Estimate of the axial force in slender beams with unknown boundary conditions using one flexural mode shape

This paper presents an experimental procedure for the axial load identification of slender prismatic beams with unknown boundary conditions by making use of one vibration frequency and of five amplitudes of the corresponding mode shape. In fact, this method does not require the knowledge of the effective length of the beam under examination, but only the flexural rigidity and mass per unit length. The proposed algorithm was verified by means of many numerical and experimental tests on tie-rods having different boundary conditions. Excellent estimates of the axial forces were obtained. Finally, the influence of the location of the instrumented sections on the estimation of the axial load was analyzed using a simply supported beam model.