Web Shear Buckling Stress

\[\tau_{cr}=\frac{k_v\pi^2E}{12(1-\nu^2)}\left(\frac{t_w}{h_w}\right)^2\]

Variables

tauCr[τcr]critical web shear buckling stress (Pa)

kvshear buckling coefficient

Emodulus of elasticity (Pa)

nu[ν]Poisson's ratio

twweb thickness (m)

hwclear web depth between flanges or stiffeners (m)

Description

What is this formula?

Web shear buckling stress estimates the elastic critical shear stress at which a thin plate-like web may buckle under shear. It is commonly used for plate girders, box girders, and thin-walled structural members.

When to use it

Use this formula when checking the shear buckling resistance of slender webs in steel beams, bridge girders, stiffened panels, or thin plate elements subjected to shear.

Example

A steel plate girder web has:

kv = 5.34

E = 200 GPa = 200000000000 Pa

ν = 0.30

tw = 0.010 m

hw = 1.20 m

Formula:

τcr = (kv*pi²*E)/(12*(1-ν²))*(tw/hw)²

Substitution:

τcr = (5.34*pi²*200000000000)/(12*(1-0.30²))*(0.010/1.20)²

Result:

τcr = 67,060,000 Pa

Result:

τcr = 67.1 MPa

Applications

Plate girder design, bridge engineering, steel structures, ship structures, box girders, stiffened web panels, and thin-walled structural analysis.

Note

This formula is an elastic plate buckling approximation. The result depends strongly on the shear buckling coefficient kv, which varies with boundary conditions, panel aspect ratio, and stiffener arrangement. Design codes may modify this theoretical value using reduction factors, post-buckling strength, yielding limits, and safety factors.