Distribution of Lateral Forces in Base-Isolated Buildings Considering Isolation System Nonlinearity

The ASCE 7 equivalent lateral force method for base-isolated buildings applies a triangular distribution of forces to the superstructure. This distribution attempts to approximately account for the observed effects of isolation system nonlinearity on the superstructure response, but a more rational approximation is needed. Using nonlinear regression analysis of median response data from nonlinear response history analysis of representative systems, improved equations are developed to estimate the lateral force distribution in the superstructure. The ASCE 7 distribution, a revision considered by a SEAONC committee, and the improved distribution developed here are evaluated. Only the improved equations are accurate over many system parameters.     

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.     

Application of an Extended Bouc-Wen Model in Seismic Response Prediction of Unbonded Fiber-Reinforced Isolators

The focus of this article is on seismic-response prediction of Stable Unbonded-Fiber Reinforced Elastomeric Isolators (SU-FREIs). The lateral load-displacement of a SU-FREI can be characterized with a gradual softening that is followed by stiffening. An extended Bouc-Wen Model is developed to simulate the response behavior of SU-FREIs under seismic events. To examine the accuracy of model, the response of a base isolated structure to different input earthquakes were simulated and compared with the results of a previous shake table study. Results of this study indicate that the proposed Bouc-Wen Model is robust and reasonably accurate in seismic analysis of SU-FREIs.     

Analysis and Design of Inter-Story Isolation Systems with Nonlinear Devices

Seismic isolation systems that mitigate seismic response are generally applied at the base of a building; however, architectural, functional, and cost considerations have motivated the application of isolation systems at inter-story locations. In this article, we systematically examine the effectiveness of inter-story isolation systems as a function of their location, and explore alternative approaches for selecting their properties. Single-story isolation systems are shown to be effective in mitigating force demands above the isolation system but less effective in mitigating forces below the isolation system. Finally, the practical aspects of designing an inter-story isolation system to accommodate light loads are discussed.     

A Procedure for the Displacement-Based Seismic Assessment of Infilled RC Frames

The aim of this study was to propose an extension of the displacement-based assessment procedure for infilled reinforced concrete (RC) frames. Two fundamental steps of the displacement-based approach were studied: the determination of the equivalent viscous damping and the definition of the limit-state displacement profile. The proposed criteria were derived by examining the results of two different numerical investigations regarding the nonlinear seismic response of single- and multi-story infilled RC frames. Lastly, the effectiveness of the method was verified through comparisons, in terms of displacement demand, with the results of nonlinear dynamic analyses.     

Equivalent Damping in Support of Direct Displacement-Based Design

The concept of equivalent linearization of nonlinear system response as applied to direct displacement-based design is evaluated. Until now, Jacobsen's equivalent damping approach combined with the secant stiffness method has been adopted for the linearization process in direct displacement-based design. Four types of hysteretic models and a catalog of 100 ground motion records were considered. The evaluation process revealed significant errors in approximating maximum inelastic displacements due to overestimation of the equivalent damping values in the intermediate to long period range. Conversely, underestimation of the equivalent damping led to overestimation of displacements in the short period range, in particular for effective periods less than 0.4 seconds. The scatter in the results ranged between 20% and 40% as a function of ductility. New equivalent damping relations for four structural systems, based upon nonlinear system ductility and maximum displacement, are proposed. The accuracy of the new equivalent damping relations is assessed, yielding a significant reduction of the error in predicting inelastic displacements. Minimal improvement in the scatter of the results was achieved, however. While many significant studies have been conducted on equivalent damping over the last 40 years, this study has the following specific aims: (1) identify the scatter associated with Jacobsen's equivalent damping combined with the secant stiffness as utilized in Direct Displacement-Based Design; and (2) improve the accuracy of the Direct Displacement-Based Design approach by providing alternative equivalent damping expressions.     

Seismic Tests and Numerical Modeling of a Rolling-ball Isolation System

For the seismic isolation of light structures, the use of laminated rubber bearings is neither economical nor, for most cases, technically suited. For the isolation of this type of structure a new system, consisting of steel balls rolling on rubber tracks, has been developed at TARRC (Tun Abdul Razak Research Centre).

This article presents the results of experimental tests carried out for the characterization of the behavior of this new device. A numerical model is also proposed that can be used to assess the seismic response of structures with this isolation system.

Comparison of the predictions of the numerical model with the experimental data shows that the model is adequate to perform the correct assessment of the seismic response of isolated structures. The results of the experimental campaign of shaking-table tests, as well as the numerical simulations, show that there is an effective reduction of the acceleration levels induced in the isolated structures.     

Seismic Design and Response of Framed Structures with Stiffening Bracing Systems

Stiffening Bracing System (SBS) is proposed as an alternative to conventional braced frames. SBS is intended to reduce the floor accelerations while maintaining uniform inter-story drift along the building height. The system ensures that additional damping devices distributed over the building’s height work efficiently. An iterative design procedure is developed to maintain a desired target performance. The procedure accounts for higher mode effects and supplemental damping. A series of nonlinear response history analyses on braced frames with various heights demonstrated the adequacy of the proposed procedure in achieving target structural performance and seismic demand prediction.     

Seismic Evaluation of Tall Buildings Using a Simplified but Accurate Analysis Procedure

A simplified analysis procedure for evaluating the nonlinear seismic responses of tall reinforced concrete (RC) buildings is examined in this study. It is called the Uncoupled Modal Response History Analysis (UMRHA) procedure. It can be viewed as an extended version of the classical modal analysis procedure, where the nonlinear response of each vibration mode is first computed, and they are later on combined into the total response of the structure. The procedure requires the knowledge of the modal hysteretic behavior, which can be obtained from a cyclic modal pushover analysis. The responses of four tall buildings in Bangkok to distant large earthquakes are computed by this procedure and compared with those obtained from the Nonlinear Response History Analysis (NLRHA) procedure. These four buildings have different heights—varying from 20 to 44 stories, different configurations of floor plan, and different arrangement of RC walls. The comparison shows that the UMRHA procedure is able to accurately compute the story shears and story overturning moments, floor accelerations, and inter-story drifts of all these tall buildings. The required computational effort is also extremely low compared to that of the NLRHA procedure. Moreover, since the UMRHA procedure computes the response of each individual vibration mode, it provides more understanding and insight into the complex nonlinear seismic responses of these tall buildings.     

Direct Displacement-Based Design of Buildings with Different Seismic Isolation Systems

A displacement-based design (DBD) procedure for buildings equipped with different seismic isolation systems is proposed. It has been derived from the Direct Dispaced-Based Design (DDBD) method recently developed by Priestley et al. [2007] Priestley, M. J. N., Calvi, G. M. and Kowalsky, M. J. 2007. Displacement-Based Seismic Design of Structures, Pavia, , Italy: IUSS Press.  [Google Scholar]. The key aspect of the proposed procedure is the definition of a target displacement profile for the structure. It is assigned by the designer to achieve given performance levels, expressed in terms of maximum displacement of the isolation system and maximum interstory drift. The proposed design procedure has been developed for four different idealized force-displacement relationships, which can describe the cyclic response of a wide variety of isolation systems, including: (i) Lead-Rubber Bearings (LRB); (ii) High-Damping Rubber Bearings (HDRB); (iii) Friction Pendulum Systems (FPS); and (iv) Combinations of lubricated Flat Sliding Bearings (FSB) with different re-centering and/or energy dissipating auxiliary devices. In this article, the background and implementation of the design procedure is presented first. It is followed by the results of validation studies based on nonlinear time-history analyses on different design configurations of base isolated buildings.     

Optimum Design Approaches for Improving the Seismic Performance of 3D RC Buildings

In this article, a number of design approaches for 3D reinforced concrete (RC) buildings are formulated in the framework of structural optimization problems and are assessed in terms of their performance under earthquake loading. In particular, three design approaches for RC buildings are considered in this study. In the first, the initial construction cost is considered as the objective function to be minimized. The second one is formulated as a minimization problem of the torsional response, while a combined formulation is also examined as the third design approach. The third approach is considered with two distinctive formulations. According to the first approach, the torsional behavior is minimized by minimizing the eccentricity between the mass and rigidity centers, while the second one is achieved by minimizing the eccentricity between the mass and strength centers. It is shown that the optimized designs obtained according to the minimum eccentricity of the rigidity center behave better in frequent (50/50 hazard level) and occasional (10/50 hazard level) earthquakes, while the designs obtained according to the minimum eccentricity of the strength center formulation was found better in rare (2/50 hazard level) events. Designs obtained through a combined formulation seem to behave equally well in the three hazard levels examined.     

Evaluation of IBC Equivalent Static Procedure for Base Shear Distribution of Seismic Isolated Structures

It has been pointed out that the static lateral response procedure for base isolated structures presented in IBC somewhat overestimates the seismic story force [Lashkari and Kircher, 1993 Lashkari, B. and Kircher, C. A. . Evaluation of SEAOC/UBC analysis procedures, Part 1: Stiff superstructure. Proceedings of a Seminar on Seismic Isolation, Passive Energy Dissipation and Active Control. Redwood City, California. ATC Report 17-1.  [Google Scholar]; Constantinou et al., 1993 Constantinou, M. C., Winters, C. W. and Theodossiou, D. . Evaluation of SEAOC and UBC analysis procedures, Part 2: Flexible Superstructure. Proceedings of a Seminar on Seismic Isolation, Passive Energy Dissipation and Active Control. Redwood City, California. ATC Report 17-1.  [Google Scholar]]. In this article IBC equivalent static method for base shear distribution of seismic isolated structures is evaluated. For this purpose one-story to six-story building models are designed according to equivalent lateral response procedure for different elastomeric isolation systems. The results of equivalent lateral response procedure in parameters such as base shear and vertical distribution of base shear are compared with results obtained from dynamic nonlinear analysis and the efficiency and limitations of its application are investigated. In general, the results of equivalent lateral response procedure in base shears are acceptable within the scope of this procedure, but the proposed triangular distribution of base shear is somewhat conservative. So a new formulation for vertical distribution of base shear is proposed which results in a more realistic distribution of shear over the height of isolated buildings. The accuracy of the new formulation is examined by comparing the resulting responses obtained from this study with those calculated by nonlinear time history analysis.     

Seismic Analysis of Non Proportionally Damped Two-Way Asymmetric Elastic Buildings Under Bi-Directional Seismic Ground Motions

This study investigates the effectiveness of the modal analysis using three-degree-of freedom (3DOF) modal equations of motion to deal with the seismic analysis of two-way asymmetric elastic systems with supplemental damping. The 3DOF modal equations of motion possessing the non proportional damping property enable the two modal translations and one modal rotation to be non proportional in an elastic state. The simple approximation method is to use the single degree-of-freedom (SDOF) modal equations of motion, which are obtained by neglecting the off-diagonal elements of the transformed damping matrix. One, one-story and one, three-story non proportionally damped two-way asymmetric buildings under the excitation of bi-directional seismic ground motions are analyzed. The analytical results are obtained by using the proposed method, noted simple approximation method, and direct integration of the equation of motion. It is seen that the proposed method can significantly improve the accuracy of the analytical results compared with those obtained by using the simple approximation method. Moreover, the proposed method does not substantially increase the computational efforts.     

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.     

Considering Soil-Nonlinearity Effect on Seismic Performance Evaluation of Structures based on Pushover Analysis

According to the most of current seismic codes, nonlinear soil behavior is commonly ignored in seismic evaluation procedure of the structures. To contribute on this matter, a pushover analysis method incorporating the probabilistic seismic hazard analysis (PSHA) is proposed to evaluate the effect of nonlinear soil response on seismic performance of a structure. The PSHA outcomes considering soil nonlinearity effect is involved in the analysis procedures by modifying the site-specific response spectrum. Results showed that incorporation of nonlinear soil behavior leads to an increase in displacement demand of structures which should accurately be considered in seismic design/assessment procedure. Results of implemented procedure are confirmed with the estimated displacement demand including soil-structure interaction (SSI).     

Seismic Response of Rolling Isolation Systems with Concave Friction Distribution

This article attempted to improve the isolation performance of a rolling isolation system by assuming that the rolling friction force gradually and linearly increased with the relative displacement between the isolator and the ground. After the rolling isolation system under different ground motions was calculated by a numerical analysis method, it obtained more regular results than that of other uneven friction distributions. Results shows that the considered concavely distributed friction force can not only dissipate the earthquake energy, but also change the structural natural period. These functions improve the seismic isolation efficiency of the structural relative displacement in comparison with the general uniform distribution of rolling friction coefficient.     

Assessment of Multi-Wythe Stone Masonry Subjected to Seismic Hazards

Heritage stone buildings are typically vulnerable to seismic events. Results of an experimental program were analyzed to evaluate the shear strength and intrinsic damping of stone masonry representative of the West Block of the Canadian Parliamentary Precinct in Ottawa. Eight representative wall specimens with different rehabilitation schemes had been tested under different static and dynamic loadings. Each wall had wythes of sandstone and limestone connected by a rubble core. The results show the shear strength of the walls could be predicted accurately and that no strengthening scheme was particularly beneficial. The effective viscous damping ratios varied between 7 and 9%.     

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.     

Equivalent Damping Ratio Equations in Support of Displacement-Based Seismic Design for Pile-Supported Wharves

This study primarily proposes new equivalent damping ratio equations based on Jacobsen’s approach for displacement-based seismic design of pile-supported wharves to account for wharf configurations and soil-pile interaction. It is found that Pivot hysteresis model and Masing rule can accurately capture nonlinear behavior of concrete and steel wharves, respectively. To verify applicability of proposed equations, analyses were conducted to three typical wharves to make a comparison of maximum displacements obtained from nonlinear time-history analyses and substitute structure method with various damping equations. The verification reveals proposed equations are better than those in practice for their higher precision in determining displacements.     

The Strength Reduction Factors for Seismic-Isolated Bridges Characterized by SDOF Bilinear Systems in Far-Fault Areas

This article presents a statistical study on strength reduction factors for seismic-isolated bridges in far-fault areas. 1410 ground motions are selected and modified to be compatible with the recommended response spectra. Then, they are divided into 60 groups to investigate the effects of PGA/PGV ratios, soil conditions and post-to-pre-yield stiffness ratio. Results show that reduction factors are significantly affected by the PGA/PGV ratio, while the latter two items are not as important as the first one. Finally, an improved equation to estimate the reduction factor is proposed, and the accuracy of the equation is verified by additional records.