Curved Webs under Combined Shear and Normal Stresses

Normal stresses, caused by bending of a girder in the direction of its curved web, have an effect equivalent to lateral pressure on the web. Except for pure shear, the problem of a curved web subjected to inplane membrane stresses is not a buckling but rather a deflection amplification problem. The membrane stresses cannot exceed a certain critical limit at which the deformation of the web theoretically reaches infinity. The behavior of curved webs is examined under different combination of membrane stresses using the linear theory of shells. The critical limit is calculated using two modified simultaneous homogenous differential equations and the Galerkin's method. The two differential equations lead to a system of linear homogenous equations from which the minimum eigenvalues of the critical load are calculated and presented in tables and curves. Approximate conservative formulas are also given for practical applications.