Dynamic amplification factors for a system with multiple-degrees-of-freedom

It is well-known that the responses of a structure are different when subjected to a static load or a sudden step load. The dynamic amplification factor (DAF), which is defined as the ratio of the amplitude of the vibratory response to the static response, is normally used to depict the dynamic effect. For a single-degree-of-freedom system (SDOF) subjected to a sudden dynamic load, the maximum value of DAF is 2. Many design guidelines therefore use 2 as an upper bound to consider the dynamic effect. For a civil engineering structure, which is normally a multiple-degrees-of-freedom (MDOF) system, the DAF may exceed 2 in certain circumstances. The adoption of 2 as the upper bond as suggested by the design guidelines therefore may lead to unsafe structural design. Very limited studies systematically investigate the DAF of a MDOF system. This study theoretically investigates the DAF of a MDOF system when it is subjected to a step load based on the fundamental theory of structural dynamics. The condition on which the DAF may exceed 2 is defined. Two numerical examples and one experimental study of a cable-stayed bridge subjected to sudden cable loss are presented to illustrate the problem.