Beam axial load identification using one vibration mode shape

This doctoral dissertation presents an experimental procedure for the evaluation of the axial load of slender beams with any given boundary condition. The comparison between the design inner force and the experimental estimate can be used to obtain the structural safety assessment. This problem has generally been dealt with by means of a global structural analysis which may lead to ill posed inverse problems. Making use Euler-Bernoulli beam model, a dynamic method was recently proved to give unique values of the axial force and of the end rotational stiffness for a beam presenting rigid end supports. Assuming that the geometry and the elastic modulus of the beam are known, this model is able to give the unknown parameters as a function of any vibration frequency and of three values of the corresponding mode shape. In the present dissertation, this approach was generalized to cover the case of generic framed structures with nodes subjected to any displacement. In particular, making use of any vibration frequency and of five amplitudes of the corresponding modal shape, the algorithm presented is able to give the value of the axial force of a generic structural component belonging to the structure under examination. Furthermore, this method does not require the measurement of the effective length of the structural component. Preliminary analytical studies were developed, using the so called continuous finite elements, to obtain the exact formulations of the condensed dynamic stiffness matrices representing the continuity with the remaining structure. The proposed algorithm was verified by means of numerous experimental tests on steel shapes in tension, with different boundary conditions. Satisfactory estimates of the axial resultants were obtained with errors not greater than 4%. Nonetheless, five amplitude records do not yield an exact formulation of the full condensed boundary stiffness matrix. In fact the exact formulation would require a greater number of data whereas five records provide for the diagonal part of the matrix only. Finally, a static method was developed to evaluate the axial resultant of a simply supported beam. In this case, three displacement components are to be measured of the beam subjected to a lateral force. In view of the greater simplicity, this method leads to identification errors up to 5%.