**Evaluation of Nonlinear Seismic Demands of High-rise RC Shear Wall Buildings Using Simplified Analysis Procedures **

**Fawad Ahmed Najam**

**Asian Institute of Technology**

School of Engineering and Technology

Thailand, December 2017

School of Engineering and Technology

Thailand, December 2017

**NUST Institute of Civil Engineering (NICE)
**

**School of Civil and Environmental Engineering (SCEE)**

**National University of Sciences and Technology (NUST)**

**H-12, Islamabad, Pakistan**

**Abstract**

An accurate determination of the nonlinear seismic demands is a primary requirement for the efficient design of new buildings and for the seismic performance evaluation of existing buildings. For this purpose, the detailed Nonlinear Response History Analysis (NLRHA) procedure is considered the most accurate and reliable procedure. However, this procedure may require significant computational effort, time, skills and other resources, especially for the complex high-rise building structures. An ordinary design office may not have necessary expertise and resources to undergo this detailed procedure for each project. Therefore, the common practicing engineers are generally interested in conceptually simple and convenient analysis procedures which are capable of clearly explaining the structural response in terms of its components, and can still provide reasonably accurate estimates in lesser time and effort. Besides being a convenient and practical way of estimating the seismic demands, such simplified analysis procedures can also serve as useful tools to understand the complex dynamic response and to gain detailed insight into the nonlinear behavior of structures.

This study presents two simplified analysis procedures to determine the nonlinear seismic demands of high-rise buildings with reinforced concrete (RC) shear walls. An approximate modal decomposition technique—referred as the Uncoupled Modal Response History Analysis (UMRHA)—is used as a starting point and basis for the conception and theoretical formulation of these simplified procedures. The key concept is that the response of different vibration modes of a structure undergo different levels of nonlinearity under the same ground motion, and therefore, should be treated differently. The first procedure—referred as the Extended Displacement Coefficient Method (EDCM)—is based on the idea that the maximum inelastic displacement of every significant vibration mode of a structure can be estimated by modifying the corresponding peak elastic displacement of that mode. This assumption provides a convenient way to determine the pushover target displacement for every significant vibration mode. The nonlinear seismic demands can be approximately determined by combining the peaks of individual modal responses obtained from the multi-mode pushover analyses at the corresponding target displacements. This proposed scheme is equivalent to extending the Nonlinear Static Procedure (NSP) prescribed in ASCE41-13 to include the response contributions from higher vibration modes. It can also be viewed as a simplified version of the Modal Pushover Analysis (MPA) procedure in which the target displacement for each significant vibration mode is estimated using the displacement modification approach.

The second simplified analysis procedure is based on the concept of equivalent linearization (EL). The primary motivation for this procedure is the realization that nonlinear modeling of structures requires great expertise and effort, which may not be devoted by the common practicing engineers. In most practical cases, the linear elastic modeling may serve the purpose of analysis within their required degree of accuracy. The theoretical formulation of the UMRHA procedure is extended by assuming that a properly tuned “equivalent linear” single-degree-of-freedom (SDF) system can approximately represent the nonlinear behavior of a vibration mode, and hence, can provide a reasonable estimate of nonlinear seismic demands of that mode. By applying this concept to every significant vibration mode of a structure, a modified version of the Response Spectrum Analysis (RSA) procedure is proposed. In this procedure, the most conventional EL approach (i.e. setting the equivalent linear stiffness to the secant stiffness of nonlinear system at maximum response amplitude, and using the additional damping determined from the equal-energy dissipation principle) is adopted. The nonlinear seismic demands are obtained by combining the peak responses of all equivalent linear modal SDF systems. Instead of direct and equal reduction of each mode’s elastic force demands by a response modification factor (R) as prescribed in the standard RSA procedure, this procedure is capable of treating each vibration mode differently depending upon its inelastic state, and therefore, has a more rational approach towards the prediction of true nonlinear responses. It also retains the convenience offered by the standard RSA procedure for practicing engineers; it does not require nonlinear analysis nor nonlinear modeling. Therefore, it can be conveniently applied both as a design procedure to estimate the seismic demands of new buildings, and as a seismic evaluation procedure for the existing buildings.

Using three case study high-rise buildings with reinforced concrete shear walls (20-, 33- and 44-story high), the accuracy of response prediction from both simplified procedures is examined for individual vibration modes, as well as for the total seismic response. In this examination, the individual modal demands computed by the UMRHA procedure and the total demands computed by the NLRHA procedure are used as benchmarks, respectively. It is observed that both simplified analysis procedures are providing reasonably accurate demand estimations for the case study buildings subjected to different input ground motions, either for those of individual vibration modes or for their sum (total demands). This satisfactory performance shows that they can be considered (and developed further for general use) as suitable simplified analysis options in cases where it is not practical to perform the detailed NLRHA procedure. Several improvements can be made in future to make these procedures applicable to buildings and structures of various types, configurations, and materials used.