Results Of Nonlinear Time History Analyses Research Articles

Sensitivity analysis of the influence of ground motion intensity levels on the seismic behavior of steel frames in assessment of the target displacement considering near-fault effects

Nonlinear time-history analysis conducted as part of a performance-based seismic design approach often require that the ground motion records are selected and then scaled to a specified level of seismic intensity. In such analyses, besides an adequate structural model, a set of acceleration time-series is needed as the most realistic representation of the seismic action. In this paper, the effects of scaling procedure on seismic demands of steel frames are investigated. To this, two special steel moment-resisting frames with considerable higher mode effects, and two sets of ground motions, including near-fault and far-fault motions are considered. Moreover, three scaling procedures are introduced for performing nonlinear dynamic time-history analysis of structures. Among different demands, lateral roof displacement and interstory drift are selected as seismic demands. The height-wise distribution of demands shows that the inelastic seismic demands of the near-fault pulse-like ground motions differ considerably from those of far-fault ones. These results show that the story drifts are mostly larger for far-fault motions in the upper story levels in comparison to near-fault records and in the lower floors, the reverse is true. Thus, the scaling procedures directly affect the results of seismic demands and choosing different methods would result in varying responses. Moreover, a low-cost and fairly effective procedure is proposed to estimate the target displacement demands of buildings from response-spectrum analyses, considering near-fault effects. The precision of this method is verified by nonlinear time-history analysis results, as the benchmark solution, and acceptable improvements have been achieved.

Structural evaluation of steel self-centering moment-resisting frames under far-field and near-field earthquakes

The design formulations, structural performance, and energy-based results of steel buildings of self-centering moment-resisting frames (SC-MRFs) with post-tensioned (PT) connections of three different energy dissipation devices including bolted top and seat angles, beam bottom flange friction devices, and bolted web friction devices are investigated under far-field and near-field earthquakes. The results of nonlinear time-history analysis using DRAIN-2DX program show that the simplified analysis used to estimate the inertial forces distributed through collector beams is not sufficiently precise since it leads to the underestimation of design beam axial forces and connection moments in exterior bays. The overestimation of design displacement demands of SC-MRFs with bottom flange friction devices results in bigger sections of beams and columns than are necessary. In addition, this SC-MRF system is not as effective as other two systems to dissipate the input energy. It is recommended to symmetrically use beam flange friction devices to achieve higher level of energy dissipation and lower fabrication costs. On the other hand, SC-MRFs with web friction devices is identified as the most efficient system to minimize the recoverable energy and SC-MRFs with top and seat angles provides medium level of energy dissipation. Different from far-field earthquakes, the input energies of SC-MRF structures under near-field ground motions are distinguishable by hikes of maximum values at the early stages of earthquakes. Furthermore, absolute energy components are substantially higher than relative energy components under near-field earthquakes. These phenomena should be considered in the formulations of energy factor and energy-based design procedures of SC-MRF systems.

Investigation of Global Equivalent Damping and Statistical Relationship of Displacement between Nonlinear Static and Dynamic Analysis of Reinforced Concrete Frame Structures

The assessment of the seismic performance of reinforced concrete (RC) frame structures using the equivalent linearization approach requires comprehensive insight into the nonlinear response of the system, and most previous researches focused on the analysis of a single-degree-of-freedom (SDOF) system. To describe the hysteretic behavior of a multi-degree-of-freedom (MDOF) system accurately, monotonic and cyclic pushover analyses for 88 RC frames structures with various configurations and design parameters are carried out and a unified hysteresis loop expression modeling the cyclic pushover results of RC frame system is developed. Then, a global equivalent damping based on Jacobsen's approach is derived, and comparisons between the displacements obtained by nonlinear static analysis (NSA) utilizing the derived global equivalent damping and those obtained by nonlinear time history analysis (NTHA) are made. Finally, a modified global equivalent damping is presented by calibrating the derived Jacobsen's equivalent damping through NTHA results. Based on the modified equivalent damping, the statistical analysis of the ratios of the results obtained by NTHA to those obtained by NSA is implemented to predicate the probabilistic seismic displacement demands of RC frame structures.

Experimental and numerical study on the DADAS dampers in steel frame structure

In this study, a structural system with seesaw motion respect to a central massive support has been considered for steel buildings, and the bottom ends of the all circumferential columns at the lowest story have been equipped with double-ADAS (DADAS) dampers, which dissipate a great portion of the seismic input energy. The hysteretic behaviour of DADAS dampers has been investigated by using finite element analysis. The damper is modelled at structural laboratory of Earthquake Engineering Research Institute in small scale and tested under harmonic loaded. Experimental results show the proper conduct of the damper prototype is under load. To show the efficiency of the proposed structural system and dampers, a series of nonlinear time history analysis (NLTHA) were performed by using a set of three-component acceleration of some selected earthquakes. Numerical results of NLTHA show that the proposed rocking structures can efficiently decrease the seismic damage in the building.

Generalized force vectors for multi-mode pushover analysis of bridges

Nonlinear static procedures (NSPs) are gaining wider use in performance based earthquake engineering practice due to their simplicity compared to rigorous nonlinear time history analysis (NTHA), and being implemented in the new generation of seismic design codes. In this study, a recently proposed Nonlinear Static Procedure (NSP) for the seismic performance assessment of building structures using the concept of generalized force vectors (GFV), is further validated through application to reinforced concrete bridges. This method, named generalized pushover analysis (GPA), maximizes the response of a chosen parameter during the seismic response, through the use of the GFV, which are a combination of modal forces representing the instantaneous force acting on the system when such parameter reaches its maximum. In this study, the original GPA implemented in buildings is adapted to bridge structures and four versions of the algorithm are tested. Two straight bridges, featuring different levels of vertical irregularity, are used as case study to validate the procedure, and the accuracy of the GPA algorithm is assessed by comparing the nonlinear static results with the “exact” prediction from NTHA. Several levels of seismic hazard, represented in the expected return period of the target spectra, are considered to test the accuracy of the method for low and high seismic demand. Furthermore, the GPA results are also compared with a commonly employed NSP, the capacity spectrum method. The results obtained for the case study suggest that GPA algorithm for bridges is suitable as a NSP approach for the seismic assessment of bridge structures, demonstrating a good fit with NTHA results and superiority with respect to the predictions of the selected traditional NSP.

Applicability of equivalent linearization methods to irregular isolated bridges

Equivalent linearization methods are widely applied to assess the seismic demands of buildings and bridges. Several regulation codes include methodologies to conduct linear analyses with equivalent structures. Normally, bridges are highly irregular structures due to the different pier heights. This study evaluates the applicability of a group of equivalent linearization methods proposed in the literature to predict the seismic response of isolated bridges with height irregularities. The isolation system is composed by lead rubber bearings. A parametric study is carried out in bridges with three types of height irregularities and combinations of relative height between piers. The bridges were subjected to a family of seismic records from a subduction zone to evaluate the equivalent elastic methods based on the results of nonlinear time-history analysis. Especial emphasis is devoted to assess the influence of the bridge irregularity on the ability of the methods to predict the nonlinear bridge demands. The results show the applicability of the equivalent linearization methods as function of the ductility demands and the height irregularity of the bridges. This study also discusses the parameter combinations that the different approaches lead to underestimate or overestimate the bridges demands.

Parametric study on the effect of structural and geotechnical properties on the seismic performance of integral bridges

In this paper practical techniques are introduced for detailed modeling of soil–pile and soil–abutment interaction effects for integral bridges (IBs). Furthermore, a parametric study is conducted to determine appropriate structural configurations and geotechnical properties to enhance the seismic performance of IBs. For this purpose, numerous nonlinear structural models of a two-span IB including dynamic soil–bridge interaction effects are built. Nonlinear time history analyses (NTHA) of the IB models are then conducted using a set of ground motions with various intensities. In the analyses, the effect of various structural and geotechnical properties such as foundation soil stiffness, backfill compaction level, pile size and orientation, abutment height and thickness are considered. The results of NTHA are then used to assess the effects of these properties on the seismic performance of IBs in terms of member forces and deformations. It is found that while the proposed modeling techniques for IBs are easy to implement in commercially available structural analysis programs, they are also computationally efficient. However, the proposed structural model may not be used to study the soil deformations along the length of the embankment. For the IB and modeling approach under consideration, the bridge seismic response is found to be insensitive to the length of the embankment and damping of the embankment soil. Furthermore, IBs built with shorter and thinner abutments as well as large steel H-piles oriented to bend about their strong axis exhibit better seismic performance.

An approximate procedure for estimating seismic demands for buildings

Methods of the estimation of the seismic demands of nonlinear structures require a sort of iterative procedures, no matter the elastic or inelastic response spectra are used in the procedure. Many studies dealt with the development of different inelastic spectra with the aim to simplify the evaluation of inelastic deformations and performance of structures. Recently, the concept of inelastic spectra has been adopted in the global scheme of the performance-based seismic design through capacity-spectrum methods (CSM). For instance, the modal pushover analysis (MPA) has been proved to provide accurate results for inelastic buildings to a similar degree of accuracy to the response spectrum analysis (RSA) in estimating peak response for elastic buildings. In this paper, a simplified nonlinear spectral analysis is made to the original MPA is proposed. The proposed procedure, which is applicable to multi-degree-of-freedom MDOF systems uses an inelastic spectrum and gives peak responses consistent with those obtained when using the nonlinear time history analysis (NL-RHA). The accuracy of the proposed procedure is verified against the nonlinear time history analysis results of two buildings. The comparison showed that the new method is capable to provide accurate peak response.

Performance-based seismic design of self-centering steel frames with SMA-based braces

This study proposes a performance-based seismic design (PBSD) method for steel braced frames with novel self-centering (SC) braces that utilize shape memory alloys (SMA) as a kernel component. Superelastic SMA cables can completely recover deformation upon unloading, dissipate energy without residual deformation, and provide SC capability to the frames. The presented PBSD method is essentially a modified version of the performance-based plastic design with extra consideration of some special features of SMA-based braced frames (SMABFs). Four six-story concentrically braced frames with SMA-based braces (SMABs) are designed as examples to illustrate the efficacy of the proposed design method. In particular, the variability in the hysteretic parameters of SMAs, such as the phase-transformation stiffness ratio and the energy dissipation factor, is considered in the PBSD method. Accordingly, four SMABFs are designed with different combinations of these hysteretic parameters. The seismic performance of the designed frames is examined at various seismic intensity levels. Results of nonlinear time-history analyses indicate that the four SMABFs can successfully achieve the prescribed performance objectives at three seismic hazard levels. The comparisons among the designed frames reveal that the SMABs with greater hysteretic parameters result in a more economical design in terms of the consumption of steel and SMA materials.

Nonlinear analysis of RC structure with massive infill wall exposed to shake table

This study aims to present nonlinear time history analysis results of double leaf cavity wall (DLCW) reinforced concrete structure exposed to shake table tests. Simulation of the model was done by a Finite Element (FE) program. Shake table experiment was performed at the National Civil Engineering Laboratory in Lisbon, Portugal. The results of the experiment were compared with numeric DLCW model and numeric model of reinforced concrete structure with unreinforced masonry wall (URM). Both DLCW and URM models have two bays and two stories. Dimensions of the tested structure and finite element models are 1:1.5 scaled according to Cauchy Froude similitude law. The URM model has no experimental results but the purpose is to compare their performance level with the DLCW model. Results of the analysis were compared with experimental response and were evaluated according to ASCE/SEI 41-06 code.

The Influence of Operator on Repeated Femoral Hip and Lumbar Spine Densitometry Measurements

In the last decade, nonlinear static procedures emerged as the reference practice-oriented analysis method for structures under seismic actions. These procedures are generally based upon two key steps: (i) performing a nonlinear static (pushover) analysis under lateral forces and (ii) evaluating the seismic demand through the so-called capacity spectrum obtained at the end of the previous step.This paper specifically deals with the latter and proposes a parametric comparison between two wide classes of methods formally based on conceptually alternative approaches for defining the demand spectra in nonlinear static analyses of dissipative structures. First of all, the paper outlines the main conceptual aspects of such alternative methods and reports their key operational details. Particularly, it proposes a dimensionless formulation of their relationships and demonstrates that both methods are based upon a small and almost common set of dimensionless parameters. Therefore, a wide parametric analysis is proposed to compare the ductility demand obtained by means of these two alternative methods with the aim of describing and quantifying the different predictions obtained by applying such methods. Finally, the results of nonlinear time-history analyses are proposed for assessing the two aforementioned methods.

Shaking table tests of a base isolated structure with Double Concave Friction Pendulum bearings

An extensive experimental testing programme named JETBIS project (Joint Experimental Testing of Base Isolation Systems) was developed within the RELUIS II project (Task 2.3.2) and RELUIS III project (Line 6) involving partners from different Italian universities. This paper describes the seismic tests performed by the research unit of University of Basilicata (UNIBAS) on an isolation system based on Double Concave Friction Pendulum (DCFP) bearings. The DCFP bearing contains two separate concave sliding surfaces and exhibits different hysteretic properties at different stages of displacement response. The main objective of this work is to evaluate the horizontal response of the DCFP isolators by means of controlled-displacement tests and shaking table tests. The experimental model was a 1/3 scaled steel framed structure with one storey and one bay in both directions. Four DCFP bearings with equal properties of the sliding surfaces were considered. In this work, three different sliding surface conditions (with and without lubrication) have been studied. The isolated base model was subjected to 8 natural earthquakes of increasing seismic intensities and considering two mass configurations (with both symmetrical and eccentric masses). The reliability of the design procedure considered for the isolation system was verified also when relevant residual displacements occurred due to previous earthquakes. In this paper, the comparisons between the experimental outcomes and the numerical results of nonlinear time-history analyses using SAP2000 are shown.

A variant of modal pushover analyses (VMPA) based on a non-incremental procedure

A variant of modal pushover analysis (VMPA) is presented to evaluate the seismic performance of the structures. The suggested procedure is based on an iterative process in which secant stiffnesses are used both at the element level and in the modal response. VMPA diverges from the existing modal pushover analyses for the following reasons: (1) mode compatible adaptive forces are applied to the structure at each iteration step, (2) the application of the equal displacement rule in combination with secant stiffness based linearization in the spectral displacement (Sd)—spectral acceleration (Sa) relation eliminates the necessity to produce a modal capacity diagram for each mode. The displacement controlled algorithm determines the single ordinate of the modal capacity diagram corresponding to the target displacement demand for the nth mode (Sdn_p, San_p) by reducing elastic spectral acceleration (San_e) to converge to the plastic acceleration (San_p). A Matlab based computer program known as DOC3D-v2 is developed to implement the proposed procedure. To verify the success of the suggested procedure, 9- and 20-storey LA SAC buildings are analysed, and the resulting demands are compared with several existing procedures, such as the extended N2, MPA and MMPA, as well as nonlinear time history analyses performed for two different set of acceleration records. VMPA yields enhanced results in terms of storey drifts, especially for the 20-storey LA building, compared with the other methods. Although the storey displacements and drifts are largely consistent with nonlinear time history analysis results, conservative estimates are obtained for the storey shear forces.

Constant-Damage Yield Strength Spectra for RC Structures Using Modified Park-Ang Damage Model

In this study, constant-damage yield strength spectrum (CDYSS), which is defined as the yield strength demand of a single-degree-of-freedom (SDOF) system of varying natural vibration period with the target constant damage index and specified ductility capacity, is derived by averaging the nonlinear time-history analysis results of a SDOF system under different earthquake ground motions. A modified Park-Ang damage model proposed by the authors, eliminating its non-convergence problem both at upper and lower limits with higher precision and smaller scatter, is adopted to calculate the damage index of the SDOF system. In the construction of CDYSS, 641 sets of earthquake ground motion records are adopted and classified into 12 groups in line with Chinese code for seismic design of buildings. The yield strength demands of SDOF systems with given ductility capacity are obtained through trial and error method. Then, the mean CDYSS and the corresponding coefficient of variation for different group of site soil conditions are calculated. The effects of ductility capacity and local site soil conditions on CDYSS are discussed. Lastly, the empirical formulas of CDYSS are developed by multivariable nonlinear regression analysis and compared with actual CDYSS.

Nonlinear static analyses based on either inelastic or elastic spectra with equivalent viscous damping: A parametric comparison

In the last decade, nonlinear static procedures emerged as the reference practice-oriented analysis method for structures under seismic actions. These procedures are generally based upon two key steps: (i) performing a nonlinear static (pushover) analysis under lateral forces and (ii) evaluating the seismic demand through the so-called capacity spectrum obtained at the end of the previous step.This paper specifically deals with the latter and proposes a parametric comparison between two wide classes of methods formally based on conceptually alternative approaches for defining the demand spectra in nonlinear static analyses of dissipative structures. First of all, the paper outlines the main conceptual aspects of such alternative methods and reports their key operational details. Particularly, it proposes a dimensionless formulation of their relationships and demonstrates that both methods are based upon a small and almost common set of dimensionless parameters. Therefore, a wide parametric analysis is proposed to compare the ductility demand obtained by means of these two alternative methods with the aim of describing and quantifying the different predictions obtained by applying such methods. Finally, the results of nonlinear time-history analyses are proposed for assessing the two aforementioned methods.

Probabilistic assessment of structures with SPSW systems and LYP steel infill plates using fragility function method

Steel plate shear walls (SPSWs) have been used as primary lateral force-resisting systems in seismic design of new and retrofit of existing buildings. Employment of low yield point (LYP) steel infill plates with considerably low yield strength and high ductility, on the other hand, has been shown in a number of studies to improve the structural performance of SPSW systems. By considering the various sources of randomness and uncertainties involved in the design and retrofit process, adoption of a probabilistic methodology can result in a robust seismic performance assessment of such structural systems. This paper presents the results of a study on the seismic performance and vulnerability of retrofitted structures employing SPSW systems and LYP steel material through probabilistic seismic demand analysis (PSDA). Three 9-story code-designed and retrofitted structural models including a moment-resisting and two SPSW frames are considered. Appropriate seismic response and ground motion intensity parameters, and damage as well as repair states are selected. Structural and nonstructural drift and acceleration fragility functions are subsequently developed based on nonlinear time-history analysis results. The effectiveness of SPSW systems in improving the seismic performance and reducing the vulnerability of buildings is demonstrated through seismic response assessment and fragility analysis. Also, it is shown that employment of relatively thicker LYP steel infill plates in seismic design and retrofit of SPSWs results in smaller damage potential and better seismic performance of such systems.

Comparison of Force-Based and Displacement-Based Design approaches for RC coupled walls in New Zealand

Reinforced concrete coupled walls are a common lateral load resisting system used in multi-storey buildings. The effect of the coupling beams can improve seismic performance, but at the same time adds complexity to the design procedure. A case study coupled wall building is designed using Force-Based Design (FBD) and Direct Displacement-Based Design (DDBD) and in the case of the latter a step by step design example is provided. Distributed plasticity fibre-section beam element numerical models of the coupled walls are developed in which coupling beams are represented by diagonal truss elements and experimental results are used to confirm that this approach can provide a good representation of hysteretic behaviour. The accuracy of the two different design methods is then assessed by comparing the design predictions to the results of non-linear time-history analyses. It is shown that the DDBD approach gives an accurate prediction of inter-storey drift response. The FBD approach, in accordance with NZS1170.5 and NZS3101, is shown to include an impractical procedure for the assignment of coupling beam strengths and code equations for the calculation of coupling beam characteristics appear to include errors. Finally, the work highlights differences between the P-delta considerations that are made in FBD and DDBD, and shows that the code results are very sensitive to the way in which P-delta effects are accounted for.

Relative Displacement Floor Spectra for Seismic Design of Non Structural Elements

Relative displacement floor spectra represent a powerful tool to evaluate the seismic displacement requirements of non-structural elements relative to their attachment points and can be used for displacement-based design of ductile components.This article examines the displacement floor spectra on single-degree of freedom systems subject to accelerograms of varying intensity. A new method is proposed to predict floor spectra on single degree of freedom supporting structures. The results of nonlinear time-history analyses of a series of case-study structures indicate that the new methodology provides good results.Future research will aim to validate this approach for multi-degrees of freedom supporting structures.

EVALUATION OF CAPACITY SPECTRUM METHOD IN ESTIMATING SEISMIC DEMANDS OF TRIPLE PENDULUM BEARINGS UNDER NEAR-FIELD GROUND MOTIONS

Simplified methods for analyzing seismically isolated structures are always used either as a design procedure or as checking criteria for the results of time history procedure. The main purpose of this study is to evaluate the accuracy of one of these methods, the capacity spectrum method (CSM), in predicting the seismic demands, such as isolator displacement and maximum base shear force, of structures with triple pendulum bearings (TPBs) under bidirectional near-field ground motions. By comparing the results of this method with those of the nonlinear time history analysis (NTHA), it can be concluded that the CSM is able to predict the maximum isolator displacement and base shear of the structure with acceptable accuracy. It should be noted that for softer soil site conditions, the values of demand calculated by CSM are sometimes underestimated compared with the results of NTHA, especially when the effective period of system exceeds 3.0 s or when the TPB works on the fifth regime of its pendulum mechanism.

Application of the Direct Displacement Based Design Methodology for Different Types of RC Structural Systems

This study investigates the direct displacement based design (DDBD) approach for different types of reinforced concrete structural systems including single moment-resisting, dual wall-frame and dual steel-braced systems. In this methodology, the displacement profile is calculated and the equivalent single degree of freedom system is then modeled considering the damping characteristics of each member. Having calculated the effective period and secant stiffness of the structure, the base shear is obtained, based on which the design process can be carried out. For each system three frames are designed using DDBD approach. The frames are then analyzed using nonlinear time-history analysis with 7 earthquake accelerograms and the damage index is investigated through lateral drift profile of the models. Results of the analyses and comparison of the nonlinear time-history analysis results indicate efficiency of the DDBD approach for different reinforced concrete structural systems.