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. 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 the results of 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.