Results Of Nonlinear Time History Analyses Research Articles

Seismic response of structures with friction pendulum inerter system (FPIS) under near-fault earthquakes

Near-fault ground motions with high acceleration peaks and long-period velocity pulses pose a serious threat to the reliability of engineering structures. To reduce the displacement of isolation layer and improve the seismic performance of superstructure under the near-fault ground motions, a composite isolation system, which is composed of friction pendulum system (FPS) and inerter system, namely FPIS, was used in this paper. Based on D’Alembert’s principle, the nonlinear motion equations of a base-isolated structure with FPIS were established. The damping effect of two different mechanical layouts of FPIS subsystems, i.e, series-parallel inerter system-I-FPS(SPIS-I-FPS) or series-parallel inerter system-II-FPS(SPIS-II-FPS), were investigated in this study. The strong nonlinearity of FPIS was considered, and the inerter system parameters were designed based on the principle of maximum damping enhancement. The fourth-order Runge-Kutta approach was used to solve the dynamic response of a multi-degree-of-freedom system under seismic excitations. The effectiveness of FPIS was verified by comparing the isolation layer displacement and the acceleration of superstructure calculated by MATLAB with the friction pendulum system and viscous damper (FPS-VD). The nonlinear time history analysis results indicate that within a certain additional damping range, the SPIS-I-FPS subsystem performs effectively than SPIS-II-FPS in reducing the superstructure acceleration and isolation layer displacement. To increase the energy dissipation efficiency of structures, it is recommended to increase the design parameters of the inerter system and control the friction coefficient of FPS within the range of 0.05∼0.10.

Seismic design and performance evaluation of steel braced frames with post-tensioned and disc-spring-based self-centering buckling-restrained braces

In this study, we focus on two types of self-centering buckling-restrained braces (SC-BRBs), which are post-tensioned (PT) SC-BRB and disc-spring-based SC-BRB, and develop a seismic design method for steel braced frames with these braces according to the displacement-based design theory. The whole independent parameters that describe the hysteretic behavior of the SC-BRBs are first determined. Then nonlinear time history analysis (NLTHA) is conducted to explore the effects of these hysteretic parameters on the ductility demands of the nonlinear single-degree-of-freedom (SDOF) system. Based on the analysis results, a ductility demand spectral model is developed, followed by a nonlinear displacement ratio spectral model. Subsequently, the seismic design procedure for SC-BRB frames is proposed based on the two spectral models. Finally, a total of 24 six-story steel frames with the two types of SC-BRBs, two target inter-story drifts, and different parameter combinations are designed at the maximum considered earthquake (MCE) level. The pushover analysis and NLTHA results indicate that a smaller strength ratio β and a larger initial stiffness ratio αs are beneficial for reducing the base shear and obtain an economical design when the designed frames achieve the same target inter-story drift. Considering the initial stiffness of the SC-BRBs is highly sensitive to machining errors, it is recommended that the value of β be taken within 0.25 to reduce the influence of the initial stiffness uncertainty of the braces on seismic design results. Moreover, controlling β within 0.25 also helps to reduce the higher-mode effect and peak floor acceleration responses of the designed structures effectively.

Comparison of Linear and Nonlinear Procedures for the Analysis of the Seismic Performance of Straight Multi-Span RC Bridges

The assessment of the seismic performance of transportation infrastructures is of primary importance for the management of the aftermath of an earthquake. To perform such an assessment, various modeling approaches characterized by different levels of accuracy are available and modern seismic design codes provide recommendations about their use. Non-linear time-history analysis (NLTHA) is acknowledged as the most reliable method, but is difficult to implement and is computationally expensive. This paper aims to investigate the viability of less complex methods, but with low computational cost, for the assessment of straight, multi-span bridges and compare their performance against the results of NLTHA in order to quantify the expected accuracy. The study is developed considering three bridge archetypes with either simply-supported or continuous-deck layouts, representative of typical features of the Italian bridge stock. The bridges are analyzed first through nonlinear dynamic analyses, to define the benchmark solution; then linear dynamic analyses, such as Linear Time-History and Response Spectrum Analysis, nonlinear static analyses, such as MPA (Modal Pushover Analysis), and Equivalent Static Analysis are considered. A comparison among the examined procedures is eventually proposed, highlighting the strengths and weaknesses of each approach.

Cyclic loading tests and numerical simulations of an assembled X-shaped flexural steel damper

This paper proposes an assembled X-shaped flexural steel damper. Welding is waived for the novel damper. As the kernel element of the damper, the X-shaped flexural steel plates have the advantages of ease of installation and replacement if necessary. In the analytical part, the effective height of the flexural steel plate was suggested, and then, the yield displacement, yield load and initial stiffness of the damper were derived. The proof-of-concept cyclic loading test was conducted using one reduced-scale specimen within a four-bar linkage experimental setup. The hysteretic performance indexes, including strength, stiffness and energy dissipation, were quantified. The high-fidelity finite element (FE) models were established by ABAQUS. The parametric study was further conducted based on the verified FE model. The considered parameters were the height and thickness of the steel plates. The testing results indicate that the proposed damper has plump hysteretic curve with good energy dissipation capacity and excellent ductility, although slight slip behavior can be found due to the gap caused by the assembling process. The results obtained from analytical method and numerical model are in good agreement with the experimental data. The results of parametric analysis show that the numerical results well agree with analytical predictions, indicating the numerical model can reflect the mechanical behavior of AXSFD. A benchmark frame building was selected to demonstrate the seismic control efficacy of the damper. The nonlinear time history analysis results indicate that the damper reduced both peak and residual interstory drift ratios for the protected structure.

Performance-based seismic design of full and partial self-centering steel braced frames using modified lateral force distribution

Design base shear and lateral force distribution are two important aspects of the seismic design process. Different design methods have been proposed to obtain the design base shear of different types of structures. However, the study related to the lateral force distribution is limited, especially for self-centering (SC) structures. The primary objective of this research is to develop a performance-based seismic design (PBSD) procedure for steel braced frames considering the modified lateral force distribution. Six-story steel braced steel frames are designed to explore the influence of the energy dissipation factor on the lateral force distribution of the frames. Results of nonlinear time-history analyses indicated that the lateral force acting on the roof increases with the decrease in energy dissipation factor. Following the parametric analyses of single-degree-of-freedom (SDOF) systems, the energy factor design spectra are established and the corresponding PBSD procedure for the steel braced frames is proposed. Finally, the four six-story braced steel frames are redesigned using the PBSD procedure with the modified lateral force distribution to illustrate the efficiency of the proposed design method. Analyses results indicate that the steel braced frames designed by the proposed design can satisfy the expected inter-story drift limit with a reasonably uniform distribution of peak inter-story drifts. Furthermore, the ‘partial’ SC system appears to be a desirable option that effectively controls the residual displacement and peak acceleration responses at the same time, and could achieve a manageable cost control compared to the full SC systems.

Comparison of Nonlinear Dynamic Analysis of Time History and Endurance Time Method in Tall Structures with Frame-Wall System

In this study, the seismic response of tall concrete structures with a special dual frame-wall concrete system is investigated using the endurance time method, and the results are compared with nonlinear time history analysis results. For this purpose, first, appropriate analytical models including buildings with concrete framed-wall system and 20, 30, and 40 stories are modeled non-linearly in PERFORM 3D software, and then, main nonlinear time history analyses are carried out for seven ground motions (accelerogram) further from the fault based on the FEMA P695 code and the endurance time accelerogram of (in) series. The results of the analysis are compared using indices (shear, relative displacement, and acceleration). The results indicate that the endurance time method is accurate in two indices of shear and acceleration, but the accuracy of the relative displacement index of the floor decreases as the number of stories of the structure increases.

Seismic response of dual concentrically braced steel frames with various bracing configurations

Steel dual structures incorporating special concentrically braced frames (SCBFs) and special moment frames (SMFs) are, in general, effective for their high lateral stiffness and ductility. As such, ductile dual CBFs are often treated as a remedy for mitigating permanent drift demands along with the potential drift concentration in isolated stories. However, despite the benefits and interest, the effect of the bracing configuration on the seismic response of the dual concentrically braced systems, designed following the current capacity design approach stipulated in AISC Seismic Provisions, in particular, has not been thoroughly examined to date. The present study aims to shed light on the impact of the bracing scheme on the seismic behavior of dual SCBFs coupled with SMFs as backup frames. For this purpose, 4- and 10-story dual SCBFs with the commonly used chevron, split X, V, and cross X type bracing configurations are designed according to ASCE 7 and AISC 341. Then, the frames are subjected to a suite of ground motions. The nonlinear time-history analysis results are contrasted and discussed in terms of the peak and permanent drift demands, horizontal floor acceleration demands along with brace ductility demands.

Risk-targeted design of seismically isolated buildings

Seismic isolation has been used to improve the seismic performance of buildings for the last decades. However, it has been shown that the code-based displacement capacity of isolation members does not provide adequate collapse probabilities for different Risk Categories of ASCE 7–16. Seismic design codes stipulate to determine maximum isolator displacement at the Risk-Targeted Maximum Considered Earthquake (MCER) level. Although the code-based isolator displacement capacity is checked with the mean displacement of the MCER level nonlinear time history analysis results, extreme event effects and incorporating uncertainties into fragility curves create additional displacement demands. Therefore, there is a need to amplify the code-based displacement capacity of isolators to obtain sufficient collapse performance. A previous study, assumed elastic behavior and rigid mass model for the superstructure, proposes an iterative probabilistic approach. In the present study, seven different seismically isolated buildings are modeled, and the nonlinear behavior of isolators and superstructures is considered in the incremental dynamic analyses achieved for all models to obtain fragility curves. Although the seismic isolation considerably decreases the spectral accelerations of the superstructure, it is shown that the R-μ-T relations for diaphragm level accelerations, transferred accelerations from base to superstructure, become more sensitive to nonlinear behavior at the superstructure mode periods. The fragility curves of five case study buildings are obtained using the FEMA P695 procedure, and it is figured out that the collapse probability of isolation units is highly correlated with the required isolator displacement to code-based maximum isolator displacement (D/DM) ratio. Then, two simple equations with high correlation coefficients are acquired to estimate the required displacement capacity for prescribed risk-target levels. Further, the obtained equations are verified for two different isolated building models, and their results are compared with the Incremental Dynamic Analysis (IDA) results. The verification results show that the given equations can be used in the preliminary design phase of seismically isolated mid-rise reinforced concrete buildings.

Accuracy of expressing the effects of hysteretic energy in terms of equivalent viscous damping according to ATC 40 and FEMA 440

A numerical study is carried out to evaluate the precision of expressing the dissipated energy by hysteretic behavior of the material (HBM) in terms of viscous damping (VD), as specified in the Capacity Spectrum Method (CSM)(ATC 40, FEMA 440) and in modal seismic analysis (MSA), by using nonlinear time history analysis (NTHA). Initially, the equivalent viscous damping (ζE1) is estimated according to the CSM. Then, by using NTHA, the reductions of several response parameters produced by HBM and VD are calculated. Based on these results, the equivalent viscous damping (ζE2) is calculated. It is shown that the values of ζE1 significantly vary with the strong motion without showing any trend; the range of variation goes from 5% to 18% tending to decrease as the height of the building increases. Results of NTHA indicate that the maximum and minimum reductions of the elastic responses produced by HBM occur for interstory shears (IS) and axial loads; they can be up to 330% and 79%, respectively, greater than the inelastic ones. The implication of this is that seismic analysis simplified procedures, in which elastic interstory shears and forces acting on members are reduced by the same amount, can lead to non-conservative designs. The maximum reductions of the elastic responses produced by VD are larger for axial loads and are quite similar for bending moments, displacements, and IS. In seismic codes the dissipated energy produced by HBM is usually expressed in terms of a fixed amount of viscous damping (5%). Results of NTHA indicate that this practice is appropriate for interstory and roof displacements, very conservative for IS and bending moments, but non-conservative for the case of axial loads; for the case of IS, the values of ζE2 range from 5.8% to 10.5%. Starting from the fact that NTHA is the most accurate analysis procedure, the results of this research indicate that expressing the effect of dissipated energy by HBM in terms of VD according to the CSM and MSA may result in non-conservative and conservative designs, respectively. If IS is the parameter of interest, a value of 8% can be reasonably used in both the CSM and MSA.

Quantification of model uncertainties of the energy-based method for dynamic column removal scenarios

The Alternative Load Path (ALP) method is widely used to assess progressive collapse resistance of reinforced concrete (RC) structures by notional removal of one or more load-bearing elements. In general, a nonlinear time history analysis (NTHA) is needed to perform such an analysis if dynamic effects are explicitly taken into account. To avoid cumbersome nonlinear dynamic analyses, the energy-based method (EBM) is a promising technique to predict the maximum dynamic responses of a structural system. In this article, the accuracy and precision of the EBM is evaluated based on a validated finite element model of a tested RC slab subjected to a sudden column removal scenario, in particular in relation to the investigation of tensile membrane action (TMA). Influences of dynamic effects are evaluated, i.e. in relation to strain rate effects, damping, and the time duration of support removals. Strain rate effects are observed to have only slight influences on the dynamic responses. The strain rate dependency of reinforcement is found to have a more significant influence on the responses in TMA stage, although also to a limited extent. The magnitude of the load has a significant influence on the dynamic response, as do increasing damping ratios due to the corresponding significant energy dissipation. Finally, the dynamic response reduces with increasing time duration of the column removal. Based on the results of the stochastic analyses, the EBM is observed to perform well based on a comparison with the results of NTHA in both flexural and TMA stages. Furthermore, in relation to the analyzed case studies on reinforced concrete slabs, the model uncertainty of the responses obtained through the EBM compared with the NTHA is found to be represented well by a lognormal distribution with mean of 0.95 and a standard deviation of 0.20, for evaluating the loads of first rupture of reinforcement. Furthermore, a lognormal distribution with mean 0.96 and standard deviation 0.13 is found appropriate to represent the model uncertainty on ultimate load-bearing capacity predictions. Model uncertainties are also obtained with respect to the model predictions for displacements at the moment of the first rupture of reinforcement, displacements at the ultimate load-bearing capacities, and both loads and displacements at second load peaks.

Seismic Performance Evaluation of Steel Buildings with Oil Dampers Using Capacity Spectrum Method

This study proposes a capacity spectrum Method (CSM)-based procedure to estimate the maximum seismic performance of steel buildings passively controlled with bilinear oil dampers. In the proposed CSM, the maximum seismic response of a building was estimated, in the acceleration-displacement response spectrum, as the intersection between the capacity curve and the damping-adjusted demand curves, using the equivalent linearization method. The building equivalent damping ratio was determined by the sum of the inherent damping, and the square root of sum of squares (SRSS) of the hysteretic damping and the viscous damping of the supplemental oil devices. The calculation steps of the proposed CSM are explained in detail based on the equivalent single degree of freedom (ESDOF) system, and its accuracy was examined by comparison with time history analysis (THA) results. Two model steel buildings of 4 and 10 stories, uniformly equipped with oil dampers along the height, were subjected to six selected earthquake ground motions scaled to be compatible with Level-2 earthquakes, as defined in the Japanese Building Standard Law. The seismic performance of the buildings was estimated by the proposed CSM procedure and compared with the results of nonlinear THA in terms of the maximum story displacements and the shear forces. It was observed that the proposed CSM scheme provided a satisfactory accuracy to assess the maximum nonlinear response of steel buildings passively controlled with oil dampers.

New performance-based plastic design and evaluation of blind bolted end-plate CFT composite frames with BRBs

The blind bolted end-plate connection to concrete-filled steel tube column (BECFT) composite frame with buckling-restrained braces (BRBs, BRB-BECFT) is a novel dual structure system that combines advantages of fast assembly ability for BECFT connections, great energy dissipation capacity for BRBs coupled with BECFT connections and superior gravity load-carrying capacity for concrete-filled steel tube (CFT) columns. Given authors’ prior experimental and theoretical studies on the BRB-BECFT structure system, and as no design method is as far introduced for this system with adequate accuracy, a new plastic design procedure based on the modified energy balance and global yield mechanism in the framework of performance-based plastic design method was proposed. The post-yielding stiffness and overall yield inter-story drift of the BRB-BECFT structure system was considered to improve the accuracy of the design base shear. Meanwhile, the BRB-BECFT structure system was decomposed into the BRB system and BECFT frame system to simplify the design process. Moreover, some formulae to avoid structural adverse yield mechanism were derived. The semi-rigid characteristic of BECFT connections was introduced into the structural global yield mechanism by work-energy principle to ensure the deformation consistency between inter-story drift and BECFT connection rotation. Finally, four prototype structures with 6, 9, 12 and, 20 stories were designed as examples to illustrate the effectiveness and robustness of the proposed design method. The results of nonlinear time-history analyses showed that the designed structures successfully achieved the pre-selected performance objectives in terms of the inter-story drift, residual drift, BECFT connection rotation, and BRB ductility demands.

Seismic evaluation of reinforced concrete bridges using capacity‐based inelastic displacement spectra

AbstractA simplified seismic evaluation method using capacity‐based inelastic displacement spectra is proposed for reinforced concrete (RC) bridges. The proposed method can not only estimate the maximum displacements of bridges, but can also discriminate the damage indices between the bridge columns, where the Park and Ang's damage index () is considered a promising performance indicator due to its good relationship with the strength capacity state and actual visual damage condition of the bridge column regardless of the imposed loading history. To realize the accuracy and reliability of the proposed method, a hypothetical case study bridge was constructed and analyzed using various structural analysis programs and seismic evaluation methods. It was found that the proposed method can receive satisfactory estimates of the maximum displacement and for both far‐field and near‐fault ground motions when compared to the nonlinear time history analysis results of the bridge. In contrast, the AASHTO's and Caltrans’ methods cannot reflect the response amplification effects caused by the frequency‐content characteristics of near‐fault ground motions and would therefore significantly underestimate the inelastic responses of bridges. When applying the proposed method to bridges having unequal‐height columns and subjected to longitudinal seismic actions, it was found that for the short column of the bridge, the AASHTO's regularity criteria (maximum bent/pier stiffness ratio of 4 for the three‐span case study bridge) would lead to a of approximately 3.5 times that of the tall column, resulting in significant damage localization and, hence, decreasing the overall lateral deformation capacity of the bridge.

Seismic response reduction of elastoplastic structures with inerter systems

Several studies have focused on the mechanism of an inerter, which is an acceleration-dependent two-terminal element, while other studies have concentrated on developing a design method for a structure with an inerter system. However, to the best of the authors’ knowledge, the nonlinearity of the primary structure has never been considered, leading to uncertainty in design results. Particularly when a structure experiences a rare earthquake, its safety becomes uncertain because of the deterioration of structural stiffness. Therefore, this study focused on seismic control of an elastoplastic structure and explored a demand-oriented design method for it. In this paper, the basic concept of an inerter system is firstly introduced. Then, various aspects of the design method are elaborated, including the performance index, design parameters, and optimal equation for elastoplastic single-degree-of-freedom (SDOF) and multiple-degree-of-freedom (MDOF) structures. Specifics of the design procedure are also described. A parameter distribution pattern is employed to reduce the computation cost for the MDOF structure. Subsequently, an elastoplastic SDOF structure and a two-dimensional steel benchmark model are employed to carry out seismic design, and the parameters of the inerter systems are obtained. Nonlinear time history analysis results indicate that the performance of structures with inerter systems satisfies the target requirements, thereby illustrating the effectiveness of the proposed design procedure. The results demonstrate that the proposed method considers the nonlinearity of a structure with an inerter system subjected to an earthquake, which improves the reliability of the seismic design and the safety of the structure. The proposed design method can be used to design structures with inerter systems that achieve their expected performance and minimize the control cost.

Seismic collapse risk of RC frames with irregular distributed masonry infills

Masonry infills are normally considered as non-structural elements in design practice, therefore, the interaction between the bounding frame and the strength contribution of masonry infills is commonly ignored in the seismic analysis work of the RC frames. However, a number of typical RC frames with irregular distributed masonry infills have suffered from undesirable weak-story failure in major earthquakes, which indicates that ignoring the influence of masonry infills may cause great seismic collapse risk of RC frames. This paper presented the investigation on the risk of seismic collapse of RC frames with irregularly distributed masonry infills through a large number of nonlinear time history analyses (NTHAs). Based on the results of NTHAs, seismic fragility curves were developed for RC frames with various distribution patterns of masonry infills. It was found that the existence of masonry infills generally reduces the collapse risk of the RC frames under both frequent happened and very strong earthquakes, however, the severe irregular distribution of masonry infills, such as open ground story scenario, results in great risk of forming a weak story failure. The strong-column weak-beam (SCWB) ratio has been widely adopted in major seismic design codes to control the potential of weak story failures, where a SCWB ratio value about 1.2 is generally accepted as the lower limit. In this study, the effect of SCWB ratio on inter-story drift distribution was also parametrically investigated. It showed that improving the SCWB ratio of the RC frames with irregularly distributed masonry infills can reduce inter-story drift concentration index under earthquakes, therefore, prevent weak story failures. To achieve the same drift concentration index limit of the bare RC frame with SCWB ratio of about 1.2, which is specified in ACI318-14, the SCWB ratio of masonry-infilled RC frames should be no less than 1.5. For the open ground story scenario, this value can be as high as 1.8.

Investigation of Uncertainties in Nonlinear Seismic Analysis of the Reinforced Concrete Shear Walls

In this study, the use of the displacement-based fibre element (DBFE) method for modelling the nonlinear seismic response of reinforced concrete shear wall structures with a variation of damping ratios and types of structural damping is evaluated. The experimental seismic responses of the CAMUS I and NEES-UCSD shear wall structures are compared with nonlinear time-history analysis results obtained using the DBFE method. Comparisons are made in terms of the absolute maximum values of the top displacement, the base shear force, the base bending moment values and minimum differences between overlaps of top displacement time-history graphs. The Hilber-Hughes-Taylor-α integration method is selected for the dynamic solution algorithm. Recommendations are made for appropriate damping ratios for stiffness-proportional, mass-proportional, and Rayleigh damping to be used for the structural damping of nonlinear seismic analyses of the shear walls. The minimum difference between experimental and numerical analysis results is obtained less than 11% using Rayleigh damping. Additionally, the optimal number of fibre elements is researched with regard to the ratio of the mean length of the fibre elements to the longitudinal length of the shear wall. When the ratio is smaller than 3%, the differences between experimental and numerical analysis results for both shear walls are less than 2% at the optimal damping ratios.

Elastic Displacement Spectrum-Based Design Approach for Precast Concrete Frame with Replaceable Energy-Dissipating Connectors

ABSTRACT A precast concrete frame with replaceable energy-dissipating connectors (REDC) is designed as an innovative system. The REDCs are placed at the top and the bottom of the beam-ends to dissipate energy during major earthquakes. A displacement spectrum-based design method is presented, which can directly determine the target period under strong earthquakes. The results of nonlinear time-history analysis of an example structure indicate that the displacement response of the innovative structure under strong earthquakes can be estimated accurately only using elastic response spectrum, without considering additional plastic parameters such as equivalent damping or ductile factor during the design process.

Shear force magnification in reinforced concrete walls of high-rise buildings designed according to Eurocode 8

The paper contains a discussion of shear force magnification in reinforced concrete (RC) walls of high-rise buildings designed according to Eurocode 8. An extensive study is performed in order to examine the applicability of Eurocode 8 procedure in determination of shear forces in RC walls of high-rise buildings. In addition, the applicability of Eurocode 8 provisions related to ductility classes for seismic design of RC high-rise buildings is investigated. 20-storey, 30-storey and 40-storey RC high-rise buildings with core wall structural system are selected as prototype buildings in presented study. 180 nonlinear time-history analyses are conducted for 60 ground motion records with a wide range of magnitudes, distances to source and various soil types including in this way uncertainties of ground motion selection. Nonlinear 3D models of the prototype buildings are constructed. Shear force magnification factors obtained by Eurocode 8 procedure are compared with the results of nonlinear time-history analyses. The current formulation of Eurocode 8 procedure yields significantly incorrect results when it is applied to RC walls of high-rise buildings. The conducted analysis has clearly indicated the possible modifications and improvements in calculation of the Eurocode 8 magnification factor ε for RC walls of the high-rise buildings. The need of introducing a single ductility class for RC walls of high-rise buildings is pointed out. The corrected magnification factor εcor defined in a more general way with variable ratio of second mode shear force to the first mode shear force at the base of the wall is proposed. Further, based on the corrected magnification factor εcor the shear force design envelopes for RC walls of high-rise buildings that best match the actual shear forces obtained from nonlinear time-history analysis are proposed.

Application of Performance-Based Plastic Design (PBPD) method for 3D steel structures

The Performance-Based Plastic Design (PBPD) method, introduced last decade, is an energy-based procedure. This method which is proposed for 2D frames has several stages. At the first stage, a pre-selected global yield mechanism and a target drift are selected. Then, the energy equilibrium equation is developed for a frame to calculate the base shear. At the end stage, designing the beams and columns is done for just one-bay of the planar frame. Since in PBPD-2D procedure the components of energy equilibrium equation are based on the planar frames, it does not consider the adjacent frames effect in 3D design problems so it is necessary to do research about developing PBPD method in 3D frames. The main scope of this paper is to apply the 3D effect on PBPD method. In the current research, the nonlinear distribution of base shear in plan has been found by nonlinear time-history analysis and processed by artificial neural networks. To fortify the results and analyses, 3D and nonlinear modeling is chosen. In the current research, the effect of earthquake power in the nonlinear base shear distribution in plan is considered by looking at the earthquake magnitude and the PGA. Since the earthquake energy is the best structural damage index, in this way, one can design 3D structures by PBPD method adjusted to the desired damage level. In this regards, three special moment frames are designed according to PBPD-2D procedure and proposed PBPD-3D procedure. The results of nonlinear time-history analysis show that the PBPD-2D method could not satisfy the weak beam- strong column criterion and the global yield mechanism in 3D designing, whereas the proposed method in this research, PBPD-3D, satisfies the mentioned criterion successfully.

Prediction of the Maximum Seismic Member Force in a Superstructure of a Base-Isolated Frame Building by Using Pushover Analysis

It is essential for the seismic design of a base-isolated building that the seismic response of the superstructure remains within the elastic range. The evaluation of the maximum seismic member force in a superstructure is thus an important issue. The present study predicts the maximum seismic member force of five- and fourteen-story reinforced concrete base-isolated frame buildings adopting pushover analysis. In the first stage of the study, the nonlinear dynamic (time-history) analysis of the base-isolated frame buildings is carried out, and the nonlinear modal responses of the first and second modes are calculated from pushover analysis results. In the second stage, a set of pushover analyses is proposed considering the combination of the first and second modal responses, and predicted maximum member forces are compared with the nonlinear time-history analysis results. Results show that the maximum member forces predicted in the proposed set of pushover analyses are satisfactorily accurate, while the results predicted considering only the first mode are inaccurate.