Analysis and modelling of the seismic behaviour of high ... - Ingegneria

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2. DUCTILITY AND SEISMIC RESPONSE OF STRUCTURES T eq ÷ T n ζ eq 4 3.5 3 2.5 2 1.5 1 0.5 α = 0 0.05 0.1 0.2 0 0 1 2 3 4 5 6 7 8 9 10 µ 0.7 0.6 0.5 0.4 0.3 0.2 0.1 α = 0 0.05 0.1 0.2 0 0 1 2 3 4 5 6 7 8 9 10 µ Figure 2.9. Variation of period and viscous damping of an equivalent linear system vs. ductility (a) (b) 29
2. DUCTILITY AND SEISMIC RESPONSE OF STRUCTURES Approximations are implicit in the various steps of this simplified analysis of an inelastic MDoF system. Implicit in Steps 1 and 2 is a lateral force distribution assumed to be fixed, and based only on the fundamental vibration mode of the elastic system; however, extensions to take into account higher mode effects have been proposed. Implicit in Step 4 is the belief that the earthquake-induced deformation of an inelastic SDoF system can be estimated satisfactorily by an iterative method requiring analysis of a sequence of equivalent linear SDoF systems, thus avoiding the dynamic analysis of the inelastic SDoF system. Both force distribution and target displacement are based on the assumption that the response is controlled by a single shape vector (the fundamental mode) and that the mode shape remains unchanged after the structure yields. Parameter studies have shown that for frame and wall structures with a first mode period of less than 2 seconds this assumption is rather accurate for elastic systems and conservative (overestimates the MDoF displacement) for inelastic systems. In all cases, the determined target displacement becomes the base line for predicting the inelastic displacement demand, which needs to be accomplished with due consideration to the hysteretic characteristic of the equivalent SDOF system. The effects of yield strength, strength and stiffness degradation, pinching during hysteretic loops, P-delta incremented forces caused by gravity loads acting on the deformed configuration of the structure can be taken into account through cumulative modification factors applied to the elastic displacement demand. The loop illustrated in Figure 2.10 assumes that stable relationships can be found between the spectral displacement demand at the first mode period of the structure and the system and element deformation demands (Gupta and Krawinkler, 2000), using the following definitions: 30 • MDoF modification factor, αMDOF, a factor that relates the elastic spectral displacement demand at the first mode period of the structure to the elastic roof drift demand of the MDoF structure, neglecting P-∆ effects. • Inelasticity modification factor, αINEL, a factor that relates the elastic roof drift demand to the inelastic roof drift demand, neglecting P-∆ effects. • P-∆ modification factor, αP∆, a factor that takes into account the effect of P- ∆ on the inelastic roof drift demand. • Storey drift modification factor, αST, a factor that relates individual storey drift demands to the roof drift demand. • Element deformations modification function, a function that relates storey drift demand to element plastic deformation demands.
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Page 3 and 4: UNIVERSITÀ DEGLI STUDI DI TRENTO D
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Page 10 and 11: INDEX 1 INTRODUCTION...............
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3. SEISMIC BEHAVIOUR OF BOLTED END
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5. SEISMIC BEHAVIOUR OF RC COLUMNS
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6. SUMMARY, CONCLUSIONS AND FUTURE
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Analysis and modelling of the seismic behaviour of high ... - Ingegneria

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