Bridge Design

Annex ABuckling and Ultimate Strength of Flat Plates

A.1 Critical Stresses and Buckling Modes of Flat Plates

A flat plate of length a and width b, with a thickness t is assumed to be supported along the four edges and loaded at the transverse edges under a non‐uniform normal stress field (σ₁ and σ₂) and a uniform shear stress distribution τ as shown in Figure A.1. This is a quite usual stress field in webs of plate girders, as referred to in Section 6.9.5.1, with normal stresses being due to bending moments and axial load and shear stresses due to shear force.

Figure A.1 Flat plate under a normal and shear stress field.

Let the case τ = 0 be considered first. The elastic critical buckling stress σ_cr is given by [1, 2]

(A.1)

where the buckling coefficient k =k(α,ψ), with α = a/b the aspect ratio of the plate and ψ = σ₂/σ₁ the stress ratio, as per Figure A.1.

A.1.1 Plate Simply Supported along the four Edges and under a Uniform Compression (ψ = 1)

The plate buckles in a single transverse half wave and with multiple longitudinal m half waves. The coefficient k, taking values defined by the buckling mode m =1,2,3, … depending on the aspect ratio α, as shown in Figure A.2, is given by

(A.2)

Figure A.2 Buckling modes and buckling mode coefficient for rectangular plates simply supported ...