Modal Combination Rule for Shock Spectrum Analysis of Bridge Structures Subjected to Barge Collisions

Owing to the differences between earthquake excitations and barge impact loads, the modal combination rules [e.g., square root of the sum of the squares (SRSS)] commonly used in seismic analysis are not appropriate for the shock spectrum analysis (SSA) technique of barge-bridge collisions. For this reason, this paper aims to develop a specialized and reasonable combination rule for the SSA method. A parametric study is first carried out to explore the modal response characteristics of bridge structures subjected to barge impact loading. It is found that the time instant (tm) corresponding to the peak value of the combined (total) dynamic response can be approximately predicted by analyzing the limited modal responses. The approximate equations are developed to predict the time instant tm for four different cases. On the basis of the estimated time instant, a new modal combination rule, called weighted algebraic sum (WAS), is proposed for the SSA method of barge-bridge collisions. The collision-induced peak responses of bridge structures derived from the SSA method with either WAS or SRSS are compared with those determined by the direct dynamic analysis technique. It is demonstrated that the WAS rule is more accurate in the barge-bridge collision spectrum analysis, particularly for the moderate- and high-energy impact events, whereas the SRSS rule is not recommended because of its lower accuracy. Also, the results obtained using the weighted function of cosine are slightly superior to those obtained using sine functions for the WAS rule.