92311182 steel code check theory enu
TRANSCRIPT
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TheorySteel Code Check
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TABLE OF CONTENTS
EC 3 ENV 1993.............................................................................................................2
EC3 code check ...................................................................................................................................................2
Material properties...........................................................................................................................................2
Consulted articles............................................................................................................................................3
Classification of sections ..........................................................................................................................4
Effective cross-section properties for class 4 cross-section ...................................................................5
Section properties.....................................................................................................................................5
Bending moment.......................................................................................................................................5
Bending, shear and axial force.................................................................................................................5Torsion check............................................................................................................................................5
Built-in beams .............. ................ ................. ................ ................. ................. ................ ................. .........6
Compression members ............................................................................................................................6
Lateral-torsional buckling .........................................................................................................................6
Use of diaphragms....................................................................................................................................6
Shear buckling check ...............................................................................................................................7
Shear buckling check for cold formed sections .......................................................................................7
Stability check for torsional buckling and torsional-flexural buckling ......................................................8
Bending and axial compression .............................................................................................................11
Battened compression members ...........................................................................................................11
EC3 - Fire Resistance ................ ................. ................ ................. ................ ................. ............... ................. .....12
Fire actions effect Efi .....................................................................................................................................12
Material properties.........................................................................................................................................13Temperature analysis - Thermal actions ......................................................................................................13
Nominal temperature-time curve ..................................................................................................................13
Net heat flux...................................................................................................................................................14
Steel Temperature.........................................................................................................................................15
Calculation model..........................................................................................................................................16
Code Check ................ ................. ................ ................. ................ ................. ................ ................ ................16
Supported sections ...........................................................................................................................................17
References..........................................................................................................................................................18
EC 3 EN 1993 .............................................................................................................20
EC3 code check .................................................................................................................................................20
Material properties.........................................................................................................................................20Consulted articles ............... ................ ................. ................. ................ ................. ................ ................. .......22
Classification of sections ........................................................................................................................23
Effective cross-section properties for class 4 cross-section .................................................................24
Section properties...................................................................................................................................24
Torsion check..........................................................................................................................................24
Built-in beams .............. ................ ................. ................ ................. ................. ................ ................. .......24
Compression members ..........................................................................................................................24
Lateral-torsional buckling .......................................................................................................................24
Use of diaphragms..................................................................................................................................25
Combined bending and axial compression............................................................................................25
Shear buckling check .............................................................................................................................26
EC3 EN Fire Resistance ............... ............... ................. ................ ................. ................. ................ ................26
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Fire actions effect Efi .....................................................................................................................................26
Material properties.........................................................................................................................................27
Temperature analysis - Thermal actions ......................................................................................................27
Nominal temperature-time curve............................................................................................................27Net heat flux............................................................................................................................................28
Steel Temperature.........................................................................................................................................29
Calculation model..........................................................................................................................................31
Code Check ................ ................. ................ ................. ................ ................. ................ ................ ................31
Supported sections ...........................................................................................................................................31
References..........................................................................................................................................................32
DIN18800.......................................................................................................................34
DIN18800 Code check .......................................................................................................................................34
Material properties.........................................................................................................................................34
Consulted articles ............... ................ ................. ................. ................ ................. ................ ................. .......35
Classification of sections ........................................................................................................................37
Net area properties ............... ............... ................. ................ ................. ................. ................ ................37Plastic interaction formula for RHS section ...........................................................................................38
Plastic interaction formula for CHS section ...........................................................................................40
Torsion check..........................................................................................................................................42
Built-in beams .............. ................ ................. ................ ................. ................. ................ ................. .......42
Calculation of the buckling length ..........................................................................................................42
Torsional buckling...................................................................................................................................42
Use of diaphragms..................................................................................................................................43
LTB Check .............. ................ ................. ................ ................. ............... ................. ................. .............44
Combined flexion for check method 2....................................................................................................48
Battened compression members ...........................................................................................................48
Effective area properties.........................................................................................................................49
Shear buckling check .............................................................................................................................50
Shear buckling check with buckling influence .......................................................................................50Cold formed thin gauge members ................................................................................................................50
Supported sections ...........................................................................................................................................51
References..........................................................................................................................................................52
ONORM B 4300.............................................................................................................54
ONORM B 4300 Code check.............................................................................................................................54
Material properties.........................................................................................................................................54
Consulted articles ............... ................ ................. ................. ................ ................. ................ ................. .......55
Supported sections ...........................................................................................................................................56
References..........................................................................................................................................................56
NEN...............................................................................................................................58
NEN6770/6771 Code check...............................................................................................................................58
Material properties.........................................................................................................................................58
Consulted articles ............... ................ ................. ................. ................ ................. ................ ................. .......58
Section properties...................................................................................................................................61
Classification of sections ........................................................................................................................62
Effective cross-section properties for class 4 cross-section .................................................................62
Torsion check..........................................................................................................................................62
Built-in beams .............. ................ ................. ................ ................. ................. ................ ................. .......62
Buckling length........................................................................................................................................62
Lateral-torsional buckling .......................................................................................................................63
Use of diaphragms..................................................................................................................................63
Battened compression members ...........................................................................................................63
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Shear buckling check .............................................................................................................................65
Shear buckling check with buckling influence .......................................................................................65
NEN6072 - Fire Resistance ...............................................................................................................................65
Fire actions effect ............... ................ ................. ................. ................ ................. ................ ................. .......66Material properties.........................................................................................................................................66
Nominal temperature-time curve ..................................................................................................................67
Steel Temperature.........................................................................................................................................67
Calculation model..........................................................................................................................................70
Code Check ................ ................. ................ ................. ................ ................. ................ ................ ................70
Supported sections ...........................................................................................................................................70
References..........................................................................................................................................................72
AISC ASD : 1989........................................................................................................73
AISC - ASD Code check ............... ................ ................. ................. ............... ................. ................ ................. ..73
Classification of sections...............................................................................................................................75
Section properties .........................................................................................................................................75
Buckling length .............. ................ ................. ................ ................. ............... ................. ................. .............75
Flexural Torsional Buckling ...........................................................................................................................75
Lateral-torsional buckling ..............................................................................................................................75
Shear buckling check ............... ................ ................. ................. ............... ................. ................ ................. ..76
Supported sections ...........................................................................................................................................77
References..........................................................................................................................................................77
AISC LRFD : 2001......................................................................................................79
AISC - LRFD Code check ................ ............... ................. ................. ................ ................. ................ ................79
Classification of sections...............................................................................................................................81
Section properties .........................................................................................................................................81
Buckling length .............. ................ ................. ................ ................. ............... ................. ................. .............81
Lateral-torsional buckling ..............................................................................................................................81Use of diaphragms ................ ................. ................ ................. ................ ................. ............... ................. .....82
Shear buckling check ............... ................ ................. ................. ............... ................. ................ ................. ..82
Supported sections ...........................................................................................................................................82
References..........................................................................................................................................................83
ANSI/AISC 360-05:2005 ................................................................................................84
ANSI/AISC 360-05 Code check.........................................................................................................................84
Classification of sections...............................................................................................................................85
Section properties .........................................................................................................................................86
Buckling length .............. ................ ................. ................ ................. ............... ................. ................. .............86
Lateral-torsional buckling ..............................................................................................................................86
Use of diaphragms ................ ................. ................ ................. ................ ................. ............... ................. .....86
Shear buckling check ............... ................ ................. ................. ............... ................. ................ ................. ..86
Supported sections ...........................................................................................................................................87
References..........................................................................................................................................................87
CM66.............................................................................................................................88
CM66 Code check .............. ................ ................. ................ ................. ............... ................. ................. .............88
Consulted articles ............... ................ ................. ................. ................ ................. ................ ................. .......88
Section properties...................................................................................................................................89
Plastic coefficient ............... ................ ................. ................. ............... ................. ................ ................. ..90
Compression members ..........................................................................................................................90
Factor kf ............... ................ ................. ................. ................ ................. ................ ................. ...............90
LTB Check .............. ................ ................. ................ ................. ............... ................. ................. .............90
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Use of diaphragms..................................................................................................................................90
Combined flexion ............... ................ ................. ................. ............... ................. ................ ................. ..90
Shear buckling check .............................................................................................................................91
Supported sections ...........................................................................................................................................91
References..........................................................................................................................................................91
CM66 - Additif 80..........................................................................................................93
CM66 - Additif 80 Code check ................ ................. ................ ................. ............... ................. ................ ........93
Consulted articles ............... ................ ................. ................. ................ ................. ................ ................. .......93
Classification of sections ........................................................................................................................94
Section check..........................................................................................................................................94
Compression members ..........................................................................................................................94
Lateral-torsional buckling .......................................................................................................................94
Use of diaphragms..................................................................................................................................94
Supported sections ...........................................................................................................................................94
References..........................................................................................................................................................95
BS5950-1:1990..............................................................................................................96
BS5950-1:1990 Code Check .............................................................................................................................96
Material properties.........................................................................................................................................96
Consulted articles ............... ................ ................. ................. ................ ................. ................ ................. .......97
Classification of sections ........................................................................................................................99
Slender cross-section .............................................................................................................................99
Section properties...................................................................................................................................99
Bending moment.....................................................................................................................................99
Bending, shear, axial force.....................................................................................................................99
Lateral torsional buckling..................................................................................................................... 100
Use of diaphragms............................................................................................................................... 101
Compression member ......................................................................................................................... 101
Shear buckling check .......................................................................................................................... 101Supported sections ........................................................................................................................................ 101
References....................................................................................................................................................... 102
BS5950-1:2000............................................................................................................103
BS5950-1:2000 Code Check .......................................................................................................................... 103
Material properties...................................................................................................................................... 103
Governing code clauses............................................................................................................................ 104
Classification of sections ..................................................................................................................... 106
Slender cross-sections ........................................................................................................................ 106
Section properties................................................................................................................................ 106
Moment capacity.................................................................................................................................. 106
Bending, shear, axial force/capacity interaction ................................................................................. 106
Lateral torsional buckling due to major axis moments ....................................................................... 107Torsional buckling about an eccentric axis (Annex G) ....................................................................... 107
Lateral buckling due axial compression.............................................................................................. 107
Combined axial and bending buckling unity check/utilisation ............................................................ 107
Torsion effects ..................................................................................................................................... 108
Supported sections ........................................................................................................................................ 108
SIA263.........................................................................................................................109
SIA263 Code check......................................................................................................................................... 109
Material properties...................................................................................................................................... 109
Consulted articles ....................................................................................................................................... 109
Section classification ........................................................................................................................... 110
Slender cross-section .......................................................................................................................... 111
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Sections properties .............................................................................................................................. 111
Lateral torsional buckling..................................................................................................................... 111
Use of diaphragms............................................................................................................................... 111
Shear buckling ..................................................................................................................................... 111Stability check ...................................................................................................................................... 112
Torsion check....................................................................................................................................... 112
Built-in beams ...................................................................................................................................... 112
SIA263 - Fire Resistance................................................................................................................................ 112
Fire actions effect Efi ................ ................. ................ ................. ............... ................. ................ ................ 112
Material properties...................................................................................................................................... 112
Temperature analysis - Thermal actions ................................................................................................... 113
Nominal temperature-time curve ............................................................................................................... 113
Net heat flux................... ................. ................ ................. ............... ................. ................ ................. .......... 113
Steel Temperature...................................................................................................................................... 113
Calculation model....................................................................................................................................... 114
Code Check ................................................................................................................................................ 115
Supported sections ........................................................................................................................................ 115
References....................................................................................................................................................... 116
GBJ 17-88 ...................................................................................................................117
The GBJ 17-88 code check ............... ................ ................. ................. ................ ................. ................ .......... 117
Material properties...................................................................................................................................... 117
Consulted articles ....................................................................................................................................... 118
Section properties................................................................................................................................ 119
Shear buckling check .......................................................................................................................... 119
Buckling curves.................................................................................................................................... 119
Buckling length..................................................................................................................................... 120
Lateral torsional buckling..................................................................................................................... 120
Local stability of compressed members.............................................................................................. 120
Shear buckling check .......................................................................................................................... 120
Supported sections ........................................................................................................................................ 121
References....................................................................................................................................................... 121
Korean steel code check ...........................................................................................122
The Korean steel code check........................................................................................................................ 122
Material properties...................................................................................................................................... 122
Consulted articles ....................................................................................................................................... 122
Section classification ........................................................................................................................... 123
Section properties................................................................................................................................ 124
Buckling length..................................................................................................................................... 124
Lateral torsional buckling..................................................................................................................... 124
Combined stresses .............................................................................................................................. 125
Shear buckling check .......................................................................................................................... 126
Supported sections ........................................................................................................................................ 126
References....................................................................................................................................................... 127
BSK 99........................................................................................................................128
BSK 99 Code check .............. ................ ................. ............... ................. ................ ................. ................. ....... 128
Consulted articles ....................................................................................................................................... 130
Classification of sections ..................................................................................................................... 130
Effective cross-section properties for class 3 cross-section .............................................................. 131
Section properties................................................................................................................................ 131
Section check....................................................................................................................................... 131
Compression members ....................................................................................................................... 131
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Stability check for torsional buckling and torsional-flexural buckling ................................................. 132
Lateral-torsional buckling .................................................................................................................... 133
Use of diaphragms............................................................................................................................... 134
Shear force ( shear buckling) .............................................................................................................. 134Supported sections ........................................................................................................................................ 135
References....................................................................................................................................................... 136
IS 800..........................................................................................................................137
IS:800 Code check ................ ............... ................. ................. ................ ................. ................ ................. ....... 137
Material properties...................................................................................................................................... 137
Consulted articles ....................................................................................................................................... 137
Classification of sections ..................................................................................................................... 138
Section properties................................................................................................................................ 138
Section check....................................................................................................................................... 139
Compression members ....................................................................................................................... 139
Stability check for torsional buckling and torsional-flexural buckling ................................................. 139
Lateral-torsional buckling .................................................................................................................... 140Use of diaphragms............................................................................................................................... 141
Supported sections ........................................................................................................................................ 141
References....................................................................................................................................................... 142
EAE code check .........................................................................................................143
Material properties...................................................................................................................................... 143
Consulted articles ....................................................................................................................................... 145
Classification of sections ..................................................................................................................... 146
Effective cross-section properties for class 4 cross-section .............................................................. 146
Section properties................................................................................................................................ 147
Torsion check....................................................................................................................................... 147
Built-in beams ...................................................................................................................................... 147
Compression members ....................................................................................................................... 147Lateral-torsional buckling .................................................................................................................... 147
Use of diaphragms............................................................................................................................... 148
Combined bending and axial compression......................................................................................... 148
Shear buckling check .......................................................................................................................... 148
Supported sections ........................................................................................................................................ 149
References....................................................................................................................................................... 149
Calculation of buckling ratio......................................................................................151
Introduction to the calculation of buckling ratio ........................................................................................ 151
Calculation buckling ratio general formula.............................................................................................. 151
Calculation buckling ratios for crossing diagonals................................................................................... 153
Continuous compression diagonal, supported by continuous tension diagonal ...................................... 154
Continuous compression diagonal, supported by pinned tension diagonal............................................. 155Pinned compression diagonal, supported by continuous tension diagonal ............................................. 156
Continuous compression diagonal, supported by continuous compression diagonal ............................. 157
Continuous compression diagonal, supported by pinned compression diagonal.................................... 158
Pinned compression diagonal, supported by continuous compression diagonal .................................... 159
Calculation of critical Euler force for VARH elements .............................................................................. 159
Definitions................................................................................................................................................... 159
Calculation of the critical Euler force ......................................................................................................... 159
Calculation buckling ratio for lattice tower members................................................................................ 162
Leg with symmetrical bracing..................................................................................................................... 163
Leg with intermediate transverse support ................................................................................................. 163
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Leg with staggered bracing........................................................................................................................ 164
Single Bracing ............................................................................................................................................ 164
Single Bracing with SBS (Secondary Bracing System) ............................................................................ 165
Cross bracing ............................................................................................................................................. 165Cross bracing with SBS ............................................................................................................................. 167
K Bracing .................................................................................................................................................... 167
Horizontal Bracing ...................................................................................................................................... 168
Horizontal Bracing with SBS ...................................................................................................................... 168
Discontinuous Cross bracing with horizontal member.............................................................................. 170
References....................................................................................................................................................... 170
Calculation of moment factors for LTB.....................................................................172
Introduction to the calculation of moment factors .................................................................................... 172
Calculation moment factors .......................................................................................................................... 172
Moment distribution generated by q load .................................................................................................. 172
Moment distribution generated by F load .................................................................................................. 174
Moment line with maximum at the start or at the end of the beam........................................................... 175
References....................................................................................................................................................... 175
LTBII: Lateral Torsional Buckling 2nd Order Analysis.............................................176
Introduction to LTBII ...................................................................................................................................... 176
Eigenvalue solution Mcr ................................................................................................................................ 176
2nd
Order analysis .............. ................ ................. ................ ................. ............... ................. ................. .......... 177
Supported National Codes ............................................................................................................................ 178
Supported Sections........................................................................................................................................ 179
Loadings .......................................................................................................................................................... 181
Imperfections................................................................................................................................................... 181
Initial bow imperfection v0 for DIN and ONORM....................................................................................... 182
Initial bow imperfection v0 for EC-EN and EAE ........................................................................................ 182
Initial bow imperfections v0 and w0 for other supported codes................................................................ 183
LTB Restraints................................................................................................................................................. 184
Diaphragms ..................................................................................................................................................... 185
Linked Beams.................................................................................................................................................. 186
Limitations and Warnings.............................................................................................................................. 186
References....................................................................................................................................................... 187
Profile conditions for code check .............................................................................189
Introduction to profile characteristics ......................................................................................................... 189
Data for general section stability check ...................................................................................................... 189
I section............... ................ ................. ................. ................ ................. ............... ................. ................ ..... 190
RHS.......... ................ ................. ................ ................. ................ ................. ............... ................. ................ 190
CHS.......... ................ ................. ................ ................. ................ ................. ............... ................. ................ 191
Angle section .............................................................................................................................................. 192
Channel section.......................................................................................................................................... 193
T section ..................................................................................................................................................... 194
Full rectangular section .............................................................................................................................. 195
Full circular section..................................................................................................................................... 196
Asymmetric I section .................................................................................................................................. 197
Z section ..................................................................................................................................................... 198
General cold formed section ...................................................................................................................... 199
Cold formed angle section ......................................................................................................................... 202
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Cold formed channel section ..................................................................................................................... 203
Cold formed Z section ................................................................................................................................ 204
Cold formed C section................................................................................................................................ 204
Cold formed Omega section ...................................................................................................................... 205Rail type KA ................................................................................................................................................ 206
Rail type KF ................................................................................................................................................ 207
Rail type KQ................................................................................................................................................ 209
Warping check............................................................................................................210
Stress check ............... ................ ................. ............... ................. ................. ................ ................. ................ .. 210
Calculation of the direct stress due to warping ......................................................................................... 211
I sections..................................................................................................................................................... 211
U sections ................................................................................................................................................... 212
sections....................................................................................................................................................... 212
Calculation of the shear stress due to warping.......................................................................................... 213
I sections..................................................................................................................................................... 213
U sections, sections ............................................................................................................................... 214
Plastic Check................................................................................................................................................... 215
Standard diagrams for warping torque, bimoment and the St.Venant torsion ...................................... 219
Torsion fixed ends, warping free ends, local torsional loading Mt............................................................ 219
Torsion fixed ends, warping fixed ends, local torsional loading Mt .......................................................... 221
Torsion fixed ends, warping free ends, distributed torsional loading mt .................................................. 223
Torsion fixed ends, warping fixed ends, distributed torsional loading mt................................................. 224
One end free, other end torsion and warping fixed, local torsional loading Mt ........................................ 225
One end free, other end torsion and warping fixed, distributed torsional loading mt............................... 226
Decomposition of arbitrary torsion line....................................................................................................... 227
Decomposition for situation 1 and situation 3 ........................................................................................... 227
Decomposition for situation 2..................................................................................................................... 228References....................................................................................................................................................... 228
Check of numerical sections .....................................................................................230
Stress check ............... ................ ................. ............... ................. ................. ................ ................. ................ .. 230
Use of diaphragms.....................................................................................................231
Adaptation of torsional constant.................................................................................................................. 231
References....................................................................................................................................................... 232
Section check for built-in beams (IFB, SFB, THQ sections).....................................234
Introduction ..................................................................................................................................................... 234
Reduction of plastic moment capacity due to plate bending ................................................................... 234
Plastic interaction formula for single bending and shear force............................................................... 236
Plastic check for plate in bending................................................................................................................ 237
Stress check for slim floor beams................................................................................................................ 238
Normal stress check................................................................................................................................... 238
Shear stress check in plate........................................................................................................................ 239
Torsion check due to unbalanced loading................................................................................................. 239
References....................................................................................................................................................... 241
Effective cross-section properties for lattice tower angle members.......................242
Effective cross-section properties for compressed lattice tower angle members................................ 242
References....................................................................................................................................................... 243
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SCIA.ESA PT Steel Code Check Theoretical Background
SCIA 1
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SCIA.ESA PT Steel Code Check Theoretical Background
SCIA 2
EC 3 ENV 1993
EC3 code check
The beam elements are checked according to the regulations given in
Eurocode 3
Design of steel structures
Part 1 - 1 : General rules and rules for buildings
ENV 1993-1-1:1992
Material properties
For standard steel grades, the yield strength fy and tensile strength fu are defined according to the thickness ofthe element (see Ref. 1, art.3.2.2.1.)
(fy, fu in N/mm, t in mm)
t
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SCIA.ESA PT Steel Code Check Theoretical Background
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fu the tensile ultimate strength
t the material thickness
Ag the gross cross-sectional area
k is a coefficient depending on the type of forming :
k = 0.7 for cold rolling
k = 0.5 for other methods of forming
n the number of 90 bends in the section
Consulted articles
The cross-section is classified according to Table 5.3.1. (class 1,2,3 or 4). The section is checked for tension (art.5.4.3.), compression (art. 5.4.4.), shear (art. 5.4.6.) and the combination of bending, shear and axial force (art.5.4.9.).
For the stability check, the beam element is checked according to art.5.5.. The following criteria are considered :
for compression : art. 5.5.1.
for lateral torsional buckling : art. 5.5.2.
for bending and axial compression : art. 5.5.4.
The shear buckling resistance is checked using the simple post-critical method from art. 5.6.3.
A more detailed overview for the used articles is given for part 5.3., 5.4., 5.5. and 5.6. in the following table. Thechapters marked with x are consulted. The chapters marked with (*) have a supplementary explanation thefollowing chapters.
5.3. Classification of cross sections
5.3.1. Basis x
5.3.2. Classification x
5.3.3. Cross-section requirements for plastic global analysis
5.3.4. Cross-section requirements when elastic global analysis is used5.3.5. Effective cross-section properties for class 4 cross-section x (*)
5.3.6. Effects of transverse forces on webs
5.4. Resistance of cross-sections
5.4.1. General x
5.4.2. Section properties (*)
5.4.3. Tension x
5.4.4. Compression x
5.4.5. Bending moment x (*)
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SCIA.ESA PT Steel Code Check Theoretical Background
SCIA 5
Effective cross-section properties for class 4 cross-section
The calculation of the effective area is performed with the direct method (sigma_d = fy,k).
For each intermediary section, the classification (and if necessary, the effective area ) is determined and theproper section check is performed. The classification (and effective area) can change for each intermediarypoint. The most critical check is displayed on the screen.
For each load case and combination, the most critical effective area properties are saved :
Aeff is the effective area of the cross section when subject to uniform compression. Weff is the effective sectionmodulus of the cross-section when subject only to moment about the relevant axis. eN is the shift of the relevantcentroidal axis when the cross section is subject to uniform compression.
With these critical properties, the stability check is performed.
For non-prismatic elements, the effective area properties are calculated on each intermediary section, also forthe stability check.
For angle sections, see chapter 'Effective cross-section properties for compressed lattice tower angle members'.
Section properties
5.4.2.2 : The net area properties are only taken into account in the Tension Check in case of lattice tower anglesections with bolted diagonal connections if the LTA functionality has been activated. For more information,reference is made to the Theoretical Background Bolted Diagonal Connections. In all other cases the net areaproperties are not taken into account.
5.4.2.3 : The shear lag effects are neglected .
Bending moment
5.4.5.3 : The holes for fasteners are neglected.
Bending, shear and axial force
The reduced design plastic resistance moment for the interaction of bending, shear and axial force, is taken fromTable 5.17. Ref. 2
Torsion check
For the cross section check inclusive torsion and warping, we refer to Chapter 'Warping check'.
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SCIA.ESA PT Steel Code Check Theoretical Background
SCIA 6
Built-in beams
For built-in beam sections (IFB, SFB, THQ sections), proper section checks are performed, taking into accountthe local plate bending. See Chapter Section check for built-in beams (IFB, SFB, THQ sections)
Compression members
5.5.1.5 For the calculation of the buckling length, we refer to chapter "Calculation of buckling ratio"
The buckling properties for a VARH element are calculated by using the critical Euler force for this member (seechapter Calculation of critical Euler force for VARH elements).
The buckling curves for steel grade S420 and S460 are taken from Ref.[5], Annex D.
Lateral-torsional buckling
For I sections (symmetric and asymmetric), RHS (Rectangular Hollow Section) sections and CHS (CircularHollow Section) sections, the elastic critical moment for LTB Mcr is given by the general formula F.2. Annex FRef. 1. For the calculation of the moment factors C1, C2 and C3 we refer to "Calculation of moment factors forLTB".
For the other supported sections, the elastic critical moment for LTB Mcr is given by
z
2t
z
2z
2
EI
LGI
I
Iw
L
EIMcr
with E the modulus of elasticity
G the shear modulus
L the length of the beam between points which have lateral restraint (= lLTB)
Iw the warping constant
It the torsional constant
Iz the moment of inertia about the minor axis
See also Ref. 3, part 7 and in particular part 7.7. for channel sections.
Haunched sections (I+Ivar, Iw+Plvar, Iw+Iwvar, Iw+Ivar, I+Iwvar) and composed rail sections (Iw+rail, Iwn+rail,I+rail, I+2PL+rail, I+PL+rail, I+2L+rail, I+Ud+rail) are considered as equivalent asymmetric I sections.
For advanced Lateral-torsional buckling analysis, see chapter LTBII: Lateral Torsional Buckling 2nd OrderAnalysis.
Use of diaphragms
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See Chapter 'Adaptation of torsional constant'.
Shear buckling check
Composed rail sections (Iw+rail, Iwn+rail, I+rail, I+2PL+rail, I+PL+rail, I+2L+rail, I+Ud+rail) are considered asequivalent asymmetric I sections.
Shear buckling check for cold formed sections
See Ref.[4] 5.8 :
The shear resistance of the web Vw,Rd shall be taken as the lesser of the shear buckling resistance V b,Rd and theplastic shear resistance Vpl,Rd.
The shear resistance of the web should be checked if:
E
f
t
s346.0
f
f83.0
ybww
_
1M
0M
y
ybw
_
The shear buckling resistance Vb,Rd is given by
1M
bvwRd,b
ftsV
The plastic shear resistance Vpl,Rd is given by
3
ftsV
0M
yw
Rd,pl
withw the relative web slenderness
fyb the basic yield strength
fy the average yield strength
sw the web length
t the web thickness
E the modulus of elasticity
fbv the shear buckling strength
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i
y1
i
l
E
42
1
yiii
l
ECGI
iA
1
),min(
f
0
0
y
y
y,cr
T,cry,crT,cry,crT,cry,crTF,cr
20
2z
2y
20
2T
mt2
0g
T,cr
TF,crT,crcr
A
cr
yb
with A the ratio Aeff/A (see Ref.[1] 5.5)
fyb the basic yield strength
cr the critical stresscr,T the elastic critical stress for torsional buckling
cr,TF the elastic critical stress for torsional-flexural buckling
G the shear modulus
E the modulus of elasticity
IT the torsion constant of the gross section
CM the warping constant
iy the radius of gyration about yy-axis
iz the radius of gyration about zz-axis
lT the buckling length of the member for torsional buckling
y0 the position of the shear center
ly the buckling length for flexural buckling about the yy-axis
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Bending and axial compression
When the torsional buckling and/or the torsional-flexural buckling is governing, the formula (6.12) from Ref.[4],article 6.5.2. is applied.
Battened compression members
The following section pairs are supported as battened compression member :
(1) 2I
(2) 2Uo(3) 2Uc
Two links (battens) are used.
The following additional checks are performed :
- buckling resistance check around weak axis of single chord with N f,Sd
- section check of single chord, using internal forces :
4
aVM
2
VV
NN
s
G
sG
SDf,G
- section check of single batten, using the internal forces :
4
aVM
2h
aVT
s
0
s
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For the calculation of Vs, the value of Ms is increased with the value of the internal force M zz.
l
a
ho
EC3 - Fire Resistance
Fire actions effect Efi
The design effects of actions for the fire situation Efi,d,t are taken from the results of the analysis. It isrecommended to use the accidental combination rules, for calculating the internal forces used in the fireresistance check.
The accidental combination is given by
)f(AQQGdj,kj,21,k1,1kGA
with Gk characteristic values of permanent actions
Qk,1 characteristic value of the (main) variable action
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Qk,j characteristic values of the other variable actions
Af(d) design values of actions from fire exposure
GA partial safety factor for permanent actions in the accidental situation
=[1.0]
1,1 2,j combination coefficients
Material properties
The material properties are depending on the steel temperature.
Strength and deformation properties :
a
,a,E
y
,p,p
y
,y,y
EE
k
f
fk
f
fk
The variation in function of the steel temperature of the value for yield strength ky,, proportional limit kp, andmodulus of elasticity kE, is given by tables in Ref.[6], table 3.1.
For cold formed members ky, is taken from Ref.[7], table III.2.5.
In the simplified calculation method, the following default properties are considered to be constant during theanalysis :
unit mass a 7850 kg/m
thermal elongation l/l 14 x 10-6 (a-20)
thermal conductivity a 45 W/mK
Temperature analysis - Thermal actions
In this part, the nominal temperature-time curves and the related net heat flux are described. See Ref.[8],Section 4, and Ref.[7], II.2.2.
Nominal temperature-time curve
The following temperature-time curves can be selected :
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with t time in [min]
g gas temperature in [C]
c the coefficient of heat transfer by convection
ISO 834 curve
Km/W25
)1t8(log34520
c
10g
external fire curve
Km/W25
20e313.0e687.01660
c
t8.3t32.0
g
hydrocarbon curve
Km/W5020e675.0e325.011080
c
t5.2t167.0
g
smoldering fire curve
20t1544g
during 20 minutes, followed by the standard ISO 834 curve
Net heat flux
r,netr,nc,netc,nd,net hhh
with hnet,d the net heat flux
hnet,c the convective heat flux
hnet,r the radiative heat flux
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n,c factor depending on NAD [1.0]
n,r factor depending on NAD [1.0]
mgcc,neth
4m4
r
8
resr,net 2732731067.5h
with configuration factor [1.0]
res resultant emissivity
= fm
f emissivity related to fire compartment
= [0.800]m emissivity related to surface material
= [0.625]
r = ggas temperature in [C]
m surface temperature of member in [C]
c coefficient of heat transfer by convection
Steel Temperature
The increase of temperature a,t in an unprotected steel member during a time interval t
thc
V/Ad,net
aa
mt,a
with Am the exposed surface area per unit length [m/m]
V the volume of the member per unit length [m/m]
The factor Am/V should not be taken as less than 10m-1
ca the specific heat of steel [J/kgK]
hnet,d the net heat flux per unit area [W/m]
t the time interval [seconds]The value should not be taken as more than 5 seconds
a the unit mass of steel [kg/m]
The increase of temperature a,t in an insulated steel member during a time interval t
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V/Adc
c
1et
31
cd
V/A
pp
aa
pp
t,g
10/t,at,g
aap
pp
t,a
with Ap the area of fire protection material per unit length [m/m]
V the volume of the member per unit length [m/m]
ca the specific heat of steel [J/kgK]
cp the specific heat of fire protection material [J/kgK]
dp the thickness of the fire protection material [m]
t the time interval [seconds]The value should not be taken as more than 30 seconds
a the unit mass of steel [kg/m]
p the unit mass of fire protection [kg/m]
a,t the steel temperature at time t
g,t the ambient gas temperature at time t
g,t the increase of the ambient gas temperature during the time interval
p the thermal conductivity of the fire protection material [W/mK]
The value a,t 0.0
For the increase of temperature a,t in an insulated steel member with intumescent coating, we refer to the NENspecifications, Chapter 'Steel Temperature'.
Calculation model
The calculation can be performed in 2 domains :
- strength domain
- temperature/time domain
In the strength domain, the strength R fi,d,t(unity check) is calculated after a given time t (e.g. strength after 45min). In the temperature/time domain, the critical steel temperature cr,d is computed. From this criticaltemperature, the fire resistance time t fi,d is calculated (the time domain).
Code Check
The section and stability checks (buckling, lateral torsional buckling) are performed according to the regulationsgiven in 'ENV 1993-1-2:1995' and/or 'Model Code on Fire Engineering - ECCS N 111'. The checks areperformed in the resistance domain or in the temperature/time domain..
Torsional buckling and shear buckling are not considered.
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For each member, the classification of the cross section, the section check and the stability check are performed.
The following checks are executed :
EC3-1-2 :
- classification of cross section : art. 4.2.2.
- resistance for tension members : art. 4.2.3.1
- resistance for compression members (class 1,2 or 3) : art. 4.2.3.2.
- resistance for beams (class 1,2) : art. 4.2.3.3.
- resistance for beams (class 3) : art.4.2.3.4.
- resistance for members (class 1,2,3) subject to bending and compression : art. 4.2.3.5.
- critical temperature : art. 4.2.4.
ECCS Model Code on Fire Engineering
- resistance for tension members : art. III.5.2.- resistance for compression members (class 1,2 or 3) : art. III.5.3.
- resistance for beams (class 1,2) : art. III.5.4.
- resistance for beams (class 3) : art. III.5.5.
- resistance for members (class 1,2,3) subject to bending and compression : art. III.5.6.
- resistance for members (class 4) : art. III.5.7.
- critical temperature : art. III.5.8.
Supported sections
I Symmetric I shapes (IPE, HEA, HEB, .)
RHS Rectangular Hollow Section
CHS Circular Hollow Section
L Angle section
U Channel section
T T section
PPL Asymmetric I shapes
Z Z section
RS Rectangular section
Cold formed sectionCOM Composed section in PRIMAW IN
O Solid tube
NUM Numerical section
The necessary data conditions for these sections are described in chapter "Profile conditions for code check
".
The COM and NUM sections are not read out of the profile library.
I RHS CHS L U T PPL RS Z O COM NUM
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Classification x x x x x x x x (1) x (1) (1) (1)
Section check class 1 x x x
Section check class 2 x x xSection check class 3 x x x x x x x x x x x x x
Section check class 4 x x x x x x
Stability check class1
x x x
Stability check class2
x x x
Stability check class3
x x x x x x x x x x x x x
Stability check class4
x x x x x x
Shear buckling check x x x x
(1) sections are classified as class 3 cross section by default.
References
1 Eurocode 3Design of steel structures
Part 1 - 1 : General rules and rules for buildings
ENV 1993-1-1:1992, 1992
2 Essentials of Eurocode 3Design Manual for Steel Structures in Building
ECCS - N 65, 1991
3 R. MaquoiELEMENTS DE CONSTRUCTIONS METALLIQUE
Ulg , Facult des Sciences Appliques, 1988
[4] ENV 1993-1-3:1996
Eurocode 3 : Design of steel structures
Part 1-3 : General rules
Supplementary rules for cold formed thin gauge members and sheeting
CEN 1996
[5] Eurocode 3
Design of steel structures
Part 1 - 1/ A1 : General rules and rules for buildings
ENV 1993-1-1:1992/A1, 1994
[6] Eurocode 3
Design of steel structures
Part 1 - 2 : General rules - Structural fire design
ENV 1993-1-2:1995, 1995
[7] Model Code on Fire Engineering
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ECCS - N 111
May 2001
[8] Eurocode 1Basis of design and actions on structures
Part 2-2 : Actions on structures - Actions on structures exposed to fire
ENV 1991-2-2:1995
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EC 3 EN 1993
EC3 code check
The beam elements are checked according to the regulations given in
Eurocode 3
Design of steel structures
Part 1 - 1 : General rules and rules for buildings
EN 1993-1-1:2005
Material properties
For standard steel grades, the yield strength fy and tensile strength fu are defined according to the thickness ofthe element (see Ref. 1, table 3.1.)
Steel Grade fy(N/mm)
fu(N/mm)
S 235 235 360
S 275 275 430
S 355 355 510
S 275 N/NL 275 390
S 355 N/NL 355 490
S 420 N/NL 420 540
S 460 N/NL 460 570
S 275 M/ML 275 380
S 355 M/ML 355 470
S 420 M/ML 420 520
S 460 M/ML 460 550
S 460 Q/QL/QL1 460 570
S 235 W 235 360
S 355 W 355 510S 235 H 235 360
S 275 H 275 430
S 355 H 355 510
S 275 NH/NLH 275 370
S 355 NH/NLH 355 470
S 460 NH/NLH 460 550
S 275 MH/MLH 275 360
S 355 MH/MLH 355 470
S 420 MH/MLH 420 500
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S 460 MH/MLH 460 530Table 1
The name of the steel grade (e.g. 'S 355 W') is used to identify the steel grade.
Remark : For cold formed section, the values for fy and fu are not influenced by the previous table
Remark : For cold formed sections, the average yield strength fya can be used (by setting the proper data flag inthe Cross Section input dialog).
The average yield strength is determined as follows :
ybuybug
ybya f2.1,fminffA
kntff
with f yb the tensile yield strength = fy
fu the tensile ultimate strength
t the material thickness
Ag the gross cross-sectional area
k is a coefficient depending on the type of forming :
k = 0.7 for cold rolling
k = 0.5 for other methods of forming
n the number of 90 bends in the section
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Consulted articles
The beam elements are checked according to the regulations given in "Eurocode 3: Design of steel structures -Part 1-1: General rules and rules for buildings - EN 1993-1-1:2005".
The cross-sections are classified according to Table 5.2. All classes of cross-sections are included. For class 4sections (slender sections) the effective section is calculated in each intermediary point, according to prEN 1993-1-5:2003, Chapter 4.4 .
The stress check is taken from art. 6.2.: the section is checked for tension (art. 6.2.3.), compression (art. 6.2.4.),bending (art. 6.2.5.), shear (art. 6.2.6.), torsion (art.6.2.7.) and combined bending, shear and axial force (art.6.2.8., art.6.2.9. and art.6.2.10.).
The stability check is taken from art. 6.3.: the beam element is checked for buckling (art. 6.3.1.), lateral torsionalbuckling (art. 6.3.2.), and combined bending and axial compression (art. 6.3.3.).
The shear buckling is checked according to prEN 1993-1-5:2003, Chapter 5.
For I sections, U sections and cold formed sections warping can be considered.
A check for critical slenderness and torsion moment is also included.
For integrated beams, the local plate bending is taken into account for the plastic moment capacity and thebending stresses in the section. The out-of-balance loading is checked.
A more detailed overview for the used articles is given in the following table. The chapters marked with x areconsulted. The chapters marked with (*) have a supplementary explanation the following chapters.
EN 1993-1-1
5.5 Classification of cross section (
*)
5.5.1. Basis x
5.5.2. Classification x
6. Ultimate limit states
6.1. General x
6.2. Resistance of cross-sections
6.2.1 General x
6.2.2 Section properties x(*)
6.2.3 Tension x
6.2.4 Compression x
6.2.5 Bending moment x
6.2.6 Shear x
6.2.7 Torsion x(*)
6.2.8 Bending and shear x
6.2.9 Bending and axial force x
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6.2.10 Bending, shear and axial force x
6.3. Buckling resistance of members
6.3.1 Uniform members in compression
x(*)
6.3.2 Uniform members in bending x
6.3.3 Uniform members in bending and axial compression x(*)
Annex A:Method 1:Interaction factors kij for interaction formula in 6.3.3.(4) x
Annex B:Method 2:Interaction factors kij for interaction formula in 6.3.3.(4) x
prEN 1993-1-3
6.1.2. Axial tension
6.1.3. Axial compression
6.1.5. Shear force
6.1.6. Torsional moment
prEN 1993-1-5
4.4. Plate elements without longitudinal stiffeners
5. Resistance to shear
5.1. Basis
5.2. Design resistance
5.3. Contribution from webs
5.4. Contribution from flanges
5.5. Verification
7.1. Interaction between shear force, bending moment and axial force
Classification of sections
For each intermediary section, the classification is determined and the proper section check is performed. Theclassification can change for each intermediary point.
For each load case/combination, the critical section classification over the member is used to perform thestability check. So, the stability section classification can change for each load case/combination.
However, for non-prismatic sections, the stability section classification is determined for each intermediarysection.
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Effective cross-section properties for class 4 cross-section
The calculation of the effective area is performed with the direct method (sigma_d = fy,k).
For each intermediary section, the classification (and if necessary, the effective area ) is determined and theproper section check is performed. The classification (and effective area) can change for each intermediarypoint. The most critical check is displayed on the screen.
For each load case and combination, the most critical effective area properties are saved :
Aeff is the effective area of the cross section when subject to uniform compression. Weff is the effective sectionmodulus of the cross-section when subject only to moment about the relevant axis. e