Hysteretic Behavior of a Bar Under Repeated Axial Loading: An Extended History

2000 ◽  
Vol 68 (3) ◽  
pp. 425-431
Author(s):  
N. Yoshida ◽  
T. Nonaka
Keyword(s):  
Analytical Study ◽  
Axial Loading ◽  
Hysteretic Behavior ◽  
Perfectly Plastic ◽  
Small Deflection ◽  
Previous Formulation ◽  
History Of ◽  
State Variation ◽  
Basic Equations ◽  
Elastic Perfectly Plastic

Analytical study is made of an elastic-perfectly plastic bar under repeated axial loading. A previous formulation on a pin-ended bar is extended here to include the effects of load eccentricity and rotational constraint at the bar ends. Basic equations are derived, based on the assumptions of planar and small deflection, and of symmetry with respect to the bar center. The end spring is allowed to yield. Numerical examples are presented to demonstrate the application of the basic equations, and adequacy is shown for any specified history of axial displacement. Diagrammatical representation of state variation provides a better understanding of the hysteretic behavior as well as the applicability of the basic equations.

Analysis on the Moment-Curvature Relationship for Prestressed UHPFRC Beams without Stirrup

2011 ◽  
Vol 255-260 ◽  
pp. 236-240
Author(s):  
Sang Mook Han ◽  
Qing Yong Guo
Keyword(s):  
Experimental Data ◽  
Tensile Strength ◽  
Steel Fibre ◽  
Fibre Reinforcement ◽  
Cracking Behavior ◽  
Perfectly Plastic ◽  
History Of ◽  
Elastic Perfectly Plastic ◽  
The Moment ◽  
Good Agreement

To simplify the analysis, an elastic perfectly plastic stress-strain law was presented for UHPFRC. The post-cracking behavior was described by the average constant post-crack tensile strength. A strain parameter μ is proposed to evaluate the performance and efficiency of steel fibre reinforcement. 8 rectangular beams were tested in this investigation. Based on the proposed constitutive model, the full history of their flexural moment-curvature relationship for UHPFRC beams was calculated and compared with experimental data on prestressed UHPFRC beams. Good agreement between calculated strengths and experimental data was obtained.

General Bounding Theorems for the Quasi-Static Deformation of a Body of Inelastic Material, With Applications to Metallic Creep

1974 ◽  
Vol 41 (4) ◽  
pp. 947-952 ◽  
Author(s):  
A. R. S. Ponter
Keyword(s):  
Creep Deformation ◽  
Static Deformation ◽  
Metallic Structures ◽  
Viscous Material ◽  
Perfectly Plastic ◽  
Small Deflection ◽  
Inelastic Material ◽  
General Displacement ◽  
Elastic Perfectly Plastic ◽  
Inelastic Strains

General displacement and work bounds are derived for the small-deflection quasi-static deformation of a body composed of a material which exhibits both elastic and inelastic strains. The bounds are described in terms of functional properties of the constitutive relationships. The results are specialized to an elastic/perfectly plastic and nonlinear viscous material and known results are recovered. Special emphasis is given to problems associated with the analysis of creep deformation of metallic structures.

scholarly journals KUHN-TUCKER CONDITIONS IN SHAKEDOWN PROBLEMS

1996 ◽  
Vol 2 (5) ◽  
pp. 14-28
Author(s):  
Juozas Atkočiūnas
Keyword(s):  
Cyclic Loading ◽  
Mathematical Programming ◽  
Safety Factor ◽  
Strain Field ◽  
Analysis Problem ◽  
Cyclic Plastic ◽  
Perfectly Plastic ◽  
History Of ◽  
Elastic Perfectly Plastic ◽  
The Moment

An elastic perfectly plastic structure at shakedown to given cyclić loading is under consideration. The stress-strain field of dissipative system in general is related to the history of loading. And only in a particular case, i.e. at the moment prior to the failure of an elastic perfectly plastic structure the distribution of the actual residual forces is unique for each prescribed history of loading (the safety factor of shakedown approaches unity). Nevertheless, there exist some domains where the plastic strains are equal to zero. The residual forces in the statically indeterminate parts of the structure may be non-unique: the stress field is only determined by the equilibrium equations. The extremum energy principle of minimum complementary energy allows to derive the actual residual forces out of all statically admissible residual forces at the moment prior to cyclic plastic failure. Then the stress-strain field analysis problem at the moment prior to the cyclic plastic failure is formulated as a problem of non-linear mathematical programming. Formulating the dual pair of non-linear programming problem (statical and kinematic formulation of analysis problem) the differential constraints are neglected or replaced by algebraic conditions. When the safety factor is approching a unity, the degeneracy of the statical formulation of the analysis problem often can occur. In this case a mathematical model is proposed for obtaining an upper bounds for the displacement at shakedown. It is pointed out that the known Kuhn-Tucker conditions of mathematical programming theory (i.e. compatibility equations of residual strains) in concert with restriction, limiting the maximum value of total energy dissipation, make up the adaptation conditions of the structure to given cyclic loading. Kuhn-Tucker conditions used in above—mentioned problem allow to correctly interprete the physical aspect of the degeneracy problem at shakedown. When the safety factor is larger than unity an artificial degeneracy situation for the statical formulation of analysis problem can be created. Then the mathematical models presented can be applied to the analysis of unloading elastoplastic structures. With this aim in view a fictitious equiplastic structure the behaviour of which is holonomic is derived. The displacements of the fictitious structure enclose the displacements of the actual structure subject to cyclic loading.

Influence of Hysteretic Behavior on Seismic Strength Demands: An Analysis for Romanian Vrancea Earthquakes

2013 ◽  
Vol 430 ◽  
pp. 362-366
Author(s):  
Iolanda Gabriela Craifaleanu
Keyword(s):  
Ground Motion ◽  
Frequency Band ◽  
Hysteretic Behavior ◽  
Seismogenic Zone ◽  
Model Parameters ◽  
Hysteretic Model ◽  
Ground Acceleration ◽  
Mean Values ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

The paper presents the results of a study performed on a large ground motion database, containing records obtained during the three strongest earthquakes that occurred during the past four decades in the Vrancea seismogenic zone. In order to express strength demands imposed by these earthquakes, constant-ductility nonlinear acceleration spectra were computed for two sets of seismic records, selected as representative for narrow frequency band and broad frequency band ground motions, respectively. The spectra, determined for various types of bilinear hysteretic models, were normalized with respect to peak ground acceleration and mean values, as well as coefficients of variation, were computed for each analysis case. The sensitivity of spectral values to the variation of strength hardening and stiffness degradation parameters was determined, with reference to the elastic-perfectly plastic model. Conclusions were drawn, separately for the two distinct types of ground motion frequency content, on the significance of the considered hysteretic model parameters for the assessment of seismic strength demands.

Deformation, Displacement, and Work Bounds for Structures in a State of Creep and Subject to Variable Loading

1972 ◽  
Vol 39 (4) ◽  
pp. 953-958 ◽  
Author(s):  
A. R. S. Ponter
Keyword(s):  
Time Constant ◽  
Variable Loading ◽  
Constant Loading ◽  
Perfectly Plastic ◽  
History Of ◽  
Elastic Perfectly Plastic

General bounds on the deformation of a structure in a state of creep are derived for an elastic/perfectly plastic/time-hardening creep material, and subject to an arbitrary history of loading. Previously derived bounds for time constant loading are recovered and extended. The bounds are specialized to cyclic histories of loading. A simple example indicates that very accurate bounds are possible in some circumstances.

Load-Deformation Behavior of Elastic Beam-Columns on Yielding Foundations

1978 ◽  
Vol 100 (1) ◽  
pp. 182-188
Author(s):  
C. Shahravan ◽  
A. I. Soler
Keyword(s):  
Tube Bundle ◽  
Compressive Load ◽  
Elastic Beam ◽  
Beam Columns ◽  
Support Plate ◽  
Perfectly Plastic ◽  
Load Carrying ◽  
Rate Form ◽  
History Of ◽  
Elastic Perfectly Plastic

The effect of an elastic-perfectly plastic foundation on compressive load carrying capacity of beam columns is considered. The configuration studied simulates a power plant condenser support plate acting as a column member to support the condenser walls against excessive deformation due to vacuum pressure. The yielding foundation represents the effect of the condenser tube bundle which can resist support plate bending through frictional action between the plate and the tubes. The equation governing lateral motion of the beam column is developed in rate form using the Green’s function for an elastic beam column. An approximate incremental solution is obtained enabling the load-deformation history of the beam column to be studied incorporating elastic-plastic loading and unloading of the foundation. “Failure” is assumed to occur when the maximum stress in the beam column reaches a preset allowable design value.

Stress concentration factors and elastic-plastic stress and strain predictions for axisymmetric internal projections on hollow tubes subjected to axial loading

1989 ◽  
Vol 24 (1) ◽  
pp. 45-54 ◽  
Author(s):  
S J Hardy ◽  
A R Gowhari-Anaraki
Keyword(s):  
Stress Concentration ◽  
Plastic Material ◽  
Low Cycle Fatigue ◽  
Axial Loading ◽  
Material Model ◽  
Published Data ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Stress Concentration Factors ◽  
Elastic Perfectly Plastic

The finite element method has been used to obtain stress concentration factor data for hollow tubes with axisym-metric internal projections subjected to axial loading. A range of geometries has been considered in the investigation, and the results are complementary to previously published data. Preliminary results from an elastic-plastic analysis of a component with an internal projection are presented. Strain predictions with an elastic-perfectly-plastic material model are found to be between those estimated using linear and Neuber rules for low cycle fatigue life predictions.

scholarly journals Hysteretic behavior modeling of elastoplastic materials

2008 ◽  
Vol 35 (1-3) ◽  
pp. 287-304
Author(s):  
Dragoslav Sumarac ◽  
Bojan Medjo ◽  
Natasa Trisovic
Keyword(s):  
Plastic Material ◽  
Rectangular Cross Section ◽  
Axial Loading ◽  
Hysteretic Behavior ◽  
Behavior Modeling ◽  
Cyclic Behavior ◽  
Preisach Model ◽  
Viscous Effects ◽  
Rectangular Tube ◽  
History Of

In the present paper the Preisach model of hysteresis is applied to model cyclic behavior of elasto-plastic material. Rate of loading and viscous effects will not be considered. The problem of axial loading of rectangular cross section and cyclic bending of rectangular tube (box) will be studied in details. Hysteretic stress-strain loop for prescribed history of stress change is plotted for material modeled by series connection of three unite element. Also moment-curvature hysteretic loop is obtained for a prescribed curvature change of rectangular tube (box). One chapter of the paper is devoted to results obtained by FEM using Finite Element Code ABAQUS. All obtained results clearly show advantages of the Preisach model for describing cyclic behavior of elasto-plastic material.

Simulation of Nonlinear Systems Having Series and Parallel Friction Elements

2011 ◽  
Author(s):  
Al Ferri ◽  
Emad Shahid
Keyword(s):  
Relative Size ◽  
Functional Relation ◽  
Prior History ◽  
Viscous Damping ◽  
Damping Term ◽  
Friction Element ◽  
Perfectly Plastic ◽  
In Series ◽  
History Of ◽  
Elastic Perfectly Plastic

The numerical response of a SDOF oscillator with a friction element and spring in series is investigated. The connection between the friction element and the spring is massless resulting in an ideal “Iwan element,” also termed an elastic/perfectly-plastic element. A methodology is proposed that avoids the complications caused by hysteresis, allowing the system to be simulated using relatively simple programming logic. A notable feature of the technique is that it yields a functional relation for the friction force that depends on the present value of the state vector, rather than on prior history of the motion. The method introduces a small, “fictitious” slider mass within the Iwan element. Simulations are presented to show how the relative size of the slider mass affects the trade off between accuracy and computational costs. It is seen that the results of the method are very accurate and easy to implement. It is also shown that the added numerical stiffness associated with the high-frequency dynamics of the slider mass can be alleviated through use of a switchable viscous damping term. The viscous damping term decreases the number of timesteps required for simulation without adversely affecting the accuracy. The paper considers SDOF systems having a single Iwan-element as well as multiple Iwan elements.

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