A higher-order beam theory for analyzing the static and dynamic behaviors of box and tubular beam-columns with the higher-order effect of axial force

Cross-sectional warping of box and tubular beam-columns is often neglected in previous studies and this treatment leads to significant errors for short beam-columns. This article develops a higher-order beam model for exactly analyzing the static and dynamic behaviors of box/tubular beams and columns by taking into account the cross-sectional warping and the higher-order effect (HOE) of axial force. Appropriate warping shapes are constructed for the box and annular cross-section, respectively. Shear deformation and rotary inertia of the corss-section are considered simultaneously, but no shear correction factor is needed. The bending, buckling, wave, and vibration are analyzed. In particular, the HOE of the axial force on the static behaviors including the deflection and critical load, and the dynamic behaviors including the phase velocity and natural frequency are analyzed for hollow-core structures or box/tubular beam-columns. The classical Euler buckling loads and natural frequencies are affected by the HOE of the axial force. The transverse waves are dispersive when the axial force is present. The presented model is also suitable for axially loaded shear deformation beams with rectangular and circular cross-sections only if the hollow-core cross-section reduces to a rectangle and a circle, respectively.