Showing papers on "Torsion (mechanics) published in 1983"

The Cauchy Problem for the R + R 2 Theories of Gravity Without Torsion

Abstract: The exterior Cauchy problem is discussed for the fourth‐order theories of gravity derived from the Lagrangian densities L=(−g)1/2 (R+ (1/2)aR2+bRμν Rμν) −κLm. When b≠0, the Cauchy problem can be solved by the standard method already used in general relativity. When b=0, the problem cannot be formulated as in the case where b≠0, since the corresponding fourth‐order theory is shown to be equivalent to a second‐order scalar–tensor theory. This scalar–tensor theory is proved to coincide with one of the models of gravity proposed by O’Hanlon in order to present a covariant version of the massive dilaton theory suggested by Fujii. This result is generalized: The models of O’Hanlon are shown to be indistinguishable from the fourth‐order theories derived from the Lagrangian densities L=(−g)1/2 F(R)−κLm, where F is any real function such that F″(R) does not identically vanish.

Introduction to Linear Elasticity

Abstract: Preface 1 Introduction and Mathematical Preliminaries 2 Traction, Stress and Equilibrium 3 Deformations 4 Material Behavior 5 Formulation, Uniqueness and Solution Strategies 6 Extension, Bending and Torsion 7 Two-Dimensional Elaticity 8 Bending of Thin Plates 9 Time-Dependent Effects 10 Energy Principles 11 Strength and Failure Criteria 12 Something New Index

Predictions of Nonlinear Fracture Process Zone in Concrete

Abstract: Crack propagation in concrete is associated with a nonlinear zone around the crack-tip. the size of this fracture process zone length may be large depending upon the size of the aggregates and the geometry of the specimen. A theoretical model to predict the extent of this nonlinear zone and a method to include the effects of this nonlinearity in predicting the fracture resistance of concrete are described. The model is based on some simple and approximate extensions of the concepts of linear elastic fracture mechanics. The model is successfully used to analyze the results of the experiments on double cantilever, double torsion and the notched-beam specimens.

Damped second-order Rayleigh-Timoshenko beam vibration in space—an exact complex dynamic member stiffness matrix

Abstract: A uniform linear beam in a uniform linear ambient medium is studied. The beam performs stationary harmonic damped nonsynchronous space vibration in simultaneous tension, torsion, bending and shear in the presence of a large static axial load. Hysteretic and viscous dampings of the beam material and ambient medium are considered. Generalized complex Kolousek functions are derived. A 12 × 12 complex symmetric stiffness matrix is established for a supported beam member excited at its ends by prescribed harmonic translations and rotations which have the same frequency but may be out of phase. This matrix allows for an exact analysis of nonproportionally damped built-up beam structures, thus avoiding assumed mode shapes and lumped or consistent masses. A general notation is suggested. Numerical examples are given, including applications of the computer program SFVIBAT-DAMP.

Shear beam load cell

Abstract: A shear beam load cell comprising a cantilevered beam member having a free end weigh section for receiving a load force to be measured, a mounting section for securing the beam member, and recesses formed in opposing sides of the cantilevered beam free end weigh section for defining an unsymmetrical I-shaped cross-section. The recesses have dimensions such that one of the recesses has its bottom wall surface insensitive to torsion. In one embodiment, the recess with the bottom surface insensitive to torsion has a depth longer than the other recess. In another embodiment, the recess with the bottom surface insensitive to torsion has a height shorter than the other recess. A strain gage sensing device is positioned in that one recess on that bottom wall surface insensitive to torsion for measuring the shear strain corresponding to the load force applied to the free end weigh section of the beam member. This shear beam load cell requires only a strain gage sensing device in that one recess connected to the four different arms of a Wheatstone bridge circuit for electrically measuring the principal shear strains associated with the load force. The dimensions of the recesses can be calculated in accordance with a formula such that the centroids for the unsymmetrical I-shaped cross-section are located in a plane substantially coinciding to the bottom wall surface of one of the recesses. The recess dimensions can then be further adjusted to correct for the actual mounting of the strain gage sensing device within the recess and for any proximity effects of the load force applied on the weigh section in relationship to the recess so that the strain gage sensing device is insensitive to twisting moments and torsion.

A high-strain biaxial-testing rig for thin-walled tubes under axial load and pressure

Abstract: It is well know that high-strain biaxial testing with axial force and pressure on thin-walled tubes can be interesting from several points of view: capability of testing over the whole range of strain or stress ratios, great versatility of testing. and because of the physical system, the measured strains and stresses are principal. Nevertheless, there are few experimental-biaxial-fatique data due to the complexity of the testing equipment involved. In this paper, an experimental testing rig capable of subjecting thin-walled tubes to combined dynamic loadings in tension-compression with torsion and tension-compression with internal-external pressure is presented. The following components are described: the mechanical and hydraulic system, servohydraulic control, specimen configuration, strain-measuring equipment and data-acquisition system. The computation of stresses and strains, as well as examples of data acquisition, are also shown.

Neutron interference: general theory of the influence of gravity, inertia and space-time torsion

Abstract: The general theory of the influence of gravity, inertia (i.e. interferometer motion) and space-time torsion on the outcome of neutron interference experiments is presented. The exact results are obtained in a general relativistic treatment based on the description of a stationary working interferometer in Riemann-Cartan space-time and on the WKB approximation for the neutron waves. Particular attention is paid to the influence on the spinor amplitude. There are two types of resulting amplitude effects; one originates in the non-integrability of the spinor connection and represents the influence of a modified Riemann-Cartan curvature; the other is caused by the influence of the interferometer rotation and acceleration and of space-time torsion during the time interval between the emission of the two coherent neutron waves. For practical purposes small effects are treated in an approximation. Two examples of a global evaluation of the expressions are given. Applications including a gravitational Aharonov-Bohm effect are discussed.

Isoperimetric Inequalities in the Torsion and Clamped Membrane Problems for Convex Plane Domains

Abstract: Bounds for the curvature of the level curve of the torsion function through an arbitrary point in a convex region D, are used to derive improved isoperimetric inequalities for maximum stress, the torsional rigidity and other functionals. These inequalities are exact if D is either a circle or an infinite strip. A similar procedure is used in the clamped membrane problem, and again improved isoperimetric inequalities are derived.

Centro‐symmetric technique for measuring shear modulus, viscosity, and surface tension of spread monolayers

Abstract: We have constructed an apparatus which enables one to measure, simultaneously, the shear modulus, the viscosity, and the surface pressure of a monomolecular film on water under a hydrostatic compression. It is particularly suitable for measurements of the static shear modulus of insoluble monolayers. A capillary wave generator/detector system was also incorporated to determine the surface pressure. The trough is a Teflon cup 12.7 cm (5.4 in.) in inner diameter with sloping interior sides. As the cup is raised, while maintaining the water elevation fixed, the film is uniformly compressed. A rotor suspended at the center from a fine torsion fiber is used to measure the mechanical properties (surface viscosity and/or surface shear modulus). To measure the quasistatic shear properties, the cup is rotated through a small angle and the residual deflection of the rotor determined. Dynamic shear response is probed by studying transient torsional oscillations following a sudden angular displacement of the torsion ...

On the correlation between solid-particle erosion and fracture parameters in SiC

Abstract: The fracture toughness,KIc, for a hot-pressed SiC and three types of reaction-bonded SiC has been measured using the Hertzian indentation technique with spherical indentors whose radii varied from 2.5 to 10 mm. Excellent agreement between the toughness measured by this technique and the publishedKIc value measured using double torsion is obtained for the hot-pressed SiC. The Vickers hardness,H, which was also measured, andKIc have been used to predict the solid-particle erosion rate, ΔW, given by ΔW ∞H a K c b where the values of the exponentsa andb depend on the details of the erosion model. The predicted rates are not in agreement with the measured rates. This discrepancy is probably due to the fact that the models are insensitive to microstructure.

Elastic beam-torsion rod connection

Abstract: A twist isolating connection between a distal end of an elastic beam disposed transversely of a vehicle sprung mass and an adjacent end of a torsion rod disposed longitudinally of the sprung mass between a suspension control arm and the elastic beam distal end, the connection including a yoke rigidly attached to the end of the torsion rod with a pair of legs straddling a platform member on the distal end of the elastic beam, and a pair of protuberances on the legs engaging opposite sides of the platform member in a common transverse plane of the sprung mass but at laterally spaced locations. The elastic beam is thus clamped between the protuberances which transfer torsional moments to the elastic beam for resistance in bending modes but which isolate the elastic beam from the torsion rod with respect to twisting of the beam due to beam bending of the torsion rod.

Spin and torsion in the very early universe

Abstract: In the very early universe with temperature T between 1024 K and 1032 K the gravitational effect of torsion is dominant if particles with spin are sufficiently polarized. The source of the torsion is the spin density and the latter is usually described by a classical theory of Weyssenhoff and Raabe. In this article the spinning particles are described quantum mechanically, i.e. with a Dirac field and the spin density is defined as the source of the torsion. The macroscopic average of the spin density is obtained by the relativistic Wigner function formalism. The expression of the spin density, as derived in this article, is different from the classical one, except when both are zero.

Arbitrary spin field equations on curved manifolds with torsion

Abstract: The authors generalise previous work (Christensen and Duff 1979) on a simple set of arbitrary spin field equations for fields propagating on curved manifolds without torsion. As a prelude to an extensive study of index theorems and anomalies in the case of non-zero torsion, new arbitrary spin field equations are developed and the consistency conditions discussed. Some of the machinery needed for future investigations of arbitrary spin fields is developed using the two-component spinor formalism.

Tension-Torsion Characteristics of the Canine Anterior Cruciate Ligament—Part II: Experimental Observations

Abstract: An experimental program was devised to determine whether the canine anterior cruciate ligament (ACL), with an apparent helical twist of its component fiber bundles, could support a torque during axial loading to failure. At the point of first significant failure, the anterior cruciate was found to develop an average maximum torque of 122 +/- 26 N-mm (mean +/- SEM) for the nine tension-torsion tests performed. A nearly linear axial force-torque curve was also observed where the average slope of all tests was 5.2 +/- 0.2 mm-1 (mean +/- SEM). The experimental axial force data was then used to determine material parameters in the constitutive equation for the fascicle and underlying bone. A nonlinear ligament model based on this response was found to reproduce the axial force data adequately and to reasonably predict the observed ligament torque over the entire subfailure loading range. The presence of a ligament torque during axial loading has implications in the design and selection of a ligament substitute. Such a substitute has already been examined in the canine in another study. The results also suggest more refined experiments which could relate the mechanical properties of a ligament to its detailed macrostructure and insertion site geometries.

Twin tension/torsion beam rotor system

Abstract: A rotor system for a helicopter including a tension/torsion component (20) which is fabricated from composite material and as a compound curved, continuous loop twin tension/torsion beam Each end of the twin tension/torsion beam (20) includes two curved (wrapped) ends which are oriented substantially orthogonally At one end the curved ends (20a, 20b) extend about the flap hinge (18), and at the other end the curved ends (20c, 20d) extend about the fold and lead/lag hinge of the rotor system To accommodate the twin tension/ torsion beam at the flap hinge a support fitting (42) is provided with lugs (44, 46) which are made compatible with the rotor hub lugs (28,30,32), and to accommodate the twin tension/torsion beam (20) at the fold and lead/lag hinge a pitch varying structure (76) is provided with twin beam engaging clevis surfaces (106)

Extended capabilities of a vibrating‐reed internal friction apparatus

Abstract: Two developments are described in a vibrating‐reed technique used for internal friction studies of foils and thin films. One is an activation procedure that enables measurements to be made on the blank reeds of fused silica used as substrates for thin films. This procedure is also relevant to the study of insulating films. The other development is an ability to make measurements on electrically conducting samples in both torsional and flexural vibration.

Proposed design procedures for shear and torsion in reinforced and prestressed concrete

Abstract: The object of this study is to propose and evaluate a design procedure for shear and torsion in reinforced and prestressed concrete beams, with the aim of clarifying and simplfying current design requirements and AASHTO requirements In previous reports in this series a three-dimensional space truss model with variable angles of inclination of the diagonals was introduced as a design model and shown by comparison with test data to be a conservative yet more accurate model than current ACI/AASHTO design approaches The general nature of this variable angle truss model makes it extremely useful to the designer in treating complex shear and torsion problems Several examples of such applictions are included in this report Specific recommendations for incorporating such models are presented in language and expressions consistent with the type of language used in AASHTO Bridge Specifications Several design examples are included both to clarify the application of the design model and to provide a comparison of the reinforcement using both the proposed changes and the current AASHTO requirements

Surface-acoustic-wave, digitized angular accelerometer

Abstract: An angular accelerometer utilizing a sensing element 10 comprising a strain member 18 and a crosswise torsion member 24, both substantially comprising flat beams 18 and 25, respectively. The strain member 18 is affixed at each end to the object whose angular acceleration is to be measured, the angular acceleration vector lying along the axis of the strain member 18. The torsion member 24 is formed with an end mass 26,26' at each end. The strain member 18 is formed from a material such as quartz whose elasticity changes in proportion to the torque it experiences. A high-frequency surface acoustic wave is sent along the strain member and the change in its frequency due to the torque in the strain member 18 is measured.

Serviceability behavior and failure mechanisms of concrete inverted t-beam bridge bentcaps

Abstract: Structural behavior of inverted T-beams differs from that of the more conventional top-loaded standard T-section. The response of prestressed members may be significantly different from that of reinforced members. Due to the lack of recommendation available for the design of beams to resist torsion, this study was conducted to provide data for designing both conventional and prestressed concrete inverted T-beam bentcaps with special attention to web reinforcement, both the amount and location of stirrups; service load cracking in response to equal and opposite torsions due to traffic loads; strength and stiffness of web and flange as the amount of combined flexure, shear, and torsion increases to the maximum capacity. Strength and serviceability behavior of inverted T-beams bentcaps is also examined with emphasis on experimental study.