Response of Complex Structures From Reed-Gage Data

1958 ◽  
Vol 25 (4) ◽  
pp. 501-508
Author(s):  
Sheldon Rubin
Keyword(s):  
Vibrational Mode ◽  
Complex Structure ◽  
Structural Response ◽  
Complex Structures ◽  
General Applicability ◽  
Single Degree Of Freedom ◽  
Peak Response ◽  
Transient Motion ◽  
Single Degree ◽  
Recorded Data

Abstract The paper considers the general applicability of the reed gage, an instrument which records the peak response to a transient motion of single-degree-of-freedom systems. These recorded data permit the calculation of peak response in each vibrational mode of a complex structure experiencing the measured excitation as a base motion. An upper bound to the maximum structural response can be obtained by summing the peak responses in each of the modes. An analysis is made of the error inherent in this superposition process. In many practical problems the distribution of mode frequencies and the form of the excitation are such that this error is not of great significance.

Single-Degree-of-Freedom Based Pressure-Impulse Diagrams for Blast Damage Assessment

2014 ◽  
Vol 567 ◽  
pp. 499-504 ◽  
Author(s):  
Zubair Imam Syed ◽  
Mohd Shahir Liew ◽  
Muhammad Hasibul Hasan ◽  
Srikanth Venkatesan
Keyword(s):  
Damage Assessment ◽  
Structural Response ◽  
Blast Loading ◽  
Computational Effort ◽  
Degree Of Freedom ◽  
Negative Phase ◽  
Single Degree Of Freedom ◽  
Pressure Impulse ◽  
Single Degree ◽  
Structural Resistance

Pressure-impulse (P-I) diagrams, which relates damage with both impulse and pressure, are widely used in the design and damage assessment of structural elements under blast loading. Among many methods of deriving P-I diagrams, single degree of freedom (SDOF) models are widely used to develop P-I diagrams for damage assessment of structural members exposed to blast loading. The popularity of the SDOF method in structural response calculation in its simplicity and cost-effective approach that requires limited input data and less computational effort. The SDOF model gives reasonably good results if the response mode shape is representative of the real behaviour. Pressure-impulse diagrams based on SDOF models are derived based on idealised structural resistance functions and the effect of few of the parameters related to structural response and blast loading are ignored. Effects of idealisation of resistance function, inclusion of damping and load rise time on P-I diagrams constructed from SDOF models have been investigated in this study. In idealisation of load, the negative phase of the blast pressure pulse is ignored in SDOF analysis. The effect of this simplification has also been explored. Matrix Laboratory (MATLAB) codes were developed for response calculation of the SDOF system and for repeated analyses of the SDOF models to construct the P-I diagrams. Resistance functions were found to have significant effect on the P-I diagrams were observed. Inclusion of negative phase was found to have notable impact of the shape of P-I diagrams in the dynamic zone.

scholarly journals An approach to quantify the influence of ground motion uncertainty on elastoplastic system acceleration in incremental dynamic analysis

2017 ◽  
Vol 20 (11) ◽  
pp. 1744-1756 ◽  
Author(s):  
Peng Deng ◽  
Shiling Pei ◽  
John W. van de Lindt ◽  
Hongyan Liu ◽  
Chao Zhang
Keyword(s):  
Dynamic Analysis ◽  
Ground Motion ◽  
Earthquake Engineering ◽  
Structural Response ◽  
Incremental Dynamic Analysis ◽  
Degree Of Freedom ◽  
Maximum Acceleration ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Performance Based Earthquake Engineering

Inclusion of ground motion–induced uncertainty in structural response evaluation is an essential component for performance-based earthquake engineering. In current practice, ground motion uncertainty is often represented in performance-based earthquake engineering analysis empirically through the use of one or more ground motion suites. How to quantitatively characterize ground motion–induced structural response uncertainty propagation at different seismic hazard levels has not been thoroughly studied to date. In this study, a procedure to quantify the influence of ground motion uncertainty on elastoplastic single-degree-of-freedom acceleration responses in an incremental dynamic analysis is proposed. By modeling the shape of the incremental dynamic analysis curves, the formula to calculate uncertainty in maximum acceleration responses of linear systems and elastoplastic single-degree-of-freedom systems is constructed. This closed-form calculation provided a quantitative way to establish statistical equivalency for different ground motion suites with regard to acceleration response in these simple systems. This equivalence was validated through a numerical experiment, in which an equivalent ground motion suite for an existing ground motion suite was constructed and shown to yield statistically similar acceleration responses to that of the existing ground motion suite at all intensity levels.

Probability Distribution of Bilinear System Response to Impulse Excitation

1966 ◽  
Vol 33 (2) ◽  
pp. 384-386
Author(s):  
Stephen F. Felszeghy ◽  
William T. Thomson
Keyword(s):  
Probability Distribution ◽  
Bilinear System ◽  
Degree Of Freedom ◽  
System Response ◽  
Single Degree Of Freedom ◽  
Peak Response ◽  
Single Degree ◽  
Impulse Excitation ◽  
Peak Value

A single-degree-of-freedom system with a bilinear spring is excited by a rectangular impulse of constant value, but whose amplitude has a probability distribution which is Gaussian. The peak response of the system under this excitation is determined, and its probability distribution is plotted as a function of its peak value.

The Random Response of a Single Degree of Freedom Generalized Maxwell Damping Structure

2015 ◽  
Vol 744-746 ◽  
pp. 1648-1653
Author(s):  
Wan Jie Zou ◽  
Chuan Gao Li ◽  
Yun Xia Zhang
Keyword(s):  
Laplace Transform ◽  
Structural Response ◽  
Second Order ◽  
Degree Of Freedom ◽  
Inverse Laplace Transform ◽  
Maximum Response ◽  
Random Response ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Response Variance

Using the model of stationary white noise excitation, defining the exact analytic method of random response and nearer value of earthquake action about single degree of freedom generalized Maxwell damping, firstly transform the motion equation into standard form, with the Laplace transform and Inverse Laplace transform method, obtained the exact analytical formula of structural response, calculate the response variance by the complex modal method and frequency domain decomposition and make comparisons, The response variance decomposition for the first standard vibrator and second order of the standard vibrator, According to the corresponding relationship between maximum response of the second order vibrator and The design response spectrum, calculated the maximum response by it, base on the maximum response proportion of the first standard vibrator and second, obtained the design of the structural response values and its corresponding earthquake force.

Inelastic Structural Response to Cascadia Subduction Zone Earthquakes

1995 ◽  
Vol 11 (1) ◽  
pp. 63-89 ◽  
Author(s):  
M. Lee Marsh ◽  
Christopher M. Gianotti
Keyword(s):  
Subduction Zone ◽  
Structural Response ◽  
Degree Of Freedom ◽  
Cascadia Subduction Zone ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Energy Demands ◽  
Cyclic Displacement ◽  
Energy Dissipated ◽  
Subduction Zone Earthquakes

The effects of postulated Cascadia subduction zone earthquakes on inelastic structural response are examined. The earthquakes considered ranged in size from those previously recorded to the largest plausible event, a magnitude 9.5 earthquake. Artificial acceleration records were generated and used as input for inelastic response history analyses of single-degree-of-freedom systems with bilinear or degrading stiffness hysteretic relationships. The results indicate that the maximum displacements are not significantly greater than those produced by previously recorded events. The inelastic energy dissipated and the numbers of displacement cycles are somewhat greater for the largest events, although the energy demands and the cyclic displacement demands are similar to those from the recorded events for magnitudes up to 8.5.

Spectral Variability and Its Relationship to Structural Response Estimated from Scaled and Spectrum-Matched Ground Motions

2016 ◽  
Vol 32 (4) ◽  
pp. 2191-2205 ◽  
Author(s):  
A. E. Seifried ◽  
J. W. Baker
Keyword(s):  
Response Spectrum ◽  
Ground Motions ◽  
Structural Response ◽  
Degree Of Freedom ◽  
Structural Systems ◽  
Spectral Variability ◽  
Single Degree Of Freedom ◽  
Inelastic Response ◽  
Single Degree ◽  
Spectral Dispersion

Conditional spectral dispersion ( CSD) is a measure of response spectrum variability that implicitly characterizes the variety of spectral shapes within a suite of ground motions. It is used here to explain the discrepancy between median structural demands estimated from different suites of scaled and spectrum-matched ground motions. Performing response history analyses with spectrum-matched ground motions is known to result in unconservatively biased median demand estimates in some cases. Herein, several suites of scaled ground motions with equivalent median intensities and varying levels of CSD are selected. A single suite of spectrum-matched ground motions is also created. These records are used to analyze the responses of inelastic single-degree-of-freedom and first-mode-dominated multiple-degree-of-freedom structural systems. Collapse capacities are also examined. A consistent trend between CSD and resulting median responses indicates that the bias phenomenon can be fully explained by an asymmetric relationship between conditional spectral ordinates at periods affecting inelastic response.

Seismic Reliability Analysis of Single-Degree-of-Freedom System when Structural Response is with Markov Property

2012 ◽  
Vol 204-208 ◽  
pp. 2690-2693
Author(s):  
Zhen Hao Zhang ◽  
Wei Jun Yang
Keyword(s):  
Reliability Analysis ◽  
Markov Property ◽  
Structural Response ◽  
Degree Of Freedom ◽  
Superposition Method ◽  
Structural System ◽  
Single Degree Of Freedom ◽  
Seismic Reliability ◽  
Single Degree ◽  
Mode Superposition Method

The stationary responses process of single-degree-of-freedom structural system is a stationary process with Markov property in displacement-speed space when the random earthquake load is simulated as flat noise or nearly flat noise. In this paper, the seismic reliability of singe-degree-of-freedom structural system of which the structural responses is with Markov property is studied according to first excursion mechanism. The explicit solution method of the structural seismic reliability is deduced. It is shown from the example that the method of this paper is correct. For the seismic reliability analysis of multiple-degree-of-freedom system, the mode-superposition method can be adopted to transform multiple-degree-of-freedom system into a series of generalized single-degree-of-freedom systems, so the method of this paper is also applicable in the theory.

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