Building collapse due to P-delta – what is the risk?

Abstract

Second-order P-delta effects require consideration as part of the seismic design and assessment of buildings, as they can amplify lateral displacement demands and potentially cause collapse through dynamic instability. International codes mitigate the likelihood of P-delta collapse by limiting the value of a P-delta stability coefficient, checked at design intensity levels. However, codes set seismic design provisions in order to limit the annual probability of collapse (i.e. the collapse risk) acknowledging that earthquake shaking can exceed design intensity levels. This paper considers the factors that are likely to affect the collapse risk due to P-delta effects. By examining the results of non-linear time-history analyses of multiple single-degree of freedom (SDOF) systems, it is shown that in addition to the stability coefficient, the hysteretic characteristics of a structure can significantly affect the annual probability of collapse. The paper also considers how the collapse risk due to dynamic instability is influenced by other design criteria, such as drift and ductility limits. It is shown that considerable risk variability can be expected depending on which criterion (ductility, drift limits or P-delta stability) is perceived to be critical during design. Furthermore, it is shown that because ductile structures typically possess a large reserve deformation capacity, the collapse risk (and the fatality risk) of such structures may in fact be dictated by P-delta stability considerations. The paper subsequently concludes that further attention to P-delta limits in future codes is warranted.