Dynamic FE simulation of four‐story steel frame modeled by solid elements and its validation using results of full‐scale shake‐table test

Dynamic finite element analyses of a four‐story steel building frame modeled as a fine mesh of solid elements are performed using E‐Simulator, which is a parallel finite element analysis software package for precisely simulating collapse behaviors of civil and building structures. E‐Simulator is under development at the National Research Institute for Earth Science and Disaster Prevention (NIED), Japan. A full‐scale shake‐table test for a four‐story frame was conducted using E‐Defense at NIED, which is the largest shaking table in the world. A mesh of the entire structure of a four‐story frame with approximately 19 million degrees of freedom is constructed using solid elements. The density of the mesh is determined by referring to the results of elastic–plastic buckling analyses of a column of the frame using meshes of different densities. Therefore, the analysis model of the frame is well verified. Seismic response analyses under 60, 100, and 115% excitations of the JR Takatori record of the 1995 Hyogoken‐Nanbu earthquake are performed. Note that the simulation does not reproduce the collapse under the 100% excitation of the Takatori record in the E‐Defense test. Therefore, simulations for the 115% case are also performed. The results obtained by E‐Simulator are compared with those obtained by the E‐Defense full‐scale test in order to validate the results obtained by E‐Simulator. The shear forces and interstory drift angles of the first story obtained by the simulation and the test are in good agreement. Both the response of the entire frame and the local deformation as a result of elastic–plastic buckling are simulated simultaneously using E‐Simulator. Copyright © 2014 John Wiley & Sons, Ltd.     

Numerical study of a full‐scale six‐story reinforced concrete wall‐frame structure tested at E‐Defense

A full‐scale shake table test on a six‐story reinforced concrete wall frame structure was carried out at E‐Defense, the world's largest three‐dimensional earthquake simulation facility, in January 2006. Story collapse induced from shear failure of shear critical members (e.g., short columns and shear walls) was successfully produced in the test. Insights gained into the seismic behavior of a full‐scale specimen subjected to severe earthquake loads are presented in this paper. To reproduce the collapse process of the specimen and evaluate the ability of analytical tools to predict post‐peak behavior, numerical simulation was also conducted, modeling the seismic behavior of each member with different kinds of models, which differ primarily in their ability to simulate strength decay. Simulated results showed good agreement with the strength‐degrading features observed in post‐peak regions where shear failure of members and concentrated deformation occurred in the first story. The simulated results tended to underestimate observed values such as maximum base shear and maximum displacement. The effects of member model characteristics, torsional response, and earthquake load dimensions (i.e., three‐dimensional effects) on the collapse process of the specimen were also investigated through comprehensive dynamic analyses, which highlighted the following seismic characteristics of the full‐scale specimen: (i) a model that is incapable of simulating a specimen's strength deterioration is inadequate to simulate the post‐peak behavior of the specimen; (ii) the torsional response generated from uniaxial eccentricity in the longitudinal direction was more significant in the elastic range than in the inelastic range; and (iii) three‐dimensional earthquake loads (X–Y–Z axes) generated larger maximum displacement than any other loading cases such as two‐dimensional (X–Y or Y–Z axes) or one‐dimensional (Y axis only) excitation. Copyright © 2011 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.     

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.     

An experimental study on seismic responses of multifunctional vibration‐absorption reinforced concrete megaframe structures

Two models are tested on a shake‐table. One of the models is a normal reinforced concrete megaframe structure and the other is a multifunctional vibration‐absorption reinforced concrete megaframe structure in which the laminated rubber bearings are placed between the major frame and the minor frames. Two earthquake motions (the El Centro wave and the Taft wave) are used during the test. This paper presents the dynamic characteristic, the seismic responses and the failure mechanism of these two models under varying peak acceleration levels for each of the earthquake motions. The test results demonstrate that the aseismic behavior of a multifunctional vibration‐absorption reinforced concrete megaframe structure is much better than that of a normal reinforced concrete megaframe structure. Copyright © 2003 John Wiley & Sons, Ltd.     

Modal response analysis of multi‐support structures using a random vibration approach

A formulation is developed for modal response analysis of multi‐support structures using a random vibration approach. The spectral moments of the structural response are rigorously decomposed into contributions from spectral moments of uncoupled modal responses. An advantage of the proposed formulation is that the total dynamic response can be obtained on the basis of mode by mode uncoupled analyses. The contributions to the total response from modal responses under individual support ground motions and under cross‐correlated pairs of support ground motions can be recognized explicitly. The application and performance of the formulation is illustrated by means of an example using a well‐established coherency spectrum model and widely known power spectra models, such as white noise and Kanai–Tajimi. The first three spectral moments of displacement, shear, and bending moment responses are computed, showing that the formulation produces the same results as the exact solution. Copyright © 2015 John Wiley & Sons, Ltd.     

Rigid‐plastic models for the seismic design and assessment of steel framed structures

This paper demonstrates the applicability of response history analysis based on rigid‐plastic models for the seismic assessment and design of steel buildings. The rigid‐plastic force–deformation relationship as applied in steel moment‐resisting frames (MRF) is re‐examined and new rigid‐plastic models are developed for concentrically‐braced frames and dual structural systems consisting of MRF coupled with braced systems. This paper demonstrates that such rigid‐plastic models are able to predict global seismic demands with reasonable accuracy. It is also shown that, the direct relationship that exists between peak displacement and the plastic capacity of rigid‐plastic oscillators can be used to define the level of seismic demand for a given performance target. Copyright© 2009 John Wiley & Sons, Ltd.     

Assessment of a capacity spectrum seismic design approach against cyclic and seismic experiments on full‐scale precast RC structures

Within the last decades, simplified methods alternative to dynamic nonlinear analysis have been developed to estimate the seismic performance of structures toward a performance‐oriented design. Considering drift as the main parameter correlated with structural damage, its estimation is of main importance to assess the structural performance. While traditional force‐based design deals with calibrated force reduction factors based on the expected structural ductility, other methods are based on the definition of a viscous damping factor defined as a function of the expected energy dissipated by the structure. An example is the capacity spectrum method. This method can be applied even without any a priori calibration or designer arbitrariness. This allows considering several peculiarities of the seismic behavior of precast structures, which may be influenced by nontraditional hysteresis of connections and members, interaction with the cladding panels, P‐δ effects, etc. The paper aims at verifying the soundness and accuracy of this method through the comparison of its predictions against the results of cyclic and pseudodynamic tests on precast structures, including single‐ and multistory buildings either stiff or flexible, obtained on full‐scale building prototypes tested within the framework of recent research projects (namely, “Precast Structures EC8,” “Safecast,” and “Safecladding”). Two simple methodologies of determination of the equivalent viscous damping from a force‐displacement cycle, based on the dissipated energy in relation to 2 different estimates of the elastic strain energy, are addressed and compared. Comments on the possible use of this procedure for the estimation of the seismic performance of precast structures are provided.     

Sloped multi‐roller isolation devices for seismic protection of equipment and facilities

The rolling motion of mutually orthogonal rollers respectively sandwiched between two bearing plates in which one or both have V‐shaped sloping surfaces makes the sloped rolling‐type isolation device have an excellent in‐plane seismic isolation performance. In this study, the sloped rolling type isolation device in which a single roller moves between two V‐shaped sloping surfaces along each principle horizontal direction is refined by incorporating multi‐roller, built‐in damping, and pounding prevention mechanisms. The associated dynamic behavior is further clarified, and a simplified twin‐flag hysteretic model, which can be easily applied in most commercial computational tools is then proposed. Seismic simulation tests on the refined isolation devices (i.e. the sloped multi‐roller isolation devices) with different design parameters such as sloping angles of bearing plates and built‐in damping capabilities, together with a raised floor system by employing the sloped multi‐roller isolation devices, were conducted. Not only is the efficiency of the sloped multi‐roller isolation devices in seismically protecting the important objects, but also the practicability and accuracy of the proposed simplified numerical model in predicting the seismic responses of the sloped multi‐roller isolation devices is experimentally verified. Copyright © 2014 John Wiley & Sons, Ltd.     

A probabilistic approach for estimating the seismic response of elasto‐plastic SDOF systems

The seismic response of elasto‐plastic structures to both recorded and generated accelerograms is characterized by a large scattering of the results, even for accelerograms with similar peak ground acceleration values and frequency content. According to current code recommendations a design value of the seismic response of an elasto‐plastic structure can be computed as the mean of the responses to a certain number of spectrum‐fitting generated accelerograms. A more effective probabilistic approach is presented herein. It allows the analyst to calculate a design value of the seismic response characterized by a predefined non‐exceedance probability using a limited number of generated accelerograms. The results of the performed analyses are presented in diagrams that can be used for structural design applications. The applicability of the proposed method is demonstrated in the case of an elasto‐plastic structural system and the results are compared with those obtained applying current code recommendations. Copyright © 2005 John Wiley & Sons, Ltd.     

Investigation of the sliding behavior between steel and mortar for seismic applications in structures

The friction developed between a steel base plate and a mortar base contributes shear resistance to the building system during a seismic event. In order to investigate the possible sliding behavior between the base plate and the mortar, a shake table study is undertaken using a large rigid mass supported by steel contact elements which rest on mortar surfaces connected to the shake table. Horizontal input accelerations are considered at various magnitudes and frequencies. The results provide a constant friction coefficient during sliding with an average value of approximately 0.78. A theoretical formulation of the friction behavior is also undertaken. The theoretical equations show that the sliding behavior is dependent on the ratio of the friction force to the input force. The addition of vertical accelerations to the system further complicates the sliding behavior as a result of the varying normal force. This results in a variable friction resistance which is a function of the amplitude, phase, and frequency of the horizontal and vertical input motions. In general, this study showed a consistent and reliable sliding behavior between steel and mortar. Copyright © 2009 John Wiley & Sons, Ltd.     

Numerical and experimental study of the performance of a single‐sided vibro‐impact track nonlinear energy sink

This paper proposes a single‐sided vibro‐impact track nonlinear energy sink (SSVI track NES) as an effective way to mitigate the effects of impulsive and seismic excitation on building structures. The SSVI track NES is a passive energy dissipation device, which consists of a mass moving along a track, the shape of which provides a nonlinear restoring force to the mass. Previous studies have analyzed the track NES, which considers the track shape to be smooth and symmetric. By introducing a discontinuity into the shape of the track (e.g., through impact), energy in the primary structure can be scattered to higher frequency responses where it can be dissipated at a faster rate. First, the SSVI track NES is analytically investigated and numerically optimized base on a two degree‐of‐freedom primary structure. The results of numerical simulations show that the SSVI track NES can be more efficient than both the track NES and tuned mass damper in reducing the response of the primary structure. Based on the analytical studies, the SSVI track NES is experimentally realized and investigated when subjected to both impulse‐like and seismic excitations, confirming the numerical predictions and validating the analytical model of the device. Finally, the robustness of the SSVI track NES is investigated numerically. The results of this investigation indicate that the SSVI track NES remains effective over a broad range of input excitation energy levels, as well as during significant changes in the stiffness of the primary structure. Copyright © 2015 John Wiley & Sons, Ltd.     

多点输入下大跨结构反应谱分析方法研究进展

在大跨度结构的抗震研究领域,多点输入反应谱方法因其形式简洁、物理意义明确、应用方便等优点而获得了广泛重视和迅速发展,并已在一些重大工程项目的抗震分析中得到了应用。本文首先详细阐述了近年来国内外多点输入反应谱分析方法的研究现状;然后介绍了多点输入反应谱法的应用情况,包括基于该方法进行的大跨度结构地震反应分析和抗震可靠度分析;最后,提出了今后研究中一些需要进一步解决的问题。     

Design,test and analysis of a light‐weight dissipative bracing system for seismic protection of structures

The paper deals with the proposal and the experimental validation of a novel dissipative bracing system for the seismic protection of structures; compared with other similar systems, it is characterized by smaller size and weight, which makes it easier to move and to install, as well as particularly suitable to be inserted in light‐framed structures (e.g. steel structures of industrial plants). The proposed system consists of an articulated quadrilateral with steel dissipaters inserted, to be connected by tendons to frame joints; the prototypes have been designed and realized for the seismic protection of a two‐storey, large‐scale, steel frame, specially designed for shaking‐table tests. The paper, after an illustration of the system, and of its design and behaviour, presents the shaking‐table tests carried out. The experimental results have fully validated the proposed system, showing its good performance in controlling the seismic response of framed structures. A numerical non‐linear model, set up and validated on the basis of the physical tests, has been used to help interpreting the experimental results, but also to perform parametrical studies for investigating the influence of the design parameters on the performance of the control system. Copyright © 2006 John Wiley & Sons, Ltd.     

Seismic performance and damage evaluation of a waffle‐flat plate structure with hysteretic dampers through shake‐table tests

Reinforced concrete waffle‐flat plate (WFP) structures present 2 important drawbacks for use as a main seismic resisting system: low lateral stiffness and limited ductility. Yet the former can serve a positive purpose when, in parallel, the flexible WFP structure is combined with a stiff system lending high‐energy dissipation capacity, to form a “flexible‐stiff mixed structure.” This paper experimentally investigates the seismic performance of WFP structures (flexible system) equipped with hysteretic dampers (stiff system) through shake‐table tests conducted on a 2/5‐scale test specimen. The WFP structure was designed only for gravitational loads. The lateral strength and stiffness provided by the dampers at each story were, respectively, about 3 and 7 times greater than those of the bare WFP structure. The mixed system was subjected to a sequence of seismic simulations representing frequent to very rare ground motions. Under the seismic simulations associated with earthquakes having return periods ranging from 93 to 1894 years, the WFP structure performed in the level of “immediate occupancy,” with maximum interstory drifts up to about 1%. The dampers dissipated most (75%) of the energy input by the earthquake.     

Development and validation of p‐y modeling approach for seismic response predictions of highway bridges

This study aims to realistically simulate the seismic responses of typical highway bridges in California with considerations of soil–structure interaction effects. The p‐y modeling approaches are developed and validated for embankments and pile foundations of bridges. The p‐y approach models the lateral and vertical foundation flexibility with distributed p‐y springs and associated t‐z and q‐z springs. Building upon the existing p‐y models for pile foundations, the study develops the nonlinear p‐y springs for embankments based on nonlinear 2D and 3D continuum finite element analysis under passive loading condition along both longitudinal and transverse directions. Closed‐form expressions are developed for two key parameters, the ultimate resistant force p_ult and the displacement y₅₀, where 0.5p_ult is reached, of embankment p‐y models as functions of abutment geometry (wall width and height, embankment fill height, etc.) and soil material properties (wall‐soil friction angle, soil friction angle, and cohesion). In order to account for the kinematic and site responses, depth‐varying ground motions are derived and applied at the free‐end of p‐y springs, which reflects the amplified embankment crest motion. The modeling approach is applied to simulate the seismic responses of the Painter Street Bridge and validated through comparisons with the recorded responses during the 1992 Petrolia earthquake. It is demonstrated that the flexibility and motion amplification at end abutments are the most crucial modeling aspects. The developed p‐y models and the modeling approach can effectively predict the seismic responses of highway bridges. Copyright © 2016 John Wiley & Sons, Ltd.     

Evaluation of vertical seismic response for a large‐scale beam‐supported aqueduct

By the theories of potential flow and structural vibration, the formulae for evaluating the ‘wet’ (with water) frequencies and mode shapes of the beam‐supported aqueduct are derived through a simplified fluid‐structure interaction analysis. The time‐history formulae of structural responses to the vertical seismic excitation are obtained. Applying the response‐spectrum principle, the equivalent vertical earthquake load exerted on the beam and the corresponding effects are also derived. Several illustrative examples are conducted. The analytical results show that: (i) The ‘wet’ frequencies of the structure are lower than the corresponding ‘dry’ (without water) frequencies due to the participating water mass, but the ‘wet’ mode shapes are identical to the corresponding ‘dry’ ones. (ii) The water mass plays an important role in the vertical seismic response, which varies with the different geological sites. For the different seismic inputs, the deeper the water is, the greater are the structural responses. (iii) The vertical seismic effects on the beam are generally not too small to be neglected and should be considered in the structural designs of a beam‐supported aqueduct. Copyright © 2002 John Wiley & Sons, Ltd.     

Comprehensive numerical analysis of fault‐structure systems – Computation of the large‐scale seismic structural response to a given earthquake scenario –

The seismic structural response is affected by temporal and spatial variations in strong ground motion. It can be evaluated through the fault‐structure system: the fault mechanism, wave propagation through the crust, amplification near the surface, and soil‐structure interaction. To analyze this system at high resolution and accuracy, we previously proposed a new multiscale analysis method and numerically verified its validity. However, the problem of the extremely large computation cost of constructing a three‐dimensional numerical model and solving the discretized governing equations still remains. Here, we introduce a new method to resolve these difficulties. By combining this new method with our multiscale analysis, we developed a tool for fault‐structure system analysis. The accuracy of this tool is verified by comparing it to a Green's function solution. Finally, we demonstrate the potential utility of the method by estimating the seismic response of a large and complex underground highway junction in a given earthquake scenario. Copyright © 2011 John Wiley & Sons, Ltd.     

Orthogonal expansion of ground motion and PDEM-based seismic response analysis of nonlinear structures

This paper introduces an orthogonal expansion method for general stochastic processes.In the method,a normalized orthogonal function of time variable t is first introduced to carry out the decomposition of a stochastic process and then a correlated matrix decomposition technique,which transforms a correlated random vector into a vector of standard uncorrelated random variables,is used to complete a double orthogonal decomposition of the stochastic processes. Considering the relationship between the Hartl...     

Verification of system identification utilizing shaking table tests of a full‐scale 4‐story steel building

This paper verifies the feasibility of the proposed system identification methods by utilizing shaking table tests of a full‐scale four‐story steel building at E‐Defense in Japan. The natural frequencies, damping ratios and modal shapes are evaluated by single‐input‐four‐output ARX models. These modal parameters are prepared to identify the mass, damping and stiffness matrices when the objective structure is modelled as a four degrees of freedom (4DOF) linear shear building in each horizontal direction. The nonlinearity in stiffness is expressed as a Bouc–Wen hysteretic system when it is modelled as a 4DOF nonlinear shear building. The identified hysteretic curves of all stories are compared to the corresponding experimental results. The simple damage detection is implemented using single‐input‐single‐output ARX models, which require only two measurements in each horizontal direction. The modal parameters are equivalent‐linearly evaluated by the recursive Least Squares Method with a forgetting factor. When the structure is damaged, its natural frequencies decrease, and the corresponding damping ratios increase. The fluctuation of the identified modal properties is the indirect information for damage detection of the structure. Copyright © 2015 John Wiley & Sons, Ltd.