Stresses in a Strip Plate Subjected to a Concentrated Load

Abstract

The object of this paper is to find a solution for the two-dimentional problem of a strip plate under a concentrated traction acting on one straight edge. By the transfomation z=tanh (πw/2t), where z=x+iy and w=φ+iψ, the strip between ψ=0 and ψ=t is conformally represented upon the half-plane y>0. In the case where a single force P acts at the origin in the (x, y) plane in the positive direction of the axis of y, the solution is given by the following equation : [numerical formula] where Δ is the "dilatation", ω is the "rotation". Transforming to (φ, ψ) plane, and by means of the equation [numerical formula] we find [numerical formula] from this equation displacements in the (φ, ψ) plane can be obtained as follows : [numerical formula] where the function "f" is the "plane harmonic function". Determining [numerical formula] we can easily calculate the stresses in a strip of width "t" subjected to a single force 2t/π·P at the origin in the positive direction of the ψ-axis, and normally distributed pressure of amount P/{1+cosh(πφ/t)} per unit length on the edge ψ=t.