Floor Spectra of Inelastic RC Frame Buildings Considering Ground Motion Characteristics

A range of reinforced concrete frame buildings with different levels of inelasticity as well as periods of vibration is analyzed to study the floor response. The derived floor acceleration response spectra are normalized by peak ground acceleration, peak floor acceleration, and ground response spectrum. The normalization with respect to ground response spectrum leads to the lowest coefficients of variation. Based on this observation as well as previous studies, an amplification function is proposed that can be used to develop design floor spectra from the ground motion spectrum, considering the building’s dynamic characteristics and level of inelasticity.     

ESTIMATION OF GROUND MOTION ACCELERATION AND BUILDING RESPONSE TO A LONG DISTANCE EARTHQUAKE

In October 1995 an earthquake with a magnitude of 7 on the Richter scale occurred in Sumatra, 450 km from Singapore. Tremors were felt by occupants of several buildings in Singapore and were recorded as an RMS acceleration value by instruments installed in a high-rise condominium. Based on this value and considering instrumental effects, site conditions and building characteristics, this paper investigates the ground motion accelerations and the building response.     

Seismic Response of Base-Isolated Benchmark Building with Variable Sliding Isolators

The seismic response of base-isolated benchmark building with variable sliding isolators like variable friction pendulum system (VFPS), variable frequency pendulum isolator (VFPI), and variable curvature friction pendulum system (VCFPS), along with conventional friction pendulum system (FPS), was studied under the seven earthquakes. The earthquakes are applied bi-directionally in the horizontal plane ignoring vertical ground motion component. The shear type base-isolated benchmark building is modeled as three-dimensional linear elastic structure having three degrees of freedom at each floor level. Time domain dynamic analysis of the benchmark building was carried out with the help of constant average acceleration Newmark-Beta method and nonlinear isolation forces was taken care by fourth-order Runge-Kutta method. The base-isolated benchmark building is investigated for uniform isolation and hybrid isolation in combination with laminated rubber bearings through the performance criteria and time history response of important structural response parameters like floor accelerations, base displacement, etc. It is observed that variable sliding isolators performed better than conventional FPS due to their varying characteristic properties which enable them to alter the isolator forces depending upon their isolator displacements thus improves the performance of the structure. The VFPS efficiently controls large isolator displacements and VFPI and VCFPS improve super structural response on the cost of isolator displacement. It is also observed that the hybrid isolation is relatively better in comparison to the uniform isolation for the benchmark building.     

Optimal Control of Structures under Earthquakes Including Soil-Structure Interaction

It is well known that the soil-structure interaction (SSI) changes the dynamic response of a structure supported on flexible soil. The analysis of optimally controlled SSI systems has certain difficulties due to the nature of the SSI and the optimal control problem. In this paper, a two-step iteration-based numerical algorithm is proposed to handle optimally controlled SSI systems under earthquakes. First, the optimal control forces are obtained by using a fixed-base system. Then, the optimal control forces are converted to the frequency domain by the Fourier transform technique to be used in the equations of the SSI system. The lateral displacement and the rocking of the foundation are obtained from the equations of the SSI system containing the optimal control forces in the frequency domain. The lateral displacement and rocking of the foundation are then converted to the time domain by the inverse Fourier transform technique, and the lateral accelerations and the rocking accelerations of the foundation are obtained by the forward finite difference method. During the second step, the optimal control forces are calculated again by using the lateral acceleration and the rocking acceleration of the foundation along with the earthquake ground motion. Using the method explained above, the optimal control forces obtained in the time domain are used in the equations of the soil-structure system from which the behavior of foundation and structure is obtained. In the final section of the paper, a numerical study is conducted for a controlled structure supported on flexible soil.     

The Numerical Study of Base-Isolated Buildings Under Near-Field and Far-Field Earthquakes

The behavior of base-isolated building frame is investigated with the help of a numerical study for far-field and near-field earthquakes with directivity and fling-step effects. Both design-level and extreme-level earthquakes are considered. Selected response parameters are peak floor displacement, acceleration, base shear, and isolator displacement. Inelastic behavior of base-isolated structure during the earthquake is investigated performing nonlinear time history analysis of a ten-story building frame. This study shows that base isolation is not effective for near-field earthquakes. Even for design-level earthquake, the frame gets significantly into inelastic range for earthquakes with fling-step effect.     

Inelastic Displacement Demand of Strength-Degraded Structures

This article presents findings from parametric studies involving nonlinear time-history analyses of inelastic systems with and without strength degradation. Results showed that estimates based on the equal-displacement and equal-energy propositions can be exceeded significantly by the inelastic displacement demands in the acceleration and velocity-sensitive regions of the response spectrum. The displacement demand behaviour is sensitive to the strength degradation and the frequency properties of the ground shaking. With a modest strength reduction factor of 2, the inelastic displacement demand would typically be constrained by the Peak Displacement Demand as indicated on the elastic displacement response spectrum for 5% damping.     

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.     

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.     

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.     

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.     

AN EVALUATION OF THE STRONG GROUND MOTION RECORDED DURING THE MAY 1, 2003 BINGÖL TURKEY,EARTHQUAKE

An important record of ground motion from a M6.4 earthquake occurring on May 1, 2003, at epicentral and fault distances of about 12 and 9 km, respectively, was obtained at a station near the city of Bingöl, Turkey. The maximum peak ground values of 0.55 g and 36 cm/s are among the largest ground-motion amplitudes recorded in Turkey. From simulations and comparisons with ground motions from other earthquakes of comparable magnitude, we conclude that the ground motion over a range of frequencies is unusually high. Site response may be responsible for the elevated ground motion, as suggested from analysis of numerous aftershock recordings from the same station. The mainshock motions have some interesting seismological features, including ramps between the P-and S-wave that are probably due to near- and intermediate-field elastic motions and strong polarisation oriented at about 39 degrees to the fault (and therefore not in the fault-normal direction). Simulations of motions from an extended rupture explain these features. The N10E component shows a high-amplitude spectral acceleration at a period of 0.15 seconds resulting in a site specific design spectrum that significantly overestimates the actual strength and displacement demands of the record. The pulse signal in the N10E component affects the inelastic spectral displacement and increases the inelastic displacement demand with respect to elastic demand for very long periods.     

Nonlinear Structural Response to Low-Cut Filtered Ground Acceleration Records

Ground acceleration records obtained from instruments in the field are often filtered to reduce noise in both low and high frequency bands before being used for structural response analyses. The structural analysis using a filtered acceleration record may elongate the fundamental period of a structure which will potentially lead to an underestimation of the nonlinear response.

The nonlinear response of single-degree-of-freedom systems to low-cut filtered ground acceleration records is investigated. Based on the results of this study, a simple criterion for selecting ground acceleration records for seismic response analyses is proposed to avoid underestimating the nonlinear structural response.     

Shaking Table Testing of a Full-Scale Prefabricated Three-Story Timber-Frame Building

Shake table tests were carried out on a 7 m × 5 m three-story, timber light-frame building (7.5 m height) at the TreesLab laboratory (Eucentre) in Pavia. The aim of the research was to evaluate the seismic behavior of a typical Italian prefabricated timber building and to study the interaction between the individual structural components tested in quasi-static manner in a previous experimental study. The 1979 Montenegro Earthquake ground motion, recorded at the Ulcinj-Hotel Albatros station, was selected as the ground motion for seismic tests. The maximum peak ground acceleration was scaled to 0.07 g, 0.27 g, 0.5 g. 0.7 g, and 1 g in order to evaluate the building’s performance at different levels of seismic input. More than 100 instruments were used to monitor the behavior of the building during seismic tests measuring acceleration, displacement, and forces. The visual inspection shows that the building did not show any damage during all seismic tests. However the data analysis (dynamic identification, capacity spectrum, inter-story drift) confirm that during the 1.00 g test the structure went beyond its linear elastic limit. The results obtained from this experimental study suggest that the design hypotheses commonly adopted in practice for seismic analysis (e.g., in terms of force distributions between the walls, and also the behavior factor q) are not always consistent with the real behavior of timber frame multi-story buildings, and should be backed by more accurate knowledge of the contributions of the individual structural components.     

Comparison of Numerical and Experimental Seismic Responses of FREI-Supported Un-reinforced Brick Masonry Model Building

Comparative study of numerically and experimentally obtained seismic responses of un-reinforced masonry building supported on in-house designed un-bonded fibre reinforced elastomeric isolator (U-FREI) are presented in this article. The effectiveness of U-FREI is established very clearly in terms of controlled dynamic response of the model building. Experimental studies are carried out on a shake table with elaborate instrumentations for measurement of acceleration and displacements at different floor levels. Numerical study of the model building supported on U-FREI is carried out to compare the results with experimental investigation. Multi-linear pivot hysteretic plasticity model is used to simulate the behavior of FREI, while plate elements are used for brick-masonry walls. Experimentally obtained force-displacement curves of FREI are used for defining the properties of multi-linear model representing FREI. The dynamic responses obtained from the numerical studies are compared with those from experimental investigations. This study indicates that the seismic responses of building supported on U-FREI can be numerically evaluated with quite reasonable accuracy. A good numerical model can be judiciously used at the preliminary design stage, followed by actual testing and construction of the base isolated building.     

Predicting the Seismic Response of Capacity-Designed Structures by Equivalent Linearization

An equivalent linearization procedure is developed for predicting the inelastic deformations and internal forces of capacity-designed structures under earthquake excitations. The procedure employs response spectrum analysis, and mainly consists of the construction of an equivalent linear system by reducing the stiffness of structural members that are expected to respond in the inelastic range. These members are well defined in structures designed with capacity principles. Maximum modal displacement demands of the equivalent linear system are determined either from the equal displacement rule, or from independent nonlinear response history analysis of SDOF systems representing inelastic modes.

Predictions obtained from the proposed equivalent linearization procedure are evaluated comparatively by using the results of nonlinear response history analysis as benchmark, linear elastic response spectrum analysis and conventional pushover analysis. The deformations and capacity controlled actions of a 12-story symmetrical plan concrete frame and a 6-story unsymmetrical plan concrete frame are obtained by each method under 96 strong ground motions. It is observed that the proposed procedure results in better accuracy in estimating the inelastic seismic displacement response parameters and capacity controlled forces than the other two approximate methods.     

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.     

Maximum Possible Ground Motion for Linear Structures

This article develops a method to generate ground motion time histories that maximize the response of a given linearly elastic structure. The root mean square (RMS) level of the input power spectral density (PSD) is used as a strong motion parameter. It is related to seismological data that is readily available. An empirical relation to estimate RMS value of the PSD from peak ground acceleration, magnitude, rupture distance, and shear wave velocity is derived from world-wide strong motion data. The ground motion is obtained by solving the inverse problem such that the structural response is maximized under the constraint of fixed value of RMS level of the input PSD enforced using a Lagrange multiplier. The proposed methodology is illustrated for a single-degree of freedom system, a six storey building and an earthen dam. It is shown that the critical PSD obtained in all the cases is a narrow band process resulting in stochastic resonance and not a Dirac-delta function with the entire energy of the system concentrated at its natural frequency. Moreover, the critical excitation samples generated using this critical PSD resembles actual earthquake acceleration time histories.     

Application of Wavelet Transforms on Characterization of Inelastic Displacement Ratio Spectra for Pulse-Like Ground Motions

In this article, a simple and effective wavelet-based procedure is implemented for describing principle features of a special class of motions, pulse-like ground motions, on inelastic displacement ratio spectra (IDRS). The computed spectra supply a simple estimation of maximum inelastic displacement demand from the corresponding elastic one. The results of analysis in this work provide a suitable platform for quantification of pulse effects into IDRS and highlight the need to better understanding of this effect on demand estimation. It is concluded that the pulse has a significant influence on IDRS of pulse-like ground motions for systems with high ductility level.     

THE USE OF SIMPLE PULSES TO ESTIMATE INELASTIC RESPONSE SPECTRA

Inelastic response spectra are estimated for elasto-plastic SDOF systems subjected to strong earthquake ground motions by applying the strength reduction factors determined for a simple pulse to the elastic response spectrum of the ground motion. This approach relies upon similarities in the strength reduction factors computed for earthquake ground motions and for short duration pulses. The accuracy of the estimated inelastic spectra obtained using 24 simple pulse waveforms is assessed in order to identify subsets of just several pulse waveforms that are suited for this purpose. Based upon the ground motions and pulses investigated, this approach appears to be equally applicable to short and long duration ground motions and those having near-fault forward directivity features.     

Inelastic Displacement Ratios for Seismic Assessment of Structures Subjected to Forward-Directivity Near-Fault Ground Motions

This article presents results of a statistical study focused on evaluating inelastic displacement ratios (i.e., ratio of maximum inelastic displacement with respect to maximum elastic displacement demand) of degrading and non degrading single-degree-of-freedom (SDOF) systems subjected to forward-directivity near-fault ground motions. C_R spectra are computed for normalized periods of vibration with respect to the predominant period of the ground motion to provide a better ground motion characterization. This period normalization allows reducing the record-to-record variability in the estimation of C_R. An equation to obtain estimates of C_R for the seismic assessment of structures exposed to forward-directivity near-fault ground motions is proposed.