Inelastic Structural Response Research Articles

Direct Displacement Based Design and Capacity Spectrum Method for Special Moment Resisting Frame

In designing seismic-resistant buildings, it is commonly used Forced-Based Design method. The concept of the Force-Based Design (FBD) method is based on an elastic analysis of the structure and indirectly shows the performance level of the structure towards the effects of the seismic forces. Therefore, it is required an approach that capable of analyzing and evaluating the performance of the inelastic structural response; it is called Performance-Based Design method. This paper uses two methods of Performance-Based Design, there are Direct Displacement-Based Design and Capacity Spectrum Method, by using pushover analysis. The objectives of the research are to analyze and compare the performance level of the building in inelastic condition by using these two methods. The structural model reinforced concrete special moment frames. Seismic design code that used in this study is SNI 1726:2012. The reviewed parameter values are displacement and story drift values, estimated plastic hinge response, and performance level of the building from two methods. As the results, all the parameter values of DDBD analysis are more significant than CSM. DDBD produces the drift and displacement values of 0.668 m with the rebar ratio is more significant than 1.00. While, the CSM produces the drift and displacement values of 0.501 m with the rebar ratio of 1.00. The failure mechanism of both methods indicates the strong column weak beam where the beams should fail before the columns. The structure performance level which refers to ATC-40 indicate that both DDBD method and CSM method are in Damage Control level despite displacement target of the two methods are different which is DDBD produces displacement target of 0.376 m while CSM produces the value of 0.345 m.

Influence of Earthquake Frequency Nonstationarity on Seismic Structural Response

Earthquake ground acceleration records exhibit nonstationarity in both amplitude and frequency content. In order to simplify the random vibration analysis, most earthquake models have often neglected the temporal variation of the frequency content. This is partly because it is difficult to incorporate this variation in ground motion models and also partly because it was believed that it had no substantial effect on structure response. The aim of this paper is to identify the temporal variation in frequency content effects, characterizing the earthquake strong ground motions, on structures. Two comparative stochastic earthquake ground motion models based on the concept of physical spectrum are used to characterize and simulate from a selected ground acceleration record two sets of artificial earthquakes exhibiting similar phases distribution and different frequency contents: the first set presents a time-variant frequency content, and the second has a time-invariant frequency content. Three hysteretic models have been considered, elasto-plastic model (bilinear), Clough’s stiffness degrading model and maximum point-oriented bilinear model. Comparative results are presented to quantify the effects of the time-variant frequency content of earthquake ground motion on the structural response of elastic and inelastic simple systems. It is found that the characteristics of elastic and inelastic structural response depend strongly on the time variation of the frequency content in the seismic input.

Effect of the high frequency components of near-fault ground motions on the response of linear and nonlinear SDOF systems: A moving average filtering approach

In this study, the effect of the high frequency components of near fault ground motions (NFGM) with forward rupture directivity effect (FRDE) on the seismic response of elastic and inelastic SDOF regular (non-isolated) and seismic isolated structures is studied. For this purpose, Moving Average filtering method is used to remove the high frequency content of the NFGM at various filtering levels. The key motive for this effort is to evaluate the appropriateness of representing the NFGMs by decomposed signals or mathematical pulse waveforms. Then, elastic and inelastic SDOF structures with various properties are subjected to the original and filtered NFGM and the responses are compared via elastic and inelastic response spectra. In addition, the efficiency of several pulse models in simulating the actual effect of NFGM on the seismic response of elastic and inelastic SDOF structures is investigated. The analyses results revealed that the high frequency content of NFGM has a significant effect on short period elastic structures and inelastic structures with high yield strength subjected to NFGM with short pulse periods. Furthermore, it is found that popular pulse models available in the literature failed to simulate the effect of the actual NFGM on the response of elastic and inelastic structures.

Effects of soil–structure interaction on inelastic response of torsionally-coupled structures

In this paper, effect of torsion on the inelastic responses of structures resting on a nonlinear flexible medium is studied. Similar studies have shown that soil–structure interaction can result in augmentation of nonlinear responses of lower stories. The focus here is on the plan-wise distribution of inelastic responses of a torsional structure considering soil–structure interaction (SSI). For this purpose, 4, 8, and 12-story steel structures consisting of special moment frames are considered on a relatively soft soil. A nonlinear set of non-uniform springs is used for modeling of SSI. For each building, different structural responses are calculated under 11 suitably scaled earthquake ground motions at the design basis and maximum considered earthquake hazard levels. The mass eccentricity ratio is varied from zero to 30%. The inelastic responses include the story drift ratios and distribution of plastic hinge rotations and performance levels of each story and frame. The results clearly show that SSI increases the drift ratio of the first story up to 30% regardless of the eccentricity value. On the other hand, SSI amplified the cumulative plastic hinge rotation of the upper stories, especially in the taller buildings. The maximum value of amplification exceeded 3 and it was very sensitive to the extent of eccentricity. The local amplification effect of combination of torsion and SSI was much more severe where it reached values over 8 in the outer frames of the buildings, with SSI having the larger share in amplification.

Numerical artifacts associated with Rayleigh and modal damping models of inelastic structures with massless coordinates

SummaryThe paper presents a detailed reexamination of the effects of three damping models on the inelastic seismic response of structures with massless degrees of freedom. The models considered correspond to (a) Rayleigh damping based on current properties (tangent stiffness), (b) Rayleigh damping based on initial properties, and (c) modal damping. The results suggest that some nonzero damping forces/moments at massless DOFs obtained in multistory frames for the case of Rayleigh damping with tangent stiffness may be numerical artifacts rather than a deficiency of the damping model. The results also indicate that significant artificial numerical oscillations in the velocities of the secondary components of MDOF structures are introduced when modal damping or mass‐proportional damping is used.

Optimal design of multiple damped-outrigger system incorporating buckling-restrained braces

The outrigger system is an effective solution in mitigating seismic responses of core-tube-type tall buildings by mobilizing the axial stiffness of the perimeter columns. The concept of damped-outrigger has been proposed which introduces dampers in the outrigger system to dissipate seismic energy. This study investigates the seismic behavior of a damped-outrigger system incorporating buckling-restrained brace (BRB-outrigger). The outrigger effect combined with the energy dissipation mechanism of the buckling-restrained brace (BRB) effectively reduce the seismic response of the building. This study proposes the methods to evaluate the inelastic seismic response of structures with multiple damped-outriggers based on a spectral analysis (SA) procedure. For the structure with BRB-outriggers, the optimal outrigger elevations, and the relationships between the axial stiffness of the BRB, the axial stiffness of the perimeter column, and the flexural rigidity of the core structure in order to minimize the seismic response are the primary research objectives of this study. Analytical models with building heights of 64 m, 128 m, 256 m, and 384 m are used to perform the SA and the nonlinear response history analysis. This study concludes with a design recommendation for preliminary design purposes.

Deep long short-term memory networks for nonlinear structural seismic response prediction

This paper presents a comprehensive study on developing advanced deep learning approaches for nonlinear structural response modeling and prediction. Two schemes of the long short-term memory (LSTM) network are proposed for data-driven structural seismic response modeling. The proposed deep learning model, trained on available datasets, is capable of accurately predicting both elastic and inelastic response of building structures in a data-driven fashion as opposed to the classical physics-based nonlinear time history analysis using numerical methods. In addition, an unsupervised learning algorithm based on a proposed dynamic K-means clustering approach is established to cluster the seismic inputs in order to (1) generate the least but the most informative datasets for training the LSTM and (2) improve the prediction accuracy and robustness of the model trained with limited data. The performance of the proposed approach is successfully demonstrated through three proof-of-concept studies that include a nonlinear hysteretic system, a real-world building with field sensing data, and a steel moment resisting frame. The results show that the proposed LSTM network is a promising, reliable and computationally efficient approach for nonlinear structural response prediction, and offers significant potential in seismic fragility analysis of buildings for reliability assessment.

Seismic Risk Assessment of an Emergency Department of a Chilean Hospital Using a Patient-Oriented Performance Model

After an earthquake, hospital emergency departments need to provide continuous health care services to respond to the eventual sudden increase in injured people. The service performance of an emergency department is influenced by internal factors, such as physical damage and staff availability, and external factors, such as an increased patient arrival rate and disruptions in its supply chain. This research presents a quantification methodology for the performance of the emergency department. The novelty of the proposed approach lies in the explicit integration of the inelastic structural and nonstructural response of the building and damage with its loss of functionality, downtime, and emergency patient treatment rate. A discrete event simulation model is used to model the flow of patients within the different units of the emergency department. The seismic risk is expressed as return periods of exceeding different levels of patient waiting times. Results show that 1,000 and 30,000 accumulated waiting hours correspond to return periods of 100 and 1,000 years, respectively. It is concluded that this model may contribute to improving the risk management of critical emergency department infrastructure.

Estimating inelastic seismic response of reinforced concrete frame structures using a wavelet support vector machine and an artificial neural network

Modern building codes increasingly enforce evaluating the inelastic response of structures to ensure their safety in major seismic events. Although an inelastic dynamic analysis provides the most realistic and accurate measure for the seismic response, its application for large-scale structures is hampered by the excessive computational burden involved. This is particularly the case for the optimization of inelastic structures subjected to dynamic loads using metaheuristic algorithms where numerous analyses are required before the design converges to the optimum. In this regard, developing predictive models with sufficient accuracy will significantly help to reduce the computational demand, thus making the seismic analysis and optimization of large structures more feasible and common practice. Motivated by this need, this paper reports a study on the capabilities of a wavelet weighted least squares support vector machine (WWLSSVM) and a feedforward, backpropagation artificial neural network (ANN) to accurately predict the inelastic seismic responses of structures. The force- and displacement-based seismic responses of an 18-story reinforced concrete frame subjected to different earthquake ground motion records scaled to the design basis earthquake and maximum considered earthquake levels are used to train the models and examine their accuracies. The first three natural periods of the frame and combinations thereof are considered as the inputs for the model. The results indicate that both models exhibit satisfactory prediction performances, with the ANN model having a slight edge on accuracy in most of the cases studied, especially when a smaller number of samples are used for training. A parametric sensitivity analysis shows that the seismic responses predicted by the ANN model generally exhibit less sensitivity to the inputs than do those predicted by the WWLSSVM model. The results also indicate that force- and displacement-based responses exhibit the highest sensitivity to the first and second natural periods, respectively.

On the structural energy distribution and cumulative damage in soil-embedded foundation-structure interaction systems

Repeated cyclic loading is well-known to have detrimental effects on inelastic response of structures. Distribution of structural energy and quantification of cumulative damage effects are very important components in performance-based seismic design approach. On the other hand, soil-foundation-structure interaction effects significantly influence inelastic response of structures through the soil contribution to modification of dynamic characteristics of the structure. Hence, this study focuses on structural energy distribution and cumulative damage effects in structures with embedded foundations considering collective effects of kinematic and inertial interactions. To achieve this goal, a soil-foundation-structure interaction system well suited for parametric study was considered: the soil surrounding the rigid foundation was modelled as a half-space, the embedded foundation was modelled using a stack of discrete disks and applying double cone model concept, and the structure was considered as a single-degree-of-freedom structure. The soil-foundation-structure interaction systems were defined according to key interaction dimensionless parameters and were then analysed subjected to 40 non-pulse far-fault ground motions. It is found that SFSI effects significantly alter total energy, viscous damping energy, and hysteretic damping energy of the structure. The results also show that considering only inertial interaction increases cumulative damage index of the structure while inclusion of kinematic interaction has a decreasing effect. Furthermore, practice-oriented correction factors to cumulative damage index of fixed-base structures are proposed to return cumulative damage index of soil-foundation-structure systems. This study can find use in damage evaluation of existing structures with embedded foundation on soft soils.

On the capacity of high, moderate and low earthquake frequency content to cause global drift ratio at level-2 of structural performance

The earthquake (EQ) frequency content can be high, moderate or low frequency, mainly depends on epicenter’s distance and local soil conditions. The EQ frequency content will affect on the inelastic response of building structures. According to Vision 2000 and FEMA 356 under particular hazard level, the building is expected to perform structural response either fully operational, immediate occupancy, life safety or near collapse. Numerical investigation of 10-stories mid-rise reinforced concrete frame structure subjected to variations of the earthquake frequency contents has been conducted. The building model is assumed to be located at Yogyakarta on the soft soil condition. The building model it was shaken by various EQ frequency contents and maximum ground accelerations (PGA) until approaching the global drift ratio (GDR) of 0.50, 0.75, 1.00, 1.25, 1.50, 1.75 and 2.00 %. Result of investigation show that the EQ high frequency is almost impossible to cause GDR ± 2.0% since it needs PGA as high as 4.01g. Under the possible maximum recorded PGA in the field, the only EQ with low frequency content which has capacity to cause maximum GDR reaches ± 2.0%. or at maximum of structural performance level. Between GDR and overall damage index (ODI) is linearly correlated, however boundaries of the performance levels according to GDR and ODI does not meet at the same point.

Seismic behavior of K-type eccentrically braced frames with high strength steel based on PBSD method

In eccentrically braced steel frames (EBFs), the links are fuse members which enter inelastic phase before other structure members and dissipate the seismic energy. Based on the force-based seismic design method, damages and plastic deformations are limited to the links, and the main structure members are required tremendous sizes to ensure elastic with limited or no damage. Force-based seismic design method is very common and is found in most design codes, it is unable to determine the inelastic response of the structure and the damages of the members. Nowadays, methods of seismic design are emphasizing more on performance-based seismic design concept to have a more realistic assessment of the inelastic response of the structure. Links use ordinary steel Q345 (the nominal yielding strength fy>=345 MPa) while other members use high strength steel (Q460 fy>=460 MPa or Q690 fy>=690 MPa) in eccentrically braced frames with high strength steel combination (HSS-EBFs). The application of high strength steels brings out many advantages, including higher safety ensured by higher strength in elastic state, better economy which results from the smaller member size and structural weight as well as the corresponding welding work, and most importantly, the application of high strength steel in seismic fortification zone, which is helpful to popularize the extensive use of high strength steel. In order to comparison seismic behavior between HSS-EBFs and ordinary EBFs, on the basis of experimental study, four structures with 5, 10, 15 and 20 stories were designed by PBSD method for HSS-EBFs and ordinary EBFs. Nonlinear static and dynamic analysis is applied to all designs. The loading capacity, lateral stiffness, ductility and story drifts and failure mode under rare earthquake of the designs are compared. Analyses results indicated that HSS-EBFs have similar loading capacity with ordinary EBFs while the lateral stiffness and ductility of HSS-EBFs is lower than that of EBFs. HSS-EBFs and ordinary EBFs designed by PBSD method have the similar failure mode and story drift distribution under rare earthquake, the steel weight of HSS-EBFs is 10%-15% lower than ordinary EBFs resulting in good economic efficiency.

An efficient framework for the inelastic performance assessment of structural systems subject to stochastic wind loads

The modeling and estimation of the inelastic response of wind excited structures is attracting growing interest with the introduction of performance-based wind engineering. While frameworks based on direct integration have been widely adopted in earthquake engineering for estimating inelastic responses, the significantly longer duration of typical windstorms, as compared to seismic events, makes this approach extremely computationally challenging in the case of wind excited systems. This is especially true in the case of modern performance-based wind engineering frameworks, which are based on probabilistic metrics estimated through simulation and therefore repeated evaluation of the system. This paper addresses this challenge through the development of a simulation framework based on dynamic shakedown theory. In particular, an efficient path-following algorithm is proposed for estimating not only the shakedown multipliers, but also the plastic strains and deformations associated with occurrence of the state of shakedown. The efficiency with which this information can be estimated for any given wind load time history enables the development of a simulation-based framework, driven by general stochastic wind load models, for the estimation of the system-level inelastic performance of the structure. The validity and practicality of the proposed framework is illustrated on a large-scale case study.

Earthquake response analysis of yielding structures coupled with vertically restrained rocking walls

SummaryThis paper investigates the inelastic response of a yielding structure coupled with a vertically restrained rocking wall. The paper first derives the nonlinear equations of motion of a yielding oscillator coupled with a vertically restrained rocking wall, and the dependability of the one‐degree of freedom idealization is validated against the nonlinear time‐history response analysis of a well‐known nine‐story moment‐resisting steel frame that is coupled with a stepping, vertically restrained rocking wall. While, the coupling of weak building frames with rocking walls is an efficient strategy that controls inelastic deformations by enforcing a uniform interstory‐drift distribution, therefore, avoiding mid‐story failures, the paper shows that even for medium‐rise buildings the effect of vertical tendons on the inelastic structural response is marginal, with the exception of increasing the vertical reactions at the pivoting points of the rocking wall. Accordingly, the paper concludes that for medium‐rise to high‐rise buildings, vertical tendons in rocking walls are not beneficial.

Inelastic response of base-isolated structures subjected to impact

While base isolation provides enhanced structural and non-structural seismic performance, there are still concerns regarding large horizontal displacements in extreme earthquakes. Excessive horizontal displacements may induce detrimental pounding of base-isolated structures against the moat wall or the restraining rim of friction pendulum bearings, resulting in yielding or even collapse of the superstructure. This paper uses a simplified two degrees-of-freedom model to investigate the inelastic responses of various base-isolated superstructure designs subjected to impact. It is found that the stiffness of the superstructure largely dictates its response to the transient impact force. The stiff superstructure is very sensitive to the impact force and develops considerably large ductility demands compared to the case with the absence of impact. However, for the flexible superstructure, the ductility demand is more dependent on system yielding under the input motion and does not increase as dramatically when impact is introduced, indicating that it is less sensitive to impact.

Ground motion scaling for seismic response analysis by considering inelastic response and contribution of the higher modes

This paper proposes a new scaling procedure to consider the inelastic response of structure along with the effect of higher modes in scaling the selected ground motions for seismic response analysis. This is done by obtaining the corresponding inelastic Single-Degree-of-Freedom (SDOF) system of the structure through performing a single-run modal pushover analysis with a load pattern consistent with the combined-modal-story-shear profile obtained from response spectrum analysis. Therefore, the effect of the higher modes and interaction between them in the nonlinear phase are reflected in the inelastic SDOF. The scaling process is performed such that the peak displacement of the inelastic SDOF system under the scaled record matches the inelastic spectral displacement (target displacement). The proposed procedure is evaluated through three regular and one irregular tall building. The results demonstrate the superiority of the proposed procedure in estimating the engineering demand parameters of structures with/without important higher modes effects.

Seismic response analysis of reinforced concrete frames using inelasticity‐separated fiber beam‐column model

SummaryEvaluating the inelastic seismic response of structures accurately is of great importance in earthquake engineering and generally requires refined simulation, which is a time‐consuming process. Because the material nonlinearity generally occurs in a small part of the whole structure, many researches focus on taking advantage of this characteristic to improve the computational efficiency and the inelasticity‐separated finite element method (IS‐FEM) proposed recently provide a generic finite element formulation for solving this kind of problems efficiently. Although the fiber beam‐column element is widely used for the simulation of reinforced concrete (RC) framed structures, the inelastic deformation is often detected in a large part of the numerical model under earthquake excitation so that it is hard to achieve high efficient computation when applying the IS‐FEM to the inelastic response analysis of RC fiber models directly. In this paper, a new numerical scheme for seismic response analysis of RC framed structures model by fiber beam‐column element is proposed based on the IS‐FEM. To implement the RC fiber model for use in IS‐FEM and improve the computational performance of proposed scheme, a method of identifying the local domains with severe section inelasticity level is proposed and a modified Kent‐Park concrete material model is developed. Because the Woodbury formula is adopted as the solver, the global stiffness matrix can keep unchanged throughout the analysis and the main computational effort is only invested on a small matrix representing local inelastic behavior. The numerical examples demonstrate the validity and efficiency of the proposed scheme.

Strip Model Analysis for Steel Plate Shear Walls in Earthquake Resistant Structures

Unstiffened Steel Plate Shear Walls (SPSWs) are very effective structural systems designed to resist lateral forces. SPSW systems consist of thin web plates infilled within frames of steel horizontal and vertical boundary elements. The thin unstiffened web plates are expected to buckle in shear and to develop diagonal tension field after buckling under the action of horizontal loads. For unstiffened steel plates, buckling in shear occurs in the elastic range at low stress levels. This behaviour provides strength, stiffness and ductility and allows to have an appropriate level of energy dissipation through tension yielding of the web plates. This paper assesses the inelastic structural response and behaviour of Steel Plate Shear Wall systems using both a modified strip model approach and a new simplified strip model for only beam connected SPSWs. Both models are developed with plasticity concentrated elements and the performed analyses include the nonlinear behaviour of strips, also considering the compressive forces effects over the strip model elements. This research indicates fundamental aspects of the seismic performance of Steel Plate Shear Wall systems, such as energy dissipation capacity, panel ductility demand, seismic inter-story drift and design load demands in Vertical Boundary Elements (VBE) and Horizontal Boundary Elements (HBE) of the frame. The results obtained from the use of these models are compared with selected experimental and numerical results to enrich the research conclusions.

Co-rotational planar beam element with generalized elasto-plastic hinges

Slender elements in framed structures may undergo large displacement and experience highly nonlinear behavior. This paper presents a two-node co-rotational flexible beam with generalized elasto-plastic hinges at the beam ends. A Condensation procedure is used to remove the internal degrees of freedom so that the formulation is easily incorporated with the standard co-rotational approach. A family of asymmetric and convex yield surfaces of super-elliptic shape is considered for the plastic behavior of the hinges. By varying the roundness factor, an infinite number of yield surfaces are obtained making it possible to select the yield function that best fit experimental data of any type of cross-section and material. The nonlinear response of bolted connections subjected to both bending and axial forces are conveniently modeled with such a yield surface. Discrete constitutive equations for the hinge plastic deformations are derived using the implicit scheme for both smooth and non-smooth cases. Numerical examples demonstrate the accuracy of the model in predicting the large displacement inelastic response of framed structures. Effect of the roundness factor on the ultimate load strongly depends on the structure typology. It was observed that cyclic loading produces pinching effect, cyclic softening and ductile behavior. Those effects are more pronounced with anisotropic yield criteria.

Estimating the response of steel structures subjected to vertical seismic excitation: Idealized model and inelastic displacement ratio

Vertical seismic excitations (VSEs) could induce severe damage to building structures and infrastructural facilities, especially to those with large-spans or long cantilevers. Thus, there is a need in engineering practice for estimating the seismic response of structures under VSEs. In this paper, a tentative investigation on VSEs-induced inelastic response of steel structures is proposed. The structure is transformed into an equivalent single-degree-of-freedom (ESDF) system in an extended pushover process, in which the vertical component of response is included. Considering the influence of gravity, a novel ESDF model with asymmetric vibrating characteristic is established. In this ESDF model, the inelastic response only occurs at the “lower” side of vibration, whereas at the other side, the system keeps elastic. Based on the idealized ESDF model and 53 recorded strong VSEs, the vertical inelastic displacement ratio (IDR) is computed. The averaged IDRs are plotted against the elastic vibrating period T, and fitted by a piece-wise function to generate the IDR spectra, in which the effects of strength reduction factor R and of post-yield stiffness ratio α are accounted for by fitting coefficients. The overall process for estimating the VSE-induced inelastic responses of steel structures, using the extended pushover procedure and the proposed IDR spectra, is summarized. In the numerical example, seismic responses of a large-span space truss subjected to VSEs are computed by means of the nonlinear RHA method and the proposed IDR-based method, respectively, the results demonstrate that the IDR-based method could yield an anticipative estimation of structural responses under severe VSEs. For mid-span displacement, error of the IDR-based method is less than 13.6%; for quantity of yielded member, error is less than 14.2%.