SCC_TB_ENU

SCIA.ESA PT Steel Code Check

THEORETICAL BACKGROUND

SCIA

Scientific Application Group

________________________________________________________________________ Release : 5.20 Module : ESASD.01 Manual : SCIA STEEL DESIGNER Steel Code Check Theoretical Background Revision : 01/2006 ________________________________________________________________________ SCIA Group n.v. Scientific Application Group Industrieweg 1007 B-3540 Herk-de-Stad (België) Tel.(+32) (0)13/55 17 75 Fax.(+32) (0)13/55 41 75 E-mail [email protected] ________________________________________________________________________ SCIA W+B Software b.v. Kroonpark 10 6831 GV ARNHEM Tel. 026 – 32 01 230 ________________________________________________________________________ SCIA sarl Parc Club des Prés Rue Papin, 29 - F-59650 Villeneuve d'Asq (France) Tel.(+33) (0) 3.20.04.10.60 Fax.(+33) (0) 3.20.04.03.36 E-mail [email protected] ________________________________________________________________________ SCIA Software GbR Emil-Figge-Str. 76-80 D-44227 Dortmund (Deutschland) Tel.(+49) 231-9742586 Fax.(+49) 231-9742587 E-mail [email protected]

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TABLE OF CONTENTS

EC 3 – ENV 1993 2

EC3 CODE CHECK 2 MATERIAL PROPERTIES 2 CONSULTED ARTICLES 3 Classification of sections 5 Effective cross-section properties for class 4 cross-section 6 Section properties 6 Bending moment 6 Bending, shear and axial force 6 Torsion check 6 Built-in beams 7 Compression members 7 Lateral-torsional buckling 7 Use of diaphragms 8 Shear buckling check 8 Shear buckling check for cold formed sections 8 Stability check for torsional buckling and torsional-flexural buckling 10 Bending and axial compression 11 Battened compression members 12 EC3 - FIRE RESISTANCE 13 FIRE ACTIONS EFFECT EFI 13 MATERIAL PROPERTIES 14 TEMPERATURE ANALYSIS - THERMAL ACTIONS 15 NOMINAL TEMPERATURE-TIME CURVE 15 NET HEAT FLUX 16 STEEL TEMPERATURE 16 CALCULATION MODEL 18 CODE CHECK 18 SUPPORTED SECTIONS 19 REFERENCES 20

EC 3 – EN 1993 22

EC3 CODE CHECK 22 MATERIAL PROPERTIES 22 CONSULTED ARTICLES 23 Classification of sections 25 Effective cross-section properties for class 4 cross-section 26 Section properties 26 Torsion check 26 Built-in beams 26 Compression members 27

Lateral-torsional buckling 27 Use of diaphragms 28 Shear buckling check 28 SUPPORTED SECTIONS 28 REFERENCES 29

DIN18800 30

DIN18800 CODE CHECK 30 MATERIAL PROPERTIES 30 CONSULTED ARTICLES 31 Classification of sections 35 Net area properties 35 Plastic interaction formula for RHS section 35 Plastic interaction formula for CHS section 38 Torsion check 40 Built-in beams 40 Calculation of the buckling length 41 Torsional buckling 41 Use of diaphragms 42 LTB Check 43 Combined flexion for check method 2 46 Battened compression members 46 Effective area properties 48 Shear buckling check 49 Shear buckling check with buckling influence 49 COLD FORMED THIN GAUGE MEMBERS 49 SUPPORTED SECTIONS 50 REFERENCES 51

ONORM B 4300 54

ONORM B 4300 CODE CHECK 54 MATERIAL PROPERTIES 55 CONSULTED ARTICLES 56 SUPPORTED SECTIONS 56 REFERENCES 57

NEN 59

NEN6770/6771 CODE CHECK 59 MATERIAL PROPERTIES 59 CONSULTED ARTICLES 60 Section properties 63 Classification of sections 63 Effective cross-section properties for class 4 cross-section 64

Torsion check 64 Built-in beams 64 Buckling length 64 Lateral-torsional buckling 65 Use of diaphragms 65 Battened compression members 66 Shear buckling check 67 Shear buckling check with buckling influence 67 NEN6072 - FIRE RESISTANCE 68 FIRE ACTIONS EFFECT 68 MATERIAL PROPERTIES 68 NOMINAL TEMPERATURE-TIME CURVE 69 STEEL TEMPERATURE 69 CALCULATION MODEL 72 CODE CHECK 72 SUPPORTED SECTIONS 73 REFERENCES 74

AISC - ASD 76

AISC - ASD CODE CHECK 76 CLASSIFICATION OF SECTIONS 78 SECTION PROPERTIES 78 BUCKLING LENGTH 79 FLEXURAL TORSIONAL BUCKLING 79 LATERAL-TORSIONAL BUCKLING 79 SHEAR BUCKLING CHECK 80 SUPPORTED SECTIONS 81 REFERENCES 81

AISC - LRFD 83

AISC - LRFD CODE CHECK 83 CLASSIFICATION OF SECTIONS 85 SECTION PROPERTIES 86 BUCKLING LENGTH 86 LATERAL-TORSIONAL BUCKLING 86 USE OF DIAPHRAGMS 87 SHEAR BUCKLING CHECK 87 SUPPORTED SECTIONS 87 REFERENCES 88

CM66 89

CM66 CODE CHECK 89 CONSULTED ARTICLES 89

Section properties 91 Plastic coefficient 91 Compression members 91 Factor kf 91 LTB Check 92 Use of diaphragms 92 Combined flexion 92 Shear buckling check 92 SUPPORTED SECTIONS 92 REFERENCES 93

CM66 - ADDITIF 80 94

CM66 - ADDITIF 80 CODE CHECK 94 CONSULTED ARTICLES 94 Classification of sections 95 Section check 95 Compression members 95 Lateral-torsional buckling 95 Use of diaphragms 96 SUPPORTED SECTIONS 96 REFERENCES 98

BS5950-1:1990 99

BS5950-1:1990 CODE CHECK 99 MATERIAL PROPERTIES 99 CONSULTED ARTICLES 100 Classification of sections 103 Slender cross-section 103 Section properties 103 Bending moment 103 Bending, shear, axial force 103 Lateral torsional buckling 104 Use of diaphragms 105 Compression member 105 Shear buckling check 105 SUPPORTED SECTIONS 105 REFERENCES 106

BS5950-1:2000 108

BS5950-1:2000 CODE CHECK 108 MATERIAL PROPERTIES 108 GOVERNING CODE CLAUSES 109 Classification of sections 112

Slender cross-sections 112 Section properties 112 Moment capacity 112 Bending, shear, axial force/capacity interaction 113 Lateral torsional buckling due to major axis moments 113 Torsional buckling about an eccentric axis (Annex G) 113 Lateral buckling due axial compression 113 Combined axial and bending buckling unity check/utilisation 114 Torsion effects 114 SUPPORTED SECTIONS 114

SIA263 115

SIA263 CODE CHECK 115 MATERIAL PROPERTIES 115 CONSULTED ARTICLES 115 Section classification 117 Slender cross-section 117 Sections properties 117 Lateral torsional buckling 118 Use of diaphragms 118 Shear buckling 118 Stability check 118 Torsion check 118 Built-in beams 119 SIA263 - FIRE RESISTANCE 119 FIRE ACTIONS EFFECT EFI 119 MATERIAL PROPERTIES 119 TEMPERATURE ANALYSIS - THERMAL ACTIONS 120 NOMINAL TEMPERATURE-TIME CURVE 120 NET HEAT FLUX 120 STEEL TEMPERATURE 120 CALCULATION MODEL 122 CODE CHECK 122 SUPPORTED SECTIONS 122 REFERENCES 123

GBJ 17-88 125

THE GBJ 17-88 CODE CHECK 125 MATERIAL PROPERTIES 125 CONSULTED ARTICLES 126 Section properties 128 Shear buckling check 128 Buckling curves 129 Buckling length 129 Lateral torsional buckling 129

Local stability of compressed members 129 Shear buckling check 130 SUPPORTED SECTIONS 130 REFERENCES 132

KOREAN STEEL CODE CHECK 133

THE KOREAN STEEL CODE CHECK 133 MATERIAL PROPERTIES 133 CONSULTED ARTICLES 134 Section classification 135 Section properties 136 Buckling length 136 Lateral torsional buckling 136 Combined stresses 137 Shear buckling check 138 SUPPORTED SECTIONS 138 REFERENCES 139

BSK 99 141

BSK 99 CODE CHECK 141 MATERIAL PROPERTIES 141 CONSULTED ARTICLES 143 Classification of sections 144 Effective cross-section properties for class 3 cross-section 144 Section properties 144 Section check 144 Compression members 145 Stability check for torsional buckling and torsional-flexural buckling 145 Lateral-torsional buckling 147 Use of diaphragms 148 Shear force ( shear buckling) 148 SUPPORTED SECTIONS 149 REFERENCES 150

IS 800 152

IS:800 CODE CHECK 152 MATERIAL PROPERTIES 152 CONSULTED ARTICLES 152 Classification of sections 154 Section properties 154 Section check 154 Compression members 154 Stability check for torsional buckling and torsional-flexural buckling 154

Lateral-torsional buckling 156 Use of diaphragms 157 SUPPORTED SECTIONS 157 REFERENCES 158

CALCULATION OF BUCKLING RATIO 159

INTRODUCTION TO THE CALCULATION OF BUCKLING RATIO 159 CALCULATION BUCKLING RATIO – GENERAL FORMULA 159 CALCULATION BUCKLING RATIOS FOR CROSSING DIAGONALS 161 CONTINUOUS COMPRESSION DIAGONAL, SUPPORTED BY CONTINUOUS TENSION DIAGONAL 162 CONTINUOUS COMPRESSION DIAGONAL, SUPPORTED BY PINNED TENSION DIAGONAL 163 PINNED COMPRESSION DIAGONAL, SUPPORTED BY CONTINUOUS TENSION DIAGONAL 164 CONTINUOUS COMPRESSION DIAGONAL, SUPPORTED BY CONTINUOUS COMPRESSION DIAGONAL 165 CONTINUOUS COMPRESSION DIAGONAL, SUPPORTED BY PINNED COMPRESSION DIAGONAL 166 PINNED COMPRESSION DIAGONAL, SUPPORTED BY CONTINUOUS COMPRESSION DIAGONAL 167 CALCULATION OF CRITICAL EULER FORCE FOR VARH ELEMENTS 167 DEFINITIONS 167 CALCULATION OF THE CRITICAL EULER FORCE 168 CALCULATION BUCKLING RATIO FOR LATTICE TOWER MEMBERS 170 LEG WITH SYMMETRICAL BRACING 171 LEG WITH INTERMEDIATE TRANSVERSE SUPPORT 171 LEG WITH STAGGERED BRACING 172 SINGLE BRACING 172 SINGLE BRACING WITH SBS (SECONDARY BRACING SYSTEM) 172 CROSS BRACING 173 CROSS BRACING WITH SBS 174 K BRACING 175 HORIZONTAL BRACING 175 HORIZONTAL BRACING WITH SBS 176 DISCONTINUOUS CROSS BRACING WITH HORIZONTAL MEMBER 176 REFERENCES 177

CALCULATION OF MOMENT FACTORS FOR LTB 179

INTRODUCTION TO THE CALCULATION OF MOMENT FACTORS 179 CALCULATION MOMENT FACTORS 179 MOMENT DISTRIBUTION GENERATED BY Q LOAD 179 MOMENT DISTRIBUTION GENERATED BY F LOAD 182 MOMENT LINE WITH MAXIMUM AT THE START OR AT THE END OF THE BEAM 183 REFERENCES 183

PROFILE CONDITIONS FOR CODE CHECK 185

INTRODUCTION TO PROFILE CHARACTERISTICS 185

DATA FOR GENERAL SECTION STABILITY CHECK 185 DATA DEPENDING IN THE PROFILE SHAPE 187 I SECTION 187 RHS 188 CHS 189 ANGLE SECTION 190 CHANNEL SECTION 191 T SECTION 193 FULL RECTANGULAR SECTION 194 FULL CIRCULAR SECTION 195 ASYMMETRIC I SECTION 196 Z SECTION 197 GENERAL COLD FORMED SECTION 199 COLD FORMED ANGLE SECTION 201 COLD FORMED CHANNEL SECTION 202 COLD FORMED Z SECTION 204 COLD FORMED C SECTION 205 COLD FORMED OMEGA SECTION 206 RAIL TYPE KA 207 RAIL TYPE KF 209 RAIL TYPE KQ 210

WARPING CHECK 213

CALCULATION OF THE DIRECT STRESS DUE TO WARPING 214 I SECTIONS 214 U SECTIONS 215 Σ SECTIONS 216 CALCULATION OF THE SHEAR STRESS DUE TO WARPING 217 I SECTIONS 217 U SECTIONS, Σ SECTIONS 218 PLASTIC CHECK 219 STANDARD DIAGRAMS FOR WARPING TORQUE, BIMOMENT AND THE ST.VENANT TORSION 223 TORSION FIXED ENDS, WARPING FREE ENDS, LOCAL TORSIONAL LOADING MT 225 TORSION FIXED ENDS, WARPING FIXED ENDS, LOCAL TORSIONAL LOADING MT 226 TORSION FIXED ENDS, WARPING FREE ENDS, DISTRIBUTED TORSIONAL LOADING MT 228 TORSION FIXED ENDS, WARPING FIXED ENDS, DISTRIBUTED TORSIONAL LOADING MT 229 ONE END FREE, OTHER END TORSION AND WARPING FIXED, LOCAL TORSIONAL LOADING MT 230 ONE END FREE, OTHER END TORSION AND WARPING FIXED, DISTRIBUTED TORSIONAL LOADING MT 230 DECOMPOSITION OF ARBITRARY TORSION LINE 232 DECOMPOSITION FOR SITUATION 1 AND SITUATION 3 233 DECOMPOSITION FOR SITUATION 2 233 REFERENCES 233

CHECK OF NUMERICAL SECTIONS 236

STRESS CHECK 236

USE OF DIAPHRAGMS 238

ADAPTION OF TORSIONAL CONSTANT 238 REFERENCES 239

SECTION CHECK FOR BUILT-IN BEAMS (IFB, SFB, THQ SECTIONS) 241

INTRODUCTION 241 REDUCTION OF PLASTIC MOMENT CAPACITY DUE TO PLATE BENDING 241 PLASTIC INTERACTION FORMULA FOR SINGLE BENDING AND SHEAR FORCE 243 PLASTIC CHECK FOR PLATE IN BENDING 244 STRESS CHECK FOR SLIM FLOOR BEAMS 245 NORMAL STRESS CHECK 245 SHEAR STRESS CHECK IN PLATE 246 TORSION CHECK DUE TO UNBALANCED LOADING 246 REFERENCES 249

EFFECTIVE CROSS-SECTION PROPERTIES FOR LATTICE TOWER ANGLE MEMBERS 250

EFFECTIVE CROSS-SECTION PROPERTIES FOR COMPRESSED LATTICE TOWER ANGLE MEMBERS 250 REFERENCES 251

SCIA.ESA PT Steel Code Check Theoretical Background

EC 3 – ENV 1993

EC3 CODE CHECK

The beam elements are checked according to the regulations given in Eurocode 3 Design of steel structures Part 1 - 1 : General rules and rules for buildings ENV 1993-1-1:1992

Material properties

For standard steel grades, the yield strength fy and tensile strength fu are defined according to the thickness 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<=250

fy fu fy fu fy fy

S235 S 235

235 360 215 340 175 320

S275 S 275

275 430 255 410 205 380

S355 S 355

355 510 335 490 275 450

S420 S 420

420 520 390 520

S460 S 460

460 550 430 550

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

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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). The average yield strength is determined as follows :

( ) ( ybuybug

ybya f2.1,fminffA

²kntff ≤−⎟⎟⎠

⎞⎜⎜⎝

⎛+= )

with fyb the tensile yield strength = fy

fu the tensile ultimate strength t the material thickness Ag the gross cross-sectional area k is a coefficient depending on the type of forming :

k = 0.7 for cold rolling k = 0.5 for other methods of forming

n the number of 90° bends in the section

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.

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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 (*) 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

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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 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

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

π+π=

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.

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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.

Use of diaphragms See Chapter 'Adaption 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

ts346.0

ff

83.0

ybww

_

1M

0M

y

ybw

_

⋅=λ

γγ

⋅≤λ

The shear buckling resistance Vb,Rd is given by

1M

bvwRd,bV

γ=

fts ⋅⋅

he plastic shear resistance Vpl,Rd is given by

T

3

ftsV

0M

ywRd,pl

γ

⋅⋅=

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with wλ ess

d strength

γM0 ce of cross-sections where

γM1 ce of cross-sections where failure is caused by buckling (=1.1)

he value for fbv is given by :

fbv

the relative web slendern

fyb the basic yield strength fy the average yiel sw the web length t the web thickness E the modulus of elasticity fbv the shear buckling strength

the partial safety factor for resistanfailure is caused by yielding (=1.1) the partial safety factor for resistan

T

w_λ

<1.40 w

ybf48.0λ

²

f67.1.40 ≥ 0

w_

yb

λ Remarks : For an arbitrary composed section, the total Vb,Rd and Vpl,Rd is taken as the sum of

sistance of each web, where the angle θ (teta) is larger than 45° (see figure) the basic yield strength is taken equal to the average yield strength

re

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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 :

( ) ( )[ ]

²iy1

²il

E²

4² T,cry,crT,cry,cr σβσ−σ+σ− 21

ii

lEC²

iA1

),min(

f

0

0

y

yy,cr

T,crTF,cr

2z

2y

2T

t20g

T,cr

TF,crT,crcr

Acr

yb

⎟⎟⎠

⎞⎜⎜⎝

⎛−=

⎟⎟⎠

⎞⎜⎜⎝

⎛π

=

σ+β

=

++=

π+=

σσ=

βσ

=

y2i2

GI⎜⎜⎝

y,crσ

00

m⎟⎟⎠

β

σ

σ

⎞⎛σ

λ

σ

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with

yb the basic yield strength σcr the critical stress

σcr,T the elastic critical s ess for torsional buckling σcr,TF the elastic critical stress for torsional-flexural buckling

G the shear modulus E the modulus of elasticity

constant of the gross section the warping constant

z the radius of gyration about zz-axis l the buckling length of the member for torsional buckling

of the shear center -axis

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

tr

IT the torsion CM

iy the radius of gyration about yy-axis i

T

y0 the position ly the buckling length for flexural buckling about the yy

Bending and axial compression

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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

) 2Uo

(3) 2Uc

The following section pairs are supported as battened compression member : (1) 2I(2

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 :

4aVM

2V V

N N

sG

sG

SDf,G

=

=

=

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

4

aVM

2haV T

s

0

s

=

=

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

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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

is. It is recommended to use the accidental combination rules, for calculating the analysinternal forces used in the fire resistance check. The accidental combination is given by

)f(AQQG dj,kj,21,k1,1kGA Σ+ψΣ+ψ+γ Σ

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with Gk characteristic values of permanent actions Qk,1 characteristic value of the (main) variable action

characteristic values of the other variable actions design values of actions from fire exposure

γGA partial safety factor for permanent actions in the accidental situation =[1.0]

1,1 2,j ients

aterial properties

Qk,j Af(d)

ψ ψ combination coeffic

M

g on the steel temperature.

trength and deformation properties :

The material properties are dependin S

aE Eθ

,a,

y

,p,p

y

,y,y

E

ff

ff

θ

θθ

θθ

=

=

=

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

t ethod, the following default properties are considered to nalysis :

unit mass ρa 7850 kg/m³

k

k

k

3 In he simplified calculation mbe constant during the a

thermal elongation ∆l/l 14 x 10-6 (θa-20) thermal conductivity λa 45 W/mK

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Temperature analysis - Thermal actions

this part, the nominal temperature-time curves and the related net heat flux are

ction 4, and Ref.[7], II.2.2.

Nominal temperature-time curve

Indescribed. See Ref.[8], Se

The following temperature-time curves can be selected :

t time in [min] gas temperature in [°C]

αc the coefficient of heat transfer by convection

ISO 834 curve

W25

t8(3420

c

g

=

++

external fire curve

with θg

•

[ ] K²m/

)1

log5 10

α

=θ

•

( )[ ] K²m/W25

20e313.0e687.01660

c

t8.3t32.0g

=α

+−−= −−

• drocar curve

θ

hy bon

( )[ ] K²/W50

e2511080

c

167.0g

=α

−= −

• smoldering fire curv

m

20e675.0 t5.2t +− −3.0θ

e

20t1544g +=θ

during 20 minutes, followed by the standard ISO 834 curve

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Net heat flux

r,nc,netc,nd,net hh r,nethγ+γ=

net,d

net,c the convective heat flux hnet,r the radiative heat flux γn,c factor depending on NAD [1.0]

γn,r factor depending on NAD [1.0]

with h the net heat flux h

( )mgcc,net θα

h = θ−

( ) ( )( )4m

4r 273273 +θ−+θ 8

resr,net 107 ⋅εΦ= −

ith

εres

εf emissivity related to fire compartment = [0.800]

= [0.625] θr = θg

gas temperature in [°C] θm surface temperature of member in [°C] αc coefficient of heat transfer by convection

Steel Temp

6.5h

w Φ configuration factor [1.0] resultant emissivity = εf εm

εm emissivity related to surface material

erature

The increase of temper member during a time interval ∆t

ature ∆θa,t in an unprotected steel

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thVc

/Ad,net

a

mt,a ∆

ρ=θ

ith nit length [m²/m] th [m³/m]

taken as less than 10m-1

t

ρa the unit mass of steel [kg/m³]

a

∆

w Am the exposed surface area per u V the volume of the member per unit leng

The factor A /V should not bem

the specific heat of steel [J/kgK] ca hnet,d the net heat flux per unit area [W/m²] ∆ the time interval [seconds]

The value should not be taken as more than 5 seconds

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

( ) ( )

V/Adc pp

aaρ=φ

c

1et

3cd

V/A

pp

t,g10/t,at,gpp

t,a

ρ

∆−−∆⎟⎠⎞⎛ φ

+

θ−θ

ρ

λ=θ φ

of fire protection material per unit length [m²/m]

p ess of the fire protection material [m] ∆t the time interval [seconds]

The value should not be taken as more than 30 seconds

t ∆θg,t the increase of the ambient gas temperature during the time

interval

∆1aap ⎜

⎝

with Ap the area V the volume of the member per unit length [m³/m] ca the specific heat of steel [J/kgK] cp the specific heat of fire protection material [J/kgK] d the thickn

ρa the unit mass of steel [kg/m³] ρp the unit mass of fire protection [kg/m³] θa,t the steel temperature at time t θg,t the ambient gas temperature at time

SCIA 17


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

∆θa,t ≥ 0.0

with intumescent e'.

The value For the increase of temperature a,t in an insulated steel member

ter 'Steel Temperatur∆θ

coating, we refer to the NEN specifications, Chap

Calculation model

The calculation can be performed in 2 domains :

m mperature, the fire resistance time tfi,d

ode Check

- strength domain - temperature/time domain In the strength domain, the strength R (unityfi,d,t check) is calculated after a given time t (e.g. strength after 45 min). In the temperature/time domain, the critical steel te perature θcr,d is computed. From this critical teis calculated (the time domain).

C

The section and stability checks (buckling, lateral torsional buckling) are performed iven 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 e temperature/time domain..

T rsional b d. For each m cross section, the section check and the s y chThe following checks are executed : EC3-1-2 : - classification of cross section : art. 4.2.2. - istan s : art. 4.2.3.1 - resistance for compression members (class 1,2 or 3) : art. 4.2.3.2. - - sistan ) : art.4.2.3.4. - resistan ss 1,2,3) subject to bending and compression : art.

3.5.

according to the regulations g

tho uckling and shear buckling are not considere

ember, the classification of the eck are performed. tabilit

res ce for tension member

resistance for beam re

s (class 1,2) : art. 4.2.3.3. ce for beams (class 3

ce for members (cla4.2.

SCIA 18


- critical : art. 4.2.4.

od ineering

ss 1,2) : art. III.5.4.

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

- resistance for members (class 4) : art. III.5.7. - al temp atu : art II.5.

SUPPORT CTIONS

temperature

E-

CCS M el Code on Fire Engresistance for tension members : art. III.5.2.

- resistance for compression members (class 1,2 or 3) : art. III.5.3. - resistance for beams (cla- resistance for beams (class 3) : art. III.5.5. - e

critic er re . I 8.

ED SE

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

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 Σ Cold formed section COM RIMAWIN Composed section in PO Solid tube NUM Numerical section

T nec conditions for these sections are described in chapter "Profile conditions for code check". The CO ry.

I RHS CHS L U T PPL

RS

Z

Σ

O

COM

NUM

he essary data

M and NUM sections are not read out of the profile libra

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

Section check cl ass 1 x x x

SCIA 19



Section check c x lass 3 x x x x x x x x x x x x

Section check c lass 4 x x x x x x

Stability check x x class 1 x

Stability check x x class 2 x

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

Stability check x x x x x class 4 x

Shear buckling x x x check x

(1) sect

REFERE

ions are classified as class 3 cross section by default.

NCES

[1]

art 1 - 1 : General rules and rules for buildings

[2] f Eurocode 3 esign Manual for Steel Structures in Building

5, 1991

[3] STRUCTIONS METALLIQUE

lg , Faculté des Sciences Appliquées, 1988

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

[5] Eurocode 3 Design of steel structures Part 1 - 1/ A1 : General rules and rules for buildings ENV 1993-1-1:1992/A1, 1994

Eurocode 3 Design of steel structures PENV 1993-1-1:1992, 1992 Essentials oDECCS - N° 6 R. Maquoi ELEMENTS DE CONU

SCIA 20


[6] Eurocode 3 Design of steel structures Part 1 - 2 : General rules - Structural fire design ENV 1993-1-2:1995, 1995

Model Code on Fire Engineering

May 2001

tions on structures - Actions on structures exposed to fire ENV 1991-2-2:1995

[7]

ECCS - N° 111

[8] Eurocode 1

Basis of design and actions on structures Part 2-2 : Ac

SCIA 21


EC 3 – EN 1993

EC3 CODE CHECK

he beam elements are checked according to the regulations given in T

Eurocode 3 Design of steel structures Part 1 - 1 : General rules and rules for buildings EN 1993-1-1:2005

Material properties

or standard steel grades, the yield strength fy and tensile strength fu are defined according to thickne , table 3.1.)

F

the ss of the element (see Ref. [1]

S eel Gradet 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

SCIA 22


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

Table 1

The name of the steel grade (e.g. 'S 355 W') is used to identify the steel grade. Remark : For cold formed section, the values for fy and fu are not influenced by the

e yield strength is determined as follows :

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 averag

( ) ( )ybuybug

ybya f2.1,fminffA

²kntff ≤−⎟⎟⎠

⎞⎜⎜⎝

⎛+=

with fyb the tensile yield strength = fy

the tensile ultimate strength l thickness

the gross cross-sectional area is a coefficient depending on the type of forming :

k = 0.5 for other methods of forming r of 90° bends in the section

Consulted articles

fu

t the materia Ag

k k = 0.7 for cold rolling

n the numbe

T hecked according to the regulations given in "Eurocode 3: D 1-1: General rules and rules for buildings - EN 1993-1-1

he beam elements are cesign of steel structures - Part:2005".

SCIA 23


The cross-sections are classified according to Table 5.2. All classes of cross-sections are i ections) the effective section is calculated in e N 1993-1-5:2003, Chapter 4.4 . T .2.: the section is checked for tension (art. 6.2.3.), c 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 cTF A check for critical slenderness and torsion moment is also included.

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

A rview for the used articles is given in the following table. The chapters marked with The chapters marked with (*) hav s the following chapters.

n of cross section (*)

ncluded. For class 4 sections (slender sach intermediary point, according to prEhe stress check is taken from art. 6ompression (art. 6.2.4.), bending (art. 6.2.5.), shear (art. 6.

ompression (art. 6.3.3.). he shear buckling is checked according to prEN 1993-1-5:2003, Chapter 5. or I sections, U sections and cold formed sections warping can be considered.

Fmchecked.

more detailed ove “x” are consulted.

upplementary explanatione a

EN 1993-1-1 5.5 Classificatio5.5.1. Basis x

5.5.2. Classification x

6. Ultimate limit states

6.1. General x

6.2. Resistance of cross-sections x 6.2.1 General

6.2.2 Section properties x(*)

6.2.3 Tension x

6.2.4 Compression x

6.2.5 Bending moment x

6.2.6 Shear x

6.2.7 Torsion x(*)

6.2.8 Bending and shear x

6.2.9 Bending and axial force x

6.2.10 Bending, shear and axial force x

SCIA 24


6.3. Buckling resistance of members 6.3.1 Uniform members in compression

x(*)

6.3.2 Uniform members in bending x

6.3.3 Uniform members in bending and axial compression x(*)

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

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

prEN 1993-1-3 6.1.2. Axial tension x

6.1.3. Axial compression x

6.1.5. Shear force x

6.1.6. Torsional moment x

rEN 1993-1-5 p 4.4. Plate elements without longitudinal stiffeners x

5. Resistance to shear x

5.1. Basis 5.2. Design resistance x

5.3. Contribution from webs x

5.4. Contribution from flanges x

5.5. Verification x

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

Classification of sections

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

F

SCIA 25


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

ion.

ve cross-section properties for class 4 cross-section

for each intermediary sect

Effecti

For each intermediary section, the classification (and if necessary, the effective area ) is ction check is performed. The classification (and effective

rea) can change for each intermediary point. The most critical check is displayed on the

n. eff 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.

ith these critical properties, the stability check is performed.

or non-prismatic elements, the effective area properties are calculated on each intermediary ction, als

Section pro ties

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

determined and the proper seascreen. 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 compressioW

W F

se o for the stability check.

per T e net area perties unt . T e shear la ffects are

orsion check

h pro are not taken into accoh g e neglected .

T

arping

or the cross section check inclusive torsion and warping, we refer to Chapter 'WFcheck'.

uilt-in beamsB

SCIA 26


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

ompression members

pbuilt-in beams (IFB, SFB, THQ sections)’

C

e buckling length, we refer to chapter "Calculation of buckling tio"

Euler force for VARH lements”).

ateral-torsional buckling

For the calculation of thraThe buckling properties for a VARH element are calculated by using the critical Euler force for this member (see chapter “Calculation of critical e

L

For I sections (symmetric and asymmetric), RHS (Rectangular Hollow Section) sections ction) sections, the elastic critical moment for LTB Mcr is

F.2. Annex F Ref. [4]. For the calculation of the moment ctors C1, C2 and C3 we refer to "Calculation of moment factors for LTB".

F r the oth ent for LTB Mcr is given by

and CHS (Circular Hollow Segiven by the general formulafa

o er supported sections, the elastic critical mom

z2

t

z2

z

EII π+

2

LEπ

odulus of elasticity odulus

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

ing constant nal constant

bout the minor axis

Re particular part 7.7. for channel sections.

+Ud+rail) are

L²GIIwIMcr =

with

E G

the mthe shear m

L the lengt

Iw the warp It the torsio Iz the moment of inertia a

S

ee also f. [5], part 7 and in

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, Iconsidered as equivalent asymmetric I sections.

SCIA 27


Use of diaphragms See Chapter 'Adaption of torsional constant'

Shear buckling check

.

il,

SUPPO

Composed rail sections (Iw+rail, Iwn+rail, I+rail, I+2PL+rail, I+PL+rail, I+2L+ra

Ud+rail) are considered as equivalent asymmetric I sections. I+

RTED SECTIONS

I Symmetric I shapes (IPE, HEA, HEB, ….) RHS r Hollow Section RectangulaCHS n Circular Hollow SectioL Angle section U Channel section T T section PPL Asymmetric I shapes Z Z section RS Rectangular section Σ Cold formed section COM PRIMAWIN Composed section inO Solid tube NUM al section Numeric

The nec re described in chapter "Profile conditions for code check".

he CO nd NUM sections are not read out of the profile library.

I

RHS

CHS

L

U

T

PPL

RS

Z

Σ

O

COM

NUM

essary data conditions for these sections a

T

M a

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

SCIA 28


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


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

Stability check class 4 x x x x x x

Shear buckling check x x x x

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

REFERENCES

Design of steel structures and rules for buildings

-1:2005

neral rules ary rules for cold-formed members and sheeting

Design of steel structures Part 1.5 : Plated structural elements prEN 1993-1-5 : 2003

4] R. Maquoi

[1] Eurocode 3

Part 1 - 1 : General rules993-1EN 1

[2] Eurocode 3

Design of steel structures Part 1-3: GeSupplementEN 1993-1-3:20XX, 2003

] Eurocode 3 [3

[

ELEMENTS DE CONSTRUCTIONS METALLIQUE Ulg , Faculté des Sciences Appliquées, 1988

SCIA 29


DIN1880

DIN18800 CODE CHECK

0

The beam elem e ven in

8800 uten

ng und Konstruktion ber 1990

ents are checked according to the r gulations gi DIN 1 Teil 1StahlbaBemessuDK 693.814.014.2, Novem

DIN 1880 tahlbaute

täts Knic on Stä nd Stabwe.814.074.5, November 1990

0 Teil 2S n Stabili fälle, ken v ben u rken DK 693 DIN 18800 Teil 3

ten Stabilitätsfälle, Plattenbeulen

November 1990

Stahlbau

DK 693.814.073.1,

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 :

SCIA 30


(fy, fu in N/mm², t in mm)

t<=40 t<=40 40<t<=80 40<t<=80 fy fu fy fu S235 240 360 215 360 S 235 St 37-2 S275 280 430 255 430 S 275 S355 360 510 325 510 S 355 St 52-3

t<=40 t<=40 40<t<=100 40<t<=100 fy fu fy fu S420 S 420

420 520 390 520

S460 460 550 430 550S 460

Consulted articles

F Tab1 n, the section is checked as slends stic) or as PL/PL (plastic/plastic). F ) auT Tab( Tab(TFor 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 :

or the section check, the cross section is classified according to DIN18800 Teil I, le 2,13,14,15 and 18.. Depending on this classificatioection, EL/EL (elastic/elastic), as EL/PL (elastic/pla

er

or the EL/EL check, DIN18800 Teil I, Element (746), (747), (748), (749), (750 re sed. he EL/PL check takes the rules from DIN18800 Teil I, Element (756), (757) and

16) ,(17). The PL/PL check is done according to DIN18800 Teil I, Element (758), le le

16),(17). he slender cross section is checked according to DIN18800 Teil 2, Element (715).

SCIA 31


• Element (304),(306) •• • pression : Element (320),(323) F used : • ctive area : Element (705),(706),(708),(709),(712),(713) •• F eil T A for the used articles is given for the relevant parts followint aves

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

ssion : Element (313),(321),(322) bending and axial compre bending (LTB) and com

or slender sections, the following criteria are calculation of effe buckling check : Element (715),(716),(718),(719) LTB check : Element (725),(726),(728),(729)

or the shear buckling check, the beam element is checked according to DIN18800 T3), (504), (602),(603)

3. he following criteria are used : Element (11

more detailed overview g able. The chapters marked with “x” are consulted. The chapters marked with (*) h

apters. a

upplementary explanation the following ch

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) ………………………………………………………………………………

x x x x x x x

Nachweis nach dem Verfahren Elastisch-Plastisch ………………………………………………

………………………………………………………………… ………………………………………

(753) ………………………………(756) ……………(757) ………………………………………

xx xx

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

x x

Teil 2 3.2. Planmässig mittiger Druck x

SCIA 32


3.2.1. Biegeknicken (304) ……………………………………………………………………………… (*)

x x

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

x x (*

3.3. Einachsige Biegung ohne Normalkraft 3.3.1. Allgemeines (307) ………………………………………………………………………………

x x

x 3.3.2. Behinderung der Verformung

*) (309) ……………………………………………………………………………… x x (

3.3.3. Nachweis des Druckgurtes als Druckstab 3.3.4. Biegedrillknicken (311) ………………………………………………………………………………

x x (*)

3.4. Einachsige Biegung mit Normalkraft x 3.4.1. Stäbe mit geringer Normalkraft x (312) ……………………………………………………………………………… x 3.4.2. Biegeknicken x (314) ……………………………………………………………………………… x 3.4.3. Biegedrillknicken (320) ………………………………………………………………………………

x x

3.5. Zweiachsige Biegung mit oder ohne Normalkraft x 3.5.1. Biegeknicken (321) ………………………………………………………………………………

)

x x

(322) ……………………………………………………………………………… x(*3.5.2. Biegedrillknicken x (323) ……………………………………………………………………………… x 4. Mehrteilige, einfeldrige Stäbes

08)……………………………………………………………………………….

x(*)4.1. Allgemeines 4.2. Häufig verwendete Formelzeichnen (404) ……………………………………………………………………………… x 4.3. Ausweichen rechtwinklig zur stofffreien Achse (405) ……………………………………………………………………………… x (406)………………………………………………………………………………. x (4 x

SCIA 33


(409)………………………………………………………………………………. x 7. Planmässig gerade Stäbe mit ebenen dünnwandigen Quenschnittsteilen 7.1. Allgemeines (701) ……………………………………………………………………………… (702) ………………………………………………………………………………

x x x x

(704) ……………………………………………………………………………… x 7.2. Berechnungsgrundlage (705) ………………………………………………………………………………

x x

x (706) ……………………………………………………………………………… (707) ………………………………………………………………………………

x

(708) ……………………………………………………………………………… (709) ………………………………………………………………………………

x x

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

x ……………………………………………………

………………………………………………………………………… ………………………………………………………………

x x (*) x

(712) ……(713) ………………7.4. Wirksame Breite beim Verfahren Elastisch-Plastisch 7.5. Biegeknicken 7.5.1. Spannungsnachweis beim Verfahren Elastisch-Elastisch (715) ………………………………………………………………………………

x x x

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

x x x x x

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

x x x x x x x

SCIA 34


Teil 3 5. Nachweise (504) ………………………………………………………………………………

(*) x

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

x x 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.

Net area properties The net area properties are not taken into account . The holes for fasteners are neglected.

Plastic interaction formula for RHS section

SCIA 35


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 lastic section modulus around y axis eWel,z elastic section modulus around z axis fy,d yield strength τy,d shear strength

SCIA 36


Vz,pl,Rd = AS τy,d Vy,pl,Rd = 2AG τy,d NSd normal force My,Sd bending moment around y axis Mz,Sd ending moment around z axis bVy,Sd hear force in y direction sVz,Sd shear force in z direction MT,Sd rsional moment to

2M ⎞⎛

Rd,pl,z

Sd,TSd,z

z

zRd,pl,z

Sd,Sd,z

Vb

V1else

0.141

V

MV

if

⎟⎟⎟⎟

⎠⎜⎜⎜⎜

⎝

+−=η

=η≤

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛+ T

b

2

Rd,pl,y

Sd,TSd,y

y

yRd,pl,y

Sd,TSd,y

Vh

MV

1else

0.141

Vh

MV

if

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛+

−=η

=η≤

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛+

Ar= ηzAS + 2ηyAG

r

Sz A

Aη=δ

Npl,Rd = Ar fy,d

SCIA 37


⎟⎠⎞

⎜⎝⎛ δ−

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

2minM

⎟⎠⎞

⎜⎝⎛ δ+

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

1minM

Rd,pl

Sd

NN

n =

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

SCIA 38


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

⎟⎠⎞

⎜⎝⎛ β

π=

β=ηπ=

srQ,pl

r

ANdtA

⎟⎠

⎜⎝

β=

+=

+=

≤

⎟⎟⎠

⎞⎜⎜⎝

⎛ π

selQ,plQ,pl

pl

v

spl

2z

2yv

2z

2yv

plQ

vQ,pl

v

W25.1,NdminM

Q

1Q3

dt2

MMM

QQQ

1

2NNcos

1MM

with Qy,Qz internal shear force

v internal normal force y,Mz internal bending moments yield strength

dimensions from CHS l elastic

Q

=η≤pl

1:4Q

⎟⎞

⎜⎛

−=η>2

v

pl

v Q1:

41

QQ

N M βs

d,t We section modulus

SCIA 39


t

d

Torsion check For the cross section check inclusive torsion and warping, we refer to Chapter 'Warping check'. The stability check (DIN 18800 T2, formula 28 & 30) for doubly symmetric I section becomes (Ref.[9], pp. 259) :

)30(0.1kM z

d,z,pl

≤+MM

kMN

)28(0.1kM

MMk

MM

NN

w,zzy

d,y,pl

y

d,

zd,z,pl

w,zzy

d,y,pl

y

d,pl

+κ

+

≤+

++

with Mz,w

MMN plzκ

κ

hw= M2

Mw he St.Venant torsion')

Built-in beams

bimoment (see chapter 'Standard diagrams for warping torque, bimoment and t

kz = 1.50

For built-in am sections (IFB, SFB, THQ sections), proper section checks are performed, t g into local plate bending. See Chapter ‘Section check for b ilt-in beam IFB, SF

beakin account the

u s ( B, THQ sections)’

SCIA 40


the bucCalculation of kling 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”). The buckling curves for steel grade S420 and S460 are taken from Ref.[10], Annex D.

Torsional buckling The slenderness for torsional buckling λvi is given by (see Ref.[6] , 7.5):

( )⎪⎪

⎭

⎪⎪

⎬

⎫

⎪⎪

⎩

⎪⎪

⎨

⎧ ⎡

+

⎥⎥⎦

⎤

⎢⎢⎣

⎟⎟⎠

⎞⎜⎜⎝

⎛−+

−++

= 222

22

0

222

2

221093.04

112

M

Mz

p

M

z

zvi

ic

zic

cic

iββ

βλ

ith al buckling length, refers to the input value for length lyz

z the system length for buckling around zz-axis Remark : the z-axis refers to the axis which goes through

z

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

β0 refers to end warping and is input by the value kxy zM the shear center

ation around major axis n around minor axis

M² = ip² + zM² w the warping constant

z l

w l0 the torsion

the system l

the shear force centre. β refers to the buckling ratio around the zz-axis

iy the radius of gyr iz the radius of gyratio ip² = iy² + iz² i I

SCIA 41


Iz the moment of inertia around minor axis t the torsional constant I

( ) ( ) ( )z

tzzzzw

IIlllIc

2200

22 039.0/ βββ +

=

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

Use of diaphragms (see also Ref.[7],3.5 and Ref.[8],3.3.4.)

ffness S for diaphragm is calculated as follows

The shear sti

LK+K

10a.=S

s

21

4

with a the frame distance

The torsiona onstant I ffness of the diaphragms :

Ls the length of diaphragm K1 factor K1 K2 factor K2

l c t is adapted with the sti

GlvorhCϑI 2

2

tidπ

+=

ith l the LTB length G the shear modulus

vorhCθ the actual rotational stiffness of diaphragm

I ,t

w

SCIA 42


LTB Check For aysmmetric I sections, RHS (Rectangular Hollow Section) sections and CHS (Circular Hollow Section) sections, the elas l 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".

epending on the input of the basic data, Mcr for symmetric I sections is given by the g l fo ula (19), or by formula according to Ref.[11] "Roik, Carl, Lindner, Biegetorsionsprobleme gerader d nnwand r S

• DIN fo ula

tic critica

Denera rm F.2. Annex F Ref. [4], by the DIN formula

ü ige täbe, Verlag von Wilhelm Ernst & Sohn, 1972".

rm (19) :

⎟⎠⎞⎜

⎝+i 25.0c⎛ 2 += p

2pk z5.0zcr ζ NM

( ) ( ) ( )z

t2

z2

002 039.0l/ +βzw2

IIllI β

=

l,l0 the LTB length β refers to rotational end-restraint ‘in plan’ (about the z-z local axis).

0 end warping zp the point of load application

the warping constant nd minor axis

It the torsional constant A the sectional area E the modulus of elasticity λvi the slenderness for torsional buckling ( see above) ζ the moment factor ( equivalent for factor C1)

c β

with z

β refers to

Iw

Iz the moment of inertia arou

( )2z

z2

ik lEIN

βπ

=

SCIA 43


• Roik, Carl & Lindner

z

tw

p2

pzcry,ki

II²l039.0Ic

²z5

²c²

z5²l

²EIMM

⋅⋅+=

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡

π++⎟⎟

⎠

⎞⎜⎜⎝

⎛π

πζ==

with ζ moment factor according to Roik, Carl, Lindner E modulus of elasticity Iz moment of inertia around weak axis zz

l system length for LTB zp application point for loading, negative value is on top and has

negative influence w warping constant

The factor ζ 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 :

I It torsional constant

- moment line according to distributed loading

SCIA 44


- moment line according to concentrated loading

SCIA 45


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

z2

t2

z2

z2

EIGIL

IIw

LEIMcr

π+

π=

with E the modulus of elasticity

estraint (= lLTB)

Iw the warping constant It the torsional constant Iz the moment of inertia about the minor axis

sections (I+Ivar, Iw+Plvar, Iw+Iwvar, Iw+Ivar, I+Iwvar) and composed rail +rail, Iwn+rail, I+rail, I+2PL+rail, I+PL+rail, I+2L+rail, I+Ud+rail) are

considered as equivalent asymmetric I sections.

Combined flexion for check method 2

G the shear modulus L the length of the beam between points which have lateral r

See also Ref. [5], part 7 and in particular part 7.7. for channel sections.

aunched Hsections (Iw

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.

Battened compression members The following section pairs are supported as battened compression member : (1) 2I (2) 2Uo (3) 2Uc

SCIA 46


Two links (battens) are used. The following additional checks are performed : - 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

2N N

yG

yG

*z

GzG

=

=

π+=

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

2Te

y

M

2hamaxV

T y

=

=

ith the value of the internal

For the calculation of maxVy, the value of Mz is increased wforce Mzz.

SCIA 47


l

a

hy

e

Effective area properties The calculation of the effective area is perfo e hod (sigma_d = fy,k) according to the El-El procedure (DIN18800 T2, 7.3.). F ssification (and if necessary, the effective area ) is determined and the proper section check is p ed. The classification (and effective a can change for each intermediary point. ost critical check is displayed on the screen. F ation, the most critical effective area properties are saved. T ea properties are the effective area properties on the p moment of inertia is the minimum. W these critical properties, the stability check is performed. For non-prismatic elements, the effective area properties are calculated on each i ediary section, also for the stability che

rmed with the direct m t

or each intermediary section, the claerformThe mrea)

or each load case and combinhe most critical effective arosition where the appropriate ith

nterm ck.

SCIA 48


Shear buckling check Com (Iw+rail, Iwn+rail, rail, I+PL+rail, I+2L+rail, I+Ud+rail) are considered as equivalent asym ctions.

Shear buckling check with buckling influen

posed rail sections I+rail, I+2PL+metric I se

ce

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

It m κ ψ

Cold formed thin gauge members

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

The following table includes a list of DASt-Richtlinie 016 (Ref.[12]are implemented in EPW by using the related DIN18800 T2 (Ref.[2]) element.

) elements which

Supported elements from DASt - 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 Bauteile 4.4.3. Allgemeiner Nachweis

421 311 422 311 423 725, 726

SCIA 49


4.5. Druck Stäbe beanspruchte einteilige4.5.1. Allgemeines

429 708-710 430 708-710 431 708-710 432 708-710 433 708-710 434 708-710 4.5.2. Planmäβig mittiger Druck 435 716 AD

ef is not used 436 manual input / input in

profile library for KSL 437 723 438 72 3 4.5.3. Einachsige B gun mit Druck ie g 440 70 7 441 718 442 72 8 4.5.3. Zweiachsige Biegung mit Druck 443 707 444 721 AD

ef is not used 445 729

SUPPORTED SECTIONS

pes (IPE, HEA, HEB, ….) I Symmetric I sha

RHS ar Hollow Section (RHS) RectangulCHS Circular Hollow Section (CHS) L Angle section U Channel section T T section

SCIA 50


PPL Asymmetric I shapes RS Rectangular section Σ Cold formed section COM Composed section in PRIMAWIN O Solid tube NUM Numerical section

The nec ese sections are described in "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 Σ O COM NUM

essary data conditions for th

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

Section check PL-PL x x

Section check E L-PL x x

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

Section check sl ender section x x x x x x

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

Stability check er section x x x x x x slend

Shear buckling x x x check x

(1) secti tion by default.

REFER CES

ons are classified as EL-EL cross sec

EN

[1]

messung und Konstruktion 1990

[2] tahlbauten

le, Knicken von Stäben und Stabwerken ber 1990

[3]

DIN 18800 Teil 1 Stahlbauten BeDK 693.814.014.2, November DIN 18800 Teil 2 SStabilitätsfälDK 693.814.074.5, Novem DIN 18800 Teil 3

SCIA 51


Stahlbauten nbeulen

[4] 3 esign of steel structures

es and rules for buildings

[5] LEMENTS DE CONSTRUCTIONS METALLIQUE

té des Sciences Appliquées, 1988

[6]

nach DIN 18 800 Teil 1 bis Teil 3 (11.90) 991

[7]

Werner-Verlag, Düsseldorf

[8] Beuth-Kommentare Stahlbauten Erläuterungen zu DIN 18 800 Teil 1 bis Teil 4, 1.Auflage Beuth Verlag, Berlin-Köln 1993

[9] Stahlbau Kalender 1999 DSTV Ernst & Sohn, 1999


Stabilitätsfälle, PlatteDK 693.814.073.1, November 1990 Eurocode DPart 1 - 1 : General rulENV 1993-1-1:1992, 1992 R. Maquoi EUlg , Facul G. Hünersen, E. Fritzsche Stahlbau in BeispieB

len erechnungspraxis

Werner-Verlag, Düsseldorf 1 E. Kahlmeyer Stahlbau nach DIN 18 800 (11.90)

SCIA 52


[11] Roik, Carl, Lindner

Biegetorsionsprobleme gerader dünnwandiger Stäbe Sohn

1972

016 und konstruktive Gestaltung von Tragwerken aus

nnwandigen kaltgeformted Bauteilen

Interaktionsbeziehungen für doppeltsymmetrische I- und Kasten- bei zweiachsiger Biegung und Normalkraft

er Stahlbau 5/1978, 6/1978

bH, Düsseldorf

Verlag von Wilhelm Ernst &

[12] DASt-Richtlinie

Bemessung düStahlbau-Verlagsgesellschaft - 1992

[13] H. Rubin,

QuerschnitteD

[14] Stahl im Hochbau 14. Auflage, Band I / Teil 2 1986, Verlag Stahleisen m

SCIA 53


ONORM B 4300

ONORM B 4300 CODE CHECK

The beam elements are checked according to the regulations given in

struktion der Tragwerke messung nach Grenzzuständen

ÖNORM B 4300-1 Stahlbau Berechnung und KonBeDK 624.014.2.046, März 1994 ÖNORM B 4300-2 Stahlbau Knicken von Stäben und Stabwerken Bedingungen für die gemeinsame Anwendung von DIN 18 800 Teil 2 und ÖNORM B 300-1 K 624.01 075.2, il 1994

4D 4.2. Apr ÖNORM B 4300-3

beulen ng r die g m endung von DIN 18 800 Teil 3 und ÖNORM B

.014.2.075.4, April 1994

PlattenBedingu en fü emeinsa e Anw4300-1DK 624 DIN 18800 Teil 1

uten messung und Konstruktion

er 1990

StahlbaBeDK 693.814.014.2, Novem

b

DIN 18800 Teil 2 Stahlbaute

äts Knick on Stä und Stabwe 3.8 4.5, N ber 1

n Stabilit fälle,

14.07en vovem

ben 990

rkenDK 69

SCIA 54


DIN 18800 Teil 3 Stahlbauten Stabilitätsfälle, Plattenbeulen

ber 1990 DK 693.814.073.1, Novem

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) The standard steel grades are : (fy, fu in N/mm², t in mm)

t<=40 t<=40 40<t<=80 40<t<=80 fy fu fu fy St 360 240 360 215 360 S235 S 235 St 430 280 430 255 430 S275 S 275 St 510 S355

360 510 325 510

S 355

t<=40 t<=40 40<t<=100 40<t<=100 fy fu fy fu S420

420 420 520 390 520

S S460 4 550 60 550 430

SCIA 55


S 460

C sulted aon rticles

F he sect ection 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 s ion is ch n, EL/EL (elastic/elastic), as EL/PL (elastic/plastic) or a L (plF EL/E 2. is used. (The 7% increase of the moment of i en into account for rolled I section - see Ref. [1], Art. 5.2.5.4.). The EL/PL c from DIN18800 Teil I, Element (756), (757) and Table

6) ,(17). The PL/PL check is done according to DIN18800 Teil I, Element (758), Table

oss section is checked according to DIN18800 Teil 2, Element (715).

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

are used : • ression : Element (304),(306) • rsional b ckl g : Element (311),(309) • and axia om ression : Element (313),(321),(322) • B) a co pression : Element (320),(323) F ns, e following criteria are used :

n of eff tiv area Element (705),(706),(708),(709),(712),(713) buckling check : Element (715),(716),(718),(719)

8),(729)

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

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

S PO

or t ion check, the cross s

ect ecked as slender sectios PL/P

theastic/plastic).

or L check, ONORM B 4300-1 Art. 5.nertia is takheck takes the rules

(1(16),(17). The slender cr Fb

comp lateral to u in bending l c p

bending (LT nd m

or slender sectio th• calculatio ec e : • • LTB check : Element (725),(726),(72

The following crit A

UP RTED SECTIONS

I , HEB, ….) Symmetric I shapes (IPE, HEARHS (RHS) Rectangular Hollow Section

SCIA 56


CHS Section (CHS) Circular HollowL Angle section U Channel section T T section PPL Asymmetric I shapesRS Rectangular section Σ Cold formed section COM section in PRIMAWIN ComposedO Solid tube NUM Numerical sections

The nec ary data conditions for these sections are described in "Profile conditions for code check". The COM and NUM sections are not read out of the profile library.

T

PPL

RS

Σ

O

COM

NUM

ess

I

RHS CHS L U

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

Section check PL-PL x

Section check EL-PL x

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

Section check s x lender section x x x x x

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

Stability check x x slender section x x x x

Shear buckling k x x x x chec

( cti EL-EL cross section by default.

REFER

1) se ons are classified as

ENCES

[1] ÖNORM B 4300-1 Stahlbau Berechnung und Konstruktion der Tragwerke Bemessung nach Grenzzuständen DK 624.014.2.046, März 1994

SCIA 57


[2] ÖNORM B 4300-2 Stahlbau Knicken von Stäben und Stabwerken

einsame Anwendung von DIN 18 800 Teil 2 und ÖNORM B 4300-1

gemeinsame Anwendung von DIN 18 800 Teil 3 -1

DK 624.014.2.075.4, April 1994

Bemessung und Konstruktion DK 693.814.014.2, November 1990

[5] DIN 18800 Teil 2

DK 693.814.074.5, November 1990

Stahlbauten Stabilitätsfä ttenDK 693.814. 1, Nove 1990

Bedingungen für die gem

DK 624.014.2.075.2, April 1994

[3] ÖNORM B 4300-3 Plattenbeulen Bedingungen für dieund ÖNORM B 4300

[4] DIN 18800 Teil 1

Stahlbauten

Stahlbauten Stabilitätsfälle, Knicken von Stäben und Stabwerken

[6] DIN 18800 Teil 3

lle, Pla beulen 073. mber

SCIA 58


NEN

EN6770/6771 CODE CHECKN

ing to the regulations given in

ber 1991

The beam elements are checked accord Staalconstructies TGB 1990 Basiseisen en basisrekenregels voor overwegend statisch belaste constructies NEN 6770, decem Staalconstructies TGB 1990 Stabiliteit NEN 6771, decem 1 an 000 ber 991-j uari 2

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.) The standard steel grades are : (fy, fu in N/mm², t in mm)

t<=40 t<=40 40<t<=100 40<t<=100 100<t<=250 100<t<=250 fy fu fy fu fy fy S235 S 235

235 360 215 340 175 320

S275 S 275

275 430 255 410 205 380

S355 S 355

355 510 335 490 275 450

S420 S 420

420 520 390 520

S460 S 460

460 550 430 550

SCIA 59


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

Consulted articles

T cording to NEN 6771 Table 1. (class 1,2,3 or 4). The section is checked on following criteria :

NEN 6770 Art. 11.2.1., NEN 6771 Art. 11.2.1. 70 Art. 11.2.2., NEN 677 rt. 11.2.2.

NEN 6770 Art. 11.2.4., NEN 6771 Art. 11.2.4. d axial force : NEN 6770 Art. 11.3., NEN 6771 t. 11.3.

For the stability check, the element is checked on following criteria : • NEN 6771 Art.12.1.1.1/ 12.1.2./12.1.3.

nal buckling : NEN 6771 Art.12.2. Art.12.3.

13.9.

he cross section is classified ac

• tension : • compression : NEN 67 1 A• shear : • bending, shear an Ar

compression : • lateral torsio• bending and axial compression: NEN 6771• shear buckling : NEN 6771 Art.13.8. /

SCIA 60


A 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 m mentary explanation the following chapters.

more detailed overview for

arked with (*) have a supple

NEN6770 11.Toetsing van de doorsnede 11.1. Algemeen

x x

11.2. Enkelvoudige krachten en momenten 11.2.1. Axiale trek

x x

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 momenten

ormaalkracht en afschuiving 11.3.1. Enkele buiging met nx x

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 doorsnede 11.1. Algemeen

xx

11.2. Enkelvoudige krachten en momenten 11.2.1. Axiale trek

x x

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

SCIA 61


12. Toetsing van de stabiliteit 12.1. Op druk belaste staven 12.1.1. Knikstabiliteit

x

*) x x (

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 staven 12.1.6.1 Algemeen 12.1.6.2. Benodigde grootheden

iddenveld van de samengestelde staaf ndvelden van de samengestelde staaf

x(*)

12.1.6.3. Toetsing van het m12.1.6.4. Toetsing van de ei12.1.6.4.2 Staven met raamwerkverband

x x xxx

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

xx x

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 staven 12.3.1. Knikstabiliteit

x x

12.3.2. Torsiestabilteit x 12.3.3. Torsieknikstabiliteit x 12.4. Op trek en buiging belaste staven 13. Toetsing van de plooistabiliteit x

x 13.1. Algemeen 13.2. Geometrie van het verstijfde en onverstijfde plaatveld x 13.3. Geometrie van de verstijvingen 13.4. Belasting in het vlak van het plaatveld 13.4.1. Normaalspanning in langsrichting

x x

13.4.2. Schuifspanningen x 13.4.3. Normaalspanningen in dwarsrichting 13.4.4. Platen in en loodrecht op hun vlak belast

SCIA 62


13.5. Belasting op verstijvingen 13.6. Ideële kritieke plooispanning van een onverstijfd plaatveld x 13.7. De plooispanning van een onverstijfd plaatveld x 13.7.1. Bepaling van de relatieve slankheid van het plaatveld x 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 inste een langsverstijving als oplegging

m13.8. Eisen waaraan plaatvelden en verstijvingen moeten voldoen x 13.8.1. Onverstijfd plaatveld x 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 knik

een x (*)

13.9.1. Algem x 13.9.2. Constructies opgebouwd uit plaatvelden al of niet verstijfd met dwarsverstijvingen

x

13.9.3. Constructies opgebouwd uit plaatvelden verstijfd met rstijfd met dwarsverstijvingen

langsverstijvingen en/of niet ve13.9.4. Berekeningen van de dwarsverstijvingen

Section properties

he influence of the bore hole is neglected. T

Classification of sections For each intermediary scheck is performe

ection, the classification is determined and the proper section d. The classification can change for each intermediary point.

or each load case/combination, the critical section classification over the member is

ad case/combination.

Fused to perform the stability check. So, the stability section classification can change for each loHowever, for non-prismatic sections, the stability section classification is determined for each intermediary section.

SCIA 63


Effective cross-section properties for class 4 cross-section The calculation of the effective area is pefy,k).

rformed with the direct method (sigma_d =

n. eff 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 compre ion. With these critical properties, the stability check is performed.

or non-prismatic elements, the effective area properties are calculated on each intermediary section, also for the stability check. F gle se ns, see ction properties for compressed lattice t wer angle mbers'.

Torsion check

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 compressioW

ss

F

or an ctio chapter 'Effective cross-seo me

For the cros d warping, we refer to Chapter 'Warping check'.

uilt-in beams

s section check inclusive torsion an

B

or built-in beam sections (IFB, SFB, THQ sections), proper section checks are

uckling length

Fperformed, taking into account the local plate bending. See Chapter ‘Section check for built-in beams (IFB, SFB, THQ sections)

B

the buckling length, we refer tochapter "Calculation of buckling tio".

t are calculated by using the critical Euler rce for this member (see “Calculation of critical Euler force for VARH elements”).

For the calculation of raThe buckling properties for a VARH elemenfo

SCIA 64


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

Lateral-torsional buckling For symmetric I sections and RHS (Rectangular Hollow Section) sections, the elastic

oment for LTB Mcr is given by the formula of Ref [2], part 12.2.5.. When the ctor α > 5000, the elastic critical moment for LTB Mcr is given by the general

fo mula in EC3, Annex F, F.2. Ref [3]. For asymmetric I sections, the elastic critical oment for LTB Mcr is given by the general formula in EC3, Annex F, F.2. Ref [3].

ment factors C1, C2 and C3 we refer to Ref.[7], tables 9

s given by

critical mfa

rmFor the calculation of the mo(case 1), 10 and 11. For the other supported sections, the elastic critical moment for LTB Mcr i

z2

t2

z2

z2

EIGIL

IIw

LEIMcr

π+

π=

with E the modulus of elasticity

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

f. [4], part 7 and in particular part 7.7. for channel sections.


Use of diaphragms

G the shear modulus

See also Re

See Chapter 'Adaption of torsional constant'.

SCIA 65


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,s;d

- section check of single chord, using internal forces :

4aQ

M

2Q

V

N N

f;s;dG

f;s;dG

f;s;dG

=

=

=

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

4M ds;k; =

aQ ds;f;

0

2haQ

V 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 66


l

a

ho

Shear buckling check Composed rail sections +rail, I+2L+rail,

Ud+rail) are considered as equivalent asymmetric I sections.

with buckling influence

(Iw+rail, Iwn+rail, I+rail, I+2PL+rail, I+PLI+


he influence of the buckling effect into the shear buckling control, is neglected when

Tthere is a bending moment present, i.e. if ψ<0.9.

SCIA 67


NEN6072 - FIRE RESISTANCE

For more info, we refer to Ref.[8], Ref.[9].

effectFire actions

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 combinatio

n is given by

rep;aa;frep;iiq;frepg;f FQG γ+ψγΣ+γ

rep characteristic values of permanent actions Qi characteristic value of the variable action

de val n (from fire exposure) partial saf for permanent actions in the special combination =1.0

γ partial safety factor for variable actions in the special

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

I an' factor for the variable action

Material properties

with G Fa;rep sign ues of special actio γf;g ety factor

f;q combination=1.0

ψ the 'momentaa

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

The yield strength is depending on the steel temperature : f d;yd;;y f

SCIA 68


- ψ=1.0 when θ ≤ 400° C

-

a

( ) 26.01e03.1

+=ψ

β when 400°C < θa ≤ 1200° C

β with 2.39482a −θ

=

θa steeltemperature in °C fy;d

;d alue for yield strength at increased temperature T e followin efault p stant during the analysis :

nit mass

design value for yield strength at room temperature fy;θ design v

h g d roperties are considered to be con

u ρ 7850 kg/m³ a thermal elongation a∆ -6 θ -20) l/l 14 x 10 (thermal conductivity λa 45 W/mK

ominal temperature-time curveN

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

with t time in [min] θg gas temperature in [°C]

Steel Temperature

T

)1t8(log34520 10g ++=θ

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

SCIA 69


( )

( ) ⎟⎠

⎟⎠

⎜⎝

−⎟⎠ 100

⎟⎞⎞⎛ +θ⎞

4a

4 2733⎜⎝a

⎜⎛⎜⎝⎛ +θ

θ−θε

=

α+α=

∆θ−ρα

=θ

t

t

rr

rc

ataa

a

1002767.5

tc

ith nit length [m²/m] th [m³/m]

ca the ic heat of steel [J/kgK]

ρa ass of steel [kg/m³]

0.5 αc coefficient of heat transfer by convection

= 25 W/(m²K)

he increase of temperature ∆θa in an insulated (non intumescent coating) steel member erval ∆

α

α

θP∆

w Am the exposed surface area per u V the volume of the member per unit leng P = Am/V θt gas temperature in [°C] θa steel temperature [°C]

specif ∆t the time interval [seconds]

the unit m εr resultant emissivity

=

Tduring a time int t

( ) ( )

iiaa

ii

M

i

ef;d;ief

t5/

a et −∆tMaa

efa

dc2c

321

1d

1cK

ρρ

=

ξ+=κ

λ=

θ∆−θ−θρ

=θ

with Ap material per unit length [m²/m]

iP κ

P

K

ξ

∆ ξ

the area of fire protection

SCIA 70


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

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

aterial [m]

The value should not be taken as more than 30 seconds ass of steel [kg/m³]

t the increase of the ambient gas temperature during the time

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

e of temperature ∆θa in an insulated (intumescent coating) steel member

uring a time interval ∆t

P ca

di the thickness of the fire protection m∆t the time interval [seconds]

ρa the unit m ρi the unit mass of fire protection [kg/m³] θa the steel temperature at time t θt the ambient gas temperature at time t ∆θ

interval

The increasd

( ) t

PicK

ataa

ef;da ∆θ−θ

ρ=θ

with Ap V Pi ca the fic heat of steel [J/kgK] Kd;ef ∆t

The value should not be taken as more than 30 seconds the unit mass of steel [kg/m³]

θ the steel temperature at time t

∆

the area of fire protection material per unit length [m²/m] the volume of the member per unit length [m³/m]

= Ap/V speci

coefficient of heat transfer of the intumescent coating the time interval [seconds]

ρa

a

θt the ambient gas temperature at time t λi;d;ef the thermal conductivity of the fire protection material

[W/mK]

SCIA 71


Calculation model

The calculation can be performed in 2 domains : - strength - temperat I he streng strength (unity check) is calculated after a given time t (e.g. strength afte e temperature/time domain, the critical steel temperature θa,cr is computed al temperature, the fire resistance time is calculated (the time domain T itical

domain ure/time domain

n t th domain, the r 45 min). In th. From this critic).

he cr steel temperature θa,cr is given by :

( )48211n

⎤⎡−

8925.0 846.3 ⎥⎦

⎢⎣ κη

l2.39 +=

e t=0 on factor

= 1.00 for beams, statically determined, 4 side exposure e exposure

= 0.85 for beams, s tica ly un eterm= 0.60 for beams, statically undeterm= 1.20 for comp ents (inclusive the buckling check) = 1.20 for compression and bending elements (inclusive the buckling and LTB check)

C

cr,aθ

with

η degree of utilization at timκ correcti

= 1.00 for tension elements

= 0.70 for beams, statically determined, 3 sidta l d ined, 4 side exposure

ined, 3 side exposure ression elem

ode Check

l buckling) are performed ted with the yield strength

r 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.

The section and stability checks (buckling, lateral torsionaaccording to the regulations given in NEN6770/6771, adapfo

SCIA 72


SUPPORTED SECTIONS

I Symmetric I shapes (IPE, HEA, HEB, ….) RHS Rectangular Hollow Section (RHS) CHS Circular Hollow Section (CHS) L Angle section U Channel section T T section PPL Asymmetric I shapes Z Z section RS Rectangular section Σ Cold formed section COM ed section in PRIMAWIN ComposO Solid tube NUM Numerical section

T nec onditions for these sections are described in "Profile conditions for c cheThe COM and NUM sections are not read out of the profile library.

T PPL RS

Z

Σ

O

COM

NUM

he ode

essary data cck".

I

RHS

CHS

L

U

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



Section check c x x x x x x x lass 3 x x x x x x

Section check c x x x x lass 4 x x



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

Stability check ass 4 x x x x x x cl

Shear buckling eck x x x x ch


SCIA 73


REFERENCES

[1] asisrekenregels voor overwegend statisch belaste

EN 6770, december 1991

[2]

ber 1991

al rules and rules for buildings NV 1993-1-1:1992, 1992

[4] R. Maquoi

ELEMENTS DE CONSTRUCTIONS METALLIQUE Ulg , Faculté des Sciences Appliquées, 1988



[7] Staalconstructies TGB 1990 Stabiliteit NEN 6771, januari 2000

Staalconstructies TGB 1990 Basiseisen en bconstructies N Staalconstructies TGB 1990 Stabiliteit NEN 6771, decem

[3] Eurocode 3 Design of steel structures Part 1 - 1 : GenerE

SCIA 74


[8] NEN 6072

Rekenkundige bepaling van de brandwerendheid van bouwdelen Staalconstructies

Rekenkundige bepaling van de brandwerendheid van bouwdelen

Belastingen en vervormingen TGB 1990

December 1991

[9] NEN 6072/A2 - Wijzigingsblad

Staalconstructies December 2001

[10] NEN 6702

December 1991

SCIA 75


A

A

ISC - ASD

ISC - ASD CODE CHECK


gn

d Codes

T ble B5.1. (compact, noncompact, or slender s T ing criteria :

,F2,F3,F4 plate girders : G2

A g n in the f able. The chapters marked with “x” are consulted. The chapters m rked with ( the following chapters.

Manual of Steel ConstructionAllowable Stress DesiPart 5 : Specification anAISC, Ninth Edition, 1989

he cross section is classified according to Taection).

he member is checked on follow

• tension : D1 • compression : E2, E3 • flexural members : F1•• combined forces : H1,H2

more detailed overview for the used articles of the relevant parts is ollowing t

ivea

*) have a supplementary explanation

B. DESIGN REQUIREMENTS B1. Gross Area x B2. Net Area (*) B3. Effective Area B4. Stability B5. Local Buckling 1.Classification of Steel Sections

2.Slender Compression Elements

(*)xx

SCIA 76


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 (*) D2. Built-up members D3. Pin-Connected Members E. COLUMN AND OTHER COMPRESSION MEMBERS E1. Effective Length and Slenderness Ratio (*) xE2. 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 Channels

x x

x

1.Members with Compact Sections 2.Members with Non-Compact Sections 3.Members with Compact or Non-Compact Sections with Unbraded Length Greater then Lc

x

F2. Allowable Stress : Weak Axis Bending of I-Shaped Members, Solid ar Plates

1.Members with Compact Sections 2.Members with Non-Compact Sections

x x x

Bars and Rectangul

F3. Allowable Stress : Bending of Box Members, Rectangular Tubes and Circular Tubes 1.Members with Compact Sections

x x

SCIA 77


2.Members with Non-Compact Sections x F4. Allowable Shear Stress x F5. Transverse Stiffeners F6. Built-up Members F7. Web-tapered Members G. PLATE GIRDERS G1. Web Slenderness Limitations G2. Allowable Bending Stress x G3. Allowable Shear Stress with Tension Field Action G4. Transverse Stiffeners G5. Combined Shear and Tension Stress H. COMBINED STRESSES H1. Axial Compression and Bending x H2. Axial Tension and Bending x APPENDIX B. DESIGN REQUIREMENTS B5. Local Buckling x

lassification of sectionsC

For each intermediary section, the classification is determined.. For each load case/combination, th critical section classification over the member is used to perform the code check. However, for non-prismatic sections, the section lassification is determined for each intermediary section.

Section pro ties

e

c

per

The influence of the bore hole is neglect

ed, i.e. only the gross area is used.

SCIA 78


Buckling length

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

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

Flexural Torsional Buckling

The buckling properties for a VARH element are calculated by ufo

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

FeE

rKL

eπ=⎟

⎠⎞

⎜⎛⎝

See Ref. [1], Commentary Chapter E1.

ateral-torsional buckling

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

L

For RHS (Rectangu s and CHS (Circular Hollow Section) , the allowable LTB stress is given in F3.

symmetrical legs, the allowable LTB stress is given in Ref. [1], ress - Design of single-angle members”.

For I sections and channel sections, the allowable LTB stress is given in F1.

lar Hollow Section) section

For angle sections withpp.309-314, “Specification for allowable st For the other supported sections, the elastic critical moment for LTB Mcr is given by

z2

t2

z2

z2

EIGIL

IIw

LEIMcr

π+

π=

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

SCIA 79


See also Ref. [4], part 7. W is mo B

ith th ment Mcr, the critical LTB stress σLT is calculated :

y

crLTB I

M=σ

th the moment of inertia about the major axis T endern , is given by

wi Iy

he sl ess ratio for LTB λLTB

LTBLTB

Eσ

π=

The allowab ss is calculated using the slenderness λLTB with the formulas g RefSee also Ref. [5], Bijlage E.

tions (I+Ivar, Iw+Plvar, Iw+Iwvar, Iw+Ivar, I+Iwvar) and composed rail rail, I+Ud+rail) are

onsidered as equivalent asymmetric I sections.


λ

le LTB streiven in .[1], E2.

Haunched secsections (Iw+rail, Iwn+rail, I+rail, I+2PL+rail, I+PL+rail, I+2L+c

C sec n (Iw+r w ra I+ il, +2PL rail, I+PL+rail, I+2L+rail, I+Ud+rail) are considered as equivalent asymm

omposed rail tio s ail, I n+ il, ra I +etric I sections.

SCIA 80


SUPPORTED SECTIONS

I

Symmetric I shapes (IPE, HEA, HEB, ….) RHS Rectangular Hollow Section (RHS) CHS HS) Circular Hollow Section (CL Angle section U Channel section T T section PPL etric I shapes AsymmRS Rectangular section Σ Cold formed section COM Composed section in PRIMAWIN O Solid tube NUM Numerical section

The nec ry data conditions for these sections are described in "Profile conditions for code check".

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

I

RHS

CHS

L

U

T

PPL

RS

Σ

O

COM

NUM

essa

T


Compact section x x x x x

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

Slender section x x x x x x

Shear buckling check x x x (1) sections are classified as non-compact section by default.

REFERENCES

[1] Manual of Steel Construction

Allowable Stress Design AISC, Ninth Edition, 1989

SCIA 81


[2] Manual of Steel Construction

Load & Resistance Factor Design AISC, First Edition, 1986

3] Manual of Steel Construction

AISC, Volume I, Second Edition, 1995

UCTIONS METALLIQUE aculté des Sciences Appliquées, 1988

] NBN B 51-001

Stalen Bouwconstructies

[

Load & Resistance Factor Design

[4] R. Maquoi

ELEMENTS DE CONSTRUlg , F

[5

BIN, 5e uitg. April 1977

SCIA 82


A

A

ISC - LRFD

ISC - LRFD CODE CHECK

T are checked according to the regulations given in

oad and Resistance Factor Design des

The cross se ompact, or slender s T owing criteria :

• flexural members : F1,Appendix F1, Appendix F2 3, Appendix G5

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

EMENTS

he beam elements

AISC – Manual of steel construction LPart 16 Specifications and CoThird Edition 2001

ction is classified according to Table B5.ection).

1. (compact, nonc

he member is checked on foll

• tension : D1 • compression : E2, E3, Appendix E3

• plate girders : Appendix G2, Appendix G• combined forces : H1,H2

ollowing table. The chaentary expl

B. DESIGN REQUIR B1. Gross Area xB2. Net Area (*) B3. Effective Area for Tension Members B4. Stability B5. Local Buckling ) (*

SCIA 83


1.Classification of Steel Sections 2.Slender Compression Elements

x

3.Slender-Element Compression Sections

x

x B6. Bracing at Support B7. Limiting Slenderness Ratios x B8. Simple Spans B9. End Restraint B10. Proportions of Beams and Girders D. TENSION MEMBERS 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 Limitations

nalysis

x *) 1.Effective Length

2.Design by Plastic Ax (

E2. Design Compressive Strength for Flexural Buckling xE3. 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 Flexure 1.Yielding 2.Lateral-Torsional Buckling

x

xx

F2. Design for Shear x F3. Web-tapered Members F4. Beams and Girders with Web Openings G. PLATE GIRDERS x

SCIA 84


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 F3. Web-tapered Members APPENDIX G. PLATE GIRDERS G1. Limitations G2. Design Flexural Strength x(*) G3. Design Shear Strength with Tension Field Action x(*) G4. Transverse Stiffeners G5. Flexure-Shear Interaction x(*)


For each intermediary section, the classification is determined..

ination, the critical section classification over the member is sed to perform the code check. However, for non-prismatic sections, the section

classification is determined for each intermediary section.

For each load case/combu

SCIA 85


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". The buckling properties for a VARH element are calculated by using the critical Euler

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

Lateral-torsional buckling

For I sections, channel sections, RHS (Rectangular Hollow Section) sections, T

s, and asymmetric I sections, the critical LTB moment is .

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

sections, rectangular sectiongiven in F1 and Appendix F1

z2

t2

z2

z2

EIGIL

IIw

LEIMcr

π+

π=

s of elasticity G the shear modulus L the length of the beam between points which have lateral restraint

Iw the warping constant It the torsional constant

Iz the moment of inertia about the minor axis

ee also Ref. [2], part 7.

with E the modulu

(= lLTB)

S

SCIA 86


Haunched sections (I+Ivar, Iw+Plvar, Iw+Iwvar, Iw+Ivar +Iw r) a composed rail sections (Iw+rail, Iwn+rail, I+rail, I+2PL+ra , I+ +ra +2L+rail, I+Ud+rail) are considered as equivalent asymmetric sec ons

, I va ndil PL il, I

I ti .

Use of diaphragms


hear buckling check

S

Compo I+rail, I+2PL+rail, I+PL+rail, I+2L+rail, I+Ud+r quivalent asymmetric I sections.

S PO TIONS

sed rail sections (Iw+rail, Iwn+rail,ail) are considered as e

UP RTED SEC

I Symmetric I shapes (IPE, HEA, HEB, ….) RHS Rectangular Hollow Section (RHS) CHS Circular Hollow Section (CHS) L Angle section U Channel section T T section PPL Asymmetric I shapes RS Rectangular section Σ Cold formed section COM Composed section in PRIMAWIN O Solid tube NUM Numerical section

The necessary data conditions for these sections are described in Appendix D. The COM and NUM sections are not read out of the profile library.

I

RHS

CHS

L

U

T

PPL

RS

Σ

O

COM

NUM

SCIA 87



Compact section x x x x x

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

Slender section x x x x x x

Shear buckling check x x x

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

EFERENCES

R

el construction nce Factor Design

Third Edition 2001

ELEMENTS DE CONSTRUCTIONS METALLIQUE

[1] AISC – Manual of ste

Load and Resista

[2] R. Maquoi

Ulg , Faculté des Sciences Appliquées, 1988

SCIA 88


C

CM66 CODE CHE

M66

CK

T are checked according to the regulations given in

ITBTP / CTICM

Consulted articles

he beam elements

Règles de calcul des constrcutions en acier

Régles CM Decembre 1966 Editions Eyrolles 1982

T t. 3,2.) and shear (art. 3,3.). F re considered : • for compression : art. 3,4. ••• for double bending and axial compression : art. 3,7. • for shear buckling : art 5,212 A verview 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.

he cross-section is checked for tension (art. 3,1), bending (ar

or the stability check, the following criteria a

for compression and bending : art. 3,5 for lateral torsional buckling : art. 3,6.

more detailed o

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

SCIA 89


3,21 Flexion simple (*) x3,22 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 (*) x3,41 Pièces comprimées a parois pleines x 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 x(*) des appuis 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(*)

SCIA 90


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

ties are not taken into account . The net area proper

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

Compression members

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”).

Factor kf

For the calculation of the buckling length, we

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

3;1lM

A172

2M

⎟⎟⎞

⎜⎜⎝

⎛−.125.0

k medf µ

⎠−+µ

=

−

SCIA 91


3.125.0I ≈ 0f Mmed .0, the formula 3,513 is used : kf −µ

+µ=

LTB Check The LTB c 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". T ffici the table for B given in Ref[1] 3,643, a g th given in Ref[1] 3,642. 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

Use of diaphragms

heck is performed for

he coend usin

ent B is calculated by interpolatinge calculated C value with table for C

considered as equivalent asymmetric I sections.

See Chapter 'Adaption of torsional sta '.

Combined flexion

con nt

The values fx is the maxi um value of the bending stress in the member for the

ending around the strong axis. The value σfy is the maximum value of the bending stress in the member for the bending around the weak axis. For non-prismatic sections the values σfx and σfy are the local (i.e. in each intermediary

stresses.


σ mb

section) bending

Compos Iw+rail, Iwn+rail, I+rail, I+2PL+rail, I+PL+rail, I+2L+rail, I+Ud+ra as equivalent asymmetric I sections.

SUPPORTED SECTIONS

ed rail sections (il) are considered

I Symmetric I shapes (IPE, HEA, HEB,

….) RHS Rectangular Hollow Section (RHS)

SCIA 92


CHS Circular Hollow Section (CHS) L Angle section U Channel section T T section PPL Asymmetric I shapes RS Rectangular section Σ Cold formed section COM Composed section in PRIMAWIN O Solid tube NUM Numerical section

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

L

U

T

PPL

RS

Σ

O

COM

NUM

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

CHS

I

RHS

Se tion check x x x xc x x x x x x x x

Buck heck x x x x x x x x x x x x ling c

Slender section buckling check x x x x x x x x

LTB Check x

Shear buckling check x x x x

REFERENCES

[1] Règles de calcul des constrcutions en acier CM

Editions Eyrolles 1982

ITBTP / CTIRégles CM Decembre 1966

SCIA 93


C 80

CM66 - ADDITIF 80 CODE CHECK

M66 - ADDITIF

T ing to the regulations given in Ad tif 80

Consulted articles

he beam elements are checked accord di

ied according to art. 5,12. (classification 'plastic' or 'elastic').

he 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.

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.

The cross-section is classifT

• for compression and bending : art. 5,32

A

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

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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 (*)

Classification of sections For each in diary section, the classification is determined and the proper section check is per for each intermediary point. For each load case/combination, the critical section classification over the member is used to perform ck. So, the stability section classification can change for e h load ca . H ever, fo sections, the stability section classification is determined for each intermediary section.

S tion che

termeformed. The classification can change

the stability chese/combinationac

ow r non-prismatic

ec ck I ectio ns specified in art. 5,1, the sections are checked according to the regulations given in Ref.[2]. I iona t, the sections are checked according to the regulations g Ref

f the s ns are not according to the conditio

f a torsiven in

l moment is presen.[2].

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

he buckling properties for a VARH element are calculated by using the critical Euler force for this member see “Calcu critical Euler force for VARH elements”).

L l bu lin

T ( lation of

ateral-torsiona ck g For the calculation of the mom nt factors C1 and C2, we ref r to "Calculation of moment factors for LTB",

e e using the EC3 values.

SCIA 95


ar, Iw+Ivar, I+Iwvar) and composed rail

ctions (Iw+rail, Iwn+rail, I+rail, I+2PL+rail, I+PL+rail, I+2L+rail, I+Ud+rail) are nsidered as equivalent asymmetric I sections.

Use of diaphragms

Haunched sections (I+Ivar, Iw+Plvar, Iw+Iwvseco


SUPPORTED SECTIONS

I Symmetric I shapes (IPE, HEA, HEB,

….) RHS Rectangular Hollow Section (RHS) CHS Circular Hollow Section (CHS) L Angle section U Channel section T T section PPL Asymmetric I shapes RS Rectangular section Σ Cold formed section COM Composed section in PRIMAWIN O Solid tube NUM Numerical section

The necessary data conditions for these sections are described in "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

Σ

O

COM

NUM

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

SCIA 96


Compression + bendinAdd 80

g x x

SCIA 97


REFERENCES

2] Règles de calcul des constrcutions en acier

bre 1966

[1] Additif 80

[ITBTP / CTICM Régles CM DecemEditions Eyrolles 1982

SCIA 98


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 inPart1. Code of practice for design in simple nd continuous construction:hot rolled section

tandard distribution BS5950 Part1 1990 revised in 1992

building

aBritish S

Material properties

rades, 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 :

rade 50 : yield strength defined between 325 and 355 N/mm² a ield strength defined between 415 and 450 N/mm²

², t in mm)

For standard steel g

Grade 43 : yield strength defined between 245 and 275 N/mm² GGr de 55 : y (pY in N/mm

Steel grade

Thickness limits

PY

t≤16 mm 275 N/Mm²

t≤40 mm

265 N/mm²

t≤63 mm

255 N/mm²

Grade 43

t≤100 mm 245 N/mm²

t≤16 mm

355 N/mm²

SCIA 99


t≤40 mm 345 N/mm²

Grade 50

t≤63 mm 340 N/mm²

t≤100 mm

325 N/mm²

t≤16 mm

450 N/mm²

t≤25 mm 430 N/mm²

t≤40 mm

415 N/mm²

Grade 55

t≤63 mm

400 N/mm²

Remark: For cold-formed section, values for P luenced by the previous table. Remark : The reduction rules from previous ta alid when the used material is defined as material for the selected code.

C

y are not infble are only v

onsulted articles

According to Art. 3.5. and table 7, cross sections are classified in 4 types: ••• ct • A reduction factor is applied to the design st aterial 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 bined moment and axial force (Art. 4.8.) and biaxial moments (Art.4.9.). For the stability check, the beam hecked for lateral torsional b d axial compression. Articles u heck are the following: • rsional buckling : Art. 4.3. • .

Plastic Compact Semi-compa Slender

rength of the m

.2.3.), com element is c

uckling, shear buckling, compression ansed for this stability c

bending with

for lateral to shear buckling : Art. 4.4.5

SCIA 100


•• bending and axial compression : Art. 4.8. A m rview of used articles is given in the following table.

ction properties

for compression : Art. 4.7. for

ore detailed ove

Part. 3 Se3.5. 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. 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 λLT, φ, η, u, v

Art. 4.3.7.5. ppendix B. A

Factors m, n Art. 4.3.7.6. Equal flanged rolled section Art. 4.3.7.7.

SCIA 101


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

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.

SCIA 102



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.

matic sections, the stability section classification is determined r each intermediary section.

lender cross-section

However, for non-prisfo

S

r sections are particularly sensitive to local buckling. British Standard code (Art. efines stress reduction factor to prevent this phenomenon. For webs subject to

axial load and for circular hollow sections, the design strength py should such that the limiting proportions for semi-compact section are met. For

sections, where a slender outstand is in compression, the design strength should be

Section properties

Slende

.6.) d3moments and

e assumed bother reduced by the factor given in Table 8.

he net area of a section is taken as its gross section neglecting the deduction due to ing Art. 4.2.3.

Bending moment

Tfastener holes: Art. 3.3. Shear area of a cross-section is calculated by us

g, it's necessary to determine the shear apacity. 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

Before any calculation of members in bendinc

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

SCIA 103


semi-compact and slender section, the simplified approach is applied following Art. 4.8.2.and Art. 4.8.3.2. (a).

Lateral torsional buckling

itical lateral torsional buckling moment is given by the general formula Art. 4.3.7. and Annex B2&3. For

The condition to be satisfied in all the cases is that

For I sections (symmetric and asymmetric PPL), rectangular sections (solid and hollow), T sections, channel sections and angle section, the cr

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].

with Mb=Sxpb and

orm moment factor) (m is an equivalent unif 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 lo and n depend on the ratio of the e ment ratio of the larger moment to the mid-s ee moThere are th ateral torsional buckling namely: ' pproach lent uniform moment method' with n=1 ' i.e. the ' ethod' with m=1 In any given ne 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 e tive len e length of the member L in the calculation of λLTB.

aded between point of lateral restraint, m=1 nd mopan fr

s at the points of restraint and on thement.

us two methods for dealing with lm an approach'

' i.e. the 'equivaequivalent slenderness m

situation, only o

ffec gth LLTB less than th

SCIA 104


H ever, as nding clarification ina future version of BS5950, it is recommende f the two following values:

ow a interim measure, ped that λLTB is taken as the smaller o

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.

aunched 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 sec ons

Use of diaphragms

H

I ti .

S daption of torsional co tan .

C

ee Chapter 'A ns t'

ompression member F bm ted o compression, we applied the recommendations given in BS 5950 and Appendix C to determine th com ressive strength.

hear buckling check

or member su it te p

S

ections (Iw+rail, Iwn+rail, I+rail, I+2PL+rail, I+PL+rail, I+2L+rail, ered as equivalent asymmetric I sections.

S OR

Composed rail sI+Ud+rail) are consid

UPP TED SECTIONS

I shapes (IPE, HEA, HEB, ….) Symmetric IRHS Rectangular Hollow Section (RHS) CHS n (CHS) Circular Hollow SectioL Angle section U Channel section T T section P Asymmetric I shapes PL

SCIA 105


RS Rectangular section Σ Cold formed section COM Composed section in PRIMAWIN O Solid tube NUM Numerical section

The nece ry data conditions for these sections are described in "Profile conditions for code check". The COM and NUM sections are not read out of the profile library.

CHS

L

U

T

PPL

RS

Σ

O

COM

NUM

ssa

I

RHS

C tion x x x x x x (1) x (1) (1) (1) lassifica x

Sect heck x ion c class 1 x x x x x x x

Section check x class 2 x x x x x x x

Section check x x x x x class 3 x x x x x x x

Section check ass 4 x x x x x x x x cl

Stability check class 1 x x x x x x x x


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



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

REFERENCES

[1] British Standard BS5950 Part 1 : 1990+Revised text 1992

Structural use of steel work in building Part1 Code of practice for design in simple and continuous construction: hot rolled sections

[2] Plastic design to BS5950 J.M. Davies & B.A. Brown The steel Construction institute

SCIA 106


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

[4] Essentials of Eurocode 3

ECCS - N° 65, 1991

Part 1 - 1 : General rules and rules for buildings 993-1-1:1992

[6] R. Maquoi

ELEMENTS DE CONSTRUCTIONS METALLIQUE

Design Manual for Steel Structures in Building

[5] Eurocode 3

Design of steel structures

ENV 1


SCIA 107


BS5950-1:

BS5950-1:2000 CODE CHECK

2000

The steel members are checke ng to the recommendations given in : British Standard BS 5950-1:2Structural use of steelwork in building Part1. Code of practice for de lled and welded sections

Material properties

d accordi

000

sign – Ro

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 Grade S355 : yield strength defined between 295 and 355 N/mm²

h defined between 410 and 460 N/mm²

mits

PY

The standard steel grades are :

Grade S460 : yield strengt

(pY in N/mm², t in mm)

Steel grade

Thickness li

t≤16 mm

275 N/Mm²

t≤40 mm

265 N/mm²

t≤63 mm

255 N/mm²

Grade S275

t≤80 mm

245 N/mm²

t<100 mm 235 N/mm2

SCIA 108


t< 150 mm 225 N/mm2

t≤16 mm 355 N/mm²

t≤40 mm 345 N/mm²

Grade S355

t≤63 mm

335 N/mm²

t≤80 mm

325 N/mm²

t<100 mm 315 N/mm2

t< 150 mm 295 N/mm2

t≤16 mm

460 N/mm²

t≤40 mm

440 N/mm²

t≤63 mm

430 N/mm²

Grade S460

t≤80 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 m the designated grades S275, S355 or S460

Governing code clauses

aterial is chosen from

According to Cl. 3.5. and tables 11 and 12, cr are classified in 4 types: •• pact • i-compact • 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 mo ial 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. Re es for this stability check are the following:

oss sections

Class 1 Plastic Class 2 Com Class 3 Sem Class 4 Slender

ment and ax

levant claus

SCIA 109


•• pression : Cl. 4.7. • W opriate, restrained or torsional buckling lengths are identified and checked to A More detailed clause references are given in the following table.

perties

for lateral torsional buckling : Cl. 4.3. for com

for bending and axial compression : Cl. 4.8. here apprnnex G

Part. 3 Section pro3.5. 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 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 p b Cl. 4.3.6.5

SCIA 110


Equivalent slenderness λLT, φ, η, u, v, βW, x

Cl. 4.3.6.7-9Annex B.

Factors m Cl. 4.3.6.6. Equal flanged rolled section l. 4.3.7 CBuckling resistance moment for single ngles a

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. 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.

SCIA 111


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.


Slender cross-sections

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.

lender sections are particularly sensitive to local buckling. BS 5950-1:2000 generally Sallows 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).

SCIA 112


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 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 potential buckling length between adjacent lateral restraints The lateral-torsional bending strength pb is calculated in accordance with Cl 4.3.6.5 and

his bending strength is dependent on the equivalent slenderness λLT ted in accordance with Cl 4.3.6.7-9.

he moment gradient (shape of the moment diagram between restraints) is allowed for

Annex B 2.1. Twhich is calculaTby 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’

ng and is not related to torsion loading or torsion moment effects. Torsional buckling may occur in any member segment between compression f ints which has intermediate restraints to the tension flange. It is therefore load comb rtal frames rafters and columns. The program carry out a stability check in accordance with BS 5950-1:2000 Cl. 5.3.4 and Annex G.

Lateral b

refers to the mode of buckli

lange restraination dependent. It is particularly important in po

will detect any potential buckling length and

uckling due axial compression T latera ember or segment between lateral res culated in accordance with Cl 4.7.4. The compressive strength pc a ng f using the strut curves appropriate to the section type, thickness and ulae of Annex pendent on the slenderness per Cl 4.7.2

he l buckling compression resistance Pc of any mtraints is cal

llowi or buckling is calculated using Cl. 4.7.5axis of buckling (Table 23) as expressed in the form

C. This compressive strength is de

SCIA 113


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.

ing and is applied to the member length ints. The second equation refers to the interaction of lateral-

rsional buckling due to the moment field and lateral buckling due to axial restraints.

-sections and Cl. 4.8.3.3.3 for CHS and RHS sections. It is permissible to take the more favourable result.

tilisation), (shape of the moment diagram between restraints) is allowed for

e 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.

The first equation refers to flexural bucklbetween major axis restratocompression and is applied to potential buckling lengths between minor axisClause 4.8.3.3.2 provides a more exact method for symmetrical I

(Lower uThe moment gradient by means of th

Torsion effects The current version of the BS 5950-1:2000 steel check does not deal with torsion

oments. Any torsion moments generated by the frame analysis will be igm nored. ost steel structures do not in fact rely on torsion effects to transmit loads.

Where it d n ry ers torsion moments as part of the primary lo system lternative checks should be made. The BS 5950-1:1990 steel check does deal with torsion.

SUPPORTED SECTIONS

Mis foun ecessa for memb to sustain ad , a

etric I shapes (UB, UC, IPE, HEA, HEB, ….) I SymmRHS Rectangular Hollow Sections (RHS) [hot rolled or cold formed] CHS Circular H Se (CHS) [hot rolled or cold formed] ollow ctionsL 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 114


SIA263

SIA263 CODE CHECK


SIA263 Construction en acier SIA263:2003

Material properties

The 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:

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

fy fu fy fu

S235 235 360 215 340 S 235 S275 275 430 255S 275

410

S355 355 5S 355

10 335 490

S460 460 55S 460

0 430 530

Consulted articles

The classification described in SIA263 is based on the calculation method. The c the method used respectively to determine the i the section and the stability check. By facility, we can alculation method in SIA263 distinguishnternal forces and to perform

SCIA 115


o on method of SIA263 and the section c According to SIA263 Table 5a-5b , cross sections are classified in 4 types: •••• s 4 The first letter of the classification denomination is related to the method used to c second letter indicates if we perform the s 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 c assification) and EC3 prescriptions. T pression, shear, combination of bending and a ement 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 :

Analyse structurale et dimensionnement

bviously make a parallel between the calculatilassification proposed in EC3.

PP (plastic-plastic) or class 1 EP (elastic-plastic) or class 2 EE (elastic-elastic) or class 3 EER (elastic-elastic reduced) or clas

alculate internal forces in the structure. The ection and the stability check with a elastic or

lassic elastic approach (EE cl

he section is checked for tension, comxial forces. For the stability check, the beam el

44.1 Généralités x 4.2 Bases de l'analyse structurale et du dimensionnement 4.3 Modélisation 4.3.1 Classification des sections

x

4.4 Résistance des sections 4.4.1 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 Stabilité 4.5.1 Flambage

x

4.5.2 Déversement des poutres fléchies x 4.5.3 Flexion et compression x

SCIA 116


4.5.4 Voilement des éléments plans comprimés x 4.5.5 Voilement des éléments plans cisaillés x 4.8 Situtation de projet incendie 4.8.1 PRINCIPES x 4.8.2 Propriétés de l'acier en cas d'incendie x 4.8.5 Méthode de calcul simplifiée x 5 Eléments de construction 5.1 POUTRES ET POTEAUX DES CLASSES DE SECTION 1 ET 2

x

5.3 Eléments comprimés à section composée 5.3.1 Barres étrésillonées ( à travers de liaison) x 5.4 Poutres composées à âme pleine 5.4.1 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 ection, the classification is determined and the proper section

ed. The classification can change for each intermediary point. For each ad case/combination, the critical section classification over the member is used to

s, the stability section lassification is determined for each intermediary section.

ction

For each intermediary scheck is performloperform the stability check. So, the stability section classification can change for each load case/combination. However, for non-prismatic sectionc

Slender cross-se

4). The using of a reduced area implies the recalculation of the shear centre position, the inertia and the elastic modulus.

rties

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.

Sections prope

SCIA 117


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


metric I profile, we don't have to perform any lateral torsional buckling heck if NEd/Npl,Rd ≤ 0.15 and the conditions provided in Table 6 SIA263 are satisfied.

SIA263 in the LTB check, we use prescriptions given in EC3 Annex F. Those rules moment for lateral torsional buckling for

) and non symmetrical (formula F.1. EC3) sections around the minor axis.

PL and, T only with compression in flange, characterised by a e 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

, I+PL+rail, I+2L+rail, I+Ud+rail) are ctions.

For double symcFor 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

allow us to determine a elastic critical symmetrical (formula F.2 EC3

In the case of I, U, Preduced area or not, w

compression web area, taken about an axis in the plane of the web. Haunched sections (I+Ivar, Iw+Plvar, Iw+Iwvar, Iw+Ivar, I+Iwvar) and composed rail ections (Iw+rail, Iwn+rail, I+rail, I+2PL+rails

considered as equivalent asymmetric I se

Use of diaphragms

e Chapter 'Adaption of torsionSe

al constant'.

Shear buckling Composed rail sections il, I+2PL+rail, I+PL+rail, I+2L+rail, I+Ud+rail) are considered as e

Stability check

(Iw+rail, Iwn+rail, I+raquivalent asymmetric I sections.

c I profile PP or EP, SIA263 provides specific formula to perform e stability check of member submitted to biaxial moment. For other sections, non

la is provided to design

For double symmetrithsymmetric or from EE and EER classification, a general formu

ember under mono-axial sollicitations. m

Torsion check

SCIA 118


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

Built-in beams For built-in beam sections (IFB, SFB, THQ sections), proper section checks are

SIA263 - FIRE RESISTANCE

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

ire actions effect EF fi

tuation Efi,d,t are taken from the results of the

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

n by

with Gk characteristic values of permanent actions

k,i characteristic value of the variable action i alues of accidental action from fire exposure

ψ2,j combination coefficients Pk characteristic value of prestressing action

Material properties

The design effects of actions for the fire si

in The accidental combination is given by

The accidental combination is give

ΣGk + Pk + Ad+ Σψ2,iQk,i

Q Ad design v

material properties are depending on the steel temperature.

Strength and deformation properties :

heT

SCIA 119


°20,aθθ

°20 θ

= ,E,a

,y,y

Ekfk

The variatio functio alue for yield strength ky,θ and modulus of elasticity kE 5. In the simplified calcu sidered to be constant ng the a

al elongation ∆l/l 14 x 10-6 (θa-20)

θ =,yfE

n in n of the steel temperature of the v,θ is given by tables in ref.[1], Figure 1

lation method, the following default properties are conduri nalysis :

thermthermal conductivity λ 45 W/mK a

Temperature analysis - Thermal actions

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'

ominal temperature-time curveN

See EC3 Chapter 'Nomi

Net heat flu

nal temperature-time curve'.

x

See EC3 Chapter 'Net h

Steel Temperature

eat flux'

See Ref.[1], Annexe C. The increase of temper ber during a time interval ∆t

ature ∆θ in an unprotected steel mema,t

thVc

/Ad,net

aa

mt,a ∆

ρ=θ∆

SCIA 120


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

ca the specific heat of steel [J/kgK] h the net heat flux per unit area [W/m²]

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

m³]

V the volume of the member per unit length [m³/m] The factor Am/V should not be taken as less than 10m-1

net,d

∆t

ρa the unit mass of steel [kg/ The increase of temperature ∆θa,t in an insulated steel member during a time interval ∆t

( ) ( )

V/c

3

paa

ρ⎠⎝

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

ific heat of steel [J/kgK] at of fire protection material [J/kgK]

the thickness of the fire protection material [m]

seconds

tion [kg/m³] θa,t the steel temperature at time t θg,t the ambient gas temperature at time t

crease of the ambient gas temperature during the time interval

e fire protection material

The value ∆

1et1cd

V/At,g

10/t,at,g

aap

ppt,a ∆−−∆

⎟⎞

⎜⎛ φ

+

θ−θ

ρ

λ=θ∆ φ

Adc p

pp

ρ=φ

with A V the volume of the member per unit length [m³/m] ca the spec cp the specific he dp

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

ρa the unit mass of steel [kg/m³] ρp the unit mass of fire protec

∆θg,t the in

λp the thermal conductivity of th[W/mK]

θa,t ≥ 0.0

SCIA 121


For the increase of temperature ∆θa,t in an insulated steel member with intumescent coating, we refer to the NEN specifications, Chapter 'Steel Temperature'.

C culatioal n model

The calculation can be performed in 2 domains : - strength- era

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 doma cri cal s eel temperature θcr,d s c puted. From this cri al t perature, the fire resistance time fi,d is calculated (the tim dom in).

Code Check

domain temp ture/time domain

nI

in, the ti t i om tic em t

e a

The section and stability checks (buckling, late l to iona buc ling are erfor ed accord the regu Ref.[1], 4.8.5. For each memb r, classification th the section eck and e tability check are performed.

ion : 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.

members (class 4) : art. 4.8.5.9.

SUPPORTED SECTIONS

ra rs l k ) p ming to lations given in

e the of e cross section, ch ths

The following checks are executed : - classification of cross sect-

- resistance for

I shapes (IPE, HEA, HEB, ….) Symmetric IRHS Rectangular Hollow Section CHS Hollow Section Circular

SCIA 122


L Angle section U Channel section T T section PPL Asymmetric I shapes Z Z section RS Rectangular section Σ Cold formed section COM Composed section O Solid tube NUM Numerical section

I

RHS

CHS

L

U

T

PPL

RS

Z

Σ

O

COM

NUM

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

Section check PP x x(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

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)

(1) sections are classified as class 3 cross section by default. (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 acier SIA263:2003

[2] SIA263/1

SCIA 123


Construction en acier / Spécification complémentaires SIA263/1:2003

SCIA 124


G 17-8

THE GBJ 17-88 CODE CHECK

BJ 8

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

National standard of the People’s Republic of China for de n of steel structures

GBJ 17-88 eijing 199

Material properties

Code sig

B 5

he used steel grades are

16Mnq • 15Mn • 15Mnq

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

sections

T • Grade3 • 16Mn •

mm): Group Diameter or thickness of bars Thickness of L-, I- and U Thickness of Plates

1 <=40 <=15 <=20 2 >40-100 >15-20 >20-40 3 >20 >40-80

T

Group Thickness f fv fce

he design values are (in N/mm²) Steel fy Steel3 1

3

215 200 190

125 115 110

320 320 320

5

235 2

23235

SCIA 125


Steel Group Thickness f fv fce fy16Mn 16Mnq

<=16 17-25 26-36

315 300 290

185 175 170

445 425 410

5 5 5

343434

15Mn 15Mnq

<=16 17-25 26-36

350 335 320

205 195 185

450 435 415

0

390

39039

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

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

fy the yield strength (N/mm²)

R aterial is defined as material for the selected code. If they are not defined as GBJ material, the f g rule is used

f = 0.91 x yield strength fv = 0.58 x yield strength

Consulted articles

fce the be

emark : The reduction rules from previous table are only valid when the used m

ollowin

tion and elements are checked according to part 4 and 5. When plastic design is allowed, part 9 is supported. A 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

The sec

more

4.1.Strength 4.1.1. 4.1.2.

*) x (x

4.2.Overall stability (*)

SCIA 126


4.2.1.

4.2.3.

4.2.2.

4.2.4.

x x x x

4.3.Local stability ) (*4.3.1. 4.3.2.

x 4.3.3. 4.3.9.

xx

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

s5.1.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.

x(*)

5.2.5. xx

5.3.Effective length and allowable slenderness ratio (*) 5.4.Local stability of compression members 5.4.1. 5.4.2.

x x x

x (*)

5.4.3. 5.4.4. x 5.4.5. 9.Plastic design 9.1.General requirements 9.1.3. 9.1.4.

x x

9.2.Calculation of members (*) 9.2.1. x

SCIA 127


9.2.2. 9.2.3. 9.2.4.

x x x

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 x members

Section properties


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

The local compressive stress σc, is considered as 0.0.

SCIA 128


Buckling curves

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

a

Buckling length

or 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 f ce for thi force for VARH elements").

L l tors

F

or s member (see "Calculation of critical Euler

atera ional buckling The LTB check is g sections : I section, U section, RHS section, T section, PPL section. For the othe e, the factor ϕb = 1.0. Haunched sections (I+Ivar, Iw+Plvar, Iw+Iwvar, Iw+Ivar, I+Iwvar) and composed rail sections (Iw il, I+2PL+rail, I+PL+rail, I+2L+rail, I+Ud+rail) are c sidered a

Local stability of compressed members

supported for the followin

r section typ

+rail, Iwn+rail, I+raon s equivalent asymmetric I sections.

d the effective area properties over the member are used to perform the stability check. However, for non-prismatic sections, the section classifica are determined for each intermedi se n to er rm he bil ch k. When the web ratio ( dept /thickness) does not conform to th requ rem nts, the web is r ulating k nd ta lity check A idth of 2 tw s each side f th web take int ac un

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.

or each load case/combination, the critical section classification anF

tion and the effective area propertiesary ctio p fo t sta ity ec

e i eeduced for calc of the section chec a s bi . w 0qrt(235/f ) ony o e is n o co t.

SCIA 129


yw f

235t20d =

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.

SUPPORTED SECTIONS

I Symmetric I shapes (IPE, HEA, HEB, ….) RHS Rectangular Hollow Section (RHS) CHS Circular Hollow Section (CHS) L Angle section U Channel section T T section PPL Asymmetric I shapes RS Rectangular section Σ Cold formed section COM Composed section in PRIMAWIN O Solid tube NUM Numerical section

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

SCIA 130


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

I

RHS

CHS

L

U

T

PPL

RS

Σ

O

COM

NUM

Plastic (single bend ing) x x

Compact section (w x x x x ith γ) x x

Non-compact secti x x x x x x x x x x on

S ction x lender se x x x x x

N kling x x x x ormal buc x x x x x x x x

LTB x x x x x

Shear buckling x x x

Plastic stability bending)

x x check (single

SCIA 131


REFERENCES

[1] Chinese Steel Code

(Chinese version)

standard of the People’s Republic of

Code for design of steel structures GBJ 17-88 Beijing 1995

GBJ 17-88

.[2] National

China

SCIA 132


KOREAN STEEL CODE CHECK

THE KOREAN STEEL CODE CHECK

aterial propertiesM

The following design values are used :

teel fy =40 mm

fy t>40 mm

St<

SS41 SPS41

240 220

SPSR41 SS50 280 260 SS55 380 380 with fy the yield strength (N/mm²)

The following steel characteristics are valid :

odulus of elasticity 210000 N/mm² shear modulus 81000 N/mm²

10-6 7850 kg/m³

m

coefficient of linear thermal expansion 12 xdensity

SCIA 133


Consulted articles

he section and elements are checked according to part 2 and 3. The shear buckling c 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.

Theck is perfromed using

TEXT 2.Allowable stress 2.1.Structural material x 2.1.1.Allowable tensile stress x 2.1.2.Allowable shear stress x 2.1.3.Allowable compressive stress x 2.1.4.Allowable bending stress (*)

x a) b) c)

x x

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

SCIA 134


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 web a)

x

Section classification For each intermediary section, the classification is determined.. 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

etermined for each intermediary section. When the element properties don’t satisfy the limiting values for the ratios, the section i sified slender. ave to be reduced for the calculation of the stresses. F tstand mpressi the part that is situated on the fixed side, remains. T e length of the part b l on the limiting ratio.

d

s clasor ou

as co

The section hon elements,

h ’ is calculated by the equation in which the ratio b’/t is equa

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.

SCIA 135


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

Section properties

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

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

Buckling length For the calculation of the buckling length, we refer to "Calculatio

he buckling properties for a VARH element are calculated by usingn of buckling ratio"

the critical Euler rce for this member(see "Calculation of critical Euler force for VARH elements") .


Tfo

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

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

z2

t

z2

z

EIILMcr

π+=

22 GILIwEIπ

with L LTB length E modulus of elasticity G shear modulus

warping constant It torsion constant Iz

Iw moment of inertia about minor axis

SCIA 136


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

y

crLTB I

M=σ

with Iy

The slendern s ratio fo

moment of inertia about major axis

es r LTB λLTB, is given by

LTBLTB

Eσ

π=λ

The allowab TB str TB with the formulas given in 2.1.3. Haunched sections (I+Ivar, Iw+Plvar, Iw+Iwvar, Iw+Ivar, I+Iwvar) and composed rail

+rail, I+rail, I+2PL+rail, I+PL+rail, I+2L+rail, I+Ud+rail) are considered as equivalent asymmetric I sections.

Combined stresses

le L ess is calculated using the slenderness L

sections (Iw+rail, Iwn

, the following formulas are used :

For compression and bending

1ftt

1f

c by ≤σ

fc

f

t

bybx

bybx

bx

c

−σ+σ

+σ

+

For tension and bending, the following formulas are used :

c ≤σ

cσ

SCIA 137


1c by ≤σ

+

1f

tt bybxt ≤σ+σ+σ

ffc

f bybx

bx

bx

σ

ith σc norm l compression stress σt normal tension stress cσb bending compression stress

tσb bending tension stress cσbx bending compression stress around x axis

tσbx bending tension stress around x axis cσby bending compression stress around y axis tσby bending tension stress around y axis ft allowable tension stress

fc allowable compression stress owable bending stress

wable bending stress around x axis f allowable bending stress around y axis


t +σ

−

t

w a

fb all

fbx alloby

Composed rail sections (Iw+rail, Iwn+rail, I+rail, I+2PL+rail, I+PL+rail, I+2L+rail, I +ra etric I sections.

SUPPORT

+Ud il) are considered as equivalent asymm

ED SECTIONS

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

RHS Rectangular Hollow Section (RHS) CHS Circular Hollow Section (CHS) L Angle section U Channel section

SCIA 138


T T section PPL Asymmetric I shapes RS Rectangular section Σ Cold formed section COM Composed section in PRIMAWIN O Solid tube NUM Numerical section

T onditions for these sections are described in "Profile conditions for cThe COM and NUM sections are not read out of the profile library.

RHS

CHS

L

U

T

PPL

RS

Σ

O

COM

NUM

he necessary data code check"

I

Slender sections x x x x x

Allowable stresses x x x x x x x x x x x x

Shear buckling x x x

REFERE ESNC

K an S d (Korean Version) 1983 Extracts Korean Standard (Internal English VersTranslated by Karam Kim - 19.03.1998

Structural Standard of B ing tecture (internal english document)

[1] ore tandar

[2]

ion)

[3] Regulations of uild Archi

SCIA 139


SCIA 140


BSK 99

BSK 99 CODE CHECK


Boverket, Byggavdelningen, 2000

M

BSK 99 StalKonstruktioner

aterial properties

F gth fyk and ten trength fuk a ness of the element (see Ref. [1 tab.2:21a and tab.2:21b) T Steel

s Poisson Unit mass (kg /m3)

Extensibility (m/m K)

Ultimtensilstrength (N/mm2)

Yield strength (N/mm2)

or standard steel grades, the characteristic yield stren sile sre defined according to the thick ],

he standard steel grades are :

Name Type E-modulu(N/mm2)

ate e

S235 Steel 210000 0.

S 235

3 7850 12*10-6 340 235

S275 Steel 210000 0.3 7850 12*10-6 410 275

S 275

S355 Steel 210000 0.3 7850 12*10-6 490 355

S 355

S420 Steel 210000 0.3

S 420

7850 12*10-6 500 420

S460

S 460

Steel 210000 0.3 7850 12*10-6 530 460

S500 Steel 210000 0.3 7850 12*10-6 590 500

S 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

SCIA 141


S690 Steel 210000

S 690

0.3 7850 12*10-6 770 690

( Steel grade Thickness fuk fyk

fyk, fuk in N/mm², t in mm)

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, S 355 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

Rem re only valid when the used material previous table.

ark : The reduction rules from previous table ais defined as material for the selected code.

SCIA 142


Consulted articles

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

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

ore detailed overview for the used articles is given for part 6:2 in the following

ed with “x” are consulted. The chapters marked with (*) have a

6:2.Calculation of the capacity of construction elements

Tforce (art. 6:25). 6

A mtable. The chapters markupplementary explanation in the following chapters. s

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

SCIA 143


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

Classification of sections 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.

Effective cross-section properties for class 3 cross-section 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

etermined 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. is the ctive a when subject to uniform compression. Weff is the effective sec e cross-section when subject only to moment about the relevant axi ability check is performed.

Section pro ties

d

Aeff effe rea of the cross section tion modulus of ths. With these properties, the section and st

per 6:22 ; 6:243 51 ; 6: into account .

Section che

; 6:2 261 : The net area properties are not taken

ck - Double symmetric I- Solid sec s (O, R S) 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):

sections (I) use the formula (6:251a) and (6:251b) tion S) and hollow sections (RHS, CH

-

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yd22

x f3 α≤τ+σ

ydx f≤σ

with α=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 lements") .

For class 3 sections, the sed, including the calculating of Idef.

Stability check for tors d torsional-flexural buckling

e

rules given in [5], part :34 are u

ional buckling an See [5], part :37. The design buckling resistance for torsional or torsional-flexural buckling shall be o tained usi he follo b ng t wing reduction factor ωc and slenderness λc :

SCIA 145


( ) ( )[ ]

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

ANN⋅σ=

ykeff fAc

116.1

²iy

²il

E²

4²21

yiii

lEC²GI

iA1

),min(

λ+=

⎟⎟⎠

⎞⎜⎜⎝

⎛−

⎟⎟⎠

⎞⎜⎜⎝

⎛π

=σ

σβσ−σ+σ−σ+σβ

=σ

++=

⎟⎟⎠

⎞⎜⎜⎝

⎛ π+=σ

σσ=σ

=λ

fyk the basic yield strength σcr the critical stress σcr,T the elastic critical stress for torsional buckling σcr,TF the elastic critical stress for torsional-flexural buckling G the shear modulus E the modulus of elasticity IT the torsion constant of the gross section

M the warping constant y the radius of gyration about yy-axis the radius of gyration about zz-axis

0

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

1=β

ω

with

C i iz

lT the buckling length of the member for torsional buckling y the position of the shear center

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Lateral-torsional buckling

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

Alterna ly to th egulations given in 6 2442. for bisymmetric sections, the elastic critica oment for LTB Mcr for I section (symme( r Hollow Section) sections and CHS (Circular Hollow Section) sections, can b ed using he rmula given by the general formula F.2. Annex F Ref. [3] For the calculation of the moment factors C1 "Calculation of m factors for TB". For the other supported sections, the elastic critical moment for LTB Mcr is given by

tivel m

e r :s tric and asymmetric), RHS

Rectangulae calculat t fo .

, C2 and C3 we refer tooment L

z2

t

z2

z2

EIL²GI

IIwEI

π+

E he m dulus f el stic y

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

It the torsional constant Iz the moment of inertia about the minor axis

Mcrπ=

L

with t o o a it G the shear modulus

Iw

SCIA 147


See also Ref. rt 7.7. for channel sections. F las used. Haunched sections (I+Ivar, Iw+Plvar, Iw+Iwvar, Iw+Ivar, I+Iwvar) and composed rail sections d+rail) are considered as equivalent asymmetric I sections.

Use of d

[ ]4 , part 7 and in particular pa

s 3 section, Izdef according to [5], part :44 isor c

(Iw+rail, Iwn+rail, I+rail, I+2PL+rail, I+PL+rail, I+2L+rail, I+U

iaphragms See Chapter 'Adaption of torsional constant'.

Shear force ( shear buckling) The shear buckling check is using the values for ωv from table 6:261 in column 2. The valu d)) taken as below :

e for λw is (according to [5], part :26, (18:26

2w

a34.500.4k1 ⎟

⎠⎜⎝

+=< τw

2w

w

kww

bbaif

bbaif

Etk.0

⎞

⎞⎛

=λ

k the modulus of elasticity fyk the yield strength a the field length bw the field height tw the web thickness

ykw fb81⋅⋅

τ

a00.434.5k1 ⎟

⎠⎜⎝

+=≥ τ

⎛

with E

SCIA 148


a

bw

ns (Iw+rail, Iwn+rail, I+rail, I+2PL+rail, I+PL+rail, I+2L+rail, ered as equivalent asymmetric I sections.

SUPPORTED SECTIONS

Composed rail sectioI+Ud+rail) are consid

Symmetric I shapes (IPE, HEA, HEB, ….) I RHS Rectangular Hollow Section CHS Circular Hollow Section L Angle section U Channel section T T section PPL Asymmetric I shapes RS Rectangular section Σ Cold formed section COM Composed section in PRIMAWIN O Solid tube NUM Numerical section

The necess nditions for these sections are described in chapter "Profile conditions for code check".

sections are not read out of the profile library.

RS

Σ

O

COM

NUM

ary data co

The COM and NUM

I RHS CHS L U T PPL


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

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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 + bending

ouble bending

x

d

Compression + bending

single bending

x x x x x x x x

Compression + LTB x

le bending

doub

Shear buckling x x x x

Torsional check x


REFERENCES

el Structures

I Swedish Institute of Steel Construction, Publication 118, 1989

Design of steel structures - 1 : General rules and rules for buildings

] R. Maquoi ENTS DE CONSTRUCTIONS METALLIQUE


orsten Höglund

C E Fritzes AB, Stockholm

[1] BSK 99 StalKonstruktioner Boverket, Byggavdelningen, 2000

[2] Swedish Regulations for SteBSK SB

[3] Eurocode 3

Part 1ENV 1993-1-1:1992, 1992

[4ELEM

[5] TK18, Dimensionering av Stalkonstruktioner Utdrag ur Handboken Bygg, kapitel K18 och K19

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[6] ENV 1993-1-3:1996

gn of steel structures Eurocode 3 : DesiPart 1-3 : General rules Supplementary rules for cold formed thin gauge members and sheeting CEN 1996

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IS 800

IS:800 CODE CHECK

The beam elements are checked according to the regulations given in IS 800 Draft version

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 Fe440W 300(<16mm), 290(16mm to 40mm), 280(>41mm to 63mm) 440 AFe440WB 300(<16m ), 280(>41mm to 63mm) 440 m), 290(16mm to 40mmFe490 350(<16mm), 330(16mm to 40mm), 320(>41mm to 63mm) 490 Fe490B (<16m m) 490 350 m), 330(16mm to 40mm), 320(>41mm to 63mFe540 410(<16mm), 390(16mm to 40mm), 380(>41mm to 63mm) 540 Fe540B mm), 380(>41mm to 63mm) 540 410(<16mm), 390(16mm to 40

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

Consulted articles

The cross-se n is clas

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

ctio sified according to Table 3.1. T8

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ore detailed overview for the used articles is given in the following table. The

hapters marked with “x” are consulted. The chapters marked with (*) have a upplementary explanation in the following chapters.

3.7. Classification of Cross Section x(*)

A mcs

6.1. Tension members x 6.2. Design strength due to Yielding of Gross section 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 n inal plastic shear resistance om x 8.4.2. Resis nce to sheta ar buckling x 9.1. Genera x l 9.2. Combi Shear aned nd 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 -

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Classification of sections For each intermediary section, the classification is determined and the proper section

sification can change for each intermediary point. tion, the critical section classification over the member is

sed to perform the stability check. So, the stability section classification can change for

ility section classification is determined each int

T ss s- ss 1 - class 2 - class 3 - class 4 The class 4 (slender) section check is not supported. For this sections a class 3 (semi-c ct) s ed.

S on pr

check is performed. The clasFor each load case/combinaueach load case/combination.

owever, for non-prismatic sections, the stabHfor ermediary section

he cro ections are classified as cla : plastic

: compact : semi-compact

: slender section

ompa ection check is perform

ecti operties T are

Section check

he net a properties are not taken into account .

of high shear for claIn the cas

fae ss 3 sectio, the allowable normal stress is reduced with a

ompression members

ctor (1-ρ). When torsional shear stress is present, the VonMisis criterium is checked.

C 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 elem

S eck for torsional buckling and torsional-flexural buckling

ents") .

tability ch

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The design buckling resistance Nb,Rd for torsional or torsional-flexural buckling shall be axis, and with relative

slenderness given by :

obtained using buckling for buckling around the weak

( ) ( )[ ]

²1

²

²

4²21

²1 ⎜⎛GI

)m

0

0

,

,,,,,,,

20

2220

220

,

,

⎟⎟⎠

⎞⎜⎜⎝

⎛−=

⎟⎟⎠

⎞⎜⎜⎝

⎛=

−+−+=

++=

⎟⎟⎠

⎞⎜⎝

+=

iy

il

E

yiii

lEC

iA

y

yycr

TcrycrTcrycrTcrycrTFcr

zy

T

mt

gTcr

TFcr

Acr

β

πσ

σβσσσσσβ

σ

πσ

σ

σ

with fyb the basic yield strength σcr the critical stress σcr,T the elastic critical stress for torsional buckling σcr,TF the elastic critical stress for torsional-flexural buckling G the shear modulus E the modulus of elasticity IT the torsion constant of the gross section CM the warping constant iy the radius of gyration about yy-axis iz the radius of gyration about zz-axis lT the buckling length of the member for torsional buckling y0 the position of the shear center ly the buckling length for flexural buckling about the yy-axis

,in( ,Tcrσ=crσ

=f ybλ

SCIA 155


torsional buckling

Lateral-

e or LTB Mcr for I sections (symmetric and asymmetric), HS (Rectangular Hollow Section) sections and CHS (Circular Hollow Section)

sections, can be calculated using the formula given by Annex F.

or 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

h elastic critical moment fT

R

F

z2

t

EI z2

2

IIw

LEIcr

π+π=

with the modulus of elasticity

G e shear modulus L the length of the beam between points which have lateral

z L²GIM

E th

SCIA 156


restraint (= lLTB) Iw the warping constant It the torsional constant Iz the moment of inertia about the minor axis


Use of diaphragms

SUPPORTED SECTIONS


tandard sections are defined :

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

The following s

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 Σ Cold formed section COM Composed section ( sheet welded, section

pairs, …) O Solid tube NUM Numerical section

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SCIA 158

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

I

RHS CHS L U T PPL RS Z Σ O COM NUM

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



Section check class 3 x x x x x x x x x x x x x

Section check class 4


Stability check c lass 2 x x x

Stability check cl x x x x x x x x x x ass 3 x x x

Stability check c lass 4

Shear buckling x check x x

) secti s are c

REFERE ES

(1 on lassified as class 3 cross section by default.

NC

1] 00 [ IS:8

2005


CALCULATION OF BUCKLING RATIO

INTRODUCTION 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

ρρρρρρρρ

ρρρρρρρρ

• for a sway structure :

4+x

x=l/L1

2

ρπ

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

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ρρρρπ

ρπρρ

21212

12

21

8+)+(+4

=x

EILC= i

iρ

φi

ii

M=C

The values for Mi and φi 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.

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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 dependant 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

l5.0s

lI

l1I1

lN4

lZ31

ls

K

31

31

K

⋅≥

⋅⋅

+

⋅⋅⋅⋅

−=

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

SCIA 162


Continuous compression diagonal, supported by pinned tension diagonal

NN

Z

Z

l/2

l1/2

l5.0s

lNlZ

75.01ls

K

1K

⋅≥

⋅⋅

−=

S

ee Ref.[4], Tab. 15, case 4.

SCIA 163


Pinned compression diagonal, supported by continuous tension diagonal

NN

Z

Z

l/2

l1/2

)1lZ

lN(

4

lZ3)IE(

1lZ

lN

l5.0s

12

21

d1

1

K

−⋅⋅

π⋅⋅

≥⋅

≤⋅⋅

⋅=


SCIA 164


Continuous compression diagonal, supported by continuous compression diagonal

N

N1

N1

l/2N

l1/2

l5.0s

lIl1I

1

lNlN

1ls

K

31

31

1

K

⋅≥

⋅⋅

+

⋅⋅

+=


SCIA 165


Continuous compression diagonal, supported by pinned compression diagonal

NN

N1

N1

l/2

l1/2

1

12

K lNlN

121ls

⋅⋅

⋅π

+=

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

SCIA 166


Pinned compression diagonal, supported by continuous compression diagonal

NN

N1

N1

l/2

l1/2

)N

lN

12(

l

lN)IE(

l5.0s

1

12

12

3

d

K

⋅+

π⋅π⋅

≥⋅

⋅=

CALCULATION OF CRITICAL EULER FORCE FOR VARH ELEMENTS

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

Definitions

A llows : 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].

VARH element is defined as fo

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forceCalculation of the critical Euler

For a VARH element (form node i to node j), we can define L beam length

i j

E modulus of Young Ncr critical Euler force Ri, Rj beam stiffness at end i and j

by :

Ii, Ij moment of inertia at end i and j A , A sectional area at end i and j

The stiffness R and R' is given

EIL

R=R

EIL

R=R

M=R

ijj

iii

′

′

Φ

II=

i

jξ

The critical Euler force is given by

LEI=N 2

i2cr α

To calculate α, the next steps are followed :

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

2. We suppose that

21>

1-ξα

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

SCIA 168


)]lncotg(+21(1)-(+[11=d

]1-)ln(sin

-[11=c=b

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

41-

)1-(=

2

2

2

2

2

ξββξ

ξ

α

ξ

ξξβ

β

α

ξββξα

ξαβ

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 αααα ′′′′

5. When a solution is found, we check if

21>

1-ξα

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

ξξξ

ξβξβξ

α

ξξξ

ξβ

α

ξξ

ξβξβξ

α

ββ

ββ

ββ

ββ

ββ

and resolve the proper equation of 4.

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CALCU TION BUCKLING RATIO FOR LATTICE TOWER MEMBERSLA

6771 is selected, the following buckling onfiguration can be selected. For each configuration, the critical slendernesses λ to be

considered, are defined.

When the national code EC3 or NEN6770/c

The values are taken from Ref.[8].

y

y

z z

v

v We defi iyy radius of gyration around yy axis izz radius of gyration around zz axis

ith the option 'Bracing members are sufficiently supported', the effective

slendernesses may be reduced as follows :

- for vv-axis :

ne :

ivv radius of gyration around vv axis

W

vv7.035.0 λ⋅+=λ

- for yy-axis : yy7.050.0 λ⋅+=λ The buckling curve 'b' is used..

SCIA 170


Leg with symmetrical bracing

vviL

=λ

Leg with intermediate transverse support

yyiL

=λ

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Leg with staggered bracing

vv

yy

i52.1)2a,1amax(

iL

⋅=λ

=λ

Single Bracing

vviL

=λ

Single Bracing with SBS (Secondary Bracing System)

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yy

2

vv

1

iLiL

=λ

=λ

Cross bracing

yy

comcom

yE

Ecom λ

com

com

com

1b

1com

sup

2bcomb'2

zz

2

yy

2

1

iL

fE

58.070.0K

L

K1125.0K

0.15.0K1125.0

FF

K1

LKLK

i,

i

L

=λ

π=

λ=λ

λ+=

⎟⎠⎞

⎜⎝⎛ +α≥

≤+⎟⎠⎞

⎜⎝⎛ +α+⎟⎟

⎠

⎞

⎝⎟⎠⎞

⎝

⋅=⋅=

=λ

=λ

11

L=α

1b 138.075.0K ⎜⎜⎛

⎜⎛ +α−=

''

vv

LLi

L

λ

SCIA 173


with Lcom Length of compressed member (L2 from figure)

com Force in compressed member (L2 from figure) Fsup Force in supporting member (member crossing member L2) E Modulus of Young fy Yield strength

Cross bracing with SBS

F

3bcomb'3

zz

'3

yy

'3

zz

2

yy

2

vv

1

LKLKL

iL

,iL

iL,

iLiL

⋅=⋅=

=λ

=λ

=λ

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'

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K Bracing

zzyy ii3

22

vv

1

L,

L,L

L

=λ

=λ

i=λ

3

zzyy

L

ii

Horizontal Bracing

L

1R0PP

R

73.0R316.0R085.0kiLk

1

2

2

vv

≤≤

=

+⋅−⋅=

=λ

with P1 Compression load P2 Tensile load

SCIA 175


Horizo Sntal Bracing with SB

L

1R0PP

R

73.0R316.0R085.0k

iLk

1

2

2

yy

≤≤

=

+⋅−⋅=

=λ

with P1 Compression load P2 Tensile load

iscontinuous Cross bracing with horizontal member

D

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N1 N2

N1N2

F F

a

a

( )α+=

⋅=λ

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 VGI

Staalbouwkundig Genootschap Staalcentrum Nederland 5684/82

SCIA 177


ate formula for effective end-fixity of

J.Aero.Sc. Vol.16 Feb.1949 pp.116 Stabiliteit voor de staalconstructeur uitgave Staalbouwkundig Genootschap

Stahlbauten : Stabilitätsfälle, Knicken von Stäben und Stabwerken November 1990

Controleregels voor lijnvormige constructie-elementen IBBC Maart 1987

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

Flambement des poteaux à inertie variable Construction Métallique 1-1981

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

[2] Newmark N.M. A simple approximcolumns

[3]

[4] DIN18800 Teil 2

[5] Rapportnr. BI-87-20/63.4.3360

[7] Y. Galéa

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CALCULATION OF MOMENT FACTORS FOR LTB

UCTION TO THE CALCULATION OF MOMENT FACTORS INTROD

or 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 end 11.

tribution is compared with some standard moment distributions. his 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.

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

CALCULATION MOMENT FACTORS

F

The current moment disT

T

load

Moment distribution generated by q

For EC3, IS800 and CM66 :

if M2

C *

C2 = 0.45 A* [1 + C* e (½ β + ½)] if M2

< 0

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

> 0

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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*

C2 = 0.45 A* [1 + C* eD* (½ β + ½)] if M2 > 0 C1 = 1.12 A* + B* E*

C2 = 0.45A*

with : l+q|M2|8

lq=A2

2*

l+q|M2|8

|M2|8=B2

*

ql

|M2|94=C2

*

)ql

|M2|-72(=D 22

*

for DIN18800 / ONORM 4300 :

β0.77-1.77=E*

for EC3 Code and IS800 :

2.70<E*0.52+1.40-1.88=E* 2ββ

for NEN6770/6771, SIA263 Code : E*=1.75-1.05*β+0.30*β² and E*<2.3 for CM66 :

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2.70<E*0.52+1.40-1.88=E* 2ββ

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loadMoment distribution generated by F

M2 < 0 C1 = A** (2.75 B** + 1) 1.35 + B** (-1.62 A** + 1) E**

C2 = 0.55 A** [1 + C** eD** (½ β + ½)] M2 > 0 C1 = 1.35 A** + B** E**

C2 = 0.55 A**

with : +Fl|M2|4

Fl=A **

+Fl|M2|4Fl=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".

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

C2 = 0.0 f IN1880 RM 4300or D 0 / ONO

β0.77-1.77=1C

for EC3 Code / IS800 :

521.40-1.88 2ββ 2.70<1C and

0.+=1C

for CM66 :

( )22 1152.013=1C

β−β+β+

−

for NEN6770/6771, SIA263 Code :

E*=1.75-1.05*β+0.30*β² and E*<2.3

REFERENCES

[1] Staalconstructies TGB 1990

Stabiliteit NEN 6771 - 1991

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

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PROFILE CONDITIONS FOR CODE CHECK

NTRODUCTION TO PROFILE CHARACTERISTICSI

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 in 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 fabri

0=rolled section (default value) 1=welded section

105 cation code

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2=cold formed section

he fabrication code is not obligatory.

hen the section is made out of 1 plate, the properties marked with (*) can be alculated by the calculation routine in the profile library. When this is not the case,

by the user in the profile library. The plastic moments are calculated with a yield strength of 240 N/mm².

T Wcthese properties have to be input

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DATA DEPENDING IN THE PROFILE SHAPE

I section

mcode 1 For

PSS Type .I. Property Description 49 H 48 B 44 t 47 s 66 R 74 W 140 wm1 61 R1 146 α 109 1

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B

s

w

t

R

R1

a

H

HS

R

Formcode 2 PSS Type .M.

Property Description 49 H 48 B 67 s 66 R

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109 2

B

sH

R

CHS

mcode 3 ForPSS Type O. .R

Property Description 64 D 65 s

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109 3

D

w

Angle section

Formcode 4 PSS Type .L.

Property Description 49 H 48 B 44 t

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61 1 R66 R 74 W1 75 W2 76 W3 109 4

B

R

R1

w1

w2

t

w3

w1

w2

C ctiohannel se n

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Formcode 5 PSS Type .U.

Property Description 49 H 48 B 44 t 47 s 66 R 68 41 61 R1 146 α 109 5

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B

s

H

t

R

R1

a

T section

Formcode 6 PSS Type .T.

Property Description 49 H 48 B 44 t 47 s 66 R 61 R1 62 R2 146 α1

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147 α2 109 6

B

s

t

R

a1

H

a2

R1

R2

Full rectangular section

Formcode 7 PSS Type .B.

Property Description 48 B 67 H

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109 7

B

H

Full circular section

ode 11 FormcPSS Type .RU.

Property Description 64 D

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109 11

D

Asymmetric I section

code 101

FormPSS Type

Property Description 49 H 48 44 47 s 42 Bt

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43 Bb 45 tt 46 tb 66 R 109 101

R

H

Bt

Bb

tt

tb

Z

section

mcode 102

For

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PSS Type .Z. Property Description 49 H 48 B 44 t 47 s 67 R 61 R1 109 102

B

s

t

H

R R1

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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. 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)

) The values for the buckling curves are defined as follows : 1 = buckling curve a 2 = buckling curve b

(1

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3 = buckling curve c 4 = buckling curve d

The conditions are that the section is an open profile. Only the geometry commands O, L etry description.

made out of 1 plate, the properties marked with (*) can be alculated by the calculation routine in the profile library. The properties from the

r tion lated 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.

mcode 110

, N, A may be used in the geom When the section isceduced sec can be calcu

ForPSS Type

Property Description 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

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B

H

e2

s

ld formed angle sectionCo

Formcode 111 PSS Type

Property Description 44 s 61 r 48 B

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68 H 109 111

B

sH

r

Cold formed channel section


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Property Description 44 s 61 r 48 B 49 H 109 112

B

sH

r

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Cold formed Z n sectio

code 113

FormPSS Type

Property Description 44 s 61 r 48 B 49 H 109 113

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B

s

H

R

Figure 1

Cold formed C section


Property Description 44 s 61 r 48 B 49 H 68 c

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109 114

B

sH

r

c

Figure 2

Cold formed Omega section


Property Description 44 s

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61 r 48 B 49 H 42 c 109 115

B

s

H

c

R

Rail type KA

Formcode 150

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PSS Type .KA.

Property Description 148 h1 149 h2 150 h3 151 b1 152 b2 153 b3 154 k 155 f1 156 f2 157 f3 61 r1 62 r2 63 r3 158 r4 159 5 r160 a 109 150

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r1

r2

r4

r3

r5

b3

k

b2

b1

f3f2

f1

h1

h3h2

R ype K

ail t F

Formcode 51 1PSS Type .KF.

Property Description 48 b 154 k 49 h 153 b3 155 f1 157 f3 148 h1

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149 h2 61 r1 62 r2 63 3 r 109 151

r1

r2r2

r2 r2

r3

k

bb3

f3

f1

h

h1 h2

Rail type KQ

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Formcode 152 PSS Type .KQ.

Property Description 48 b 154 k 49 h 153 b3 155 f1 149 h2150 3 h61 r1 109 152

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b

k

b3

r1

h3

h2

f1

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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

3

f

f

τ+τ+τ+τ=τ

σ+σ+σ+σ=σγ

≤τ+σ

γ≤τ

γ≤σ

with

fy the yield strength σtot,Ed the total direct stress

τtot,Ed the total shear stres γM = γM0 (class 1,2 and 3 section)

= γM1 (class 4 section) γM0 the partial safety f tance of cross-sections

where failure is caused by yielding (=1.1) the partial safety where failure is caused by buckling (=1.1)

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

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

Mz,Ed the direct stress due to the bending moment around z axis on the relevant effectiv

σw,Ed the direct stress due to warping on the gross cross-section τVy,Ed the shear stress due ss

s

actor for resis

γM1 factor for resistance of cross-sections

σN,Ed

σe cross-section

to shear force in y direction on the gro

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

cross-section τt,Ed the shear stress du t. Venant) torsion on the

gross cross-section τw,Ed the shear stress due the gross cross-section

The warping effect is considered for standard I sections and U sections, and for Σ (= “cold formed sections”) sections. The def ctions and U sections, and Σ sections are described in "Profile conditions T her standard sections ( RHS, CHS rectangular sections) are considered as warping free. See also Ref.[2], Bild 7.4.40.

C ULATION OF THE DIRECT STRESS DUE TO WARPING

e to uniform (S

to warping on

inition of I se for code check".

he ot , Angle section, T section and

ALC

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

m,w C

MwEd

wM=σ

w the bimoment wM the unit warping Cm the warping constant

I sections

with M

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:

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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 4hb1

⋅⋅=

with b the section width hm the section height (see figure)

U sections

w

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

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

Σ sections

The direct stress

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.

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

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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])

∫=τs

0Mw

m

xs tdstC

M

with the warping torque (see "Standard

warping torque, bimoment on")

I sections

Ed,w

Mxs diagrams for and the St.Venant torsi

wM

the unit warping Cm

t the warping constant the element thickness

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

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For I sections, we have the following :

A4wtbtdsw M

2/b

0∫ M =

⋅⋅=

U sections, Σ sections

Starting from the wM diagram, we calculate the value

f critical points. The shear stres due to warping is calculated in these critical points (see circles in f

∫s

0M tdsw

or thes

igures)

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PLASTIC CHECK

For doubly symmetric I sections of class 1 and class 2 (plastic check), the interaction f la given in Ref.[10] is used. ormu

b

tw

tf

h Hy y

z

z

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Used variables Section Properties A sectional area b width H heigth of section tf flange thickness tw web thickness h = H - tf Aw = 1.05 (h+tf) tw for rolled section Aw = h tw for welded sections

ff tb2A ⋅⋅=

AAf

f =α

fw 1 α−=α

Wz,pl plastic section modulus around z axis

Wy,pl plastic section modulus around y axis

Material Properties fy,d yield strength τy,d shear strength Internal forces NSd normal force My,Sd bending moment around y axis Mz,Sd bending moment around z axis Mw,Sd bimoment Vy,Sd shear force in y direction Vz,Sd shear force in z direction Mxp,Sd torque due to St. Venant Mxs,Sd warping torque

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Plastic capacities Npl,Rd = A fy,d Mz,pl,Rd = Wz,pl fy,d Vz,pl,Rd = Aw τy,d

d,y

2w2

fRd,pl,xp 2t

hbt τ⎟⎟⎠

⎞⎜⎜⎝

⎛+=

M

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

2hMM Rd,pl,zRd,pl,w =

Vy,pl,Rd = Af τy,d

2hVM Rd,pl,yRd,pl,xs =

Rd,pl

Sd

NN

n =

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 =

Rd,pl,z

Sd,zz V

Vv =

Rd,pl,xp

Sd,xpxp M

Mm =

Rd,pl,xs

Sd,xsxs M

Mm =

SCIA 221


Shear force reduction

( )

wwz

2zw

xp2zz

1s5.0for β

12

mv

ρ−>

−β=ρ

+=β

=

( )( )

ffy

2yf

xp2

yxsy

1s5.0for β

12

mvm

ρ−=>

−β=ρ

++=β

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

( )

2s

np1

s4smm

mmmm

1

ww

ww

ffwz

wz

wzs

α−

≤

αα

+⎟⎟⎠

⎞⎜⎜⎝

⎛+−

−=λ

⎟⎟⎠

⎞⎜⎜⎝

⎛α

−λ−αλ=δww

swws snp1s4

Unity checks :

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( )

( )

( )

( ) ( )

( ) ( )1

smp

sm

s2ns21m

and

1s

mpsm

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

≤−+⎭⎬⎫

⎩⎨⎧

α

α−α+±

≤++⎭⎬⎫

⎩⎨⎧

α

α−α+±

α>

≤++

⎪⎪⎭

⎪⎪⎬

⎫

⎪⎪⎩

⎪⎪⎨

⎧

α

δ−α

+α−α+

α≤

m

m

R e values between must be >0.

STANDARD DIAGRAMS FOR WARPING TORQUE, BIMOMENT AND THE

{ }emark : th

ST.VENANT TORSION

The following 6 standard situations are given in the literature (Ref.[2], Ref.[3]). The value λ is defined as follows :

m

t

CEIG

⋅⋅

=λ

with Mx the total torque

= Mxp + Mxs Mxp the torque due to St. Venant

Mxs the warping torque w the bimoment

IT the torsional constant CM the warping constant E the modulus of elasticity

M

SCIA 223


G the shear modulus

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

x M

L

aMLt ⋅

bM t ⋅

M

M

xb

xa

=

=

Mxp for a side ⎟⎟

⎠

⎞⎜⎜⎝

⎛λ

λλ

−⋅= )xcosh()Lsinh()bsinh(

LbMM txp

Mxp for b side ⎟⎟

⎠

⎞⎜⎜⎝

⎛λ

λλ

+−⋅= )'xcosh()Lsinh()asinh(

LaMM txp

Mxs for a side ⎟⎟

⎠

⎞⎜⎜⎛

λλλ

⋅= )xcosh()Lsinh()bsinh(MM txs

⎝

Mxs for b side ⎟⎟

⎠

⎞⎜⎜⎝

⎛λ

λλ

−⋅= )'xcosh()Lsinh()asinh(MM txs

Mw for a side ⎟⎟⎠⎝ λλ )Lsinh(⎞

⎜⎜⎛

λλ

⋅= )xsinh()bsinh(MM tw

Mw for b side ⎟⎟⎠⎝ λλ )Lsinh(⎞

⎜⎜⎛

λλ

⋅= )'xsinh()asinh(MM tw

SCIA 225


Tor Mtsion fixed ends, warping fixed ends, local torsional loading

Mx

LaMM

LbM ⋅M

txb

txa

⋅=

=

Mxp for a

⎟⎠⎞

⎜⎝

⋅= MM txpside⎛ −

λ−+λ 3D

L1k2kb

Mxp foside

r b ⎟⎠

⎜⎝

−λ

⋅= 4DL

MM txp ⎞⎛ −λ− 1ka2k

Mxs foside

r a 3DMM t ⋅= xs

Mxs for b

4DMM txs ⋅= sideMw for a side 1DMM t ⋅= w λ

Mw for b side 2DMM tw ⋅

λ=

SCIA 226


( )

( )

( )

( )

)2Ltanh(2L

)2Ltanh(

2L)b

)2Ltanh(2

sin

2k

)2Ltanh(

2L

)Lsinh()bsinh()asinh(bsin

k

)Lsinh()2k4D

sinh3D

)'xsinh(1k)asinh()x(2k

sinh1D

λλ

−

λ⋅⋅λ

λ+=

λ⋅⋅λ

λ−λ−

+

λ⋅

=

=

λ+λ+λ⋅

)Lsinh(21

)Lsinh( λ−

−−

λsinh()asinh(ba)bsinh()ah(

)2Ltanh(2L)

2Ltanh(2

−λ−λ+λ

λλ

−+

λ

2a1

)Lsinh()bsinh()ah( −

−λ

λ+λ

1 =

'xcosh(1k)asinh()xcosh( λ+λ−λ)Lsinh(

)'xcosh(1k)xcosh(2k)b(λ

λ⋅−λ+λ)Lsinh( λ

sinh2D =

)Lsinh()'xsinh(1k)xsinh(2k)b(

λλ⋅+λ+λ

=

SCIA 227


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

Mx

2LmM

2LmM

txb

txa

⋅=

⋅=

Mxp

⎟⎟⎠

⎞⎜⎜⎝

⎛λ

λ−λ+−λ⋅

λ=

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

2L(mM t

xp

Mxs ⎟⎠

⎜⎝ λλ )Lsinh(

⎟⎞

⎜⎛ λ−λ

−⋅=)'xcosh()xcosh(mM t

xs

Mw ⎟⎟⎠

⎞⎜⎜⎝ λ

−⋅λ )Lsinh(

12⎛ λ+λ sinh()xsinh(mt=

)'xw M

SCIA 228


Torsion fixed ends, war istributed torsional loading mtping fixed ends, d

Mx

2LmM

2LmM

txb

txa

⋅=

⋅=

Mxp

⎟⎟⎠

⎞⎜⎜⎝

⎛λ

λ−λ−+−λ⋅

λ=

)Lsinh()'xcosh()xcosh()k1()x

2L(mM t

xp

Mxs ⎟⎟⎠

⎞⎜⎜⎝

⎛λ

λ−λ−−⋅

λ=

)Lsinh()'xcosh()xcosh()k1(mM t

xs

Mw ⎟⎟⎠

⎞⎜⎜⎝

⎛λ

λ+λ−−⋅

λ=

)Lsinh()'xsinh()xsinh()k1(1mM 2

tw

)2Ltanh(

2L

1kλ

λ

−=

SCIA 229


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

Mx

txa MM =

Mxp

⎟⎟⎠

⎞⎜⎜⎝

⎛λλ

−⋅=)Lcosh()'xcosh(1MM txp

Mxs ⎟⎟⎠

⎞⎜⎜⎝

⎛λλ

⋅=)Lcosh()'xcosh(MM txs

Mw ⎟⎟⎠

⎞⎜⎜⎝

⎛λλ

−⋅λ

=)Lcosh()'xsinh(MM t

w

ne end free, other end torsion and warping fixed, distributed torsional loading mtO

SCIA 230


Mx

Lmt ⋅ M xa =

Mxp

⎟⎟⎠

⎞⎜⎜⎝

+λλ−λ⋅λ

)xcosh(L'xt ⎛mλ

λλλ+=

)Lcosh()xsinh())Lsinh(L1(M xp

Mxs ⎟⎟⎠

⎞⎜⎜⎝

⎛λ

λλλ+−λλ⋅

λ=

)Lcosh()xsinh())Lsinh(L1()xcosh(LmM t

xs

Mw ⎟⎟⎠

⎞⎜⎜⎝

⎛λ

λλλ+−λλ+⋅

λ=

)Lcosh()xcosh())Lsinh(L1()xsinh(L1

²mM t

w

SCIA 231


DECOMPOSITION OF ARBITRARY TORSION LINE

There the EPW 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

he following end conditions are considered :

standard situations. T • 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

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Decomposition for situation 1 and situation 3

The arbitrary total torque line is decomposed into the following standard situations : • 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

rsional loadings Mtn and the distributed loading mt. The value Mt0 is added to the Mxp alue.

Decomposition for situation 2

tov

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

ules – Supplementary rules for cold formed thin heeting

CEN 1996

[1] ENV 1993-1-3:1996

Eurocode 3 : Design of steel structures Part 1-3 : General rgauge members and s

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[2] Stahl im Hochbau 14. Auglage Band I/ Teil 2 Verlag Stahleisen mbH, Düsseldorf 1986

[3] Kaltprofile 3. Auflage Verlag Stahleisen mbH, Düsseldorf 1982

Carl, Lindner Biegetorsionsprobleme gerader dünnwandiger Stäbe Verlag von Wilhem ernst & Sohn, Berlin 1972 D erg K ne und Kranba n Ausführung B . Teubner, Stut

] D t-Richtlinie 01B ssung und konstruktive Gestaltung von Tragwerken aus d wandigen kaltStahlbau-Verlagsgesellschaft, Köln 1992

[7] Esa Prima Win Steel Code Check Manual SCIA EPW 3.10

[8] C. Petersen Stahlbau : Grundlagen der Berechnung und baulichen Ausbildung von Stahlbauten Friedr. Vieweg & Sohn, Braunschweig 1988

Design of steel structures Part 1 - 1 : General rules and rules for buildings ENV 1993-1-1:1992, 1992

[4] Roik,

[5] ietrich von Bra hnen – Berechnung Konstruktio.G tgart 1988

[6 AS 6 emeünn geformten Bauteilen

[9] Eurocode 3

SCIA 234


[10] I. Vayas, Interaktion der plastischen Grenzschnittgrössen doppelsymmetrischer I-Querschnitte Stahlbau 69 (2000), Heft 9

SCIA 235


CHECK OF NUMERICAL SECTIONS

STRESS CHECK

The stress calculation for a numerical section is as follows :

z

zVz

y

yVy

zMz W

=σ zz

x

VzVytot

2tot

2totvm

AV

AV

M

AN

3

=τ

=τ

=σ

τ+τ=τ

τ+σ=σ

with σvm the VonMises stress, the composed stress σtot the total normal stress τtot the total shear stress σN the normal stress due to the normal force N

normal stress due to the bending ent Myy around y axis

σMz the norma stress due to the bending

τVy the shear stress due to shear force Vy in y direction

τVz the shear stress due to shear force Vz in z direction

MzMyNtot σ+σ+σ=σ

N

y

yyMy W

=σ

M

σMy the mom

moment Mzz around z axis

SCIA 236


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 237


USE OF APHRAGMS

ADAPTION OF TORSIONAL CONSTANT

DI

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(IE ⋅3C

100b

C2.1C

125bif100b

C

sEIkC

C1

CC

GlvorhCI

s

sk,P

a100k,A

a

2a

100k,A

effk,M

k,Pk,Ak,M

2

2

tid,t

=

−⋅

≈

⎥⎦⎤

⎢⎣⎡=

≤⎥⎦⎤

⎢⎣⎡=

=

+

π+=

ϑ

ϑ

ϑ

ϑ

ϑϑϑϑ

ϑ

with l the LTB length G the shear modulus vorhCθ the actual rotational stiffness of diaphragm CθM,k the rotational stiffness of the diaphragm CθA,k the rotational stiffness of the connection between the diaphragm

and the beam CθP,k the rotational stiffness due to the distortion of the beam k numerical coefficient

200b125if a <<5 ⋅

I

111+=

vorhC

C

SCIA 238


= 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 h beam height t thickness beam flange s thickness beam web

REFERENCES

SCIA 239



00 (11.90) Werner-Verlag, Düsseldorf

] Beuth-Kommentare Stahlbauten Erläuterungen zu DIN 18 800 Teil 1 bis Teil 4, 1.Auflage Beuth Verlag, Berlin-Köln 1993

[2] E. Kahlmeyer Stahlbau nach DIN 18 8

[3

SCIA 240


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].

R PLASTIC MOMENT CAPACITY DUE TO PLATE BENDINGEDUCTION OF

bu

e1

e2=bo

bo

tu

0.5 q0.5 q

SCIA 241


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 242


( ) ( )

( )

µ−−=λ

γ−=µ

µ−λ−+λµ+µ

−=ψ

ψ=

11

tftqee

b6ee²ee233t²1

AA

uyu

M21

u

2121u

ueff,u

• for SFB beam :

with e1, e2, tu, bu see the figures above q load on flange, plate (as N/m) fy yield strength γM partial safety factor ψ see formula ψu = ψ ψo analog to ψu, but with

bu=bo

e1=bo

tu=to

e2=tw

PLASTIC INTERACTION FORMULA FOR SINGLE BENDING AND SHEAR

oouueff AAA ψ+ψ=

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 :

SCIA 243


SCIA 244

y,pl

fm

Rd,z,pl

Sd,z

m

v

Rd,y,pl

Sd,y

W2hA

0.1VV

AA

MM

=β

≤⎟⎟⎠

⎞⎜⎜⎝

⎛⋅+⎟

⎟⎠

⎞⎜⎜⎝

⎛β

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 ≤⎟⎟⎠

⎞⎜⎜⎝

⎛ −⎟⎟⎠

⎞⎜⎜⎝

⎛ ξ+γ+⎟

⎟⎠

⎞⎜⎜⎝

⎛ ξ+γ

with e1, e2, tu see figures q load on flange, plate (as N/m)

= qmax+qmin


SCIA 245

ξ (Ksi) q

qq minmax −=

fy yield strength γM partial safety factor

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 :


SCIA 246

( )

12tIx

2ee)q,q(M

2t

IM

f

3u

21minmaxx

u

x

xy

M

y2yyx

2x

=

−=

±=σ

γ≤σ+σσ−σ

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

=τ

γ≤τ+σ

Torsion check due to unbalanced loading

• for IFB and SFB beams :


SCIA 247

12bEtEI

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

=

=

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛±=

=τ

⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛

−±=

=τ

γ≤τ+τ

with to, bo see figures hf = h+tu/2-to/2 (see figure) It torsional constant for complete section E modulus of Young G shear modulus L system length for Lyz Q,e see figure


SCIA 248

Q

e

• for THQ beams :

2V

be1

4qL Rd,z,pl

f

≤⎟⎟⎠

⎞⎜⎜⎝

⎛ξ±

with e, bf see figure hf = h+tu/2-to/2 (see figure) q load on flanges, plate (as N/m)

= qmax+qmin ξ (Ksi)

qqq minmax −

=


SCIA 249

q maxq min

bf

ee

REFERENCES

[1] Multi-Storey Buildings in Steel

Design Guide for Slim Floors with Built-in Beams ECCS N° 83 - 1995


SCIA 250

EFFECTIVE CROSS-SECTION PROPERTIES FOR LATTICE TOWER ANGLE MEMBERS

EFFECTIVE CROSS-SECTION PROPERTIES FOR COMPRESSED LATTICE TOWER ANGLE MEMBERS

The 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 :


SCIA 251

bb

f235

43.0KK4.28

tb

eff

y

c

c

pp

p

ρ=

=ε

=

ε

λ=λ

=λ

For rolled angle :

2

p

p

pp

p

98.0213.1

91.02213.191.0

0.191.0

λ=ρ⇒>λ

λ−=ρ⇒≤λ<

=ρ⇒≤λ

For cold formed angle :

2

p

p

p

p

p

98.0213.1

3

404.05

213.1809.0

0.1809.0

λ=ρ⇒>λ

⎟⎟⎠

⎞⎜⎜⎝

⎛ λ−

=ρ⇒≤λ<

=ρ⇒≤λ

with t the thickness b the nominal width fy the yield strength in Mpa

REFERENCES


SCIA 252

[1] EN 50341-1:2001

Overhead electrical lines exceeding AC 45 kV Part 1: General requirements


SCIA 253

SCC_TB_ENU

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