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

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2. DUCTILITY AND SEISMIC RESPONSE OF STRUCTURES demands on beam-to-column connections, shear force demands in deep reinforced concrete beams, shear force demands in unreinforced masonry wall piers, etc; • estimates of the deformation demands for elements that have to deform inelastically in order to dissipate the energy imparted to the structure by ground motion; • consequences of strength deterioration of individual elements on the behaviour of a structural system; • identification of the critical regions in which the deformation demands are expected to be high and that have to become the focus of detailing; • identification of strength discontinuities in plan and elevation that will lead to changes in the dynamic characteristic in the inelastic range; • estimates of the interstorey drifts that account for strength or stiffness discontinuities and that may be used to control damage and to evaluate P- delta effects. Clearly, this benefits come at the cost of additional analysis effort, associated with incorporation of all important elements, the modelling of their inelastic load- deformation characteristic, and the execution of incremental inelastic analysis, preferably with a three-dimensional (3D) analytical model. At this time adequate analytical tools for this purpose ere either cumbersome or not available, but several good tools are under development, primarily through the recent publication of the FEMA 273 document (1997), that includes extensive recommendations for load- deformation modelling of individual elements and for acceptable values of force and deformation parameters for performance evaluation. Based on the capacity spectrum method originally developed by Freeman et al. (1975) and Freeman (1978), the NSP procedure could be summarized in the following steps (Chopra and Goel, 1999): 1. Develop the relationship between base shear Vb and roof (N th floor) displacement uN, depicted in Figure 2.6, commonly known as pushover curve. u N F V b Pushover Curve u V N b Figure 2.6. Development of a pushover curve 25
2. DUCTILITY AND SEISMIC RESPONSE OF STRUCTURES 26 2. Convert the pushover curve to a capacity diagram, see Figure 2.7, where N m φ j j1 j j1 j = 1 * j = 1 1 N 1 N 2 mjφ j1 2 mjφ j1 j = 1 j = 1 N m φ 2 Γ = Μ = ( 2.6 ) and mj = lumped mass at the j th floor level, φj1 is the j th -floor element of the * fundamental mode φj, N is the number of floors, and M1 is the effective modal mass for the fundamental vibration mode. V b Pushover Curve u N A = V b M 1 * Capacity Diagram u N D = Γ1 φ N1 Figure 2.7. Conversion of a pushover curve to a capacity diagram 3. Convert the elastic response (or design) spectrum from the standard pseudo-acceleration A versus natural period TN format to the A-D format, where D is the deformation spectrum ordinate, defined as 2 N 2 T D = ⋅ A ( 2.7 ) 4π 4. Plot the demand diagram and capacity diagram together and determine the displacement demand as illustrated in Figure 2.8. Involved in this step are dynamic analyses of a sequence of equivalent linear systems with successively updated values of the natural vibration period Teq and equivalent viscous damping ξeq. To define the above-mentioned quantities we have to consider an inelastic SDoF system with bi-linear force- deformation relationship on initial loading. The stiffness of the elastic branch is k and that of the yielding branch is αk.
Page 1 and 2: Dipartimento di Ingegneria Meccanic
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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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