Accuracy and Limitations of the Method of Equivalent Linearization for Hysteretic Multi-Storey Structures

1988 ◽  
pp. 3-21 ◽  
Author(s):  
H. J. Pradlwarter ◽  
G. I. Schuëller
Keyword(s):  
Equivalent Linearization

Performance analysis of global local mean square error criterion of stochastic linearization for nonlinear oscillator

2019 ◽  
Author(s):  
Nguyen Cao Thang ◽  
Luu Xuan Hung
Keyword(s):  
Performance Analysis ◽  
Mean Square Error ◽  
Nonlinear Oscillators ◽  
Degree Of Freedom ◽  
Equivalent Linearization ◽  
Mean Square ◽  
Error Criterion ◽  
Stochastic Linearization ◽  
Local Mean ◽  
Mean Square Error Criterion

The paper presents a performance analysis of global-local mean square error criterion of stochastic linearization for some nonlinear oscillators. This criterion of stochastic linearization for nonlinear oscillators bases on dual conception to the local mean square error criterion (LOMSEC). The algorithm is generally built to multi degree of freedom (MDOF) nonlinear oscillators. Then, the performance analysis is carried out for two applications which comprise a rolling ship oscillation and two degree of freedom one. The improvement on accuracy of the proposed criterion has been shown in comparison with the conventional Gaussian equivalent linearization (GEL).

scholarly journals Displacement Demand for Nonlinear Static Analyses of Masonry Structures: Critical Review and Improved Formulations

Buildings ◽  
2021 ◽  
Vol 11 (3) ◽  
pp. 118
Author(s):  
Gabriele Guerrini ◽  
Stylianos Kallioras ◽  
Stefano Bracchi ◽  
Francesco Graziotti ◽  
Andrea Penna
Keyword(s):  
Time History ◽  
Nonlinear Static Analysis ◽  
Equivalent Linearization ◽  
Eurocode 8 ◽  
Masonry Structures ◽  
Equivalent Viscous Damping ◽  
Inelastic Displacement ◽  
N2 Method ◽  
Nonlinear Static ◽  
Nonlinear Time History

This paper discusses different formulations for calculating earthquake-induced displacement demands to be associated with nonlinear static analysis procedures for the assessment of masonry structures. Focus is placed on systems with fundamental periods between 0.1 and 0.5 s, for which the inelastic displacement amplification is usually more pronounced. The accuracy of the predictive equations is assessed based on the results from nonlinear time-history analyses, carried out on single-degree-of-freedom oscillators with hysteretic force–displacement relationships representative of masonry structures. First, the study demonstrates some limitations of two established approaches based on the equivalent linearization concept: the capacity spectrum method of the Dutch guidelines NPR 9998-18, and its version outlined in FEMA 440, both of which overpredict maximum displacements. Two codified formulations relying on inelastic displacement spectra are also evaluated, namely the N2 method of Eurocode 8 and the displacement coefficient method of ASCE 41-17: the former proves to be significantly unconservative, while the latter is affected by excessive dispersion. A non-iterative procedure, using an equivalent linear system with calibrated optimal stiffness and equivalent viscous damping, is then proposed to overcome some of the problems identified earlier. A recently developed modified N2 formulation is shown to improve accuracy while limiting the dispersion of the predictions.

Calculation of Nonlinear Systems Under Narrow Band Excitation Using Equivalent Linearization and Path Continuation

2021 ◽  
Author(s):  
Alwin Förster ◽  
Lars Panning-von Scheidt
Keyword(s):  
Nonlinear Systems ◽  
Narrow Band ◽  
Gaussian White Noise ◽  
Random Excitation ◽  
Mean Value ◽  
Equivalent Linearization ◽  
Efficient Procedure ◽  
Stochastic Excitations ◽  
Wide Range ◽  
The One

Abstract Turbomachines experience a wide range of different types of excitation during operation. On the structural mechanics side, periodic or even harmonic excitations are usually assumed. For this type of excitation there are a variety of methods, both for linear and nonlinear systems. Stochastic excitation, whether in the form of Gaussian white noise or narrow band excitation, is rarely considered. As in the deterministic case, the calculations of the vibrational behavior due to stochastic excitations are even more complicated by nonlinearities, which can either be unintentionally present in the system or can be used intentionally for vibration mitigation. Regardless the origin of the nonlinearity, there are some methods in the literature, which are suitable for the calculation of the vibration response of nonlinear systems under random excitation. In this paper, the method of equivalent linearization is used to determine a linear equivalent system, whose response can be calculated instead of the one of the nonlinear system. The method is applied to different multi-degree of freedom nonlinear systems that experience narrow band random excitation, including an academic turbine blade model. In order to identify multiple and possibly ambiguous solutions, an efficient procedure is shown to integrate the mentioned method into a path continuation scheme. With this approach, it is possible to track jump phenomena or the influence of parameter variations even in case of narrow band excitation. The results of the performed calculations are the stochastic moments, i.e. mean value and variance.

Impact of Damping Scaling Factors on Direct Displacement-Based Design

2016 ◽  
Vol 32 (2) ◽  
pp. 843-859 ◽  
Author(s):  
Cuiyan Kong ◽  
Mervyn J. Kowalsky
Keyword(s):  
Response Spectra ◽  
Equivalent Linearization ◽  
Base Shear ◽  
Limit States ◽  
Scaling Factors ◽  
Equivalent Viscous Damping ◽  
Direct Displacement Based Design ◽  
Displacement Response Spectra ◽  
Performance Limit States ◽  
Displacement Based

Damping scaling factors (DSFs) play an important role in direct displacement-based design (DDBD) as they provide a means to establish displacement response spectra for damping values beyond 5%. Response spectra for multiple damping values are needed for DDBD as the approach relies on equivalent linearization, expressed in the form of effective stiffness and equivalent viscous damping, to establish design forces for prescribed performance limit states. In the past, DSFs based on the Eurocode have been employed for DDBD; however, recent research has resulted in more robust DSF models. This paper examines the accuracy of the current DSF equation used in DDBD across the parameters that are important for structural design. A nonlinear regression analysis is performed based on the data obtained by the Rezaeian et al. (2014) model, and a base shear adjustment factor (SAF) is proposed for application to the DDBD base shear equation.

scholarly journals EQUIVALENT LINEARIZATION OF LIQUEFIED SANDY SOIL

1983 ◽  
Vol 1983 (340) ◽  
pp. 59-65
Author(s):  
Masaru HOSHIYA ◽  
Etsuro SAITO
Keyword(s):  
Sandy Soil ◽  
Equivalent Linearization

scholarly journals Evaluation of Seismic Demand for Substandard Reinforced Concrete Structures

2018 ◽  
Vol 12 (1) ◽  
pp. 9-33
Author(s):  
Nicholas Kyriakides ◽  
Ahmad Sohaib ◽  
Kypros Pilakoutas ◽  
Kyriakos Neocleous ◽  
Christis Chrysostomou ◽  
...  
Keyword(s):  
Reinforced Concrete ◽  
Seismic Performance ◽  
Performance Prediction ◽  
Brittle Failure ◽  
Failure Modes ◽  
Shaking Table ◽  
Equivalent Linearization ◽  
Diagram Method ◽  
Capacity Curves ◽  
Non Linear

Background: Reinforced Concrete (RC) buildings with no seismic design exhibit degrading behaviour under severe seismic loading due to non-ductile brittle failure modes. The seismic performance of such substandard structures can be predicted using existing capacity demand diagram methods through the idealization of the non-linear capacity curve of the degrading system, and its comparison with a reduced earthquake demand spectrum. Objective: Modern non-linear static methods for derivation of capacity curves incorporate idealization assumptions that are too simplistic and do not apply for sub-standard buildings. The conventional idealisation procedures cannot maintain the true strength degradation behaviour of such structures in the post-peak part, and thus may lead to significant errors in seismic performance prediction especially in the cases of brittle failure modes dominating the response. Method: In order to increase the accuracy of the prediction, an alternative idealisation procedure using equivalent elastic perfectly plastic systems is proposed herein that can be used in conjunction with any capacity demand diagram method. Results: Moreover, the performance of this improved equivalent linearization procedure in predicting the response of an RC frame is assessed herein. Conclusion: This improved idealization procedure has been proven to reduce the error in the seismic performance prediction as compared to seismic shaking table test results [1] and will be further investigated probabilistically herein.

Sign in / Sign up

Export Citation Format

Share Document