Static strain energy and dynamic amplification factor on multiple degree of freedom systems

Many references and design codes propose the use of a dynamic amplification factor applied to the static response of a structure for estimating its dynamic response. This is the case of the present recommendations on cable stayed bridges or other references for evaluating the dynamic effects produced by the accidental loss of a segment during the cantilever construction of a precast concrete bridge. This paper deals with the dynamic amplification factor of multiple degree of freedom systems under the action of a rectangular pulse load of infinite duration. A theoretical study of the possible maximum values that the dynamic amplification factor can reach has been carried out, establishing the relation between this factor and the strain energy of the system under the load statically applied. This relation allows us to determine if the dynamic amplification factor can exceed the value of 2.0 and to derive a simple method for comparing the dynamic effects of different pulse loads. Finally, a numerical example illustrates this method applied to determine which rectangular pulse load, produced by the accidental loss of a segment of a bridge, can produce a larger and a smaller dynamic amplification factor on a cantilever precast segmental bridge under construction. In this example, the possible maximum dynamic amplification factor obtained has been 3.24.