Dynamic amplification factors in instantaneously loaded structures

Dynamic amplification factors are used to include dynamic effects in equivalent static analyses. Theoretical boundaries for the dynamic amplification factor in instantaneously loaded structures, with and without initial velocity, are determined using the pseudo-static method and a compatibility criterion is derived for various structural responses and pulse loading shapes. For instantaneously loaded structures without initial velocity, the dynamic amplification factor can exceed the widely assumed upper boundary of 2 and is possible in some situations with practical relevance. For instantaneously loaded structures with an initial velocity, such as for debris impact loading, the dynamic amplification factor does not have an upper boundary and its value depends on the ratio of the drop height of the impacting object and the dynamic displacement of the impacted structure, as well as on the structural response type. The developed analytical model agrees well with experimental results of debris loading on ductile steel beams and can be used in the design against impact loading. The compatibility criterion between the structural response type and the loading pulse shape, for instantaneous loading, shows that a linear response is only compatible with a triangular pulse, and a rigid-plastic response with a rectangular pulse. This result deviates from the linear response and rectangular loading pulse currently used in EN 1991-1-7:2006 and in the JCSS Probabilistic Model Code for vehicular impact, and may lead to an underestimation of the dynamic effects in dynamic analyses.