Verification Manual - StabLab.pdf

8/9/2019 Verification Manual - StabLab.pdf

http://slidepdf.com/reader/full/verification-manual-stablabpdf 1/50

Verification Manual



2

Content

1 Theoretical background ...........................................................................................................3

2 Stress analysis ..........................................................................................................................3

2.1 Geometrically linear (first order) theory .......................................................................... 4

WE-01 Compressed member ......................................................................................... 4

WE-02 Member subjected to bending ........................................................................... 6

WE-03 Member in torsion (concentrated twist moment) .............................................. 9

WE-04 Member in torsion (torsion by transverse concentrated load on mono-

symmetric I section) ..................................................................................................... 14

2.2 Geometrically nonlinear (second order) theory ............................................................. 19

WE-05 Member subjected to bending and compression ............................................. 19

WE-06 Member subjected to biaxial bending and compression ................................. 22

3 Stability analysis ....................................................................................................................26

WE-07 Lateral torsional buckling (double symmetric section & constant bending

moment) ........................................................................................................................... 26

WE-08 Lateral torsional buckling (double symmetric section & triangular bending

moment distribution) ........................................................................................................ 28

WE-09 Lateral torsional buckling (mono-symmetric section & constant moment) ....... 30

WE-10 Lateral torsional buckling (mono-symmetric section & triangular moment

distribution) ...................................................................................................................... 34

WE-11 Lateral torsional buckling (C section & equal end moments) ............................. 38

WE-12 Lateral torsional buckling (C section & equal end moments) ............................. 41

WE-13 Flexural-torsional buckling (U section) .............................................................. 44

WE-14 Interaction of flexural buckling and LTB (symmetric I section & equal end

moments and compressive force)..................................................................................... 48



3

1 Theoretical background

The StabLab software uses the 14 degrees of freedom general thin-walled beam-columnfinite element (referred as Beam7 ) publ ished by Rajasekaran in the fo l lowing textbook:

CHEN, W.F. ATSUTA, T.: Theory of Beam-Columns: Space behavior and

design , Vol .2 McGraw-Hil l , 1977, pp . 539 -564

Later more researchers used and developed this element, for example:

PAPP, F.: Computer aided design of steel beam-column structures, Doctoral

thesis , Budapest Universi ty of Technology & Herio t -Wat t Universi ty of

Edinburgh, 1994-1996

The general beam-column finite element takes the effect of warping into consideration;

therefore i t is reasonable to use i t in both of the geometrically nonlinear stress analysis

and the e last ic s tabi l i ty ana lysis of spa t ia l s tee l s t ruc tures .

The verification of this analysis model is presented by comparisons with two types ofindependent resul ts :

Calculation by hand – where analytical solution is available

Calculation by triangular shell f inite element (referred as Shell3 ) – an equivalent

model is created where the plate elements of the beam member are modeled bytriangular shell f inite elements, the analysis is performed by the ConSteel software

(www.constee lsof tware .com)

2 Stress analysis

The stress analysis (computation of deflections, internal forces and reactions) of simple

structural members are verified by

Geometr ica l ly l inear ( f i rs t order) theory

Geometrica l ly non- l inear (second order) theory



4

2.1 Geometrically linear (first order) theory

The analysis of simple structural members using the StabLab software (based on the

Beam7 f ini te element) are checked in the following Worked Examples (WE-01 to WE-

04) .

WE-01 Compressed member

Figure 1 shows a compressed member. The displacement of the end of themember and the compressive stress are calculated by hand, by Shell3 element and by the StabLab software.

A) Calculat ion by hand

Sectional area A 11250 m m2

Grade of material S235

E 2 10 000 N

mm2

Length of member L 4000 m m

Compressive force Fx

1000 kN

Compressive stress x

Fx

A88.889

N

mm2

End moving ex

x

L

E 1.693 mm

F ig .1 Stress analysis of compressed member



5

B) Computation by Shel l3 e lement

F i g.2 Axial deflection of the compressed member – Shell3

C) Computation by StabLab

F i g.3 Axial deflection of the compressed member- Beam7

Evaluation

Table 1 shows the axial displacement of the free end of the simply supported

compressed member calculated by hand and computed by Shell3 element and by

the StabLab software . The resul ts a re accura te.

Tab.1 Stress analysis of compressed member

section property theory1 StabLab

Beam72 1 /2 Shell3

3 1 /3

HEA300

L=4000mme x [mm] 1,693 1,684 1 ,005 1,717 0 ,986



6

WE-02 Member subjected to bending

Figure 4 shows a structural member which is loaded by uniformlydistributed load. The vertical displacement of the middle cross-section and themaximum bending moment of the member are calculated by hand, by Shell3

element and by the StabLab software.


Section : welded symmetric I section

flange b 200 mm tf 1 2 m m

web hw 400 mm tw 8 mm

Elastic modulus E 210000 N

mm2

Length of member L 8000 m m

Load p 30 kN

m

Inertia moment Iy 2 b tf

hw

2

tf

2

2

tw

hw3

12 246359467 mm

4

Maximum deflection ez.max5

384

p L4

E Iy 30.927 mm

Maximum bending moment My.max p L

2

8240 kN m

F i g.4 Structural member loaded by uniformly distributed load in the

vertical plane (welded I section with 200- 12 f lange and 400-8 web)



7


Figure 5 shows the deflections of the member with the numerical value ofthe maximum deflection (self-weight is neglected).

F i g.5 Deflections of the member subjected to bending (with δ=50mm FE size)


Figure 6 shows the deflections of the member with the numerical value of

the maximum deflection. Figure 7 shows the bending diagram with themaximum bending moment at the middle cross-section (self-weight isneglected).

F i g.6 Deflections of the member subjected to bending (with n=16 FE)



8

F i g.7 Bending moment diagram of the member subjected to bending

Evaluation

Table 2 shows the maximum value of the vert ical deflections calculated by hand

and computed by Shel l3 e lement and by the StabLab software. The results are

accurate .

Tab.2 Stress analys is of member subjected to bending

section property theory1

StabLab Shel l33

Beam72

n result 1 /2 δ result 1 /3

Welded I

200-10 ;

400-8

ez .m a x [mm] 30.927

4 29,373 1 ,053 100 31,200 0 ,991

6*

30,232 1 ,023 50 31,3760 ,986

8 30,533 1 ,013 25 31,4270 ,984

16 30,823 1 ,003

My .m a x [kNm] 2404 240

1 ,0006* 240

8 240

16 240

*) given by the automatic mesh generation (default)

Notes

In the table n denotes the number of the finite element in the Beam7 model,δ denotes the size of the finite ele ments in [mm] in the Shell3 model.

The distributed load on the Beam7 model is concentrated into the FE nodes,therefore the deflections depend on the number of the fi nite elements.

The Shell3 model involves the effect of the shear deformation, therefore itshows larger deflections.



9

WE-03 Member in torsion (concentrated twist moment)

Figure 8 shows a simple fork supported structural member which is loaded by a concentrated twist mome nt at the mi ddle cross -s ection. The me mber wasanalysed by hand, by Shell3 element and by the StabLab software.


Section: Welded symm etric I section


web hw 300 mm tw 1 0 m m

Sectional properties (by GSS m odel) It1

32 b tf

3 hw tw3 919200 mm

4

hs hw tf 316 mm

Iz 2 t f b

3

12 72000000 mm

4

I Iz

hs2

4 1797408000000mm

6

h hw 2 t f 332 mm

Elastic m odulus E 210000 N

mm2

G E

2 1 0.3( ) 80769

N

mm2

Parameter G ItE I

0.4441

m

Concentrated torsional mom ent Mx 2 5 kN m

Member length L 4000 m m

Cross-secti on positi on L2L

22000 mm

Parameters z L

22000 mm

z0 0 mm

Rotation* max

Mx

2

E I

L2

Lz

sinh L2 sinh L( )

sinh z( )

0.067 rad

max.deg max 3.852 deg

F i g.8 Simple fork supported structural member loaded by

concentrated twist moment at the middle cross-section



10


Figure 9 shows the deformation of the member with the numerical value ofthe maximum rotation (self-weight is neglected). Figure 10 shows the axialstress distribution in the middle cross-section.

F ig .9 Maximum rotation of the middle cross -section

Bimoment* B Mx

sinh L2 sinh L( )

sinh z( ) 20.009kN m2

Torsinal moment* Mt Mx

L2

L

sinh L2 sinh L( )

cosh z0

3.696kN m

M Mx

sinh L2 sinh L( )

cosh z0 8.804kN m

Check equilibrium Mx.int Mt M 12.5kN m

Warping stress ef h

2

tf

2 158 mm

max ef b

2 23700 mm

2

x.maxB

Imax 263.8 N

mm2

*) Csellár, Halász, Réti: Thin-walled steel struc tures, Muszaki Könv kiadó 1965, Budapest ,

Hungary , pp. 129-131 (in hungarian)



11

F i g.10 Axial stress distribution in the middle cross -section (with 25mm FE)


Figure 11 shows the deflections of the member with the numerical value of

the maximum rotation (self-weight is neglected). Figure 12 shows the bimo me nt diagram with the ma ximu m bimo me nt at the mi ddle cross -section. Figure 13 shows the warping normal stress in the middle cross-section.

F i g.11 Rotation of the member due to concentrated twist moment





13

Notes

In the table n denotes the number of finite element in the Beam7 model, δ denotes the size of the finit e elements in [mm] in the Shell3 model.A stiffener was applied in the shell model at mid-span in order to avoid anylocal deformation due to the introduction of the concentrated twist.



14

WE-04 Member in torsion (torsion by transverse concentrated load on mono-

symmetric I section)

Figure 14 shows a simple fork supported member with mono-symmetricwelded I section which is loaded by a concentrated transverse force in the centroidof the middle cross-section. The member was analysed by hand, by Shell3 elementand by the StabLab software.


Section : Welded monsymmetric I section

top flange b1 200 mm tf1 12 m m


bottom flange b2 100 mm tf2 12 m m

Sectional properties Iz1 tf1

b13

12 8000000 mm

4 Iz2 tf2

b23

12 1000000 mm

4

Iz Iz1 Iz2 9000000 mm4

It1

3 b1 tf1

3 b2 tf2

3 hw tw

3 241067 mm

4

f

I

z1Iz1 Iz2

0.889 hs hw

t

f12

t

f22 412 mm

I f 1 f Iz hs2

1.5088 1011

mm6

ZS 248.4 mm (by GSS model of ConSteel)

zD 123.4 mm (by GSS model of ConSteel)

Elastic modul us E 210000 N

mm2

G E

2 1 0.3( ) 80769

N

mm2

Parameter G It

E I 0.784

1

m


Transverse force Fy 10 kN

F i g.14 Simple fork supported member with mono-symmetricwelded I section loaded by concentrated transverse force in the

centroid



15

Torsional moment Mx Fy zD 1.234kN m

Cross-secti on positi on L2

L

23000 mm

z L

23000 mm z0 0 mm

Rotation* max

Mx

2

E I

L2

Lz

sinh L2 sinh L( )

sinh z( )

3.172 deg

Bimoment* B Mx

sinh L2 sinh L( )

sinh z( ) 0.773kN m2

Torsinal moment* Mt Mx

L2

L

sinh L2 sinh L( )

cosh z0

0.501kN m

M Mx

sinh L2 sinh L( )

cosh z0 0.116kN m

Check equilibrium Mx.int Mt M 0.617kN m

Warping stress 2 18311 mm2

(by GSS model of ConSteel)

.2B

I2 93.8

N

mm2

Bending moment Mz FyL

4 15 k N m

Bending stress Mz2

Mz

Iz

b2

2 83.33

N

mm2

Axial stress in bottom flange x2

.2

Mz2

177.14 N

mm2

*) Csellár, Halász, R éti: Thin-walled s teel struc tures, Muszaki Könv kiadó 1965, Budapest,

Hungary, pp. 129-131 (in Hungarian)



16


Figure 15 shows the deformation of the member with the numerical value ofthe maximum rotation (self-weight is neglected).

F i g.15 Maximum rotat ion of the middle cross -section


Figure 16 shows the deformed member with the numerical value of themaximum rotation (self-weight is neglected). Figure 17 shows the bimomentdiagram with the maximum bimoment at the middle cross-section. Figure 18

shows the warping normal stress in the middle cross-section.

F i g.16 Rotation of the member due to concentrated transverse force in thecentroid of the middle cross-section (n=16)



17

F i g.17 Bimoment of the member (n=16)

F i g.18 Warping normal stress in the middle cross-section (n=16)







20


B) Computation by StabLab

Figure 20 shows the second order bending moment di agram of themember which was computed by the StabLab software using the Beam7 finite element model.

F i g.20 Bending moment diagram of the member (n=16)

Section:IPE 360

Sectional properties (ProfilARBED) A 7273 mm2

Iz 10430000 mm4


mm2

L 8000 m mLength of member

Distributed load intensity p 1 kN

m

Compressive force Fx 200 kN

Crirical foce F

cr.x

2

E Iz

L2

337.8 kN

Bending moment by first order theory Mz1 p L

2

88 kN m

Moment amplifier factor 1

1Fx

Fcr.x

2.452

Bending moment by second order theory Mz2 M z1 19.61kN m

Maximum compressive stress ymax 85 m m

c.max

Fx

A

Mz2

Iz ymax 187.3

N

mm2





22

WE-06 Member subjected to biaxial bending and compression

Figure 21 shows a simple fork supported member with IPE360 equivalentwelded section (flange: 170-12,7; web: 347-8) subjected to biaxial bending aboutthe minor axis due to concentrated end moments and to compressive force.

Deflections of middle cross-section of the member are calculated by hand, byShell3 model and by the StabLab software using Beam7 model.

F i g.21 Simple fork supported member with IPE360 section

subjected to biaxial bending and compression



23

A) Calculat ion by hand (using approximated method)

*) Chen, W. and Atsuta, T.: Theory of Beam-Columns, Vol. 2: Space

behavior and design, McGRAW -HILL 1977, p . 192

Section:IPE360 equivalent welded I section

Sectional properties (by EPS model ) A 6995 m m2

Iy 155238000 mm4

Iz 10413000 mm4

It 291855 mm4

I 313000000000 mm6

r 0

Iy

A

Iz

A 153. 887mm


mm2

G E

2 1 0.3( ) 80769

N

mm2

L 8000 m mLength of member

P 100 kNCompressive force

My 4 5 k N m Mz 7.5 kN mEnd

moments

Critical axial forces Pcr.y

2

E Iy

L2

5027 kN

Pcr.z

2

E Iz

L2

337.2 kN

Pcr.1

r 02

2

E I

L2

G It

1423.5 kN

Displacements*

C

2

8

My Mz

Pcr.y Pcr.z P

Pcr.y

Pcr.z P

Pcr.z

Pcr.y P

4

Pcr.z Pcr.y

P

My2

Pcr.z P

Mz2

Pcr.y P r 0

2Pcr. P

0.087

umax1

Pcr.z P

2

8Mz C My

55.53 mm

vmax1

Pcr.y P

2

8My C Mx

11.25mm

max C 4.991 deg



24


Figure 22 shows the second order deflection of t he member which was

computed by Shell3 finite element model.

F i g.22 Deformation of the member by Shell3 FE model ( δ=43mm)


Figure 23 shows the second order deflection of t he member which wascomputed by the StabLab software using the Beam7 finite element model.

F i g.23 Deformation of the member by Beam7 FE model (n=16)



25

Evaluation

Table 6 shows the second order bending moment and the maximum axial

compressive stress value of the middle cross-section calculated by approximatedtheory and computed by Shell3 e lement and by the StabLab software. The accuracyof the approximated hand calculation is a bit pure, but the StabLab results of

Beam7 model comparing with the Shell3 model are accurate .

Tab.6 Second order stress analysis of member in bending and compression

sect ion displacement theory

(approximati

on)

StabLab

Beam7 Shel l3

n result δ result

IPE360equivalent

welded I

section

170-12,7

347-8

ey .m a x [mm] 55,53

2 53,00 43 51,174 53,38 25 53,03

6* 53,46

009,1)25(3

)16(7

Shell

n Beam

16 53,50

e z .m a x [mm] 11,25

2 11,10 43 10,81

4 11,10 25 10,83

6* 11,10 025 ,1

)25( csShell

)16 n( csBeam

16 11,10

φ .m a x [deg] 4,991

2 4,172 43 4,2874 4,216 25 4,433

6* 4,229 956,0

)25(3

)16(7

Shell

n Beam 16 4,239


Notes

In the Table 6 n denotes the number of the finite elements of the Beam7 model, δ denotes the maximum size of the shell finite elements of the Shell3 model in [mm].



26

3 Stability analysis

The s tabi l i ty ana lysis of s imple s t ruc tura l members using the StabLab sof tware based on

the Beam7 f ini te element models are checked by hand calculation and optionally by the

Shell3 f ini te element models in the following Worked Examples (WE-07 to WE-12 ) .

WE-07 Lateral torsional buckling (double symmetric section & constant

bending moment)

Figure 24 shows a simple fork supported member with welded section(flange: 200-12; web: 400-8) subjected to bending about the major axis due toconcentrated end moments. Critical moment of the member is calculated by

hand and by the StabLab software using the Beam7 model.


Section : welded symmetric I section



Sectional properties Iz 2 tf b

3

12 16000000 mm4

It1

32 b tf

3 hw tw

3 298667 mm

4

I

tf b3

24hw tf

2 678976000000 mm

6


mm2

G E

2 1 0.3( ) 80769

N

mm2


Critical moment Mcr

2

E Iz

L2

I

Iz

L2

G It

2 E Iz

241.31kN m

F ig .24 Simple fork supported member subjected to bending aboutthe major axis (LTB)



27


Figure 25 shows the member subjected to lateral torsional bucklingwhich was computed by the StabLab software using the Beam7 f initeelement model.

F i g.25 LTB of simple supported structural member (n=16)

Evaluation

Table 7 shows the cri t ical moment for la teral torsional buckling of the member

which calculated by hand and computed by the StabLab software using the Beam7

model. The result is accurate .

Tab.7 Stability analysis of member in bending (LTB, L=6000mm)

section critical force theory1

Beam72

n result 1 /2

Welded I200-12 ; 400-

8

Mc r [kNm] 241,31

2 243,24 0 ,992

4 241,87 0 ,998

6* 241,79 0 ,998

16 241,77 0 ,998


Note

In the Table 7 n denotes the number of the finite elements of the Beam7 model.



28

WE-08 Lateral torsional buckling (double symmetric section & triangular

bending moment distribution)Figure 26 shows a simple fork supported member with welded section

(flange: 200-12; web: 400-8) subjected to transverse force at middle cross sectionin the main plane of the member. The critical force is calculated by hand and bythe StabLab software using Beam7 model.


Section: welded symmetric I section

flange b 200 mm tf 1 2 mm


Sectional properties Iz 2 tf b

3

12 16000000 mm

4

It1

32 b tf

3 hw tw

3 298667 mm

4

I

tf b3

24hw tf 2

678976000000 mm6


mm2

G E

2 1 0.3( ) 80769

N

mm2


Critical force C1 1.365

Mcr C1

2

E Iz

L2

I

Iz

L2

G It

2

E Iz

329.387kN m

Fcr 4

Mcr

L 219.6 kN

F i g.26 Simple fork supported member subjected to transverse force (LTB)



29


Figure 27 shows the LTB of the member subjected to t ransverse force.The critical force is computed by the St abLab software using Beam7 finite element model.

F i g.27 LTB of simple supported structural member subjected to

transverse force (n=16)

Evaluation

Table 8 shows the cri t ical force for la teral torsional buckling of the member which

calculated by hand and computed by the StabLab software using Beam7 model.

The result is accurate .

Tab.8 Stability analysis of member in Bending (LTB, L=6000mm)


Beam72

n result 1 /2

Welded I200-12 ; 400-

8

Pc r [kN] 219,6

2 220,90 ,994

4 219,90 ,999

6* 219,71 ,000

16 219,71 ,000


Note

In the Table 8 n denotes the number of the finite elements of the Beam7

model.



30

WE-09 Lateral torsional buckling (mono-symmetric section & constant

moment)Figure 28 shows a simple fork supported member with welded mono-

symmetric I section (flange: 200-12 and 10 0-12; web: 400-8) subjected to equal endmoments. The critical moment is calculated by hand, by Shell3 finite element and by the StabLab software using Beam7 finite element.

F ig .28 Simple fork supported member with mono-symmetric I section subjected to equal end moments (LTB)



31


Section: welded mono-symmetric I section

top flange b1 200 mm tf1 1 2 m mweb hw 400 mm tw 8 mm

bottom flange b2 100 mm tf2 1 2 m m

Sectional properties ZS 248.4 mm (by GSS model of

ConSteel)

zD 123.4 mm (by GSS model of

ConSteel)

Iz1 tf1

b13

12 8000000 mm

4 Iz2 tf2

b23

12 1000000 mm

4

Iz Iz1 Iz2 9000000 mm4

Iy 186493000 mm4 (by GSS model of

ConSteel)

It1

3 b1 tf1

3 b2 tf2

3 hw tw

3 241067 mm

4

f

Iz1

Iz1 Iz2 0.889

hs hw

tf1

2

tf2

2 412 mm

I f 1 f Iz hs2

150883555556 mm6

e hw tf2tf1

2

ZS 169.6 mm

A1 b1 tf1 2400 mm2

A2 b2 tf2 1200 mm2

qx1

Iy

zD Iz1 A1 e3

A2 hs e 3

tw

4e

4hs e

4

51.725 mm

z j zD 0.5qx 149.262 mm


mm2

G E

2 1 0.3( ) 80769

N

mm2


Critical moment Mcr

2

E I

z

L2

I

Iz

L2

G I

t

2

E Iz z j2 z j

220.77kN m



32

B) Computation by Shell3 element

Figure 29 shows the LTB of the mono-symmetric member subjected toequal end moments. The critical force is computed by Shell3 finiteelement model.

F i g.29 LTB of simple supported mono-symmetric structural member subjected to equal end moments (δ=50mm)


Figure 30 shows the LTB of the mono-symmetric member subjected toequal end moments. The critical moment is computed by the StabLabsoftware using Beam7 finite element model.

F i g.30 LTB of simple supported mono-symmetric structural member

subjected to equal end moments (n=16)



33

Evaluation

Table 9 shows the cri t ical moment for la teral torsional buckling of the member

which calculated by hand, by Shell3 model and computed by the StabLab softwareusing Beam7 model . The resul t i s accura te .

Tab.9 Stability analysis of mono-symmetric member subjected to equal end

moments


Beam72

Shel l33


Welded

mono-

symmetric I200-12 ; 400-

8 ; 100-12

Mc r [kNm] 220,77

2 221,67 0 ,996 50 219,77 1 ,005

4 220,37 1 ,002 25 217,13 1 ,016

6* 220,30 1 ,002

16 220,28 1 ,002


Note


model, δ denotes the maximum shell FE size.



34

WE-10 Lateral torsional buckling (mono-symmetric section & triangular

moment distribution)

Figure 31 shows a simple fork supported member with welded mono-

symmetric I section (flange: 200-12 and 100-12; web: 400-8) subjected totransverse force at the middle cross- section of the member. The critical force iscalculated by hand, by Shell3 finite element and by the StabLab software usingBeam7 finite element.

F i g.31 Simple fork supported member with mono-symmetricwelded I section subjected to transverse force (LTB)



35


Section: welded monsymmetric I section

top flange b1 200 mm tf1 1 2 m m


bottom flange b2 100 mm tf2 1 2 m m

Sectional properties ZS 248.4 mm (by GSS model of ConSteel)

zD 123.4 mm (by GSS model of ConSteel)

Iz1 tf1

b13

12 8000000 mm

4 Iz2 tf2

b23

12 1000000 mm

4

Iz Iz1 Iz2 9000000 mm4

Iy 186493000 mm4

(by GSS model of ConSteel)

It13

b1 tf13 b2 tf2

3 hw tw3 241067 mm4

f

Iz1

Iz1 Iz2 0.889

hs hw

tf1

2

tf2

2 412 mm

I f 1 f Iz hs2

150883555556 mm6

e hw tf2tf1

2 ZS 169.6 mm

A1 b1 tf1 2400 mm2

A2 b2 tf2 1200 mm2

qx1

Iy

zD Iz1 A1 e3

A2 hs e 3

tw

4e

4hs e 4

51.725 mm

z j zD 0.5qx 149.262 mm

Elastic m odulus E 210000 N

mm2

G E

2 1 0.3( ) 80769

N

mm2

Member length L 6000 m mCoefficients* C1 1.365 C3 0.411

Critical moment Mcr C1

2

E Iz

L

2

I

I

z

L2

G It

2

E Iz

C3 z j 2 C3 z j

213.88kN m

Fcr 4Mcr

L 142.59 kN

*) G. Sedlacek, J. Naumes: Excerpt from the Background Document to

EN 1993-1-1 Flexural buckling and lateral buckling on a common basis:

Stability assessments according to Eurocode 3 CEN / TC250 / SC3 / N1639E - rev2



36


Figure 32 shows the LTB of the mono-symmetric member subjected totransverse force. The critical force is computed by Shell3 finite elementmodel.

F i g.32 LTB of s imple supported mono-symmetric structural member subjected to transverse force (δ=25mm)


Figure 33 shows the LTB of the mono-symmetric member subjected totransverse force. The critical force is computed by the StabLab software

using Beam7 finite element model.

F i g.33 LTB of simple supported mono-symmetric structural member

subjected to transverse force (n=16)



37

Evaluation

Table 10 shows the cri t ical force for la teral torsional buckling of the member

which calculated by hand, by Shell3 model and computed by the StabLab softwareusing Beam7 e lement. The result is accurate .

Tab.10 Stability analysis of mono-symmetric member subjected to transverse

force


Beam72

Shel l33


Welded

mono-

symmetric I200-12 ; 400-

8 ; 100-12

Fc r [kNm] 142,59

2 143,13 0 ,996 50 141,5 1 ,008

4 142,13 1 ,003 25 139,4 1 ,023

8* 141,99 1 ,004

16 141,98 1 ,004


Note


model, δ denotes the maximum shell FE size.



38

WE-11 Lateral torsional buckling (C section & equal end moments)

Figure 34 shows a simple fork supported member with cold-formed Csection (150x100x30x2) subjected to equal end moments. The critical moment is

calculated by hand and by the St abLab software using Beam7 model.

F i g.34 Simple fork supported member with cold-formed C section subjected to equal and moments (LTB)





40


Figure 34 shows the LTB of the member with C section subjected toequal end moments. The critical moment is computed by the StabLabsoftware using Beam7 finite element model.

F i g.34 LTB of simple supported C structural member subjected toequal end moments (n=16)

Evaluation

Table 11 shows the cri t ical end moment for la teral torsional buckling of the C

member calculated by hand and computed by the StabLab software using Beam7 model. The result is accurate .

Tab.11 Stability analysis of the C member subjected to equal end moments


Beam72

n result 1 /2

Cold formed

C150x100x30x2

Mc r [kNm] 94,108

2 94,070 ,994

4 93,42 1 ,007

6* 93,381 ,008

16 93,381 ,008


Note

In the Table 11 n denotes the number of the finite elements of the Beam7 model.



41

WE-12 Lateral torsional buckling (C section & equal end moments)

Figure 35 shows a simple fork supported member with cold-formed Csection (150x200x30x2) subjected to equal end moments. The critical moment is

calculated by hand and by the StabLab software using Beam7 model.

F i g.35 Simple fork supported member with cold-formed C section

subjected to equal and moments (LTB)



42



Figure 36 shows the LTB of the member with C section subjected toequal end moments. The critical moment is computed by the StabLab

software using Beam7 finite element model.

Section : Cold-formed C sectionwidth of flange b 200 mmdepth d 150 mmwidth of stiffener d1 30 m m

pla te thickness t 2 mm

Cross-sectional properties (by ConSteel GSS model )

Iy 6362658 mm4

Iz 5269945 mm4

It 1734 mm4

I 35770000000 mm6

e 85.2 m m es 112.8 mm

Sectional radius* Af d t( ) t 296 mm

2

If t d t( )

3

12540299 m m

4

As d1t

2

t 58 m m2

Is

t d1t

2

3

12As

d

2

t

2

d1t

2

2

2

209399 mm4

Aw b t

2

t 398 mm2

Iw Awd

2

t

2

2

2179448 mm4

h b t

2 199 mm

qx1

Iz

e Af e2

If 2es As es2

Is 2 e h( ) Iw t

2e

4h e( )

4

30.737 mm

zD 187.8 mm

z

j

z

D

0.5q

x

203.168 mm

Length of member L 4 000 m m

Critical moment Mcr

2

E Iz

L2

I

Iz

L2

G It

2

E Iz

z j2

z j

288.68kN m





44

WE-13 Flexural-torsional buckling (U section)

Figure 37 shows a simple fork supported member with cold-formed Usection (120x120x4) subjected to compressive force. The critical force is

calculated by hand, by Shell3 model and by the StabLab software using Beam7

element.

F i g.37 Simple fork supported member with cold-formed U section

subjected to compressive force ( f lexural-torsional buckling)



45


Section: Cold-formed U sectionwidth of fla nge b 120 mmdepth d 120 mmplate thickness t 4 mm


mm2

G E

2 1 0.3( ) 80769

N

mm2

Length of member L 4 000 m m

Cross-sectional properties (by ConSteel GSS model)

A 1408 mm2

Iz 2180000 mm4

iz 39.4 mm

Iy 3699100 mm4

iy 51.3 mm

It 7927 mm4

I 5264600000 mm6

y 90.1 mm

i iy2

iz2

y2

110.915 mm

i p

Iy Iz

A64.618 mm

Critical forces Pcr.y

2

E Iy

L2

479.176 kN

P1

i2

2

E I

L2

G It

107.48 kN

Critical compressive force

Pcr

i

2

2 i p2

Pcr.y P

i

4

4 i p4

Pcr.y P

2

Pcr.y P

i

2

i p2

92.768 kN



46


Figure 38 shows flexural torsional buckling of the member with Usection subjected to compressive force. The critical force is computed byShell3 finite element model.

F i g.38 FTB of the simple supported U structural member subjected tocompressive force (δ=25mm)


Figure 39 shows the flexural torsional buckling of the member with U

section subjected to compressive force. The critical force is computed bythe StabLab software using Beam7 finite element model.

F i g.39 FTB of the simple supported U structural member subjected tocompressive force (n=16)



47

Evaluation

Table 13 shows the cri t ical compressive force for flexural la teral buckling of the

member which calculated by hand, by Shell3 model and computed by the StabLabsoftware using Beam7 e lement . The resul ts a r e accura te .

Tab.13 Stability analysis of member subjected to compressive force


StabLab

Beam72

Shell33


U

120x120x4cold formed

Pc r [kN] 92,77

2 93,24 0 ,995 50 94,42 0 ,983

4 92,86 0 ,999 25 93,55 0 ,992

6* 92,84 0 ,999

16 92,83 0 ,999


Notes

In the Table 13 n denotes the number of the finite elements of the Beam7 model, δ denotes the maximum size of the shell finite elements in the Shell3 model in [mm].



48

WE-14 Interaction of flexural buckling and LTB (symmetric I section &

equal end moments and compressive force)

Figure 40 shows a simple fork supported member with welded symmetric I

section (200-12, 400-8) subjected to compressive force and equal end moments.The critical moment with constant compressive force is calculated by hand and bythe StabLab software using Beam7 model.

F i g.40 Simple fork supported member with welded I section subjected to constant compressive force and equal end moments

(interaction)





Documents

Verification Manual - StabLab.pdf