Out-of-plane behavior of curved beams: Exact solution

The governing differential equations of out-of-plane deformation for a planar curved beam with variable curvature and cross-section are solved exactly by using the initial value method. The differential equations include the shear deformation effect. The analytical expressions of the elements of the fundamental matrix are obtained for a general case. The inverse of the fundamental matrix is given for a parabolic beam with variable cross-section. It is also possible to use these analytical expressions in order to obtain the results for a curved beam with any loading and boundary conditions. The results can be obtained for a curved beam carrying any distributed loads. Examples in the literature are solved and the results obtained in this study are compared with those.