Blast dynamics of beam-columns via analytical approach

Problems involving forced transverse vibrations of beam-columns have many applications in different fields of engineering. This paper presents an analytical procedure allowing the prediction of the blast dynamic response of a beam-column to a combined action of axial and transverse loads. The solution is based on the continuous formulation and the Euler-Bernoulli beam theory. The response of the beam-column in the quasi-static, dynamic and impulsive regimes is analysed using the developed analytical model. The analysis shows that the number of modes of vibration needed to produce an accurate estimate of the beam-column behaviour may vary depending on the loading regime. Various types of spatial load distributions and time histories of transverse loads commonly used in engineering practice for modelling of extreme loads are discussed. The significance of the axial force and the shape of the transverse load time history for the beam-column response is shown using the response spectrum and pressure-impulse diagram methods. The initial imperfections in the beam-column geometry and applied loads are introduced into the analysis and their effects are also examined. The results obtained by the analytical model are compared to the results of a nonlinear finite element analysis performed in ABAQUS. Certain discrepancies between the beam-column response yielded by the analytical solution and the finite element model were observed at high levels of axial force and quasi-static transverse loading conditions.