Nonlinear Response History Analysis Research Articles

Tall building performance‐based seismic design using SCEC broadband platform site‐specific ground motion simulations

AbstractThe scarcity of strong ground motion records presents a challenge for making reliable performance assessments of tall buildings whose seismic design is controlled by large‐magnitude and close‐distance earthquakes. This challenge can be addressed using broadband ground‐motion simulation methods to generate records with site‐specific characteristics of large‐magnitude events. In this paper, simulated site‐specific earthquake seismograms, developed through a related project that was organized through the Southern California Earthquake Center (SCEC) Ground Motion Simulation Validation (GMSV) Technical Activity Group, are used for nonlinear response history analyses of two archetype tall buildings for sites in San Francisco, Los Angeles, and San Bernardino. The SCEC GMSV team created the seismograms using the Broadband Platform (BBP) simulations for five site‐specific earthquake scenarios. The two buildings are evaluated using nonlinear dynamic analyses under comparable record suites selected from the simulated BBP catalog and recorded motions from the NGA‐West database. The collapse risks and structural response demands (maximum story drift ratio, peak floor acceleration, and maximum story shear) under the BBP and NGA suites are compared. In general, this study finds that use of the BBP simulations resolves concerns about estimation biases in structural response analysis which are caused by ground motion scaling, unrealistic spectral shapes, and overconservative spectral variations. While there are remaining concerns that strong coherence in some kinematic fault rupture models may lead to an overestimation of velocity pulse effects in the BBP simulations, the simulations are shown to generally yield realistic pulse‐like features of near‐fault ground motion records.

Influence of superstructure modeling approach on the response prediction of buildings with LRBs considering heating effects

The aim of this study is to investigate the variation in response quantities of buildings seismically isolated by lead rubber bearings (LRBs), depending on how the superstructure is modeled in the analyses. For this purpose, two distinct seismically isolated structures with 4- and 9-stories are idealized by (i) a single-degree-of-freedom model (SDOF), (ii) a two-degree-of-freedom model (2DOF), (iii) a 3D model and subjected to near-fault earthquake excitations through nonlinear response history analyses (NRHA). In all of the structural models, the hysteretic behavior of LRBs is represented by a deteriorating force–displacement curve in which the strength of bearing decreases gradually during cyclic motion due to the lead core heating. Analyses are performed by OpenSees and the response quantities considered are floor drifts and floor accelerations for superstructures and maximum isolator displacements for isolation systems. In order to assess the influence of the superstructure modeling approach on selected response quantities, results of analyses with SDOF, 2DOF, and 3D models are compared with each other. Furthermore, in order to highlight the significance of hysteretic representation used to model LRBs, a non-deteriorating force–displacement curve, where lead core heating phenomenon is ignored, is also considered to idealize LRBs in the case of a 3D superstructural model. Results showed that the SDOF model overestimates the isolator displacements obtained from the 3D model and the 2DOF model is effective only in estimating mid-story response quantities of the 3D model.

Seismic response of rocking isolated railway bridge piers with sacrificial components

In this study, sacrificial components were incorporated into self-centering railway bridge piers to improve the lateral stiffness. The seismic response of this new detail was investigated. First, the method to compute the initial uplift moment of the self-centering pier is given. In addition, shaking table tests were conducted on a free-rocking pier without sacrificial components, which was used to validate a two-spring numerical model. Good agreement was obtained between the numerical results and experimental data. Furthermore, the validated model was employed to investigate the influence of sacrificial components on the seismic response of rocking piers. For this purpose, two models were developed, with and without sacrificial components. Nonlinear response history analysis was then performed on both models under three historical motions. The results showed that compared to the one without sacrificial components, the rocking pier with sacrificial components has comparable displacement at the top of the pier, and maximum uplift moment at high amplitude motion. Therefore, incorporating sacrificial components into the rocking pier can increase the lateral stiffness at service load and low amplitude frequent earthquakes but can produce comparable response at high seismic excitation. These results provide support for performance-based seismic design of self-centering rocking piers.

Application of the Incremental Modal Pushover Analysis to Bridges Subjected to Near-Fault Ground Motions

Near-fault events can cause severe damage to civil structures, including bridges. Many studies have demonstrated that the seismic assessment is not straightforward. Usually, dealing with near-fault ground motion, the structural analysis is performed using Nonlinear Response-History Analysis (NRHA) but in the last years, many authors have tested existing pushover-based procedures originally developed and validated using far-field events. Between those procedures, the Incremental Modal Pushover Analysis (IMPAβ) is a pushover-based procedure specifically developed for bridges that, in this work, was applied to a case study considering near-fault pulse-like ground motion records. The records were analyzed and selected from the European Strong Motion Database. In the paper the results obtained with IMPAβ together with other standard pushover procedures, are compared with NRHA and incremental dynamic analyses; the vertical component of the motion has been also considered. Results obtained with the bridge case study demonstrate that the vertical seismic action has a minor influence on the structural response and that IMPAβ is confirmed as a very effective pushover-based method that can be applied also for near-fault events.

Application of Conditional Mean Spectrum in the Seismic Assessment of a Braced Frame Steel Structure

Detailed engineering of critical infrastructure and tall buildings require that their response be estimated from nonlinear response history analysis (NLRHA) by subjecting the structure to suites of earthquake accelerograms. Selection of ground motion records due to future earthquake events represents an important step in the robust assessment of structural response. As per the current practice, both site-specific uniform hazard spectrum (UHS) and conditional mean spectrum (CMS) are employed as the target spectra for ground motion record selection. The CMS approach is superior considering that it represents realistic seismic events and also consider the multiple natural periods of the structure. The paper presents the application of conditional mean spectrum in the seismic assessment of an eight-story ordinary braced steel structure built on an example site. The NLRHA was conducted using the ground motions spectrally matched to the CMS at different conditioning periods. It was found that the CMS spectrally matched to larger modal period always result in larger seismic demands. A comparison was also made between seismic demands obtained from UHS & CMS indicating that the structural response parameters are almost the same in both cases except the story shears & drifts which is dominated by UHS in lower floors and by CMS in upper floors.

Fast fragility analysis of plan-asymmetric structures considering soil-structure interaction using flexible base 2 degrees of freedom Modal Pushover Analysis (F2MPA)

As an alternative to the very time consuming Non-Linear Response History Analysis (NLRHA) approach, this research aimed to employ the F2MPA (Flexibly-supported 2 DOF Modal Pushover Analysis) approach in developing fragility curves of flexibly-supported plan-asymmetric structures. To do this task, the F2MPA approach is employed to approximately calculate the seismic non-linear response of soil-RC plan asymmetric building systems considering the eccentricity and soil structure interaction (SSI) simultaneously with lower computational costs. Using an appropriate hysteretic model, the F2MPA-based IDA (Incremental Dynamic Analysis) procedure, developed in this study, can accurately estimate the seismic response of the superstructure considering stiffness deterioration, strength loss and pinching behavior of RC members. To examine the applicability of the proposed method, an 8-story RC dual lateral load resistant building under an ensemble of near-fault pulse-like events is used. The comparison of the NLRHA-based and F2MPA-based fragility functions showed a good agreement. Considering the time effectiveness of the proposed approximate method (less than the 0.01 of the NLRHA method), the method is found to be very attractive for practical soil-asymmetric structures. Negligence of the SSI effect for a given structure could be taken into consideration if this approximate fragility analysis does not highlight major SSI effects.

Selection and Scaling of Ground Motions Using Multicriteria Optimization

AbstractAlthough large ground motion databases are widely available today, in many occasions, the selection of ground motion records still hampers the use of nonlinear response history analysis in ...

Damping spectra for estimating inelastic deformations from modal response spectrum analysis

SummaryThe focus of this study is estimating inelastic deformations of building frames by conducting response spectrum analysis. Damping spectra (Rμ–ξ–T spectra) are derived first for SDOF systems defined with their initial period or initial stiffness, in order to attain equal maximum displacements of the companion inelastic systems. Mean spectral relations and their standard deviations are calculated for 566 horizontal pairs of near‐fault ground motions. They are further classified with respect to ductility reduction factor Rμ as well as the earthquake magnitude and soil type, which are found to have notable influence on the effect of damping in reducing maximum displacement. Optimal damping scaling factors are then calculated for converting the standard 5% damped linear elastic spectra to inelastic spectra. Finally, maximum deformations of MDOF building frames are estimated by using the optimal spectral factors through mode superposition analysis. The results are compared with the results obtained from nonlinear response history analysis under different sets of strong ground motions. Mean inelastic deformations are predicted with reasonable accuracy with the proposed procedure. Hence, damping spectra furnishing optimal damping ratios are suggested as a practical tool for assessing the seismic performance of newly designed, code conforming structures.

Three-dimensional nonlinear response history analyses for earthquake damage assessment: A reinforced concrete wall building case study

Nonlinear dynamic analysis techniques have made significant progress in the last 20 years, providing powerful tools for assessing structural damage and potential building collapse mechanisms. The fact that several reinforced concrete shear wall residential buildings underwent severe structural damage in walls at the lower building levels during the 2010 Maule earthquake (Chile) presents a scientific opportunity to assess the predictive quality of these techniques. The objective of this research is to compare building responses using two completely different three-dimensional nonlinear dynamic models and study in detail the observed damage pattern and wall collapse of one reinforced concrete shear wall building in Santiago, Chile. The first model is a mixed fiber-shell model developed in MATLAB, and the second is a shell finite element model developed in the software DIANA. Results of both models are consistent with the hypothesis that high axial loads trigger a limited ductility failure in critical walls at roof-to-base drift ratios less than 0.34% with little capacity of hysteretic energy dissipation, which contradicts the ductile design philosophy of current code provisions.

Characterization of ground motion intensity for the seismic fragility assessment of plan-irregular RC buildings

The identification of ground motion intensity measures (IMs) that are characterized by virtues such as efficiency, sufficiency, scaling robustness and hazard computability, has been the subject of extensive research over the past several years. In the process, there have evolved, numerous non-structure specific as well as structure specific descriptors of ground shaking severity. Most of the studies that investigated the optimality of such descriptors were, however, restricted to the seismic response of single or multi-storey planar frame buildings under unidirectional excitation. The study herein aims to examine, the efficiency and sufficiency of a wide spectrum of IMs, in predicting the maximum interstorey drift demands on plan-irregular RC moment frame buildings subjected to bi-directional ground motion. This is accomplished through a cloud analysis-based framework that integrates nonlinear response history analysis and statistical regression analysis. Further, the use of scalar bi-directional shaking intensity measures (BSIMs) derived from a vector of intensities corresponding to each horizontal component of ground motion using popular combination schemes such as geometric averaging, arithmetic averaging, SRSS and use of envelope values, is examined from the perspective of their ability to predict drift demands. Observations from the study reveal that IMs based on the geometric averaging of spectral ordinates over a range of periods are superior to the other descriptors considered, in terms of the aforementioned attributes and that combining the intensities of the two orthogonal components by geometric averaging leads to an optimal BSIM that could be used in place of vector IMs. The heteroscedasticity in the maximum interstorey drift response under different levels of the BSIM is further investigated using a Multiple Stripe Analysis framework. The optimal BSIM is observed to perform reasonably well at all target intensity levels, making it an excellent candidate to base fragility and vulnerability functions upon.

Efficient intensity measures and machine learning algorithms for collapse prediction of tall buildings informed by SCEC CyberShake ground motion simulations

In contrast to approaches based on scaling of recorded seismograms, using extensive inventories of numerically simulated earthquakes avoids the need for any selection and scaling of motions which implicitly requires assumptions on intensity measures (IMs) that correlate with structural response. This study has the objectives to examine seismogram features that control the collapse response of tall buildings and to develop efficient and reliable collapse classification algorithms. To that end, machine learning techniques are applied to the results of nonlinear response history analyses of a 20-story tall building performed using about two million simulated ground motions. Feature selection of ground motion IMs generally confirms current understanding of collapse predictors based on previous studies using scaled recorded motions. In addition, interrogations of the large collection of hazard-consistent simulations demonstrate the utility of different IMs for collapse risk assessment in a way that is not possible with recorded motions. Finally, a small subset of IMs is identified and used in development of an efficient collapse classification algorithm which is tested on benchmark simulated data at several sites in the Los Angeles basin.

Fiber‐based hysteretic model for simulating strength and stiffness deterioration of steel hollow structural section columns under cyclic loading

SummaryAn efficient component model has been developed that captures strength and stiffness deterioration of steel hollow structural section (HSS) columns. The proposed model consists of two fiber‐based segments at a member's ends along with an elastic segment in between. The fibers exhibit nonlinear uniaxial stress–strain behavior, which is explicitly defined by uniaxial monotonic tensile and cyclic round coupon tests. The postbuckling behavior of an HSS column is traced through a proposed uniaxial effective stress–strain constitutive formulation, which includes a softening branch in compression and an energy‐based deterioration rule to trace the influence of cyclic deterioration in the inelastic cyclic straining. These may be inferred by uniaxial stub‐column tests. The component model captures the coupling between the column axial force and flexural demands. Consistent model parameters for a number of steel materials used in the steel construction in North America and Japan are proposed along with the associated model calibration process. The efficiency of the proposed model in predicting the hysteretic behavior of HSS columns is demonstrated by comparisons with physical steel column tests subjected to various loading histories, including representative ones of ratcheting prior to earthquake‐induced collapse. The proposed model is implemented in an open‐source finite element software for nonlinear response history analysis of frame structures. The effectiveness of the proposed model in simulating dynamic instability of steel frame buildings is demonstrated through nonlinear response simulations of a four‐story steel frame building, which was tested at full‐scale through collapse. Limitations as well as suggestions for future work are discussed.

Composite behavior in RC buildings retrofitted using buckling-restrained braces with elastic steel frames

Seismically retrofitting reinforced concrete (RC) building with a combination of buckling-restrained braces (BRBs) and elastic steel frames offers a practical solution that provides additional lateral stiffness and energy dissipation capacity. However, the available methods to vertically distribute the BRB sizes based on equivalent linearization do not consider the additional stiffness due to the composite behavior between the RC frame and the elastic steel frame, which may lead to an overly conservative estimate of the BRB stiffness demands. This study proposes a retrofit design method incorporating the composite behavior. Numerical models considering the detailed composite behavior are developed and calibrated against quasi-static cyclic loading tests, and a simplified evaluation method is proposed. A four-story RC school building is used as a benchmark model, and the proposed retrofit design method is validated using nonlinear response history analysis. The analysis results suggest that taking the composite behavior into account by using the proposed retrofit design method more accurately estimates the lateral stiffness of the retrofitted structure and leads to a more economic retrofit.

Maximum inelastic displacement of mainshock-damaged structures under succeeding aftershock

To facilitate the rapid, though, reliable assessment of mainshock-damaged structures against the succeeding aftershock excitations, the γ-index is introduced, defined as the ratio of the residual displacement of a structure under the mainshock excitation over the aftershock-induced maximum inelastic displacement of the damaged structure. Over 200 mainshock-aftershock sequences from very dense and stiff soil profiles were chosen to perform nonlinear response history analyses of single degree of freedom systems and the influence of structural, strong ground motion and site-specific parameters on the γ-index was assessed. An equation for the γ-index is proposed to predict the performance of the damaged structure under aftershocks.

Multi-Objective Optimization of Three Different SMA-LRBs for Seismic Protection of a Benchmark Highway Bridge against Real and Synthetic Ground Motions

Many researchers have taken advantage of adding shape memory alloy (SMA) wires to base isolators to control displacements and residual deformations. In the literature, different arrangements of SMA wires wrapped around the rubber bearings can be found, as examples, straight, cross and double-cross arrangements. SMA wires with various configurations and radii lead to the different characteristics of the isolator system and thus various shear hysteresis. Therefore, the aim of this study is to evaluate the performance of these three SMA wire’s configurations in the seismic retrofitting of a benchmark highway bridge by implementing them in the bridge’s existing lead rubber bearings (LRB). This system is referred to as SMA-LRB isolator. Firstly, because of the crucial influence of the wire’s radius, this parameter is determined using a multi-objective optimization algorithm (non-dominated sorting genetic algorithm (NSGA)-II). This algorithm simultaneously minimizes the deck acceleration and mid-span displacement. Secondly, the optimized SMA-LRBs are implemented in the highway bridge and nonlinear dynamic analysis is conducted. For the nonlinear response history analysis, two strong ground motion records are selected from the PEER database, by studying the site’s conditions. In addition, ten synthetic ground acceleration time histories are generated. The result illustrates that the double-cross SMA-LRB reduces the maximum and residual displacements more than two other devices; however, it causes the largest base shear force and deck acceleration. Besides, the cross-configuration results in the least displacement reduction and has the least shear force and acceleration. To find SMA-LRB with the best overall performance, a multi-objective decision-making method is utilized and the straight SMA-LRB is recognized as the most effective isolator.

Effect of skew on the minimum support length requirements of single-span bridges with seat-type abutments

Skew bridges are known to be susceptible to girder unseating during earthquakes, and empirical equations for minimum support length are used in their design. To determine the degree of conservatism or un-conservatism in these equations, a rigorous model of a skewed bridge was developed in OpenSees and validated against a comprehensive dataset from shake table experiments. The validated model was then used to perform a parameter study on a series of single-span, simply supported, prototype bridges with seat-type abutments. Nonlinear response history analyses were performed that included impact and friction effects at the abutments and were repeated for both far-field and near-field motions. It was found that the additional support length required to prevent unseating is a linear function of skew angle over the range 0°–60° for both types of motions. This is contrary to common practice, which uses a quadratic function (American Association of State Highway and Transportation Officials, AASHTO) or the inverse of cosine of angle of skew (Federal Highway Administration (FHWA)). Consequently, common practice appears to be underestimating support length requirements by up to 50% at midrange skew angles of 30°–40°.

Seismic Response of Long-Span Domes Supported by Multi-Storey Substructures

This paper investigates the seismic response characteristics of long-span domes. The natural periods of the prominent modes are longer than medium-span domes, which leads to a greater contribution from the higher modes to the response of the long-span dome. The acceleration distributions, particularly the vertical acceleration distributions are sensitive to the dominant mode shapes of these higher modes. This leads to inaccuracies when applying the previously proposed response evaluation methods. The vibration modes of multi-storey supporting substructures also affect the excited vibration modes of the roof. In this paper, the dynamic characteristics and seismic response of 150m-span domes supported by multi-storey substructures are studied. The effects of the post- yield stiffness of multi-storey substructures are also analysed by considering two structural systems, buckling- restrained braced frames (BRBF) and damped spine frames. A simple design procedure to evaluate the equivalent static loads using amplification factors and incorporating the effects of higher modes is proposed based on response spectrum analysis and equivalent linearisation procedures. The accuracy of the proposed method is evaluated by comparing the responses with those obtained from non-linear response history analysis.

Inelastic seismic response of box-girder bridges due to torsional ground motions

The torsional components of strong ground motions (TGMs) may result in unanticipated displacement and force demand particularly in highway bridges due to their complex dynamic characteristics. For this purpose, the present study investigates the effects of TGMs on the inelastic seismic response of continuous concrete box-girder highway bridges with seat type abutments. Three-dimensional finite element (3D FE) models of bridges with varying skew angles, number of bent columns, and column height-to-diameter ratios were developed using OpenSees, and a series of nonlinear response history analyses were conducted. Comparison of seismic response of bridges subjected to only translational and both translational and TGMs revealed that TGMs may result in uneven and asymmetric failure of the shear keys. Therefore, deck rotations are significantly amplified due to induced instantaneous eccentricity when deck comes in contact with shear key(s). The amplified impact forces due to TGMs further amplify the deck rotations, which in return result in higher inelastic displacement and force demand. Last but not the least, the induced torsion due to TGM combined with axial-flexure-shear interactions may result in complex failure modes, higher shear stresses, and reduction in lateral deformation and flexural capacity of the bridge columns.

A comparative study of seismic diaphragm design forces for RC dual system buildings

The reinforced concrete (RC) diaphragm damage observed during the Northridge earthquake (1994) has motivated numerous analytical and experimental studies focused on evaluating the seismic performance of this important building component. The ASCE/SEI 7-16 recently introduced an alternative methodology to determine diaphragm design forces that considered various diaphragm systems. However, this formulation was developed for typical North American structures (on frames or dual systems combined with gravity framing), which substantially differ from other worldwide common typologies that may not include gravity framing. Throughout this study, the accuracy of the existing code provisions and other alternative methods is evaluated by using three-dimensional computer models of eight symmetric-plan reinforced concrete buildings that are between five and 15 stories high and have non-gravity frames (i.e. all frames are part of the seismic force resisting system) for RC-floor systems. These models are subjected to non-linear response history analysis that considers sets of far-field records. Benchmark values, defined as the mean value of the time responses and their dispersion, are compared with the forces of design codes and procedures. General conclusions indicate that existing provisions underestimate diaphragm design forces for all the systems considered, but the results can substantially improve if a low diaphragm reduction factor is used. Alternative procedures capture the magnitude but not the height distribution. Finally, the level of non-linear behavior of the structural elements was verified; beams exhibit high inelastic response, but the overall structure and the vertical elements mostly kept elastic.

Seismic design of low-rise steel building frames with self-centering panels and steel strip braces

This paper develops a practical seismic design approach for an emerging lateral force resisting system consisting of self-centering panels and steel strip braces. The system combines the favorable re-centering feature of conventional self-centering building frames and the energy absorption capacity and high initial stiffness of concentrically braced frames. The system also overcomes the detrimental frame expansion effect that occurs in conventional self-centering building frames. Following the proposed design approach, multiple designs to achieve different performance objectives were performed for a representative three-story building in which the considered lateral force resisting system is used to resist the seismic forces. Nonlinear response history analyses were performed for the designs to evaluate the applicability and adequacy of the proposed design approach. Based on the analyses conducted in this research, it was found that the considered system designed using the proposed approach can meet both transient and residual inter-story drift requirements specified for the selected performance objectives. While an initial design per the proposed design approach may be inadequate, the re-design strategy recommended can help transform the design to an acceptable one after only one round of modification. Moreover, the high-mode effect appears nonnegligible in the considered system and this effect should be considered in the proposed approach through the use of the lateral distribution factor of seismic forces specifically for self-centering systems.