Equivalent SDOF Research Articles

An Improved Seismic Intensity Measure of Inelastic Spectral Acceleration Based on MPA to Reduce the Dispersion in IDA

We present a new seismic intensity measure (IM) to reduce the dispersion in incremental dynamic analysis (IDA), which commonly use the elastic spectral acceleration as the IM. We propose using the inelastic spectral acceleration based on the principles of modal pushover analysis (MPA) as the seismic IM of ground motion. Unlike other methods of computing inelastic spectral acceleration, this new metric is calculated from the result of equivalent single degree-of-freedom (SDF) systems under the lateral force mode using the uncoupled modal response history analysis procedure. These equivalent SDF systems consider the constantly changing elastic–plastic hysteretic behaviour of the structure itself with different seismic intensities. The results indicate that the improved IDA method can more accurately estimate nonlinear structural responses in many intensity levels covering the entire range of structural responses—all the way from elastic behaviour to global dynamic instability. When the structure enters into the inelastic range, the seismic performance of the IDA’s dispersion using the inelastic spectral acceleration as the seismic IM is better than that using peak ground acceleration or elastic spectral acceleration.

Reduced-order models for vertical human-structure interaction

For slender and lightweight structures, the vibration serviceability under crowd- induced loading is often critical in design. Currently, designers rely on equivalent load models, upscaled from single-person force measurements. Furthermore, it is important to consider the mechanical interaction with the human body as this can significantly reduce the structural response. To account for these interaction effects, the contact force between the pedestrian and the structure can be modelled as the superposition of the force induced by the pedestrian on a rigid floor and the force resulting from the mechanical interaction between the structure and the human body. For the case of large crowds, however, this approach leads to models with a very high system order. In the present contribution, two equivalent reduced-order models are proposed to approximate the dynamic behaviour of the full-order coupled crowd-structure system. A numerical study is performed to evaluate the impact of the modelling assumptions on the structural response to pedestrian excitation. The results show that the full-order moving crowd model can be well approximated by a reduced-order model whereby the interaction with the pedestrians in the crowd is modelled using a single (equivalent) SDOF system.

A linearized approach for the seismic response analysis of flexible cable net structures

Cable net structures are characterized by significant geometrical nonlinear properties. The linear modal superposition method (LMSM), which ignores the effect of nonlinearity, is believed not suitable for the seismic response analysis of this kind of structures. To conquer the drawback of LMSM, a non-iterative linearization method (NILM) is proposed in this paper. An energy parameter named the “stiffness parameter” is utilized in generating the nonlinear equivalent single degree of freedom (ESDF) systems for the dominant vibration modes of cable nets. The nonlinear stiffness of an ESDF system is simulated by a quadratic function about the equivalent displacement. Based on a stochastic linearization process, the relationship between the equivalent linear stiffness and the displacement response of a modal ESDF system is established. Then the structural responses are computed according to the design response spectra through a non-iterative procedure. Finally, the effectiveness of the proposed NILM is illustrated by a numerical example that carried out on a trapezoid-shaped cable net supported curtain wall structure. It is demonstrated that the proposed NILM, which takes the stiffness hardening effect into consideration, could not only yield better results than the LMSM does, but also exhibit satisfying timesaving property over the nonlinear RHA.

RC beams under blast load: Reliability and sensitivity analysis

Abstract The effects of blast loading on structures can be very dangerous: damages and failures are expected with serious threats to structural safety and human life. Materials stresses and strains are often pushed to the limit and the modelling of these phenomena can be very complex. In order to design blast-resistant structures it is very important to determine what are the key parameters of this problem. This paper presents a reliability and parametric analysis of the response of reinforced concrete (RC) beams under blast loads. The main aim is to highlight the key parameters of the problem in order to produce information useful for the design of reliable blast-resistant RC structures. The beam has been idealised as an equivalent SDOF system, in which strain-rate effects are accounted for. This approach is convenient from a computational point of view and it has been validated by a direct comparison with a more sophisticated finite element model and with experimental results found in literature. Then a sensitivity analysis of the parameters involved in beam response under blast load has been developed. Slenderness (which has a direct effect on stiffness) and peak load prove to be the most important parameters, but span length (which has an important influence on the mass) is also a key parameter. Other variables such as concrete strength and reinforcement ratio do not seem to have a strong correlation with the beam response.

Vibration control of platform structures with magnetorheological elastomer isolators based on an improved SAVS law

This paper presents a study on the vibration control of platform structures with magnetorheological elastomer (MRE) isolators. Firstly, a novel MRE isolator design is put forward based on the mechanical properties of MREs, and subsequently a single-degree-of-freedom (SDOF) dynamic model and a multiple-degree-of-freedom (MDOF) dynamic model for platform systems incorporating such isolators are developed. In order to overcome the shortcomings of the conventional on–off control law, an improved semi-active variable stiffness (SAVS) control law is proposed. The proposed SAVS scheme makes full use of the continuously variable stiffness of MREs, and it takes into account the influence of the sampling interval such that the field-dependent restoring force is made to do negative work during the whole sampling interval as far as possible. The results of numerical simulations demonstrate that the improved SAVS control law can achieve better vibration-control effectiveness than the on–off control law. The comparative results are discussed through examining the mechanisms of these two control laws in light of the power spectral density and the energy input. For an MDOF platform a simplified approach is proposed to combine the local response signals with an equivalent SDOF representation to generate the control parameters for individual isolators, and the effectiveness of such a scheme is also verified through numerical simulation.

A nonlinear SDOF model for the simplified evaluation of the displacement demand of low-rise URM buildings

The determination of displacement demands for masonry buildings subjected to seismic action is a key issue in the performance-based assessment and design of such structures. A technique for the definition of single-degree-of-freedom (SDOF) nonlinear systems that approximates the global behaviour of multi-degree-of-freedom (MDOF) 3D structural models has been developed in order to provide useful information on the dependency of displacement demand on different seismic intensity measures. The definition of SDOF system properties is based on the dynamic equivalence of the elastic properties (vibration period and viscous damping) and on the comparability with nonlinear hysteretic behaviour obtained by cyclic pushover analysis on MDOF models. The MDOF systems are based on a nonlinear macroelement model that is able to reproduce the in-plane shear and flexural cyclic behaviour of pier and spandrel elements. For the complete MDOF models an equivalent frame modelling technique was used. The equivalent SDOF system was modelled using a suitable nonlinear spring comprised of two macroelements in parallel. This allows for a simple calibration of the hysteretic response of the SDOF by suitably proportioning the contributions of flexure-dominated and shear-dominated responses. The comparison of results in terms of maximum displacements obtained for the SDOF and MDOF systems demonstrates the feasibility and reliability of the proposed approach. The comparisons between MDOF and equivalent SDOF systems, carried out for several building prototypes, were based on the results of time-history analyses performed with a large database of natural records covering a wide range of magnitude, distance and local soil conditions. The use of unscaled natural accelerograms allowed the displacement demand to be expressed as a function of different ground motion parameters allowing for the study of their relative influence on the displacement demand for masonry structures.

Equivalent Linear Model for Existing Soil-Structure Systems

The concept of equivalent linearization is extended for the soil-structure systems, in which the strength ratio (defined as the ratio of the yielding strength to the elastic strength demand) is known rather than the ductility ratio. The nonlinear soil-structure system is replaced by a linear single-degree-of-freedom (SDOF) system, which can capture the response of the actual system with sufficient accuracy. The dynamic characteristics of the equivalent linear SDOF system are determined through a statistical approach. The super-structure is modeled by an inelastic SDOF system with bilinear behavior, and the homogeneous half space beneath the structure by a discrete model, following the Cone Model. To cover a wide range of soil-structure systems, a comprehensive parametric study is conducted using a set of nondimensional parameters for the soil-structure system. The accuracy of the equivalent linear parameters is then assessed. The results confirm that the proposed equivalent linear model can capture the simultaneous effects of soil-structure interaction (SSI) and nonlinearity in the super-structure concerning the maximum inelastic response of the soil-structure system.

Investigation of Blast Effects on Double-Skinned Composite Steel Tubular Columns

In recent years, concrete filled double skin steel tube (CFDST) members have gained interest due to its attractive properties such as ease of construction, light weight, high strength and good seismic resistance, and thus it is expected that these members have the potential of being used in construction of buildings. However, there is lack of understanding about the inelastic behaviors of CFDST members under blast loads. In this paper, based on the ConWep airblast loading model, the blast resistance of typical circular CFDST columns used in engineering field is investigated and the multiple failure modes of CFDST columns under blast loading are analyzed. The influence of explosive charge weights and column axial loading condition on the response of CFDST columns are investigated through parametric study. Finally, the direct shear and flexural failure modes of CFDST columns are analyzed, and uncoupled P-I (pressure-impulse) diagrams are obtained based on an equivalent single degree of freedom (SDOF) system. This study helps to understand the non-linear behaviors of CFDST columns subjected to blast loading.

Analysis of axially restrained water storage tank under blast loading

The water storage tank was proposed as a multi-functional facade system characterizing energy saving and blast resisting. The energy saving performance, not presented in this paper, has been evaluated by experimental and numerical methods. The aim of this study is to propose simplified methods to reasonably predict the response of water storage tank under blast loading. Based on the equivalent single-degree-of-freedom (SDOF) method, the shock spectrum and dimensionless pressure–impulse (P–I) diagram were established, which can be used to evaluate the damage levels of water storage tanks subject to blast loading. The equivalent SDOF method cannot capture the varying deflection shape of structure during motion, herein the Lagrange equation method that allows for multiple deflection shape functions was proposed to predict the structural response. It was shown that the Lagrange equation method was better than the SDOF method since it could provide conservative predictions in all response regimes. Furthermore, the varying dynamic increase factor (DIF) with strain rate was incorporated into the Lagrange equation method to capture the strain rate effects.

강재압축재의 방폭성능에 대한 중력하중효과의 해석적 연구

Equivalent Single-Degree-of-Freedom(SDOF) analysis, most used for blast-resistant design, does not consider the effects of gravity load on the performance evaluation of blast resistance of structural members. However, since there exists gravity load on columns and walls of structures, the blast resistance of structural members should be evaluated considering gravity load on them. In this paper, an approach to reflect the gravity load effects on the equivalent SDOF analysis for dynamic blast response of structural members is proposed. For this purpose, the parametric studies using finite element analysis were performed by varying maximum blast load, blast load duration, and gravity load with constant the resistance and natural period of a structural member. The finite element analysis results were compared with the equivalent SDOF analysis results and the blast response of the structure member was estimated by conducting finite element analyses for various gravity loads. Finally, a graphical solution for ductility of a structural member with the variables of blast load, gravity load and structural member properties was developed. The blast response of structural members under gravity load could be estimated reasonably and easily by using this graphical solution.

Assessing reparability: simple tools for estimation of costs and performance loss of earthquake damaged reinforced concrete buildings

SummaryTools for assessing building reparability via the estimation of expected performance loss (PL) and associated costs for repair of existing RC building classes damaged by an earthquake are presented. The assessment approach relies on the availability of a number of suitably developed: (i) capacity curves for representative building classes; (ii) curves relating global ductility demand μ to the expected PL for the same classes; and (iii) PL–cost for repair relationship calibrated on database collecting cost data of more than 2300 buildings damaged after 2009 L'Aquila earthquake. The tools are developed applying a simplified procedure involving the simulated design of existing building classes, the assumption of predefined collapse mechanism types and the analyses of the seismic behavior of equivalent SDOF systems representative of ‘intact’ and ‘damaged’ structures after an earthquake. The use of these tools may give useful preliminary indications to decision makers for establishing reparability priorities in the aftermath of damaging earthquakes or to insurance companies to value sound insurance premium for existing building classes. Copyright © 2014 John Wiley & Sons, Ltd.

Free Vibration of the Damping Beam Using Co-simulation Method Based on the MFT

The particle damping technique has been in development for several decades, and has been used successfully in many fields. However, it is difficult to predict its damping characteristics due to complex collisions and friction mechanisms, as well as high non-linear damping characteristics in dense particles. The focus of these current main achievements is centralized on the equivalent single degree of freedom (SDOF) system under free and forced vibration. In this paper, a brand new co-simulation approach for the continuum structure system based on the multiphase flow theory (MFT) of gas solid is developed by the COMSOL Multiphysics live link for MATLAB. A simple continuum structure system, (i.e., the cantilever particle damped beam) is made as an experiment. It is further shown that the damping capacity of a cantilever beam depends not only on the exerted location of the particle damper, but also the quantity of the filling. An experimental verification is performed, and an acceptable accordance is achieved between the theoretical results and the experimental data. It can be shown that the theoretical work in this paper is valid. The co-simulation method simplifies the complicated modelling problem, and offers the possibility to analyse the vibro-acoustic response prediction for complicated particle-damping composite structures.

Experimental study of laminated glass window responses under impulsive and blast loading

Laminated glass panes are widely adopted as blast-resistant glass windows to mitigate the hazard from ejecting fractured glass fragments. The response of laminated glass windows under blast loads is often predicted by equivalent static analysis or simplified equivalent single degree of freedom (SDOF) analysis. The equivalent SDOF and equivalent static analyses are also respectively adopted in UFC and ASTM design guide for glass window designs. Owing to the inherent problems, the SDOF analysis can only predict the global responses of glass windows and the predictions are not necessarily always satisfactory. Therefore the accuracy and applicability of the SDOF analysis is sometimes questioned. Often numerical simulations and/or experimental tests have to be carried out for reliable predictions of laminated glass window responses to blast loads. In this study, experimental tests on laminated glass windows subjected to impact and blast loads were carried out to evaluate the accuracy of available analyses and design methods. Pendulum impact tests were conducted first on laminated panes of various thicknesses. Full-scale field blast tests were performed on laminated glass windows of dimension 1.5 m × 1.2 m. Glass pane deflections were monitored by mechanical linear voltage displacement transducer (LVDT) and high-speed cameras. The responses of the tested windows are compared with the estimations of SDOF models and design standards in this paper. Available blast testing data by other researchers are also included together with the current testing data to evaluate the accuracy of the SDOF and equivalent static analyses defined in the design guides. The adequacy of these simplified approaches in predicting laminated glass window responses to blast loads is discussed.

Shaking table tests of an arch-pillars system and design of strengthening by the use of tie-rods

In arches and vaults, tie-rods play a decisive role in counterbalancing horizontal thrusts produced by both permanent and seismic loadings. In this paper, the effectiveness of flexible tie-rods to improve the seismic response of arch-pillars system is assessed by means of shaking table tests and simple analytical models, developed in the framework of displacement-based design. The reduced scale model, made of rigid blocks with dry joints, has been tested without tie-rod and considering different configurations of strengthening. Both experimental and theoretical results have proved the importance, in particular for this kind of flexible masonry structure, of improving displacement capacity rather then strength, because in this latter case other brittle mechanisms could be activated. The paper shows the possibility of describing the dynamic seismic response of rocking masonry structures, characterized by complex mechanisms made of many blocks and hinges, by an equivalent nonlinear SDOF system.

Analysis of MDOF Pseudo-Dynamic Test Design of High Flexible Structure

In order to point out the main factors in MDOF pseudo-dynamic test design of high-rise flexible, the key points in pseudo-dynamic test design using equivalent MDOF system were analyzed based on the theoretic derivation and numerical simulation, and the problems to notice in test design were pointed out, the pseudo-dynamic test results validity of high piers based on equivalent SDOF system was discussed, and the impact of high mode to the earthquake response of high-rise flexible structure was acquired. The results of numerical simulation of lumped-mass model prove that the contribution of high mode to the displacement of high flexible structure is little, and the displacement is mainly provided by the first-order mode, which is nothing to do with the selection of seismic waves. However, the high mode have great influence on seismic base shear and base moment of high flexible structure, and the influence level is associated with the properties of seismic wave spectrum. Under one specific earthquake wave, the second-order vibration may play a main contribution to seismic base shear and base moment of high-rise flexible structure. Therefore, it is proper to use equivalent two-degree of freedom system in pseudo-dynamic test of high piers. However, if using equivalent SDOF system, the structural displacement response is correct while the strain data and experimental phenomenon may be untrue. The conclusion proposed is significant in guiding the pseudo dynamic test design of high-rise flexible structure and ensuring the rationality of test.

Seismic Fragility Analysis of Lightning Arresterusing Capacity Spectrum Method

Abstract In this paper, seismic fragility analysis of lightning arrester is performed using capacity spectrum method(CSM). Since seismic fragility analysis of structure with many structural members is required to calculate many inelastic responses for several tens or hundreds of ground motions, simple method such as CSM is more appropriate than response history analysis(RHA). In general, accuracy of seismic response evaluated by CSM is less than that by RHA. In order to increase accuracy of CSM, equivalent SDOF method and performance point calculation technique are applied to CSM. Seismic fragility method proposed by Shinozuka et al. is used. In order to evaluate site effect of ground motions on seismic fragility, 60 different site classification earthquakes are selected as input ground motions. From the seismic fragility curves of lightning arrester evaluated by CSM and RHA, it can be observed that the seismic fragility curves evaluated by CSM are very similar to those by RHA. Also, it can be observed that main seismic failure mode of lightning arrest is bushing breakage.

Research on the Static and Dynamic Characteristics of the Sliding Rail Joint Surfaces of the Fe-Based Porous Oily Material

The dynamic characteristics of joint interfaces have significant effect on both static and dynamic behaviors of the whole machine tool structures. A test system for identifying the unit area dynamic characteristic parameters of Fe-based joint interfaces in still and motion states were represented based on Equivalent Single Degree Of Freedom (ESDOF) system theory. Compared with the stiffness and damping parameters in stationary state, the stiffness is reduced and the damping is increased in motion. When the velocity increased, the equivalent stiffness and damping parameters of joint interface are both increased.

Study on Dynamic and Virtual Prototyping of Artillery Ramming Device

In order to create a virtual prototype model to meet the engineering analysis, the dynamical model of ramming device in the automatic loading system is built and solvedby using an equivalent SDOF mechanical model, then three-dimensional model is built and imported to RecurDyn, a simulation software,then the virtual prototype is established completely, the result of simulation show that the virtual prototype model is reasonableand can be used for analysis and research of dynamics.

A Microscale Approach for the Seismic Response of MDOF Structures Including Soil-Foundation-Structure Interaction

In this article, a three-dimensional microscale computational framework utilizing the discrete element method is presented to analyze the seismic response of soil-foundation- MDOF structure systems. The proposed approach is used to explore the response of MDOF structures on a square embedded footing founded on a dry granular deposit. Computational simulations were conducted to investigate the response of the system to several base excitations. The impact of replacing a MDOF structure with its equivalent single degree of freedom (ESDOF) structure while accounting for soil-foundation-structure interaction (SFSI) is investigated. Detrimental or beneficial effect of SFSI on the response is also examined.

Optimal integrated seismic design of structural and viscoelastic bracing‐damper systems

SUMMARYPassive structural control techniques are generally used as seismic rehabilitation and retrofit methodologies for existing structures. A poorly explored and exciting opportunity within structural seismic control research is represented by the possibility to design new structural forms and configurations, such as slender buildings, without compromising the structural performance through an integrated design approach. In this paper, with reference to viscous dampers, an integrated seismic design procedure of the elastic stiffness resources and viscoelastic properties of a dissipative bracing‐damper system is proposed and developed to ensure a seismic design performance, within the displacement‐based seismic design, explicitly taking into account the dynamic behaviour both of the structural and control systems. The optimal integrated seismic design is defined as the combination of the variables that minimizes a suitable index, representing an optimized objective function. Numerical examples of the proposed integrated cost‐effectiveness seismic design approach both on an equivalent SDOF system and a proportionally damped MDOF integrated system are developed defining the design variables, which minimize the cost index. Validation of the effectiveness of the proposed integrated design procedure is carried out by evaluating the average displacement of the time‐history responses to seven unscaled acceleration records selected according to EC8 provisions. Copyright © 2014 John Wiley & Sons, Ltd.