Showing papers on "Torsion (mechanics) published in 1972"
Book•
01 Jan 1972
TL;DR: In this article, the authors present a general framework for the analysis of deformable bodies, including bending, deformation, and deformation of a twisted circular shaft with respect to bending.
Abstract: Preface to the second edition Preface to the second edition with SI units Preface to the first edition Chapter One Fundamental Principles of Mechanics 1.1 Introduction 1.2 Generalized procedure 1.3 The fundamental principles of mechanics 1.4 The concept of force 1.5 The moment of a force 1.6 Conditions for equilibrium 1.7 Engineering applications 1.8 Friction 1.9 Examples 1.10 Hooke's joint 1.11 Final remarks Problems Chapter Two Introduction to Mechanics of Deformable Bodies 2.1 Analysis of deformable bodies 2.2 Uniaxial loading and deformation 2.3 Statically determinate situations 2.4 Statically indeterminate situations 2.5 Computer analysis of trusses 2.6 Elastic energy Castigliano's theorem 2.7 Summary Problems Chapter Three Forces and Moments Transmitted by Slender Members 3.1 Introduction 3.2 General method 3.3 Distributed loads 3.4 Resultants of distributed loads 3.5 Differential equilibrium relationships 3.6 Singularity functions 3.7 Fluid forces 3.8 Three-dimensional problems Problems Chapter Four Stress and Strain 4.1 Introduction 4.2 Stress 4.3 Plane stress 4.4 Equilibrium of a differential element in plane stress 4.5 Stress components associated with arbitrarily oriented faces in plane stress 4.6 Mohr's circle representation of plane stress 4.7 Mohr's circle representation of a general state of stress 4.8 Analysis of deformation 4.9 Definition of strain components 4.10 Relation between strain and displacement in plane strain 4.11 Strain components associated with arbitrary sets of axes 4.12 Mohr's circle representation of plane strain 4.13 Mohr's circle representation of a general state of stress 4.14 Measurement of strains 4.15 Indicial notation Problems Chapter Five Stress-strain-temperature Relations 5.1 Introduction 5.2 The tensile test 5.3 Idealizations of stress-strain curves 5.4 Elastic stress-strain relations 5.5 Thermal strain 5.6 Complete equations of elasticity 5.7 Complete elastic solution for a thick-walled cylinder 5.8 Strain energy in an elastic body 5.9 Stress concentration 5.10 Composite materials and anisotropic elasticity 5.11 Criteria for initial yielding 5.12 Behavior beyond initial yielding in the tensile test 5.13 Fracture of ductile specimens and structures 5.14 Fracture of brittle specimens and structures 5.15 Fatigue 5.16 Criteria for continued yielding 5.17 Plastic stress-strain relations 5.18 Viscoelasticity Problems Chapter Six Torsion 6.1 Introduction 6.2 Geometry of deformation of a twisted circular shaft 6.3 Stresses obtained from stress-strain relations 6.4 Equilibrium requirements 6.5 Stress and deformation in a twisted elastic circular shaft 6.6 Torsion of elastic hollow circular shafts 6.7 Stress analysis in torsion combined stresses 6.8 Strain energy due to torsion 6.9 The onset of yielding in torsion 6.10 Plastic deformations 6.11 Residual stresses 6.12 Limit analysis 6.13 Torsion of rectangular shafts 6.14 Torsion of hollow, thin-walled shafts Problems Chapter Seven Stresses Due to Bending 7.1 Introcustion 7.2 Geometry of deformation of a symmetrical beam subjected to pure bending 7.3 Stresses obtained from stress-strain relations 7.4 Equilibrium requirements 7.5 Stress and deformation in symmetrical elastic beams subjected to pure bending 7.6 Stresses in symmetrical elastic beams transmitting both shear force and bending moment 7.7 Stress analysis in bending combined stresses 7.8 Strain energy due to bending 7.9 The onset of yielding in bending 7.10 Plastic deformations 7.11 Bending of unsymmetrical beams 7.12 Shear flow in thin-walled open sections shear center Problems Chapter Eight Deflections Due to Bending 8.1 Introduction 8.2 The moment-curvature relation 8.3 Integration of the moment-curvature relation 8.4 Superposition 8.5 The load-deflection differential equation 8.6 Energy methods 8.7 Limit analysis Problems Chapter Nine Stability of Equilibrium: Buckling 9.1 Introduction 9.2 Elastic stability 9.3 Examples of instability 9.4 Elastic stability of flexible columns 9.5 Elastic postbuckling behavior 9.6 Instability as a mode of failure 9.7 Necking of tension members 9.8 Plastic buckling Problems Answers to Selected Problems Index s
512 citations
TL;DR: In this article, a study of three essentially different mechanisms of energy absorption was carried out to determine whether such devices are feasible and the results showed that at plastic strains in the range 3% to 12% it was possible to develop energy dissipation of the order of 2000-7500 lb in/in3 per cycle (14-50 x 106 N/M2 per cycle).
Abstract: A structure designed to resist earthquake attack must have a capacity to dissipate kinetic energy induced by the ground motion. In most structures this energy absorption is developed in the vicinity of beam to column connections. Recent research has shown that connections are not reliable when subject to cyclic loading, such as results from earthquake attack. Connections in steel frames deteriorate due to local instabilities in adjacent flanges, and in reinforced concrete frames alternating shear loads produce diagonal tension and bond failures which progressively reduce the strength of the connection.
Much work in building research and earthquake engineering in laboratories throughout the world is directed toward increasing the reliability and energy absorption capacity of structural connections. In this paper an alternative approach to this problem is described. This approach is to separate the load carrying function of the structure from the energy absorbing function and to ask if special devices could be incorporated into the structure with the sole purpose of absorbing the kinetic energy generated in the structure by earthquake attack.
To determine whether such devices are feasible a study has been undertaken of three essentially different mechanisms of energy absorption. These mechanisms all utilized the plastic deformation of mild steel. They included the rolling of strips, torsion of square and rectangular bars, and the flexure of short thick beams. These mechanisms were selected for intensive study since they were basic to three different types of device each of which was designed for a separate mode of operation in a structural system.
The characteristics of these mechanisms which were of primary importance in this study were the load displacement relations, the energy absorption capacity and the fatigue resistance. This information was obtained with a view to the development of devices for specific structural applications.
This report describes the tests used to explore the basic mechanisms and the data obtained. It also include s a brief description of tests on scale models of a device which was designed to be located in the piers of a reinforced concrete railway bridge.
It has been shown by the tests that the plastic torsion of mild steel is an extremely efficient mechanism for the absorption of energy. It was found that at plastic strains in the range 3% to 12% it was possible to develop energy dissipation of the order of 2000-7500 lb in/in3 per cycle (14-50 x 106 N/M2 per cycle) with lifetimes within the range of 1000 to 100 cycles. It was also shown that the mode of failure in torsion is an extremely favourable one for use in an energy absorbing device in that it took the form of a gradual decay. The other two mechanisms studied were both less efficient and less reliable than torsion and had capacities of 500-2000 lb in/in3 per cycle (3.5 - 14 x 106 N/M2 per cycle) and life times of around 200 to 20 cycles. Nevertheless they lend themselves to more compact devices than does the torsional mechanism and furthermore the devices may be located in regions in a structure where they are readily accessible for replacement after attack.
384 citations
TL;DR: In this article, the elastic flexural-torsional buckling of simply supported tapered I-beams is studied and it is found that the changes in the torsional stiffness with the degree of taper are small, and consequently the elastic critical loads do not vary greatly.
Abstract: In this paper, the differential equation for the nonuniform torsion of tapered I-beams is derived by analyzing the deformations of the flanges, and this equation is used to study the elastic flexural-torsional buckling of simply supported tapered I-beams For constant flange beams which are tapered in depth, it is found that the changes in the torsional stiffness with the degree of taper are small, and that consequently the elastic critical loads do not vary greatly The elastic critical loads of constant depth beams which have tapered flanges decrease significantly as the degree of taper increases Torsion tests were carried out on tapered depth cantilevers and the results of these were in close agreement with the theoretical predictions Buckling tests were carried out on simply supported I-beams which were tapered in flange width, thickness or web depth, and the experimental critical loads confirmed the theoretical predictions
89 citations
TL;DR: In this paper, a triaxial torsion was used to test the liquefaction potential of a saturated sand sample in the presence of shear strain on the vertical piston.
72 citations
TL;DR: In this article, the authors considered the problem of determining stresses and deformations in elastic thin-walled, prismatical beams, subject to axial end forces and end bending and twisting moments, within the range of applicability of linear theory.
Abstract: The paper considers the problem of determining stresses and deformations in elastic thin-walled, prismatical beams, subject to axial end forces and end bending and twisting moments, within the range of applicability of linear theory. The technically most significant aspect of the work has to do with the analysis of the effect of anisotropy of the material, which is associated with previously not determined modes of coupling between stretching, bending, and twisting. Use of the general formulas of the theory is illustrated for a class of shells consisting of an 'ordinary' material (unable to support stress moments with axes normal to the middle surface of the shell, and unable to undergo transverse shear deformation). Here explicit formulas are obtained for certain types of open as well as of closed-cross-section beams.
57 citations
TL;DR: In this paper, the fracture criterion of critical COD was verified by using the results of the burst tests in titanium and aluminum alloy cryogenic pressure vessels, and the model was applied to the analysis of experimental data obtained from flat plates and cylindrical shells under axial tension, internal pressure, and torsion.
54 citations
TL;DR: In this article, the fully anti-symmetric problem for a cylindrical shell with a circumferential crack is considered, and the solution of the problem is reduced to a system of singular integral equations of the first kind.
Abstract: The fully anti-symmetric problem for a cylindrical shell with a circumferential crack is considered. The solution of the problem is reduced to that of a system of singular integral equations of the first kind. As an example the torsion of the cylinder is discussed and membrane and bending components of the stress intensity factor ratio are given.
52 citations
01 Jan 1972
TL;DR: In this paper, the authors developed a failure model for reinforced and prestressed concrete beams applicable to general cross sectional shapes including on one side small solid sections used in buildings, on the other side large sections such as box sections occurring in prestressed reinforced concrete bridges.
Abstract: Since about ten years experimental and theoretical research into the behavior of reinforced and prestressed concrete beams subjected to torsion and combined torsion-bending-shear has been intensified world wide (see e. g. [9]). For the past seven years such a program has been under way at the Institute of Structural Engineering, Swiss Federal Institute of Technology, Zurich. The aim of the project is to develop a failure model for reinforced and prestressed concrete beams applicable to general cross sectional shapes including on one side small solid sections used in buildings, on the other side large sections such as box sections occurring in prestressed concrete bridges. Results of the experimental and theoretical studies have been reported in references [1] to [5].
46 citations
TL;DR: In this article, a particular class of strain energy functions is discussed in relation to the finite deformation of solid and tubular cylinders of incompressible isotropic elastic material, and the predictions of the theory correspond closely with data from experiments on the combined torsion and extension of a solid cylinder of natural rubber.
Abstract: A particular class of strain-energy functions is discussed in relation to the finite deformation of solid and tubular cylinders of incompressible isotropic elastic material. It is shown that the predictions of the theory correspond closely with data from experiments on the combined torsion and extension of a solid cylinder of natural rubber. This deformation is universal, i.e. it can be maintained in any isotropic elastic solid by the application of suitable surface tractions. The axial and torsional shear deformations of a circular cylindrical tube, however, cannot be so maintained unless the constitutive law conforms with certain conditions. The material constants occurring in the strain-energy function considered here are shown to satisfy inequalities ensuring the existence of these deformations.
42 citations
TL;DR: In this paper, Biot's theory of consolidation is applied to beam-like structural elements by using the procedure of Michell, consisting of representation of stress and deformation components as rational integral functions of the axial coordinate z.
01 Jan 1972
TL;DR: BreBreuer and Gottlieb as mentioned in this paper proved that explicit characterization of spherical curves is a necessary and sufficient condition for a curve to be a spherical curve, without any precondition on the curvature and torsion.
Abstract: It will be proved that the "explicit characterization" of spherical curves recently obtained by S. Breuer and D. Gottlieb (Proc. Amer. Math. Soc. 27 (1971), pp. 126-127) is, without any precondition on the curvature and torsion, a necessary and sufficient condition for a curve to be a spherical curve. The proof is based on an earlier result of the present author on spherical curves (Monatsh. Math. 67 (1963), pp. 363-365).
TL;DR: In this article, a time independent incremental constitutive law corresponding to hypoelasticity is examined with particular reference to its description of failure, and material constants applicable to plain concrete are determined and the resulting law is shown to describe the behavior up to and including failure for both triaxial and combined torsion and compression loading.
TL;DR: In this paper, the nonlinear basic equations which govern the motion of beams are developed on the basis of three-dimensional theory of thermo-elastodynamics in terms of a reference state.
TL;DR: In this paper, the development and use of an experimental apparatus for testing materials in torsion at high rates of strain is described, where constant strain-rate data can be obtained at shear strain rates from 10 2 to 10 4 s −1, and the operation and instrumentation of a torsional split Hopkinson pressure-bar is presented along with a discussion of the accuracy and reliability of data obtained with this apparatus.
Abstract: The development and use of an experimental apparatus for testing materials in torsion at high rates-of-strain is described. Constant strain-rate data can be obtained at shear strain rates from 10 2 to 10 4 s −1 . The operation and instrumentation of a torsional split Hopkinson pressure-bar is presented along with a discussion of the accuracy and reliability of data obtained with this apparatus. In particular, the use of specimens having very short gage lengths to obtain data at high strain-rates is investigated experimentally. Data from high strain-rate tests on 2024-T351 aluminum alloy using specimens having gage lengths varying from 0–5 to 0–05 in. are all consistent and show this material to be slightly strain-rate dependent in torsion.
TL;DR: In this article, the authors make use of a recent advance in the theory of Mellin transforms to find the stress intensity factors and crack energy of a symmetric array of edge cracks in a circular cylinder under torsion.
TL;DR: An application of the finite element method to inelastic analysis of the Saint-Venant torsion problem, using a triangular element formulated on the basis of the hybrid stress approach, is described in this article.
Abstract: An application of the finite element method to inelastic analysis of the Saint-Venant torsion problem, using a triangular element formulated on the basis of the hybrid stress approach, is described. The stress field in the element is defined by a stress function which is assumed to vary linearly within the element. The warping function on the element boundary is also defined by a linear expression. Numerical results indicate that the method gives an accurate stress solution and is appropriate to the elastic-plastic analysis of bars of arbitrary cross-section which may include multiply connected regions. It is further shown that such phenomena as planar orthogonal plastic anisotropy, strain-hardening and unloading of relevant twisted bar can be treated in a unified manner.
01 Sep 1972
TL;DR: In this paper, the Flory-Huggins theory of the swelling of a crosslinked rubber by a liquid of low molecular weight is applied to the problem of a cylinder subjected to combined axial extension and torsion about the axis.
TL;DR: In this article, the effect of torsion on the swelling of a rubber cylinder in a low molecular-weight liquid was investigated and the results were less than the predicted values by amounts varying from 12% to 23%, depending to some extent on the type of rubber and on the degree of crosslinking.
TL;DR: In this article, the torsion of an infinitely long elastic shaft bonded to an elastic disk of finite width and of different elastic constants is considered, and the dominant kernel of the integral equation is of generalized Cauchy-type and the solution has a singularity of the form (c2−x2)−γ, where 2c is the width of the disk and 0 < γ < 12.
TL;DR: In this paper, a regular perturbation procedure and the Rayleigh-Ritz method are used to study the finite torsion of cylinders made of slightly compressible neo-Hookean materials.
Abstract: A regular perturbation procedure and the Rayleigh-Ritz method are used to study the finite torsion of cylinders made of slightly compressible neo-Hookean materials. Two cases are considered: 1. the length of the cylinder is not permitted to change during torsion and 2. the net axial force on the cylinder vanishes. The perturbation procedure fails for certain constitutive relations whereas, in principle, the Rayleigh-Ritz method has general applicability. When it works, the success of the perturbation procedure depends on prior knowledge of the problem for an incompressible material (the zeroth order nonlinear problem). The solution of problem 2. is considerably more complicated than the solution of problem 1. since the complete approximation of order n for problem 2. requires extensive work on the approximation of order ( n + 1).
TL;DR: The wedge-crack growth model proposed by Williams for creep rupture has been modified by inclusion of the Cottrell criterion for crack instability as discussed by the authors, which can be applied to conditions of high-strain-rate deformation where the grain size may be established by dynamic recrystallization.
Abstract: The wedge-crack growth model proposed by Williams for creep rupture has been modified by inclusion of the Cottrell criterion for crack instability. By combining this model with empirical relationships between strain rate, grain-boundary sliding rate, stress, and grain size, it can be applied to conditions of high-strain-rate deformation where the grain size may be established by dynamic recrystallization. Comparison of predicted rupture times with experimental results obtained in torsion indicates that control of ductility by wedge-crack growth is reasonable under these conditions and that the occurrence of dynamic recrystallization significantly decreases crack growth rates.
01 Jan 1972
TL;DR: In this paper, reinforced concrete beams loaded in combined torsion, bending and shear are compared to a study of the ultimate load-carrying capacity of reinforced concrete structures.
Abstract: Reinforced concrete beams loaded in combined torsion, bending and shear : a study of the ultimate load-carrying capacity
TL;DR: In this article, an analysis of coupled torsion-flapping rotor blade vibrations in response to atmospheric turbulence revealed that at high rotor advance ratios anticipated for future high speed pure or convertible rotorcraft both flapping and torsional vibrations can be severe.
Abstract: An analysis of coupled torsion-flapping rotor blade vibrations in response to atmospheric turbulence revealed that at high rotor advance ratios anticipated for future high speed pure or convertible rotorcraft both flapping and torsional vibrations can be severe. While appropriate feedback systems can alleviate flapping, they have little effect on torsion. Dynamic stability margins have also no substantial influence on dynamic torsion loads. The only effective means found to alleviate turbulence caused torsional vibrations and loads at high advance ratio was a substantial torsional stiffness margin with respect to local static torsional divergence of the retreating blade.