A Base Isolation System for Developing Countries Using Discarded Tyres Filled with Elastomeric Recycled Materials

This article studies the performance of economic base isolators using tyres filled with elastomeric recycled materials. The research was conducted to analyze base isolators to be used in developing nations, where the application of conventional elastomeric rubber bearings due to economic reasons is limited.

The tested isolators are made of kart tyres filled with different recycled elastomeric materials and aggregates. Dynamic and static tests proved acceptable vertical to horizontal stiffness ratio of the bearings and shake table tests showed an excellent enhancement of the base isolated structural response compared to the corresponding fixed base structure.     

Inelastic Demand Spectra of Bi-Linear Models for Capacity Spectrum Method and Response of Simple Structures under Near-Source Records

A very useful tool for the preliminary design of structures is the elastic demand spectrum that can be used in the capacity spectrum method. A pseudo-acceleration relationship has to be assumed when constructing a demand spectrum. This assumption results in large errors for long period structures with large damping ratios and the conventional demand spectra require a substitute elastic structure. In the present study, the conventional demand spectra are extended to bi-linear models. Pseudo-acceleration is still assumed but results in acceptably small errors, when a constant viscous damping coefficient for a single-degree-of-freedom (SDF) structure is calculated from the tangent stiffness and the damping ratio is set at 5% in both elastic and yield phases. For nonlinear structures, tangent stiffness dependency of damping force could be acceptable because energy absorption is primarily the result of structural nonlinear deformation. To extend the conventional demand spectra to a bi-linear model, effective period calculated from the secant stiffness has to be used. The use of effective period introduces no approximation because the peak displacement of the SDF structure is computed from nonlinear analysis in the time domain. The method presented in this study is also valid if damping coefficient proportional to initial elastic spectra is used. In this case, the pseudo-acceleration is defined as the base shear coefficient that is required to produce the peak displacement of the SDF structure in a static manner. We present demand spectra of bi-linear models for a number of near-source records from large earthquakes, and spectral ratios of two horizontal components. The effects of different types of ground motion on the response reduction factor due to inelastic deformation are investigated.     

Characterization of Ductility and Inelastic Displacement Demand in Base-Isolated Structures Considering Cyclic Degradation

New designed or retrofitted structures with the use of isolation system may exhibit nonlinear deformations during strong ground motions. Inelastic displacement ratio of base-isolated structures is studied in this paper by employing two degree of freedom model taking into account inelastic behavior of isolators and superstructure. Parametric study is conducted to evaluate influence of isolator and superstructure properties on inelastic displacement ratio according to two sets of near-fault and far-fault ground motions. Accuracy of proposed equations in the literature to evaluate inelastic displacement ratio are studied, as well. Furthermore, cyclic degradation effects are investigated by considering stiffness and strength degradation and pinching in hysteresis model of superstructure. Eventually, inelastic responses of isolated structures with two types of isolators (lead rubber bearing and friction pendulum bearing) are compared.     

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”.     

Cumulative Ductility Spectra for Seismic Design of Ductile Structures Subjected to Long Duration Motions: Concept and Theoretical Background

A seismic design procedure that does not take into account the maximum and cumulative plastic deformation demands that a structure will likely undergo during severe ground motion could lead to unreliable performance. Damage models that quantify the severity of repeated plastic cycling through plastic energy are simple tools that can be used for practical seismic design. The concept of constant cumulative ductility strength spectra, developed from one such model, is a useful tool for performance-based seismic design. Particularly, constant cumulative ductility strength spectra can be used to identify cases in which low-cycle fatigue may become a design issue, and provides quantitative means to estimate the design lateral strength that should be provided to a structure to adequately control its cumulative plastic deformation demands during seismic response. Design expressions can be offered to estimate the strength reduction factors associated to the practical use of constant cumulative ductility strength spectra.     

DAMAGE AND DUCTILITY DEMAND SPECTRA ASSESSMENT OF HYSTERETIC DEGRADING SYSTEMS SUBJECT TO STOCHASTIC SEISMIC LOADS

Damage phenomena observed in structures subject to intense seismic events are the result of stiffness and strength degradation. This paper studies the damage assessment of hysteretic degrading structures described by means of the Bouc-Wen model, modified to represent the mechanical degradation induced by severe earthquakes. In order to consider randomness of seismic action, the analysis is performed by adopting a stochastic approach and the Park and Ang damage functional is also evaluated in stochastic way. A parametric analysis is carried out with the aim to analyse the effect of mechanical characteristics and measure parameters of earthquake intensity on seismic response and damage level. Damage spectra are finally obtained and they are used to develop, on the basis of the Performance Based Seismic Design, ductility demand spectra.     

ANALYTICAL MODELS FOR BRICK MASONRY INFILLED R/C FRAMES UNDER LATERAL LOADING

Proposed in this paper are two analytical models for predicting the inelastic response of unreinforced brick masonry infills in reinforced concrete frames subjected to mono-tonic and reversed cyclic loading. The first model is based on the traditional diagonal strut concept, while the second one is a simple isoparametric element with shear deformation only. All the essential characteristics of the hysteretic behaviour of the panel, including strength and stiffness degradation, pinching and slippage, are explicitly taken into account. The models are implemented in a general-purpose program for the inelastic time-history analysis of structures, and are used for studying the seismic behaviour of typical multistorey frames with various arrangements of infill panels, including structures with an open ground storey. The results of the analysis are in agreement with both experimentally observed behaviour and with experience regarding seismically damaged buildings.     

Constant Ductility Energy Factors for the Near-Fault Pulse-Like Ground Motions

This study is focused on the constant ductility energy factors for bilinear system under the near-fault pulse-like ground motions. The variation of energy factors is studied in consideration of the earthquake magnitude, rupture distance, damping ratios, and post-yield stiffness ratios. The results indicate that the near-fault pulse-like ground motions would increase the energy dissipation of structures. The energy factors are significantly influenced by the earthquake magnitude. The damping ratios have more obvious influences on the energy factors than the post-yield stiffness ratios. A predictive model is proposed for the application of constant ductility energy factors for near-fault pulse-like ground motions.     

Nonlinear Response of RC Framed Buildings with Isolation and Supplemental Damping at the Base Subjected to Near-Fault Earthquakes

The nonlinear seismic response of base-isolated framed buildings subjected to near-fault earthquakes is studied to analyze the effects of supplemental damping at the level of the isolation system, commonly adopted to avoid overly large isolators. A numerical investigation is carried out with reference to two- and multi-degree-of-freedom systems, representing medium-rise base-isolated framed buildings. Typical five-story reinforced concrete (RC) plane frames with full isolation are designed according to Eurocode 8 assuming ground types A (i.e., rock) and D (i.e., moderately soft soil) in a high-risk seismic region. The overall isolation system, made of in-parallel high-damping-laminated-rubber bearings (HDLRBs) and supplemental viscous dampers, is modeled by an equivalent viscoelastic linear model. A bilinear model idealizes the behavior of the frame members. Pulse-type artificial motions, artificially generated accelerograms (matching EC8 response spectrum for subsoil classes A or D) and real accelerograms (recorded on rock- and soil-site at near-fault zones) are considered. A supplemental viscous damping at the base is appropriate for controlling the isolator displacement, so avoiding overly large isolators; but it does not guarantee a better performance of the superstructure in all cases, in terms of structural and non structural damage, depending on the frequency content of the seismic input. Precautions should be taken with regard to near-fault earthquakes, particularly for base-isolated structures located on soil-site.     

AN ALGORITHM FOR COMPUTING ISODUCTILE RESPONSE SPECTRA

The computation of constant ductility (or isoductile) response spectra for single-degree-of-freedom systems can require numerous individual response history analyses. Recognising that the same ductility response may be obtained for different strength oscillators of a given period, greater computational effort is required to reduce the possibility that a desired solution is not overlooked. Even a single solution may not exist if a local discontinuity in the strength-ductility relationship coincides with the desired value of ductility. This paper describes a two-phase algorithm to identify the highest strength solution for which the corresponding ductility equals (or does not exceed) the desired ductility. The first phase adopts a “check-reject” approach to reject intervals of strength where the possibility of unidentified higher-strength solutions is considered to be remote, thereby narrowing the strength interval in which the solution will be found. The second phase identifies a solution within this interval as rapidly as possible using a bisection approach. The algorithm is implemented in the USEE software program. The efficiency and accuracy of the algorithm are demonstrated by comparison to results obtained with other software programs.     

ELASTIC EARTH PRESSURES ON RIGID WALLS UNDER EARTHQUAKE LOADING

Elastic dynamic earth pressures induced by earthquakes are computed by analyzing a wall-foundation-backfill system. Both foundation and backfill are considered viscoelastic; the foundation is a semi-infinite space and the backfill, a uniform layer of constant thickness. A simple analytical solution is developed by assuming an approximate backfill-foundation interface condition and adopting the least squares method. The response functions computed indicate the large influence of the various system parameters on earth pressure, including the foundation characteristics,as well as wall geometry and mass. The transient response of the system is also studied by obtaining spectra for base shear. A large number of seismic records are analyzed to obtain average spectra and a total of three correction functions are used to take into account the foundation stiffness and density as well as wall inertia. A simple design method is proposed to estimate the maximum base shear.     

DESIRABLE STRENGTH DISTRIBUTION FOR ASYMMETRIC STRUCTURES WITH STRENGTH-STIFFNESS DEPENDENT ELEMENTS

Recent studies have shown that for many reinforced concrete lateral force-resisting elements (LFRE) stiffness is dependent on strength, and as a result strength assign-ment to these elements would affect both the strength and stiffness distributions in a structure. As a consequence, stiffness distribution cannot be considered known prior to strength assignment. This implies that in assigning strength to LFRE, the designer has the ability not only to prescribe the strength distribution, but also indirectly control the stiffness distribution in the structure. In this paper, a study is made on the seis-mic performance of a number of single-story structures to reconfirm that the “balanced CV-CR location” criterion, previously suggested by the writers, constitutes a desirable strength/stiffness distribution for minimising torsional response of asymmetric reinforced concrete structures.     

SEISMIC DESIGN AND ANALYSIS OF A KNEE BRACED FRAME BUILDING

A five-storey steel frame incorporating dissipative knee elements is designed using the Eurocode 8 pushover analysis method. The non-linear analysis makes use of a novel knee element model capable of accurately simulating the bending and shear behaviour observed in full-scale tests. The performance of the structure is assessed using non-linear time-history analysis. This shows that the knee elements can be designed to yield under small earthquakes or early in a strong one (maximising their energy dissipation) while still being able to withstand a large event without collapse. Knee elements thus have the potential to give excellent seismic performance in steel framed structures. The time history analysis results are compared to those obtained with the three different pushover analysis methods (Eurocode 8, FEMA 356 and ATC 40). The FEMA 356 method, which includes a more accurate representation of the structure's significant post-yield stiffness, gave the closest agreement with the time history analyses, while the Eurocode 8 method gave rather conservative results and the ATC 40 method appears non-conservative for this type of structure.     

STRENGTH REDUCTION FACTORS FOR DUCTILE STRUCTURES WITH PASSIVE ENERGY DISSIPATING DEVICES

In recent years, current seismic codes started contemplating the design of structures with passive energy dissipating devices. One important issue for the rational seismic design of these devices and the structure that contains them is the formulation of numerical methods to estimate their design seismic forces. From the study of the dynamic response of single-degree-of-freedom systems subjected to accelerograms recorded in Mexico during the last two decades, expressions to estimate the strength reduction factor that should be used to reduce the elastic design strength spectra for 5 percent damping, to establish the design seismic forces for structures having different combinations of plastic and viscous energy dissipating capacities, are formulated.     

DUCTILITY REDUCTION FACTOR OF MDOF SHEAR-BUILDING STRUCTURES

In this paper, the results of recent studies on inelastic seismic response of MDOF shear-building structures are presented. In the last few decades, the concept of response modification factor R has been introduced and developed to account for inelastic nonlinear behaviour of structures under earthquakes. In this paper, an attempt has been made to adjust and extend this concept through introducing a modifying factor R _T . This factor is used for dynamic analysis of MDOF structures, including the calculation of inelastic response spectra. Sensitivity analysis was carried out to identify the parameters that have influence on R _T . It has been demonstrated that R _T is predominantly a function of number of stories, and accordingly a relationship has been suggested. Finally, an approximate approach has been developed for evaluating the seismic strength and ductility demands of MDOF structures.     

Seismic Performance and Modeling of a Half-Scale Base-Isolated Wood Frame Building

The concept of base isolation is a century old, but application to civil engineering structures has only occurred over the last several decades. Application to light-frame wood buildings in North America has been virtually non existent with one notable exception. This article quantitatively examines issues associated with application of base isolation in light-frame wood building systems including: (1) constructability issues related to ensuring sufficient in-plane floor diaphragm stiffness to transfer shear from the superstructure to the isolation system; (2) evaluation of experimental seismic performance of a half-scale base-isolated light-frame wood building; and (3) development of a displacement–based seismic design method and numerical model and their comparison with experimental results. The results of the study demonstrate that friction pendulum system (FPS) bearings offer a technically viable passive seismic protection system for light-frame wood buildings in high seismic zones. Specifically, the amount and method of stiffening the floor diaphragm is not unreasonable, given that the inter-story drift and accelerations at the upper level of the tested building were very low, thus resulting in the expectation of virtually no structural, non structural, or contents damage in low-rise wood frame buildings. The nonlinear dynamic model was able to replicate both the isolation layer and superstructure movement with good accuracy. The displacement-based design method was proven to be a viable tool to estimate the inter-story drift of the superstructure. These tools further underscore the potential of applying base isolation systems for application to North America's largest building type.     

Cyclic Response of Concrete Beams Reinforced by Plain Bars

There are many reinforced concrete structures throughout the world that have been built in the past decades that lack appropriate seismic details and reinforced by plain bars. To study the behavior of such buildings, seven beams have been tested under cyclic and monotonic load. The specimens include substandard specimens, with deficient seismic details and reinforced by plain bars, specimens designed in accordance with ACI-318-99 but reinforced by plain bars, and standard specimens reinforced by deformed bars. The tests indicate that the substandard specimens sustain relatively large slip of longitudinal bars, separation of specimen relative to foundation and sliding at large deformation phase, low initial stiffness ratio, limited lateral displacement capacity, and loss of nominal yield strength. The specimens reinforced by plain bars in accordance with ACI-318-99 perform almost similar to standard specimens with deformed bars, in terms of elastic stiffness and lateral displacement ductility; but, they sustain larger slip, and smaller yield strength. Failure of all specimens reinforced by plain bars is characterized by flexural cracks without visible shear failure. Residual shear strength of substandard specimens is modeled by dowel action of longitudinal bars to predict a lower limit for lateral strength of the specimens.     

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.     

Non-Iterative Equivalent Linearization Based on Secant Period for Estimating Maximum Deformations of Existing Structures

The capacity spectrum method of ATC-40 uses the secant period as the equivalent period of equivalent linear systems. Therefore, it results in a direct graphical comparison. The maximum inelastic displacement and acceleration demands of structures can be simultaneously obtained from the intersection of the demand and capacity diagrams. However, for evaluation of existing structures, the demands need to be determined through iterations since the equivalent period and damping of the equivalent linear systems currently available are both a function of the (displacement) ductility ratio, which is unknown and is the target of evaluation. In addition, the equivalent damping used in the capacity spectrum method is independent of periods of vibration. It may lead to poor estimations of maximum responses especially for short-period systems. This article proposes two equivalent linear systems based on the secant period to estimate the maximum displacement and acceleration responses of existing structures. Both the recommended equivalent period and damping are defined by the strength ratio (elastic lateral strength/yield lateral strength), rather than the ductility ratio. Because the strength ratio of existing structures is a known parameter, the maximum displacement and acceleration responses of these structures can be determined without iterations. Besides, effects of periods of vibration on the equivalent linear systems are also included in this study. The equivalent damping is derived from statistical analyses for bilinear single-degree-of-freedom (SDOF) systems with different periods of vibration, strength ratios and post-yield stiffness based on 72 earthquake ground motions recorded on firm sites. Procedures and examples for applications of the proposed equivalent linear systems on nonlinear static analysis procedures are also provided.     

Design of Passive Viscous Fluid Control Systems for Nonlinear Structures Based on Active Control

A practical procedure is developed for the design of passive control systems using viscous fluid dampers for nonlinear structures. The design methodology takes advantage of the modification of the damping, strength, and stiffness properties of the structure to achieve the desired relative displacement and absolute acceleration response. For this purpose, a study of poles in the complex plane is used to determine the required changes in the dynamic properties of nonlinear structures. Furthermore, a relatively simple relation between the ductility demands of highly damped single- and multiple-degree-of-freedom (SDF and MDF respectively) systems is established to reduce the computational burden of the proposed design method.