Axial Force Identification of Short Beam Members with Unknown Boundary Conditions Incorporating Rotational Inertia

Accurate identification of axial forces in beam structures with unknown boundary conditions is important for structural assessment and safety monitoring. Most existing methods are based on Euler–Bernoulli beam theory and neglect the effect of rotational inertia. This simplification may reduce the accuracy of axial force identification for short beam members. To address this limitation, this study develops an axial force identification method that accounts for rotational inertia effects. First, a free-vibration governing equation for axially loaded beam members is derived based on the Reissner energy approach. Compared with the Euler–Bernoulli beam, the derived equation further accounts for the effect of rotational inertia. Then, based on the proposed dynamic formulation, an axial force identification method applicable to beam members with unknown boundary conditions is established by utilizing measured natural frequencies and mode shapes. Finally, the effectiveness and accuracy of the proposed method are systematically validated through both numerical simulations and experimental investigations on beam members. Numerical results indicate that incorporating rotational inertia improves axial force identification accuracy compared with conventional approaches, particularly for short beam members and higher-order modes. Experimental results further confirm its effectiveness, with a maximum identification error reduction of 7.69%.