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.     

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.     

Ductility-Equivalent Viscous Damping Relationships for Beam-to-Column Partial-Strength Steel Joints

This paper seeks to contribute to the development and improvement of displacement-based design procedures, proposing improved ductility-equivalent viscous damping relationships for steel moment-resisting framed structures with dissipative beam-to-column partial-strength joints. These relationships can be used directly in procedures like the Direct Displacement-Based Seismic Design (DDBD) that uses effective stiffness, ductility-equivalent viscous damping relationships, and period-displacement relationships in a performance-based design approach. To this end, a finite element model of a steel beam-to-column sub-assemblage, characterized by an extended end-plate, is developed in ABAQUS. The model, which is validated against monotonic and cyclic experimental data obtained in previous research, is employed to carry out non-linear time-history (NLTH) analyses, using real records scaled to target several levels of ductility demand. A procedure is then proposed and applied to determine the ductility-equivalent viscous damping relationships of the sub-assemblages. The equivalent linearization technique is applied to the non-linear responses obtained in the NLTH analyses, using an elastic single degree of freedom structure and the elastic displacement spectra. The influence of joints mechanisms and of the dynamic characteristics of the structure in the equivalent viscous damping is investigated, and an expression for ductility-equivalent viscous damping is proposed. The proposed expression represents a clear improvement in relation to the existing expressions available in literature.     

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).     

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 Static Nonlinear Procedure for the Evaluation of the Elastic Buckling of Anchored Steel Tanks Due to Earthquakes

Ground-supported steel tanks experienced extensive damage in past earthquakes. The failure of tanks in earthquakes may cause severe environmental damage and economic losses. This study deals with the evaluation of the elastic buckling of above-ground steel tanks anchored to the foundation due to seismic shaking. The proposed nonlinear static procedure is based on the capacity spectrum method (CSM) utilized for the seismic evaluation of buildings. Different from the standard CSM, the results are not the base shear and the maximum displacement of a characteristic point of the structure but the minimum value of the horizontal peak ground acceleration (PGA) that produces buckling in the tank shell. Three detailed finite element models of tank-liquid systems with height to diameter ratios H/D of 0.40, 0.63, and 0.95 are used to verify the methodology. The 1997 UBC design spectrum and response spectra of records of the 1986 El Salvador and 1966 Parkfield earthquakes are used as seismic demand. The estimates of the PGA for the occurrence of first elastic buckling obtained with the proposed nonlinear static procedure were quite accurate compared with those calculated with more elaborate dynamic buckling studies. For all the cases considered, the proposed methodology yielded slightly smaller values of the critical PGA for the first elastic buckling compared to the dynamic buckling results.     

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.     

EVALUATION OF CAPACITY SPECTRUM METHOD FOR ESTIMATING THE PEAK INELASTIC RESPONSES

The accuracy of the capacity spectrum method (CSM) depends on the precise estimation of equivalent period and damping ratio as well as the modification of the demand spectrum. In this paper, the CSM provided in ATC-40 for estimating the peak inelastic responses is evaluated. First, the effect of equivalent period and damping ratio estimation on the accuracy of the CSM is assessed. Analyses results indicate that the difference between estimation methods is large when the structural nonlinearity is large, but becomes negligible as the hardening ratio increases. Next, the reduction factors provided in ATC-40 and Eurocode are evaluated. It is found that the acceleration responses obtained using the factor of Eurocode is closer to the actual ones than those obtained using the factors of ATC-40. Finally, the demand spectrum is constructed using the peak absolute acceleration and pseudo-acceleration. The results obtained using the peak absolute acceleration is found to be generally larger than those obtained using the pseudo-ones. Since the original CSM generally underestimates the response, the use of peak absolute acceleration in the construction of demand spectrum produces the response relatively closer to the exact one. However, the use of peak absolute acceleration overestimates the response more when the original CSM overestimates the response.     

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.     

GROUND MOTION DOMINANT FREQUENCY EFFECT ON THE DESIGN OF MULTIPLE TUNED MASS DAMPERS

Utilising the Kanai-Tajimi and Clough-Penzien spectrums and the pseudo-excitation algorithm in the frequency domain, parametric study is performed to examine the effect of the dominant frequency of ground motion on the optimum parameters and effective-ness of multiple tuned mass dampers (MTMD) with identical stiffness and damping coefficient but with unequal mass. The examination of the optimum parameters is con-ducted through the minimisation of the minimum values of the maximum displacement and acceleration dynamic magnification factors of the structure with the MTMD. The optimum parameters of the MTMD include the optimum frequency spacing reflecting the robustness, the average damping ratio and the tuning frequency ratio. Minimisation of the minimum values of the maximum displacement and acceleration dynamic mag-nification factors, nondimensionalised respectively by the maximum displacement and acceleration dynamic magnification factors of the structure without the MTMD, is used to measure the effectiveness of the MTMD. The results indicate that in the two cases where both the total mass ratio is below 0.02 and the total mass ratio is above 0.02, but the dominant frequency ratio of ground motion is below unity (including unity), the earthquake ground motion can be modelled by a white noise. It is worth noting, however, that for the total mass ratio above 0.02, the Kanai-Tajimi Spectrum or Clough-Penzien spectrum needs to be employed to design the MTMD for seismic structures in situations where the dominant frequency ratio of ground motion is beyond unity.     

Estimation of the Displacement of Viscously Damped Pinching Hysteretic Structures Subjected to Near-fault Ground Motions

To fulfill a displacement-based design or response prediction for nonlinear structures, the concept of equivalent linearization is usually applied, and the key issue is to derive the equivalent parameters considering the characteristics of hysteretic model, ductility level, and input ground motions. Pinching hysteretic structures subjected to dynamic loading exhibit hysteresis with degraded stiffness and strength and thus reduced energy dissipation. In case of excitation of near-fault earthquake ground motions, the energy dissipation is further limited due to the short duration of vibration. In order to improve the energy dissipation capability, viscous-type dampers have been advantageously incorporated into these types of structures. Against the viscously damped pinching hysteretic structure under the excitation of near-fault ground motions, this study aims to develop a seismic response estimation method using an equivalent linearization technique. The energy dissipation of various hysteretic cycles, including stationary hysteretic cycle, amplitude expansion cycle, and amplitude reduction cycle, is investigated, and empirical formulas for the equivalent damping ratio is proposed. A damping modification factor that accounts for the near-fault effect is introduced and expanded to ensure its applicability to structures with damping ratios less than 5%. An approach for estimating the maximum displacement of a viscously damped pinching hysteretic structure, in which the pinching hysteretic effect of a structure and the near-fault effect of ground motions are considered, is developed. A time history analysis of an extensive range of structural parameters is performed. The results confirm that the proposed approach can be applied to estimate the maximum displacement of a viscously damped pinching hysteretic structure that is subjected to near-fault ground motions.     

Elastic Displacement Spectrum-Based Design Approach for Buckling-Restrained Braced Frames

The design focus for a buckling-restrained braced frame (BRBF) is that the buckling-restrained braces (BRBs) dissipate most of the seismic energy while the main frame retains a degree of elastic stiffness under a major earthquake. An elastic displacement spectrum based design method is presented in this article, which can directly determine the sectional area of the BRBs. The yield displacement in the roof of the main frame is taken as the target displacement under a major earthquake. An elastic displacement design spectrum is used to solve the target period of the BRBF. To validate this method, a six-story buckling-restrained braced steel frame is designed using the proposed method, and a series of nonlinear response history analyses (RHAs) are performed to verify the design result. The example shows that the required BRB area can be simply and accurately determined by the proposed method. The error between the given target displacement and the RHA results is 4.0% and 21.3% for BRBFs designed with BRB yield strength of 235 Mpa and 100 Mpa, respectively.     

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.     

INELASTIC SEISMIC RESPONSE ANALYSIS BASED ON ENERGY DENSITY SPECTRA

Energy balance is used to characterise the seismic energy in inelastic structures where energy input to the structure is decomposed into strain energy, kinetic energy, damping energy, and plastic energy. The exact quantification of plastic energy is derived based on force analogy method for moment-resisting frames. A method of generating energy density spectra is then proposed based on yield displacement of a single degree of freedom system. The effects of different structural vibration characteristics are then studied on energy density spectra. These effects include variations of yield displacement level, earth-quake scaling factor, and damping ratio, which proves to be useful in improving the basic understanding of energy characteristics in structural dynamic response. Finally, the use of energy density spectra is demonstrated on a multi-degree of freedom structure to show the practical applications of these spectra.     

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.     

Beam-Column Joint Model for Nonlinear Analysis of Non-Seismically Detailed Reinforced Concrete Frame

An efficient and simplified plane beam-column joint model that can describe the strength deterioration, stiffness degradation, and pinching effect was developed for the nonlinear analysis of non-seismically detailed reinforced concrete frames. The proposed beam-column joint model is a super-element consisting of eight spring components and one panel zone component, representing the bond-slip mechanism of the longitudinal reinforcement and the shear deformation mechanism of the joint concrete core region, respectively. In order to represent the dynamic response at the system level, the elastic constitutive law is applied to the eight connector springs, while the Bouc-Wen-Baber-Noori (BWBN) model is adopted to describe the hysteretic behavior of the panel zone component. For the implementation of the finite element analysis, the algorithmically consistent tangent of the BWBN model is derived as a uni-axial constitutive model, while the initial stiffness of the panel zone component is determined by the concrete compression strut assumption. The accuracy and efficiency of the proposed beam-column joint model were calibrated at both the component and structural levels by comparing the simulated results with the experimental data for non-seismically detailed joint sub-assemblages and a reinforced concrete plane frame.     

SEISMIC DESIGN AND RESPONSE OF BARE AND MASONRY-INFILLED REINFORCED CONCRETE BUILDINGS. PART II: INFILLED STRUCTURES

The effects of masonry infills on the global seismic response of reinforced concrete structures is studied through numerical analyses. Response spectra of elastic SDOF frames with nonlinear infills show that, despite their apparent stiffening effect on the system, infills reduce spectral displacements and forces mainly through their high damping in the first large post-cracking excursion. Parametric analyses on a large variety of multi-storey infilled reinforced concrete structures show that, due to the hysteretic energy dissipation in the infills, if the infilling is uniform in all storeys, drifts and structural damage are dramatically reduced, without an increase in the seismic force demands. Soft-storey effects due to the absence of infills in the bottom storey are not so important for seismic motions at the design intensity, but may be very large at higher motion intensities, if the ultimate strength of the infills amounts to a large percentage of the building weight. The Eurocode 8 provisions for designing the weak storey elements against the effects of infill irregularity are found to be quite effective, in general, for the columns, but unnecessary and often counterproductive for the beams.     

A Multi-Mode Method for Estimation of Floor Response Spectra

A new simplified procedure for estimation of floor response spectra (FRS) is proposed. This methodology enriches the most common procedures using nonlinear response-history analysis to predict FRS by including a direct multi-mode technique to estimate FRS. A novel feature of the procedure is that the coupling effect is considered to establish equivalent modal systems and the FRS are developed by incorporating capacity spectrum method in conjunction with ductility-based FRS for each modal system. Both the proposed method and the traditional method are applied to three steel moment frame structures, and a reasonable accuracy is demonstrated.     

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.