The Plastic Deformation of Built-in Beams Due to Distributed Dynamic Loading

1964 ◽  
Vol 31 (3) ◽  
pp. 507-514 ◽  
Author(s):  
M. F. Conroy
Keyword(s):  
Plastic Deformation ◽  
Initial Phase ◽  
Plastic Material ◽  
Yield Condition ◽  
Bending Moment ◽  
Transverse Load ◽  
Infinite Length ◽  
Central Segment ◽  
Transverse Shearing ◽  
Shearing Deformation

This paper is concerned with the initial phase of behavior of a long built-in beam when subject to a dynamic transverse load which is uniformly distributed over a central segment. The beam is assumed to be made of a rigid, ideally plastic material and the yield condition is assumed to depend only upon the bending moment. The effects of transverse shearing deformation, rotary inertia and strain rate are neglected. In the analysis, the beam is taken to be of infinite length. Four possible types of initial phase of motion are found. The conditions under which the results of this analysis are applicable to finite built-in beams are defined and the behavior of finite beams when these conditions are not satisfied is briefly discussed.

The Behavior of Long Beams Under Impact Loading

1950 ◽  
Vol 17 (1) ◽  
pp. 27-34
Author(s):  
P. E. Duwez ◽  
D. S. Clark ◽  
H. F. Bohnenblust
Keyword(s):  
Plastic Deformation ◽  
Cross Sections ◽  
Constant Velocity ◽  
Bending Moment ◽  
Infinite Length ◽  
Longitudinal Impact ◽  
Deflection Curve ◽  
Transverse Impact ◽  
Cold Rolled ◽  
Annealed Copper

Abstract This paper presents the results of a theoretical and experimental investigation of the plastic deformation of long beams which are subjected to a concentrated transverse impact of constant velocity. In the theoretical analysis, the beam is supposed to be of infinite length, and plane cross sections are assumed to remain plane. The bending moment is assumed to depend on the curvature according to a function that is obtained from the stress-strain curve of the material. The theory neglects both the lateral displacement of the cross sections against each other due to the shearing force and the rotary kinetic energy of the motion of the beam. The theory shows that a strain is not propagated along a beam at constant velocity, as in the case of longitudinal impact. The strain depends on the ratio between the square of the distance from the point of impact and the time. This is correct regardless of the shape of the moment - curvature curve. If certain approximations are applied to the bending moment - curvature curve, the theory provides a method of computing the deflection curve of a beam at any instant during impact. An experimental study has been made in which the deflection curves of long simply supported beams have been obtained during impact. The deflection characteristics of a cold-rolled steel and an annealed-copper beam have been computed by approximating the bending moment - curvature curves. It is shown that for materials such as cold-rolled low-carbon steel, for which plastic deflection is localized at the point of impact, the observed deflection curve is closely approximated by computing a curve based on the assumption that the beam remains elastic. For a soft material like annealed copper, plastic deformation extends over a relatively large distance from the point of impact and, taking plastic deformation into account, a satisfactory agreement is obtained between theory and experimental results.

On the plastic theory of plates

1957 ◽  
Vol 241 (1225) ◽  
pp. 153-179 ◽  
Keyword(s):  
Plastic Material ◽  
Yield Condition ◽  
Middle Surface ◽  
Transverse Load ◽  
Flow Rule ◽  
Transverse Shear Strain ◽  
Elastic Plates ◽  
Field Equations ◽  
Rigid Plastic ◽  
Tresca Yield Condition

This paper presents a theory of the small deformations of a thin uniform plate under transverse load. The plate is made of non-hardening rigid-plastic material obeying the Tresca yield condition and associated flow rule. The basic assumptions are similar to those made in the conventional engineering theory of thin elastic plates, and the effects of transverse shear strain and rotatory inertia are neglected. Hitherto, the theory has been developed only under conditions of circular symmetry, and the object of the present paper is to remove this restriction. Attention is confined here to the derivation and classification of the field equations. The field equations involve the stress moments and the middle-surface curvature rates as the associated generalized stresses and strain rates. These equations are first referred to Cartesian co-ordinates. The condition of isotropy requires the coincidence of the directions of principal stress moment and curvature rate. One of these two families of directions is characteristic for the equations appropriate to certain plastic régimes. The field equations are therefore referred to curvilinear co-ordinates taken along these directions. A detailed study is made of discontinuities in the field quantities. The field equations are either parabolic or elliptic for the principal plastic régimes.

The Elastic-Plastic Stress Distribution Within a Wide Curved Bar Subjected to Pure Bending

1955 ◽  
Vol 22 (3) ◽  
pp. 305-310
Author(s):  
Bernard W. Shaffer ◽  
Raymond N. House
Keyword(s):  
Stress Distribution ◽  
Convex Surface ◽  
Plastic Material ◽  
Circumferential Stress ◽  
Yield Condition ◽  
Bending Moment ◽  
Stress Distributions ◽  
Elastic Plastic ◽  
Tresca Yield Condition ◽  
Plastic Stress

Abstract Analytical expressions are obtained for the radial and circumferential stress distributions within a wide curved bar made of a perfectly plastic material when it is subjected to a uniformly distributed bending moment. The elastic stress distributions are based on the use of the Airy stress function, whereas the plastic stress distributions in this problem of plane strain are based on the use of the Tresca yield condition. It is found that as the bending moment increases in the direction which tends to straighten the initially curved bar, an elastic-plastic boundary develops first around the concave surface. It meets a second boundary, which starts sometime later around the convex surface, when the bar is completely plastic. The elastic region within the bar decreases at a fairly uniform rate as the bending moment increases to within approximately 90 per cent of the fully plastic bending moment but then it degenerates very much more rapidly until it no longer exists when the bar is completely plastic. The position of the neutral surface is independent of the applied bending moment when the stress distribution is within the completely elastic and the completely plastic ranges. Within the elastic-plastic range, however, it moves away from and then toward the center of curvature as the bending moment increases.

Visualization of Processes of Plastic Deformation Initiation in Conditions of Pure Tension and Pure and Simple Bending

2015 ◽  
Vol 240 ◽  
pp. 3-10
Author(s):  
Henryk Jodłowski ◽  
Stefan Bućko ◽  
Piotr Gibas
Keyword(s):  
Plastic Deformation ◽  
Initial Phase ◽  
Bending Moment ◽  
Plastic Deformations ◽  
Interference Fringes ◽  
Tension Tests ◽  
Plastic Deformation Process ◽  
Bending Process ◽  
34Crnimo6 Steel ◽  
Maximal Strain

The rules and capabilities of macro-strains identification method with the use of optical interference for identifying initial phase of plastic deformation process in steels with material instability were discussed in the work. It was also shown how the technique run in presentation of the initial phase of yielding progress. As the example for illustration of discussed method real capabilities the course of plastic deformations beginning in the tension tests of 15CrMo and 34CrNiMo6 steel samples was shown as well as the course of test of pure and simple bending for the steel 15CrMo beam. Namely, the sequence of interference fringes pictures showing the formation of plastic strains correlating to the points on the tensile test curve was presented. For bending process the pictures were correlated with the point on the graph of dimensionless bending moment versus maximal strain measured by the strain gauge

Finite Element Modeling of Self-Loosening of Bolted Joints

2004 ◽  
Author(s):  
Ming Zhang ◽  
Yanyao Jiang ◽  
Chu-Hwa Lee
Keyword(s):  
Finite Element ◽  
Contact Pressure ◽  
Bending Moment ◽  
Shear Loading ◽  
Transverse Load ◽  
Fe Model ◽  
Bolted Joint ◽  
Cyclic Bending ◽  
Second Stage ◽  
Cyclic Bending Moment

A three-dimensional finite element (FE) model with the consideration of the helix angle of the threads was developed to simulate the second stage self-loosening of a bolted joint. The second stage self-loosening refers to the graduate reduction in clamping force due to the back-off of the nut. The simulations were conducted for two plates jointed by a bolt and a nut and the joint was subjected to transverse or shear loading. An M12×1.75 bolt was used. The application of the preload was simulated by using an orthogonal temperature expansion method. FE simulations were conducted for several loading conditions with different preloads and relative displacements between the two clamped plates. It was found that due to the application of the cyclic transverse load, micro-slip occurred between the contacting surfaces of the engaged threads of the bolt and the nut. In addition, a cyclic bending moment was introduced on the bolted joint. The cyclic bending moment resulted in an oscillation of the contact pressure on the contacting surfaces of the engaged threads. The micro-slip between the engaged threads and the variation of the contact pressure were identified to be the major mechanisms responsible for the self-loosening of a bolted joint. Simplified finite element models were developed that confirmed the mechanisms discovered. The major self-loosening behavior of a bolted joint can be properly reproduced with the FE model developed. The results obtained agree quantitatively with the experimental observations.

Effect of structural deformations and bend angle on the collapse load of pipe bends subjected to in-plane closing bending moment

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Silambarasan R. ◽  
Veerappan A.R. ◽  
Shanmugam S.
Keyword(s):  
Plastic Material ◽  
Large Strain ◽  
Bending Moment ◽  
Bend Angle ◽  
Plastic Collapse ◽  
Collapse Load ◽  
Pipe Bend ◽  
Content Type ◽  
Structural Deformations ◽  
Bend Angles

Purpose The purpose of this study is to investigate the effect of structural deformations and bend angle on plastic collapse load of pipe bends under an in-plane closing bending moment (IPCM). A large strain formulation of three-dimensional non-linear finite element analysis was performed using an elastic perfectly plastic material. A unified mathematical solution was proposed to estimate the collapse load of pipe bends subjected to IPCM for the considered range of bend characteristics. Design/methodology/approach ABAQUS was used to create one half of the pipe bend model due to its symmetry on the longitudinal axis. Structural deformations, i.e. ovality (Co) and thinning (Ct) varied from 0% to 20% in 5% steps while the bend angle (ø) varied from 30° to 180° in steps of 30°. Findings The plastic collapse load decreases as the bend angle increase for all pipe bend models. A remarkable effect on the collapse load was observed for bend angles between 30° and 120° beyond which a decline was noticed. Ovality had a significant effect on the collapse load with this effect decreasing as the bend angle increased. The combined effect of thinning and bend angle was minimal for the considered models and the maximum per cent variation in collapse load was 5.76% for small bend angles and bend radius pipe bends and less than 2% for other cases. Originality/value The effect of structural deformations and bend angle on collapse load of pipe bends exposed to IPCM has been not studied in the existing literature.

The Influence of Rotatory Inertia and Transverse Shear on the Dynamic Plastic Behavior of Beams

1979 ◽  
Vol 46 (2) ◽  
pp. 303-310 ◽  
Author(s):  
Norman Jones ◽  
J. Gomes de Oliveira
Keyword(s):  
Transverse Shear ◽  
Shear Force ◽  
Yield Criterion ◽  
Yield Condition ◽  
Bending Moment ◽  
Plastic Behavior ◽  
Plastic Response ◽  
Rotatory Inertia ◽  
Perfectly Plastic ◽  
Theoretical Procedure

The theoretical procedure presented herein examines the influence of retaining the transverse shear force in the yield criterion and rotatory inertia on the dynamic plastic response of beams. Exact theoretical rigid perfectly plastic solutions are presented for a long beam impacted by a mass and a simply supported beam loaded impulsively. It transpires that rotatory inertia might play a small, but not negligible, role on the response of these beams. The results in the various figures indicate that the greatest departure from an analysis which neglects rotatory inertia but retains the influence of the bending moment and transverse shear force in the yield condition is approximately 11 percent for the particular range of parameters considered.

Effect of Bend Angle on Gross Plastic Deformation of Pipe Bends: A Finite Element Based Study

2015 ◽  
Author(s):  
Anindya Bhattacharya ◽  
Sachin Bapat ◽  
Hardik Patel ◽  
Shailan Patel
Keyword(s):  
Plastic Deformation ◽  
Finite Element ◽  
Failure Mechanisms ◽  
Bending Moment ◽  
Bend Angle ◽  
Piping System ◽  
Plastic Collapse ◽  
Collapse Load ◽  
Pipe Bend ◽  
Bend Angles

Bends are an integral part of a piping system. Because of the ability to ovalize and warp they offer more flexibility when compared to straight pipes. Piping Code ASME B31.3 [1] provides flexibility factors and stress intensification factors for the pipe bends. Like any other piping component, one of the failure mechanisms of a pipe bend is gross plastic deformation. In this paper, plastic collapse load of pipe bends have been analyzed for various bend parameters (bend parameter = tRbrm2) under internal pressure and in-plane bending moment for various bend angles using both small and large deformation theories. FE code ABAQUS version 6.9EF-1 has been used for the analyses.

scholarly journals Justification of the Rheological Model of Process of Plastic Material Injection by the Rollers

2019 ◽  
Vol 23 (3) ◽  
pp. 101-114
Author(s):  
Katarzyna Szwedziak ◽  
Igor Stadnyk ◽  
Sergey Golyachuk ◽  
Żaneta Grzywacz
Keyword(s):  
Rheological Model ◽  
Plastic Material ◽  
Structural Parameters ◽  
Structural Elements ◽  
Reduced Viscosity ◽  
Physical Experiments ◽  
Nonlinear Character ◽  
Shearing Deformation ◽  
Working Bodies ◽  
The Relationship

AbstractIt is justified thatproblems related to the changes in structural and mechanical properties of plastic material and influence of structural elements of equipment and modes of implementation of the for-mation process on them are considered detail, taking into account empirical data, theoretical dependencies and results of physical experiments. It was established that during the mechanical influence of rollers with grooves on a structured dispersion plastic material in the node of injection of the molding machine, internal shear, and shearing deformation have a preponderant value. Accordingly, the productivity of machines is determined mainly by the structural parameters of the working bodies geometry, kinematics, and contact area. It is shown that increasing the pressure in the plastic material causes a decrease in its volume, but the relationship between pressure and volume has a nonlinear character. It has been established that regardless the variety of flour from which the plastic material was prepared for bagels, its moisture content and the duration of fermentation reduced viscosity of the effective plastic material along with the increase of the shear stress. The paper describes the refined rheological model of the Bingham body deformation, which develops instantaneously, and the velocity of the common elastic deformation in the dough is a simultaneous function of stresses and temperatures, which are close to exponential ones.

The Torsionless Bending of a Hollow Beam by a Transverse Load

1937 ◽  
Vol 4 (1) ◽  
pp. A25-A30
Author(s):  
W. L. Schwalbe
Keyword(s):  
Cross Sections ◽  
Equilateral Triangle ◽  
Bending Moment ◽  
Longitudinal Section ◽  
Transverse Load ◽  
Shearing Stress ◽  
Numerical Work ◽  
Hollow Beam ◽  
Transverse Loads ◽  
Hollow Beams

Abstract The author discusses the bending of hollow beams when subjected to transverse loads, and points out that shearing stresses and strains in the cross sections are necessary, and a particular longitudinal section remains plane only if the resultant of the shearing stress, and hence the plane of the applied bending moment, possesses a particular location. The author determines the location of this resultant shearing stress by applying a method based on St. Venant’s theory. Applications of the method are made to two hollow sections. One of the sections is that of an equilateral triangle which serves as a measure of accuracy for the numerical work presented by the author, since the location of the resultant of the shearing stresses is known by symmetry.

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