Dynamic instability of axially loaded elements: General considerations and seismic loading

The phenomenon of dynamic instability of steel beams under harmonic axial loading is analysed, in particular to identify those elements in equilibrium under static axial loads, i.e. loaded below the Euler load, but that could fail under dynamic conditions, possibly compromising the entire structural stability. In the literature, the general problem of dynamic instability was comprehensively presented by Bolotin, who defined instability regions. Bolotin's method was extended herein and more accurate instability regions derived. In some conditions, depending on the ratio between the frequency of the exciting load and the beam transversal natural frequency, an elastic beam could sustain a dynamic axial load greater than the Euler load. The influence of geometric and material non-linearity on the shape of the instability regions has been evaluated herein through time series analyses. Then, response spectrum analyses were conducted to highlight possible effects of dynamic instability due to seismic loading. Two building typologies were considered: multi-storey buildings with cross bracing and existing industrial buildings. The results show that in the case of elements of the bracing system of new-designed multi-storey buildings, the dynamic instability is generally not an issue due to the high frequency of the single elements compared to the frequency of the fundamental mode of vibrations of the whole building. In the case of existing industrial buildings not designed to sustain seismic actions, some slender elements, with frequency of vibration compatible with the fundamental frequencies of the building, may undergo dynamic instability with possible detrimental effects in the whole building response.