Zig-zag theory for concrete beams with corrugated steel webs

Owing to the large difference between the longitudinal and transverse stiffness of corrugated steel webs (CSWs), concrete beams with CSWs are idealized as sandwich beams with an orthotropic core in this study. A zig-zag displacement is then assumed to describe the deformation along the beam thickness along with a layer-wise parabolic distribution of the transverse shear stress. A new composite beam theory for a concrete beam with CSWs is finally developed, and the governing equations are derived using the variational principle of mixed energy. The transverse shear stress in the proposed theory automatically satisfies the traction-free condition at both the top and bottom surfaces of the beam. The continuity conditions of the displacements and shear stresses at the interfaces between two adjacent layers are also maintained, and thus there is no need to introduce a shear correction factor. Finally, analytical solutions for CSWs under four common boundary conditions are derived. These solutions are verified by numerical methods, and the results show that the proposed theory in this study can predict the deformation and stress of the concrete beams with CSWs more accurately.