Modified Capacity Spectrum Method Research Articles

Nonlinear seismic analysis of irregular base isolated structures using a new modified lateral load pattern

Nowadays, seismic isolation systems are increasingly used by engineers for retrofitting existing structures and designing new ones. Nevertheless, limited studies have been conducted on the performance evaluation of the nonlinear static analysis methods for estimating the seismic demands of the base isolated structures. The current study proposes a new modified lateral load pattern for seismic analysis of base isolated structures using modified capacity spectrum method (MCSM). Moreover, this study investigates the applicability of the modal pushover analysis (MPA) and modified capacity spectrum methods for assessing the base isolated structures with setback irregularity. To this end, two types of steel moment resisting structures including 3-story (low-rise) and 9-story (medium-rise) with different irregularities in elevation are considered. All the structures are isolated by three types of lead rubber bearing (LRB) isolators with various stiffnesses. In order to consider the effect of ground motion, two types of near-fault and far-fault ground motions are selected. To evaluate the performance of the MCSM and MPA methods, the structural seismic demands estimated by these methods are compared with their benchmark values obtained by the nonlinear time history analysis method. The obtained results show the superiority of the modified capacity spectrum method and the effectiveness of the new modified lateral load pattern presented for this method.

Performance Evaluation of a New NSP for Estimation of Seismic Demands of Nonlinear Irregular BRB Frames

Nonlinear static procedures are commonly used to compute seismic demands of structural systems. This paper combines the modified capacity spectrum method (MCSM) and modal pushover analysis (MPA) and proposes a new nonlinear static method called MPA–MCSM. To evaluate the accuracy of the proposed method, 30 different buckling-restrained braced (BRB) structures which consist of 3-, 9- and 20-story BRB frames with irregularities in plan and in elevation are selected. Each structure was analyzed subjected to seven pairs of ground motions. As a measure for the performance assessment of the proposed method, four structural seismic demands: (1) peak roof displacement, (2) story drift, (3) story shear and (4) base shear, are computed for each considered structure. The accuracy of MPA–MCSM responses is checked against the results obtained from nonlinear time-history analysis (NL-THA). The results reveal that MPA–MCSM provides conservative seismic demands for BRB frames.

Masonry vaults strengthened with a GFRP reinforced mortar coating: evaluation of the resisting peak ground acceleration

The reinforcement of existing masonry vaults against seismic actions is an extremely timing issue and it has already involved many researchers in experimental testing and numerical modelling. However, up to now, the results of the research have been expressed and compared in terms of load-displacement capacity curves. But the designers, in the practice, need to assess the resisting peak ground acceleration of the vault (PGA), so to compare it with the seismic demand. In the paper, a strategy to evaluate this parameter, based on the modified Capacity Spectrum Method and accounting for the level of the vault in the building is proposed. The procedure is applied to a case study of a masonry building with barrel vaults, comparing the performances of plain vaults and vaults strengthened with a GFRP (Glass Fiber Reinforced Polymer) reinforced mortar coating. The results evidenced significant improvements in terms of PGA after the reinforcement, attaining to values from 3.1 to 3.3 times that of the unreinforced vault.

Error Estimation of Nonlinear Equivalent Static Analysis for 3D-BRB Frames

Capacity Spectrum Method (CSM) as a nonlinear equivalent static method is one of the practical procedures which is usually used to estimate the seismic demands for design and evaluation of structural systems. This paper proposes a nonlinear equivalent static method called MPA-MCSM which combines the Modified Capacity Spectrum Method, MCSM, and the Modal Pushover Analysis, MPA. The accuracy of the developed algorithm is investigated for response prediction of Buckling Restrained Brace (BRB) frames with irregularities in elevation. The accuracy assessment of the proposed method is evaluated based on the computation of four seismic demands; peak roof displacement, story drift, base shear and story shear for each considered structure. The accuracy of MPAMCSM responses is checked against the results obtained from nonlinear time-history analysis. Thirty different models consist of 3-, 9- and 20-story structures subjected to 7 pairs of ground motions were analyzed. The results reveal that MPA-MCSM provides conservative seismic demands and has a good accuracy for BRB frames.

Assessment of the seismic capacity increase of masonry buildings strengthened through the application of GFRM coatings on the walls

The results of a numerical investigation on the seismic performances of masonry buildings strengthened through the application of a glass fibre-reinforced mortar (GFRM) coating are presented. Four different building configurations were modelled (two and three storey, regular and non-regular in plan); solid brick and rubble stone masonry were considered. A simplified modelling method (equivalent frame method) was adopted, with concentration of the non-linear response in shear and bending 'plastic hinges'. Some difficulties needed to be faced for strengthened masonry, so to consider the effect of the reinforcement in available commercial computer codes. The non-linear static analysis provided the capacity curves of the structures. Moreover, by applying the modified capacity spectrum method, it was possible to compare the performances in terms of maximum resisting ground acceleration. The results evidenced for the reinforced buildings increase ranging from 1.8 to 2.6 times that of unreinforced ones, proving the effectiveness of the reinforcement technique.

Seismic vulnerability assessment of strengthened Glass Fiber Reinforced Concrete (GFRC)

This paper presents the effect of using Carbon Fiber Reinforced Polymers (CFRP) as retrofitting material on seismic behavior of Plain Cement Concrete (PCC) and Glass Fiber Reinforced Concrete (GFRC). The experimental work was carried out in two steps. In first step, cylindrical specimens of size 150 mm × 300 mm were cast by using both PCC and GFRC. In second step, the specimens were wrapped by CFRP in three different patterns. All the specimens were tested under monotonic compressive loading. The test results were later used in the non-linear static cyclic analysis of reinforced concrete frame modeled in a finite element based analytical tool. Seismic vulnerability assessment was then carried out using a modified capacity spectrum method to develop analytical curves for the frames. The results showed significant improvement in seismic performance of frames strengthened by CFRP. Collapse hazard level for unconfined GFRC structure was increased by 20.73% as compared to unconfined PCC structure. There was 21 to 28% improvement observed in collapse hazard level in confined PCC structures as compared to their unconfined counterparts. However, confinement of GFRC structures resulted in only 8% increase in collapse hazard level as compared to unconfined GFRC structures.

A Pushover Seismic Analysis and Retrofitting Method Applied to Low-Rise RC School Buildings

The proposed method, called the Taiwan Earthquake Assessment for Structures by Pushover Analysis (TEASPA), is a modified capacity spectrum method developed in the NCREE handbook after the 1999 Chi-Chi earthquake. In this study, the evaluation of TEASPA is carried out using results from an experimental campaign comprised of two pushover tests inlow-rise reinforced concrete (RC) school buildings and the ASCE 41 capacity spectrum method. In addition, three problems related to retrofitting design are also discussed. Those are the removal of short columns in the structure, the optimal selection of the RC jacketing's position, and waterproofing problems in the RC jacketing method. The base shear-roof displacement curve, peak ground acceleration, and failure mechanism are calculated from each analysis. The results show that TEASPA is capable of providing accurate results for assessing a low-rise RC building's capacity and is more appropriate to pushover tests. Moreover, the solutions related to retrofitting problems are provided.

Accuracy of nonlinear static procedures for the seismic assessment of shear critical structures

SummaryThe nonlinear behavior of reinforced concrete (RC) members represents a key issue in the seismic performance assessment of structures. Many structures constructed in the 1980s or earlier were designed based on force limits; thus they often exhibit brittle failure modes, strength and stiffness degradation, and severe pinching effects. Field surveys and experimental evidence have demonstrated that such inelastic responses affect the global behavior of RC structural systems. Efforts have been made to consider the degrading stiffness and strength in the simplified nonlinear static procedures commonly adopted by practitioners. This paper investigates the accuracy of such procedures for the seismic performance assessment of RC structural systems. Refined finite element models of a shear critical bridge bent and a flexure‐critical bridge pier are used as reference models. The numerical models are validated against experimental results and used to evaluate the inelastic dynamic response of the structures subjected to earthquake ground motions with increasing amplitude. The maximum response from the refined numerical models is compared against the results from the simplified static procedures, namely modified capacity spectrum method and coefficient method in FEMA‐440. The accuracy of the static procedures in estimating the displacement demand of a flexure‐critical system and shear‐critical system is discussed in detail. Copyright © 2015 John Wiley & Sons, Ltd.

A Modified Capacity Spectrum Method with Direct Calculation of Seismic Intensity of Points on Capacity Curve

A direct methodology for solving the seismic intensity of each point on the capacity curve is proposed. By utilizing the procedure, a continuous curve between the structural response and the seismic intensity, the structural response function, can be easily generated. Unlike previous procedures that search for the performance point of a determined seismic intensity, the proposed methodology easily draws the full curve without iterations. The procedure is applicable to both a smooth design spectrum and an actual response spectrum. Examples indicate the methodology is accurate and fast, and convenient to be combined with existing procedures, such as Modal Pushover Analysis.

성능기반설계에 기초한 성능영향인자 변화에 따른 기둥의 거동분석

철근 콘크리트 구조물의 명확한 성능평가를 수행하기 위해 재료 및 구조적 특성이 구조물에 미치는 영향에 대한 분석이 필요하다. 구조물의 성능에 영향을 미치는 성능영향인자는 구조물의 재료적 특성인 콘크리트 강도, 종방향 주철근, 횡구속 철근, 구조적 특성인 형상비, 축하중에 대하여 총 5가지로 정의하였다. 각각의 성능영향인자 변화에 따른 고유치 해석과 비선형 정적해석을 수행하여 각각의 성능영향인자들이 구조물의 항복 변위와 항복 기저전단력 및 연성비의 정적성능에 미치는 영향을 분석하였다. 또한 비선형 정적해석의 결과를 이용하여 FEMA-440에서 제안된 수정된 능력스펙트럼법을 이용하여 성능평가를 수행하였고, 이에 따라 구조물의 성능점을 도출하였으며 각각의 성능영향인자가 미치는 영향을 분석하였다. 성능영향인자 변화에 따른 해석 결과, 고유치해석과 비선형 정적해석의 따른 고유주기와 연성비는 구조적 특성이 재료적 특성에 비해 구조물에 더 큰 영향을 미치는 것으로 나타났고, 그 중 형상비의 영향이 가장 크게 작용하였으며, 수정된 능력스펙트럼법을 이용한 성능평가 결과, 고유주기와 연성비와 마찬가지로 구조적 특성 중 형상비의 영향이 가장 크게 작용하였다.

Comparison of displacement coefficient method and capacity spectrum method with experimental results of RC columns

AbstractFor the performance‐based seismic design of buildings, both the displacement coefficient method used by FEMA‐273 and the capacity spectrum method adopted by ATC‐40 are non‐linear static procedures. The pushover curves of structures need to be established during processing of these two methods. They are applied to evaluation and rehabilitation of existing structures. This paper is concerned with experimental studies on the accuracy of both methods. Through carrying out the pseudo‐dynamic tests, cyclic loading tests and pushover tests on three reinforced concrete (RC) columns, the maximum inelastic deformation demands (target displacements) determined by the coefficient method of FEMA‐273 and the capacity spectrum method of ATC‐40 are compared. In addition, a modified capacity spectrum method which is based on the use of inelastic design response spectra is also included in this study. It is shown from the test specimens that the coefficient method overestimates the peak test displacements with an average error of +28% while the capacity spectrum method underestimates them with an average error of ‐20%. If the Kowalsky hysteretic damping model is used in the capacity spectrum method instead of the original damping model, the average errors become ‐11% by ignoring the effect of stiffness degrading and ‐1.2% by slightly including the effect of stiffness degrading. Furthermore, if the Newmark–Hall inelastic design spectrum is implemented in the capacity spectrum method instead of the elastic design spectrum, the average error decreases to ‐6.6% which undervalues, but is close to, the experimental results. Copyright © 2003 John Wiley & Sons, Ltd.

Capacity spectrum method based on inelastic demand spectra

By means of a graphical procedure, the capacity spectrum method compares the capacity of a structure with the demands of earthquake ground motion on it. In the present version of the method, highly damped elastic spectra have been used to determine seismic demand. A more straightforward approach for the determination of seismic demand is based on the use of the inelastic strength and displacement spectra which can be obtained directly by time-history analyses of inelastic SDOF systems, or indirectly from elastic spectra. The advantages of the two approaches (i.e. the visual representation of the capacity spectrum method and the superior physical basis of inelastic demand spectra) can be combined. In this paper, the idea of using inelastic demand spectra within the capacity spectrum method has been elaborated and is presented in an easy to use format. The approach represents the so-called N2 method formulated in the format of the capacity spectrum method. By reversing the procedure, a direct displacement-based design can be performed. The application of the modified capacity spectrum method is illustrated by means of two examples. Copyright © 1999 John Wiley & Sons, Ltd.