Fig. 1. Geometry of frame and dimensions of member cross-sections (in mm).

Fig. 2. Effect of consideration of P–Δ effects and stiffness modelling on vulnerability curves from a single earthquake (Kalamata 1986 earthquake N10W).

Fig. 3. Vulnerability curves for the seven input motions and scenario A.

Fig. 4. Comparison of average vulnerability curves for three groups of records.

Fig. 5. Comparison of average vulnerability curve given by all seven earthquakes to that given by the three motions with (a) the highest A/V ratios and (b) the longest durations.

Fig. 6. Average vulnerability curves for the three spatial distribution scenarios.

Fig. 7. Failure mode relative frequencies for two intensity levels and three spatial scenarios. (Ci=failure of column at ith storey, Di−j=exceedance of 3% drift between levels i and j).

Fig. 8. Effect of random critical drift on average vulnerability curve for (a) scenario A, and (b) scenario B.

Fig. 9. Example of patterns of plastic hinges and failed members for frame subjected to AEGL for (a) A′=0.75g, t=3.78 s, δ_cr=3% (δ_max=3.0%), and (b) A′=0.90g, t=3.84 s, δ_cr=6.2% (δ_max=3.2%).

Fig. 10. Vulnerability curves obtained for the SLS.

Fig. 11. Average SLS vulnerability curves.

Fig. 12. Hazard curves used in the present study, plotted in terms of the probability of exceeding a given value of A in t_d years.

Fig. 13. Increase of probability of failure with design life for the ULS.

Fig. 14. Variation in resistance and loads for the ULS, conditional to failure having occurred.

Fig. 15. Variation in resistance and loads for the SLS, conditional to failure having occurred, for (a) the yield rotation criterion, and (b) the 0.5% critical drift criterion.

Fig. 16. Derivation of actual q-factor for structures which fail (0.82% of total).

Table 1. Properties of normal distributions assumed for modelling the random material properties

Table 2. Input motions used in analyses

Table 3. Probabilities of failure for different scenarios