Inelastic response analysis of reinforced concrete structures using modified force analogy method

A modified force analogy method (MFAM) is developed to simulate the nonlinear inelastic response of reinforced concrete (RC) structures. Beam–column elements with three different plastic mechanisms are utilized to simulate inelastic response caused by moment and shear force. A multi‐linear hysteretic model is implemented to simulate the nonlinear inelastic response of RC member. The P‐Δ effect of the structure is also addressed in MFAM. Static and dynamic inelastic response of structure, damage condition and failure type for structural element, structural limit state and collapse time can also be simulated using MFAM. Compared with the general algorithm, the MFAM provides less computational time especially in the case of large structural system. It is also easier to be written as computer program. Three test data groups, which include cyclic loading test data of a non‐ductile RC bridge column, a two‐storey RC frame, and dynamic collapse test data of a non‐ductile RC portal frame, are selected to confirm the effectiveness of applying MFAM to simulate the inelastic behaviour of structures. Copyright © 2007 John Wiley & Sons, Ltd.     

An improvement to linear‐elastic procedures for seismic performance assessment

An improved linear‐elastic analysis procedure is developed in this paper as a simple approximate method for displacement‐based seismic assessment of the existing buildings. The procedure is mainly based on reducing the stiffness of structural members that are expected to respond in the inelastic range in a single global iteration step. Modal spectral displacement demands are determined from the equal displacement rule. Response predictions obtained from the proposed procedure are evaluated comparatively by using the results of benchmark nonlinear response history analysis, and both the conventional and the multi‐mode pushover analyses. In comparative evaluations, a twelve‐story RC plane frame and a six‐story unsymmetrical‐plan RC frame are employed by using 91 ground motion components. It is observed that the proposed procedure estimates the flexural deformation demands in deformation‐controlled members and the shear forces in force‐controlled members with reasonable accuracy. Copyright © 2010 John Wiley & Sons, Ltd.     

Pushover analysis of reinforced concrete frames considering shear failure at beam-column joints

Since most current seismic capacity evaluations of reinforced concrete(RC) frame structures are implemented by either static pushover analysis(PA) or dynamic time history analysis,with diverse settings of the plastic hinges(PHs) on such main structural components as columns,beams and walls,the complex behavior of shear failure at beam-column joints(BCJs) during major earthquakes is commonly neglected.This study proposes new nonlinear PA procedures that consider shear failure at BCJs and seek to assess the actual damage to RC structures.Based on the specifications of FEMA-356,a simplified joint model composed of two nonlinear cross struts placed diagonally over the location of the plastic hinge is established,allowing a sophisticated PA to be performed.To verify the validity of this method,the analytical results for the capacity curves and the failure mechanism derived from three different full-size RC frames are compared with the experimental measurements.By considering shear failure at BCJs,the proposed nonlinear analytical procedures can be used to estimate the structural behavior of RC frames,including seismic capacity and the progressive failure sequence of joints,in a precise and effective manner.     

基于柔度法的异形截面钢筋混凝土构件非线性分析

钢筋混凝土异形截面构件在住宅建筑中已被广泛应用,但适合此类长细比较小的异形截面构件空间分析模型并不成熟.目前国内外学者提出的基于有限单元柔度法的纤维单元模型,还不能考虑剪切变形对构件刚度的影响,对于短肢剪力墙这类长细比较小的构件是不适用的.本文建立了考虑剪切变形的基于柔度法的弹塑性纤维单元,对L形钢筋混凝土构件进行了算例分析.模拟计算结果与试验结果显示出良好的一致性,L形截面构件在侧力作用下会发生斜弯曲现象,钢筋混凝土构件在纯弯矩作用下杆件具有伸长特性.     

Hybrid experimental performance of a full‐scale two‐story buckling‐restrained braced RC frame

This paper proposes a novel implementation of buckling‐restrained braces (BRB) in new reinforced concrete (RC) frame construction. Seismic design and analysis methods for using a proposed steel cast‐in anchor bracket (CAB) to transfer normal and shear forces between the BRB and RC members are investigated. A full‐scale two‐story RC frame with BRBs (BRB‐RCF) is tested using hybrid and cyclic loading test procedures. The BRBs were arranged in a zigzag configuration and designed to resist 70% of the story shear. The gusset design incorporates the BRB axial and RCF actions, while the beam and column members comply with ACI 318‐14 seismic design provisions. Test results confirm that the BRBs enhanced the RCF stiffness, strength, and ductility. The hysteresis energy dissipation ratios in the four hybrid tests range from 60% to 94% in the two stories, indicating that BRBs can effectively dissipate seismic input energy. When the inter‐story drift ratio for both stories reached 3.5% in the cyclic loading test, the overall lateral force versus deformation response was still very stable. No failure of the proposed steel CABs and RC discontinuity regions was observed. This study demonstrates that the proposed design and construction methods for the CABs are effective and practical for real applications. Copyright © 2016 John Wiley & Sons, Ltd.     

Seismic retrofit of reinforced concrete frames using buckling‐restrained braces with bearing block load transfer mechanism

A new method of retrofitting reinforced concrete (RC) frames with buckling‐restrained braces (BRBs) to improve frame strength, stiffness and energy dissipation is proposed. Instead of typical post‐installed anchors, load is transferred between the BRB and RC frame through compression bearing between an installed steel frame connected to the BRB, and high‐strength mortar blocks constructed at the four corners of the RC frame. This avoids complex on‐site anchor installation, and does not limit the allowable brace force by the anchor strength. Cyclic displacements of increasing amplitudes were imposed on two RC frame specimens retrofitted with different BRB strength capacities. In one of the frames, the bearing blocks were reinforced with wire mesh to mitigate cracking. A third RC frame was also tested as a benchmark to evaluate the retrofit strength and stiffness enhancements. Test results indicate that the proposed method efficiently transferred loads between the BRBs and RC frames, increasing the frame lateral strength while achieving good ductility and energy‐dissipating capacity. When the bearing block was reinforced with wire mesh, the maximum frame lateral strength and stiffness were more than 2.2 and 3.5 times the RC frame without the BRB respectively. The BRB imposes additional shear demands through the bearing blocks to both ends of the RC beam and column member discontinuity regions (D‐regions). The softened strut‐and‐tie model satisfactorily estimated the shear capacities of the D‐regions. A simplified calculation and a detailed PISA3D analysis were shown to effectively predict member demands to within 13.8% difference of the measured test results. Copyright © 2016 John Wiley & Sons, Ltd.     

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

Evaluating 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.     

Experimental and analytical investigations of steel panel dampers for seismic applications in steel moment frames

A ductile Vierendeel frame can be constructed by incorporating steel panel dampers (SPDs) into a moment‐resisting frame (MRF). Thus, the stiffness, strength, and ductility of the lateral force–resisting system can be enhanced. The proposed 3‐segment SPD possesses a center inelastic core (IC) and top and bottom elastic joints. This paper discusses the mechanical properties, capacity design method, and buckling‐delaying stiffeners for the SPDs through the use of cyclic loading tests on 2 specimens. Tests confirm that SPDs' cyclic force vs deformation relationships can be accurately predicted using either the Abaqus or PISA3D model analyses. The paper also presents the capacity design method for boundary beams connected to the SPDs of a typical SPD‐MRF. The seismic performance of an example 6‐story SPD‐MRF is evaluated using nonlinear response history analysis procedures and 240 ground accelerations at 3 hazard levels. Results indicate that under 80 maximum considered earthquake ground accelerations, the mean‐plus‐one standard deviation of the shear deformation of the ICs in the SPDs is 0.055 rad, substantially less than the 0.11 rad deformational capacity observed from the SPD specimens. The experimental cumulative plastic deformation of the proposed SPD is 242 times the yield deformation and is capable of sustaining a maximum considered earthquake at least 8 times before failure. This paper introduces the method of using one equivalent beam‐column element for effective modeling of the 3‐segment SPD. The effects of the IC's relative height and stiffness on the overall SPD's elastic and postelastic stiffness, elastic deformation limits, and inelastic deformational demands are discussed.     

System identification and damage evaluation of degrading hysteresis of reinforced concrete frames

In this study, signal processing approaches and nonlinear identification are used to measure seismic responses of reinforced concrete (RC) structures using the shaking table test. To analyze structural nonlinearity, an equivalent linear system with time‐varying model parameters, singular spectrum analysis to elucidate residual deformation, and wavelet packet transformation analysis to yield the energy distribution among components are adopted to detect the nonlinearity. Then, damage feature extraction is conducted using both the Holder exponent and the Level‐1 detail of the discrete wavelet component. Finally, the modified Bouc‐Wen hysteretic model and the system identification process are employed to the shaking table test data to evaluate the physical parameters, including the stiffness degradation, the strength deterioration and the pinching hysteresis. Finally, the identified stiffness and strength degradation functions from the test data of RC frames in relation to the degree of ground shaking, damage index and the identified nonlinear features are discussed. Based on the proposed method, both signal‐based and model‐based identifications, the relationship between the damage occurrence and severity of structural damage can be identified. Copyright © 2010 John Wiley & Sons, Ltd.     

Accuracy of nonlinear static procedures for the seismic assessment of shear critical structures

The nonlinear behavior of reinforced concrete (RC) members represents a key issue in the seismic performance assessment of structures. Many structures constructed in the 1980s or earlier were designed based on force limits; thus they often exhibit brittle failure modes, strength and stiffness degradation, and severe pinching effects. Field surveys and experimental evidence have demonstrated that such inelastic responses affect the global behavior of RC structural systems. Efforts have been made to consider the degrading stiffness and strength in the simplified nonlinear static procedures commonly adopted by practitioners. This paper investigates the accuracy of such procedures for the seismic performance assessment of RC structural systems. Refined finite element models of a shear critical bridge bent and a flexure‐critical bridge pier are used as reference models. The numerical models are validated against experimental results and used to evaluate the inelastic dynamic response of the structures subjected to earthquake ground motions with increasing amplitude. The maximum response from the refined numerical models is compared against the results from the simplified static procedures, namely modified capacity spectrum method and coefficient method in FEMA‐440. The accuracy of the static procedures in estimating the displacement demand of a flexure‐critical system and shear‐critical system is discussed in detail. Copyright © 2015 John Wiley & Sons, Ltd.     

Seismic collapse analysis of reinforced concrete framed structures using the finite element method

A new finite element code using the Adaptively Shifted Integration (ASI) technique with a linear Timoshenko beam element is applied to the seismic collapse analysis of reinforced concrete (RC) framed structures. This technique can express member fracture as a plastic hinge located at either end of an element with simultaneous release of the resultant forces in the element. Contact between members is also considered in order to obtain results that agree more closely with actual behavior, such as intermediate‐layer failure. By using the proposed code, sufficiently reliable solutions have been obtained, and the results reveal that this code can be used in the numerical estimation of the seismic design of RC framed structures. Copyright © 2003 John Wiley & Sons, Ltd.     

Analytical investigations of seismic responses for reinforced concrete bridge columns subjected to strong near-fault ground motion

Strong near-fault ground motion, usually caused by the fault-rupture and characterized by a pulse-like velocity- wave form, often causes dramatic instantaneous seismic energy (Jadhav and Jangid 2006). Some reinforced concrete (RC) bridge columns, even those built according to ductile design principles, were damaged in the 1999 Chi-Chi earthquake. Thus, it is very important to evaluate the seismic response of a RC bridge column to improve its seismic design and prevent future damage. Nonlinear time history analysis using step-by-step integration is capable of tracing the dynamic response of a structure during the entire vibration period and is able to accommodate the pulsing wave form. However, the accuracy of the numerical results is very sensitive to the modeling of the nonlinear load-deformation relationship of the structural member. FEMA 273 and ATC-40 provide the modeling parameters for structural nonlinear analyses of RC beams and RC columns. They use three parameters to define the plastic rotation angles and a residual strength ratio to describe the nonlinear load- deformation relationship of an RC member. Structural nonlinear analyses are performed based on these parameters. This method provides a convenient way to obtain the nonlinear seismic responses of RC structures. However, the accuracy of the numerical solutions might be further improved. For this purpose, results from a previous study on modeling of the static pushover analyses for RC bridge columns (Sung et al. 2005) is adopted for the nonlinear time history analysis presented herein to evaluate the structural responses excited by a near-fault ground motion. To ensure the reliability of this approach, the numerical results were compared to experimental results. The results confirm that the proposed approach is valid.     

An innovative methodology for seismic retrofitting of existing RC buildings by metal shear panels

In the present paper, the seismic upgrading of existing reinforced concrete (RC) structures by means of steel and pure aluminium shear panels is examined. After a preliminary experimental evaluation of the performance of the bare RC structure, a design approach based on the capacity spectrum method has been developed according to the procedure provided in the ATC 40 American guidelines. First, the geometrical configuration of the applied shear panels has been defined according to simplified analytical relationships, while appropriate steel members have been designed to allow the insertion of shear panels in the existing RC structure. Then, complex finite element models have been implemented in order to check the reliability of the proposed design procedure. Also, a numerical evaluation of the global response of the upgraded structure has been processed aiming at evaluating the interaction between the RC structure and the metal devices. Finally, the effectiveness of the applied shear panels has been proven by means of full‐scale experimental tests, which confirmed the significant improvement of the RC structure performance, in terms of strength, stiffness and deformation capacity. Copyright © 2008 John Wiley & Sons, Ltd.     

Development and validation of a metallic haunch seismic retrofit solution for existing under‐designed RC frame buildings

The feasibility and efficiency of a seismic retrofit solution for existing reinforced concrete frame systems, designed before the introduction of modern seismic‐oriented design codes in the mid 1970s, is conceptually presented and experimentally investigated. A diagonal metallic haunch system is introduced at the beam–column connections to protect the joint panel zone from extensive damage and brittle shear mechanisms, while inverting the hierarchy of strength within the beam–column subassemblies and forming a plastic hinge in the beam. A complete step‐by‐step design procedure is suggested for the proposed retrofit strategy to achieve the desired reversal of strength hierarchy. Analytical formulations of the internal force flow at the beam–column‐joint level are derived for the retrofitted joints. The study is particularly focused on exterior beam–column joints, since it is recognized that they are the most vulnerable, due to their lack of a reliable joint shear transfer mechanism. Results from an experimental program carried out to validate the concept and the design procedure are also presented. The program consisted of quasi‐static cyclic tests on four exterior, ? scaled, beam–column joint subassemblies, typical of pre‐1970 construction practice using plain round bars with end‐hooks, with limited joint transverse reinforcement and detailed without capacity design considerations. The first (control specimen) emulated the as‐built connection while the three others incorporated the proposed retrofitted configurations. The experimental results demonstrated the effectiveness of the proposed solution for upgrading non‐seismically designed RC frames and also confirmed the applicability of the proposed design procedure and of the analytical derivations. Copyright © 2006 John Wiley & Sons, Ltd.     

Damage index based on stiffness degradation of low‐rise RC walls

Widely used damage indices, such as ductility and drift ratios, do not account for the influences of the duration of strong shaking, the cumulative inelastic deformation or energy dissipation in structures. In addition, the formulation and application of most damage indices have until now been based primarily on flexural modes of failure. However, evidence from earthquakes suggests that shear failure or combined shear‐flexure behavior is responsible for a large proportion of failures. Empirical considerations have been made in this paper for evaluating structural damage of low‐rise RC walls under earthquake ground motions by means of a new energy‐based low‐cycle fatigue damage index. The proposed empirical damage index is based on the results of an experimental program that comprised six shake table tests of RC solid walls and walls with openings; results of six companion walls tested under QS‐cyclic loading were used for comparison purposes. Variables studied were the wall geometry, type of concrete, web shear steel ratio, type of web shear reinforcement, and testing method. The index correlates the stiffness degradation and the destructiveness of the earthquake in terms of the duration and intensity of the ground motions. The stiffness degradation model considers simultaneously the increment of damage associated to the low‐cycle fatigue, energy dissipation, and the cumulative cyclic parameters, such as displacement demand and hysteretic energy dissipated. Copyright © 2014 John Wiley & Sons, Ltd.     

A rate‐dependent constitutive model of high damping rubber bearings: modeling and experimental verification

In this study, a constitutive model of high damping rubber bearings (HDRBs) is developed that allows the accurate representation of the force–displacement relationship including rate‐dependence for shear deformation. The proposed constitutive model consists of two hyperelastic springs and a nonlinear dashpot element and expresses the finite deformation viscoelasticity laws based on the classical Zener model. The Fletcher–Gent effect, manifested as high horizontal stiffness at small strains and caused by the carbon fillers in HDRBs, is accurately expressed through an additional stiffness correction factor α in the novel strain energy function. Several material parameters are used to simulate the responses of high damping rubber at various strain levels, and a nonlinear viscosity coefficient η is introduced to characterize the rate‐dependent property. A parameter identification scheme is applied to the results of the multi‐step relaxation tests and the cyclic shear tests, and a three‐dimensional function of the nonlinear viscosity coefficient η with respect to the strain, and strain rate is thus obtained. Finally, to investigate the accuracy and feasibility of the proposed model for application to the seismic response assessment of bridges equipped with HDRBs, an improved real‐time hybrid simulation (RTHS) test system based on the velocity loading method is developed. A single‐column bridge was used as a test bed and HDRBs was physically tested. Comparing the numerical and RTHS results, advantage of the proposed model in the accuracy of the predicted seismic response over comparable hysteretic models is demonstrated. Copyright © 2016 John Wiley & Sons, Ltd.     

钢筋混凝土桥墩刚度和强度折减系数确定

目的是解析地预测钢筋混凝土桥墩在反复荷载作用下的非线性滞回特性。使用实验中得到的力一位移滞回曲线,对随轴压比,配筋率和配箍率的变化而变化的刚度和强度折减系数,进行了回归分析,并提出了其表达式。按照提出的理论力一位移滞回模型,能够预测现存钢筋混凝土桥墩的刚度和强度折减情况。     

Inelastic displacement demand of bridge columns considering shear–flexure interaction

Reinforced concrete bridge columns exhibit complex hysteretic behavior owing to combined action of shear, bending moment, and axial force under multi‐directional seismic shakings. The inelastic displacement of columns can be increased by shear–flexure interaction (SFI). This paper develops a simple yet reliable demand model for estimating the inelastic displacement and ductility based on the nonlinear time history analyses of 24 full‐size columns subject to a suite of near‐fault ground motions. A coupled hysteretic model is used to simulate the shear‐flexure interactive (SFI) behavior of columns and the accumulated material damage during loading reversals, including pinching, strength deterioration, and stiffness softening. Guided by rigorous dimensional analysis, the inelastic displacement responses of bridge columns are presented in dimensionless form showing remarkable order. A dimensionless nonlinearity index is derived taking into account of the column strength, ground motion amplitude, and softening or hardening post‐yield behavior. Strong correlation is revealed between the normalized inelastic displacement and the dimensionless structure‐to‐pulse frequency, the dimensionless nonlinearity index as well as the aspect ratio. Two regressive equations for displacement and ductility demands are proposed and validated against the simulation results. The SFI effects are discussed and included explicitly through the aspect ratio in the proposed model. This study offers a new way to realistically predict the inelastic displacement of columns directly from structural and ground motion characteristics. Copyright © 2010 John Wiley & Sons, Ltd.     

Inelastic earthquake response of single‐story asymmetric buildings: an assessment of simplified shear‐beam models

The inelastic seismic torsional response of simple structures is examined by means of shear‐beam type models as well as with plastic hinge idealization of one‐story buildings. Using mean values of ductility factors, obtained for groups of ten earthquake motions, as the basic index of post‐elastic response, the following topics are examined with the shear‐beam type model: mass eccentric versus stiffness eccentric systems, effects of different types of motions and effects of double eccentricities. Subsequently, comparisons are made with results obtained using a more realistic, plastic hinge type model of single‐story reinforced concrete frame buildings designed according to a modern Code. The consequences of designing for different levels of accidental eccentricity are also examined for the aforementioned frame buildings. Copyright © 2003 John Wiley & Sons, Ltd.     

Collapse of a nonductile concrete frame: Shaking table tests

Post‐earthquake reconnaissance has reported the vulnerability of older reinforced concrete (RC) columns lacking details for ductile response. Research was undertaken to investigate the full‐range structural hysteretic behavior of older RC columns. A two‐dimensional specimen frame, composed of nonductile and ductile columns to allow for load redistribution, was subjected to a unidirectional base motion on a shaking table until global collapse was observed. The test demonstrates two types of column failure, including flexure‐shear and pure flexural failure. Test data are compared with various simplified assessment models commonly used by practicing engineers and researchers to identify older buildings that are at high risk of structural collapse during severe earthquake events. Comparison suggests that ASCE/SEI 41‐06 produces very conservative estimates on load–deformation relations of flexure‐shear columns, while the recently proposed ASCE/SEI 41‐06 update imposes significant modifications on the predictive curve, so that improved accuracy has been achieved. Copyright © 2008 John Wiley & Sons, Ltd.