The slender web of a plate girder buckles in shear at a low stress — but that is not failure. The buckled web keeps carrying load as a diagonal tension band. Vary the web dimensions and stiffener spacing to see the post-buckling ultimate shear strength produced by this tension field action.
Parameters
Web depth d
mm
Height of the web plate between the flanges
Web thickness t
mm
Thinner buckles earlier but gains more from the tension field
Stiffener spacing a
mm
Spacing between transverse stiffeners. Closer is stronger
Yield stress f_y
MPa
Yield stress of the steel (about 235 for mild steel)
Young's modulus E
GPa
Nearly constant at about 205 GPa for structural steel
Results
—
Web slenderness d/t
—
Stiffener aspect ratio a/d
—
Elastic shear buckling τ_cr (MPa)
—
Shear buckling factor Cv
—
Ultimate shear strength Vu (kN)
—
Tension-field reserve ratio
—
Web panel and diagonal tension field — animation
A web panel bounded by the top and bottom flanges and two vertical stiffeners. Over the diagonal buckling waves, a tension field (blue arrows) runs corner to corner, while the stiffeners carry compression.
Ultimate shear strength Vu including tension field action. Inside the bracket, the first term C_v is the pre-buckling shear capacity and the second term is the diagonal tension-field contribution carried after buckling. a: stiffener spacing. The ratio over the buckling-only capacity Vcr = τ_cr·d·t measures the size of the tension-field bonus.
What is Tension Field Action?
🙋
A bridge "plate girder" — seen from the side it is a thin steel plate with lots of slender posts standing on it. That thin plate, doesn't it buckle?
🎓
Good question. It does buckle, actually. The thin plate in the middle of a plate girder is called the "web", and under shear it buckles into diagonal wrinkles at a fairly low stress. Here is the key point though — that buckling is not "failure". Even after it buckles, the web keeps right on carrying load.
🙋
Wait — it buckled but it doesn't break? How does a wrinkled plate carry force?
🎓
Picture a deck chair. The fabric, when pulled taut, can hold a person. Fabric is poor at being pushed but very strong at being pulled. The buckled web is the same: the wavy plate reorganises into a "tension band" that runs diagonally from corner to corner of the panel. That diagonal tension band carries the load. We call this "tension field action". The reason Vu stays far above τ_cr in the tool on the left is exactly this tension field.
🙋
I see! So what does that tension band "hook onto" to pull taut? Fabric needs a frame.
🎓
Exactly that. The anchors of the tension band are the top and bottom flanges and the vertical stiffeners on each side. When the tension field pulls on the diagonal, the reaction puts the stiffeners into compression — the same role as the compression posts of a Pratt truss. That is why a plate girder carries rows of evenly spaced stiffeners. They are not decoration — they are the "frame" of the tension field.
🙋
When I make the stiffener spacing a smaller, Vu jumps up in the tool. What is the reasoning behind that?
🎓
Two things are at work. First, packing the stiffeners closer makes each panel smaller, which raises the shear buckling coefficient kv — so buckling itself becomes harder to trigger. Second, the tension band becomes steeper, so the second term of the ultimate-strength formula (the root of 1 + (a/d)²) becomes much more effective. So "adding stiffeners" lifts both the pre-buckling and the post-buckling strength — a cost-effective way to strengthen the girder.
🙋
Then if I count on tension field action, can I just keep making the web thinner and thinner?
🎓
Be careful there. The tension field develops only if the flanges and stiffeners can hold firm as anchors. An end panel has a neighbouring panel on one side only, so the tension field cannot be relied on fully — many codes say "do not count tension field action in end panels". You also have to check the stiffeners themselves against buckling and the extra bending the tension field puts into the flanges. Post-buckling strength is economical when used well, but it only stands up together with the check on the anchor side.
Frequently Asked Questions
Tension field action is the phenomenon in which the slender web of a plate girder, after buckling in shear, keeps carrying load as a diagonal tension band. The web buckles into diagonal waves at a low shear stress tau_cr, but this is not failure. The buckled web reorganises into a tension band running from corner to corner of the panel, anchored against the flanges and the transverse stiffeners, and carries load far beyond the buckling stress — the same way the fabric of a deck chair pulls taut on the diagonal to support a person.
The intermediate (transverse) stiffeners act as the anchors of the tension field. The post-buckling tension band stretches diagonally inside the panel bounded by the top and bottom flanges and the two stiffeners. The stiffeners then take compression, like the posts of a Pratt truss. Spacing the stiffeners more closely raises both the shear buckling coefficient kv and the tension-field ultimate strength Vu, so the girder is strengthened efficiently. That is why steel girders carry rows of stiffeners.
Cv is the elastic shear buckling stress tau_cr divided by the web shear yield stress tau_y (capped at 1.0). It represents how much of the shear yield strength the web can use before it buckles. A slender web (large d/t) has a small Cv and buckles early. When Cv is below 1, tension field action carries the remaining strength, the (1 - Cv) part. In this tool's ultimate-strength formula, the second term inside the bracket is the tension-field contribution.
Yes, conditionally. The tension field develops only if the flanges and stiffeners are stiff and strong enough to anchor the tension band. End panels (between the girder end and the first stiffener) have an anchor on one side only, so many design codes do not allow tension field action in end panels. Stiffener buckling and the extra flange bending caused by the tension field must also be checked. This tool gives an estimate of the post-buckling strength of an interior panel and should be used together with a detailed code-based check.
Real-World Applications
Plate girder bridges: In a steel plate-girder bridge, the top and bottom flanges carry the bending and the thin web carries the shear. Making the web thick adds steel weight and cost, so modern economical design uses a thin web and counts on the post-buckling strength from tension field action. Vertical stiffeners are placed at even spacing along the span to raise the shear buckling coefficient and to provide anchors for the tension field. Closer stiffener spacing near the supports, where the shear is largest, is standard practice.
Long-span building beams: In built-up I-section girders used to span gymnasiums, warehouses and factories, the shear buckling and post-buckling strength of the web become governing issues. When openings are cut in the web to pass ducts and pipes, the reinforcement around the opening and the disturbance to the tension field flow must be checked together.
Crane girders and runway beams: The runway beam of an overhead crane and the main girder of a gantry crane carry moving loads and repeated shear. When the web buckles and rebounds repeatedly, a phenomenon known as "plate breathing" arises, which makes fatigue cracks at the welds around the stiffeners more likely. In a design that relies on post-buckling strength, attention to fatigue is especially important.
Aircraft and ship thin-plate structures: The concept of tension field action was originally developed for thin-web aircraft beams (the Wagner beam). In structures that use extremely thin plates for lightness — aircraft wing spars, fuselage frames, ship bulkheads — actively exploiting the post-buckling strength is the standard design philosophy. The physics behind this tool's steel-girder formulas is the same.
Common Misconceptions and Pitfalls
The biggest misconception is assuming "shear buckling = failure of the web". τ_cr is only the stress at which elastic buckling begins; it is not the ultimate strength. For a slender web, τ_cr comes out far below the yield stress, but because the tension field rises after buckling, the actual ultimate shear strength Vu can be more than twice τ_cr·d·t. Treating buckling as an immediate failure leads to unnecessarily thick webs and added steel weight. Conversely, jumping to the conclusion that the diagonal wrinkles of a buckled web are a "defect" is also wrong — if the design counts on post-buckling behaviour, the waviness itself is expected.
Next, thinking "tension field action can be used unconditionally in any panel". The tension field develops only when the flanges and stiffeners on both sides serve as anchors. An end panel has no neighbouring panel on the outside, so the anchor on one side is weak; many design codes require end panels to be checked with the buckling stress (Cv only) and do not allow tension field action there. Where the stiffener spacing is extremely wide (large a/d), or where the flanges are too slender to resist the extra bending, the tension field cannot be fully relied on either. The Vu in this tool is an estimate that assumes an interior panel with sound anchors.
Finally, the misconception that "as long as the ultimate strength is satisfied, any stiffener will do". Because the reaction of the tension field puts the stiffeners into compression, the stiffeners need a section (the required second moment of area and area) that will not itself buckle. If the stiffeners are weak, the tension-field anchor fails first and the web cannot develop its post-buckling strength. In addition, the vertical component of the tension field imposes local extra bending on the flanges. The ultimate shear strength calculation is the starting point — the design is complete only when the stiffness and strength of the stiffeners, the extra flange bending, and the fatigue of the welds are all checked together.
How to Use
Enter web depth (d) in mm and web thickness (t) in mm to establish web slenderness d/t ratio
Set intermediate stiffener spacing (a) in mm to calculate stiffener aspect ratio a/d
Input steel yield strength (fy) in MPa—typically 250 MPa for Grade 250 or 355 MPa for Grade 355
Simulator calculates elastic shear buckling stress τ_cr using (π²E)/(12(1−ν²))(t/d)² and shear buckling coefficient Cv
Ultimate shear strength Vu is computed from Cv × 0.6fy × d × t, accounting for post-buckling tension field reserve
Review tension-field reserve ratio to confirm the buckled web remains stable before failure
Worked Example
Steel plate girder with d=1200 mm, t=8 mm, intermediate stiffener spacing a=2400 mm, fy=355 MPa. Web slenderness d/t=150, aspect ratio a/d=2.0. Elastic buckling stress τ_cr≈42 MPa (E=200 GPa, ν=0.3). Shear buckling factor Cv≈0.82 accounts for post-buckling strength. Ultimate shear strength Vu=(0.82 × 0.6 × 355 × 1200 × 8)/1000≈1,680 kN. Tension-field reserve ratio 1.18 indicates the web safely exceeds design shear demand before diagonal tension field collapse.
Practical Notes
Slender webs (d/t > 100) are economical in plate girders because tension field action recovers post-buckling strength lost to elastic instability
Stiffener spacing a/d between 1.0 and 3.0 is typical; closer stiffeners reduce buckling stress but add cost
Cv drops sharply when d/t exceeds 60; use intermediate stiffeners to maintain shear capacity in deep, thin webs
Always verify local web buckling and flange lateral-torsional buckling separately—tension field action does not apply to those modes
AISC 360-16 and EN 1993-1-5 both recognize tension field contribution; check code limits on stiffener rigidity and weld details