Matjaž Dolšek

SOFT STOREY EFFECTS IN UNIFORMLY INFILLED REINFORCED CONCRETE FRAMES

A large number of multi-storey reinforced concrete frame buildings with masonry infill walls, which were uniformly distributed over the height of the building, collapsed in the 1999 Kocaeli (Turkey) earthquake, due to complete failure of the first storey or the bottom two stories. In the paper it is demonstrated that a soft storey mechanism is formed in such structural systems if the intensity of ground motion is above a certain level. It is likely that collapse will occur if the global ductilities of the bare frames, as well as the ductilities of the structural elements, are low, and if the infill walls are relatively weak and brittle.

Simplified method for seismic risk assessment of buildings with consideration of aleatory and epistemic uncertainty

A simplified method for seismic risk assessment with consideration of aleatory and epistemic uncertainties is proposed based on the widely used closed-form solution for estimating the mean annual frequency of exceeding a limit state (LS). The method for the determination of fragility parameters involves a non-linear static analysis of a set of structural models, which is defined by utilising Latin hypercube sampling, and non-linear dynamic analyses of equivalent single degree-of-freedom models. The set of structural models captures the epistemic uncertainties, whereas the aleatory uncertainty due to the random nature of the ground motion is, as usual, simulated by a set of ground motion records. Although the method is very simple to implement, it goes beyond the widely used assumption of independent effects due to aleatory and epistemic uncertainty. Thus, epistemic uncertainty has a potential influence on both fragility parameters, and not only on dispersion, as has been assumed in some other approximate methods. The proposed method is applied to an example of a four-storey reinforced concrete building, where it is shown that the effects of epistemic uncertainties, in addition to aleatory uncertainty, increase with the severity of the LS, so that, for the near collapse LS, the risk with consideration of both sources of uncertainty is more than double if compared to the risk, which was determined solely by the consideration of aleatory uncertainty.

Progressive Incremental Dynamic Analysis for First-Mode Dominated Structures

Incremental dynamic analysis (IDA) is a widely used method for assessing structural performance under earthquake excitations. It enables direct evaluation of the record-to-record variability in structural response through a set of ground-motion records. If the number of ground-motion records is large then, the method becomes computationally demanding. To facilitate its practical application, a precedence list of ground-motion records has been introduced, aiming at selecting the most representative ground-motion records for IDA analysis. In progressive IDA analysis, the IDA curves are computed progressively, starting from the first ground-motion record in the precedence list. After an acceptable tolerance has been achieved, the analysis is terminated. This approach may significantly reduce the computational effort for first-mode-dominated structures, since the seismic response can be computed only for a certain number of ground-motion records from the precedence list to achieve an acceptable level of confidence in the prediction of the summarized (16th, 50th, and 84th fractiles) IDA curves. The proposed implementation of incremental dynamic analysis, which is demonstrated using an example of a 4-story reinforced concrete frame, can also be used for the selection of ground-motion records from a very large set of records, provided that all the records properly represent the seismic scenario for a given site. DOI: 10.1061/(ASCE)ST.1943-541X.0000282.

Evaluation of factors influencing the earthquake-resistant design of reinforced concrete frames according to Eurocode 8

Abstract The impact of factors which affect the performance of regular-reinforced concrete frame buildings designed according to the Eurocodes is investigated. The introduction of a sequence of variants of a structure, which gradually takes into account the design factors, makes it possible to measure the level of impact of an individual design factor on the global structural and performance parameters. The proposed procedure was applied to several regular reinforced concrete frame buildings, which were designed for ductility class medium and located in a region with moderate seismicity. A comparison between the reduction factor and the behaviour factor revealed that the behaviour factor defined in Eurocode 8, which significantly affects the design seismic action, is based more on the expert elicitation rather than on a firm scientific basis. Furthermore, based on the results of the investigated buildings it is shown that the design factors which are simply adopted in the design often have a significant impact on the resulting structures and their performance, whereas some other design factors, which require analysis of the structure and a lot of labour by engineers, often have only a minor effect on the performance of a structure.

A Practice-Oriented Approach for Probabilistic Seismic Assessment of Building Structures

A relatively simple probabilistic approach for the seismic performance assessment of building structures combines the SAC-FEMA method, which is a part of the broader PEER probabilistic framework and permits probability assessment in closed form, with the N2 method, which is based on the pushover analysis of a multi-degree-of-freedom model and the response spectrum analysis of an equivalent single-degree-of-freedom (SDOF) model. In the probabilistic approach the most demanding part of the PEER probabilistic framework, i.e. the Incremental Dynamic Analysis (IDA), is replaced by the much simpler Incremental N2 (IN2) analysis which requires less input data and less effort but, nevertheless, generally provides an acceptable accuracy. The incremental N2 (IN2) curve is intended to approximate a summarized IDA curve. Predetermined default values for dispersion measures are needed for the practical implementation of the simplified approach. In the paper, the simplified approach is summarized and applied to the seismic performance assessment of two variants of an asymmetric three-storey reinforced concrete frame building. The first variant represents a building designed for vertical loads only, without consideration of seismic codes (the “SPEAR building”, tested and analyzed within the European project SPEAR), whereas the second variant represents a building with the same geometry but designed according to Eurocode 8 (EC8) considering design ground acceleration on rock of 0.25g and soil type C. The probabilities of exceedance of the near collapse (NC) limit state are estimated and discussed. The results of the analyses indicate that the building designed according to the EC8 is able to survive a ground motion which is about 3.1 times stronger than in the case of the SPEAR building, while the probability of the exceedance of the NC limit state is about 25 times smaller.

Pushover-based loss estimation of masonry buildings with consideration of uncertainties

A seismic loss estimation methodology for masonry buildings is introduced. It enables the estimation of losses based on the simulated damage at the building’s level with consideration of epistemic and aleatoric uncertainties. The modelling uncertainties are incorporated through a set of structural models, which are defined by utilizing the Latin Hypercube Sampling technique. The damage of the building is simulated by the pushover analyses, whereas the relationship between the engineering demand parameter at the level of the building and the seismic intensity is estimated by incremental dynamic analysis, which is performed for the single-degree-of-freedom model taking into account the ground motion randomness and the modelling uncertainties. The loss estimation methodology requires the use of the fragility functions, which were in the case of masonry walls established from the experimental database, whereas for the other components, they were adopted according to FEMA P-581. The proposed method is demonstrated by means of an example of a three-storey masonry building. It is shown that consideration of the effect of modelling uncertainty increased the probability of collapse in 50 years and the expected annual loss, respectively, for factors of 1.5 and 1.25.

Pushover-Based Analysis in Performance-Based Seismic Engineering – A View from Europe

In this chapter, it is claimed that pushover-based methods, although subject to several limitations, often represent a rational practice-oriented tool for the estimation of the seismic response of structures. It is shown that the relations between quantities controlling the seismic response can be easily understood if a pushover-based analysis is presented graphically in the acceleration – displacement (AD) format. One of the pushover-based methods, i.e., the N2 method , which is implemented in Eurocode 8 , as well as its extensions, is very briefly summarized. Additionally, some recent pushover-based applications are listed. Finally, as an example of the application of pushover analysis, the seismic performance assessment of a multistorey building with consideration of aleatory and epistemic uncertainties is presented.

A Toolbox and Web Application for the Seismic Performance Assessment of Buildings

A software tool, known as a PBEE toolbox, for the seismic performance assessment of buildings, which was developed in Matlab in conjunction with the software framework OpenSees, and a web application for the prediction of approximate IDA curves are presented in this chapter. Although, in its present version, the PBEE toolbox supports only simple nonlinear models, its capabilities exceed usual software tools for computational simulation, since it enables seismic performance assessment of buildings with various procedures and adopts an open-source philosophy so that it can be easily extended or modified to suit specific user requirements. The capabilities of the PBEE toolbox and the web application, which involves the response database of a single-degree-of-freedom system with a quadrilateral force-displacement relationship, are demonstrated by means of an assessment of the seismic response parameters of an eight-storey reinforced concrete frame, using incremental dynamic analysis, progressive incremental dynamic analysis, approximate incremental dynamic analysis, and the N2 method. It is shown that, for the case of the presented example, all the methods produce similar results, although each method has some advantages and some disadvantages.

DEMAND HAZARD ANALYSIS: A TOOL FOR ASSESSING THE ADEQUACY OF CAPACITY DESIGN APPROACH FOR DEFINITION OF THE DESIGN SHEAR FORCES IN THE FRAME BUILDINGS

The risk-based design of buildings using nonlinear analysis is a challenging task. A question how to design components for non-simulated failure still remains unsolved. The simplified possibility is to use the capacity design which prevents shear failure of the components according to deterministic approach. In this paper an attempt has been made to obtain additional insight regarding this issue. For this purpose, the demand hazard analysis was performed for an example of an eight-storey reinforced concrete building. The ground motions were selected to match different target spectra. In addition to the uniform hazard spectrum, the conditional spectra conditioned to the first, second and third vibration periods were used. It was found that the return period of the design shear force according to capacity design vary significantly depending on location of the column as well as on the set of ground motions. However, for the investigated building it can be concluded that conditional spectrum with consideration of the first period of structure can be sufficient for determination of design

RISK-BASED DESIGN CHECK FOR COLLAPSE SAFETY USING FEW GROUND MOTIONS

The 3R method (Response analysis, Record selection, Risk-based decision making), which is used to check the adequacy of structural collapse safety by few nonlinear dynamic analyses, is briefly presented. The 3R method uses characteristic ground motions, which are selected by two-step selection procedure. Hazard-consistent set of ground motions is selected in the first step, while in the second step a subset of a few ground motions is obtained on the basis of the seismic response analysis of equivalent single-degree-of-freedom model, which is not computationally demanding. All ground motions are scaled to single intensity level, which corresponds to target collapse risk. The objective of the method is not precise assessment of collapse risk, but decision making whether the collapse risk is lower or greater in comparison to the target collapse risk. For this reason simple decision model may be introduced. If collapse is observed for less than half of characteristic ground motions, it can be decided that the reliability of structure against collapse is appropriate and vice versa. For an example of reinforced concrete dual structural system it is shown that an intensity-based assessment can provide sufficiently accurate risk-based decision making. Marko Brozovic and Matjaž Dolsek