The influence of the in-plane warping on the behavior of thin-walled beams

The paper presents a theoretical study of the importance of the in-plane deformation on the structural behavior of thin-walled isotropic and composite beams which are subjected to bending and torsional moments. To separate the effects of the out-of-plane warping and the in-plane warping, the overall solution methodology is based on a generic combination of two complementary “inner” and “outer” solutions. The inner model is based on numerical optimization tools which are employed to determine the in-plane deformation that will ensure a stationary (minimum) state of the total potential energy. The outer model performs global solution for cross-sections that are rigid in their own plane but includes the out-of-plane warping. The overall solution is capable of determining the influence of the in-plane warping on any existing approximate numerical scheme that do not include this deformation component. The results correlate well with known analytic solutions for isotropic tubes under pure bending. A parametric study of the relative importance of the in-plane warping as a function of the geometry and the loading parameters in rectangular thin-walled isotropic and composite beams is also presented along with some buckling considerations.