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SHEAR BUCKLING RESISTANCE OF CANTILEVER GIRDERS WITH CORRUGATED WEB

Witold BASIŃSKI

Witold BASIŃSKI

Faculty of Civil Engineering. The Silesian University of TechnologyGliwice, Poland
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BASIŃSKI, Witold
  
20 mai 2019
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Catégorie d'article: research-article
Publié en ligne: 20 mai 2019
Pages: 63 - 79
Reçu: 19 juil. 2018
Accepté: 24 janv. 2019
DOI: https://doi.org/10.21307/acee-2019-006
Mots clés
© 2019 Witold BASIŃSKI, published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Figure 1.

Cantilever SIN girders: a) static scheme, b) flat plates on the support in the SIN girder
Cantilever SIN girders: a) static scheme, b) flat plates on the support in the SIN girder

Figure 2.

Cantilever girders with corrugated web a) models M 1.12, M 2.12 b) models M 1.22, M 1.32, M 1.42, M 1.52, M 2.22, M 2.32, M 2.42, M 2.52; c) d) end stiffeners
Cantilever girders with corrugated web a) models M 1.12, M 2.12 b) models M 1.22, M 1.32, M 1.42, M 1.52, M 2.22, M 2.32, M 2.42, M 2.52; c) d) end stiffeners

Figure 3.

a) Girder 2.32 on the test stand; b) steel frame FR
a) Girder 2.32 on the test stand; b) steel frame FR

Figure 4.

Location of strain gauges on the girder web M 2.52
Location of strain gauges on the girder web M 2.52

Figure 5.

Strain in the direction 60° relative to the axis of the web a) girder M 1.32; b) girder M 2.12
Strain in the direction 60° relative to the axis of the web a) girder M 1.32; b) girder M 2.12

Figure 6.

Diagram of global displacements y of tested girders
Diagram of global displacements y of tested girders

Figure 7.

Load – displacements paths P(y) of girders a) M 1.12 (2×300×20); b) M 2. 12 (2×300×20 mm)
Load – displacements paths P(y) of girders a) M 1.12 (2×300×20); b) M 2. 12 (2×300×20 mm)

Figure 8.

Load – displacements paths P(y) of girders a) M 1.52 (2×300×25 mm); b) M 2. 52 (2×300×25 mm)
Load – displacements paths P(y) of girders a) M 1.52 (2×300×25 mm); b) M 2. 52 (2×300×25 mm)

Figure 9.

Failure modes of cantilever SIN girders: a) M 1.12 (2×300×20 mm); b) M 2. 52 (2×300×25 mm)
Failure modes of cantilever SIN girders: a) M 1.12 (2×300×20 mm); b) M 2. 52 (2×300×25 mm)

Figure 10.

Numerical models
Numerical models

Figure 11.

Boundary conditions and load application to numerical model
Boundary conditions and load application to numerical model

Figure 12.

Comparison of LDPs P(y): a) tests M 1.42; b) FEM 1250×2
Comparison of LDPs P(y): a) tests M 1.42; b) FEM 1250×2

Figure 13.

Comparison of LDPs P(y): a) test M 2.52; b) FEM 1500×2
Comparison of LDPs P(y): a) test M 2.52; b) FEM 1500×2

Figure 14.

Comparison of failure modes: a) experimental girder M 1.12 (500×2: stiffener 2×300×20); b) numerical model 500×2 (stiffener: 2×300×20)
Comparison of failure modes: a) experimental girder M 1.12 (500×2: stiffener 2×300×20); b) numerical model 500×2 (stiffener: 2×300×20)

Figure 15.

Failure modes of numerical models: a) 1000×2 (stiffener 2×300×25); b) 1000×2.5 (stiffener 2×300×25)
Failure modes of numerical models: a) 1000×2 (stiffener 2×300×25); b) 1000×2.5 (stiffener 2×300×25)

Figure 16.

Comparison of failure modes: a) experimental girder M 1.52 (1500×2: stiffener 2×300×25); b) numerical model 1500×2 (stiffener: 2×300×25)
Comparison of failure modes: a) experimental girder M 1.52 (1500×2: stiffener 2×300×25); b) numerical model 1500×2 (stiffener: 2×300×25)

Figure 17.

Normalized shear resistance in function of the slenderness
Normalized shear resistance in function of the slenderness

Current numerical program

hw [mm] tw [mm] Flange [mm] Suport stiffener [mm] w [mm] L [mm] Number of models
1 2 3 4 5 7 8
500 2; 2.6; 3 300×15 2×300×20 1500 6350 3
1000 2; 2.6; 3 300×15 2×300×25 1500 6350 3
1250 2; 2.6; 3 300×15 2×300×25 1500 6350 3
1500 2; 2.6; 3 300×15 2×300×25 1500 6350 3

Experimental results of girders

Girder Web hw x tw [mm] Flange [mm] Suport stiffener Failure modes Limit load PeB [kN] First buckling load Pu,Rd [kN] PeB /Pu,Rd [%]
2 3 4 5 6 7 8 9
M 1.12 500×2 300×15 2×300×20 L 184 147 0.80
M 2.12 500×2 300×15 2×300×25 L 181 151 0.82
M 1.22 1000×2 300×20 2×300×25 I 342 298 0.87
M 2.22 1000×2 300×15 2×300×25 L 343 296 0.86
M 1.32 1000×2.6 300×20 2×300×25 I 478 380 0.79
M 2.32 1000×2.6 300×15 2×300×25 I 492 390 0.79
M 2.42 1000×3 300×15 2×300×25 I 694 510 0.73
M 1.42 1250×2 300×15 2×300×25 I 348 304 0.87
M 1.52 1500×2 300×15 2×300×25 I 468 400 0.85
M 2.52 1500×2 300×15 2×300×25 I 459 399 0.87

Numerical results of girders

Girder h w x t w [mm] Support Stiffener Failure modes Limit load P u,Rd [kN] First buckling load P eB [kN] P eB /P u,Rd [%]
1 2 3 4 5 6
500×2 2×300×20 L 154.1 149.1 0.97
500×2.5 2×300×20 L 192.2 186.8 0.97
500×3 2×300×20 L 231.3 224.6 0.97
1000×2 2×300×25 L 308.1 297.2 0.96
1000×2.5 2×300×25 I 384.3 371.3 0.97
1000×3 2×300×25 I 462.2 445.3 0.96
1250×2 2×300×25 I 384.6 360.1 0.94
1250×2.5 2×300×25 I 480.4 449.9 0.94
1250×3 2×300×25 I 576.5 539.5 0.94
1500×2 2×300×25 I 460.8 419.2 0.91
1500×2.5 2×300×25 I 575.6 531.9 0.92
1500×3 2×300×25 I 687.5 635.7 0.92

Material properties

Girder f ¯ y [MPa] f ¯ u [MPa] Percentage total elongation at maximum force (Fm ) [%] Percentage total elongation at fracture [%] f ¯ y [MPa] f ¯ u [MPa] Percentage total elongation at maximum force (Fm ) [%] Percentage total elongation at fracture [%] E [GPa]
web flange
1 2 3 4 5 6 7 8 9 10
M 1.12 334.7 430.6 16.1 22.1 297.5 443.1 23.9 30.3 196
M 2.12 337.9 429.1 15.7 20.8 311.2 476.7 24.5 30.8 188
M 1.22 339.4 435.4 15.9 22.2 287.2 448 24.1 31.4 200
M 2.22 336.3 427.3 14.9 22.5 323.5 461.4 23.1 29.6 234
M 1.32 312.5 453.9 13.8 20.2 264.2 460.9 22.6 28.0 199
M 2.32 324.6 451.5 13.6 19.2 293.9 442.1 25.1 32.3 241
M 2.42 445.9 544.1 10.7 14.6 301.5 439.8 21.3 27.7 205
M 1.42 267.2 360.9 13.4 19.9 302.8 440.4 22.9 30.8 199
M 1.52 299.1 380.5 16.8 23.3 312.5 445.6 24.1 30.0 200
M 2.52 281.0 375.5 17.2 24.6 306.7 449.3 21.9 28.6 203

Comparison investigations, FEM analysis with design [6, 1] and proposed resistances (17)

Girder hw x tw [mm] τINV [MPa] τFEM [MPa] τ I N V τ Y τ F E M τ Y τ n , S B τ Y τ n , E C τ Y τ n , B A τ Y τ n , B A τ I N V τ n , B A τ F E M
1 2 3 4 5 6 7 8 9 10
500×2 147.0 149.1 0.80 0.92 0.79 0.86 0.86 1.09 0.93
500×2.5 149.4 0.92 0.79 0.91 0.86 0.93
500×3 149.7 0.92 0.79 0.95 0.86 0.93
1000×2 149.0 148.6 0.78 0.92 0.79 0.83 0.86 1.10 0.94
1000×2.5 152.0 148.5 0.90 0.92 0.79 0.88 0.86 0.96 0.94
1000×3 170.0 148.4 0.75 0.91 0.79 0.93 0.86 1.26 0.94
1250×2 121.6 144.0 0.86 0.89 0.79 0.82 0.85 1.01 0.96
1250×2.5 144.0 0.89 0.79 0.88 0.85 0.96
1250×3 143.9 0.89 0.79 0.92 0.86 0.96
1500×2 133.0 139.7 0.88 0.86 0.79 0.82 0.84 0.96 0.98
1500×2.5 141.8 0.87 0.79 0.87 0.85 0.97
1500×3 141.3 0.87 0.79 0.92 0.85 0.97
AVG. 0.83 0.90 0.79 0.88 0.85 1.06 0.95
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