Linear Response Spectrum Analysis Research Articles

Seismic Analysis of High Rise Building with Transfer Floor

A transfer floor is the floor system which supports a vertical as well as lateral load resisting system and transfer its loading to different underneath system. Transfer floor distribute the load from closely spaced columns to the columns with long span. This study presented, a seismic analysis of high rise building with transfer floor. A number of proto type models of high rise building were analyzed using linear response spectrum analysis. The models were analyzed using structural software for building analysis ETABS 2016 software. The analyzed models has transfer slab system at different floor levels in high rise building. In this paper, five different models of 10 storey building had studied by providing a transfer slab at different floor levels such as first floor, second floor, third floor, fourth floor and fifth floor of the building. And the vertical position of transfer slab with respect to building height was investigated. The seismic response of high rise building such as storey shear, storey moment, storey displacement, inter-storey were numerically evaluated. Key Words: Transfer slab, Response spectrum analysis, Storey shear, Storey moment, ETABS 2016.

Critical issues in existing RC deck stiffened arch bridges under seismic actions

Existing Reinforced Concrete arch bridges represent still today an important part of transportation network. The peculiarities of such bridges make particularly complex the assessment of their behaviour under both static and dynamic actions and, therefore, their safety. This work concentrates on a specific arch bridge typology known as the “Maillart –Type Arch Bridges” or “Deck-Stiffened Arch Bridges”, characterized by a very stiff deck beam and a slender and wide vault. As well as for the RC structures designed during 50s of the last century, where some important details for concrete elements were not considered, RC Deck-Stiffened Arch Bridges could be subjected to similar structural deficiencies. Moreover, the current loading conditions provide actions that were not considered in the original design or have changed over the time, such as the seismic actions or the moving loads due to the vehicular traffic.For the evaluation of the main critical issues related to the current performance of the “Maillart–Type Arch Bridges”, this study, starting from a “simulated design” according to the design rules and the mandatory codes in force at the construction time, defines a large building inventory of simulated bridges (3000 samples) characterized by different values of the most significant geometrical parameters. Firstly, each bridge of the inventory is modelled and studied by means of a linear Response Spectrum Analysis (RSA) implemented in the software SAP2000. The large number of structural analyses allowed to investigate the seismic behaviour of such a bridge typology, assess and localize the most frequent failure modes. The results of the RSA allowed developing preliminary fragility functions at the Ultimate Limit State, based on shear or flexural failure of single elements of the bridges. Lastly, Non-Linear Time History Analyses (NLTHA) were carried out on two representative case studies extracted from the simulated inventory and the results were examined in terms of fragility curves obtained according to the Cloud methodology for four Damage States. Despite the different approaches (RSA on large scale and NLTHA on two prototypes), a comparison of the fragility curves for equivalent Damage States was also proposed and a good agreement was found. These fragility curves are a first step for the assessment of the seismic vulnerability of “Maillart–Type Arch Bridges” and can be useful for planning seismic risk mitigation interventions for such a bridge typology.

Seismic responses of hyperbolic cooling towers under horizontal and vertical earthquake

Following the dynamic property analysis and elaboration, linear response spectrum analysis (RSA) and response history analysis (RHA) were conducted on a representative hyperbolic cooling towers (HCT) in present study. The seismic responses in tower shell were illustrated in detail, including the internal force amplitude, modal contribution, influence from damping ratio, comparison of results got from RSA and RHA and especially the latitude distributions of internal forces. The results show that the eigenmodes could be classified in a new method into four types according to their mode shapes and only the lateral bending modes and vertical stretching modes are meaningful for horizontal and vertical earthquake correspondingly. The bending modes and seismic deformation display the same feature which is global lateral bending accompanied by minute circular flow displacement of section. This feature also decides the latitude distributions of internal forces as sine or cosine. Moreover, the following method is also proposed for approximate estimation of internal force amplitudes without time-consuming response history analysis: getting the response spectrums of the selected ground accelerations and then comparing values of response spectrums at the natural period of first lateral bending mode because it is always prime dominant for horizontal seismic responses.

Performance based Dynamic Analysis of Basalt Fiber Reinforced Over Conventional Concrete with Linear Response Spectrum Analysis

Performance based Dynamic Analysis of Basalt Fiber Reinforced Over Conventional Concrete with Linear Response Spectrum Analysis

Importance of Target Spectrum Basis in Earthquake Ground Motion Scaling

AbstractSeismic demand on structures may be estimated using linear response spectrum analysis, linear response history analysis, or nonlinear response history analysis. For response history analysi...

Extended spectrum-based pushover analysis for predicting earthquake-induced forces in tall buildings

Achievements have been made in the development of effective and accurate simplified methods for predicting the seismic demand of tall buildings. However, most of these methods are primarily focused on the estimation of seismic deformation of buildings, while no analysis and calculation of earthquake-induced forces in the structures have been presented. Based on the spectrum-based pushover analysis (SPA) for estimating the seismic demand of tall buildings, where the complicated vibration mode coupling in the nonlinear vibration of structures is simplified, an extended spectrum-based pushover analysis (ESPA) is developed for the fast prediction of earthquake-induced forces of tall buildings. In ESPA, a linear response spectrum analysis procedure is incorporated into SPA to consider the modal combination in the linear stage of vibration. A case study of two high-rise, special steel moment-resisting frame buildings subjected to different levels of ground-motion intensity is conducted to investigate the applicability and accuracy of the ESPA method. Comparisons of the results of earthquake-induced forces are made among ESPA, nonlinear response time history analysis (NLRHA), N2 method, modal pushover analysis (MPA) and consecutive modal pushover analysis (CMP). It is seen that the earthquake-induced forces, including bending moments and shear forces, predicted by the proposed ESPA method agree very well with those of NLRHA.

Analyzing the seismic response of nonlinear cable net structure by the linear response spectrum analysis method

Pre-tensioned cable net systems are being increasingly used in building façades. Due to the geometrical nonlinearities exhibited by the cables, people have to resort to the nonlinear response history analysis approach for analyzing the seismic responses of cable net structures. This article studies the effectiveness of linear response spectrum analysis method for nonlinear cable net systems. An energy-based parameter is used to describe the structural stiffness, based on which the equivalent single-degree-of-freedom systems for cable net structures with various irregularities could be established. By means of a pseudo-energy-equivalent approach, the nonlinear equivalent single-degree-of-freedom systems are transformed into linear ones, whose seismic responses are reasonable approximations of the accurate nonlinear results. It is revealed that the vibrating period of the equivalent linearized system is close to that of the nonlinear equivalent single-degree-of-freedom system, indicating that the nonlinear effects on seismic responses of cable net structures are not serious. Inspired by the theoretical analysis, large-scale numerical computations are carried out to check the accuracy of linear response spectrum analysis for nonlinear cable net structures. In the numerical computation, four cable net models are excited by 80 seismic records. Considering 19 different degrees of earthquake intensity, a total number of 6080 nonlinear response history analyses are executed, and the results are compared with those obtained from the linear response spectrum analysis. From the numerical results, the linear response spectrum analysis yields proper overestimations of seismic responses with errors within 35%, which may lead to slightly conservative yet acceptable designs in engineering practice. Given all the aforementioned discussions, it is concluded that the linear response spectrum analysis method is effective for seismic response analysis and aseismic design of nonlinear cable net structures.

Nonlinear seismic modeling of reinforced concrete cores including torsion

Reinforced concrete (RC) cores are used in many residential multi-story buildings as the primary seismic force resisting system (SFRS). Due to architectural limitations, these buildings are often torsionally flexible. To assess the effect of torsion on the nonlinear seismic response of RC cores, a wide-column model (WCM) with fiber elements is used. The nonlinear warping and the nonlinear biaxial (P-Mx-My) cyclic behaviors of the WCM are validated against experimental results and exhibit excellent agreement. According to modal and linear time history analyses, the model can adequately capture the dynamic characteristics and seismic response of core structures, including torsion. The WCM is then extended to the nonlinear range to perform three-dimensional (3D) time history analyses of a typical RC building structure located in Eastern North America (ENA) that is subjected to high-frequency ground motions. Three different building configurations with increasing torsional flexibility (B=1.7, B=2.1 and B=2.5, according to the current National Building Code of Canada) are studied to investigate the effect of torsion on the seismic behavior. The nonlinear envelopes of key response parameters are similar to the design envelopes obtained from the linear response spectrum analysis of a shell elements model (B=1.7) with proper inelastic force modification factors. Aside from the story torque, the shear and moment demands remain relatively constant, regardless of the torsional flexibility value. The effective shear stiffness must be carefully selected in the WCM to avoid large questionable rotations.

Inelastic Displacement Spectra for Bridges Using the Substitute-Structure Method

AbstractThe design of bridge structures for seismic loading by displacement-based procedures has become preferred over force-based procedures in modern specifications. One key step in displacement-based design (DBD) is the estimation of inelastic displacement. Current AASHTO specifications rely on a linear response spectrum analysis with an amplification factor, Rd, for conventionally designed bridges and on the substitute structure method (SSM) for analysis of isolated bridges to estimate inelastic displacements. Both methods are used in this study for a selected site and target acceleration response spectrum. The procedures for both are outlined in detail. Displacement spectra from nonlinear response history analyses (NLRHA) are generated for seven ground-motion sets and compared to results from the two simplified methods. The SSM is shown to produce inelastic displacement estimates that more closely match NLRHA results than do results from the AASHTO Rd method over a wide range of periods for the speci...

The effects of L’aquila earthquake on the St. Gemma church in Goriano Sicoli: part II—fem analysis

In order to integrate the study undertaken in the companion paper, the main outcomes of a linear response spectrum analysis carried out by the FEM numerical model of the St. Gemma church in Goriano Sicoli are presented in current paper. The proposed model has been calibrated on the basis of ambient vibration tests carried out on the building in the damaged state. Numerical model reliability has been proved by its capability to reproduce the crack pattern observed on the church as it was provoked by the occurred earthquake. The structural response of the church has been investigated by interpreting the stress distribution with the aim of understanding the zone where the major stress concentrations occur. The purpose of the study is to provide useful indications on the main structural vulnerability of this type of building in order to extend the main outcomes to similar churches belonging to the same regional area, in order to get appropriate fragility curves.

Design of Base Isolated School Building with Elastomeric Bearing

In this paper, a school building which is to be located in Coimbatore region is taken. A four storied (G+3) school building having plan dimension of 16m x 54m is considered. The structure is modeled as single degree of freedom. The analysis of the structure is made by linear dynamic response spectrum method and the dynamic responses are found. From linear response spectrum analysis used in this study, the total base shear forces and storey shear forces in the columns and the absolute and relative storey drifts are found and the column having critical value is found judicially. Elastomeric bearing is designed for that column. The aim of this study is to obtain dynamic characteristics which are natural frequencies and mode shape of the structure using modal analysis and to carry out analytical modal analysis of the structure. Response spectrum analysis is carried out. Design procedures used for base isolated systems are discussed and form the basis for preliminary design procedures.

Comparison of shear lag in structural steel building with framed tube and braced tube

Under lateral loads Framed Tube (FT) system exhibits reduction of cantilever efficiency due to the effect of shear lag. Braced Tube (BT) represents a valuable solution to overcome shear lag problems by stiffening the exterior frame with diagonal braced members. This study investigates the effect of shear lag on BT and FT under wind load. Shear lag and top-level displacement results are compared with previous findings by researchers on FT and BT systems. The investigation of the effect of various configurations in BT on the reduction the shear lag is another objective of this study. The efficiency of each structure is evaluated using the linear response spectrum analysis to obtain shear lag. STADD Pro software is used to run the dynamic analysis of the models. Results show there is relatively less shear lag in all the BT configurations compared to the FT structural system. Moreover, the comparison of the obtained result with those derived by previous studies shows that shear lag is not proportional to lateral displacement. With respect to results, optimum BT configuration in term of lower shear lag caused by lateral loads is presented.

A Conceptual Design Approach of Coupled Shear Walls

Earthquake causes considerable damage to a large number of RCC high-rise buildings and tremendous loss of life. Therefore, designers and structural engineers should ensure to offer adequate earthquake resistant provisions with regard to planning, design, and detailing in high-rise buildings to withstand the effect of an earthquake and minimize disaster. As an earthquake resistant system, the use of coupled shear walls is one of the potential options in comparison with moment resistant frame (MRF) and shear wall frame combination systems in RCC high-rise buildings. Furthermore, it is reasonably well established that it is uneconomical to design a structure considering its linear behavior during earthquake. Hence, an alternative design philosophy needs to be evolved in the Indian context to consider the postyield behavior wherein the damage state is evaluated through deformation considerations. In the present context, therefore, performance-based seismic design (PBSD) has been considered to offer significantly improved solutions as compared to the conventional design based on linear response spectrum analysis.

Response spectrum analysis for regular base isolated buildings subjected to near fault ground motions

This paper presents a response spectrum analysis procedure suitable for base isolated regular buildings subjected to near fault ground motions. This procedure is based on the fact that the isolation system may be treated separately since the superstructure behaves as a rigid body on well selected isolation systems. The base isolated building is decomposed into several single-degree of freedom systems, the first one having the total weight of the building is isolated while the remainder when superposed they replicate approximately the behavior of the superstructure. The response of the isolation system is governed by a response spectrum generated for a single isolated mass. The concept of the procedure and its application for the analysis of base isolated structures is illustrated with an example. The present analysis procedure is shown to be accurate enough for the preliminary design and overcomes the limits of applicability of the conventional linear response spectrum analysis.

A novel approach to evaluate the equivalent dynamic stiffness of guy clusters in telecommunication masts under ground excitation

Telecommunication structures are essential components of communication and post-disaster networks and critically important facilities require reliable earthquake-resistant design procedures in seismically active regions. Calculation of the nonlinear seismic response of tall guyed masts using detailed time-step finite element methods is far more complex than linear response spectrum analysis that is routinely used in structural engineering practice. It is recognized that detailed computational procedures are not always necessary, in particular when the goal of the analysis is to provide a global earthquake-resistant design check on a regular structure with predictable response: this is when rational simplified methods are called upon to calculate the seismic demand. However, up until now, no such method exists for tall guyed masts that can account for the dynamic cable–mast interactions which dominate seismic effects in these structures. In the study reported here, the writers explore the dynamic behavior of guy cables under harmonic and seismic support ground motion through detailed computational modeling and propose a novel frequency-dependent method to evaluate the equivalent dynamic stiffness of guy clusters. This development will contribute efficiently towards a new robust rational model of general applicability for simplified seismic analysis of tall guyed telecommunication masts. Detailed numerical simulations involving 57 guy cables from eight existing towers with varying heights of 150–607 m were used in the study. A mathematical procedure was developed to replace the nonlinear time-variant cable stiffness with an equivalent linear frequency-dependent spring/mass system, based on the response spectrum of individual guy cables and the frequency content of the seismic excitation. Comparison of the main response indicators of these equivalent models and the detailed nonlinear finite element analysis results confirmed the reasonable and consistent engineering accuracy of the proposed simplified method with considerable savings in analysis effort.

Evaluation of peak structural responses based on consistent elastic and inelastic design spectra

AbstractMany structures built in seismically active regions are expected to behave nonlinearly during an earthquake event. Because of the complex and cumbersome nature of nonlinear time history structural analysis, more recent research has been focused on a way of producing inelastic response spectra that will accurately estimate the peak structural responses. In this paper, peak acceleration and displacement values for three different two‐dimensional steel frames were determined using linear and nonlinear time history analysis, and the results were then compared with peak responses found using elastic and inelastic response spectrum analysis. In order to compare the accuracy of these methods, 12 ground motions were adjusted using spectral matching to produce 12 different ground motion histories with nearly identical 5% damped elastic design spectra for the University of Utah location in Salt Lake City, as specified by the United States Geological Survey. It was determined that linear response spectrum analysis proves to be a fairly accurate estimate of time history peak responses. While inelastic response spectrum analysis was found to provide a somewhat less accurate estimation of time history peak responses, the method still shows promise as a simpler and less computationally intensive alternative to time history analysis. Copyright © 2009 John Wiley & Sons, Ltd.

Simplified Nonlinear Modeling for Seismic Assessment of Complex Bridges

A common procedure used for the seismic assessment of complex bridges is a three-dimensional linear-response spectrum analysis. The linear nature of such an analysis can lead to erroneous results and misdiagnosis of vulnerable components. Analysis that accounts for the nonlinear behavior of components is desirable, but the human resource effort required to properly model an entire bridge is usually more than what most owners would like to invest. The use of simplified nonlinear modeling as a complement to larger linear models is discussed, providing the engineer with a true sense of structure response during the seismic event. The result is a proper diagnosis of vulnerabilities without a large analytical design effort. Three bridge case studies illustrate examples of nonlinear assessment of retaining walls, reinforced concrete connections, steel members, and viscous damping devices.

Experimental Study on Seismic Responses of Piping Systems With Friction—Part 2: Simplified Analysis Method on the Effect of Friction

Abstract Friction between pipe and support structure is generally known to reduce seismic response of the piping systems. Vibration tests using large-scale piping model with friction support were carried out to evaluate the reduction effect. The piping response was mainly governed by the first modal deformation. The simplified analysis method based on linear response spectrum analysis was developed and confirmed to be applicable. In this method, the reduction effect by friction is treated as equivalent viscous damping ratio. This paper deals with the analysis method, and the comparison between the experimental results and analytical ones.

A Procedure to Incorporate Effects of Seismic Events in a Quasi-Static Piping System Inelastic Analysis

Inelastic analysis of a prototypic liquid metal fast breeder reactor (LMFBR) piping system is generally performed without explicit consideration of time-dependent seismic loading. This paper presents an approximate procedure to simulate dynamic seismic loading as an equivalent static load for inelastic analysis. This procedure utilizes the results of the available linear seismic response spectrum analysis to calculate external (statically equivalent) loads. These statically equivalent loads are selected such that they produce internal forces and moments comparable to those predicted by the linear response spectrum analysis.

Scram and nonlinear reactor system seismic analysis for a liquid metal fast reactor

Earthquake vibrations cause large forces and stresses that can significantly increase the scram time required for safe shutdown of a nuclear reactor. The horizontal deflections of the reactor system components cause impact between the control rods and their guide tubes and ducts. The resulting frictional forces, in addition to other operational forces, delay the travel time of the control rods. To obtain seismic responses of the various reactor system components (for which a linear response spectrum analysis is considered inadequate) and to predict the control rod drop time, a non-linear seismic time history analysis is required. Nonlinearities occur due to the clearances or gaps between various components. When the relative motion of adjacent components is large enough to close the gaps, impact takes place with large impact accelerations and forces. This paper presents the analysis and results for a liquid metal fast rector system which was analyzed for both scram times and seismic responses such as bending moments, accelerations and forces. The reactor system was represented with a one-dimensional nonlinear mathematical model with two degrees of freedom per node (translational and rotational). The model was developed to incorporate as many reactor components as possible without exceeding computer limitations. It consists of 12 reactor components with a total of 71 nodes, 69 beam and pin-jointed elements and 27 gap elements. The gap elements were defined by their clearances, impact spring constants and impact damping constants based on a 50% co-efficient of restitution. The horizontal excitation input to the model was the response of the containment building at the location of the reactor vessel supports. It consists of a 10 sec safe shutdown eathquake (SSE) acceleration-time history at 0.005 sec intervals and with a maximum acceleration of 0.408 g. The analysis was performed with two Westinghouse special purpose computer programs. The first program calculated the reactor system seismic responses and stored the impact forces on tape. The impact forces on the control rod driveline were converted into vertical frictional forces by multiplying them by a coefficient of friction, and then these were used by the second program for the scram time determination. The results give time history plots of various seismic responses, and plots of scram times as a function of control rod travel distance for the most critical scram initiation times. The total scram time considering the effects of the earthquake was still acceptable but about four times longer than that calculated without the eathquake. The bending moment and shear force responses were used as input for the structural analysis (stresses, deflections, fatigue) of the various components, in combination with the other applicable loading conditions.