Stress distribution and wrinkling of webs under non-uniform and asymmetric edge loading

Non-uniform edge loading can cause unwanted wrinkling of a web. Here, Airy stress functions are obtained by a modified Fourier series method for webs under non-uniform and different edge loading on each side. The stress distributions of a web under non-uniform edge loading only on one side are subjected to the effect of Saint-Venant’s principle. For the web of small aspect ratio under non-uniform edge loading, the stress distribution converges to a uniform distribution or a linear distribution with both the resultant force and the resultant moment being equal to those of the applied loading. Conditions of wrinkling and the corresponding wrinkling modes of a web are found when the edge loadings are different on each side. The non-uniformities and shapes of the applied edge loadings result in different wrinkling conditions. Moreover, the non-uniformities together with the shapes of the applied edge loadings on each side affect the wrinkling conditions.