The tall, thin web of a plate girder can buckle under shear long before the steel yields. Adjust the web depth, thickness and stiffener spacing to see the elastic shear buckling stress, the shear yield stress and the web shear capacity update in real time, and find out whether buckling or yielding governs.
Parameters
Web depth d
mm
Height of the web plate between the two flanges
Web thickness t_w
mm
The thinner the web, the more slender and the easier it buckles
Stiffener spacing a
mm
Length of one panel between transverse stiffeners
Yield strength F_y
MPa
Steel yield strength (235 for mild steel, 355+ for high-strength steel)
Results
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Panel aspect ratio a/d
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Shear buckling coefficient k_v
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Elastic shear buckling stress τ_cr (MPa)
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Shear yield stress τ_y (MPa)
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Web shear capacity (kN)
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Failure mode
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Plate girder elevation — web shear buckling
A web held between two flanges is divided into panels by vertical transverse stiffeners. A panel loaded in shear folds into inclined wrinkles under the diagonal compression. The colour shows whether buckling governs (orange) or yielding governs (green).
Shear yield stress τ_y (von Mises criterion) and the governing stress τ_gov. If τ_cr is less than τ_y, buckling governs; if greater, yielding governs.
$$V=\tau_{gov}\,d\,t_w$$
Web shear capacity V (the shear force one panel can carry), found by multiplying the governing stress by the web cross-sectional area.
What is the Plate Girder Web Shear Buckling Simulator?
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I hear "plate girder" a lot for bridge beams. How is it different from an ordinary rolled H-section beam?
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Roughly speaking, a plate girder is a large beam built up by welding steel plates together. Two "flange" plates on top and bottom, with one tall "web" plate in between, forming an I-shaped section. The flanges carry the bending, the web carries the shear. The advantage is that you can build girders 2 or 3 metres deep — far bigger than any rolled H-section — with exactly the plate thicknesses you need.
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I see. So the web is the plate that takes the shear. But what does it mean for it to "buckle" in shear? I thought buckling only happened under compression.
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Good question. The thing is, pure shear on a panel is equivalent to a compression along one diagonal and a tension along the other. So there is a "compression" hidden inside the shear. A tall, thin web is a slender plate, so when that diagonal compression acts on it, it folds suddenly into inclined wrinkles at a stress well below where the steel would yield. That is web shear buckling.
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So it buckles before it even yields. When I make the "web thickness" thinner on the left, the buckling stress τ_cr drops fast.
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Exactly. The buckling stress is proportional to the square of the web slenderness — to (t_w/d)². So halving the thickness drops the buckling stress to a quarter. You want a thin web to save weight, but the thinner it is, the sooner buckling comes — that is the dilemma of plate girder design. A common field problem is shaving the web too thin to lighten the girder and ending up short of shear capacity.
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How do you stop a thin web from buckling? Is making it thicker the only option?
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The other powerful move is intermediate stiffeners. You weld vertical plates across the web at intervals, dividing the tall web into shorter, more nearly square panels. The buckling stress is proportional to the buckling coefficient k_v, which depends on the panel shape (aspect ratio a/d), and a more nearly square panel has a larger k_v. So by spacing stiffeners closer to shrink a/d, you can raise the buckling strength without thickening the web. The "buckling stress vs stiffener spacing" chart below shows the stress rising as the spacing shrinks.
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If the web does buckle, is that girder finished?
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Not necessarily. A slender web, even after it buckles, can still carry more load through a tension "membrane" that forms along the panel diagonal. This is called tension field action, and it can be taken into design as a post-buckling reserve. But the elastic shear buckling stress this tool gives you is the key threshold at which buckling begins, and it is the basic value for setting stiffener spacing. The first step is to judge here whether buckling or yielding governs.
Frequently Asked Questions
The web is a tall, thin plate that carries the shear. Pure shear on a panel is equivalent to a compression along one diagonal and a tension along the other. That diagonal compression folds a thin web into a pattern of inclined wrinkles. The thinner the plate, the sooner it buckles, and the buckling stress can be well below the shear yield stress of the steel. That is why, in plate girders, this elastic shear buckling often governs the strength instead of yielding.
The shear buckling coefficient k_v depends on the shape of the web panel — its aspect ratio a/d, where a is the stiffener spacing and d is the web depth. For a/d >= 1, k_v = 5.34 + 4.0/(a/d)²; for a/d < 1, k_v = 4.0 + 5.34/(a/d)². The closer the panel is to square, the larger k_v and the higher the buckling stress. Closer stiffener spacing (a smaller a/d) raises k_v and so the web's buckling strength.
Intermediate transverse stiffeners are welded vertically across the web to divide a tall web into shorter, more nearly square panels. The buckling stress depends strongly on the panel aspect ratio: reducing a/d increases the buckling coefficient k_v and so the buckling stress. Moving the stiffener-spacing slider in this tool shows the buckling stress rising as the spacing is reduced. It helps you decide between adding stiffeners or increasing the web thickness.
No. A slender web does not fail immediately when it buckles in elastic shear. After buckling, a tension membrane forms along the panel diagonal and carries additional load — a post-buckling reserve known as tension field action. The elastic shear buckling stress computed by this tool is, however, the key threshold at which buckling begins, and it is the basis for stiffener-spacing design and serviceability checks.
Real-World Applications
Plate girder bridges: The most common girder form for road and railway bridges is the welded-up plate girder. Shear force is largest near the supports, so web buckling governs there. Designers space the stiffeners closer near the supports to make the panels more nearly square and secure the buckling stress, while at midspan — where bending governs and shear is small — the stiffener spacing is widened to cut cost. The result is a deliberately graded stiffener layout.
Long-span building beams and transfer girders: Tall welded-up girders are used for the steel beams that span the large spaces of gymnasiums, factories and commercial buildings, and for transfer girders that pick up an upper-storey column and carry its load to a different column. These also need the same web shear buckling check, and where openings (penetrations for pipes and ducts) are introduced, panel subdivision and stiffening become even more important.
Crane runway girders: The girder that supports the rails on which an overhead crane travels is a typical plate girder. As the crane moves, the position of the shear force changes and the girder carries repeated load, so the web and stiffeners are checked for both buckling and fatigue. Where the concentrated wheel load travels, local web buckling (patch loading) also needs attention.
Design checks and inspection of existing bridges: Existing plate girder bridges sometimes show diagonal out-of-plane deformation in the web — the trace of buckling. An elastic shear buckling estimate like this tool gives a first read on how much margin the current stiffener layout has against buckling, helping to decide whether strengthening (adding stiffeners) is needed. A detailed check uses non-linear FEM analysis that accounts for initial imperfections and residual stresses.
Common Misconceptions and Pitfalls
The most common mistake is assuming the web is governed by shear yielding. For beams with a thick, shallow web — such as rolled H-sections — shear yielding does govern. But for plate girders, where the web is thin and tall, elastic shear buckling occurs before yielding and governs the strength. As the comparison of τ_cr and τ_y in this tool shows, at the default condition (a high web slenderness) the buckling stress τ_cr is the smaller of the two, so buckling is the governing mode. Computing the shear capacity simply as "web area × shear yield stress" overestimates it on the unsafe side.
Next, the misconception that "adding stiffeners means the web cannot buckle". Intermediate stiffeners divide the web into panels and raise the buckling coefficient k_v, but the stiffeners themselves must have enough stiffness and strength. A stiffener with too little stiffness simply moves out of plane together with the web when it buckles, and the panel subdivision has no effect. Also, shear buckling depends strongly not only on the stiffener spacing a but on the web thickness t_w. If t_w is too thin, no amount of closer stiffener spacing will raise the buckling stress far enough. It is essential to decide the stiffener spacing and the web thickness together.
Finally, treating the elastic buckling stress as the ultimate strength. What this tool computes is the elastic shear buckling stress of an ideal flat plate with no initial imperfections. A real web has initial out-of-plane deformation from fabrication and welding residual stresses, so buckling actually begins "gradually" at a somewhat lower stress. On the other hand, after buckling there is the post-buckling reserve of tension field action along the panel diagonal, so the ultimate strength can be higher than the elastic buckling stress. Use the elastic shear buckling stress as a guide and a threshold for setting stiffener spacing, and confirm the ultimate design with the code formulas of each national standard or with non-linear analysis.
How to Use
Enter web depth (d) in mm, typically 800–2000 for plate girders, and web thickness (tw) in mm, usually 8–16 for steel grade 350.
Set panel aspect ratio (a/d) by defining stiffener spacing (a) relative to depth; ratios of 1.0–1.5 are common in highway bridge design.
Input steel yield strength (fy) in MPa: 250 for mild steel, 350 for high-strength, 450 for premium grades.
Read elastic shear buckling stress τ_cr using AISC formula k_v = 5.34 + 4.0(d/a)², then τ_cr = k_v × π² × E / (12(1−ν²) × (d/tw)²).
Compare τ_y (shear yield ≈ 0.58fy) against τ_cr to identify buckling or yield governs; panel capacity in kN follows from stress × web area.
Worked Example
Plate girder with d=1200 mm, tw=12 mm, a=1400 mm (a/d=1.17), fy=350 MPa, E=200 GPa. Panel aspect ratio a/d=1.17 gives k_v=5.34+4.0/(1.17)²=7.94. Elastic buckling stress τ_cr=7.94×9870×200/(12×0.92×(1200/12)²)=142 MPa. Shear yield τ_y=0.58×350=203 MPa. Since τ_cr < τ_y, web buckling governs. Shear capacity=(142 MPa×1200 mm×12 mm)/1000=2038 kN.
Practical Notes
Transverse stiffeners reduce buckling by lowering d/a ratio; spacing ≤1.5d is standard in AISC for Class I webs to prevent initial buckling below yield.
Post-buckling tension field action increases capacity 20–40% beyond elastic τ_cr; account for this in design reserves per EN 1993-1-5.
Thin webs (d/tw >150) on narrow-flange beams are prone to buckling; check hybrid girders with thicker bottom flange separately under combined bending and shear.
Web bearing plates and corner notches create stress concentrations; verify local stresses near stiffener terminations independently.