Plate Buckling Analysis
Determine the elastic critical buckling stress of a flat rectangular plate under uniform compression with configurable boundary conditions.
About This Calculator
This calculator finds the elastic critical buckling stress of a flat rectangular plate loaded in uniform compression along two opposite edges, and compares it with yield to show which governs. Method: the plate’s flexural rigidity is D = E t³ / (12 (1 − ν²)). The elastic critical stress is σ_cr = k π² E (t / b)² / (12 (1 − ν²)), where b is the loaded width and k the buckling coefficient for the edge conditions: 4.0 with all edges simply supported (for plates longer than they are wide), about 6.97 with the unloaded edges clamped, and about 0.43 with one unloaded edge free. If σ_cr is below yield, elastic buckling governs; otherwise yield governs. The applied stress is reported as a utilisation, with the aspect ratio a / b for reference. Inputs are the plate width, thickness and length, Young’s modulus, Poisson’s ratio, yield strength, buckling coefficient and applied compressive stress. Assumptions and limits: a perfectly flat, elastic plate with uniform stress and idealised edges. Thin plates can carry load beyond first buckling, which design codes allow for through an effective width, while initial distortion from welding reduces strength. For design, use BS EN 1993-1-5 or DNV-RP-C201. Shear, bending and combined stresses are not covered. Typical uses: deck plating, web and flange panels of fabricated girders, panels between stiffeners, and thin-walled compression members. For a stiffened panel, check each plate panel between the stiffeners here, then check the stiffeners themselves as struts, for example with the column buckling calculator.
Referenced Standards
- Timoshenko and Gere, Theory of Elastic Stability
- BS EN 1993-1-5, Plated structural elements
- DNV-RP-C201, Buckling strength of plated structures