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Lateral Torsional Buckling of I-beams
A Parametric Study of Elastic Critical Moments in Structural
Design Software
Master of Science Thesis in the Master’s Programme Structural Engineering and
Building Technology

MARTIN AHNLÉN
JONAS WESTLUND

Department of Civil and Environmental Engineering
Division of Structural Engineering
Steel and Timber Structures
CHALMERS UNIVERSITY OF TECHNOLOGY
Göteborg, Sweden 2013
Master’s  Thesis  2013:59

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7.2.3 Geometry
Two IPE-beams with different lengths are investigated.

 IPE500, 8 meter
 IPE500, 16 meter



In COLBEAM, LTBeam and SAP2000 the sectional properties are accessed from
databases in the programs. In ADINA the section is defined manually by the  “general
cross-section” command, and the properties   are   taken   from  ArcelorMittal’s product
catalogue (ArcelorMittal 2013).



Table 7.1 Section properties of studied IPE500 beams.

ADINA

(general section)

COLBEAM LTBeam SAP2000

hw [mm] - 468 468 468

hf [mm] - 200 200 200

tf [mm] - 16.0 16.0 16.0

tw [mm] - 10.2 10.2 10.2

r [mm] - 21 21 -

A [mm2] 11600 11550 11552 11600

Iy [mm4] 4.82e8 4.82e8 4.819855e8 4.82e8

Iz [mm4] 2.142e7 2.142e7 2.14169e7 2.142e7

It [mm4] 8.93e5 * 8.901e5 8.91e5

Iw [mm6] 1.249e12 1.25e12 1.254258e12 *

* Calculated implicitly by the program

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7.2.4 Point of load application, PLA
In the study concerning the C1-factor, all loads are assumed to act in the shear centre.
When studying C2, the loads are applied either on top of the upper flange or under the
lower flange. All three points are located on the symmetry line along the z-axis.



SC SC SC


Figure 7.1 Three different PLA used in the study; on top of the upper flange, in

the shear centre and under the lower flange.


7.2.5 Lateral boundary conditions
In the 3-factor formula, the lateral boundary conditions are controlled by the factors kz
(lateral bending) and kw (warping). Since COLBEAM and SAP2000 cannot treat these
degrees of freedom separately, the studies are limited to situations where kz=kw. In
such situations, the factors are just denoted k.
Three different cases of lateral boundary conditions are investigated.

(1) Both ends free, k=1.0
(2) One end free and one end fixed, k=0.7
(3) Both ends fixed, k=0.5



7.2.6 Studied load cases
7.2.6.1 Load Case I - End-moments



M M


Figure 7.2 Load Case I; The beam is subjected to end-moment loading.


7.2.6.2 Load Case II - Simply supported, concentrated load

F

0.5L 0.5L


Figure 7.3 Load Case II; The beam is simply supported about major axis and
subjected to a concentrated load in the mid-span.

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E2.2 Fixed about major axis
E2.2.1 ADINA






E2.2.2 COLBEAM





Concentrated load in mid-span

Length [m] k C_1 M_cr [kNm] C_2
Top 8 1 1,761 216,726 1,463
Bottom 8 1 1,761 1095,447 1,434

Top 8 0,7 1,446 316,138 1,100
Bottom 8 0,7 1,446 1399,695 1,049

Top 8 0,5 1,070 427,761 0,879
Bottom 8 0,5 1,070 1698,676 0,850

Distributed load

Length [m] k C_1 M_cr [kNm] C_2
Top 8 1 2,667 269,626 1,922
Bottom 8 1 2,667 1539,071 1,276

Top 8 0,7 2,286 421,064 1,412
Bottom 8 0,7 2,286 2032,786 0,91

Top 8 0,5 1,762 633,710 1,038
Bottom 8 0,5 1,762 2375,161 0,626

Concentrated load in mid-span

Length [m] k M_cr [kNm] C_2
Top 8 1 117,500 1,565
Bottom 8 1 660,300 1,565

Top 8 0,7 207,700 1,189
Bottom 8 0,7 1049,000 1,189

Top 8 0,5 384,000 0,938
Bottom 8 0,5 1685,000 0,938

Distributed load

Length [m] k M_cr [kNm] C_2
Top 8 1 117,700 1,562
Bottom 8 1 659,500 1,562

Top 8 0,7 229,700 1,016
Bottom 8 0,7 948,900 1,016

Top 8 0,5 470,600 0,652
Bottom 8 0,5 1375,000 0,652

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E2.2.3 LTBeam




Concentrated load in mid-span

Length [m] k C_1 M_cr [kNm] C_2
Top 8 1 1,722 214,980 1,431

Bottom 8 1 1,722 1055,800 1,403

Top 8 0,7 1,420 314,300 1,080
Bottom 8 0,7 1,420 1359,800 1,031

Top 8 0,5 1,054 425,720 0,866
Bottom 8 0,5 1,054 1657,100 0,836

Distributed load

Length [m] k C_1 M_cr [kNm] C_2
Top 8 1 2,607 305,370 1,572

Bottom 8 1 2,607 1698,900 1,536

Top 8 0,7 2,249 476,530 1,155
Bottom 8 0,7 2,249 2279,400 1,128

Top 8 0,5 1,741 721,510 0,829
Bottom 8 0,5 1,741 2687,200 0,810

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