SUMMARYThe modal pushover analysis (MPA) procedure, presently restricted to one horizontal component of ground motion, is extended to three-dimensional analysis of buildings-symmetric or unsymmetric in plansubjected to two horizontal components of ground motion, simultaneously. Also presented is a variant of this method, called the practical modal pushover analysis (PMPA) procedure, which estimates seismic demands directly from the earthquake response (or design) spectrum. Its accuracy in estimating seismic demands for very tall buildings is evaluated, demonstrating that for nonlinear systems this procedure is almost as accurate as the response spectrum analysis procedure is for linear systems. Thus, for practical applications, the PMPA procedure offers an attractive alternative whereby seismic demands can be estimated directly from the (elastic) design spectrum, thus avoiding the complications of selecting and scaling ground motions for nonlinear response history analysis.

The modal-pushover-based-scaling (MPS) procedure, currently restricted to scale one component of ground motion records, is extended herein to scale two horizontal components. The accuracy and efficiency of the MPS procedure is evaluated here by applying it to an existing nine-story building, symmetric in plan. The computer model developed for the building is validated against motions of the building recorded during the Chino Hills earthquake (2008). It is demonstrated that nonlinear response history analysis (RHA) of the building for a small set of records scaled by the MPS procedure provided a highly accurate estimate of the engineering demand parameters (EDPs), accompanied by significantly reduced record-to-record variability of the responses. Furthermore, the MPS procedure is shown to be much superior to the procedure specified in the ASCE/SEI 7-05 standard for scaling two components of ground motion records.

The accuracy of the three-dimensional modal pushover analysis (MPA) procedure in estimating seismic demands for unsymmetric-plan buildings due to two horizontal components of ground motion, simultaneously, is evaluated. Eight low-and medium-rise structures were considered. Four intended to represent older buildings were designed according to the 1985 Uniform Building Code, whereas four other designs intended to represent newer buildings were based on the 2006 International Building Code. The median seismic demands for these buildings to 39 two-component ground motions, scaled to two intensity levels, were computed by MPA and nonlinear response history analysis (RHA), and then compared. Even for these ground motions that deform the buildings significantly into the inelastic range, MPA offers sufficient degree of accuracy. It is demonstrated that PMPA, a variant of the MPA procedure, for nonlinear systems is almost as accurate as the well-known standard response spectrum analysis procedure is for linear systems. Thus, for practical applications, the PMPA procedure offers an attractive alternative to nonlinear RHA, whereby seismic demands can be estimated directly from the (elastic) design spectrum. In contrast, the nonlinear static procedure specified in the ASCE/SEI 41-06 Standard is demonstrated to grossly underestimate seismic demands for some of the unsymmetric-plan buildings considered. Figure 2. First triplet of periods and modes of vibration of the UBC85 buildings (only roof motion is shown).by the letters A, B, and C followed by the number of stories and the design code: plan A is rectangular with two axes of symmetry, plan B is symmetric about the y-axis, and plan C is unsymmetric about both x-and y-axes. The buildings have similar plan areas and floor weights, with a span length of 30 ft and a story height of 13 ft. Design code forces for the buildings, assumed to be located in Bell, CA (33.996 N, 118.162 W), were determined, but their member sizes were governed by drift instead of strength requirements [9]. Figure 3. First triplet of periods and modes of vibration of the IBC06 buildings (only roof motion is shown). ModelingNonlinear RHA, MPA, and code pushover analyses were implemented for these buildings using the PERFORM-3D computer program [10] modeled with the following features: (1) beams and columns were modeled by a linear element with tri-linear plastic hinges at the ends of the elements that include in-cycle strength deterioration, but not cyclic stiffness degradation. Axial load-moment interaction for the columns was represented by the plasticity theory;(2) panel zones were modeled as four rigid links hinged at the corners with a rotational spring that represents the strength and

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