Validation - LTBeam

CTICM

LTBeam – Report on Validation Tests

July 2002

LTBEAM REPORT ON VALIDATION TESTS

1.

INTRODUCTION

2.

COMPARISON TE TESTS LT LTBEAM/ANSYS 2.1 Presentation 2.2 Overview table of tests 2.3 Results 2.4 Conclusion

3.

COMPARISON TE TESTS LT LTBEAM/DRILL 3.1 Presentation 3.2 Results 3.3 Conclusion

4.

COMPA OMPARI RISO SON N WIT WITH H TES TESTS TS RESU RESUL LTS FROM FROM LITER ITERAT ATUR URE E 4.1 Presentation 4.2 Results 4.3 Conclusion

5.

TAPER APERED ED BEAM BEAMS S : COM COMPA PARI RISO SON N LTB LTBEA EAM M/FIN /FINE ELG 5.1 Presentation 5.2 Results 5.3 Conclusion

6.

GENERAL CONCLUSION

Page 1 / 21

CTICM

1.


July 2002

INTRODUCTION

In order to validate the calculation modules of L TBEAM, comparisons between LTBEAM results and results obtained from other software have been undertaken. Up to now, the following actions have been carried out :

♦ Comparison tests LTBEAM/ANSYS ♦ Comparison tests LTBEAM/DRILL ♦ Comparison with tests results from literature ♦ Comparison LTBEAM/FINELG for tapered beams

2.

COMPARISON TE TESTS LT LTBEAM/ANSYS

2.1

Presentation

In this section are presented results of validation tests of LTBEAM by comparison with results obtained from F.E. simulations with ANSYS V5.6 carried out at CTICM (many thanks to Pierre-Olivier MARTIN ). ). Steel properties considered in calculations calculations are : E = 210000 MPa and ν = 0,3. Tests are classified in the following sets : ü ü ü ü ü ü ü

Set 40 : Set 50 : Set 60 : Set 70 70 : Set 80 : Set 100 : Set 11 110 :

Use of "Formatted data" Beams with intermediate support(s) Cantilever beams Beams un under un uniformly di distributed lo load Beam with intermediate lateral restraint(s) T Beams Boundary re restraint co conditions.

For a best overview of the 65 tests performed, a summary table of tests parameters is given hereafter. For each test, the following information is given in the hereafter tables : ü ü

the test number the dimensions of the section : bf1

tf1 h

tw tf2

h: tf1 tf1 : tf2 tf2 : tw :

Height : h Uppe Upperr fla flang ngee wid width th : bf1 bf1 and and thi thick ckne ness ss Lowe Lowerr fla flang ngee wid width th : bf2 bf2 and and thi thick ckne ness ss Web thickness

(no radius at flange-to-web junctions) bf2

ü ü

the LTB restraints conditions and the loading the results of the calculations : o o

o

the critical load factor calculated by LTBeam : µLTB , the critical load factor calculated by ANSYS : µANS , the difference between results, calculated with the formula : ∆ =

µ ANS − µ LTB µ ANS

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CTICM


July 2002

Some in for mation about numeri cal simu lati ons with A NSYS

For all tests, finite elements SHELL 63 are used for modelling and are defined in the mid-plane of walls. A appropriate density of meshing is used. For example, 6923 nodes and 6610 elements are defined for Test 60. The figure hereafter gives an idea of the meshing used for this example and most of the others. This figure also shows how beam elements (BEAM 4) are used at support locations and point load locations in order to stiffen the cross-section and to avoid local buckling effects. ANSYS performs an Eigenvalue Buckling Analysis to find out the critical load factor µANS . All ANSYS data files have been stored and are available.

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CTICM

2.2


July 2002

Overview table of tests

Beam

N° Test

n a p s 1

40 41 44 50 51 52 53 54 55 56 57 58 60-1 60-2 60-3 61-1 61-2 61-3 62-1 62-2 62-3 65-1 65-2 65-3 66-1 66-2

X X X

s n a p s 2

Vertical supports

r e v e l i t n a C

s t r o p p u s e l p m i S

s t r o p p u s d e x i F

s t r o p p u s d e x i M

r e v e l i t n a C

Section

n o i t c e s m r o f i n U

X X X X X X X X X X X X X X X X X X X X X X X X X

m r o f i n u n o N

X X X

X X X X X X X X X

n o i t c e s

X X X X X X X X X X X X X X

X X X X X X X X X X X X X X X X X X X X X X X X

. t e m m y s e l b u o D

LTB restraints

. t e m m n y o s i o t c n e o s M T

X X X X X X X X X X X X X X X X X X X X X X X X X X

s t n i a r t s e r e t a i d e m r e t n I

s t n i a r t s e r c i t s a l E

t n i a r t s e r t n i o P

t n i a r t s e r s u o n i t n o C

e r t n e c r a e h s t A

X X X X X X X X X X X X X X X X X X X X X X X X X X

Loads

l e v e l e g n a l f t A

s d n e t a l a i c e p S

d a o l t n i o P

d a o l m r o f i n U

X X X X X X X X X X X X X X X

e r t n e c r a e h s t A

Others

l e v e l e g n a l f T A

X X X X X X X X X X X X

n a p s n i e s a e l e r s s e n f f i t S

X

X X X X X X X X

X X X

X X X X X X X X X

X X

X X X Page 4 / 21

CTICM 66-3 67-1 67-2 67-3 70 71 72 75 76 77 80 82 83 84-1 84-2 84-3 85 86 87 88-1 88-2 88-3 89 90 91 92 100 101 102 103 110-1 110-2 110-3 111-1 111-2 111-3 112-1 112-2 112-3

X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X

X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X

LTBeam – Report on Validation Tests X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X

X X X X X X X X X X X X X X X X X X X X

X X X X X X X X X

X X X X X X X X X X X X X X X X

July 2002 X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X

X X X X X X X X X X X X X X X X X X X X X X X X X X X X X

X X X X X X

X X X X X X X X X X

X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X

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CTICM

2.3


July 2002

Results

All tests with LTBeam have been performed with N=100 beam elements, except when specified otherwise. Set 40 :

Formatted data

N°

40

Section

Boundary conditions and loading

Double symmetrical I section. Height h varies from 536 mm at the origin to 236 mm at the end of the beam. bf1 = bf2 = 200 mm tf1 = tf2 = 18 mm tw = 12 mm

L = 15 m. F = -10 kN. Supports and load are applied at the shear centre line. At each end, v and θ fixed, v’ and θ’ free.

F

Results

µLTB

µANS

∆

4,9701

5,0229

0,11 %

27,588

27,901

0,11 %

9,4421

9,4957

0,56 %

L

N=300 q

41

L = 15 m. q = -0,2 kN/m Supports and load are applied at the shear centre line. At each end, v and θ fixed, v’ and θ’ free.

Idem Test 40 L

N=300

44

Double symmetrical I section. h = 310 mm bf1 = bf2 = 190 mm tf1 = tf2 = 13,5 mm tw = 10,5 mm

Fz

Link node z

8m

x 10 m

DOF transmitted by the link : UX, UY, UZ (v) directly transmitted ; RX (θ) transmitted by a spring (k = 1,5 kNm), RY not transmitted, RZ (v’) transmitted by a spring (k = 3,75 kNm). Fz = -10 kN At each end, v, θ, v’ and θ’ fixed. Supports, link and load are applied at the shear centre line.

15 m

Two cantilever beams, connected by a link N=300

Page 6 / 21

CTICM

Set 50 :


N°

50

July 2002

Beams with intermediate support(s) Section


Double symmetrical I section. h = 300 mm. bf1 = bf2 = 200 mm tf1 = tf2 = 15 mm tw = 10 mm

F

F

L/2

L = 19,5 m. F = -10 kN. Supports and load are applied at the shear centre line. At each support, v and θ fixed, v’ and θ’ free.

Results

µLTB

µANS

∆

14,966

14,852

0,76 %

9,4556

9,4102

0,48 %

9,48

9,4112

0,73 %

12,881

12,810

0,55 %

7,7618

7,7024

0,77 %

L/2 q2

51

Idem Test 50

L = 19,5 m. q1 = -1,0 kN/m and q2 = -3 kN/m. Supports and load are applied at the shear centre line. At each support, v and θ fixed, v’ and θ’ free.

q1

L/4

L/2

L

q

52

Idem Test 50 L/2

L/2 F

53

Idem Test 50 L/2

L/2

q

54

Idem Test 50 L/2

L/2

L = 19,5 m. q = -3 kN/m. Supports and load are applied at the shear centre line. At each support, v and θ fixed, v’ and θ’ free. L = 19,5 m. F = -10 kN. Supports and load are applied at the shear centre line. At each support, v and θ fixed, v’ and θ’ free.

L = 19,5 m. q = -3 kN/m. Supports and load are applied at the shear centre line. At each support, v and θ fixed, v’ and θ’ free.

Page 7 / 21

CTICM

N°

55


Section

Mono symmetrical I section. h = 300 mm. bf1 = 150 mm bf2 = 200 mm tf1 = 12 mm tf2 = 15 mm tw = 10 mm

July 2002



F

L/2

Idem Test 55 L/2

57


L/2

F

L/2

L/2

q

58

Idem Test 57 L/2

µANS

∆

8,1018

8,0646

0,46 %

4,7482

4,7196

0,61 %

9,2944

9,2530

0,45 %

5,7547

5,7099

0,78 %

L/2

q

56

Results

µLTB

L/2




Page 8 / 21

CTICM

Set 60 :


N°

Section

F

µLTB

Results

µANS

∆

L = 10,0 m. F = -10 kN.

Upper flange

1,8358

1,8483

0,6 %

At beam fixing, v, θ, v’ and θ’ fixed.

Shear centre

2,3334

2,3434

0,43 %

Lower flange

2,6707

2,6763

0,21 %

L = 10,0 m. q = -2 kN/m.

Upper flange

3,0032

3,0023

0,03 %


Shear centre

4,238

4,2184

0,5 %

Lower flange

5,3647

5,3230

0,8 %

L = 10,0 m. q1 = -2 kN/m, q2 = -5 kN/m

Upper flange

5,1517

5,1772

0,5 %


Shear centre

7,5604

7,5509

0,12 %

Lower flange

9,3689

9,3341

0,37 %

L

q

61-1 Idem Test 60 61-2

L

61-3

q2

q1

62-1 Idem Test 60

62-3

Loading location


Double symmetrical I section. 60-1 h = 300 mm. bf1 = bf2 = 200 mm 60-2 tf1 = tf2 = 15 mm tw = 10 mm 60-3

62-2

July 2002

Cantilever beams

L/2

L/4 L

Page 9 / 21

CTICM

N°


Section

F

µLTB

Results

µANS

∆

L = 10,0 m. F = -10 kN.

Upper flange

1,2065

1,2119

0,47 %


Shear centre

1,3272

1,3315

0,32 %

Lower flange

1,5669

1,566

0,06 %

L = 10,0 m. q = -2 kN/m.

Upper flange

1,9341

1,9307

0,18 %


Shear centre

2,2432

2,2343

0,40 %

Lower flange

3,0548

3,0310

0,78 %

L = 10,0 m. q1 = -2 kN/m, q2 = -5 kN/m

Upper flange

3,3469

3,3530

0,18 %


Shear center

3,9331

3,9291

0,10 %

Lower flange

5,1556

5,1277

0,54 %

L

q

66-1 Idem Test 65 66-2

L

66-3

q2

q1

67-1 Idem Test 65

67-3

Loading location


Mono symmetrical I section. 65-1 h = 300 mm. bf1 = 200 mm bf2 = 150 mm 65-2 tf1 = 15 mm tf2 = 12 mm tw = 10 mm 65-3

67-2

July 2002

L/2

L/4 L

Page 10 / 21

CTICM

Set 70 :


N°

70

July 2002

Beams under constant distributed loading Section


Boundary conditions and loading q

L

L = 15 m. q = -2,3 kN/m. Supports and load are applied at the shear centre line. At each support, v and θ fixed, v’ and θ’ free.

Results

µLTB

µANS

∆

2,3077

2,3041

0,15 %

12,125

12,138

0,11 %

5,5322

5,5215

0,19 %

1,6167

1,6102

0,40 %

6,1237

6,0955

0,46 %

3,4311

3,4171

0,41 %

q

71

Idem Test 70

L

q

72

Idem Test 70 L

75


q

L

L = 15 m. q = -2,3 kN/m. Supports and load are applied at the shear centre line. At each end, v, θ, v’ and θ’ fixed. L = 15 m. q = -2,3 kN/m. Supports and load are applied at the shear centre line. At beam fixing, v, θ, v’ and θ’ fixed. At beam support, v and θ fixed, v’ and θ’ free. L = 15 m. q = -2,3 kN/m. Supports and load are applied at the shear centre line. At each support, v and θ fixed, v’ and θ’ free.

q

76

Idem Test 75

L q

77

Idem Test 75 L

L = 15 m. q = -2,3 kN/m. Supports and load are applied at the shear centre line. At each end, v, θ, v’ and θ’ fixed. L = 15 m. q = -2,3 kN/m. Supports and load are applied at the shear centre line. At beam fixing, v, θ, v’ and θ’ fixed. At beam support, v and θ fixed, v’ and θ’ free.

Page 11 / 21

CTICM

Set 80 :


N°

80

Section

Double symmetrical I section. h = 500 mm. bf1 = bf2 = 280 mm tf1 = tf2 = 19 mm tw = 12,5 mm

Idem Test 80

q L/2 L Lateral restraint

L/4

L

q

83

Idem Test 80 L/4

L/4

L q

84-1 Idem Test 80 84-2

L/4

84-3

L

Idem Test 80

L/4

L

q

86

Idem Test 80

L/4

L

L = 18 m. q = -3 kN/m. Supports, restraint and load are applied at the shear centre line. At each support and at lateral restraint, v and θ fixed, v’ and θ’ free. L = 18 m. q = -3 kN/m. Supports, restraint and load are applied at the shear centre line. At each support and at lateral restraint, v and θ fixed, v’ and θ’ free. L = 18 m. q = -3 kN/m. Supports, restraints and load are applied at the shear centre line. At each support and at each lateral restraint, v and θ fixed, v’ and θ’ free. L = 18 m. Restraint q = -3 kN/m. location : Supports and load are applied at the shear centre Up flange line. Shear cent At each support, v and θ fixed, v’ and θ’ free. At lateral restraint, v fixed, θ, v’ and θ’ free. Lo flange

q

85

Results


q

82

July 2002

Beams with intermediate lateral restraint(s).

L = 18 m. q = -3 kN/m. Supports, restraint and load are applied at the shear centre line. At each support, v and θ fixed, v’ and θ’ free. At lateral restraint, θ fixed, v, v’ and θ’ free. L = 18 m. q = -3 kN/m. Supports, restraint and load are applied at the shear centre line. At each support, v and θ fixed, v’ and θ’ free. At lateral restraint, v fixed by a spring (k = 10 kN/m), θ, v’ and θ’ free.

µLTB

µANS

∆

7,0221

6,9718

0,72 %

5,1471

5,1208

0,51 %

10,12

10,041

0,78 %

5,1471

5,1207

0,51 %

4,7699

4,7467

0,49 %

3,0058

2,9876

0,61 %

3,9349

3,9209

0,35 %

2,4661

2,4573

0,36 %

Page 12 / 21

CTICM

N°


Section

Boundary conditions and loading q

87

Idem Test 80 L/4 L q

88-1 Idem Test 80 88-2

L/4

88-3

89

L

q

Idem Test 80 L

90

q

Idem Test 80 L

91

q

Idem Test 80 L

92

Mono symmetrical section. h = 500 mm. bf1 = 280 mm bf2 = 180 mm tf1 = 19 mm tf2 = 15 mm tw = 12,5 mm

July 2002

q

Results

µLTB

µANS

∆

2,8378

2,8316

0,22 %

3,5544

3,5462

0,23 %

3,3176

3,3101

0,22 %

3,1143

3,1072

0,23 %

2,6682

2,6610

0,27 %

L = 18 m. q = -3 kN/m. Supports, restraints and load are applied at the shear centre line. At each support, v and θ fixed, v’ and θ’ free. Continuous lateral restraint, θ free, v fixed by continuous spring (k = 2 kN/m/m).

2,5868

2,5775

0,36 %

L = 18 m. q = -3 kN/m. Supports and load are applied at the shear centre line. At each support, v and θ fixed, v’ and θ’ free. Continuous lateral restraint, θ free, v fixed by continuous spring (k = 0,75 kN/m/m). Continuous restraint applied at upper flange.

2,5453

2,5482

0,11 %

Idem Test 91

1,842

1,8389

0,17 %

L = 18 m. q = -3 kN/m. Supports, restraint and load are applied at the shear centre line. At each support, v and θ fixed, v’ and θ’ free. At lateral restraint, θ fixed by a spring (k = 40 kNm), v, v’ and θ’ free. L = 18 m. q = -3 kN/m. Restraint Supports and load are applied at the shear centre location : Up flange line. At each support, v and θ fixed, v’ and θ’ free. At lateral restraint, v fixed by a spring (k = 100 Shear cent kN/m), θ fixed by a spring (k = 50 kNm), v’ and θ’ Lo flange free. L = 18 m. q = -3 kN/m. Supports, restraints and load are applied at the shear centre line. At each support, v and θ fixed, v’ and θ’ free. Continuous lateral restraint, v free, θ fixed by continuous spring (k = 1 kNm/m).

L

Page 13 / 21

CTICM


July 2002

T Beams

Set 100 : N°

Section


Results

µLTB

µANS

∆

1,425

1,4266

0,11 %

1,2044

1,2052

0,07 %

1,2564

1,2611

0,37 %

1,039

1,0429

0,37 %

f

F

100 tf

h

tw

h = 150 mm tf = 10 mm

L = 10m. F = -5 kN/m. Supports and load are applied on the shear centre line. At each support, v and θ fixed, v’ and θ’ free.

L

bf = 120 mm tw = 8 mm q

101

L = 10m. q = -1 kN/m. Supports and load are applied on the shear centre line. At each support, v and θ fixed, v’ and θ’ free.

Idem Test 100 L

102

h

F

tw tf

L = 10m. F = -5 kN/m. Supports and load are applied on the shear centre line. At each support, v and θ fixed, v’ and θ’ free.

L

f h = 150 mm tf = 10 mm

bf = 120 mm tw = 8 mm q

103

Idem Test 102 L

L = 10m. q = -1 kN/m. Supports and load are applied on the shear centre line. At each support, v and θ fixed, v’ and θ’ free.

Page 14 / 21

CTICM


Set 110 : N°

July 2002

Boundary restraint conditions Section

Loading location

µLTB

µANS

∆

L = 15 m. q = -2,3 kN/m.

Upper flange

5,2142

5,2608

0,88 %

At beam fixing, v, θ and v’ fixed; θ’ free.

Shear centre

9,2548

9,2914

0,39 %

Lower flange

16,212

16,187

0,15 %

2,5514

2,5606

0,36 %

2,8606

2,8706

0,35 %

3,2065

3,2161

0,30 %

3,1042

3,099

0,17 %

3,9822

3,9821

0,0 %

5,0317

5,0340

0,05 %


Results

q

110


L

q

111

Idem Test 110 L

L = 15 m. Upper flange q = -2,3 kN/m. Supports are applied at the shear centre line. Shear centre At each support, v, θ and θ’ fixed; v’ free. Lower flange

q

112

Idem Test 110 L

L = 15 m. Upper flange q = -2,3 kN/m. Supports are applied at the shear centre line. Shear centre At each support, v, θ and v’ fixed; θ’free. Lower flange

2.4

Conclusions

Differences between LTBEAM and ANSYS results are lower than 1% for all tests.

Page 15 / 21

CTICM


3.

COMPARISON TESTS LTBEAM/DRILL

3.1

Presentation

July 2002

DRILL is a F.E. software (Germany) dedicated to elastic stability of beams. Commercial Intertech (ASTRON Division), partner in the ECSC Project, has got this software and has carried out somme stability analysis of a simply supported beam under uniform bending moment continuously restraint at upper flange by a spring. These results have been compared with LTBEAM results hereafter. Section : IPE 400

L = 10 m

E = 210 000 N/mm 2

G = 81 000 N/mm 2

M

R v :

M

continuous restraint stiffness for lateral displacement v [in kN/m/m] Location at the extreme fibre of the upper flange

R θ : continuous restraint stiffness for axial rotation θ [in kNm/m]

∆ =

LTBEAM/DRILL

3.2

Results µcr : multiplicateur critique

M = 10 kNm

M = -10 kNm

Rv

Rθ

DRILL

LTBeam

∆

DRILL

LTBeam

∆

0 0 0 0

0.0 3.5 7.0 10.5

11.86 15.41 18.29 20.77

11.89 15.44 18.31 20.78

0.27% 0.17% 0.09% 0.07%

11.86 15.41 18.29 20.77

11.89 15.44 18.31 20.78

0.27% 0.17% 0.09% 0.07%

500 500 500 500

0.0 3.5 7.0 10.5

79.75 80.62 81.47 82.31

79.89 80.75 81.60 82.44

0.17% 0.16% 0.16% 0.16%

15.17 23.03 30.43 35.96

15.23 23.09 30.48 36.04

0.39% 0.25% 0.15% 0.21%

1000 1000 1000 1000

0.0 3.5 7.0 10.5

102.35 103.23 104.10 104.96

102.48 103.36 104.23 105.09

0.13% 0.13% 0.12% 0.12%

15.38 23.68 31.69 36.58

15.44 23.74 31.75 36.66

0.37% 0.25% 0.18% 0.21%

1500 1500 1500 1500

0.0 3.5 7.0 10.5

124.92 125.81 126.69 127.57

125.05 125.95 126.83 127.70

0.10% 0.11% 0.11% 0.10%

15.45 23.93 32.19 36.91

15.51 23.99 32.25 37.00

0.41% 0.24% 0.18% 0.24%

Note:

DRILL :

10 elements ; tolerance 10-6

LTBeam : 100 elements ; tolerance 10

3.3

-6

Conclusions

Differences between LTBEAM and DRILL results are lower than 0,5% for all tests.

Page 16 / 21

CTICM


July 2002

4.

COMPARISON WITH TESTS RESULTS FROM LITERATURE

4.1

Presentation

LTBEAM results have been compared with those found in the following reference : Braham M. – " Le déversement élastique des poutres en I à section monosysmétrique soumises à un gradient de moment de flexion" – Revue Construction Métallique n°1-2001 – CTICM Tests concern a simply supported beam with equal/unequal end moments M1 and M2 (M2 ≤ M1) with a ratio ψ = M2/M1.

M1

M2=ψ M1

Three cross-sections are tested : - a double symmetrical I cross-section - a mono-symmetrical I cross section - a T cross-section Tests have been carried out with various software and FE codes, and by various authors. The reader will refer to the above reference for more information about the authors, the programmes used for the numerical simulations, conditions in which these simulations have been performed and cross-section dimensions.

4.2

Results

4.2.1

Double symmetrical I cross-section

Section properti es :

Iw cm6 125930

It cm4 15.57

Iz cm4 602.7

Iy cm4 7999

A cm2 51.89

zs cm 0

βz cm 0

E daN/cm2 2100000

G daN/cm2 800000

Resul ts (fr om Tabl e 3 of t he reference paper ):

Elastic critical bending Moment left side (M1) in kNm Psi = Length According to Mohri According to Braham CTICM M2/M1 in m. Abaqus Mohri ELTBTB FinelG IBDSQ Abaqus Ansys LTBEAM

1

-1

Note :

3 4 5 6 7 8 3 4 5 6 7 8

240 150.53 107.56 83.22 67.8 57.23 654 408.4 290 225.4 183.23 154.26

240.43 150.9 107.97 83.03 67.38 57.45 657.22 411.46 293.45 227.48 184.53 154.61

239.7 149.8 106.9 82.65 67.29 56.77 655.5 408.7 290.9 224.2 182 153

240 150.1 107.2 82.9 67.5 56.97 656 409.5 292 225 182.6 153.6

148.4 82.3 56.7 388.2 220.6 152

239.8 149.8 107 82.7 67.3 56.8 655.9 408.9 291 224.3 182.1 153.1

∆% 0.10% 0.10% 0.38% 0.14% 0.29% 0.39% 0.03% 0.90% 0.20% 0.11% 0.54% 0.26%

∆ is the dif ference (absolu te val ue) to the mean valu e of other avail able resul ts for t he case under considerati on.

Page 17 / 21

CTICM

4.2.2


July 2002

Mono-symmetrical I cross-section


Iw cm6 25081

It cm4 12.39

Iz cm4 335.05

Iy cm4 3134.9

A cm2 43.53

zs cm 8.8

betaz cm 10.77

E G 2 daN/cm daN/cm2 2100000 800000

Resul ts (fr om Tabl e 4 of t he reference paper ) :

Psi = Length M2/M1 in m. 1

0.5

0

-0.5

-0.75

-1

Note :

3 4 5 6 7 8 3 4 5 6 7 8 3 4 5 6 7 8 3 4 5 6 7 8 3 4 5 6 7 8 3 4 5 6 7 8

Elastic critical bending Moment left side (M1) in kNm According to Mohri According to Braham CTICM Conci Mohri ELTBTB FineIG IBDSQ Abaqus Ansys LTBEAM

223.8 125.9 94.4 69.9 57.5 49.3 285 174 117.5 94.4 74.3 66.1 391 243 168 130 104 86.5 405 273 201 159.4 131.9 112.2

174.8 125.9 100.7 85.3 74.3 66.01

216.35 133.18 94.086 71.485 57.037 47.377 286.58 177.64 124.96 94.604 75.255 62.432 393.47 243.87 172.23 130.82 104.35 86.577 405.57 270.12 201.71 160.1 132.33 112.13 260.91 182.63 145.11 120.37 102.83 90.377 174.84 124.92 102.09 86.27 74.68 66.17

220.6 135.4 94.8 71.9 57.46 47.67 290.7 178.5 125 94.8 75.7 62.8 399 246 172 131 105 87.1 398.9 267.5 200.7 160 132.5 112.5 250.7 175.9 137.9 114.9 99.4 88.05 167.5 119.5 94.7 79.7 69.4 61.9

220.1 135.2 94.75 71.9 57.5 47.7 290.1 178.3 125 94.8 75.9 63 398.7 246 173 131 105 87.3 404 270.5 202.6 161.3 133.3 113.1 254.9 179 140.2 116.8 101 89.4 170.2 121.4 96.3 81 70.5 62.9

220.6 135.4 94.9 72 57.6 47.8 290.7 178.6 125.1 94.9 75.9 63 394 246 173 131 105 87.3 400 268.4 201.3 160.6 132.9 112.8 251.8 176.8 138.6 115.5 99.9 88.6 168.4 120.1 95.3 80.1 69.8 62.3

133.8 71.44 47.6 176.3 94.2 62.7 388.55 242.5 171.1 130.3 104.5 86.8 263.2 160 112.6

119 80.5 63

223.8 137.2 95.77 72.4 57.7 47.73 294.4 180.8 126.3 95.49 76.1 62.94 396 246.6 173.3 131.5 104.9 86.89 385.5 269.2 203.6 162.2 133.8 113.2 247.7 178.8 140.8 117.1 100.9 89.03 168.1 122 96.89 81.18 70.41 62.51

220.1 135.6 94.9 72 57.5 47.7 291.2 178.8 125.1 94.9 75.9 62.9 400 246.7 173.2 131.5 105.2 87.3 399.2 267.7 200.8 160.1 132.6 112.6 250.8 176 137.9 114.9 99.4 88.06 167.6 119.5 94.8 79.7 69.4 61.9

∆% 0.35% 1.40% 0.12% 0.59% 0.06% 0.38% 0.56% 0.60% 0.91% 0.17% 0.50% 0.60% 1.42% 0.75% 0.81% 0.53% 0.50% 0.43% 0.16% 0.43% 0.50% 0.26% 0.14% 0.04% 0.95% 1.47% 1.87% 1.74% 1.39% 1.16% 1.78% 1.91% 2.93% 2.81% 2.96% 2.58%


Page 18 / 21

CTICM 4.2.3


July 2002

T cross-section


Iw cm6 319.45

It cm4 9.45

Iz cm4 301.77

Iy cm4 3134.9

A cm2 35.83

zs cm 7.98

betaz cm 11.63

E daN/cm2 2100000

G daN/cm2 800000

Resul ts (fr om Tabl e 5 of t he reference paper ) :

Psi = Length M2/M1 in m. 1

0.5

0

-0.5

-0.75

-1

3 4 5 6 7 8 3 4 5 6 7 8 3 4 5 6 7 8 3 4 5 6 7 8 3 4 5 6 7 8 3 4 5 6 7 8

Elastic critical bending Moment left side (M1) in kNm According to Mohri According to Braham CTICM Conci Mohri ELTBTB FineIG IBDSQ Abaqus Ansys LTBEAM

208.63 128.86 86.93 62.71 51.66 43.46 272.38 162.99 123.79 86.93 66.07 57.37 359.31 217.32 168.29 118.23 99.35 78.24 57.95 60.85 65.37 62.71 62.09 64.33

30.14 30.42 29.21 28.98 26.82 24.34

205.38 124.81 87.09 65.64 52.02 42.73 271.01 166.44 115.92 87.08 68.81 56.38 364.5 224.37 157.45 119.13 94.72 78.03 79.83 77.59 81.47 79.91 75.85 71.19 49.58 48.16 50.87 50.06 47.6 44.73 35.89 35.28 35.02 34.12 33.27 31.16

182.5 112.7 79.2 60.2 48.2 40 240.2 148.4 104.3 79.3 63.5 52.76 324 202.9 143.7 109.7 88 73.1 117.5 110.1 101.3 92.1 87.4 81.8 62.1 59.7 57 54.2 52 50.3 41.8 40.42 39.46 38.35 37.18 35.93

182.7 112.7 79.2 60.2 48.2 40 324.1 202.9 143.6 109.6 87.9 73 97.4 90.73 86.41 83.05 79.88 76.45 -

43.9 41.3 39.55 38.1 36.78 35.51

183 113 79.9 60.5 48.4 40.2 324 203 144 110 88.3 73.4 95.53 88.34 83.69 80.2 77.23

111.7 59.9 39.9 147.1 78.9 52.5 318 200.5 142.4 108.8 87.34 72.62 70 68.3 68

32.8 32.4 32.4

326.2 205.1 145.3 110.8 88.7 73.57

189.6 116.4 81.5 61.7 49.3 40.8 249 153 107.4 81.4 65 53.8 335 209 147.5 112.3 89.9 74.5 93.5 85.9 81.1 77.5 74.6 71.9 58.7 54.4 51.7 49.6 47.9 46.5 42.5 39.6 37.7 36.2 35 33.8

∆% 1.48% 0.76% 1.17% 0.28% 0.80% 0.60% 4.67% 2.07% 6.34% 1.99% 1.70% 1.74% 0.21% 0.47% 1.17% 0.02% 0.79% 0.09% 4.30% 3.58% 3.05% 0.27% 2.47% 0.63% 5.12% 0.87% 4.14% 4.85% 3.82% 2.14% 12.04% 9.87% 5.28% 5.26% 4.44% 6.06%

Note :


4.3

Conclusions

In all cases, LTBEAM results are quite acceptable. For some cases of T-sections, especially negative ψ values, the difference may appear rather large, but for these cases the dispersion of results from all software is rather wide and it can be observed that some results from other authors are somewhat questionnable; However, LTBEAM results are in the range. Of course, we have no information on the modelling, on the meshing and on the real section properties used for most of the simulations performed by other authors than CTICM. Page 19 / 21

CTICM


July 2002

5.

TAPERED BEAMS : COMPARISON LTBEAM/FINELG

5.1

Presentation

The results with FINELG software reported herefater have been performed by C. Heck at Liege University in the frame of the Research Contract n°7210 PR 183 with the European Community for Steel and Coal – 1999~2002 (Working Document LTB31). FINELG is a F.E. code developed by the MSM Department of Liege University. Tests concern a simply supported I tapered beam under unequal end moments M1 and M2.

M1

M2

The web height varies linearily from hw1 (where M1 is applied) to hw2. The other section properties are :

∆=

bf = 250 mm

tf = 20 mm

tw = 14 mm

µ LTBEAM − µ FINELG µ FINELG

where µ is the critical load factor.

5.2

Results

N°Test Span (m) hw1 (mm) hw2 (mm) M1 (kN.m)

M2 (kN.m)

FinelG

LTBeam

P1-1A P1-2A P1-3A P1-4A P1-5A P1-6A

5 5 5 5 5 5

400 400 400 400 400 400

800 800 800 800 800 800

200 200 200 200 200 200

-800 -600 400 600 800 200

4.482 6.352 5.155 3.847 3.062 7.694

4.4885

P3-1A P3-4A P3-6A

5 5 5

200 200 200

1000 1000 1000

200 200 200

-1200 1000 200

2.801 2.48 7.271

2.8043 2.4826

P1-1A P1-6A P3-1A

10 10 10

400 400 200

800 800 1000

200 200 200

-800 200 -1200

1.486 2.603 0.948

1.4857

5.3

6.3617 5.1608 3.8522 3.0661 7.7026

7.276 2.6019 0.9475

∆ 0.15% 0.15% 0.11% 0.14% 0.13% 0.11% 0.12% 0.10% 0.07% -0.02% -0.04% -0.05%

Conclusion

With all differences lower than 0,2%, the comparison is quite satisfactory.

Page 20 / 21

CTICM

6.


July 2002

GENERAL CONCLUSION

In the very most of the cases, the difference between LTBEAM results and those from numerical simulations performed with various F.E. software by CTICM or other authors is lower than 1%. For the few cases where this difference is higher, a wide dispersion already exists for the available results from literature and LTBeam results are in the range. Many other comparisons, not presently reported here, have been made with available results with a very good conclusion - Tapered beams with unequal end moments – Comparison LTBEAM/FINELG The general conclusion from the above comparison work is that LTBEAM results are quite satisfactory and that the reliability of LTBEAM seems quite good. However, users are invited to transmit to CTICM all information about cases for which unsatisfactory results would be found by LTBEAM in order to retrieve the origin of the discrepancy and, if necessary, to correct the programme.

YG _____________________

Page 21 / 21

Validation - LTBeam

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