Showing papers on "Torsion (mechanics) published in 2000"

A new constitutive framework for arterial wall mechanics and a comparative study of material models

Abstract: In this paper we develop a new constitutive law for the description of the (passive) mechanical response of arterial tissue. The artery is modeled as a thick-walled nonlinearly elastic circular cylindrical tube consisting of two layers corresponding to the media and adventitia (the solid mechanically relevant layers in healthy tissue). Each layer is treated as a fiber-reinforced material with the fibers corresponding to the collagenous component of the material and symmetrically disposed with respect to the cylinder axis. The resulting constitutive law is orthotropic in each layer. Fiber orientations obtained from a statistical analysis of histological sections from each arterial layer are used. A specific form of the law, which requires only three material parameters for each layer, is used to study the response of an artery under combined axial extension, inflation and torsion. The characteristic and very important residual stress in an artery in vitro is accounted for by assuming that the natural (unstressed and unstrained) configuration of the material corresponds to an open sector of a tube, which is then closed by an initial bending to form a load-free, but stressed, circular cylindrical configuration prior to application of the extension, inflation and torsion. The effect of residual stress on the stress distribution through the deformed arterial wall in the physiological state is examined. The model is fitted to available data on arteries and its predictions are assessed for the considered combined loadings. It is explained how the new model is designed to avoid certain mechanical, mathematical and computational deficiencies evident in currently available phenomenological models. A critical review of these models is provided by way of background to the development of the new model.

Measurement of Newton's constant using a torsion balance with angular acceleration feedback.

Abstract: We measured Newton's gravitational constant G using a new torsion balance method. Our technique greatly reduces several sources of uncertainty compared to previous measurements: (1) It is insensitive to anelastic torsion fiber properties; (2) a flat plate pendulum minimizes the sensitivity due to the pendulum density distribution; (3) continuous attractor rotation reduces background noise. We obtain G = (6.674215+/-0.000092) x 10(-11) m3 kg(-1) s(-2); the Earth's mass is, therefore, M = (5.972245+/-0.000082) x 10(24) kg and the Sun's mass is M = (1.988435+/-0.000027) x 10(30) kg.

D-branes, B fields and twisted K theory

Abstract: In this note we propose that D-brane charges, in the presence of a topologically non-trivial B-field, are classified by the K-theory of an infinite dimensional C*-algebra. In the case of B-fields whose curvature is pure torsion our description is shown to coincide with that of Witten.

Solar collector and tracker arrangement

Abstract: A solar energy collector and tracker has at least one north-south oriented torsion tube (32) supporting an array of flat rectangular solar panels (34). At least one pier (36), supported in the earth, has a pivot member (40) in which the torsion tube (32) is journalled. A linear actuator (42) has a body portion mounted on a footing (45) separate from the pier footing and supported in the earth at a distance spaced from pier, and has a rod (44) coupled to a torque arm (46) on the torsion tube. The actuator (42) can be horizontally or vertically oriented. The torsion tube is of generally square cross section. The horizontal driver can be used to drive multiple rows of solar panels, with a linkage mechanism (68) connecting the torque arms (46) of the multiple rows. The linkage mechanism (68) can include a series of rigid link members articulated to one another, permitting use on uneven terrain. Wires can be concealed within the tubular members.

Helical and Localised Buckling in Twisted Rods: A Unified Analysis of the Symmetric Case

Abstract: We review the geometric rod theory for the case of a naturallystraight, linearly elastic, inextensible, circular rod suffering bendingand torsion but no shear. Our primary focus is on the post-bucklingbehaviour of such rods when subjected to end moment and tension.Although this is a classic problem with an extensive literature, datingback to Kirchhoff, the usual approach tends to neglect the physicalinterpretation of solutions (i.e., rod configurations) to the modelsproposed. Here, we explicitly compute geometrical properties of buckledrods. In a unified approach, making use of Kirchhoff's dynamic analogy,both the classical helical and the more recently investigated localisedbuckling are considered. Special attention is given to a consistenttreatment of concepts of link, twist and writhe.

Seat belt retractor

Abstract: The object is to provide a seat belt retractor which, by a relatively simple structure, makes it possible to increase the freedom with which an EA load is set and to set the EA load more stably. A seat belt retractor according to the present invention in which a torsion pipe (20) is disposed inside an annular space between a spool (4) and a torsion bar (7), with the left end portion of the torsion pipe (20) being connected and secured to securing pins (21) and (22). The right end portion of the torsion pipe (20) engages an externally threaded shaft (15) at a locking base (14) in a direction of rotation and can move axially relative to the externally threaded shaft (15). When the spool (4) rotates relative to the locking base (14) in a direction in which a webbing is extracted, the torsion bar (7) and the torsion pipe (20) are both twisted and deformed, so that impact energy is absorbed. Since the twisting and deformation of the torsion pipe (20) makes it shorter in length, the right end portion of the torsion pipe (20) disengages from the externally threaded shaft (15), so that energy is absorbed by twisting and deforming the torsion bar (7) alone.

Intermediate Mechanics of Materials

Abstract: Introduction.- 1.1 The Engineering design process 1.2 Design optimization 1.2.1 Predicting the behaviour of the component.- 1.2.2 Approximate solutions.- 1.3 Relative magnitude of different effects.- 1.4 Formulating and solving problems.- 1.4.1 Use of procedures.- 1.4.2 Inverse problems.- 1.4.3 Physical uniqueness and existence arguments.- 1.5 Review of elementary mechanics of materials.- 1.5.1 Definition of stress components.- 1.5.2 Transformation of stress components.- 1.5.3 Displacement and strain.- 1.5.4 Hooke's law.- 1.5.5 Bending of beams.- 1.5.6 Torsion of circular bars.- 1.6 Summary.- Problems.- 2 Material Behaviour and Failure.- 2.1 Transformation of stresses.- 2.1.1 Review of two-dimensional results.- 2.1.2 Principal stresses in three dimensions.- 2.2 Failure theories for isotropic materials.- 2.2.1 The failure surface.- 2.2.2 The shape of the failure envelope.- 2.2.3 Ductile failure (yielding).- 2.2.4 Brittle failure.- 2.3 Cyclic loading and fatigue.- 2.3.1 Experimental data.- 2.3.2 Statistics and the size effect.- 2.3.3 Factors influencing the design stress.- 2.3.4 Effect of combined stresses.- 2.3.5 Effect of a superposed mean stress.- 2.3.6 Summary of the design process.- 2.4 Summary.- Problems.- 3 Energy Methods.- 3.1 Work done on loading and unloading.- 3.2 Strain energy.- 3.3 Load-displacement relations.- 3.3.1 Beams with continuously varying bending moments.- 3.3.2 Axial loading and torsion.- 3.3.3 Combined loading.- 3.3.4 More general expressions for strain energy.- 3.3.5 Strain energy associated with shear forces in beams.- 3.4 Potential energy.- 3.5 The principle of stationary potential energy.- 3.5.1 Potential energy due to an external force.- 3.5.2 Problems with several degrees of freedom.- 3.5.3 Non-linear problems.- 3.6 The Rayleigh-Ritz method.- 3.6.1 Improving the accuracy.- 3.6.2 Improving the back of the envelope approximation.- 3.7 Castigliano's first theorem.- 3.8 Linear elastic systems.- 3.8.1 Strain energy.- 3.8.2 Bounds on the coefficients.- 3.8.3 Use of the reciprocal theorem.- 3.9 The stiffness matrix.- 3.9.1 Structures consisting of beams.- 3.9.2 Assembly of the stiffness matrix.- 3.10 Castigliano's second theorem.- 3.10.1 Use of the theorem.- 3.10.2 Dummy loads.- 3.10.3 Unit load method.- 3.10.4 Formal procedure for using Castigliano's second theorem.- 3.10.5 Statically indeterminate problems.- 3.10.6 Three-dimensional problems.- 3.11 Summary.- Problems.- 4 Unsymmetrical Bending.- 4.1 Stress distribution in bending.- 4.1.1 Bending about the x-axis only.- 4.1.2 Bending about the y-axis only.- 4.1.3 Generalized bending.- 4.1.4 Force resultants.- 4.1.5 Uncoupled problems.- 4.1.6 Coupled problems.- 4.2 Displacements of the beam.- 4.3 Second moments of area.- 4.3.1 Finding the centroid.- 4.3.2 The parallel axis theorem.- 4.3.3 Thin-walled sections.- 4.4 Further properties of second moments.- 4.4.1 Coordinate transformation.- 4.4.2 Mohr's circle of second moments.- 4.4.3 Solution of unsymmetrical bending problems in principal coordinates.- 4.4.4 Design estimates for the behaviour of unsymmetrical sections.- 4.4.5 Errors due to misalignment.- 4.5 Summary.- Problems.- 5 Non-linear and Elastic-Plastic Bending.- 5.1 Kinematics of bending.- 5.2 Elastic-plastic constitutive behaviour.- 5.2.1 Unloading and reloading.- 5.2.2 Yield during reversed loading.- 5.2.3 Elastic-perfectly plastic material.- 5.3 Stress fields in non-linear and inelastic bending.- 5.3.1 Force and moment resultants.- 5.4 Pure bending about an axis of symmetry.- 5.4.1 Symmetric problems for elastic-perfectly plastic materials.- 5.4.2 Fully plastic moment and shape factor.- 5.5 Bending of a symmetric section about an orthogonal axis.- 5.5.1 The fully plastic case.- 5.5.2 Non-zero axial force.- 5.5.3 The partially plastic solution.- 5.6 Unsymmetrical plastic bending.- 5.7 Unloading, springback and residual stress.- 5.7.1 Springback and residual curvature.- 5.7.2 Reloading and shakedown.- 5.8 Limit analysis in the design of beams.- 5.8.1 Plastic hinges.- 5.8.2 Indeterminate problems.- 5.9 Summary.- Problems.- 6 Shear and Torsion of Thin-walled Beams.- 6.1 Derivation of the shear stress formula.- 6.1.1 Choice of cut and direction of the shear stress.- 6.1.2 Location and magnitude of the maximum shear stress.- 6.1.3 Welds, rivets and bolts.- 6.1.4 Curved sections.- 6.2 Shear centre.- 6.2.1 Finding the shear centre.- 6.3 Unsymmetrical sections.- 6.3.1 Shear stress for an unsymmetrical section.- 6.3.2 Determining the shear centre.- 6.4 Closed sections.- 6.4.1 Determination of the shear stress distribution.- 6.5 Pure torsion of closed thin-walled sections.- 6.5.1 Torsional stiffness.- 6.5.2 Design considerations in torsion.- 6.6 Finding the shear centre for a closed section.- 6.6.1 Twist due to a shear force.- 6.6.2 Multicell sections.- 6.7 Torsion of thin-walled open sections.- 6.7.1 Loading of an open section away from its shear centre.- 6.8 Summary.- Problems.- 7 Beams on Elastic Foundations 7.1 The governing equation.- 7.1.1 Solution of the governing equation.- 7.2 The homogeneous solution.- 7.2.1 The semi-infinite beam.- 7.3 Localized nature of the solution.- 7.4 Concentrated force on an infinite beam.- 7.4.1 More general loading of the infinite beam.- 7.5 The particular solution.- 7.5.1 Uniform loading.- 7.5.2 Discontinuous loads.- 7.6 Finite beams.- 7.7 Short beams.- 7.8 Summary.- Problems.- 8 Membrane Stresses in Axisymmetric Shells.- 8.1 The meridional stress.- 8.1.1 Choice of cut.- 8.2 The circumferential stress.- 8.2.1 The radii of curvature.- 8.2.2 Sign conventions.- 8.3 Self-weight.- 8.4 Relative magnitudes of different loads.- 8.5 Strains and Displacements.- 8.5.1 Discontinuities.- 8.6 Summary.- Problems.- 9 Axisymmetric Bending of Cylindrical Shells.- 9.1 Bending stresses and moments.- 9.2 Deformation of the shell.- 9.3 Equilibrium of the shell element.- 9.4 The governing equation.- 9.4.1 Solution strategy.- 9.5 Localized loading of the shell.- 9.6 Shell transition regions.- 9.6.1 The cylinder/cone transition.- 9.6.2 Reinforcing rings.- 9.7 Thermal stresses.- 9.8 The ASME pressure vessel code.- 9.9 Summary.- Problems.- 10 Thick-walled Cylinders and Disks.- 10.1 Solution method.- 10.1.1 Stress components and the equilibrium condition.- 10.1.2 Strain, displacement and compatibility.- 10.1.3 The elastic constitutive law.- 10.2 The thin circular disk.- 10.3 Cylindrical pressure vessels.- 10.4 Composite cylinders, limits and fits.- 10.4.1 Solution procedure.- 10.4.2 Limits and fits.- 10.5 Plastic deformation of disks and cylinders.- 10.5.1 First yield.- 10.5.2 The fully-plastic solution.- 10.5.3 Elastic-plastic problems.- 10.5.4 Other failure modes.- 10.5.5 Unloading and residual stresses.- 10.6 Summary.- Problems.- 11 Curved Beams.- 11.1 The governing equation.- 11.1.1 Rectangular and circular cross sections.- 11.1.2 The bending moment.- 11.1.3 Composite cross sections.- 11.1.4 Axial loading.- 11.2 Radial stresses.- 11.3 Distortion of the cross section.- 11.4 Range of application of the theory.- 11.5 Summary.- Problems.- 12 Elastic Stability.- 12.1 Uniform beam in compression.- 12.2 Effect of initial perturbations.- 12.2.1 Eigenfunction expansions.- 12.3 Effect of lateral load (beam-columns).- 12.4 Indeterminate problems.- 12.5 Suppressing low-order modes ..- 12.6 Beams on elastic foundations.- 12.6.1 Axisymmetric buckling of cylindrical shells.- 12.6.2 Whirling of shafts.- 12.7 Energy methods.- 12.7.1 Energy methods in beam problems.- 12.7.2 The uniform beam in compression.- 12.7.3 Inhomogeneous problems.- 12.8 Quick estimates for the buckling force.- 12.9 Summary.- Problems.- A The Finite Element Method.- A.1 Approximation.- A.1.1 The 'best' approximation.- A.1.2 Choice of weight functions.- A.1.3 Piecewise approximations.- A.2 Axial loading ..- A.2.1 The structural mechanics approach.- A.2.2 Assembly of the global stiffness matrix.- A.2.3 The nodal forces.- A.2.4 The Rayleigh-Ritz approach.- A.2.5 Direct evaluation of the matrix equation.- A.3 Solution of differential equations.- A.4 Finite element solutions for the bending of beams.- A.4.1 Nodal forces and moments.- A.5 Two and three-dimensional problems.- A.6 Computational considerations.- A.6.1 Data storage considerations.- A.7 Use of the finite element method in design.- A.8 Summary.- Problems.- B Properties of Areas.- C Stress Concentration Factors.- D Answers to Even Numbered Problems.- Index.

Long-life torsion fatigue with normal mean stresses

Abstract: Relatively simple fatigue tests have been performed on two common engineering materials, cast ductile iron and low-carbon steel, using two stress states, cyclic torsion and cyclic torsion with static axial and hoop stresses. Tests were designed to discriminate between normal stress and hydrostatic stress as the most suitable mean stress correction term for high cycle fatigue analysis. Microscopy shows that cracks in low-carbon steel nucleate and grow on maximum shear planes, while for cast iron pre-existing flaws grow on maximum normal stress planes. The data illustrate that tensile normal stress acting on a shear plane significantly reduced fatigue life and is an appropriate input for fatigue analysis of ductile materials. Static normal stresses did not significantly affect the fatigue life for the cast iron because the net mean stress on the maximum normal stress plane was zero. Mean torsion significantly reduced the fatigue strength of the cast iron. A critical plane long-life parameter for nodular iron which accounts for both stress state and mean stress is proposed, and is found to accurately correlate experimental data.

Experimental validation of smeared analysis for plain concrete in torsion

Abstract: This is the second of two papers concerned with the development and the application of a smeared crack model for the description of the behavior of concrete elements in torsion. The first paper presented the development of an efficient model for the torsional analysis of concrete that utilizes a special numerical technique, which is properly adapted to include the smeared crack approach. This paper presents the validation of the analytical model by providing comparisons between analytically predicted behavior curves and experimentally obtained ones. The experimental data used in this paper comprise a series of tests in pure torsion conducted for this purpose and a database of experimental information compiled from works around the world, in an attempt to establish the validity of the proposed approach based on a broad range of parametric studies. From the comparisons between the predicted and the measured data, it is concluded that the proposed approach describes very well the behavior of concrete element...

3D Wind-Excited Response of Slender Structures: Closed-Form Solution

Abstract: Along-wind, crosswind, and torsional vibrations of structures are different aspects of the same physical phenomenon. Despite this fact, each aspect has been the object of numerous studies involving lines of research that have frequently been independent of each other. These independent lines of research have often been characterized by notable inconsistencies and clashes. This paper proposes a single coherent formulation that provides compact expressions for estimating the along-wind, crosswind, and torsional response based on a generalized gust factor approach. It presents the wind-loading model and uses a generalized equivalent spectrum technique to derive closed-form solutions of the 3D wind-excited response of slender structures and structural elements. This extends a solution previously obtained for along-wind vibrations to the crosswind and torsional response. Numerical examples are provided that illustrate the simplicity and precision of this method. Because of this simplicity and precision, the method is suitable for use in design offices as a means of providing rapid estimates of the dynamic response of slender structures to gust buffeting actions. In particular, the estimates of the crosswind and torsional response will allow the designers to make more informed decisions on when to conduct physical model studies in boundary-layer wind tunnels.

Comparative study of large strain methods for assessing failure characteristics of selected food gels

Abstract: Vane rheometry was compared with uniaxial compression and torsion in evaluating the effects of strain rate on failure shear stress and deformation of soybean protein (tofu) and gellan gum gels. A Haake VT 550 viscotester was used for torsion and vane tests, and compression was performed with an Instron/MTS universal testing machine. Strain or angular deformation at failure was independent of strain rate in the three testing modes. In vane rheometry, failure shear stress increased with increasing low shear rates (< 0.100 s−1) and was rate independent at higher rates. This strain rate dependency was also evident in compression, varying with the material. For torsion, fracture stress appeared to be rate independent. Shear fracture stresses measured in torsion and compression were in good agreement at strain rates above 0.025 s−1 and 0.100 s−1 for tofu and gellan gels, respectively. Shear stresses from the vane method were lower than shear stresses of torsion and compression. Similar texture maps of the food gels studied were generated by plotting stress and strain or angular deformation values of the three testing methods. The findings validate the vane technique as an alternative to torsion and compression for rapid textural characterization of viscoelastic foods.

On a moderate rotation theory of thin-walled composite beams

Abstract: A small strain and moderate rotation theory of laminated composite thin-walled beams is formulated by generalizing the classical Vlasov theory of sectorial areas. The proposed beam model accounts for axial, bending, torsion and warping deformations and allows one to predict critical loads and initial post-buckling behaviour. A finite element approximation of the theory is also carried out and several numerical applications are developed with reference to lateral buckling of composite thin-walled members. The sensitivity of critical load to second-order effects in the pre-buckling range is pointed out.

Shear lag of thin-walled curved box girder bridges. technical note

Abstract: Thin-walled curved box girders are widely used in grade separation and viaduct bridges. This note investigates the influence of shear lag for these girders, including longitudinal warping. The longitudinal warping displacement functions of the flange slabs are approximated by a cubic parabolic curve instead of a quadratic curve of Reissner's method. On the basis of the thin-walled curved bar theory and the potential variational principle, the equations of equilibrium considering the shear lag, bending, and torsion (St. Venant and warping) for a thin-walled curved box girder are established. The closed-form solutions of the equations are derived, and Vlasov's equation is further developed. The obtained formulas are applied to calculate the shear lag effects for curved box girder bridges. Numerical examples are presented to verify the accuracy and applicability of the method.

Polysulfide anions II: structure and vibrational spectra of the S4(2-) and S5(2-) anions. Influence of the cations on bond length, valence, and torsion angle.

Abstract: The influence of the cations on bond length, valence, and torsion angle of S4(2-) and S5(2-) anions was examined in a series of solid alkali tetra- and pentasulfides by relating their Raman spectra to their known X-ray structures through a force-field analysis. The IR and Raman spectra of BaS4.H2O and the Raman spectra of (NH4)2S4.nNH3, gamma-Na2S4, and delta-Na2S5 are presented. The similarity of spectra of gamma-Na2S4 with those of BaS4.H2O suggests similar structures of the S4(2-) anions in these two compounds with a torsion angle smaller than 90 degrees. The variations of SS bond length, SSS valence angle, and dihedral angle of Sn2- anions are related to the polarization of the lone pair and electronic charge of the anion by the electric field of the cations. A correlation between the torsion angle and the SSS valence angle is shown as that previously reported between the length of the bond around which the torsion takes place and the dihedral angle value. These geometry changes are explained by the hyperconjugation concept and the electron long-pair repulsion.

Shear Lag of Thin-Walled Curved Box Girder Bridges

Abstract: This note investigates the influence of shear lag for thin-walled curved box girders, including longitudinal warping. The longitudinal warping displacement functions of the flange slabs are approximated by a cubic parabolic curve instead of a quadratic curve of Reissner’s method. On the basis of the thin-walled curved bar theory and the potential variational principle, the equations of equilibrium considering the shear lag, bending, and torsion (St. Venant and warping) for a thin-walled curved box girder are established. The closed-form solutions of the equations are derived, and Vlasov’s equation is further developed. The obtained formulas are applied to calculate the shear lag effects for curved box girder bridges. Numerical examples are presented to verify the accuracy and applicability of the present method.

Smeared Crack Analysis for Plain Concrete in Torsion

Abstract: This is the first of two papers addressing the efficient approach of the torsional behavior of concrete elements through smeared crack analysis. This paper presents the development of an analytical model for the behavior of concrete elements in increasing torsion. The model is based on a special numerical technique that employs constitutive relations expressed in terms of normal stress and crack width, for the behavior of the crack process zones. The width of a crack process zone is considered as a material property and is estimated through comparisons between analytical and experimental data. The method is not restricted by the cross section shape because the analysis includes numerical mapping. Examination of the objectivity of the proposed analysis in relation to the used mesh density is included in the study. The proposed approach is also applicable to concrete elements subjected to torsion combined with flexure, shear, and axial force. Validation of the analytical model derived in this paper is demonstrated in a companion paper using extensive comparisons between predicted and experimentally obtained behavior curves and ultimate torque values.

SIF and threshold for small cracks at small notches under torsion

Abstract: The basic approach to the problem of torsional fatigue strength of pieces containing defects is based on the stress concentration factor concept. However, experiments have shown that the torsional fatigue limit of specimens containing small holes is controlled by the threshold condition for small cracks emanating from small notches. Therefore, the ratio of torsional to bending fatigue limit (τw /σw ) for specimens containing small defects must be studied from the viewpoint of fracture mechanics. The scope of this paper is to address the calculation of the stress intensity factor for a small crack emanating from a three-dimensional hole under a biaxial state of stress by using the weight function method and to apply it to the fatigue limit prediction. The results obtained are in good agreement with experimental results on specimens with defects.