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Plate Shear Buckling Stress Formulae and Calculator

Flat Plates Stress, Deflection Design Equations and Calculators

Plate Shear Buckling Stress Calculator and Equations

Critical Shear Stress at which a plate first buckles calculator.

Long Rectangular Plates. In 1891, Bryan (1891) presented the analysis of the elastic critical stress for a rectangular plate simply supported along all edges and subjected to a uniform longitudinal compressive stress. The elastic critical stress of a long plate segment is determined by the plate width-to-thickness ratio b/t, by the restraint conditions along the longitudinal boundaries, and by the elastic material properties (elastic modulus, E, and Poisson's ratio µ).

Preview Plate Shear Stress Buckling Calculator

The elastic critical stress, at which a plate first buckles, is expressed as

Eq. 1
${\displaystyle {\mathrm{\tau <!--\; \tau \; -->}}_{cr}=\frac{K_s{\mathrm{\pi <!--\; \pi \; -->}}^2\mathrm{\eta <!--\; \eta \; -->}E}{12(1-<!--\; -\; -->{\mathrm{\mu <!--\; \mu \; -->}}^2)}{\left(\frac{t}{b}\right)}^2}$

A great deal of work has been done relative to the value of the plasticity correction factor. The expression for η must involve a measure of the stiffness of the materials in the elastic and inelastic ranges. A simple means of obtaining a value of η is to take the ratio of the shear secant modulus to the shear modulus.

Eq. 2
${\displaystyle \mathrm{\eta <!--\; \eta \; -->}=\frac{G_s}{D}}$

Figure 1, Plate

Figure 2, Shear Buckling Coefficient, K_s

Where

E = modulus of elasticity
K_s = non-dimensional shear buckling coefficient
η = plasticity correction factor
µ = poisson's ratio
c = clamped
s = simple supported
a = long side
b = short side
t = thickness

• Bell Helicopter Structural Design Manual, 1977

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