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.

中文翻译：

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具有多个自由度的系统的动态放大因子

众所周知，结构的响应在承受静态载荷或突然的阶跃载荷时会有所不同。通常将动态放大因子（DAF）定义为振动响应与静态响应的振幅之比，以描述动态效果。对于承受突然动态负载的单自由度系统（SDOF），DAF的最大值为2。因此，许多设计准则都将2作为考虑动态效果的上限。对于通常是多自由度（MDOF）系统的土木工程结构，DAF在某些情况下可能会超过2。因此，根据设计指南的建议采用2作为上限键可能会导致结构设计不安全。非常有限的研究系统地研究了MDOF系统的DAF。这项研究基于结构动力学的基本理论，从理论上研究了MDOF系统在承受阶跃载荷时的DAF。定义了DAF可能超过2的条件。给出了两个数值示例和一个斜拉桥遭受突然电缆损失的实验研究，以说明这一问题。