CALIBRATION OF FORCE REDUCTION FACTORS OF RC BUILDINGS

A comprehensive study is undertaken to assess and calibrate the force reduction factors (R) adopted in modern seismic codes. Refined expressions are employed to calculate the R factors “supply” for 12 buildings of various characteristics represent a wide range of medium-rise RC buildings. The “supply” values are then compared with the “design” and “demand” recommended in the literature. A comprehensive range of response criteria at the member and storey levels, including shear as a failure criterion, alongside a detailed modelling approach and an extensively verified analytical tool are utilised. A rigorous technique is employed to evaluate R factors, including inelastic pushover and incremental dynamic collapse analyses employing eight natural and artificial records. In the light of the information obtained from more than 1500 inelastic analyses, it is concluded that including shear and vertical motion in assessment and calculations of R factors is necessary. Force reduction factors adopted by the design code (Eurocode 8) are over-conservative and can be safely increased, particularly for regular frame structures designed to lower PGA and higher ductility levels.     

Seismic Vulnerability Assessment of Modular Steel Buildings

Contemporary seismic design is based on dissipating earthquake energy through significant inelastic deformations. This study aims at developing an understanding of the inelastic behavior of braced frames of modular steel buildings (MSBs) and assessing their seismic demands and capacities. Incremental dynamic analysis is performed on typical MSB frames. The analysis accounts for their unique detailing requirements. Maximum inter-story drift and peak global roof drift were adopted as critical response parameters. The study revealed significant global seismic capacity and a satisfactory performance at design intensity levels. High concentration of inelasticity due to limited redistribution of internal forces was observed.     

SEISMIC BEHAVIOUR OF PERIMETER AND SPATIAL STEEL FRAMES

The present study deals with the seismic performance of partial perimeter and spatial moment resisting frames (MRFs) for low-to-medium rise buildings. It seeks to establish perimeter configuration systems and hence the lack of redundancy can detrimentally affect the seismic response of framed buildings. The paper tackles this key issue by com-paring the performance of a set of perimeter and spatial MRFs, which were “consistently designed”. The starting point is the set of low-(three-storey) and medium-rise (nine-storey) perimeter frames designed within the SAC Steel Project for the Los Angeles, Seattle and Boston seismic zones. Extensive design analyses (static and multi-modal) of the perimeter frame buildings and consistent design of spatial frame systems, as an alternative to the perimeter configuration, were conducted within this analytical study. The objectives of the consistent design are two-fold, i.e. obtaining fundamental periods similar to those of the perimeter frames, i.e. same lateral stiffness under design horizon-tal loads, and supplying similar yield strength. The seismic behaviour of perimeter and spatial configuration structures was evaluated by means of push-over non-linear static analyses and inelastic dynamic analyses (non linear time histories). Comparisons be-tween analysis results were developed in a well defined framework since a clear scheme to define and evaluate relevant limit states is suggested. The failure modes, either local or global, were computed and correlated to design choices, particularly those concerning the strength requirements (column overstrength factors) and stiffness (elastic stability indexes). The inelastic response exhibited by the sample MRFs under severe ground motions was assessed in a detailed fashion. Conclusions are drawn in terms of local and global performance, namely global and inter-storey drifts, beam and column plas-tic rotations, hysteretic energy. The finding is that the seismic response of perimeter and spatial MRFs is fairly similar. Therefore, an equivalent behaviour between the two configurations can be obtained if the design is “consistent”.     

IDENTIFICATION AND VERIFICATION OF SEISMIC DEMAND FROM DIFFERENT HYSTERETIC MODELS

The goal of this paper is to develop a modified Bouc-Wen hysteretic model from cyclic loading test data for reinforced columns, including the behavior of stiffness degradation, strength deterioration, pinching and softening effects of RC members. Seismic demands on this inelastic single degree of freedom system when subjected to both near-fault ground motion and far-field ground motion excitations were examined.

The cyclic loading test of reinforced concrete columns was experimentally observed and a system identification computer program was developed to solve each control parameter of the hysteretic model. A least-squared method for identifying parameters of the model is proposed in this paper. The hysteretic constitutive law produces a smoothly varying hysteresis such as the control-parameters for strength deterioration, stiffness degradation, pinching and softening effects. Two implementations of (1) flexure damage and (2) shear damage were conducted to provide better understanding of hysteretic behavior of RC structural members. A pseudo-dynamic experiment was also developed to verify the model parameters.

Based on the developed hysteretic model, the seismic demand of this inelastic model was investigated by using both near-fault ground motion data and far-field ground motion data as input motion. An R-μT inelastic response spectrum from different hysteretic models was generated.     

Displacement Ductility Limits for Pile Foundations in Cohesionless Soils

The displacement ductility limit for seismic design of concrete piles is determined for the range of cohesionless soils expected in practice. The curvature ductility capacity associated with specified performance limit states, namely, the “serviceability” and “damage-control” limits, is determined based on the current provisions for confining steel. An analytical model is applied to assess the displacement ductility factor at the specified curvature ductility level. The investigated parameters include the soil stiffness, pile diameter, longitudinal reinforcement ratio, axial force level, and pile above-ground height. A set of design displacement ductility factors is recommended and verified to ensure the satisfactory seismic performance.     

A PROCEDURE FOR ESTIMATING INPUT ENERGY SPECTRA FOR SEISMIC DESIGN

In this paper, the damage potential of an earthquake ground motion is evaluated in terms of the total power of the acceleration of the ground motion. By assuming an appropriate spectral shape for the input energy spectrum, and using the well-known Parseval theorem for evaluating the total power of a random signal, the peak amplification factor for the equivalent input energy velocity spectrum can be determined. It is shown that the peak amplification factor for the input energy spectrum depends on the peak-ground-acceleration to peak-ground-velocity ratio and duration of the strong motion phase of the ground motion. Values for the equivalent input energy velocity amplification factor vary from about 2 to 10 for most of the recorded ground motions used in this study. Although a considerable scatter of data is observed in this study, the peak amplification factor predicted by the Fourier amplitude spectrum of the ground acceleration provides a fairly good estimate of the mean value of the peak input energy compared to that determined from inelastic dynamic time history analyses, particularly for systems with high damping and low lateral strength. The peak amplification factor derived in this paper provides a more consistent approach for estimation of seismic demand when compared to an earlier empirical expression used for the formulation of duration-dependent inelastic seismic design spectra, even though only a slight difference in the required lateral strength results from the use of the new formula.     

Simple Models for Inelastic Seismic Analysis of Asymmetric Multistory RC Buildings

A simple stick model is presented for the inelastic seismic analysis in 3D of two-way eccentric multistory RC buildings. It has 3 DoFs per floor, point hinges at the ends of the vertical elements connecting floors, elastic story stiffness derived from the corresponding story force-interstory deformation relations of the elastic 3D structure under inverted-triangular floor loading (by torques for torsional stiffness, by horizontal forces for the lateral ones), story yield forces derived from the total resistant shear of the story vertical elements, but no coupling between lateral and torsional inelasticity. It is evaluated on the basis of comparisons of response histories of floor displacements to those from full nonlinear models in 3D of four actual buildings. Alternative locations of the story vertical element with respect to the floor mass center are examined: (a) the floor “center of twist” of the elastic 3D building under inverted-triangular floor torques; (b) the story “effective center of rigidity,” through which application of inverted triangular lateral forces does not induce twisting of floors; (c) the centroid of the secant stiffness of the story vertical members at yielding and (d) the centroid of the lateral force resistance of story vertical elements. Among alternatives (a)–(d), the floor “center of twist” provides the best agreement with floor displacement response-histories from full 3D nonlinear models. This means that the static eccentricity that matters for torsional response may be taken as that of the floor “center of twist.” The center of resistance comes up as the second-best choice.     

Statistical Characterization of Structural Demand under Earthquake Loading. Part 1: Robust Estimation of the Central Value of the Data

This article is the first of two companion articles addressing the statistical characterization of seismic demand. Performance-based earthquake engineering methodologies often require the characterization of central value estimates of structural demand. Since outliers can occur in the data, central value estimates should be determined by robust estimation methods. The performance of 50 robust central value estimators is evaluated, for different sample sizes, using the chord rotation, curvature, shear force, and inter-story drift demands obtained after analyzing five reinforced concrete structures under real earthquake records scaled to several intensities. Based on the results, seven estimators are proposed for different sample sizes.     

A Simplified Drift-Based Assessment Procedure for Regular Confined Masonry Buildings in Seismic Regions

This article presents a simplified procedure for assessing the seismic performance of existing low-to-medium rise confined masonry (CM) buildings, which are a typical construction type in Latin-America. The procedure consists of the estimation of the peak roof and first-story inelastic drift demand of CM buildings. The expected peak inelastic displacement demand is related to drift-based fragility curves, which express the probability of being or exceeding two key damage states in the masonry panels, developed from a relatively large experimental database. The proposed procedure could be very useful for obtaining rapid estimates of expected performance during future earthquake events and for assessing the seismic vulnerability of regular confined masonry structures.     

Estimating the Higher-Mode Response of Ductile Structures

While the importance of higher-mode actions is appreciated within the engineering community, the affect that ductile nonlinear response has on higher-mode characteristics and the subsequent implications this has for design has received little attention. In this article, the manner in which the higher-mode response of frame-wall structures is affected by inelastic behavior is closely examined and a means of accounting for this in design is proposed. The work focuses firstly on the characteristics of the higher modes present at the development of peak response and then considers how these characteristics would affect the total forces in the building. The study utilizes a series of nonlinear time-history analyses of two different groups of RC frame-wall structures subject to a suite of real records. It is shown that a new modal analysis approach that incorporates transitory inelastic modal characteristics gives significantly improved predictions of peak base shear in frame-wall structures than more traditional modal analysis methods which use elastic higher-mode characteristics. The issues associated with the use of transitory inelastic modal characteristics are discussed and various challenges that would need addressing for the prediction of other response parameters and structural types are identified.     

Definition of Seismic Input for Out-of-Plane Response of Masonry Walls: I. Parametric Study

Response of masonry walls to out-of-plane excitation is a complex, yet inadequately addressed theme in seismic analysis. The seismic input expected on an out-of-plane wall (or a generic “secondary system”) in a masonry building is the ground excitation filtered by the in-plane response of the walls and the floor diaphragm response. More generally, the dynamic response of the primary structure, which can be nonlinear, contributes to the filtering phenomenon. The current article delves into the details and results of several nonlinear dynamic time-history analyses executed within a parametric framework. The study addresses masonry structures with rigid diaphragm response to lateral loads. The scope of the parametric study is to demonstrate the influence of inelastic structural response on the seismic response of secondary systems and eventually develop an expression to estimate the seismic input on secondary systems that explicitly accounts for the level of inelasticity in the primary structure in terms of the displacement ductility demand. The proposed formulation is discussed in the companion article.     

SEISMIC RISK ASSESSMENT OF RC STRUCTURES WITH THE “2000 SAC/FEMA” METHOD

The applicability of a new, fully probabilistic approach to seismic design and assessment of reinforced concrete (RC) structures is investigated. Fundamental advantages of the method are mathematical simplicity and comparatively light computational effort. The original formulation, which was developed for steel structures, is first illustrated; ah extension which allows consideration of multiple failure mechanisms, typical of RC structures, is then proposed. The applicability of the method is demonstrated through an example: the seismic risk of a four storey RC building that was not designed for seismic resistance is evaluated. Three failure mechanisms are considered: joint failure, column shear failure and drift failure.     

Importance of Degrading Behavior for Seismic Performance Evaluation of Simple Structural Systems

This study focuses on effect of degradation characteristics on seismic performance of simple structural systems. Equivalent single degree of freedom systems are used for which the structural characteristics are taken from existing reinforced concrete (RC) frame buildings. Simulation of degrading behavior is achieved by considering actual experimental data. To obtain the seismic response of degrading structural systems, two different approaches are used: inelastic spectral analysis and fragility analysis. According to the results obtained from both approaches, degrading behavior is dominant for mid-rise RC frame buildings as it significantly amplifies seismic demand. Hence, in performance-based assessment approaches, analytical modeling of such degrading structures should be carried out carefully.     

Displacement-Based Design of an Energy Dissipating System for Seismic Upgrading of Existing Masonry Structures

A displacement-based method for the design of an energy dissipating system is proposed in this article. The device, which is composed of added concrete walls equipped with hysteretic Added Damping and Stiffness (ADAS) dampers, is aimed at upgrading the seismic behavior of existing masonry structures. The design method is based upon a simplified model of the overall structure-dissipating system. The proposed displacement-based design procedure was tested by means of inelastic response-time history analyses considering different masonry structures. The results of the analyses were compared with the seismic behavior expected from the design.     

SEISMIC RESPONSE OF REINFORCED CONCRETE FRAMES INFILLED WITH WEAKLY REINFORCED MASONRY PANELS

The research work presented in this paper is related to the seismic response of RC frames infilled with weak masonry panels, as it is traditional in many seismic prone countries in southern Europe. More specifically, the benefits derived from the insertion of a light reinforcement, in the mortar layers or in the external plaster, are studied in some detail.

Tests have been performed on different types of single bay, single storey, infilled frames to investigate the in-plane response at different earthquake intensity levels and the out-of-plane strength as a function of the in-plane damage. A series of parametric simulations have then been performed, calibrating the models used in the test results, to evaluate the effects of the different panels characteristics on the response of whole buildings, with different infill patterns. Both in-plane and the out-of-plane response have been considered. The results are described in terms of peak ground acceleration required to induce given limit states of serviceability or damage relatively far from the collapse of the structure, which is governed by the RC frame design more than by the infill panels properties.     

Experimental Evaluation of Seismic Performance of Squat RC Structural Walls with Limited Ductility Reinforcing Details

This article describes an experimental study carried out on of reinforced concrete (RC) walls of less confining reinforcement than that recommended by ACI 318. A total of eight RC walls with boundary elements comprising of five walls with aspect ratio of 1.125 and three walls with aspect ratio of 1.625 were tested by subjecting them to low levels of axial compression loading and simulated seismic loading, to examine the structural performance of the walls with limited transverse reinforcement. Conclusions are reached concerning the failure mode, drift capacity, strength capacity, components of top deformation, and energy dissipation characteristics of walls on the seismic behavior with limited transverse reinforcement. The influences of axial loading, transverse reinforcement in the wall boundary elements, and the presence of construction joints at the wall base on the seismic behavior of walls are also studied in this paper. Lastly, reasonable strut-and-tie models are developed to help in understanding the force transfer mechanism in the walls tested.     

Seismic Vulnerability Analysis of RC Bridges Based on Kriging Model

This paper presents a Kriging model-based method for seismic vulnerability analysis of reinforced concrete (RC) bridges. It aims at reducing the computational effect when the Monte Carlo technique is used for establishing the structural vulnerability curves. The general procedure of the proposed method is put forward firstly. In the procedure, the uncertainties existing in the structures and ground motions are both taken into account, and the uniform design (UD) technique is adopted for generating the random samples. The reliability of the proposed method is demonstrated by the vulnerability analysis of an single degree of freedom (SDOF) system using the Latin hypercube simulation (LHS) method. Vulnerability analysis of an RC bridge system is then carried out using the proposed method. The vulnerability curves of the bridge obtained by the Kriging model-based method are compared with those obtained by the LHS method. Additionally, three simulation schemes adopting different UD tables are employed to investigate the convergence and stability of the proposed method. The results show that the proposed method used for the seismic vulnerability analysis of RC bridges can reduce the computational effort and time to a large extent without much compromise on the accuracy.     

Statistical Characterization of Structural Demand under Earthquake Loading. Part 2: Robust Estimation of the Dispersion of the Data

Performance-based earthquake engineering methodologies often require a probabilistic model of structural demand. Since observations masking the probability distribution of the majority of the data are frequently found, robust estimation methods are proposed to estimate the probabilistic model parameters (i.e., central value and dispersion). The performance of thirty-three robust dispersion estimators is evaluated, for different sample sizes, using the chord rotation, curvature, shear force, and inter-story drift demands obtained after analyzing five reinforced concrete structures under real earthquake records scaled to several intensities. Based on the results, combinations involving dispersion and central value (defined in a companion article) estimators are proposed.     

Simple Iterative Use of Lyapunov's Solution for the Linear Optimal Seismic Design of Passive Devices in Framed Buildings

This article presents a Lyapunov-based analysis/redesign approach for the optimal seismic design of added viscous dampers in 3D framed structures. The optimal solution minimizes the total added damping while the mean squared drifts at the peripheral frames are constrained to allowable values under a white noise excitation. The proposed approach uses Lyapunov equation for analysis and an optimality criterion that dictates “fully stressedness” for redesign. Hence, the design process is actually comprised of an iterative solution of a set of algebraic equations. Three examples are solved so as to highlight the advantages of the proposed approach — a 3-story shear frame, an 8-story, 3-bay by 3-bay setback frame, and a 10-story industrial frame.     

Experimental Study on the Seismic Performance of Superimposed RC Shear Walls with Enhanced Horizontal Joints

The seismic performance of superimposed reinforced concrete (RC) shear walls is decreased by rocking behavior and damage concentration at the horizontal joint. An enhanced horizontal joint method is proposed to improve the corresponding seismic performance. To validate the reliability of the proposed method, three full-scale superimposed walls and a cast-in-place shear wall (for comparison) are designed and tested under the quasi-static load. The test results indicate that the rocking phenomenon can be prevented using the proposed method, and the seismic performance of superimposed RC shear walls with enhanced horizontal joints is comparable to that of the cast-in-place RC shear walls.