The shear buckling failure and strength of a web panel stiffened by stiffeners with corrosion damage were examined according to the degree of corrosion of the stiffeners, using the finite element analysis method. For this purpose, a plate girder with a four-panel web girder stiffened by vertical and longitudinal stiffeners was selected, and its deformable behaviors and the principal stress distribution of the web panel at the shear buckling strength of the web were compared after their post-shear buckling behaviors, as well as their out-of-plane displacement, to evaluate the effect of the stiffener in the web panel on the shear buckling failure. Their critical shear buckling load and shear buckling strength were also examined. The FE analyses showed that their typical shear buckling failures were affected by the structural relationship between the web panel and each stiffener in the plate girder, to resist shear buckling of the web panel. Their critical shear buckling loads decreased from 82% to 59%, and their shear buckling strength decreased from 88% to 76%, due to the effect of corrosion of the stiffeners on their shear buckling behavior. Thus, especially in cases with over 40% corrosion damage of the vertical stiffener, they can have lower shear buckling strength than their design level.
In steel plate girder bridges with more than 50–70 years’ service period, severe corrosion damaged structural members have been found near their supports from their corrosive environmental condition, such as higher humidity caused by poor air circulation, dust deposition, and rain water or antifreeze penetration from drainage type expansion joints [
A collapsed steel plate girder bridge in Japan [
After collapse [
Inside before collapse [
In this study, therefore, a stiffener was only selected as a corroded member of a plate girder. Nonlinear FE analyses of web panels stiffened by stiffeners were conducted, to compare their shear buckling behaviors according to the degree of corrosion of their stiffeners. Thus, a plate girder with a four-panel web panel stiffened by vertical and longitudinal stiffeners was selected. After their post-shear buckling behaviors, their shear buckling failures were compared, as well as their change in shear buckling strength. Then, the effect of the corroded stiffener of the web panel on the shear buckling failure was evaluated.
To numerically analyze the shear buckling behaviors of the web panel with stiffener, a four-panel web plate girder stiffened by vertical stiffeners and longitudinal stiffeners was selected, with a total height of 1,256 mm (stiffened web panel, with height and width of 1000 mm), a total length of 4,420 mm, flange width of 200 mm, flange thickness of 22 mm, and web thickness of 6 mm, as shown in Figure
Dimensions of web panel and stiffener for FE analysis.
In this study, the FE analysis models were classified into three cases, depending on the analysis conditions. For the first FE analysis case, a plate girder with longitudinal stiffener was selected to examine the shear buckling behaviors affected by the vertical stiffener; thus only the vertical stiffener was considered to be corroded from the lower flange in the plate girder. For the second FE analysis case, the vertical stiffener and end-longitudinal stiffener were considered to be corroded from the lower flange and center of the end-longitudinal stiffener, to examine the effect between the corroded vertical stiffener and the end-longitudinal stiffener on their shear buckling behaviors. For the third FE analysis case, a left-longitudinal stiffener (end-longitudinal stiffener) and right-longitudinal stiffener (next-longitudinal stiffener) were considered to be corroded with the vertical stiffener, to examine the relationship between left-longitudinal stiffener and right-longitudinal stiffener. Thus, in the vertical and left-longitudinal stiffener corrosion model, the corroded height of the vertical stiffener changed from 0 mm to 1000 mm in 100 mm units (10% of the vertical stiffener height), and the corroded width of the left-longitudinal stiffener changed from 0 mm to 1000 mm from the center of longitudinal stiffener in 200 mm units (20% of vertical stiffener height) for a symmetric web panel, as shown in Figure
Corrosion damage condition of web stiffener for FE analysis.
Vertical and end-longitudinal stiffener corrosion model (V-stiffener cases, V-L stiffener cases)
Vertical and left-right longitudinal stiffener corrosion model (V-L-R stiffener cases)
For the FE analysis model, they are identified as follows: the first letter indicates the analysis case (VL: vertical and left-longitudinal stiffener corrosion model, V-L-R: vertical and left-right longitudinal stiffener corrosion model), the second letter, H, indicates the corrosion height of the vertical stiffener (e.g., H200 indicates a corroded vertical stiffener of 200 mm from the lower flange), the third letter, L, indicates the width of the left-longitudinal stiffener (e.g., L200 indicates an end-longitudinal stiffener of 200 mm), and the fourth letter, R, indicates the width of the right-longitudinal stiffener (e.g., R200 indicates the next-longitudinal stiffener of 200 mm).
Therefore, in this study, the corrosion ratio of vertical and longitudinal stiffeners for each FE analysis can be summarized as follows: Vertical stiffener corrosion model (V-stiffener cases). Vertical and left-longitudinal stiffener corrosion model (V-L stiffener cases). Vertical and left-right longitudinal stiffener corrosion model (V-L-R stiffener cases).
In order to examine the shear buckling failure of the web panel related to the locally corroded stiffener condition in the plate girder using nonlinear FE analysis (finite element analysis), the FE analysis program MARC Mentat 2010 was used for each of the stiffener corrosion cases. To determine their critical shear buckling loads, buckling modes, elastic buckling analysis was anteriorly conducted before postbuckling analysis. Then, their incremental nonlinear analyses with elastic buckling modes were sequentially processed. In this FE analysis model, an 8-node solid element was used, as shown in Figure
Boundary and load condition of the FE analysis model (V-LH600L400).
For boundary conditions of the FE analysis model, both the lower flanges of the end panel (Boundary A) only were released to rotate in the transverse direction, while the other translations and rotations were prevented. For its symmetrical behavior, five points of the upper flange (Boundary B) in the plate girder model were not allowed to translate in the transverse direction, and a center point (Boundary C) at the lower flange was not allowed to translate in the longitudinal direction. For the shear bucking of the web panel, shear load was applied to the center flange of the FE analysis model. Each FE analysis case was considered corrosion damage conditions of their vertical and longitudinal stiffeners. For vertical stiffener corrosion models, a lower part of vertical stiffener was removed as corrosion damage as 100 mm units from the lower flange in the plate girder. For longitudinal stiffener corrosion models with vertical stiffener corrosion, center part of end-longitudinal stiffener and right-longitudinal stiffener (next-longitudinal stiffener) was removed with the corrosion damage of vertical stiffeners according to FE analysis condition. For V-LH600L400 model, therefore, vertical stiffener was removed to 600 mm from lower flange and 400 mm length of end-longitudinal stiffener was removed as corrosion damage as shown in Figure
To validate the FE analysis model used in this study, shear loading test results of a plate girder with similar dimension were compared, according to test boundary conditions and loading procedure [
Validation model of the FE analysis.
Comparison of the displacement at mid-span.
To examine the shear buckling failure mode of the web panel stiffened by vertical and longitudinal stiffeners depending on the corroded stiffener condition, shear buckling failure modes at shear bulking strength were compared. Figures
V-stiffener model with V: 0% corrosion damage (VH00).
Out-of-plane displacement contour
Maximum principal stress distribution contour
V-stiffener model with V: 50% corrosion damage (VH500).
Out-of-plane displacement contour
Maximum principal stress distribution contour
V-stiffener model with V: 100% corrosion damage (VH1000).
Out-of-plane displacement contour
Maximum principal stress distribution contour
V-L stiffener model with V: 50% and L: 20% corrosion damage (V-LH500L200).
Out-of-plane displacement contour
Maximum principal stress distribution contour
V-L stiffener model with V: 50% and L: 40% corrosion damage (V-LH500L400).
Out-of-plane displacement contour
Maximum principal stress distribution contour
V-L stiffener model with V: 50% and L: 60% corrosion damage (V-LH500L600).
Out-of-plane displacement contour
Maximum principal stress distribution contour
V-L stiffener model with V: 50% and L: 80% corrosion damage (V-LH500L800).
Out-of-plane displacement contour
Maximum principal stress distribution contour
V-L-R stiffener model with V: 50%, L: 40%, and R: 40% corrosion damage (V-LH500L400R400).
Out-of-plane displacement contour
Maximum principal stress distribution contour
V-L-R stiffener model with V: 50%, L: 40%, and R: 80% corrosion damage (V-LH500L400R800).
Out-of-plane displacement contour
Maximum principal stress distribution contour
In the case of the vertical and left-longitudinal stiffeners corrosion model, as shown in Figures
To more clearly identify this tendency, out-of-plane displacements were also compared according to the corroded stiffener condition, in company with comparing the displacements at the center of a plate girder. Figure
Displacement and out-of-plane displacement distribution of each case.
Out-of-plane displacement of V-stiffener series
Displacement of V-stiffener series
Out-of-plane displacement of V-L stiffener series
Displacement of V-L stiffener series
Out-of-plane displacement of V-L-R-stiffener series
Displacement of V-L-R-stiffener series
For the vertical and left-longitudinal stiffener corrosion model, the corrosion height of the vertical stiffener changed from 0 mm to 1000 mm in 100 mm units, and the corroded width of the end-longitudinal stiffener also changed from 0 mm to 1000 mm from the center of longitudinal stiffener in 200 mm units. Basically, their critical shear buckling load and shear buckling strength decreased, depending on the corroded stiffener height, as shown in Tables
Shear buckling values for V-LL00 stiffener series.
Corrosion of longitudinal stiffener | Corrosion of vertical stiffener |
Critical shear buckling load ( |
Shear buckling strength ( |
With corrosion/without corrosion | ||||
---|---|---|---|---|---|---|---|---|
Height (mm) | Ratio | Load (kN) | Ratio | Load (kN) | Ratio |
|
|
|
Width: 0 mm, |
0 | 0 | 545 | 1.00 | 810 | 1.00 | 1.00 | 1.00 |
100 | 0.1 | 537.5 | 0.99 | 810 | 1.00 | 0.99 | 1.00 | |
200 | 0.2 | 532.5 | 0.98 | 805 | 0.99 | 0.98 | 0.99 | |
300 | 0.3 | 531 | 0.97 | 792.5 | 0.98 | 0.97 | 0.98 | |
400 | 0.4 | 523 | 0.96 | 760 | 0.94 | 0.96 | 0.94 | |
500 | 0.5 | 503.5 | 0.92 | 735 | 0.91 | 0.92 | 0.91 | |
600 | 0.6 | 482.8 | 0.89 | 727.5 | 0.90 | 0.89 | 0.90 | |
700 | 0.7 | 467.2 | 0.86 | 717.5 | 0.89 | 0.86 | 0.89 | |
800 | 0.8 | 458.05 | 0.84 | 715 | 0.88 | 0.84 | 0.88 | |
900 | 0.9 | 455.95 | 0.84 | 712.5 | 0.88 | 0.84 | 0.88 | |
1000 | 1.0 | 446.35 | 0.82 | 712.5 | 0.88 | 0.82 | 0.88 |
Shear buckling values for V-LL200 stiffener series.
Corrosion of longitudinal stiffener | Corrosion of vertical stiffener |
Critical shear buckling load ( |
Shear buckling strength ( |
With corrosion/without corrosion | ||||
---|---|---|---|---|---|---|---|---|
Height (mm) | Ratio | Load (kN) | Ratio | Load (kN) | Ratio |
|
|
|
Width: 200 mm, |
0 | 0 | 513 | 1.00 | 810 | 1.00 | 0.94 | 1.00 |
100 | 0.1 | 504 | 0.98 | 810 | 1.00 | 0.92 | 1.00 | |
200 | 0.2 | 494.35 | 0.96 | 802.5 | 0.99 | 0.91 | 0.99 | |
300 | 0.3 | 487.3 | 0.95 | 777.5 | 0.96 | 0.89 | 0.96 | |
400 | 0.4 | 485.35 | 0.95 | 750 | 0.93 | 0.89 | 0.93 | |
500 | 0.5 | 469.8 | 0.92 | 722.5 | 0.89 | 0.86 | 0.89 | |
600 | 0.6 | 443.6 | 0.86 | 710 | 0.88 | 0.81 | 0.88 | |
700 | 0.7 | 425.5 | 0.83 | 695 | 0.86 | 0.78 | 0.86 | |
800 | 0.8 | 416.95 | 0.81 | 685 | 0.85 | 0.77 | 0.85 | |
900 | 0.9 | 414.8 | 0.81 | 685 | 0.85 | 0.76 | 0.85 | |
1000 | 1.0 | 409.25 | 0.80 | 685 | 0.85 | 0.75 | 0.85 |
Shear buckling values for V-LL400 stiffener series.
Corrosion of longitudinal stiffener | Corrosion of vertical stiffener |
Critical shear buckling load ( |
Shear buckling strength ( |
With corrosion/without corrosion | ||||
---|---|---|---|---|---|---|---|---|
Height (mm) | Ratio | Load (kN) | Ratio | Load (kN) | Ratio |
|
|
|
Width: 400 mm, |
0 | 0 | 489.15 | 1.00 | 810 | 1.00 | 0.90 | 1.00 |
100 | 0.1 | 479.55 | 0.98 | 810 | 1.00 | 0.88 | 1.00 | |
200 | 0.2 | 469.15 | 0.96 | 797.5 | 0.98 | 0.86 | 0.98 | |
300 | 0.3 | 461.8 | 0.94 | 770 | 0.95 | 0.85 | 0.95 | |
400 | 0.4 | 459.85 | 0.94 | 745 | 0.92 | 0.84 | 0.92 | |
500 | 0.5 | 449.35 | 0.92 | 717.5 | 0.89 | 0.82 | 0.89 | |
600 | 0.6 | 420.8 | 0.86 | 695 | 0.86 | 0.77 | 0.86 | |
700 | 0.7 | 396.9 | 0.81 | 682.5 | 0.84 | 0.73 | 0.84 | |
800 | 0.8 | 385.1 | 0.79 | 667.5 | 0.82 | 0.71 | 0.82 | |
900 | 0.9 | 382.5 | 0.78 | 665 | 0.82 | 0.70 | 0.82 | |
1000 | 1.0 | 380.05 | 0.78 | 665 | 0.82 | 0.70 | 0.82 |
Shear buckling values for V-LL600 stiffener series.
Corrosion of longitudinal stiffener | Corrosion of vertical stiffener |
Critical shear buckling load ( |
Shear buckling strength ( |
With corrosion/without corrosion | ||||
---|---|---|---|---|---|---|---|---|
Height (mm) | Ratio | Load (kN) | Ratio | Load (kN) | Ratio |
|
|
|
Width: 600 mm, |
0 | 0 | 475.15 | 1.00 | 805 | 1.00 | 0.87 | 0.99 |
100 | 0.1 | 465.65 | 0.98 | 802.5 | 1.00 | 0.85 | 0.99 | |
200 | 0.2 | 453.25 | 0.96 | 777.5 | 0.97 | 0.83 | 0.96 | |
300 | 0.3 | 443.6 | 0.94 | 745 | 0.93 | 0.81 | 0.92 | |
400 | 0.4 | 438.9 | 0.94 | 725 | 0.90 | 0.81 | 0.90 | |
500 | 0.5 | 435.65 | 0.92 | 705 | 0.88 | 0.80 | 0.87 | |
600 | 0.6 | 409.85 | 0.86 | 692.5 | 0.86 | 0.75 | 0.85 | |
700 | 0.7 | 383.25 | 0.81 | 677.5 | 0.84 | 0.70 | 0.84 | |
800 | 0.8 | 364.05 | 0.79 | 667.5 | 0.83 | 0.67 | 0.82 | |
900 | 0.9 | 357.4 | 0.78 | 652.5 | 0.81 | 0.66 | 0.81 | |
1000 | 1.0 | 356.5 | 0.78 | 652.5 | 0.81 | 0.65 | 0.81 |
Shear buckling values for V-LL800 stiffener series.
Corrosion of longitudinal stiffener | Corrosion of vertical stiffener |
Critical shear buckling load ( |
Shear buckling strength ( |
With corrosion/without corrosion | ||||
---|---|---|---|---|---|---|---|---|
Height (mm) | Ratio | Load (kN) | Ratio | Load (kN) | Ratio |
|
|
|
Width: 800 mm, |
0 | 0 | 455.5 | 1.00 | 802.5 | 1.00 | 0.84 | 0.99 |
100 | 0.1 | 446.65 | 0.98 | 785 | 0.98 | 0.82 | 0.97 | |
200 | 0.2 | 434.3 | 0.95 | 745 | 0.93 | 0.80 | 0.92 | |
300 | 0.3 | 424 | 0.93 | 717.5 | 0.89 | 0.78 | 0.89 | |
400 | 0.4 | 419.25 | 0.92 | 697.5 | 0.87 | 0.77 | 0.86 | |
500 | 0.5 | 417.1 | 0.92 | 680 | 0.85 | 0.77 | 0.84 | |
600 | 0.6 | 397.45 | 0.87 | 672.5 | 0.84 | 0.73 | 0.83 | |
700 | 0.7 | 371.9 | 0.82 | 665 | 0.83 | 0.68 | 0.82 | |
800 | 0.8 | 350.45 | 0.77 | 637.5 | 0.79 | 0.64 | 0.79 | |
900 | 0.9 | 337.95 | 0.74 | 625 | 0.78 | 0.62 | 0.77 | |
1000 | 1.0 | 335 | 0.74 | 622.5 | 0.78 | 0.61 | 0.77 |
Shear buckling values for V-LL1000 stiffener series.
Corrosion of longitudinal stiffener | Corrosion of vertical stiffener |
Critical shear buckling load ( |
Shear buckling strength ( |
With corrosion/without corrosion | ||||
---|---|---|---|---|---|---|---|---|
Height (mm) | Ratio | Load (kN) | Ratio | Load (kN) | Ratio |
|
|
|
Width: 100 mm, |
0 | 0 | 440.25 | 1.00 | 750 | 1.00 | 0.81 | 0.93 |
100 | 0.1 | 431.65 | 0.98 | 742.5 | 0.99 | 0.79 | 0.92 | |
200 | 0.2 | 419.80 | 0.95 | 730 | 0.97 | 0.77 | 0.90 | |
300 | 0.3 | 410.10 | 0.93 | 702.5 | 0.94 | 0.75 | 0.87 | |
400 | 0.4 | 406.20 | 0.92 | 690 | 0.92 | 0.75 | 0.85 | |
500 | 0.5 | 404.00 | 0.92 | 675 | 0.90 | 0.74 | 0.83 | |
600 | 0.6 | 387.35 | 0.88 | 660 | 0.88 | 0.71 | 0.81 | |
700 | 0.7 | 363.7 | 0.83 | 635 | 0.85 | 0.67 | 0.78 | |
800 | 0.8 | 344.25 | 0.78 | 625 | 0.83 | 0.63 | 0.77 | |
900 | 0.9 | 330.85 | 0.75 | 617.5 | 0.82 | 0.61 | 0.76 | |
1000 | 1.0 | 324.20 | 0.74 | 612.5 | 0.82 | 0.59 | 0.76 |
Shear buckling load and ratio of vertical and end-longitudinal stiffener corrosion model.
L-stiffener: 0% corrosion damage
L-stiffener: 20% corrosion damage
L-stiffener: 40% corrosion damage
L-stiffener: 60% corrosion damage
L-stiffener: 80% corrosion damage
L-stiffener: 100% corrosion damage
Shear buckling ratio of V-L stiffener corrosion series for no corrosion damage.
For the vertical and left-right longitudinal stiffener corrosion model, the corrosion height of the vertical stiffener changed from 0 mm to 500 mm in 100 mm units, and the corrosion width of the left-longitudinal stiffener changed from 200 mm to 800 mm in 200 mm units, and the right-longitudinal stiffener changed to 400 mm and 800 mm. As for the vertical and left-longitudinal stiffener corrosion model, they also show similar shear buckling behaviors with the change in the shear buckling value as shown in Tables
Shear buckling values for the V-L-RL200R400 stiffener series.
Corrosion of longitudinal stiffener | Corrosion of vertical stiffener |
Critical shear buckling load ( |
Shear buckling strength ( |
With corrosion/without corrosion | |||||
---|---|---|---|---|---|---|---|---|---|
End (mm) | Inner (mm) | Height (mm) | Ratio | Load (kN) | Ratio | Load (kN) | Ratio |
|
|
200 |
400 |
0 | 0 | 515.5 | 1.00 | 770 | 1.00 | 0.95 | 0.95 |
100 | 0.1 | 507.5 | 0.98 | 770 | 1.00 | 0.93 | 0.95 | ||
200 | 0.2 | 498.7 | 0.97 | 770 | 1.00 | 0.92 | 0.95 | ||
300 | 0.3 | 486.35 | 0.94 | 767.5 | 1.00 | 0.89 | 0.95 | ||
400 | 0.4 | 472.55 | 0.92 | 747.5 | 0.97 | 0.87 | 0.92 | ||
500 | 0.5 | 455.75 | 0.88 | 727.5 | 0.94 | 0.84 | 0.90 |
Shear buckling values for the V-L-RL200R800 stiffener series.
Corrosion of longitudinal stiffener | Corrosion of vertical stiffener |
Critical shear buckling load ( |
Shear buckling strength ( |
With corrosion/without corrosion | |||||
---|---|---|---|---|---|---|---|---|---|
End (mm) | Inner |
Height (mm) | Ratio | Load (kN) | Ratio | Load (kN) | Ratio |
|
|
200 |
800 |
0 | 0 | 509 | 1.00 | 755 | 1.00 | 0.93 | 0.93 |
100 | 0.1 | 507 | 1.00 | 755 | 1.00 | 0.93 | 0.93 | ||
200 | 0.2 | 496.65 | 0.98 | 755 | 1.00 | 0.91 | 0.93 | ||
300 | 0.3 | 476.1 | 0.94 | 752.5 | 1.00 | 0.87 | 0.93 | ||
400 | 0.4 | 455.7 | 0.90 | 745 | 0.99 | 0.84 | 0.92 | ||
500 | 0.5 | 438.75 | 0.86 | 720 | 0.95 | 0.81 | 0.89 |
Shear buckling values for the V-L-RL400R400 stiffener series.
Corrosion of longitudinal stiffener | Corrosion of vertical stiffener |
Critical shear buckling load ( |
Shear buckling strength ( |
With corrosion/without corrosion | |||||
---|---|---|---|---|---|---|---|---|---|
End (mm) | Inner |
Height (mm) | Ratio | Load (kN) | Ratio | Load (kN) | Ratio |
|
|
400 |
400 |
0 | 0 | 488.4 | 1.00 | 770 | 1.00 | 0.90 | 0.95 |
100 | 0.1 | 481.35 | 0.99 | 770 | 1.00 | 0.88 | 0.95 | ||
200 | 0.2 | 472.8 | 0.97 | 770 | 1.00 | 0.87 | 0.95 | ||
300 | 0.3 | 463.5 | 0.95 | 767.5 | 1.00 | 0.85 | 0.95 | ||
400 | 0.4 | 454.7 | 0.93 | 742.5 | 0.96 | 0.83 | 0.92 | ||
500 | 0.5 | 438.6 | 0.90 | 707.5 | 0.92 | 0.80 | 0.87 |
Shear buckling values for the V-L-RL400R800 stiffener series.
Corrosion of longitudinal stiffener | Corrosion of vertical stiffener |
Critical shear buckling load ( |
Shear buckling strength ( |
With corrosion/without corrosion | |||||
---|---|---|---|---|---|---|---|---|---|
End (mm) | Inner |
Height (mm) | Ratio | Load (kN) | Ratio | Load (kN) | Ratio |
|
|
400 |
800 |
0 | 0 | 488.35 | 1.00 | 765 | 1.00 | 0.90 | 0.94 |
100 | 0.1 | 482.4 | 0.99 | 762.5 | 1.00 | 0.89 | 0.94 | ||
200 | 0.2 | 473.7 | 0.97 | 762.5 | 1.00 | 0.87 | 0.94 | ||
300 | 0.3 | 459.95 | 0.94 | 762.5 | 1.00 | 0.84 | 0.94 | ||
400 | 0.4 | 444.6 | 0.91 | 737.5 | 0.96 | 0.82 | 0.91 | ||
500 | 0.5 | 428.6 | 0.88 | 707.5 | 0.92 | 0.79 | 0.87 |
Shear buckling values for the V-L-RL600R400 stiffener series.
Corrosion of longitudinal stiffener | Corrosion of vertical stiffener |
Critical shear buckling load ( |
Shear buckling strength ( |
With corrosion/without corrosion | |||||
---|---|---|---|---|---|---|---|---|---|
End (mm) | Inner |
Height (mm) | Ratio | Load (kN) | Ratio | Load (kN) | Ratio |
|
|
600 |
400 |
0 | 0 | 475.45 | 1.00 | 770 | 1.00 | 0.87 | 0.95 |
100 | 0.1 | 468 | 0.98 | 770 | 1.00 | 0.86 | 0.95 | ||
200 | 0.2 | 457.35 | 0.96 | 770 | 1.00 | 0.84 | 0.95 | ||
300 | 0.3 | 444.55 | 0.94 | 740 | 0.96 | 0.82 | 0.91 | ||
400 | 0.4 | 432.8 | 0.91 | 702.5 | 0.91 | 0.79 | 0.87 | ||
500 | 0.5 | 423.1 | 0.89 | 682.5 | 0.89 | 0.78 | 0.84 |
Shear buckling values for the V-L-RL600R800 stiffener series.
Corrosion of longitudinal stiffener | Corrosion of vertical stiffener |
Critical shear buckling load ( |
Shear buckling strength ( |
With corrosion/without corrosion | |||||
---|---|---|---|---|---|---|---|---|---|
End (mm) | Inner (mm) | Height (mm) | Ratio | Load (kN) | Ratio | Load (kN) | Ratio |
|
|
600 |
800 |
0 | 0 | 476.3 | 1.00 | 755 | 1.00 | 0.87 | 0.93 |
100 | 0.1 | 469.3 | 0.99 | 755 | 1.00 | 0.86 | 0.93 | ||
200 | 0.2 | 458.45 | 0.96 | 755 | 1.00 | 0.84 | 0.93 | ||
300 | 0.3 | 442.25 | 0.93 | 742.5 | 0.98 | 0.81 | 0.92 | ||
400 | 0.4 | 426.55 | 0.90 | 702.5 | 0.93 | 0.78 | 0.87 | ||
500 | 0.5 | 414.35 | 0.87 | 680 | 0.90 | 0.76 | 0.84 |
Shear buckling values for the V-L-RL800R400 stiffener series.
Corrosion of longitudinal stiffener | Corrosion of vertical stiffener |
Critical shear buckling load ( |
Shear buckling strength ( |
With corrosion/without corrosion | |||||
---|---|---|---|---|---|---|---|---|---|
End (mm) | Inner |
Height (mm) | Ratio | Load (kN) | Ratio | Load (kN) | Ratio |
|
|
800 |
400 |
0 | 0 | 458.45 | 1.00 | 772.5 | 1.00 | 0.84 | 0.95 |
100 | 0.1 | 450.45 | 0.98 | 772.5 | 1.00 | 0.83 | 0.95 | ||
200 | 0.2 | 438.3 | 0.96 | 745 | 0.96 | 0.80 | 0.92 | ||
300 | 0.3 | 424.45 | 0.93 | 707.5 | 0.92 | 0.78 | 0.87 | ||
400 | 0.4 | 413.8 | 0.90 | 682.5 | 0.88 | 0.76 | 0.84 | ||
500 | 0.5 | 407.8 | 0.89 | 667.5 | 0.86 | 0.75 | 0.82 |
Shear buckling values for the V-L-RL800R800 stiffener series.
Corrosion of longitudinal stiffener | Corrosion of vertical stiffener |
Critical shear buckling load ( |
Shear buckling strength ( |
With corrosion/without corrosion | |||||
---|---|---|---|---|---|---|---|---|---|
End (mm) | Inner |
Height (mm) | Ratio | Load (kN) | Ratio | Load (kN) | Ratio |
|
|
800 |
800 |
0 | 0 | 460.8 | 1.00 | 755 | 1.00 | 0.85 | 0.93 |
100 | 0.1 | 451.85 | 0.98 | 755 | 1.00 | 0.83 | 0.93 | ||
200 | 0.2 | 439 | 0.95 | 742.5 | 0.98 | 0.81 | 0.92 | ||
300 | 0.3 | 422.6 | 0.92 | 707.5 | 0.94 | 0.78 | 0.87 | ||
400 | 0.4 | 409.55 | 0.89 | 682.5 | 0.90 | 0.75 | 0.84 | ||
500 | 0.5 | 401.4 | 0.87 | 665 | 0.88 | 0.74 | 0.82 |
Shear buckling load and ratio of the V-L-R stiffener corrosion model.
L-stiffener: 20–40% corrosion damage
L-stiffener: 20–80% corrosion damage
L-stiffener: 40-40% corrosion damage
L-stiffener: 40–80% corrosion damage
L-stiffener: 60–40% corrosion damage
L-stiffener: 60–80% corrosion damage
L-stiffener: 80–40% corrosion damage
L-stiffener: 80-80% corrosion damage
Shear buckling ratio of V-L-R stiffener corrosion series for no corrosion damage.
Shear buckling behaviors of the web panel can be classified as before elastic shear buckling behavior, and post-shear buckling behavior, after elastic shear buckling behavior. Before elastic shear buckling, equal tensile and compressive principal stresses in the web panel develop prior to incipient buckling under shear load. After elastic shear buckling, the diagonal tension stresses (diagonal tension stresses) resist the additional shear load. Elastic shear buckling load is calculated by (
Shear buckling strength determined from post-shear buckling behaviors can be considered from AISC [
For calculation by AASHTO and AISC design specifications, the critical shear buckling load of web panel (1000
Comparison of the shear buckling strengths for each analysis case.
This study examined the shear buckling failure and strength of web panels stiffened by stiffeners, to evaluate the effect of corroded stiffeners on shear buckling behaviors, according to the local corrosion damage of the stiffener. Therefore, for stiffener corrosion cases in the plate girder, nonlinear FE analyses were conducted, and their shear buckling behaviors were compared, as well as the change in the shear buckling strength of the web panel, depending on the degree of corrosion of the vertical and longitudinal stiffeners. For shear buckling failure mode, basically, they were shown to have a typical shear buckling failure mode, related to the shear resistance of a web panel with a diagonal tension field. Their tensile field band shapes were more clearly going down in a tension field direction of the web panel affected by weak stiffened damaged stiffeners, depending on the degree of corrosion damage of the vertical stiffener. This tendency can be found in the load out-of-plane displacement in the center web panel, and the maximum out-of-plane displacement also changed, according to the mechanical relationship between the web panel and the vertical and longitudinal stiffeners in the plate girder. Their critical shear buckling load and shear buckling strength decreased, depending on the corroded height of the vertical stiffener and the corroded width of the longitudinal stiffener from 82% to 59% of the critical shear buckling load, and from 88% to 76% of the shear buckling strength, since the shear buckling behaviors of the web panel are determined by the shear resistance of the web panel stiffened by each stiffener. For over 40% corrosion damage of the vertical stiffener, the corrosion ratio of the vertical stiffener should be considered to repair or reinforce the web panel with a corroded stiffener, since their shear buckling strengths can decrease below the design value.
In this study, the shear buckling behaviors of a web panel stiffened by stiffener with corrosion damage were examined. Their shear buckling failure behaviors and the change in the shear buckling strength were found to be insufficient for all web panel conditions with stiffener. For more effective results on the shear buckling behavior of web panel, various design conditions of the web panel and the corrosion conditions should be considered.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2014R1A1A2055900 and NRF-2014R1A1A2058765).