Research Article  Open Access
Locally Corroded Stiffener Effect on Shear Buckling Behaviors of Web Panel in the Plate Girder
Abstract
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 fourpanel 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 postshear buckling behaviors, as well as their outofplane 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.
1. Introduction
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 [1–3]. For a steel plate girder bridge, vertical and longitudinal stiffeners are basically installed to improve the shear buckling strength of their web panel. However, stiffeners also are not free from corrosion damage, depending on timedependent maintenance. In the collapsed plate girder bridge caused by severe corrosion damage in Japan in 2009 [3, 4], severely corroded longitudinal and vertical stiffeners were also found, as shown in Figure 1. For shear buckling problems, various studies were conducted to examine the shear bucking behaviors of web panel and to suggest design guideline of web panel under shear loading [5–12]. Several studies on shear buckling problem with local corrosion damage in web panel were also carried out, since corrosion damage of the web panel is related to decrease in the shear buckling strength and shear failure behavior [2, 3, 13–17]. In case of a corroded plate girder, sectional damage of stiffeners affected by corrosion damage can also relate to shear buckling behaviors of the web panel. However, it is difficult to consider all the corroded cases of a plate girder. If all cases were considered, the corrosion damage effect of a stiffener on the shear buckling behaviors of a plate girder is not clear.
(a) After collapse [3]
(b) Inside before collapse [4]
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 fourpanel web panel stiffened by vertical and longitudinal stiffeners was selected. After their postshear 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.
2. FE Analysis Model of Plate Girder with Corroded Stiffener
2.1. Analysis Cases of the Corroded Stiffener in the FE Analysis
To numerically analyze the shear buckling behaviors of the web panel with stiffener, a fourpanel 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 2. All the stiffeners were considered identical, of 12 mm thickness and 90 mm width.
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 endlongitudinal stiffener were considered to be corroded from the lower flange and center of the endlongitudinal stiffener, to examine the effect between the corroded vertical stiffener and the endlongitudinal stiffener on their shear buckling behaviors. For the third FE analysis case, a leftlongitudinal stiffener (endlongitudinal stiffener) and rightlongitudinal stiffener (nextlongitudinal stiffener) were considered to be corroded with the vertical stiffener, to examine the relationship between leftlongitudinal stiffener and rightlongitudinal stiffener. Thus, in the vertical and leftlongitudinal 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 leftlongitudinal 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 3(a). In the vertical and leftright longitudinal stiffener corrosion model, the corroded height of the vertical stiffener changed from 0 mm to 500 mm in 100 mm units (10% of the vertical stiffener height), and the corroded width of the leftlongitudinal stiffener changed from 200 mm to 800 mm in 200 mm units (20% of vertical stiffener height), and the rightlongitudinal stiffener changed to 400 mm and 800 mm for a symmetric web panel, as shown in Figure 3(b). However, the corroded widths of the leftlongitudinal stiffener and rightlongitudinal stiffener were not the same for all analysis cases, to examine the relationship between the endlongitudinal stiffener and the nextlongitudinal stiffener.
(a) Vertical and endlongitudinal stiffener corrosion model (Vstiffener cases, VL stiffener cases)
(b) Vertical and leftright longitudinal stiffener corrosion model (VLR stiffener cases)
For the FE analysis model, they are identified as follows: the first letter indicates the analysis case (VL: vertical and leftlongitudinal stiffener corrosion model, VLR: vertical and leftright 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 leftlongitudinal stiffener (e.g., L200 indicates an endlongitudinal stiffener of 200 mm), and the fourth letter, R, indicates the width of the rightlongitudinal stiffener (e.g., R200 indicates the nextlongitudinal 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:(1)Vertical stiffener corrosion model (Vstiffener cases).(2)Vertical and leftlongitudinal stiffener corrosion model (VL stiffener cases).(3)Vertical and leftright longitudinal stiffener corrosion model (VLR stiffener cases).
2.2. FE Analysis Model
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 8node solid element was used, as shown in Figure 4. For material properties of the FE analysis model, the tensile strength test results were used with a nominal yield stress of 260 MPa, Young’s modulus of 206,000 MPa, and Poisson’s ratio of 0.3. Elasticperfectly plastic behaviors and the von Mises yield criterion were applied as the material plasticity.
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 endlongitudinal stiffener and rightlongitudinal stiffener (nextlongitudinal stiffener) was removed with the corrosion damage of vertical stiffeners according to FE analysis condition. For VLH600L400 model, therefore, vertical stiffener was removed to 600 mm from lower flange and 400 mm length of endlongitudinal stiffener was removed as corrosion damage as shown in Figure 4.
3. Shear Buckling Failure Depending on the Corroded Stiffener Condition
3.1. FE Model Validation
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 [18]. Figure 5 shows validation model of the FE analysis. Figure 6 presents a comparison of the displacement at midspan of the test result data and the FE analysis result. As shown in Figure 6, its displacement was found to be in agreement with that of the test result. Therefore, the shear buckling behavior of the plate girder with stiffener can be examined using this FE analysis model.
3.2. Shear Buckling Failures of Web Panel with Corroded Stiffener
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 7–15 show their outofplane displacement contours and maximum principal stress contours. As shown in Figures 7–15, a typical shear buckling failure mode can be found with a diagonal tension field through the shear resistant behaviors of the web panel. By increasing the damage of the vertical stiffener, a wider and larger diagonal tension field band was present, owing to the increase caused in the shear resistant width of the web panel. Pronounced outofplane deformation also appeared at the corroded vertical stiffener, by reduction of the shear resistance of the vertical stiffener to restrict the shear buckling of the web panel; thus its tensile field shape was shown to be going down in the tension field direction of the web panel, according to decrease in the vertical stiffener by corrosion damage. For the 100% damage vertical stiffener, in particular, shear buckling failure mode of the wide web panel was present, due to increase in the width of the web panel by the disappearing vertical stiffener.
(a) Outofplane displacement contour
(b) Maximum principal stress distribution contour
(a) Outofplane displacement contour
(b) Maximum principal stress distribution contour
(a) Outofplane displacement contour
(b) Maximum principal stress distribution contour
(a) Outofplane displacement contour
(b) Maximum principal stress distribution contour
(a) Outofplane displacement contour
(b) Maximum principal stress distribution contour
(a) Outofplane displacement contour
(b) Maximum principal stress distribution contour
(a) Outofplane displacement contour
(b) Maximum principal stress distribution contour
(a) Outofplane displacement contour
(b) Maximum principal stress distribution contour
(a) Outofplane displacement contour
(b) Maximum principal stress distribution contour
In the case of the vertical and leftlongitudinal stiffeners corrosion model, as shown in Figures 10–13, their shear buckling failure modes were shown to be similar to those of the vertical stiffener corrosion model. A diagonal tension field was also present in the upper web panel of the longitudinal stiffener, according to increase in the corrosion damage of the longitudinal stiffener, except for the endlongitudinal stiffener case with 20% corrosion damage, and their tensile field shapes were shown to be more clearly going down in a tension field direction of the web panel affected by weak stiffened damaged stiffeners, according to decrease in the vertical stiffener by corrosion damage. The shear resistance of the endlongitudinal stiffener with 20% corrosion damage was not affected, and a similar diagonal tension field developed, even though corrosion damage occurred in the endlongitudinal stiffener. The vertical stiffener corrosion model with leftright longitudinal stiffener corrosion also showed a similar tendency to those of the vertical stiffener corrosion model with longitudinal stiffener corrosion, since the shear resistance of the web panel decreased by corrosion damage of the longitudinal stiffener of the next web panel, as shown in Figures 14–15.
To more clearly identify this tendency, outofplane displacements were also compared according to the corroded stiffener condition, in company with comparing the displacements at the center of a plate girder. Figure 16 shows the outofplane displacements and displacements of representative stiffener corrosion cases, as shown in Figures 7–15. Outofplane displacements at the center points of the end (left) web panel appeared to increase, and their critical buckling loads and shear buckling strengths decreased with reduced stiffness effect of the stiffener for the shear resistant strength of the web plane, as shown in the loaddisplacement relationship curve in Figure 16. In their load outofplane displacement relationships, as shown in their shear buckling failure mode contours in Figures 7–15, distortional shear buckling behaviors of the web panel affected by the remaining vertical and longitudinal stiffeners presented as askew bends of the web plane to resist shear stress in the web panel. Since the point where the maximum outofplane displacement occurred changed, according to the mechanical relationship between the web panel and the vertical and longitudinal stiffeners in the plate girder, their load outofplane displacements at the center of the left web panel also showed different levels to the shear loading level, and irregular distribution in the same plane of the web panel.
(a) Outofplane displacement of Vstiffener series
(b) Displacement of Vstiffener series
(c) Outofplane displacement of VL stiffener series
(d) Displacement of VL stiffener series
(e) Outofplane displacement of VLRstiffener series
(f) Displacement of VLRstiffener series
3.3. Shear Buckling Strength Related to Corroded Stiffener Condition
3.3.1. Vertical and LeftLongitudinal Stiffener Corrosion Model (VL Cases)
For the vertical and leftlongitudinal 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 endlongitudinal 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 1–6 and Figure 17. Their critical shear buckling load and shear buckling strength were also affected, according to the corroded width of the longitudinal stiffener. Thus, the critical shear buckling loads changed from 545.0 kN to 324.2 kN, and shear buckling strengths decreased from 810.0 kN to 612.5 kN. This means the critical buckling load can decrease to 59% and 76% of those of the web panel stiffener without corrosion damage, according to the condition of the longitudinal stiffener. For each longitudinal stiffener corrosion case, their shear buckling values relatively sharply decreased, after 50% corrosion damage of the vertical stiffener, like that of the vertical stiffener corrosion model. Figure 18 summarizes the shear buckling ratio of each vertical and endlongitudinal stiffener corrosion model for no corrosion damage in the stiffener. For critical shear buckling load, it decreased from 82% to 59% of that of no corrosion damage in the stiffener. For shear buckling strength, it decreased from 88% to 76% of that of no corrosion damage in the stiffener.






(a) Lstiffener: 0% corrosion damage
(b) Lstiffener: 20% corrosion damage
(c) Lstiffener: 40% corrosion damage
(d) Lstiffener: 60% corrosion damage
(e) Lstiffener: 80% corrosion damage
(f) Lstiffener: 100% corrosion damage
3.3.2. Vertical and LeftRight Longitudinal Stiffener Corrosion Model (VLR Cases)
For the vertical and leftright 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 leftlongitudinal stiffener changed from 200 mm to 800 mm in 200 mm units, and the rightlongitudinal stiffener changed to 400 mm and 800 mm. As for the vertical and leftlongitudinal stiffener corrosion model, they also show similar shear buckling behaviors with the change in the shear buckling value as shown in Tables 7–14 and Figure 19. As the shear stiffness of the enlarged shear web panel decreased from the disappearing longitudinal stiffener of the inner web panel (right web panel) by corrosion damage, their critical shear buckling loads and shear buckling strengths highly decreased by slightly more than those of the vertical and left longitudinal stiffener corrosion model (VL cases). For the same vertical stiffener corrosion, they thus have about 4~6% decreased shear buckling values affected by the next (near) longitudinal stiffener (longitudinal stiffener of the next panel). Figure 20 summarizes the shear buckling ratio of each vertical and leftright longitudinal stiffener corrosion model for no corrosion damage in the stiffener.








(a) Lstiffener: 20–40% corrosion damage
(b) Lstiffener: 20–80% corrosion damage
(c) Lstiffener: 4040% corrosion damage
(d) Lstiffener: 40–80% corrosion damage
(e) Lstiffener: 60–40% corrosion damage
(f) Lstiffener: 60–80% corrosion damage
(g) Lstiffener: 80–40% corrosion damage
(h) Lstiffener: 8080% corrosion damage
3.4. Evaluation of Shear Buckling Strength of Web Panel Related to Corroded Stiffener
Shear buckling behaviors of the web panel can be classified as before elastic shear buckling behavior, and postshear 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 (1), using the buckling coefficient with regard to the boundary conditions [19]:where is the elastic modulus, is Poisson’s ratio, is the web thickness, is the web height, and is the buckling coefficient determined from the boundary conditions and the aspect ratio.
Shear buckling strength determined from postshear buckling behaviors can be considered from AISC [20] and AASHTO [21] design specifications. In AISC [20], the nominal shear strength () is given by (2) and (3) at the limit of the tension field yielding. For the shear coefficient () of (3), it is suggested to be given by (4a), (4b), (4c):where the buckling coefficient () is suggested to be given by In AASHTO [21], the nominal shear resistance () is given by (2), on the basis of the fully plastic strength (), as shown in (6). The fully plastic shear strength () and the shear coefficient () of (6) are suggested to be given by (7) and (8a), (8b), and (8c), respectively:where the buckling coefficient () is suggested to be as shown in
For calculation by AASHTO and AISC design specifications, the critical shear buckling load of web panel (1000 1000 mm) using (4a), (4b), and (4c) was calculated as 402 kN, and the shear buckling strength of the web panel was calculated as 709 kN for AASHTO, and 731 kN for AISC. In this study, vertical stiffener cases with 0~100% corrosion damage have been considered to examine the effect of corrosion damage of the stiffener on shear buckling behaviors of the web panel. However, it is difficult for a vertical stiffener to fully corrode (100% corrosion) under a real atmospheric corrosion environment. Therefore, the shear buckling strength of vertical stiffener cases with 0~50% corrosion damage was considered, to compare the shear buckling values of the web panel stiffened by stiffeners with design values. Figure 21 shows a comparison of the shear buckling strengths for each analysis case of the stiffener corrosion model. As shown in Figure 21, on the whole, shear buckling strengths of the web panels stiffened by stiffeners were shown to be higher than the design value, except for the multiply severely corroded stiffener cases. However, after 40% corrosion damage of the vertical stiffener, its shear buckling strength can decrease below the design value. Therefore, the corrosion ratio of the vertical stiffener should be checked, to repair or reinforce the web panel with a corroded stiffener.
4. Conclusions
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 outofplane displacement in the center web panel, and the maximum outofplane 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.
Conflict of Interests
The authors declare that there is no conflict of interests regarding the publication of this paper.
Acknowledgment
This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF2014R1A1A2055900 and NRF2014R1A1A2058765).
References
 National Institute for Land and Infrastructure Management, “Research on local corrosion of highway steel bridges,” Technical Note 294, National Institute for Land and Infrastructure Management, 2006 (Japanese). View at: Google Scholar
 I.T. Kim, M.J. Lee, J.H. Ahn, and S. Kainuma, “Experimental evaluation of shear buckling behaviors and strength of locally corroded web,” Journal of Constructional Steel Research, vol. 83, pp. 75–89, 2013. View at: Publisher Site  Google Scholar
 J.H. Ahn, I.T. Kim, S. Kainuma, and M.J. Lee, “Residual shear strength of steel plate girder due to web local corrosion,” Journal of Constructional Steel Research, vol. 89, pp. 198–212, 2013. View at: Publisher Site  Google Scholar
 T. Shimozato, Y. Tamaki, J. Murakoshi, and M. Takahasi, “Real time monitoring of bridge collapse due to intense corrosion,” Magazine of Korean Society of Steel Construction, vol. 22, no. 5, pp. 13–17, 2010 (Korean). View at: Google Scholar
 D. M. Porter, K. C. Rockey, and H. R. Evans, “The collapse behavior of plate girders loaded in shear,” Structural Engineer, vol. 53, no. 8, pp. 313–325, 1975. View at: Google Scholar
 S. C. Lee, J. S. Davidson, and C. H. Yoo, “Shear buckling coefficients of plate girder web panels,” Computers & Structures, vol. 59, no. 5, pp. 789–795, 1996. View at: Publisher Site  Google Scholar
 S.K. Jung and D. W. White, “Shear strength of horizontally curved steel Igirders—finite element analysis studies,” Journal of Constructional Steel Research, vol. 62, no. 4, pp. 329–342, 2006. View at: Publisher Site  Google Scholar
 I. Estrada, E. Real, and E. Mirambell, “Shear resistance in stainless steel plate girders with transverse and longitudinal stiffening,” Journal of Constructional Steel Research, vol. 64, no. 11, pp. 1239–1254, 2008. View at: Publisher Site  Google Scholar
 N. C. Hagen and P. K. Larsen, “Shear capacity of steel plate girders with large web openings—part II: design guidelines,” Journal of Constructional Steel Research, vol. 65, no. 1, pp. 151–158, 2009. View at: Publisher Site  Google Scholar
 M. F. Hassanein, “Finite element investigation of shear failure of lean duplex stainless steel plate girders,” ThinWalled Structures, vol. 49, no. 8, pp. 964–973, 2011. View at: Publisher Site  Google Scholar
 M. M. Alinia, A. Gheitasi, and M. Shakiba, “Postbuckling and ultimate state of stresses in steel plate girders,” ThinWalled Structures, vol. 49, no. 4, pp. 455–464, 2011. View at: Publisher Site  Google Scholar
 A. Bedynek, E. Real, and E. Mirambell, “Tapered plate girders under shear: tests and numerical research,” Engineering Structures, vol. 46, pp. 350–358, 2013. View at: Publisher Site  Google Scholar
 J.H. Ahn, S. Kainuma, and I.T. Kim, “Shear failure behaviors of a web panel with local corrosion depending on web boundary conditions,” ThinWalled Structures, vol. 73, pp. 302–317, 2013. View at: Publisher Site  Google Scholar
 T. E. Dunbar, N. Pegg, F. Taheri, and L. Jiang, “A computational investigation of the effects of localized corrosion on plates and stiffened panels,” Marine Structures, vol. 17, no. 5, pp. 385–402, 2004. View at: Publisher Site  Google Scholar
 D. Ok, Y. Pu, and A. Incecik, “Computation of ultimate strength of locally corroded unstiffened plates under uniaxial compression,” Marine Structures, vol. 20, no. 12, pp. 100–114, 2007. View at: Publisher Site  Google Scholar
 R. Rahgozar, “Remaining capacity assessment of corrosion damaged beams using minimum curves,” Journal of Constructional Steel Research, vol. 65, no. 2, pp. 299–307, 2009. View at: Publisher Site  Google Scholar
 J. E. Silva, Y. Garbatov, and C. Guedes Soares, “Ultimate strength assessment of rectangular steel plates subjected to a random localised corrosion degradation,” Engineering Structures, vol. 52, pp. 295–305, 2013. View at: Publisher Site  Google Scholar
 J.H. Ahn, W.H. Lee, and I.T. Kim, “Shear buckling of the web panel in the plate girder with circular local section damage,” in Proceedings of the 25th Annual Conference Korean Society of Steel Construction, vol. 25, pp. 91–92, 2014 (Korean). View at: Google Scholar
 S. P. Timoshenko and J. M. Gere, Theory of Elastic Stability, McGrawHill, New York, NY, USA, 2nd edition, 1961. View at: MathSciNet
 American Institute of Steel Construction, Seismic Provisions for Structural Steel Buildings, AISC, Chicago, Ill, USA, 2005.
 American Association of State Highway and Transportation Officials, LRFD Bridge Design Specifications, AASHTO, Washington, DC, USA, 1st edition, 1994.
Copyright
Copyright © 2015 Jungwon Huh et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.