A simplified method for collapse capacity assessment of moment-resisting frame and shear wall structural systems

doi:10.1016/j.engstruct.2010.12.028

Engineering Structures

Volume 33, Issue 4, April 2011, Pages 1107-1116

https://doi.org/10.1016/j.engstruct.2010.12.028 Get rights and content

Abstract

A simplified methodology for predicting the median and dispersion of collapse capacity of moment-resisting frame and shear wall structural systems subjected to seismic excitations is proposed. The method is based on nonlinear static (pushover) analysis. Simple mathematical models denoted as “generic structures” are utilized to model moment-resisting frames and shear walls. After examining a wide range of structural parameters of the generic structures, a comprehensive database of collapse fragilities and pushover curves (using ASCE 7-05 lateral load pattern) are generated. Based on the obtained pushover curves, closed-form equations for estimation of median and dispersion of building collapse fragility curves are developed using multivariate regression analysis. Comparing the estimates of the median collapse capacity calculated from the closed-form equations with the actual collapse capacities determined from nonlinear response-history analysis indicates that the simplified methodology is reliable. The effectiveness of this methodology for predicting the median collapse capacity of frame and wall structures is further demonstrated with two case studies of structural systems designed based on current seismic provisions.

Introduction

Prediction of collapse potential of structures under earthquake loads has always been a crucial aspect of earthquake engineering. Collapse potential can be employed as a key decision parameter for engineers to design new structures and also to evaluate seismic performance of existing ones when subjected to earthquakes. Accurate collapse prediction is important since collapse of structural systems is the primary source of life and monetary losses during and after an earthquake [1]. There are several analytical methods currently available to assess the collapse capacity of structures under earthquake ground motions [2], [3], [4]. These methods are representative of various analytical approaches such as simplification of the whole structure to an equivalent single-degree-of-freedom system [5], [6], [7], [8], [9], use of a step-by-step finite-element analysis of the whole structure for detection of abrupt structural response increase [10], [11], [12] and recently emerged incremental dynamic analysis [13], [14], [15], [16], [17]. The work presented in this paper is particularly analogous to the approach used to develop “SPO2IDA” [18] based on SDOF systems to approximate MDOF system response and the research by Chou [19] that uses a closed-form equation to estimate median collapse capacity from maximum roof deformation. However, the approach and results presented in this paper use generic MDOF system to estimate the collapse capacity of buildings that is different from the aforementioned studies in which an equivalent SDOF system is utilized to estimate the collapse capacity.

Incremental dynamic analysis (IDA) has been introduced as a procedure developed for accurate estimation of seismic behavior of structures through collapse, provided that deterioration of structural components is accurately captured in the mathematical model of the structure. An incremental dynamic analysis requires performing a series of nonlinear time-history analyses in which the scale factors of selected ground motions are gradually increased until the collapse capacity of the structure is reached. In the context of this paper collapse is associated with a sidesway mode in which a story or a number of stories of a structure displace sufficiently laterally and $P$ –Delta effects accelerated by component deterioration fully offset the first story shear resistance. As a result, dynamic instability occurs and the structural system loses its gravity load resistance.

Although IDA has become a common analysis method for researchers who are interested in determining the seismic vulnerability and collapse capacity of structures under extreme loads, this method has not been so popular among structural engineers for actual buildings. The reason is that the IDA method requires a large number of nonlinear response-history analyses of the structure using a set of representative ground motions, each scaled to many intensity levels covering the entire range of structural response [20]. Recognizing the technical difficulties of the IDA method including (1) selection of appropriate ground motions for different seismic zones and hazard levels, (2) realistic interpretation of dynamic response of a structure and (3) time consuming computational efforts required to conduct IDA, this paper proposes approximate relationships for collapse capacity prediction of regular buildings by utilizing simple nonlinear static (pushover) analysis method and by considering the number of stories and natural period of the structural system.

In this study, two types of structural systems are considered. The first one is moment-resisting frames and the second one is shear walls. Both structural systems are subjected to IDA using a set of 40 large-magnitude–small-distance ground motions in order to determine their dynamic collapse capacity [15]. On the other hand, both types of structural systems are analyzed using the pushover analysis method to identify their nonlinear static response in terms of yielding, plastic, and ultimate drift ratios. Based on statistical evaluation of obtained results from dynamic and static analyses, the best-fitted first-order regression models are proposed for relating both structural characteristics and pushover parameters to the expected median collapse capacity of the structural systems. By employing the generated relationships, dynamic collapse capacity can be simply estimated based on information obtained from a pushover analysis of the structure.

For accurate collapse prediction, it is also important to consider characteristics of ground motions that may affect the dynamic structural response. A value that quantifies the effect of a ground motion on a structure is called an intensity measure (IM). The spectral acceleration at the first mode period of a structure, $S_{a} (T_{1})$ , has been proven as a widely acceptable IM. Recent studies by Baker and Cornell [21] have shown that a significant difference can be observed among the dynamic responses of a structure analyzed using a set of ground motions all with the same $S_{a} (T_{1})$ . Baker and Cornell [21] have demonstrated that the vector-valued IM of $S_{a} (T_{1})$ and $ε$ is a more precise representation for ground motion intensity compared to the scalar value of $S_{a} (T_{1})$ . As a result, the effect of the $ε$ parameter of ground motions is considered in this paper in order to improve collapse estimation relationships. Two case study buildings are used to validate the proposed relationships for simplified collapse estimation. It is demonstrated that the developed relationships can predict the collapse capacity of structures well with an acceptable level of error in prediction.

Section snippets

Generic structural systems

In order to predict the collapse capacity of regular structures, simple mathematical models of structural systems denoted as “generic structures” are used in this study. The generic structures have been categorized as: generic moment-resisting frames (denoted as MRF) and generic shear walls (denoted as SW). Based on the number of stories, $N$ , equal to 4, 8, and 12, the generic structures are representative of low-, medium-, and high-rise buildings, respectively. The generic structures are

Incremental dynamic analysis

Incremental dynamic analysis (IDA) is a powerful means to evaluate the seismic behavior of structures. IDA involves performing a series of nonlinear dynamic time-history analyses for each ground motion record by scaling it to the several levels of intensity measure (IM) to encompass the full range of structural behavior starting from elastic to nonlinear inelastic, and finally until global dynamic instability [16]. The results of these time-history analyses for one ground motion create one IDA

Nonlinear static (pushover) analysis

The nonlinear static (pushover) analysis method has become a popular method for predicting seismic deformation demands as well as local/global capacity of structures. This analysis method is widely used among practicing engineers for seismic performance evaluation of structures against probable collapse during an earthquake [4]. According to ASCE/SEI 41-06, if the nonlinear static procedure is selected for seismic evaluation, a mathematical model of the structure should be subjected to

Statistical data reduction and regression

Based on the incremental dynamic analysis and nonlinear static analysis methods, a comprehensive structural response database has been developed for a wide range of combinations in structural parameters. Due to large amount of information in both generic type structures used in this study a data reduction approach is important. Despite variations in the natural period of structural systems and their yield base shear coefficient, different realizations for each of three previously defined

Effect of ground motion characteristics

According to recent findings on effects of different ground motion characteristics on structural response [21], [32], [33], it is important to consider other properties of a ground motion for seismic response evaluation of the structural systems. Spectral acceleration at the predominant period of the structure is now commonly used as an effective and practical parameter for intensity measure, but it should be noted that considerable difference still exists among the seismic responses of a given

Application and case study

In order to evaluate the accuracy of proposed collapse capacity estimation relationships, two case study buildings have been selected and studied. Both case studies comprise steel moment-resisting frames whose behavior under heavy seismic excitation (i.e., near collapse) was tested in laboratory environment. Due to lack of similar tests for shear walls, especially those with flexural dominant failure, case studies for such lateral load-resisting system were not included as case studies.

The

Conclusions

This paper presents a methodology for estimation of collapse capacity of structural systems using nonlinear static (pushover) analysis. The authors understand the approximations involved in estimating the collapse potential of structural systems. Furthermore, it is known that nonlinear static analysis has limited capability in demonstrating the dynamic behavior of a structure as it cannot capture the effect of higher modes of vibration and the cyclic deterioration in structural components.

Acknowledgements

This work was supported in part by the National Science Foundation award CMMI-0654409. Their support is gratefully acknowledged. Any opinions, findings and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect those of the National Science Foundation.

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A simplified method for collapse capacity assessment of moment-resisting frame and shear wall structural systems

Abstract

Introduction

Section snippets

Generic structural systems

Incremental dynamic analysis

Nonlinear static (pushover) analysis

Statistical data reduction and regression

Effect of ground motion characteristics

Application and case study

Conclusions

Acknowledgements

J Eng Struct

Assessment of probability of collapse and design for collapse safety

J Earthq Eng Struct Dyn

Methods to assess the seismic collapse capacity of building structures: state of the art

J Struct Eng

Amplification factors for inelastic P–delta effects in earthquake analysis

J Earthq Eng Struct Dyn

Dynamic instability of simple structural systems

J Struct Eng

Collapse of a model for ductile reinforced concrete frames under extreme earthquake motions

J Earthq Eng Struct Dyn

Evaluation of damage and P–delta effects for systems under earthquake excitation

J Struct Eng

Seismic damage and collapse assessment of composite moment frames

J Struct Eng

Hysteretic models that incorporate strength and stiffness deterioration

J Earthq Eng Struct Dyn

Incremental dynamic analysis

J Earthq Eng Struct Dyn

Direct estimation of seismic demand and capacity of multidegree-of-freedom systems through incremental dynamic analysis of single degree of freedom approximation

ASCE J Struct Eng

Amplification factors for inelastic $P$ –delta effects in earthquake analysis

Evaluation of damage and $P$ –delta effects for systems under earthquake excitation