Seismic reliability analysis of plane frame structures

This paper presents a practical and simplified reliability analysis method for plane frame structures subject to in-plane earthquake ground accelerations. The frame modelling is based on the approach used in the computer program TABS77. A condensation technique is used in TABS77 to transform the frame structure into a stick model with lumped mass at each floor level. Dynamic characteristics of the structure such as natural frequencies and mode shapes are also obtained using TABS77. The earthquake ground acceleration is represented by a segment of stationary Gaussian random process with mean zero and a Kanai-Tajimi power spectrum. The power spectrum together with the dynamic characteristics of the structure are utilized in the random vibration analysis to derive the covariance matrices of the structural response. A simplified limit analysis procedure is utilized to determine the failure mechanism and the corresponding storey shear capacity of the frame structure. For this failure mechanism, the limit state probability of each storey, i.e. the storey limit state probability, can be evaluated. Then, the limit state probability of the structure is measured in terms of the largest storey limit state probability. The fragility curve for the frame structure is generated by evaluating the limit state probabilities at different levels of peak ground acceleration. From the hazard curve for a site and the fragility curve for a structure, the annual limit state probability of the structure can also be evaluated. A five-storey building assumed to be located in New York City is used for numerical illustration.