An adaptive modal pushover analysis procedure to evaluate the earthquake performance of high-rise buildings

Abstract

Today, in light of the advances in structural design/systems and high strength materials, as well as innovative structural concepts, a rapid growth in the construction of tall buildings within urban areas is taking place. Force-based linear design procedures have given way to a performance-based design approach. In this context, the Pacific Earthquake Engineering Research Center (PEER) is leading the Tall Buildings Initiative (TBI), which has developed safe and convenient written guidelines containing principles for the performance-based design of tall buildings, as well as having funded and coordinated a range of short- to intermediate-term projects between 2006 and 2009. Meanwhile, participants in the TBI—namely, the Los Angeles Tall Buildings Structural Design Council (LATBSDC), the Structural Engineers Association of Northern California (SEAONC) and the Council of Tall Buildings and Urban Habitat (CTBUH)—have published guidelines about the performance-based design of tall buildings. PEER published a document entitled "Guidelines for Performance-Based Seismic Design of Tall Buildings", which describes performance-based design principles and characteristic criteria for tall buildings. In parallel with these international developments, a draft code for the design of tall buildings in Istanbul, known as "Yüksek Yapılar Deprem Yönetmeliği", was published in 2008. A consensus has been reached about the necessity of performing a three-dimensional (3D) nonlinear time history analysis (NTHA) with biaxial components of ground motions in the final design of tall buildings. Nonetheless, some difficulties in implementing NTHA exist, on the basis that it is a complex and time consuming process faced with many uncertainties. For this reason, there is a need to develop analyzing methods that are both quick and with a reasonable degree of accuracy with respect to NTHA. The nonlinear static procedure (NSP) has become a practical analytical tool to estimate seismic demands of building-type structures. Most NSPs are precisely designated as conventional pushover analyses, in which an invariant lateral force distribution corresponding to the fundamental mode shape is subjected to the structure. However, applicability of conventional pushover analysis is limited to low-rise buildings without vertical or torsional irregularities, the behavior of which is not affected by higher modes. Multimode pushover analysis procedures are approximate methods, which can overcome the drawbacks of conventional NSPs by taking account of higher mode effects as well as obtain results that are closer to NTHA when compared with conventional NSPs. In this thesis, a variant of modal pushover analysis (VMPA-A), which is capable of taking account of the higher mode effects, is developed for use in the performance-based evaluation of tall buildings. The so-called DOC3D-v2, which is a MATLAB-based computer program, was developed to implement VMPA in order to analyze 3D frame and/or shear wall-type structural systems. DOC3D-v2 takes into account concentrated and distributed plasticity for the frame-type elements, as well as considers the second-order effects of axial loads on the members. Furthermore, the beam-column element of DOC3D-v2 considers the nonlinear interaction of shear-flexural deformations. The applicability of the physical substructuring approach is one of the substantial features of DOC3D-v2 for reducing the computation time. The suggested procedure is based on an iterative process, in which secant stiffness is used both at the element level and in the modal response. VMPA diverges from the existing modal pushover analyses for the following reasons: i) In the adaptive version (VMPA-A), mode-compatible adaptive forces are applied to the structure at each iteration step. In this way, the compatibility of force and displacement vectors may be satisfied. For the non-adaptive case (VMPA), the force vector is invariant during the analysis process. ii) The application of the equal displacement rule, in combination with secant stiffness-based linearization, eliminates the necessity to produce a capacity diagram for each mode. The analysis is performed for a unique displacement for each mode. The algorithm of VMPA-A is handled in respect of two-dimensional (2D) and 3D structural systems. The algorithm for the planar system is implemented in the spectral displacement-spectral acceleration (Sd-Sa) format. The displacement-controlled algorithm determines the single ordinate of the modal capacity diagram, which corresponds to the target displacement demand for the nth mode (Sdn_p, San_p) by reducing elastic spectral acceleration (San_e) to converge with plastic acceleration (San_p). To verify the success of the suggested procedure, nine- and 20-story LA SAC buildings are analyzed, with the resulting demands compared with several existing procedures, such as the extended N2, MPA (modal pushover analysis) and MMPA, while NTHAs are performed for two different sets of acceleration records. The first set consists of 44 strong ground motion records, which are downloaded from the PEER NGA Database for the ground acceleration level (ag=0.75g). The second set is taken from the European Database and consists of 20 strong ground motion records, which are analyzed for four different acceleration levels (ag= 0.10, 0.50, 0.75, 1.00g). The evaluated demand parameters are story displacements, drifts, shear forces and the distribution of column and beam curvatures. VMPA-A yields enhanced results in terms of story drifts, especially for the 20-storey LA building, compared with the other methods. Although the story displacements and drifts are largely consistent with NTHA results, conservative estimates are obtained for the story shear forces. The 2D algorithm is extended for use with 3D structures in relation to bidirectional ground motions. The theoretical background of VMPA-A has a lot of similarities with MPA. Nonetheless, MPA has some deficiencies such as i) invariant load patterns compatible with an nth-mode shape, which corresponds to the linear elastic eigenvalues applied to the structure, and ii) the MPA procedure, which is applied separately for the x and y components of the ground motion. For each case, the demand parameters of interest are combined by a CQC combination rule. Next, the effects of two ground motion components are combined using an SRSS combination rule. Applying modal combination rules twice may cause erroneous results. These drawbacks are eliminated in VMPA-A for the following reasons: i) the use of adaptive force patterns, due to the changes in the dynamic characteristics with increasing structural damage, provides the compatibility of force and displacement vectors for each three-degree-of-freedom (x,y ve z); ii) the VMPA method is implemented in relation to the hybrid spectrum, whose abscissas and ordinates have no physical meaning, namely and , respectively. The slope of the spectrum for a specific vibration mode corresponds to the eigenvalue of the mode, as with the Sd-Sa spectrum. The two orthogonal components of the ground motion can be taken into account simultaneously. As a natural consequence of this, the two-time application of modal combination rules is reduced to one in VMPA-A. A 45-story coupled shear wall (SW) system is used as a calibration example for 3D VMPA-A. Thirty historical earthquake acceleration records, including fault normal and fault parallel components that are scaled according to the ASCE 7.05 spectrum within the selected period range, are used and compared with the VMPA results. The results obtained from the average of NTHAs are compared with those of VMPA-A. The predictions obtained for the lateral displacement and drift in the weak direction are in close agreement with the mean of the NTHA. However, some discrepancy is encountered in the perpendicular direction. Conservative estimates are reached for the story shear forces' weak direction and the corresponding overturning moments. The predictions in perpendicular direction, story shear forces and overturning moments are better, with the exception of lower stories. Although the ultimate tension and compression strains for two representative SW parts are consistent with the NTHA results at the lower stories, where nonlinear behavior occurs, the relative differences are quite high for the upper part of the structure. Similar results are obtained for the curvature distribution of the coupling beams. The third application of VMPA is on an existing 21-story, reinforced concrete building, with three basements, one ground floor and 17 typical floors, under bidirectional ground motion. Thirty ground motions are selected from the PEER NGA database, then scaled in accordance with the 2007 Turkish Earthquake Code spectrum with consideration to the location and soil conditions of the building, for use in NTHAs. Here, cracked rigidities are used for SWs. This reflects the predictions of lateral drifts and displacements with respect to the average of the NTHA in both orthogonal directions. Similarly, with the 45-story example, conservative estimates have been reached for story shears and overturning moments. First mode behavior dominates the story overturning moments, especially at lower stories. Again, similar to the 45-story example, although the nonlinear strains of selected SW fibers are in close agreement with NTHA in lower stories, the errors increase in the upper parts. The curvatures are successfully estimated and first mode response governs the total.