This paper investigates a number of computational issues related to the use of nonlinear static procedures in fragility analysis of structures. Such approaches can be used to complement nonlinear ...dynamic procedures, reducing the computational and modelling effort. Specifically, this study assesses the performance of the Capacity Spectrum Method (CSM) with real (i.e. recorded) ground motions (as opposed to code-based conventional spectra) to explicitly account for record-to-record variability in fragility analysis. The study focuses on single-degree-of-freedom systems, providing a basis for future multi-degree-of-freedom system applications. A case-study database of 2160 inelastic oscillators is defined through parametric backbones with different elastic periods, (yield) base shear coefficients, values of the ductility capacity, hardening ratios, residual strength values and hysteresis rules. These case studies are analysed using 100 real ground motions. An efficient algorithm to perform the CSM with real spectra is proposed, combined with a cloud-based approach (Cloud-CSM) to derive fragility relationships. Simple criteria to solve the issue of multiple CSM solutions (i.e. two or more points on the backbone satisfying the CSM procedure) are proposed and tested. It is demonstrated that the performance point selection can be carried out based on a particularly efficient intensity measure detected via optimal intensity measure analysis. The effectiveness of the proposed Cloud-CSM in fragility analysis is discussed through extensive comparisons with nonlinear time-history analyses, the code-based N2 method, and a simple method involving an intensity measure as a direct proxy for the performance displacement. The Cloud-CSM provides errors lower than ±20% in predicting the median of the fragility curves in most of the analysed cases and outperforms the other considered methodologies in calculating the fragility dispersion.
•The CSM is applied for the fragility analysis of parametric SDoF systems.•An algorithm to perform the CSM with real spectra is described.•A criterion to select the Performance Point in multiple-solution cases is proposed.•CSM provides errors lower than ±20% on the median fragility with respect to NLTHA.•CSM outperforms other nonlinear static approaches in estimating fragility dispersion.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK, ZRSKP
•Applicability of the nonlinear static procedure when applied to existing URM buildings.•Critical analysis and comparison of nonlinear static procedures proposed in international Standards.•Seismic ...assessment in presence of structural irregularity and not rigid diaphragms.•Criteria to properly define damage levels associated to the global response of URM buildings.•Refinements for the target displacement evaluation of URM buildings.
The nonlinear static procedure (NSP) is commonly adopted by practitioners for the seismic assessment of unreinforced masonry (URM) buildings, although a systematic validation of the procedure when applied to this type of buildings still lacks in the literature. The aim of this paper is to contribute to the validation and the improvement of the NSP when used for the seismic assessment of irregular URM buildings.
The effectiveness of the NSP is tested on numerical models representative of URM buildings that present both in plan and in elevation irregularities. The concept of irregularity is also extended to that consequent to the presence of flexible/stiff diaphragms, so frequent in existing URM buildings. To this aim a total of 13 numerical models representative of 3 and 4 stories URM buildings were developed. The results derived by the application of the NSP are compared with the nonlinear dynamic procedure, considered as the reference solution.
Based on the findings of the present research, original contributions are provided to: (1) the load patterns to apply for the pushover analysis; (2) the identification of damage levels; (3) the evaluation of the target displacement and the corresponding intensity measure that causes its attainment.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
•Proposed a modified first-mode-based pushover analysis procedure to assess the seismic performance of SMRF buildings.•Clarify the features of the responses by the modal pushover analysis.•Clarify ...the merits and demerits of the conventional nonlinear static procedures on estimating the dynamic responses of buildings.•Improved and reasonable accuracy of the proposed pushover analysis procedures was verified compared to the existing ones.
With the aim of performance-based design of building structures, nonlinear response history analysis (NRHA) procedures are required to reliably obtain the realistic responses of the buildings which, however, involve much complex procedures and reduce the feasibility of the practical uses. Nonlinear static procedure (NSP) analysis conventionally solely based on the first-mode of the structure are typically adopted in the design practice for approximately assessing seismic performances. Modal pushover analysis (MPA) and other modified NSP procedures were developed to include the higher-mode-effects in the NSP analysis, while they are still not feasible for the general practical uses. The study proposed a relatively simple procedure, named the modified first-mode-based pushover analysis (MFPA), for accurately assessing various seismic performances of steel buildings under MCE-level events through a single-step pushover process with a novel load pattern until a target displacement. Against mathematical approaches, a wide range of model building cases, including five-, ten-, fifteen-, and twenty-story buildings of special moment resisting frames (SMRFs) with two types of story heights were designed and examined in the study to verify the validity of the MFPA procedures. The results verified that the proposed MFPA procedures enabled to consistently more accurately assess the peaks and distributions of the inter-story responses of buildings obtained by the NRHA compared to other NSP and MPA approaches, and form an alternative method for the practical applications.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
This paper presents, firstly, an overview of the nonlinear static procedures (NSPs) given in different codes and research studies available in the literature, followed by the results achieved by the ...authors to evaluate the reliability of the safety level that they guarantee. The latter is estimated by adopting the fragility curve concept. In particular, 125 models of a masonry building case study are generated through a Monte Carlo process to obtain numerical fragility curves by applying various NSPs. More specifically, among the NSPs, the N2 method (based on the use of inelastic response spectra) with different alternatives and the capacity spectrum method (CSM)—based on the use of overdamped response spectra—are investigated. As a reference solution to estimate the reliability of the nonlinear static approach, nonlinear dynamic analyses (NLDAs) are carried out using the cloud method and a set of 125 accelerograms; the results are post-processed to derive fragility curves under the assumption of a lognormal distribution. The focus of this investigation is to quantify the influence that the NSP method’s choices imply, such as the criteria adopted to calculate the displacement demand of a structure or those for the bilinearization of the pushover curve. The results show that the N2 methods are all non-conservative. The only method that provides a good approximation of the capacity of the analyzed URM structures as derived from NLDAs is the CSM. In particular, bilinearization is proven to have a relevant impact on the results when using the N2 method to calculate displacement capacities, whereas the CSM method is not affected at all by such an assumption. The results obtained may have a significant impact on engineering practice and in outlining future directions regarding the methods to be recommended in codes.
Performance-based design plays a significant role in the structural and earthquake engineering community to ensure both safety and economic feasibility. Its application to masonry building ...design/assessment is limited and requires straightforward rules considering the characteristics of masonry behavior. Nonlinear static procedures mainly cover regular frame system structures, and their application to both regular and irregular masonry buildings require further investigation. The present paper addresses two major issues: (i) the definition of irregularity in masonry buildings, and (ii) the applicability of classical nonlinear static procedures to irregular masonry buildings. It is observed that the irregularity definition is not comprehensive and has different descriptions among the seismic codes as well as among researchers, particularly in the case of masonry buildings. The lack of global language may result in the misuse of the procedures, while adjustments may be essential due to irregularity effects. Therefore, irregularity indices given by different codes and research studies are discussed. Furthermore, an overview of nonlinear static procedures implemented within the framework of the performance-based approach and improvements proposed for its application in masonry buildings is presented.
The Improved Modal Pushover Analysis (IMPA) is a multimode procedure that has the advantage of redefining the lateral load applied, when comparing with the multimode current methods; hence, instead ...of considering the elastic deformed shape, it is possible to consider the deformed shape of the structure when it is behaving inelastically, as a pattern. The IMPA was proposed in the past and was successfully applied in the seismic assessment of bridges, the main objective of this work being to explore IMPA in buildings. For this purpose the seismic demands of two asymmetric plan buildings are herein estimated by means of IMPA and compared to Nonlinear Dynamic Analyses (NDA) and to current reference Nonlinear Static Procedures (NSPs): Modal Pushover Analysis (MPA) and two other NSPs that are proposed in American and European seismic codes (ASCE/SEI 41-06 NSP and N2 method respectively). In the latter, an extended version (extended N2) is considered, taking into account both the torsional and the higher mode effects.
The seismic response of the two buildings herein studied is obtained through two different approaches: the first regarding only one component of ground motion, while the second considers both components of ground motion acting simultaneously. The seismic assessment of both buildings is performed in terms of pushover curves, top displacement ratios, lateral displacements profiles, interstorey drifts, normalized top displacements and shear forces.
•An extension of IMPA is proposed for asymmetric plan buildings.•The individual performance of MPA, extended N2, ASCE41-06 NSP and IMPA was evaluated.•The NSPs were applied to two asymmetric plan buildings, and compared with NDA.•There is a general improvement with IMPA in relation to MPA.
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Pushover analysis technique is a key tool for the performance-based seismic design that has been largely adopted in the new generation of seismic codes. Therefore, more precise and reliable ...performance predictions are highly demanded. Improved upper-bound (IUB) pushover analysis is one of the advanced nonlinear static procedures (NSPs) that has been recently developed. This procedure adequately estimates the response of regular and tall buildings. In this study, IUB is extended to assess the seismic response of irregular buildings with setbacks. To this end, an adjustment of the IUB lateral load distribution is implemented by integrating a third mode of vibration to control the response of these complex buildings. Fifteen multi-storey steel frames with different types of setbacks including a reference structure are used to test the accuracy of the proposed procedure by comparing its results to those from other NSPs and the nonlinear time history analysis (NTHA). The findings show the superior capacity of the extended IUB in predicting the seismic response of buildings with different levels and types of setbacks.
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EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
The so-called N2 method is a widely used nonlinear static method for the seismic design and/or assessment of different building typologies. In this paper, the idea of reversing the so-called N2 ...method currently adopted in the Annex B of Eurocode 8 (the code on which the present paper is based) in a direct displacement-based procedure is presented in a simple alternative format. In this way, it is possible to obtain the percentage of the seismic action associated to any performance displacement. By doing so, it is also possible to determine the target displacement without the need for an iterative procedure. The proposed method presents several advantages for professional engineering practice in respect to the seismic vulnerability assessment of new and existing buildings. The comparison of the original N2 method with the proposed one is illustrated by means of a test structure example.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
A common analysis method of soil-structure systems in seismic design procedures such as FEMA-440 is to replace the entire soil-structure system by a fixed-base oscillator with an equivalent ...fundamental period and damping ratio to consider inertial effect of soil-structure interaction. It is generally believed by researchers that ignoring kinematic effect of soil-structure interaction is conservative to determine response of structures and FEMA-440 supports this idea by defining a reduction factor applying to elastic response spectra. Also, the improvements of nonlinear static procedures in FEMA-440 are achieved for fixed-base structures and the soil effects are not perfectly obtained in coefficients and relations of these procedures. Thus, it seems necessary to assess the accuracy of proposed procedures of FEMA-440 to include soil-structure interaction. In this paper, the accuracy of equivalent replacement oscillator and nonlinear static Procedures of Equivalent Linearization and Coefficient methods, defined in FEMA-440, to analyze soil-structure systems with surface and embedded foundations are evaluated. Both kinematic and inertial effects of soil-structure interaction are investigated by conducting a parametric study using 20 ground motions recorded on soft soil site E, on which the more SSI effects are probable.
One of the most determinant components of any seismic safety assessment procedure is the estimate of the nonlinear seismic demand, particularly if such procedure is probabilistic rather than ...deterministic. Indeed, the prediction of the seismic demand of RC structures is dictated by a number of variables, related to the seismic action or to the geometrical and material properties, with different relevancy and uncertainty levels. From a macro-viewpoint one can distinguish the different approaches for nonlinear demand prediction in two major groups: nonlinear static and dynamic. Whereas the latter is widely recognised as the most accurate approach, the former, particularly by means of nonlinear static procedures (NSPs), represents a valid alternative tool for performance-based seismic assessment of structures, quite accepted among the scientific community worldwide. Significant effort has therefore been made, over the past few years, to improve those simplified methods and several different proposals in terms of application methodology have come up. Simultaneously, validation studies have thoroughly been carried out, even though focusing mainly on regular, building structures, rather than typically irregular bridges, and have focused the validation through the direct comparison of response prediction. The capability of such procedures within a probabilistic framework that yields the collapse probability of randomly sampled RC viaducts is herein investigated. A commonly employed nonlinear static procedure (N2) is further validated against nonlinear dynamic analysis using two distinct probabilistic procedures, described and tested in a companion paper, which account differently for the uncertainty of the concerned variables (geometry, material properties, earthquake records, intensity level). A case study of seven bridge configurations, with different (ir)regularity levels, is considered together with a relatively large set of real earthquake records and random simulation is carried out using the Latin Hypercube Sampling scheme. The conclusions have further probed the suitability of nonlinear static analysis in estimating seismic demand by leading, under probabilistic conditions, to slightly conservative probabilities of collapse of RC bridges with respect to nonlinear dynamic analysis.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK, ZRSKP
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