Estimation Accuracy of Absolute Maximum Elasto-Plastic Displacements of MDOF Oscillators Based on a Modal Combination Rule With Post-Yielding Modal Properties and Linear Response Spectrum Values

2018 ◽  
Author(s):  
Tomoyo Taniguchi ◽  
Yoshihiko Toda ◽  
Yusuke Ono ◽  
Kyosuke Mukaibo
Keyword(s):  
Response Spectrum ◽  
Time History ◽  
Degree Of Freedom ◽  
Estimation Accuracy ◽  
Absolute Maximum ◽  
Earthquake Excitation ◽  
Linearized System ◽  
The Absolute ◽  
Plastic Displacement ◽  
Mode 3

Taniguchi, et al. [1] developed an analytical method for evaluating the absolute maximum elasto-plastic displacements of multi-degree-of-freedom (MDOF) oscillators under the action of base excitation based on a modal combination. Its essence is that 1) modal frequencies, shapes and damping during yielding of any member of the MDOF oscillators are readily specified by the modal analysis with the secondary stiffness of the members being yielded, 2) assuming that a bilinear hysteresis may describe the force-displacement relationship of each mode, an equivalently linearized system consisting of a single-degree-of-freedom (SDOF) oscillator is introduced to approximate the absolute maximum elasto-plastic displacement of each mode, 3) the absolute maximum elasto-plastic displacement of the MDOF oscillator is evaluated by the Square Root of Sum of Squares rule (SRSS-rule) by combining the maximum elasto-plastic displacement of each mode approximated by the proposed equivalently linearized system. This study first provides small modification in the equivalently linearized system. Then, employing a couple of MDOF oscillators whose spring at arbitrary storey may yield and an accelerogram, the maximum elasto-plastic displacement of the MDOF oscillator is calculated by the proposed method and is compared with that computed by the time history analysis. Their comparison suggests that the proposed method can reasonably evaluate the absolute maximum elasto-plastic displacement of the MDOF oscillator subjected to earthquake excitation as the conventional SRSS-rule does that for the linear MDOF oscillators.

scholarly journals Mode superposition in multi-degree of freedom systems using earthquake response spectrum data

1962 ◽  
Vol 52 (2) ◽  
pp. 405-416 ◽  
Author(s):  
H. C. Merchant ◽  
D. E. Hudson
Keyword(s):  
Response Spectrum ◽  
Weighted Average ◽  
Strong Motion ◽  
Design Criterion ◽  
Degree Of Freedom ◽  
Dynamic Responses ◽  
Base Shear ◽  
Earthquake Excitation ◽  
True Value ◽  
The Absolute

ABSTRACT Dynamic responses of a series of typical three-degree of freedom structures to strong-motion earthquake excitation were calculated by analog computer techniques and were compared with approximate responses obtained by a superposition of individual modes derived from response spectrum curves. The results indicate that a suitably weighted average of the sum of the absolute values of the individual modes and the square root of the sum of the squares of the modes will give a practical design criterion for the base shear forces in multi-story buildings. For critical designs, this weighted average reduces to the absolute sum of the modes, which is found to be close to the true value for a significantly high proportion of typical earthquake-structure combinations.

scholarly journals High voltage circuit breaker supported on a base isolating tripod for earthquake protection

1989 ◽  
Vol 22 (3) ◽  
pp. 145-154
Author(s):  
B. F. Safi ◽  
L. T. Pham ◽  
M. J. Busby
Keyword(s):  
Response Spectrum ◽  
Circuit Breaker ◽  
Time History ◽  
Degree Of Freedom ◽  
Design Parameters ◽  
Circuit Breakers ◽  
Helical Springs ◽  
Safe Level ◽  
Induced Motion ◽  
Earthquake Protection

The 1987 Bay of Plenty earthquake caused the total destruction of a 220 kV circuit breaker. Failures occurred in the porcelain columns supporting the Interrupter Heads. There are many other circuit breakers of the same type in the national grid. To protect these circuit breakers from earthquake damage, a proposal is made to replace the existing support stand with a base isolating tripod. On the tripod, Helical Springs and oil filled dampers are used to control the earthquake induced motion of the circuit breaker. By controlling this motion the forces on the porcelain support column are reduced to a safe level. The design is modelled using a multi degree of freedom system subjected to Response Spectrum and Time History analyses. The model produces results which are consistent with tests, and confirms the design parameters selected by a single degree of freedom approximation. The result is an economical tripod stand design which is expected to protect the circuit breaker from earthquake ground accelerations up to twice the level of the 1940 El Centro earthquake. This level of earthquake is considerably stronger than the 1987 Bay of Plenty earthquake.

Design Tool for Base-Isolated Structures Modeled as Single-Degree-of-Freedom Oscillators

1997 ◽  
Vol 50 (11S) ◽  
pp. S125-S132
Author(s):  
Gustavo O. Maldonado
Keyword(s):  
Response Spectrum ◽  
Time History ◽  
Design Tool ◽  
Degree Of Freedom ◽  
Iteration Step ◽  
Complex Conjugate ◽  
Equivalent Linearization ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Isolated Structures

A stochastic equivalent linearization technique combined with a ground response spectrum approach is proposed to approximate the inelastic response of base-isolated structures. These structures are modeled by nonlinear oscillators with a single degree of freedom. The main advantage of the proposed methodology is the fast calculation of approximate results in comparison with the slow, but more accurate time history analyses. The Bouc-Wen constitutive model is used to represent the inelastic behavior of the isolators. The equations of motion are linearized by an iterative stochastic technique involving the a-priori unknown response statistics. At each iteration step, the modal contributions from one real and one pair of complex conjugate modes are combined by a response spectrum approach to obtain the maximum responses of interest. The process requires the use of conventional spectra (pseudo-acceleration and relative velocity) as well as the relative displacement spectrum of a massless oscillator. Floor response spectrum results above the isolators are calculated by the proposed approach and are compared against the results obtained by a simulation involving time history analyses.

scholarly journals Development of equivalent linear systems for single-degree-of-freedom structures with magneto-rheological dampers for seismic design application

2017 ◽  
Vol 28 (19) ◽  
pp. 2675-2687 ◽  
Author(s):  
Yunbyeong Chae ◽  
James M Ricles ◽  
Richard Sause
Keyword(s):  
Response Spectrum ◽  
Damping Ratio ◽  
Time History ◽  
Analysis Procedure ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Design Response Spectrum ◽  
Simplified Analysis ◽  
Magneto Rheological

Numerous studies have been conducted for magneto-rheological dampers, but the application of magneto-rheological dampers in seismic design is limited due to the lack of a systematical design procedure. In this article, a simplified analysis procedure is proposed to estimate the response of a single-degree-of-freedom structure with diagonal bracing and a magneto-rheological damper without performing the time history analysis. The proposed simplified analysis procedure is based on the equivalent linear system of a magneto-rheological damper. The equivalent damping ratio and the effective period of the single-degree-of-freedom system are determined from the loss factor and the effective stiffness of the magneto-rheological damper based on the quasi-static model. Design response spectrum is utilized to calculate the displacement of the single-degree-of-freedom system. The equivalent damping ratio and the effective stiffness of the single-degree-of-freedom system are dependent on the displacement of the system; thus, the proposed procedure is iterated until the displacement from the design response spectrum converges. The accuracy of the simplified analysis procedure is evaluated by comparing the estimated response from this procedure with the response from the time history analysis. The results show a good agreement between two methods, demonstrating the robustness of the proposed simplified analysis procedure.

Anti-Seismic Reliability Analysis of Quayside Container Crane

2010 ◽  
Vol 118-120 ◽  
pp. 487-491
Author(s):  
Yu Long Jin ◽  
Tian Xing Wu ◽  
Zeng Guang Li
Keyword(s):  
Reliability Analysis ◽  
Response Spectrum ◽  
Time History ◽  
Earthquake Excitation ◽  
Seismic Reliability ◽  
Container Crane ◽  
Analysis Theory ◽  
History Analysis ◽  
Load Carrying ◽  
Quayside Container Crane

Towards the safety reliability problems of the quayside container crane under earthquake excitations, the anti-seismic reliability analysis has been carried out. Because of hugeness and complexity of the structure, it is absolutely impossible to carry on seismic testing with prototype. Thus, a FEM mechanical model of quayside container crane is presented by using the ANSYS codes. Based on the modal response spectrum method and the time-history analysis theory, the load-carrying performance is investigated under earthquake excitations. The results show that neither the displacement response nor the stress response is large under the earthquake excitation in every direction, which could satisfy seismic design requirements.

An application of spectral techniques

1970 ◽  
Vol 3 (4) ◽  
pp. 173-178
Author(s):  
R. Shepherd ◽  
R. E. McConnel
Keyword(s):  
Response Spectrum ◽  
Time History ◽  
Response Spectra ◽  
Degree Of Freedom ◽  
Elastic Response ◽  
Design Stage ◽  
Seismic Load ◽  
Simple Method ◽  
Conservation Of Energy ◽  
Spectral Techniques

Techniques of seismic load prediction
using response spectra have been in general
used for many years and the normal mode-response spectrum approach forms the background to a majority of modern earthquake resistant design codes. It is widely appreciated that in the general case of multi-degree of freedom systems, extension of the approach to the prediction of structural response in the post-elastic range
is invalid. Consequently analyses based on the system, using a time history of ground acceleration as the excitation, have been developed. However, some structures may be modelled reasonably accurately by a single degree of freedom system and in these circumstances spectral techniques may be applied justifiably to post-elastic seismic response calculations. Predictions of the post-elastic response of a viaduct pier, making use of earthquake response spectra, are described in this paper. A simple method involving consideration of conservation of energy and a second approach based on the reserve energy technique are reviewed and the behaviour predicted by applying each to the proposed pier is compared with the response determined from a computer analysis involving numerical integration of the equations of motion of the system. It is shown that in the case of the particular structure examined the results of the spectral technique considerations are of the same order as those obtained from more complex analyses, thereby supporting the contention that, at least for some structures, estimates of post-elastic seismic behaviour based on response spectra applications may be of value, particularly at the initial design stage when a full computer based analysis may not be warranted.

Analysis of Maximum Elasto-Plastic Response of Multi-Degree-of-Freedom Oscillators Based on a Modal Combination of Equivalently Linearized Response of Each Mode

2016 ◽  
Author(s):  
Tomoyo Taniguchi ◽  
Hiroki Nishiraku ◽  
Yusuke Ono
Keyword(s):  
Analytical Method ◽  
Degree Of Freedom ◽  
Base Excitation ◽  
Plastic Response ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Linearized System ◽  
Plastic Displacement ◽  
Relationship Of ◽  
Force Displacement

This study develops a new analytical method for evaluating maximum elasto-plastic displacement of multi-degree-of-freedom (MDOF) oscillators under the action of base excitation based on a modal combination. The essence is that modal frequencies, shapes and damping during yielding of any member of the MDOF oscillators are readily specified by the modal analysis with the secondary stiffness of the members being yielded. In addition, assuming that a bilinear hysteresis may describe the force-displacement relationship of each mode, an equivalently linearized system consisting of a single-degree-of-freedom (SDOF) oscillator is introduced to approximate maximum elsato-plastic displacement of each mode. Employing the SRSS-rule, the maximum elasto-plastic displacement of the MDOF oscillator subjected to Kobe-NS accelerogram is calculated and compared with that computed by the commercial software. Applicability of the proposed method to evaluating maximum elasto-plastic displacement of the MDOF oscillator is thoroughly discussed.

Seismic response analysis of steel–concrete hybrid wind turbine tower

2021 ◽  
pp. 107754632110075
Author(s):  
Junling Chen ◽  
Jinwei Li ◽  
Dawei Wang ◽  
Youquan Feng
Keyword(s):  
Wind Turbine ◽  
Response Spectrum ◽  
Ground Motions ◽  
Time History ◽  
Seismic Action ◽  
Response Spectrum Method ◽  
Spectrum Method ◽  
Wind Turbine Tower ◽  
Ground Types ◽  
Nonlinear Time History

The steel–concrete hybrid wind turbine tower is characterized by the concrete tubular segment at the lower part and the traditional steel tubular segment at the upper part. Because of the great change of mass and stiffness along the height of the tower at the connection of steel segment and concrete segment, its dynamic responses under seismic ground motions are significantly different from those of the traditional steel tubular wind turbine tower. Two detailed finite element models of a full steel tubular tower and a steel–concrete hybrid tower for 2.0 MW wind turbine built in the same wind farm are, respectively, developed by using the finite element software ABAQUS. The response spectrum method is applied to analyze the seismic action effects of these two towers under three different ground types. Three groups of ground motions corresponding to three ground types are used to analyze the dynamic response of the steel–concrete hybrid tower by the nonlinear time history method. The numerical results show that the seismic action effect by the response spectrum method is lower than those by the nonlinear time history method. And then it can be concluded that the response spectrum method is not suitable for calculating the seismic action effects of the steel–concrete hybrid tower directly and the time history analyses should be a necessary supplement for its seismic design. The first three modes have obvious contributions on the dynamic response of the steel–concrete hybrid tower.

Seismic evaluation of single-storey steel buildings

1999 ◽  
Vol 26 (4) ◽  
pp. 379-394 ◽  
Author(s):  
M S Medhekar ◽  
DJL Kennedy
Keyword(s):  
Seismic Performance ◽  
Response Spectrum ◽  
Time History ◽  
Analytical Models ◽  
Steel Buildings ◽  
Concentrically Braced Frames ◽  
Braced Frame ◽  
Seismic Zones ◽  
Concentrically Braced Frame ◽  
Concentrically Braced

The seismic performance of single-storey steel buildings, with concentrically braced frames and a roof diaphragm that acts structurally, is evaluated. The buildings are designed in accordance with the National Building Code of Canada 1995 and CSA Standard S16.1-94 for five seismic zones in western Canada with seismicities ranging from low to high. Only frames designed with a force modification factor of 1.5 are considered. Analytical models of the building are developed, which consider the nonlinear seismic behaviour of the concentrically braced frame, the strength and stiffness contributions of the cladding, and the flexibility, strength, and distributed mass of the roof diaphragm. The seismic response of the models is assessed by means of a linear static analysis, a response spectrum analysis, a nonlinear static or "pushover" analysis, and nonlinear dynamic time history analyses. The results indicate that current design procedures provide a reasonable estimate of the drift and brace ductility demand, but do not ensure that yielding is restricted to the braces. Moreover, in moderate and high seismic zones, the roof diaphragm responds inelastically and brace connections are overloaded. Recommendations are made to improve the seismic performance of such buildings.Key words: analyses, concentrically braced frame, dynamic, earthquake, flexible diaphragm, low-rise, nonlinear, seismic design, steel.

Seismic Vulnerability Analysis of FRP Retrofitting Industrial Buildings

2015 ◽  
Vol 724 ◽  
pp. 353-357
Author(s):  
Jian Zhu ◽  
Ping Tan ◽  
Pei Ju Chang
Keyword(s):  
Seismic Vulnerability ◽  
Response Spectrum ◽  
Time History ◽  
Seismic Intensity ◽  
Fiber Reinforced Polymers ◽  
Infill Wall ◽  
Intensity Index ◽  
Industrial Buildings ◽  
Dynamic Time ◽  
Masonry Infill Wall

This study focus on derivation of such vulnerability curves using Fiber Reinforced Polymers technologies retrofitted conventional RC industrial frames with masonry infill wall. A set of stochastic earthquake waves which compatible with the response spectrum of China seismic code are created. Dynamic time history analysis is used to compute the random sample of structures. Stochastic damage scatter diagrams based different seismic intensity index are obtained. Seismic vulnerability of FRP-reinforced RC industrial frames is lower than unreinforced frames obviously, and seismic capability of frames using FRP technologies is enhanced especially under major earthquake.

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