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 fatality risk, which is linked to the annual probability of collapse (i.e. the collapse risk) that is in turn related to the design intensity, 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 and the implications for fatality risk. By examining the results of non-linear time-history analyses of many single-degree of freedom (SDOF) systems, it is shown that in addition to the so-called P-delta stability coefficient, the hysteretic characteristics of a structure can significantly affect the annual probability of collapse. Collapse fragility functions due to P-delta effects are defined for two different hysteretic models deemed to be representative of well-detailed steel and reinforced concrete buildings. Subsequently, the implications of the results for seismic design are considered. It is argued that future codes should utilise P-delta collapse fragility curves when setting limits to P-delta stability coefficients. This could help ensure that the annual fatality risk associated with dynamic instability is limited to acceptable levels.