Plate Girder Web Shear Buckling Stress
Plate Girder Web Shear Buckling Stress
Deep, thin-walled plate girder webs are efficient at carrying shear because most of the material is concentrated in the flanges for bending, leaving a thin web that does the shear work. That efficiency comes with a catch: a thin web can buckle elastically in shear well before it reaches its material shear strength, so girder design has to check plate buckling as a distinct limit state from yielding.Unstiffened, slender webs on long-span plate girders (bridges, crane girders, deep transfer girders) are the classic case where shear buckling governs; when it does, the fix is transverse stiffeners that break the panel into shorter, stockier sub-panels rather than simply thickening the whole web, which would add substantial weight and cost.
The elastic critical shear buckling stress of a rectangular plate panel is tau_cr = k_s·pi^2·E/(12·(1-nu^2))·(t_w/h_w)^2, from classical plate buckling theory. where k_s is the shear buckling coefficient (depends on panel aspect ratio and stiffening), E is the steel modulus of elasticity, nu is Poisson's ratio, t_w is the web thickness, h_w is the web depth (unsupported panel dimension), and tau_cr is the resulting critical shear buckling stress.
Inputs
t_w := 10 mm=10 mm
h_w := 1000 mm=1 m
E := 200 GPa=200000 MPa
nu := 0.3=0.3
k_s := 5.34=5.34
Plugging the panel geometry and material properties into the classical plate-buckling formula gives the shear stress at which the web panel is predicted to buckle elastically.
tau_cr := k_s·pi^2·E/(12·(1-nu^2))·(t_w/h_w)^2=96.53 MPa
Results
The critical buckling stress found here (roughly 97 MPa) is well below typical steel shear yield strength (around 150 MPa for common grades), confirming that this thin, deep web panel is genuinely buckling-governed rather than yield-governed. If tau_cr comes out below the demand shear stress, the standard remedies are adding intermediate transverse stiffeners (which raises k_s substantially) or increasing the web thickness — stiffening is almost always the more material-efficient choice for long panels. Post-buckling tension-field action can still add reserve capacity beyond this elastic buckling point in stiffened girders, but that requires a separate, more involved check.
Assumptions & limitations
- Elastic buckling only — no post-buckling tension-field reserve strength included.
- Web panel is assumed simply supported along its edges by the flanges and stiffeners.
- k_s corresponds to an idealized long, unstiffened panel aspect ratio; actual value depends on stiffener spacing.
- Residual stresses and initial imperfections are not explicitly modeled.