AbstractBridges with deck supported on either sliding or elastomeric bearings are very common in mid‐seismicity regions. Their main seismic vulnerabilities are related to the pounding of the deck against abutments or between the different deck elements. A simplified model of the longitudinal behavior of those bridges will allow to characterize the reaction forces developed during pounding using the Pacific Earthquake Engineering Research Center framework formula. In order to ensure the general applicability of the results obtained, a large number of system parameter combinations will be considered. The heart of the formula is the identification of suitable intermediate variables. First, the pseudo acceleration spectral value for the fundamental period of the system (Sa(Ts)) will be used as an intensity measure (IM). This IM will result in a very large non‐explained variability of the engineering demand parameter. A portion of this variability will be proved to be related to the relative content of high‐frequency energy in the input motion. Two vector‐valued IMs including a second parameter taking this energy content into account will then be considered. For both of them, a suitable form for the conditional intensity dependence of the response will be obtained. The question of which one to choose will also be analyzed. Finally, additional issues related to the IM will be studied: its applicability to pulse‐type records, the validity of scaling records and the sufficiency of the IM. Copyright © 2009 John Wiley & Sons, Ltd.