Response Spectrum Analysis Method Research Articles

A Design of Mechanical Frequency Converter Linear and Non-linear Spring Combination for Energy Harvesting

In this study, the improvement of energy harvesting from wideband vibration with random change by using a combination of linear and nonlinear spring system is investigated. The system consists of curved beam spring for non-linear buckling, which supports the linear mass-spring resonator. Applying shock acceleration generates a snap through action to the buckling spring. From the FEM analysis, we showed that the snap through acceleration from the buckling action has no relationship with the applied shock amplitude and duration. We use this uniform acceleration as an impulse shock source for the linear resonator. It is easy to obtain the maximum shock response from the uniform snap through acceleration by using a shock response spectrum (SRS) analysis method. At first we investigated the relationship between the snap-through behaviour and an initial curved deflection. Then a time response result for non-linear springs with snap through and minimum force that makes a buckling behaviour were obtained by FEM analysis. By obtaining the optimum SRS frequency for linear resonator, we decided its resonant frequency with the MATLAB simulator.

Minimum failure cost-based energy dissipation system designs for buildings in three seismic regions – Part I: Elements of failure cost analysis

This and the companion papers are focused on the optimal utilization of viscous dampers for performance improvement of building structures by minimizing the failure/life-cycle costs. The cost minimization is a natural choice as the primary motivation for introducing the multi-objective performance based design concept in the earthquake engineering community was to reduce the observed unacceptable levels of damage costs in buildings for moderate intensity but more frequent earthquakes. This paper describes an approach to calculate the failure and life-cycle costs associated with different levels of damage and their consequences considering the random occurrences of seismic events and uncertainties in the calculated response. The inter-story drift is used as an effective response variable to define fragilities and failure costs, although it is realized that damage of some components may be better expressed in terms of the acceleration response. Since a life-cycle cost-based optimization methodology could be computationally demanding especially for yielding structures, the use a response spectrum method of analysis is considered for the response and failure cost calculations. Comparison of the numerical results, for three example buildings in Los Angeles, Seattle and Boston, obtained by the approximate response spectrum method and accurate time-stepping method utilizing an ensemble of base motions indicates that the response spectrum methods can provide a good estimate of the failure cost for a quick performance-based evaluation of different design alternatives. The companion paper utilizes this failure cost and performance evaluation approach to determine optimal designs of damping systems.

Study on Seismic Resistant Properties of the Integral Structure after Adding Steel Storey on Top of the Multistoried Brick-Concrete Architecture

The whole quality, stiffness and damping of the structure have changed a lot after retrofitting with steel adding layer. It should make seismic response analysis for the overall structure. Use finite element analysis software SATWE to set up finite element models for a three-layer masonry structure with steel top-adding layer. Bottom layer shear, bottom layer axial force and the horizontal displacement of Y direction are obtained by using response spectrum analysis method and time history analysis method. Analysis results indicate that the stories with sudden change in stiffness show less resistance against the earthquake and require special attention in design. Under earthquakes, the analysis to determine the integrated performance of the structure is necessary.

“STATIC &DYNAMIC ANALYSIS OF MULTISTORY BUILDING USING COMPOSITE STRUCTURE”

Steel concrete composite construction means the concrete slab is connected to the steel beam with the help of shear connectors so that they act as a single unit. In the present work steel concrete composite with RCC options are considered for comparative study of G+15 story commercial building which is situated in earthquake zone-III and for earthquake loading, the provisions of IS: 1893(Part1)-2002 is considered. A three dimensional modeling and analysis of the structure are carried out with the help of SAP 2000 software. Equivalent Static Method of Analysis and Response spectrum analysis method are used for the analysis of both Composite & R.C.C. structures. The results are compared and found that composite structure more economical)

COMPARISON OF BRACINGS AND SHEAR WALLS AS SEISMIC STRENGTHENING METHODS TO BUILDINGS WITH PLAN IRREGULARITIES

Failure of reinforced concrete structures during the past earthquakes has taught us the importance of evaluation of the seismic capacity of the existing buildings. Presence of irregularities is considered as a major deficiency in the seismic behavior of structures. One such forms of irregularity is the presence of re-entrant corners which causes stress concentration due to sudden changes in stiffness and torsion in the buildings due to plan asymmetry. Strengthening the notch of the re-entrant cornered buildings is very essential to ensure a good seismic performance of such buildings. Introduction of bracings and stiff shear walls are the popular methods of strengthening the buildings against their poor seismic performance. This paper aims at comparing the efficiency of these two methods of strengthening of irregular buildings. For this purpose, eight storey buildings are modeled and analyzed by response spectrum and pushover analysis methods using ETABS software. Analysis is carried out for different configurations of bracings and shear walls as strengthening elements with varying stiffness. Results of the analysis confirm the reduction in roof top displacement with the increase in the stiffness of the strengthening elements. Further, for a similar performance level the efficiency and economy of both strengthening methods are compared using a cost comparison analysis. Results of the analysis have showed that shear walls prove to be more economical compared to bracings for a given performance level.

Static and Dynamic Analysis of Concrete Gravity Dam by ANSYS

Dam is the most important building in water conservancy, which generates enormously social and economic benefits in the national economy by providing green energy to all walks of the national daily life, and playing a important role in flood control for the safety of peoples lives and properties. However, as dam outburst will bring disastrous consequences to the downstream place, it is very important to ensure the safety of dam. By the large general software ANSYS for static analysis and the response spectrum analysis method for the dynamic analysis, this paper gives the security evaluation of a RCC gravity dam project, and provides some reference for similar engineering analysis.

Effect of higher modes on the seismic response and design of moment-resisting RC frame structures

Recently, extensive research has been conducted regarding higher-mode effects on the response of multi degree-of-freedom (MDOF) systems. The research has been focused mainly on structures with a lateral force resisting system consisting of slender walls, since these types of buildings are expected to be mostly affected by higher-mode phenomena according to structural dynamics, and simplified expressions have been proposed for slender-wall structures to account for higher-mode response in estimating shear forces. Current seismic design practice assumes the same reduction factor for all modes, even though there is strong evidence that inelasticity affects higher modes of vibration unequally. Additionally, simplified design methods are based only on the fundamental mode of vibration neglecting the effect of higher modes or considering them as elastic. In this paper, higher-mode contributions on the overall response of a nine-storey moment resisting frame (MRF), for which a domination of the first mode is expected, are investigated. The accuracy of a modified Modal Response Spectrum Analysis (mMRSA) method and other available methods is evaluated by comparing the results with the ones of the nonlinear response history analysis. Modal behaviour (reduction) factors are directly calculated for the first three modes and the validity of common assumptions is examined. The assessment of the methods is not restricted to deformations, but is extended to storey inertial forces and shears as well, which have attracted less interest from structural engineers, even though they are considered responsible for numerous structural and non-structural failures during major recent earthquakes and are critical for the design of several structures, such as precast buildings. The results suggest that the storey inertial forces and accelerations at all storeys and shear forces at higher storeys are significantly underestimated by methods neglecting or non-properly accounting for higher modes, even for first-mode dominated structures. The contribution of higher modes depends on the ground motion characteristics, the overstrength associated with each mode and the response quantity examined.

Response Spectrum Analysis of a Large-Span Hangar Subjected to Multi-Dimensional Seismic Inputs

The multi-dimensional seismic response of a single-span hangar was studied by response spectrum analysis method. The lateral displacements of the structure, forces of its supporting columns and its roof structure were calculated and compared with each other for cases of one-, two- and three-dimensional (1D, 2D and 3D) seismic inputs. The results show that, compared with the case of 1D earthquake input, the effects of horizontally 2D earthquake inputs on the internal forces and displacements of its supporting columns in the primary direction of input are obvious when it is along the symmetrical axis of the hangar and their effects in the secondary direction of input are even more important which results in great increases of the internal forces and displacements in that direction. The vertical seismic input has almost no effect on the internal forces and displacements of columns. The internal forces in different parts of the roof structure are controlled by horizontal or vertical inputs, respectively, and, compared with those from horizontally or vertically 1D inputs, the responses from 3D inputs are increased and the effects should be considered in seismic design.

Seismic Performance Reliability Analysis of Frame Structure with Special-Shaped Columns

The displacement response of special-shaped column frame structure on the elasto-plastic state was obtained with the Pushover method. Using Park-Ang model to calculate the damage level of each floor, and then using the improved mean response spectrum analysis method to compute the mean square response of the maximum elasto-plastic structure interlayer displacement and the probability of different damage levels. The result shows that the seismic performance of special-shaped column structure will be better reflected when the structure is analyzed with the methods mentioned above and these methods have some theoretical significance.

Seismic Analysis for the Suspended Converter Valve Tower of the UHV

Based on the ANSYS software, a finite element model of a single converter valve tower of the UHV (Ultra High Volt) is built, the structure dynamic characteristics of the converter valve tower is analyzed by the modal analysis method, the earthquake response of the converter valve tower is calculated by the response spectrum analysis method. The prestress effect and the large deformation effect are taken into account in the calculation process, and the seismic responses under some complex loads which combine the earthquake loads and the gravity load are calculated. The results show that lots of natural frequencies of the converter valve tower, which is designed as a flexible structure, very low. The fundamental vibration modes are pendulum sways in X- and Y-direction. The displacements of the horizontal sway response of the converter valve tower are larger than other direction displacements. This conclusion must be considered in the reasonable arrangement design of the valve hall.

Response of tall cantilever wall buildings to strong pulse type seismic excitation

SUMMARYThis paper investigates the seismic response of tall cantilever wall buildings subjected to pulse type ground motion, with special focus on the relation between the characteristics of ground motion and the higher‐modes of response. Buildings 10, 20, and 40 stories high were designed such that inelastic deformation was concentrated at a single flexural plastic hinge at their base. Using nonlinear response history analysis, the buildings were subjected to near‐fault seismic ground motions and simple closed‐form pulses, which represented distinct pulses within the ground motions. Euler–Bernoulli beam models with lumped mass and lumped plasticity were used to model the buildings. The response of the buildings to the closed‐form pulses fairly matched that of the near‐fault records. Subsequently, a parametric study was conducted for the buildings subjected to three types of closed‐form pulses with a broad range of periods and amplitudes. The results of the parametric study demonstrate the importance of the ratio of the fundamental period of the structure to the period of the pulse to the excitation of higher modes. The study shows that if the modal response spectrum analysis approach is used — considering the first four modes with a uniform yield reduction factor for all modes, and with the square root of sum of squares modal combination rule — it significantly underestimates bending moment and shear force responses. A response spectrum analysis method that uses different yield reduction factors for the first and the higher modes is presented. Copyright © 2011 John Wiley & Sons, Ltd.

Seismic Design and Response of Crane-Supporting and Heavy Industrial Steel Structures

This paper presents an analytical study of the seismic behavior of two different types of industrial buildings; a regular mill-type crane-supporting steel structure and an irregular heavy industrial building housing a vertical mechanical process. For both structures, the seismic response is examined through elastic time-history dynamic analyses in order to validate the predictions from the equivalent static force procedure and the response spectrum analysis method prescribed in current building codes. The analyses also serve to assess the inelastic demand in crane-supporting structure. For the crane-supporting structure, analyses are performed for sites in Montreal and Vancouver in Canada and in Seattle in the United States. The results show that the median horizontal displacement and acceleration from the time-history analyses are generally well predicted by the code analysis methods. Inelastic response in these buildings is likely to develop in the form of buckling of the lower column segment, a failure mode that exhibits limited ductility. For the tall irregular building, the analyses are performed for the Montreal site only. The results show the equivalent static method provides fair displacements estimate, but may lead to unconservative predictions of column and brace forces. Response spectrum analysis method, as prescribed in design codes, appears to provide appropriate prediction of the seismic response of such highly irregular structures. For both building types, a good prediction from response spectrum and time-history analysis methods is possible only when a sufficient number of modes are used.

Probabilistic Risk Assessment of Fan Type Cable Stayed Bridges Against Earthquake Forces

A fragility analysis of a fan type cable stayed bridge using a probabilistic risk analysis (PRA) procedure is presented to determine its probability of failure under random ground motion. Seismic input to the bridge support is considered to be a band-limited white noise at the bedrock. For the response analysis, the bridge deck is modeled as a beam supported on springs at different points. The stiffnesses of the springs are determined by a separate 2D static analysis of the cable—tower—deck system. A continuum method of analysis using dynamic stiffness is used to determine the dynamic properties of the bridges.The responses of the bridge deck are obtained by the response spectrum method of analysis for multiple-degrees-of-freedom system. The fragility analysis includes uncertainties of responses due to the variation in ground motion, material properties, modeling and method of analysis. Uncertainties of the capacity of the structure are considered, such as ductility factor variation and damage concentration effects. Failure of the bridge is assumed to take place when the bridge deck moment at any section within a supported span reaches the yield value. The probability of failure of the bridge deck is determined by the first order second moment (FOSM) reliability method. A three-span double-plane symmetrical cable stayed bridge is used as an illustrative example. The fragility curves for the bridge deck failure are obtained under a number of parametric variations which include ratio of the components of ground motion, spatial correlation of ground motion, angle of incidence of earthquake, ductility ratio and coefficients of variation of the uncertainty factors. The results of the study show that these factors have considerable effect on the probability of failure of the bridge.

11803 摩擦支持部を有する2自由度系の簡易耐震設計法に関する研究(OS5 運動と制御(1),オーガナイズドセッション)

The frictional behaviour is effective for dissipating seismic energy. Therefore, in recent years, the installation of a frictional isolator in industrial facilities has been investigated. In the present paper, the easy estimation of seismic respose for a 2-dof friction system based on a friction response spectrum and modal analysis method are proposed. Moreover, the applicable range of the proposed method is clarified by comparison with the result of non-linear time history analysis. The proposed method can obtain the seismic response of a 2-dof friction system immediately without non-linear time history analysis.

摩擦系応答スペクトルを用いた2自由度摩擦系の地震応答推定(機械力学,計測,自動制御)

The frictional behaviour is effective for dissipating seismic energy. Therefore, in recent years, the installation of a frictional isolator in industrial facilities has been investigated. However, the seismic response of the friction system is obtained only by non-linear time history analysis. A great deal of time is required for non-linear analysis. The present study deals with the easy estimation of seismic response for a multi-dof system with friction. In the previous study, the authors suggested the easy estimation of the seismic response of a 1-dof friction system using a friction response spectrum. In addition, the modal analysis method for a 2-dof friction system when the mass ratio of the structure by support is nearly zero was proposed. First, the present paper proposed the estimation method of a seismic response for a 2-dof friction system based on a friction response spectrum and modal analysis method. Secondly, the applicable range of the proposed method is suggested by comparison with the result of non-linear time history analysis. The proposed method can obtain the seismic response of a 2-dof friction system immediately without non-linear time history analysis.

Applicability of pushover methods for the seismic analysis of single‐column bent viaducts

AbstractAn overview of the applicability of a typical single‐mode pushover method (the N2 method) and two typical multi‐mode pushover methods (the modal pushover analysis (MPA) and incremental response spectrum analysis (IRSA) methods) for the analysis of single column bent viaducts in the transverse direction is presented. Previous research, which was limited to relatively short viaducts supported by few columns, has been extended to longer viaducts with more bents.The single‐mode N2 method is accurate enough for bridges where the effective modal mass of the fundamental mode is at least 80% of the total mass. The applicability of this method depends on (a) the ratio of the stiffness of the superstructure to that of the bents and (b) the strength of the bents. In short bridges with few columns, the accuracy of the N2 method increases as the seismic intensity increases, whereas in long viaducts (e.g. viaducts with lengths greater than 500 m) the method is in general less effective.In the case of the analyzed moderately irregular long viaducts, which are common in construction design practice, the MPA method performed well. For the analysis of bridges where the modes change significantly, depending on the seismic intensity, the IRSA method is in principle more appropriate, unless a viaduct is torsionally sensitive. In such cases, all simplified methods should be used with care. Copyright © 2008 John Wiley & Sons, Ltd.

Seismic Performance of Concentrically Braced Steel Frames in Multistory Buildings with Mass Irregularity

The influence of mass irregularity on building seismic response is examined for an eight-story concentrically braced steel frame with different setback configurations resulting in sudden reductions in plan dimensions and seismic weight along the height of the structure. Three locations of mass discontinuity were considered (25, 50, and 75% of the building height), together with two ratios of seismic weight (200 and 300%). A reference regular structure was also considered for comparison. The design of each structure was performed according to the proposed 2005 National Building Code of Canada NBCC provisions using two analysis methods: The equivalent static force procedure and the response spectrum analysis method. Although severe, the mass irregularity conditions considered in this study were found to have a limited negative impact on the seismic performance of the structures designed with the static analysis method. The performance of irregular structures exhibiting lower performance could be improved by...

A simplified fragility analysis of fan type cable stayed bridges

A simplified fragility analysis of fan type cable stayed bridges using Probabilistic Risk Analysis (PRA) procedure is presented for determining their failure probability under random ground motion. Seismic input to the bridge support is considered to be a risk consistent response spectrum which is obtained from a separate analysis. For the response analysis, the bridge deck is modeles as a beam supported on spring at different points. The stiffnesses of the springs are determined by a separate 2D static analysis of cable-tower-deck system. The analysis provides a coupled stiffness matrix for the spring system. A continuum method of analysis using dynamic stiffness is used to determine the dynamic properties of the bridges. The response of the bridge deck is obtained by the response spectrum method of analysis as applied to multidegree of freedom system which duly takes into account the quasi-static component of bridge deck vibration. The fragility analysis includes uncertainties arising due to the variation in ground motion, material property, modeling, method of analysis, ductility factor and damage concentration effect. Probability of failure of the bridge deck is determined by the First Order Second Moment (FOSM) method of reliability. A three span double plane symmetrical fan type cable stayed bridge of total span 689 m, is used as an illustrative example. The fragility curves for the bridge deck failure are obtained under a number of parametric variations. Some of the important conclusions of the study indicate that (i) not only vertical component but also the horizontal component of ground motion has considerable effect on the probability of failure; (ii) ground motion with no time lag between support excitations provides a smaller probability of failure as compared to ground motion with very large time lag between support excitation; and (iii) probability of failure may considerably increase soft soil condition.

Response Spectrum Analysis of Suspension Bridges for Random Ground Motion

The response spectrum method of analysis for suspension bridges subjected to multicomponent, partially correlated stationary ground motion is presented. The analysis is based on the relationship between the power spectral density function and the response spectrum of the input ground motion and fundamentals of the frequency domain spectral analysis. The analysis duly takes into account the spatial correlation of ground motions between the supports, the quasi-static component of the response, and the modal correlation between different modes of vibration. A suspension bridge is analyzed under a set of important parametric variations in order to (1) compare between the responses obtained by the response spectrum method of analysis and the frequency domain spectral analysis; and (2) investigate the behavior of suspension bridges under seismic excitation. The parameters include the spatial correlation of ground motion, the angle of incidence of the earthquake, the ratio between the three components of ground motion, the number and nature of modes considered in the analysis, and the nature of the power spectral density function of ground motion. It is shown that the response spectrum method of analysis provides a fair estimate of responses under parametric variations considered in the study.

Nonlinear seismic response of reinforced‐concrete free‐standing towers with application to TV towers on flexible foundations

AbstractReinforced‐concrete (R/C) free‐standing towers such as TV towers are often analysed using elastic analyses as fixed‐base cantilever beams, ignoring the effect of soil–structure interaction. To take the capacity of structures after yielding into account, most designers usually prefer to decrease the peak values of the elastic response spectrum for the maximum credible earthquake (MCE) anticipated at the site by a factor called the ductility capacity factor, which varies with the design earthquake level and the structural characteristics of the structure neglecting the effect of supporting soil. To investigate the effect of foundation flexibility on the response of R/C free‐standing towers deforming into their inelastic range during intense ground shaking, a linear sway‐rocking model is applied in numerical modelling of the soil–structure system. The effect of concrete cracking and reinforcement yielding on the elements used in the structure modelling is taken into account by introducing a nonlinear model for R/C frame elements using the moment–curvature (M–ϕ) relation. A method called pseudo‐dynamic analysis is presented to quantify the inelastic seismic response spectrum of a soil–R/C free‐standing system using response spectrum analysis method and push‐over analysis technique. The earthquake responses of cracked and uncracked systems for a practical TV tower and a practical range of soil shear wave velocity are calculated and compared with the objective of understanding how soil–structure interaction influences structural responses. Copyright © 2002 John Wiley & Sons, Ltd.