f3

f

with =1.1

Compression members

6:232 : For the calculation of the buckling length, we refer to "Calculation of buckling ratio". The buckling properties for a VARH element are calculated by using the critical Euler force for this member (see "Calculation of critical Euler force for VARH elements") .

For class 3 sections, the rules given in [5], part :34 are used, including the calculating of Idef.


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See [5], part :37.

The design buckling resistance for torsional or torsional-flexural buckling shall be obtained using the following reduction factor c and slenderness c :

2c

c

0

0

y

yy,cr

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

20

2z

2y

20

2T

mt2

0gT,cr

TF,crT,crcr

crcr

cr

ykeffc

116.1

²iy

1

²il

E²

4²21

yiii

lEC²GI

iA1

),min(AN

NfA

with fyk the basic yield strength




G the shear modulus










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The calculation of cr based on [6], part 6.2.3.(5).


Alternatively to the regulations given in 6:2442. for bisymmetric sections, the elastic critical moment for LTB Mcr for I sections (symmetric and asymmetric), RHS (Rectangular Hollow Section) sections and CHS (Circular Hollow Section) sections, can be calculated using the formula given by the general formula F.2. Annex F Ref. 3.

For the calculation of the moment factors C1, C2 and C3 we refer to "Calculation of moment factors for LTB".


z2

t

z2

z2

EIL²GI

IIw

LEIMcr


G the shear modulus







SCIA 134

For class 3 section, Izdef according to [5], part :44 is used.


Use of diaphragms


Shear force ( shear buckling)

The shear buckling check is using the values for v from table 6:261 in column 2.

The value for w is (according to [5], part :26, (18:26d)) taken as below :

2w

w

2w

w

k

yk

w

ww

ab

34.500.4k1baif

ab00.434.5k1

baif

Ef

tb

k81.0

with Ek the modulus of elasticity

fyk the yield strength

a the field length

bw the field height

tw the web thickness


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a

bw





L Angle section

U Channel section

T T section



Cold formed section


O Solid tube






Section check double bending


Class 3 support x x x x x x

Buck:ling check x x x x x x x x x x x x

LTB check x x x x x x x x x x x x

Compression + bendingdouble bending

x

Compression + bending

x x x x x x x x


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single bending

Compression + LTBdouble bending

x

Shear buckling x x x x

Torsional check x


References[1] BSK 99

StalKonstruktionerBoverket, Byggavdelningen, 2000

[2] Swedish Regulations for Steel StructuresBSKSBI Swedish Institute of Steel Construction, Publication 118, 1989



[5] Torsten HöglundK18, Dimensionering av StalkonstruktionerUtdrag ur Handboken Bygg, kapitel K18 och K19C E Fritzes AB, Stockholm



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IS 800

IS:800 Code check


IS 800 Draft version (for 3rd Revision)

Material properties

The following steel grades are supported :

Grade/ Classification Yield stress(Mpa) Ultimate tensile stress(Mpa)

A/Fe410WA 250(<20mm), 240(20mm to 40mm), 230(>40mm) 410

B/Fe410WB 250(<20mm), 240(20mm to 40mm), 230(>40mm) 410

C/Fe410WC 250(<20mm), 240(20mm to 40mm), 230(>40mm) 410

Fe440 300(<16mm), 290(16mm to 40mm), 280(>41mm to 63mm) 440

Fe440B 300(<16mm), 290(16mm to 40mm), 280(>41mm to 63mm) 440





The string in the column ‘Grade/Classification’ is used to determine the proper yield stress reduction.

Consulted articles

The cross-section is classified according to Table 3.1.

The section is checked for tension (Section 6), compression (Section 7), bending (Section 8) and the combination of forces (Section 9).

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

3.7. Classification of Cross Section x(*)

6.1. Tension members x

6.2. Design strength due to Yielding of Gross section


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7.1. Design Strength x

8.2. Design strength in bending x

8.2.1. Laterally supported beam

8.2.1.1. Section with slender webs x

8.2.1.2. When factored shear force < 0.6 Vd x

8.2.1.3. When factored shear force > 0.6 Vd x

8.2.2. Laterally unsupported beam x

8.2.2.1. Elastic Lateral Torsional Buckling moment x

8.4. Shear x

8.4.1. The nominal plastic shear resistance x

8.4.2. Resistance to shear buckling x

9.1. General x

9.2. Combined Shear and bending x

9.3. Combined Axial Force and Bending Moment x

Appendix F x

Remarks

- the design of slender compression elements is outside the scope of this implementation

- the shear buckling check is only using the Simple Post Critical Method



For each load case/combination, the critical section classification over the member is used to perform the stability 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 intermediary section

The cross sections are classified as

- class 1 : plastic

- class 2 : compact

- class 3 : semi-compact

- class 4 : slender section

The class 4 (slender) section check is not supported. For this sections a class 3 (semi-compact) section check is performed.

Section properties



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Section check

In the case of high shear for class 3 section, the allowable normal stress is reduced with a factor (1-). When torsional shear stress is present, the VonMisis criterium is checked.

Compression members

For the calculation of the buckling length, we refer to "Calculation of buckling ratio". The buckling properties for a VARH element are calculated by using the critical Euler force for this member (see "Calculation of critical Euler force for VARH elements") .


The design buckling resistance Nb,Rd for torsional or torsional-flexural buckling shall be obtained using buckling for buckling around the weak axis, and with relative slenderness given by :

²1

²

²

4²21

²1

),min(

0

0

,

,,,,,,,

20

2220

220

,

,,

iy

il

E

yiii

lECGI

iA

f

y

yycr

TcrycrTcrycrTcrycrTFcr

zy

T

mt

gTcr

TFcrTcrcr

Acr

yb

with fyb the basic yield strength




G the shear modulus



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The elastic critical moment for LTB Mcr for I sections (symmetric and asymmetric), RHS (Rectangular Hollow Section) sections and CHS (Circular Hollow Section) sections, can be calculated using the formula given by Annex F.

For the calculation of the moment factors C1, C2 and C3 we refer to "Calculation of moment factors for LTB".


z2

t

z2

z2

EIL²GI

IIw

LEIMcr


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G the shear modulus







Use of diaphragms


Supported sections

The following standard sections are defined :




L Angle section

U Channel section

T T section


Z Z section


Cold formed section

COM Composed section ( sheet welded, section pairs, …)

O Solid tube




In the following matrix is shown which sections are supported for the different analysis parts in the Indian steel Code check :


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




Section check class 4

Stability check class 1 x x x

Stability check class 2 x x x

Stability check class 3 x x x x x x x x x x x x x




References[1] IS:800

2005


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EAE code checkThe beam elements are checked according to the regulations given in

Instrucción EAE

Documento 0 de la Instrucción de Acero Estructural

Comisión Permanente de Estructuras de Acero

November 2004

Material propertiesFor standard steel grades, the yield strength fy and tensile strength fu are defined according to Capítulo VI of Ref. 1.

Steel Grade fy (N/mm²)

fu (N/mm²)

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 355 510

S 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

S 460 MH/MLH 460 530

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



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Remark : For cold formed sections, the average yield strength fya can be used (by setting the proper data flag in the Cross Section input dialog) according to Ref.[4].

The average yield strength is determined as follows :

ybuybug

ybya f2.1,fminffA

²kntff








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Consulted articles

The beam elements are checked according to the regulations given in " Instrucción EAE, Documento 0 de la Instrucción de Acero Estructural, Comisión Permanente de Estructuras de Acero, November 2004".

The cross-sections are classified according to Artículo 20 of Capítulo V. All classes of cross-sections are included. For class 4 sections (slender sections) the effective section is calculated in each intermediary point, according to Artículo 20 of Capítulo V.

The member check is executed according to Capítulo IX. The stress check is taken from art. 34.: the section is checked for tension (art. 34.2.), compression (art. 34.3.), bending (art. 34.4.), shear (art. 34.5.), torsion (art. 34.6.) and combined bending, shear and axial force (art. 34.7.1., art. 34.7.2. and art. 34.7.3.).The stability check is taken from art. 35.: the beam element is checked for buckling (art. 35.1.), lateral torsional buckling (art. 35.2.), and combined bending and axial compression (art. 35.3.). 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 the bending 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” are consulted. The chapters marked with (*) have a supplementary explanation the following chapters.

Instrucción EAE

20. Clasificación de las secciones transversales (*)

20.2. Clasificación de las secciones transversales metálicas x20.3. Criterios de asignación de Clase en secciones metálicas no rigidizadas x20.7. Características de la sección reducida en secciones transversales esbeltas x

34. Estado límite de resistencia de las secciones

34.1. Principios generales del cálculo x34.1.2. Características de las secciones transversales x

(*)

34.2. Esfuerzo axil de tracción x

34.3. Esfuerzo axil de compresión x34.4. Momento flector x34.5. Esfuerzo cortante x34.6. Torsión x

(*)


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34.7. Interacción de esfuerzos

34.7.1. Flexión y cortante x34.7.2. Flexión y esfuerzo axil x34.7.3. Flexión, cortante y esfuerzo axil x35. Estado límite de inestabilidad

35.1. Elementos sometidos a compresión x(*)

35.2. Elementos sometidos a flexión x35.3. Elementos sometidos a compresión y flexión x

(*)

35.5. Abolladura del alma a cortante x35.7. Interacción

35.7.1. Cortante, flexión y esfuerzo axil x

For cold formed sections prEN 1993-1-3 is applied.

6.1.2. Axial tension

6.1.3. Axial compression

6.1.5. Shear force

6.1.6. Torsional moment









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Aeff is the effective area of the cross section when subject to uniform compression. Weff is the effective section modulus of the cross-section when subject only to moment about the relevant axis. eN is the shift of the relevant centroidal axis when the cross section is subject to uniform compression.With these critical properties, the stability check is performed.


Section properties


The shear lag effects are neglected .

Torsion check


Built-in beams

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

Compression members

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



For I sections (symmetric and asymmetric), RHS (Rectangular Hollow Section) sections and CHS (Circular Hollow Section) sections, the elastic critical moment for LTB Mcr is given by the general formula F.2. Annex F Ref. 5. For the calculation of the moment factors C1, C2 and C3 we refer to "Calculation of moment factors for LTB".


z2

t

z2

z2

EIL²GI

IIw

LEIMcr


G the shear modulus


SCIA 148








Use of diaphragms


Combined bending and axial compression

For prismatic members the value My,Ed is the maximum value of the bending moment around the strong axis in the member. The value Mz,Ed is the maximum value of the bending moment around the weak axis in the member.

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

Interaction Method Calculation of Czz

By default for Czz the formula given in Ref.[1] is used:

In this formula however the position of the factor eLT is incorrect. For exact analysis the formula according to Ref.[9] can be used:




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L Angle section

U Channel section

T T section


Z Z section


Cold formed section


O Solid tube











x x x


x x x




x x x x x x



References1 Instrucción EAE

Documento 0 de la Instrucción de Acero EstructuralComisión Permanente de Estructuras de AceroNovember 2004

2 Essentials of Eurocode 3Design Manual for Steel Structures in BuildingECCS - N° 65, 1991


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[6] Eurocode 3Design of steel structuresPart 1 - 2 : General rules - Structural fire designENV 1993-1-2:1995, 1995

[7] Model Code on Fire EngineeringECCS - N° 111May 2001

[8] Eurocode 1Basis of design and actions on structuresPart 2-2 : Actions on structures - Actions on structures exposed to fireENV 1991-2-2:1995


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Calculation of buckling ratioIntroduction to the calculation of buckling ratio

For the calculation of buckling ratio, several methods can be applied.

The general method is described in chapter "Calculation buckling ratio – general formula". For crossing diagonals, the buckling ratio is explained in chapter "Calculation buckling ratios for crossing diagonals". For VARH elements, the critical Euler force is calculated according to the method given in chapter "Calculation of critical Euler force for VARH elements". For lattice tower members, see the chapter "Calculation buckling ratio for lattice tower members".

Calculation buckling ratio – general formula

For the calculation of the buckling ratios, some approximate formulas are used. These formulas are treated in reference [1], [2] and [3].

The following formulas are used for the buckling ratios (Ref[1],pp.21) :

for a non sway structure :

24)+11+5+24)(2+5+11+(212)2+4+4+24)(+5+5+(

=l/L21212121

21212121

for a sway structure :

4+x

x=l/L1

2

with L the system length

E the modulus of Young

I the moment of inertia

Ci the stiffness in node i

Mi the moment in node i

Fi the rotation in node i

21212

12

21

8+)+(+4

=x

EILC= i

i

i

ii

M=C


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The values for Mi and i are approximately determined by the internal forces and the deformations, calculated by load cases which generate deformation forms, having an affinity with the buckling form. (See also Ref.[5], pp.113 and Ref.[6],pp.112).The following load cases are considered:

load case 1 : on the beams, the local distributed loads qy=1 N/m and qz=-100 N/m are used, on the columns the global distributed loads Qx = 10000 N/m and Qy =10000 N/m are used.

load case 2 : on the beams, the local distributed loads qy=-1 N/m and qz=-100 N/m are used, on the columns the global distributed loads Qx = -10000 N/m and Qy= -10000 N/m are used.

The used approach gives good results for frame structures with perpendicular rigid or semi-rigid beam connections. For other cases, the user has to evaluate the presented bucking ratios. In such cases a more refined approach (from stability analysis) can be applied.


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Calculation buckling ratios for crossing diagonals

For crossing diagonal elements, the buckling length perpendicular to the diagonal plane, is calculated according to Ref.[4], DIN18800 Teil 2, table 15. This means that the buckling length sK is dependent on the load distribution in the element, and it is not a purely geometrical data anymore. In the following chapters, the buckling length sK is defined,

with sK buckling length

l member length

l1 length of supporting diagonal

I moment of inertia (in the buckling plane) of the member

I1 moment of inertia (in the buckling plane) of the supporting diagonal

N compression force in member

N1 compression force in supporting diagonal

Z tension force in supporting diagonal

E elastic modulus


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Continuous compression diagonal, supported by continuous tension diagonal

NN

Z

Z

l/2

l1/2

l5.0slIl1I1

lN4lZ31

ls

K

31

31

K

See Ref.[4], Tab. 15, case 1.


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Continuous compression diagonal, supported by pinned tension diagonal

NN

Z

Z

l/2

l1/2

l5.0slNlZ75.01ls

K

1K



SCIA 156

Pinned compression diagonal, supported by continuous tension diagonal

NN

Z

Z

l/2

l1/2

)1lZlN(4

lZ3)IE(

1lZlN

l5.0s

12

21

d1

1

K



SCIA 157

Continuous compression diagonal, supported by continuous compression diagonal

NN

N1

N1

l/2

l1/2

l5.0slIl1I1lNlN1

ls

K

31

31

1

K



SCIA 158

Continuous compression diagonal, supported by pinned compression diagonal

NN

N1

N1

l/2

l1/2

1

12

K lNlN

121ls

See Ref.[4], Tab. 15, case 3 (2).


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Pinned compression diagonal, supported by continuous compression diagonal

NN

N1

N1

l/2

l1/2

)NlN

12(llN)IE(

l5.0s

1

12

12

3

d

K

See Ref.[4], Tab. 15, case 3 (3).

Calculation of critical Euler force for VARH elements

Definitions

A VARH element is defined as follows :

The member has the properties of a symmetric I secion (formcode=1), where only the height is linear variable along the member. The system length for buckling around the local yy axis (strong axis), is equal to member length.For this non-prismatic section, the critical Euler force is given in Ref[7].

Calculation of the critical Euler force


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For a VARH element (form node i to node j), we can define:

L beam length

Ii, Ij moment of inertia at end i and j

Ai, Aj

sectional area at end i and j

E modulus of Young

Ncr critical Euler force

Ri, Rj

beam stiffness at end i and j

The stiffness R and R' is given by:

EIL

R=R

EIL

R=R

M=R

ijj

iii

II=

i

j

The critical Euler force is given by

LEI=N 2

i2cr

To calculate , the next steps are followed :

1. Calculate L, Ii, Ij, Ri, Rj, R'i, R'j, ξ

2. We suppose that

21>

1-

3. Calculate a, b, c and d as follows


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)]lncotg(+21(

1)-(+[11=d

]1-)ln(sin

-[11=c=b

)]lncotg(-211)(-(+[11=a

41-

)1-(=

2

2

2

2

2

4. For a beam in non-sway system, we solve

0=RRbc)-(ad+Rd+Ra+1 jiji

For a beam in sway system, we solve

0=bc))-(ad-d+c-b-(aRR+-)d-(1R+)a-(1R 2ji

22j

2i

5. When a solution is found, we check if

21>

1-

6. If not, then recalculate a,b,c en d as follows :

])-(

))+21(-)-

211)((-(

+[11=d

])-(

1)-(2-[11=c=b

]-

))+21(-)-

211)((-(

+[11=a

-

-

2

-2

-

2

and resolve the proper equation of 4.


SCIA 162

Calculation buckling ratio for lattice tower membersWhen the national code EC-ENV is selected, the following buckling configuration can be selected. For each configuration, the critical slenderness to be considered, is defined.The values are taken from Ref.[8].

y

y

z z

v

v

We define :

iyy radius of gyration around yy axis

izz radius of gyration around zz axis

ivv radius of gyration around vv axis

With the option 'Bracing members are sufficiently supported', the effective slendernesses may be reduced as follows :

- for vv-axis : vv7.035.0

- for yy-axis : yy7.050.0 The buckling curve 'b' is used..


SCIA 163

Leg with symmetrical bracing

vviL

Leg with intermediate transverse support

yyiL


SCIA 164

Leg with staggered bracing

vv

yy

i52.1)2a,1amax(

iL

Single Bracing

vviL


SCIA 165

Single Bracing with SBS (Secondary Bracing System)

yy

2

vv

1

iLiL

Cross bracing


SCIA 166

yy

comcom

yE

E

comcom

com

com

11

1b

1com

sup1b

2bcomb'2

zz

'2

yy

'2

vv

1

iL

fE

58.070.0K

LL

K1125.0K

K1125.0

FF

K1138.075.0K

LKLKL

iL

,iLiL

with Lcom Length of compressed member (L2 from figure)

Fcom Force in compressed member (L2 from figure)

Fsup Force in supporting member (member crossing member L2)

E Modulus of Young

fy Yield strength


SCIA 167

Cross bracing with SBS

3bcomb'3

zz

'3

yy

'3

zz

2

yy

2

vv

1

LKLKL

iL

,iL

iL

,iLiL

with Lcom Length of compressed member (L3 from figure)

Fcom Force in compressed member (L3 from figure)

Fsup Force in supporting member (member crossing member L3)

Kb See Chapter 'Cross bracing'

K Bracing


SCIA 168

zz

3

yy

3

zz

2

yy

2

vv

1

iL

,iL

iL

,iLiL

Horizontal Bracing

L

1R0PP

R

73.0R316.0R085.0kiLk

1

2

2

vv

with P1 Compression load

P2 Tensile load

Horizontal Bracing with SBS


SCIA 169

L

1R0PP

R

73.0R316.0R085.0k

iLk

1

2

2

yy

with P1 Compression load

P2 Tensile load


SCIA 170

Discontinuous Cross bracing with horizontal member

N1 N2

N1N2

F F

a

a

cos)2N1N(,FmaxFia,

ia2

Sd

vvyy

with F normal force to check

FSd actual compression force in horizontal member

N1 tensile force in diagonal

N2 compression force in diagonal

References

[1] Handleiding moduul STACO VGIStaalbouwkundig GenootschapStaalcentrum Nederland5684/82

[2] Newmark N.M. A simple approximate formula for effective end-fixity of columnsJ.Aero.Sc. Vol.16 Feb.1949 pp.116


SCIA 171

[3] Stabiliteit voor de staalconstructeuruitgave Staalbouwkundig Genootschap

[4] DIN18800 Teil 2Stahlbauten : Stabilitätsfälle, Knicken von Stäben und StabwerkenNovember 1990

[5] Rapportnr. BI-87-20/63.4.3360Controleregels voor lijnvormige constructie-elementenIBBC Maart 1987

[6] Staalconstructies TGB 1990Basiseisen en basisrekenregels voor overwegend statisch belaste constructiesNEN 6770, december 1991

[7] Y. GaléaFlambement des poteaux à inertie variableConstruction Métallique 1-1981

[8] NEN-EN 50341-3-15Overhead electrical lines exceeding AC 45 kV - Part 3: Set of National Normative AspectsNumber 15: National Normative Aspects (NNA) for The Netherlands


SCIA 172

Calculation of moment factors for LTB

Introduction to the calculation of moment factors

For determining the moment factors C1 and C2 for lateral torsional buckling (LTB), we use the standard tables which are defined in Ref.[1] Art.12.25.3 table 9.1.,10 and 11.

The current moment distribution is compared with some standard moment distributions. This standard moment distributions are moment lines generated by a distributed q load, a nodal F load, or where the moment line is maximum at the start or at the end of the beam.

The standard moment distributions which is closest to the current moment distribution, is taken for the calculation of the factors C1 and C2.

The factor C3 is taken out of the tables F.1.1. and F.1.2. from Ref.[2] - Annex F.

Calculation moment factors

Moment distribution generated by q load

For EC3, IS800 and CM66 :

if M2 < 0

C1 = A* (1.45 B* + 1) 1.13 + B* (-0.71 A* + 1) E*

C2 = 0.45 A* [1 + C* eD* (½ + ½)]

if M2 > 0

C1 = 1.13 A* + B* E*

C2 = 0.45A*

For DIN18800 and ONORM4300 :

if M2 < 0

C1 = A* (1.45 B* + 1) 1.12 + B* (-0.71 A* + 1) E*


SCIA 173

C2 = 0.45 A* [1 + C* eD* (½ + ½)]

if M2 > 0

C1 = 1.12 A* + B* E*

C2 = 0.45A*

with :l+q|M2|8

lq=A2

2*

ql|M2|94=C

2*

l+q|M2|8|M2|8=B

2* )

ql|M2|-72(=D 2

2*

for DIN18800 / ONORM 4300 :

0.77-1.77=E*

for EC3 Code and IS800 :

2.70<E*0.52+1.40-1.88=E* 2

for NEN6770/6771, SIA263 Code :

E*=1.75-1.05*+0.30*² and E*<2.3

for CM66 :

2.70<E*0.52+1.40-1.88=E* 2


SCIA 174

Moment distribution generated by F load

FM2 M1 = Beta M2

l

M2 < 0

C1 = A** (2.75 B** + 1) 1.35 + B** (-1.62 A** + 1) E**

C2 = 0.55 A** [1 + C** eD** (½ + ½)]

M2 > 0

C1 = 1.35 A** + B** E**

C2 = 0.55 A**

with : +Fl|M2|4

Fl=A ** +Fl|M2|4|M2|4=**B

Fl|M2|38=C **

)Fl

|M2|-32(=D 2**

The values for E** can be taken as E* from chapter "Moment distribution generated by q load".


SCIA 175

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

M2 M1 = Beta M2

l

C2 = 0.0

for DIN18800 / ONORM 4300

0.77-1.77=1C

for EC3 Code / IS800 :

2.70<1C and0.52+1.40-1.88=1C 2

for CM66 :

22 1152.013=1C

for NEN6770/6771, SIA263 Code :

E*=1.75-1.05*+0.30*² and E*<2.3

References[1] Staalconstructies TGB 1990

StabiliteitNEN 6771 - 1991

[2] Eurocode 3 : Design of steel structures Part 1-1 : General rules and rules for buildingsENV 1993-1-1:1992


SCIA 176

LTBII: Lateral Torsional Buckling 2nd Order Analysis Introduction to LTBII

For a detailed Lateral Torsional Buckling analysis, a link was made to the Friedrich + Lochner LTBII application Ref.[1].

The Frilo LTBII solver can be used in 2 separate ways:

1) Calculation of Mcr through eigenvalue solution

2) 2nd Order calculation including torsional and warping effects

For both methods, the member under consideration is sent to the Frilo LTBII solver and the respective results are sent back to SCIA-ESA PT.

A detailed overview of both methods is given in the following chapters.

Eigenvalue solution Mcr

The single element is taken out of the structure and considered as a single beam, with:

- Appropriate end conditions for torsion and warping

- End and begin forces

- Loadings

- Intermediate restraints (diaphragms, LTB restraints)

The end conditions for warping and torsion are defined as follows:

Cw_i Warping condition at end i (beginning of the member)

Cw_j Warping condition at end j (end of the member)

Ct_i Torsion condition at end i (beginning of the member)

Ct_j Torsion condition at end j (end of the member)

To take into account loading and stiffness of linked beams, see chapter “Linked Beams”.

For this system, the elastic critical moment Mcr for lateral torsional buckling can be analyzed as the solution of an eigenvalue problem:

0KK ge


SCIA 177

With

Critical load factor

Ke Elastic linear stiffness matrix

Kg Geometrical stiffness matrix

For members with arbitrary sections, the critical moment can be obtained in each section, with: (See Ref.[3],pp.176)

)x(MxM

MmaxM

yycr

yycr

With

Critical load factor

Myy Bending moment around the strong axis

Myy(x) Bending moment around the strong axis at position x

Mcr(x) Critical moment at position x

The calculated Mcr is then used in the Lateral Torsional Buckling check of SCIA-ESA PT.

For more background information, reference is made to Ref[2].

2nd Order analysis


SCIA 178

The single element is taken out of the structure and considered as a single beam, with:

- Appropriate end conditions for torsion and warping

- End and begin forces

- Loadings

- Intermediate restraints (diaphragms, LTB restraints)

- Imperfections

To take into account loading and stiffness of linked beams, see chapter “Linked Beams”.

For this system, the internal forces are calculated using a 2nd Order 7 degrees of freedom calculation.

The calculated torsional and warping moments (St Venant torque Mxp, Warping torque Mxs and Bimoment Mw) are then used in the Stress check of SCIA-ESA PT (See chapter “Warping Check – Stress Check”).

Specifically for this stress check, the following internal forces are used:

- Normal force from SCIA-ESA PT

- Maximal shear forces from SCIA-ESA PT / Frilo LTBII

- Maximal bending moments from SCIA-ESA PT / Frilo LTBII

Since Lateral Torsional Buckling has been taken into account in this 2nd Order stress check, it is no more required to execute a Lateral Torsional Buckling Check.

For more background information, reference is made to Ref[2].

Supported National CodesThe following codes are supported for the analysis of Mcr.

- EC3 - ENV

- EC3 - EN

- DIN18800

- ONORM

- NEN

- SIA

- IS

- EAE

For the following national codes, the 2nd Order analysis approach is supported.

- EC3 - ENV

- EC3 - EN

- DIN18800

- ONORM

- NEN

- SIA

- EAE


SCIA 179

Supported Sections

The following table shows which cross-section types are supported for which type of analysis:

FRILO LTBII CSS SCIA-ESA PT CSS Eigenvalue analysis

2nd

Order

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

Thin walled geometric asymmetric I x x

Haunched sections x x

Welded I+Tl x x

Sheet welded Iwn x x

HAT Section 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 sections are replaced by equivalent asymmetric I sections, by ignoring the middle flanges.

The following picture illustrates the relation between the local coordinate system of SCIA-ESA PT and Frilo LTBII. Special attention is required for U sections due to the inversion of the y and z-axis.


SCIA 180

For more information, reference is made to Ref[2]


SCIA 181

Loadings

The following load impulses are supported:

- Point force in node (if the node is part of the exported beam)

- Point force on beam

- Line force in beam

- Moment in node (if the node is part of the exported beam)

- Moment on beam

- Line moment in beam (only for Mx in LCS)

The supported load impulses and their eccentricities are transformed into the local LCS of the exported member.

The dead load is replaced by an equivalent line force on the beam.

Load eccentricities are replaced by torsional moments.

The forces in local x-direction are ignored, except for the torsional moments.

Note: In Frilo LTBII a distinction is made between the centroid and the shear center of a cross-section. Load impulses which do not pass through the shear center will cause additional torsional moments.

Imperfections

In the 2nd Order LTB analysis the bow imperfections v0 (in local y direction) and w0 (in local z direction) can be taken into account.

v0

y, v0

zy

For DIN, ONORM, EC-EN and EAE the imperfections can be calculated according to the code. The codes indicate that for a 2nd Order calculation which takes into account LTB, only the imperfection v0 needs to be considered.


SCIA 182

The sign of the imperfection according to code depends on the sign of Mz in SCIA-ESA PT.

Initial bow imperfection v0 for DIN and ONORM

The imperfection is calculated according to Ref.[6] article 2.2

For prismatic uniform members:

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-uniform members, the bow imperfection is considered at the centre of the buckling system length L.

Initial bow imperfection v0 for EC-EN and EAE

The imperfection is calculated according to Ref.[4] article 5.3.4(3)

00 ekv


SCIA 183

With

k Factor taken as 0,5

e0 Bow imperfection of the weak axis

The value of e0 is taken from following table:

Buckling curve eo /L – elastic analysis eo/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

Initial bow imperfections v0 and w0 for other supported codes

For all other supported codes (EC-ENV, NEN and SIA) as well as DIN, ONORM, EC-EN and EAE the user can manually input the imperfections v0 and w0.


SCIA 184

LTB Restraints

LTB restraints are transformed into 'Supports' (Ref.[2] p22), with horizontal elastic restraint Cy:

Cy = 1e15 kN/m

The position of the restraint z(Cy) is depending on the position of the LTB restraint (top/bottom).

The use of an elastic restraint allows the positioning of the restraint since this is not 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 Frilo LTBII solver. (see Chapter “Supported Sections”)


SCIA 185

Diaphragms

Diaphragms are transformed into 'Elastic Foundations' of type ‘elastic restraint’ (Ref.[2] p25). Both a horizontal restraint Cy and a rotational restraint C are used.

The elastic restraint Cy [kN/m^2] is calculated as follows (Ref.[2] p52 and Ref.5 p40):

2

LSCy

With

S Shear stiffness of the diaphragm

L Diaphragm length along the member

The above formula for Cy is valid in case the bolt pitch of the diaphragm is set as ‘br’. For a bolt pitch of ‘2br’ the shear stiffness S is replaced by 0,2 S (Ref.5 p22).

The shear stiffness S for a diaphragm is calculated as follows (Ref.7,3.5 and Ref.8,3.3.4.):

LK+K

10a.=S

s

21

4

With a Frame distance

Ls Length of the diaphragm

K1 Factor K1 of the diaphragm

K2 Factor K2 of the diaphragm

The position of the restraint z(Cy) is depending on the position of the diaphragm.

Specifically for U-sections, an elastic restraint Cz is used with position y(Cz) due to the rotation of U-sections in the Frilo LTBII solver. (see Chapter “Supported sections”)


SCIA 186

The rotational restraint C [kNm/m] is taken as vorhC (see Chapter “Adaptation of Torsional Constant”)

Linked Beams

Linked beams are transformed into 'Supports' (Ref.[2] p22), with elastic restraint.

The direction of the restraint is dependent on the direction of the linked beam:

If the linked beam has an angle less then 45° with the local y-axis of the beam under consideration, the restraint is set as Cy. In all other cases the restraint is set as Cz.

The position of the restraint z(Cy) or y(Cz) is depending on the application point of the linked beam (top/bottom).

The position is only taken into account in case of a flexible restraint (Ref.[2] p23).

The end forces of the linked beam are transformed to point loads on the considered 1D member,

- in z -direction for linked beams considered as y-restraint

- in y- direction for linked beams considered as z-restraint

Specifically for U-sections, if the linked beam has an angle less then 45° with the local y-axis of the beam under consideration, the restraint is set as Cz. In all other cases the restraint is set as Cy. This is due to the rotation of U-sections in the Frilo LTBII solver. (see Chapter “Supported Sections”)

Limitations and Warnings

The FRILO LTB solver is used with following limitations

- Only straight members are supported

- LTBII analysis is done for the whole 1D member, not for a part of the member, not for more members together


SCIA 187

- When a LTB system length is inputted which differs from the member length, a warning will be given.Intermediate lateral restraints should be defined through LTB restraints, diaphragms and linked beams.

During the analysis, the Frilo LTBII solver may return a warning message. The most important causes of the warning message are listed here.

Eigenvalue solution Mcr

- Lateral Torsional Buckling is not governing – relative slenderness < 0,4

Due to the low relative slenderness, no LTB check needs to be performed. In this case it is not required to use the Frilo LTBII solver.

- Design Torsion! Simplified analysis of lateral torsional buckling is not possible.

Due to the torsion in the member it is advised to execute a 2nd order analysis instead of an eigenvalue calculation.

- Bending of U-section about y-axis!

The program calculates the minimum bifurcation load only.

2nd Order Analysis

- Load is greater then minimum bifurcation load (Error at elastic calculation – system is instable in II.Order )

The loading on the member is too big, a 2nd order calculation cannot be executed.

- You want to calculate the structural safety with Elastic-Plastic method. This analytical procedure cannot be used for this cross-section. It is recommended to use the Elastic-Elastic method.

Plastic calculation is not possible, use imperfection according to code elastic instead of plastic.

For more information, reference is made to Ref[1] and [2].

References

[1] Frilo LTBII softwareFriedrich + Lochner Lateral Torsional Buckling 2nd Order AnalysisBiegetorsionstheorie II.Ordnung (BTII)


SCIA 188

http://www.frilo.de

[2] Friedrich + Lochner LTBII ManualBTII HandbuchRevision 1/2006

[3] J. Meister

Nachweispraxis Biegeknicken und Biegedrillknicken

Ernst & Sohn, 2002

[4] Eurocode 3

Design of steel structures

Part 1 - 1 : General rules and rules for buildings

EN 1993-1-1:2005

[5] J. Schikowski

Stabilisierung von Hallenbauten unter besonderer Berücksichtigung der Scheibenwirkung von Trapez- und Sandwichelementdeckungen, 1999http://www.jschik.de/

[6] DIN 18800 Teil 2

Stahlbauten

Stabilitätsfälle, Knicken von Stäben und Stabwerken

November 1990

[7] E. Kahlmeyer

Stahlbau nach DIN 18 800 (11.90)

Werner-Verlag, Düsseldorf

[8] Beuth-Kommentare

Stahlbauten

Erläuterungen zu DIN 18 800 Teil 1 bis Teil 4, 1.Auflage

Beuth Verlag, Berlin-Köln 1993


SCIA 189

Profile conditions for code checkIntroduction to profile characteristics

The standard profile sections have fixed sections properties and dimensions, which have to be present in the profile library.The section properties are described in chapter "Data for general section stability check".

The required dimension properties are described in chapter "Data depending On the profile shape".

Data for general section stability check

The following properties have to be present in the profile library for the execution of the section and the stability check :

Description Property number

Iy moment of inertie yy 8

Wy elastic section modulus yy 10

Sy statical moment of area yy 6

Iz moment of inertia zz 9

Wz elastic section modulus zz 11

Sz statical moment of area zz 7

It* torsional constant 14

Wt* torsional resistance 13

A0 sectional area 1

Iyz centrifugal moment 12

iy radius of gyration yy 2

iz radius of gyration zz 3

Mpy plastic moment yy 30

Mpz plastic moment zz 31

fab fabrication code0=rolled section (default value)1=welded section2=cold formed section

105

The fabrication code is not obligatory.

When the section is made out of 1 plate, the properties marked with (*) can be calculated by the calculation routine in the profile library. When this is not the case, these properties have to be input by the user in the profile library.

The plastic moments are calculated with a yield strength of 240 N/mm².


SCIA 190

Data depending On the profile shape

I section

Formcode 1

PSS Type .I.

Property Description

49 H

48 B

44 t

47 s

66 R

74 W

140 wm1

61 R1

146

109 1

B

s

w

t

R

R1

a

H

RHS

Formcode 2


SCIA 191

PSS Type .M.


49 H

48 B

67 s

66 R

109 2

B

sH

R

CHS

Formcode 3

PSS Type .RO.


SCIA 192


64 D

65 s

109 3

D

w

Angle section

Formcode 4

PSS Type .L.


49 H

48 B

44 t

61 R1

66 R


SCIA 193

74 W1

75 W2

76 W3

109 4

B

R

R1

w1

w2

t

w3

w1

w2

Channel section

Formcode 5

PSS Type .U.


49 H

48 B

44 t

47 s

66 R

68


SCIA 194

41

61 R1

146

109 5

B

s

H

t

R

R1

a

T section

Formcode 6

PSS Type .T.


49 H

48 B

44 t

47 s

66 R

61 R1

62 R2

146 1

147 2

109 6


SCIA 195

B

s

t

R

a1

H

a2

R1

R2

Full rectangular section

Formcode 7

PSS Type .B.


48 B

67 H

109 7


SCIA 196

B

H

Full circular section

Formcode 11

PSS Type .RU.


64 D

109 11


SCIA 197

D

Asymmetric I section

Formcode 101

PSS Type


49 H

48

44

47 s

42 Bt

43 Bb

45 tt

46 tb

66 R

109 101


SCIA 198

R

H

Bt

Bb

tt

tb

Z section

Formcode 102

PSS Type .Z.


49 H

48 B

44 t

47 s

67 R

61 R1

109 102


SCIA 199

B

s

t

H

R R1

General cold formed section

Each section is considered as a composition of rectangular parts. Each part represents a plate unit which is considered as element for defining the effective width. The start and end parts are considered as unstiffened elements, the intermediate parts are considered as stifffened parts.


SCIA 200

This way of definition of the section assumes that the area is concentrated at its centre line. The rounding in the corners are ignored.

Description Property number Value

form code 109 110

Dy* 22

Dz* 23

CM* 26

buckling curve around yy axis 106 (1)

buckling curve around zz axis 107 (1)

buckling curve for LTB 108 (1)

(1) The values for the buckling curves are defined as follows :

1 = buckling curve a

2 = buckling curve b

3 = buckling curve c

4 = buckling curve d

The conditions are that the section is an open profile. Only the geometry commands O, L, N, A may be used in the geometry description.

When the section is made out of 1 plate, the properties marked with (*) can be calculated by the calculation routine in the profile library. The properties from the reduced section can be calculated by the code check.

When the section is made out of more then 1 plate, the properties marked with (*) can NOT be calculated by the calculation routine in the profile library. The properties from the reduced section can be calculated, except for the marked properties. These properties have to be input by the user in the profile library.

Formcode 110

PSS Type


44 s

61 r

48 B

142 sp

143 e2

68 H

109 110

Remark :r is rounding, special for KLS section (Voest Alpine)

sp is number of shear planes


SCIA 201

B

H

e2

s


SCIA 202

Cold formed angle section

Formcode 111

PSS Type


44 s

61 r

48 B

68 H

109 111

B

sH

r


SCIA 203

Cold formed channel section

Formcode 112

PSS Type


44 s

61 r

48 B

49 H

109 112

B

sH

r


SCIA 204

Cold formed Z section

Formcode 113

PSS Type


44 s

61 r

48 B

49 H

109 113

B

s

H

R

Cold formed C section

Formcode 114

PSS Type


SCIA 205


44 s

61 r

48 B

49 H

68 c

109 114

B

sH

r

c

Cold formed Omega section

Formcode 115

PSS Type



SCIA 206

44 s

61 r

48 B

49 H

42 c

109 115

B

s

H

c

R

Rail type KA

Formcode 150

PSS Type .KA.


148 h1

149 h2

150 h3


SCIA 207

151 b1

152 b2

153 b3

154 k

155 f1

156 f2

157 f3

61 r1

62 r2

63 r3

158 r4

159 r5

160 a

109 150

r1

r2

r4

r3

r5

b3

k

b2

b1

f3f2

f1

h1

h3h2

Rail type KF

Formcode 151


SCIA 208

PSS Type .KF.


48 b

154 k

49 h

153 b3

155 f1

157 f3

148 h1

149 h2

61 r1

62 r2

63 r3

109 151

r1

r2r2

r2 r2

r3

k

bb3

f3

f1

h

h1 h2


SCIA 209

Rail type KQ

Formcode 152

PSS Type .KQ.


48 b

154 k

49 h

153 b3

155 f1

149 h2

150 h3

61 r1

109 152

b

k

b3

r1

h3

h2

f1


SCIA 210

Warping check

Stress check

In cross sections subject to torsion, the following is checked:

Ed,wEd,tEd,VzEd,VyEd,tot

Ed,wEd,MzEd,MyEd,NEd,tot

M

y2Ed,tot

2Ed,tot

0M

yEd,tot

M

yEd,tot

f1.13

3f

f

withfy the yield strength

tot,Ed the total direct stress

tot,Ed the total shear stress

M = M0 (class 1,2 and 3 section)= M1 (class 4 section)

M0 the partial safety factor for resistance of cross-sections where failure is caused by yielding (=1.1)

M1 the partial safety factor for resistance of cross-sections where failure is caused by buckling (=1.1)

N,Ed the direct stress due to the axial force on the relevant effective cross-section

My,Ed the direct stress due to the bending moment around y axis on the relevant effective cross-section

Mz,Ed the direct stress due to the bending moment around z axis on the relevant effective cross-section

w,Ed the direct stress due to warping on the gross cross-section

Vy,Ed the shear stress due to shear force in y direction on the gross cross-section

Vz,Ed the shear stress due to shear force in z direction on the gross cross-section

t,Ed the shear stress due to uniform (St. Venant) torsion on the gross cross-section

w,Ed the shear stress due to warping on the gross cross-section

The warping effect is considered for standard I sections and U sections, and for (= “cold formed sections”) sections. The definition of I sections and U sections, and sections are described in ‘Profile conditions for code check’.

The other standard sections ( RHS, CHS, Angle section, T section and rectangular sections) are considered as warping free. See also Ref.[2], Bild 7.4.40.


SCIA 211

Calculation of the direct stress due to warping

The direct stress due to warping is given by (Ref.[2] 7.4.3.2.3, Ref.[3])

m

MwEd,w C

wM

with Mw the bimoment

wM the unit warping

Cm the warping constant

I sections

For 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. The diagram of wM is given in the following figure:

The direct stress due to warping is calculated in the critical points (see circles in figure).

The value for wM can be calculated by (Ref.[5] pp.135) :

mM hb41w

with b the section width

hm the section height (see figure)


SCIA 212

U sections

For U sections, the value of wM is given in the tables as wM1 and wM2 (Ref. [2], Tafel 7.89). These values are added to the profile library. The diagram of wM is given in the following figure :

The direct stress due to warping is calculated in the critical points (see circles in figure).

sections

The 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.


SCIA 213

The critical points for each part are shown as circles in the figure.

Calculation of the shear stress due to warping

The shear stress due to warping is given by (Ref.[2] 7.4.3.2.3, Ref.[3])

s

0M

m

xsEd,w tdsw

tCM

with Mxs the warping torque (see "Standard diagrams for warping torque, bimoment and the St.Venant torsion")

wM the unit warping

Cm the warping constant

t the element thickness

I sections

The shear stress due to warping is calculated in the critical points (see circles in figure)


SCIA 214

For I sections, we have the following :

A4wtbtdsw M

2/b

0M

U sections, sections

Starting from the wM diagram, we calculate the value

s

0M tdsw

for the critical points.

The shear stress due to warping is calculated in these critical points (see circles in figures)


SCIA 215

Plastic CheckFor doubly symmetric I sections of class 1 and class 2 (plastic check), the interaction formula given in Ref.[10] is used.


SCIA 216

b

tw

tf

h Hy y

z

z

Used variables

Section Properties

A sectional area

b width

H heigth of section

tf flange thickness

tw web thickness

h = H - tfAw = 1.05 (h+tf) tw for rolled section

Aw = h tw for welded sections

ff tb2A

AA f

f

fw 1 Wz,pl plastic section modulus around z axis

Wy,pl plastic section modulus around y axis

Material Properties

fy,d yield strength

y,d shear strength


SCIA 217

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,d

Mz,pl,Rd = Wz,pl fy,d

Vz,pl,Rd = Aw y,d

d,y

2w2

fRd,pl,xp 2t

hbtM

My,pl,Rd = Wy,pl fy,d

2hMM Rd,pl,zRd,pl,w

Vy,pl,Rd = Af y,d

2hVM Rd,pl,yRd,pl,xs

Rd,pl

Sd

NNn

Rd,pl,y

Sd,yy M

Mm

Rd,pl,z

Sd,zz M

Mm

Rd,pl,w

Sd,ww M

Mm

Rd,pl,y

Sd,yy V

Vv


SCIA 218

Rd,pl,z

Sd,zz V

Vv

Rd,pl,xp

Sd,xpxp M

Mm

Rd,pl,xs

Sd,xsxs M

Mm

Shear force reduction

wwz

2zw

xp2zz

1s5.0for

12

mv

ffy

2yf

xp2

yxsy

1s5.0for

12

mvm

Sign

p=sign ( Mz,Sd x Mw,Sd)

2s

np1

s4smm

mmmm

1

ww

ww

ffwz

wz

wzs

ww

swws snp1s4

Unity checks :


SCIA 219

1

sm

psm

s2ns21m

and

1s

mp

sm

s2ns21m

snif

1s

msm

s2s²ns1m

snif

f

w

f

z

2

ff

wwfy

f

w

f

z

2

ff

wwfy

ww

f

w

f

z

2

ff

wwwwfy

ww

Remark : the values between must be >0.

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

The following 6 standard situations are given in the literature (Ref.[2], Ref.[3]).

The value is defined as follows :

m

t

CEIG

with Mx the total torque= Mxp + Mxs

Mxp the torque due to St. Venant

Mxs the warping torque

Mw the bimoment

IT the torsional constant



G the shear modulus

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


SCIA 220

Mx

LaMM

LbMM

txb

txa

Mxp for a side

)xcosh()Lsinh()bsinh(

LbMM txp

Mxp for b side

)'xcosh()Lsinh()asinh(

LaMM txp

Mxs for a side

)xcosh()Lsinh()bsinh(MM txs

Mxs for b side

)'xcosh()Lsinh()asinh(MM txs

Mw for a side

)xsinh()Lsinh()bsinh(MM t

w

Mw for b side

)'xsinh()Lsinh()asinh(MM t

w


SCIA 221

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

Mx

LaMM

LbMM

txb

txa

Mxp for a side

3DL

1k2kbMM txp

Mxp for b side

4DL

1ka2kMM txp

Mxs for a side 3DMM txs

Mxs for b side 4DMM txs

Mw for a side1DMM t

w

Mw for b side2DMM t

w


SCIA 222

)2Ltanh(2L

)2Ltanh(

2L

)Lsinh()bsinh()asinh(

2ba

)2Ltanh(2

1)Lsinh(

)bsinh()asinh(

2k

)2Ltanh(2L

)2Ltanh(

2L

)Lsinh()bsinh()asinh(

2ba

)2Ltanh(2

1)Lsinh(

)bsinh()asinh(

1k

)Lsinh()'xcosh(1k)asinh()xcosh(2k4D

)Lsinh()'xcosh(1k)xcosh(2k)bsinh(3D

)Lsinh()'xsinh(1k)asinh()xsinh(2k2D

)Lsinh()'xsinh(1k)xsinh(2k)bsinh(1D


SCIA 223

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

Mx

2LmM

2LmM

txb

txa

Mxp

)Lsinh()'xcosh()xcosh()x

2L(

mM t

xp

Mxs

)Lsinh()'xcosh()xcosh(m

M txs

Mw

)Lsinh()'xsinh()xsinh(1

mM 2

tw


SCIA 224

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

Mx

2LmM

2LmM

txb

txa

Mxp

)Lsinh()'xcosh()xcosh()k1()x

2L(

mM t

xp

Mxs

)Lsinh()'xcosh()xcosh()k1(

mM t

xs

Mw

)Lsinh()'xsinh()xsinh()k1(1

mM 2

tw

)2Ltanh(

2L

1k


SCIA 225

One end free, other end torsion and warping fixed, local torsionalloading Mt

Mx

txa MM

Mxp

)Lcosh()'xcosh(1MM txp

Mxs

)Lcosh()'xcosh(MM txs

Mw

)Lcosh()'xsinh(M

M tw


SCIA 226

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

Mx

LmM txa

Mxp

)Lcosh()xsinh())Lsinh(L1()xcosh(L'x

mM t

xp

Mxs

)Lcosh()xsinh())Lsinh(L1()xcosh(L

mM t

xs

Mw

)Lcosh()xcosh())Lsinh(L1()xsinh(L1

²m

M tw


SCIA 227

Decomposition of arbitrary torsion line

Since the SCIA-ESA PT solver does not take into account the extra DOF for warping, the determination of the warping torque and the related bimoment, is based on some standard situations.

The following end conditions are considered:

warping free

warping fixed

This results in the following 3 beam situations :

situation 1 : warping free / warping free

situation 2 : warping free / warping fixed

situation 3 : warping fixed / warping fixed

Decomposition for situation 1 and situation 3

The arbitrary total torque line is decomposed into the following standard situations :


SCIA 228

n number of torsion lines generated by a local torsional loading Mtn

one torsion line generated by a distributed torsional loading mt

one torsion line with constant torque Mt0

The values for Mxp, Mxs and Mw are taken from the previous tables for the local torsional loadings Mtn and the distributed loading mt. The value Mt0 is added to the Mxp value.

Decomposition for situation 2

The arbitrary total torque line is decomposed into the following standard situations :

one torsion line generated by a local torsional loading Mtn

one torsion line generated by a distributed torsional loading mt

The values for Mxp, Mxs and Mw are taken from the previous tables for the local torsional loading Mt and the distributed loading mt.

References[1] 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 sheetingCEN 1996

[2] Stahl im Hochbau14. Auglage Band I/ Teil 2Verlag Stahleisen mbH, Düsseldorf 1986

[3] Kaltprofile3. AuflageVerlag Stahleisen mbH, Düsseldorf 1982

[4] Roik, Carl, LindnerBiegetorsionsprobleme gerader dünnwandiger StäbeVerlag von Wilhem ernst & Sohn, Berlin 1972

[5] Dietrich von BergKrane und Kranbahnen – Berechnung Konstruktion AusführungB.G. Teubner, Stuttgart 1988

[6] DASt-Richtlinie 016Bemessung und konstruktive Gestaltung von Tragwerken aus dünnwandigen kaltgeformten BauteilenStahlbau-Verlagsgesellschaft, Köln 1992

[7] Esa Prima WinSteel Code Check ManualSCIA


SCIA 229

EPW 3.10

[8] C. PetersenStahlbau : Grundlagen der Berechnung und baulichen Ausbildung von StahlbautenFriedr. Vieweg & Sohn, Braunschweig 1988


[10] I. Vayas,Interaktion der plastischen Grenzschnittgrössen doppelsymmetrischer I-QuerschnitteStahlbau 69 (2000), Heft 9


SCIA 230

Check of numerical sections

Stress check

The stress calculation for a numerical section is as follows:

z

zVz

y

yVy

z

zzMz

y

yyMy

xN

VzVytot

MzMyNtot

2tot

2totvm

AV

AV

WM

WM

AN

3

with vm the VonMises stress, the composed stress

tot the total normal stress

tot the total shear stress

N the normal stress due to the normal force N

My the normal stress due to the bending moment Myy around y axis

Mz the norma stress due to the bending moment Mzz around z axis

Vy the shear stress due to shear force Vy in y direction

Vz the shear stress due to shear force Vz in z direction

Ax the sectional area

Ay the shear area in y direction

Az the shear area in z direction

Wy the elastic section modulus around y axis

Wz the elastic section modulus around z axis


SCIA 231

Use of diaphragms Adaptation of torsional constant

See Ref.[1], Chapter 10.1.5., Ref.2,3.5 and Ref.3,3.3.4..

When diaphragms (steel sheeting) are used, the torsional contant It is adapted for symmetric/asymmetric I sections, channel sections, Z sections, cold formed U, C , Z sections.

The torsional constant It is adapted with the stiffness of the diaphragms :

12³sI

)th(IE3

C

200b125if100b

C25.1C

125bif100b

CC

sEI

kC

C1

C1

C1

vorhC1

GlvorhCII

s

sk,P

aa

100k,A

a

2a

100k,A

effk,M

k,Pk,Ak,M

2

2

tid,t

with l the LTB length

G the shear modulus

vorhC the actual rotational stiffness of diaphragm

CM,k the rotational stiffness of the diaphragm

CA,k the rotational stiffness of the connection between the diaphragm and the beam

CP,k the rotational stiffness due to the distortion of the beam

k numerical coefficient= 2 for single or two spans of the diaphragm= 4 for 3 or more spans of the diaphragm

EIeff bending stiffness of per unit width of the diaphragm

s spacing of the beam

ba the width of the beam flange (in mm)

C100 rotation coefficient - see table


SCIA 232

h beam height

t thickness beam flange

s thickness beam web

References[1] ENV 1993-1-3:1996

Eurocode 3 : Design of steel structures Part 1-3 : General rulesSupplementary rules for cold formed thin gauge members and sheetingCEN 1996

[2] E. KahlmeyerStahlbau nach DIN 18 800 (11.90)Werner-Verlag, Düsseldorf


SCIA 233

[3] Beuth-KommentareStahlbautenErläuterungen zu DIN 18 800 Teil 1 bis Teil 4, 1.AuflageBeuth Verlag, Berlin-Köln 1993


SCIA 234

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

For the national codes EC3, NEN6770/6771, DIN18800 and SIA263, special checks are performed for built-in beams, according to Ref.[1].

Reduction of plastic moment capacity due to plate bending

bu

e1

e2=bo

bo

tu

0.5 q0.5 q


SCIA 235

bu

e1

e2=bo

bo

tu

0.5 q0.5 q

to

bu

e1

bo

tu

0.5 q0.5 q

e2=0

to

When the lower plate is loaded by q-load (uniform distributed load), the effective area of the loaded plate (flange) for the calculation of the plastic capacity is reduced as follows :

for THQ and IFB beams :


SCIA 236

11

tftqee

b6ee²ee233t²

1

AA

uyu

M21

u

2121u

ueff,u

for SFB beam :

oouueff AAA

with e1, e2, tu, bu see the figures above

q load on flange, plate (as N/m)

fy yield strength

M partial safety factor

see formula

u =

o analog to u, but withbu=bo

e1=bo

tu=toe2=tw

Plastic interaction formula for single bending and shear force

The following plastic interaction formula can be used, when single bending around yy-axis My,Sd, in combination with shear force Vz,Sd, is acting :

y,pl

fm

Rd,z,pl

Sd,z

m

v

Rd,y,pl

Sd,y

W2hA

0.1VV

AA

MM


SCIA 237

with My,Sd, Vz,Sd internal forces

Mpl,y,Rd plastic bending capacity around yy axis

Vpl,z,Rd plastic shear capacity in z direction

Av shear area (see figure)

Am = A - | Ao,x - Au,x | (see figure)

hf = h+tu/2-to/2 (see figure)

Wpl,y plastic section modulus around yy axis - reduced if necessary

Plastic check for plate in bending

The following condition for the plate in bending must be verified :

0.1

tee

tf1q

tf1q

43

u

21

uy

M

2

uy

M

with e1, e2, tu see figures

q load on flange, plate (as N/m)= qmax+qmin

(Ksi)

qqq minmax

fy yield strength

M partial safety factor


SCIA 238

0.5 q (1+Ksi)0.5 q (1-Ksi)

Stress check for slim floor beams

Normal stress check

At the edges of the bottom plate, the following composed stress check is performed :

12t

Ix

2ee

)q,q(M

2t

IM

f

3u

21minmaxx

u

x

xy

M

y2yyx

2x


SCIA 239

Shear stress check in plate

In the middle of the bottom plate, transverse shear stress is checked :

u

minmax

M

y2x

t)q,q(

23

f²3

Torsion check due to unbalanced loading

for IFB and SFB beams :

12bEt

EI

GIEI

h2L

LLtanh

2QeLM

htbM

23

LL

LLtanh

12

QeLM

ItM

3f

3oo

o

t

ofk

k

kmax,w

foo

max,wmax,w

k

kmax,t

t

omax,tmax,t

M

ymax,wmax,t

with to, bo see figures


It torsional constant for complete section

E modulus of Young


SCIA 240

G shear modulus

L system length for Lyz

Q,e see figure

Q

e

for THQ beams :

2V

be1

4qL Rd,z,pl

f

with e, bf see figure


q load on flanges, plate (as N/m)= qmax+qmin

(Ksi)

qqq minmax


SCIA 241

q maxq min

bf

ee

References[1] Multi-Storey Buildings in Steel

Design Guide for Slim Floors with Built-in BeamsECCS N° 83 - 1995


SCIA 242

Effective cross-section properties for lattice tower angle membersEffective cross-section properties for compressed lattice tower angle membersThe effective cross-section properties shall be based on the effective width beff of the leg. See Ref.[1], Chapter J.2.3.

b

The effective width shall be obtained from the nominal width of the leg, assuming uniform stress distribution :

bb

f235

43.0KK4.28

tb

eff

y

c

c

pp

p

For rolled angle :


SCIA 243

2

p

p

pp

p

98.0213.1

91.02213.191.0

0.191.0

For cold formed angle :

2

p

p

p

p

p

98.0213.1

3

404.05

213.1809.0

0.1809.0

with t the thickness

b the nominal width

fy the yield strength in Mpa

References[1] EN 50341-1:2001

Overhead electrical lines exceeding AC 45 kV Part 1: General requirements

Steel Code Check Theory Enu

Documents

torsional buckling

crosssection properties

torsionalflexural buckling

scia software

axial compression

compression members

cold formed sections

scia group