Showing papers on "Bending moment published in 1971"

Bend propagation by a sliding filament model for flagella

Abstract: 1. If active sliding occurs between flagellar filaments, as suggested for the sliding filament mechanism for muscular contraction, it will generate positive bending in one direction along the flagellum and negative bending in the opposite direction. Bends will therefore be propagated automatically if the sliding process is activated by bending. 2. The active bending moment required to match the viscous bending moments resulting from the uniform propagation of bending waves can be generated by a simple relationship between the curvature of the flagellum at any point and the magnitude of the moment per unit length generated by the active sliding process at that point. 3. This propagation mechanism incorporates features of the two mechanisms proposed previously for flagellar-bend propagation. The major difficulties which arise when these propagation mechanisms are developed in terms of a ‘local-bending’ model for flagellar bending are avoided when a ‘sliding filament’ model is used. 4. The elastic constants of the flagellum have a minor role in bend propagation, and without additional assumptions their magnitudes cannot be obtained from measurements of the parameters of flagellar bending-wave propagation.

Buckling of a thin annular plate under uniform compression

Abstract: thin rods, is solved. The analysis yields a set of stability criteria involving the system parameters such as the body moments of inertia, the length and mass distribution of the elastic rods, the lowest natural frequencies of the rods, and the satellite spin velocity. The power of the method is illustrated by the relative ease with which closed-form stability criteria are derived and by the amount of information which can be extracted from their ready physical interpretation. In particular, the analysis shows that, for stability, the spinning motion is to be imparted about the axis of maximum moment of inertia. This is the well-known "greatest moment of inertia" requirement. Moreover, the initial spin velocity flc should not be merely lower than the first natural frequencies Aiu and Air associated with the transverse vibration of the rods (as the frequency of simple harmonic excitation of the rods should be if resonance is to be prevented), but the ratios Os/AiM and fi./Ai,, are dictated by the system parameters. Of course, for very stiff rods the natural frequencies AI« and AIV may be sufficiently high that the satisfaction of criteria (40) is ensured. References

Reinforced concrete beams under load reversals

Abstract: A SERIES OF 12 REINFORCED CONCRETE CANTILEVER BEAMS WERE SUBJECTED TO REVERSALS OF OVERLOAD TO DETERMINE THE EFFECT OF LOAD HISTORY ON THE STRENGTH, DUCTILITY, AND MODE OF FAILURE OF THE BEAMS, THE RESULTS SHOWED THAT THE BEHAVIOR OF THE SPECIMENS UNDER LOAD REVERSAL WAS INFLUENCED PRIMARILY BY SHEER. CHANGES IN BEAM GEOMETRY OR LOAD HISTORY WHICH REDUCED THE SHEAR FORCE OR INCREASED THE SHEAR CAPACITY OF THE BEAM SIGNIFICANTLY INCREASED THE ENERGY ABSORBING CAPACITY AND THE NUMBER OF CYCLES TO FAILURE. /AUTHOR/

Cross-Section of Human Lower Leg Bones Viewed from Strength of Materials

Abstract: The bones of the lower leg were examined from the viewpoint of strength of materials. The area, the moment of inertia of area and the polar moment of inertia of area of the cross-section at the middle of the lower leg bones were calculated. The resistance of the bone against the normal force, against the bending moment and against the torsion can be shown by these properties of the cross-section. The properties of the shape of the bones do not correlate with the age of the specimen. The sexual dimorphism is clear. The fibula is very much weaker than the tibia. The index of cross-section has no direct correlation with the strength of bones nor with the curvature of tibia shaft.

Postcracking stiffness of reinforced concrete beams in torsion and bending

Abstract: THEORETICAL EXPRESSIONS FOR THE POSTRCRACKING STIFFNESS OF RECTANGULAR REINFORCED CONCRETE BEAMS IN TORSION AND BENDING ARE DESCRIBED AND SIMPLIFIED. THEY ARE BASED ON A SPACE TRUSS MODEL. IT IS SHOWN THAT THE POSTRCRACKING TORSIONAL STIFFNESS IS NOT GREATLY INFLUENCED BY BENDING WHILE THE POSTCRACKING FLEXURAL STIFFNESS DEPENDS ON THE AMOUNT OF TORSION. REALIZING THAT THE DROP IN TORSIONAL STIFFNESS AFTER CRACKING IS GREATER THAN THE DROP IN FLEXURAL STIFFNESS, THE TORSIONAL MOMENTS AFTER CRACKING WILL BE SMALLER IN MANY CASES THAN THE ONES PREDICTED BY THE UNCRACKED STIFFNESS VALUES. THE TORSIONAL REINFORCEMENT MAY THUS BE REDUCED BY MEANS OF THE TOOLS PROVIDED IN THIS PAPER. /ACI/

A finite element procedure for large deflection analysis of plates with initial deflections

Abstract: The concepts of the matrix displacement approach to finite element structural analysis are extended to analyze the large deflection behavior of plates with initial deflections. The initial deflections are considered to be of the order of magnitude of the plate thickness. The large deflection phenomena are accounted for by considering the influence of the element membrane forces due to initial deflection and large bending on element flexure stiffness matrices. The effects of element membrane forces due to initial deflection and large bending are characterized in the nonlinear stiffness formulations by the zero, first, and second order incremental stiffness matrices. Representations of the nonlinear effects are formulated for a conforming rectangular plate finite element. The formulations are appropriate for both the iterative and incremental approaches. Large deflection behaviors are predicted for rectangular plates with different length-width ratios and various boundary conditions. Comparisons with some available alternative analytic solutions are provided. Examples are performed by a piecewise linear incremental approach. A reduction scheme which removes certain degrees of freedom from the problem statement is incorporated into the numerical procedure.

Optimized Components in Frame Synthesis

Abstract: The incorporation of optimized thin-walled beam elements into procedures for the minimum-weight design of indeterminate elastic planar frame structures is examined. It is shown that all frame structures composed of beam elements with thin-walled cross sections will be fully stressed in the sense that each element should be proportioned to be on the verge of local instability under at least one independent load condition. This fact leads to a formulation of the design requirements as an inequality-constrained minimization problem with the only variables being moments of inertia of the elements. Solutions are examined numerically by use of a nonlinear programing technique. The formulation also suggests a simple and efficient direct iterative procedure for obtaining designs which are fully-stressed with respect to both local buckling and yielding. For the examples considered, both procedures are shown to produce identical results. Nomenclature A = cross-sectional area D = depth of beam cross section E = Young's rnodulus / = moment of inertia K = buckling coefficient M = bending moment 9fTl = maximum absolute value of M in element W = weight Z = section modulus kAjki = constants I — length t = thickness p = specific weight ay = yield stress a = Wl/Z

Process for multiple bending of rods and a bending machine for carrying out this process

Abstract: The multiple bending of rods or other elongated elements into loops in which a rod (or rods) is supported on an abutment and is bent by means of a bending tool which is guided on a circular path around a bolt which determines the bending radius. The rod (or rods) which is to be bent is held by a clamping element which is fixed in relation to the rod (or rods) at least before the individual bends whereby before each individual bend a straight line distance between the bending tool of the bending machine and the clamping element is reduced, by means of a drive, by the length of the loop side piece required for the next single bend.

Experimental Stress Analysis of 24-In. Tees

Abstract: This paper describes the experimental stress analysis and low cycle fatigue test of one 24-in. dia, schedule 40 carbon steel, ASA Standrd B16.9 tee performed by Combustion Engineering, Inc. This program is part of the Oak Ridge National Laboratory Piping Program for the development of design criteria for nuclear service piping components. The tee was instrumented with 230 rectangular strain gage rosettes. Elastic data was obtained for 12 loading conditions consisting of internal pressure and orthogonal pure moment and orthogonal direct forces applied individually to the free branch and run ends of the tee. One of the run ends of the tee was “built in” throughout the test. All loads were applied through pipe extensions welded to the tee. The tee was tested to failure in a low cycle fatigue test with an in-plane bending moment on the branch pipe. The tee was pressurized to the design pressure of 1025 psig during the fatigue test. A cyclic stress of approximately ±83,600 psi was imposed on the tee and a through-the-wall fatigue crack occurred at 18,532 cycles. Significant test results are summarized and compared with design values tabulated in the current issue of the Nuclear Power Piping Code, USAS B31.7-1969.

Variational Equation of Motion for Coupled Flexure and Torsion of Bars of Thin-Walled Open Section Including Thermal Effect

Abstract: Literature on flexure and torsion of bars of thin-walled open section is reviewed. The use of the variational equation of motion in solving problems of structural dynamics is further advocated. The variational equation of motion, together with the associated stress-displacement relations, is then derived for coupled flexure and torsion of the open section. Thermal effect is included, leading to a thermal twisting moment in addition to the usual thermal bending moments. For the special case of an open section with one axis of symmetry and with symmetrical heat input, only flexure is shown to be thermally inducible. The general result then reduces to the simple variational equation of flexural motion used in a separate study of the thermal flutter of a spacecraft boom.

Post-Buckling Behavior of Stiffened Plates with Small Initial Curvature under Combined Loads,

Abstract: : The post-buckling behavior of a stiffened plate with small initial curvature is discussed in this paper. The stiffened plate is idealized by an equivalent orthotropic plate. The basic differential equations are derived and solved under two sets of boundary and loading conditions. Non-dimensional design curves giving the center deflection, critical load, effective breadth, and bending moment are presented for different values of the inplane load, lateral load, virtual aspect ratio, stiffeners characteristics and initial deflection. A computer program is also presented in order to obtain the results for values of the parameters not covered in the design curves. An example on the use of the design curves is given in which the results are compared under different boundary conditions and different initial deflections. (Author)

On the creep analysis of pressurized circular cylindrical shells

Abstract: Numerical analysis of the steady state creep of a pressurized circular cylindrical shell is developed on the basis of Mises' criterion and the power law of creep. The representations of stress, membrane force and bending moment expressed in terms of the components of displacement are linearized by expanding them in the neighborhood of a certain approximate value of displacement. The equations of equilibrium substituted with these expressions are replaced by the corresponding difference equations, in order to obtain the simultaneous linear equations with respect to the small perturbation of the components of displacement. The approximate values assumed previously are improved by using the resulting solutions. More accurate values of these variables are obtained by repeating the procedure. This method may be interpreted as a modification of the Newton-Raphson method for non-linear simultaneous equations. Calculations are carried our for clamped circular cylindrical shells with open ends subjected to internal pressure. The effect of the shell geometry and that of non-linearity of the creep law are elucidated. The numerical results thus obtained are also compared with existing solutions for sandwich shells.

Dynamic response of circular plates subjected to transverse impulsive loads

Abstract: The behaviours of dynamical stresses acting in the circular plate subjected to transverse impulsive loads are investigated. The cases are treated where a rigid body with spring collides with the circular plate having a hole at its center along its inner edge. The relationships between dynamic load factors (D.L.F.) with respect to bending moments, solid viscosities and spring are obtained. Experiments are carried out and theoretical results are compared with experimental ones.

Moment-curvature relationships for prestressed concrete in constant-moment zones

Abstract: Synopsis The paper deals with a theoretical formulation of moment-curvature curves for prestressed concrete members subjected to constant bending moment. The theory takes into consideration the variation of curvature between cracks caused by concrete tension and makes possible the prediction of both the curvature at a crack and the average curvature along the length of the member. A report is included of tests on seven single-span pre-tensianed beams which show that the theory accurately predicts the moment-curvature relationship.

Transfer of Unbalanced Moment and Shear From Flat Plates to Columns

Abstract: A REFINEMENT OF CURRENT METHODS FOR CALCULATING THE STRENGTH OF SLAB-COLUMN JUNCTIONS CARRYING UNBALANCED MOMENT AND SHEAR IN FLAT PLATE CONCRETE STRUCTURES IS DESCRIBED. THE SLAB SECTIONS FRAMING INTO EACH COLUMN FACE ARE IDEALIZED AS BEAM SECTIONS WHICH CAN DEVELOP THE ULTIMATE BENDING MOMENT, TORQUE, OR SHEAR APPROPRIATE FOR THE GIVEN LOADING CONDITION. THIS PROCEDURE PREDICTS THE STRENGTHS MEASURED IN LABORATORY TESTS, SIMULATING CONNECTIONS AT BOTH INTERIOR AND EXTERIOR COLUMNS. IT IS SHOWN THAT, IN ADDITION TO FLEXURE, TWO MODES OF FAILURE ARE POSSIBLE, MOMENT-TORSION AND SHEAR-TORSION. /ACI/

On the Stresses around an Elliptic Hole in a Cylindrical Shell

Abstract: A theoretical analysis is presented for the membrane and bending stresses around an elliptic hole in an infinitely long, thin circular cylindrical shell The shell is loaded by a uniformly distributed bending moment around the elliptic cutout The method of solution is a perturbation technique and the results obtained are valid, if the hole is small in size compared to the shell

Negative moment behavior of composite beams

Abstract: COMPOSITE BEAM TESTS, WERE CONDUCTED TO: (1) INVESTIGATE THE EFFECT OF THE AMOUNT OF LONGITUDINAL STEEL IN THE SLAB OF A COMPOSITE BEAM WHEN SUBJECTED TO NEGATIVE BENDING MOMENT CONDITIONS, AND (2) DETERMINE WHETHER OR NOT IT IS POSSIBLE TO SIMULATE THE NEGATIVE MOMENT REGION OF CONTINUOUS COMPOSITE BEAMS BY USING SIMPLE BEAMS WHICH DUPLICATE THE SECTION PROPERTIES OF THE PROPOSED NEGATIVE MOMENT REGION. STATIC TESTS TO FAILURE WERE MADE ON 21 WF 62 BEAMS COMPOSITE WITH A 6 X 60 FT. REINFORCED CONCRETE SLAB. BASED ON THE TESTS DESCRIBED, THE FOLLOWING WAS CONCLUDED: (1) THE TENSILE CAPACITY OF THE LONGITUDINAL STEEL REINFORCEMENT OF THE SLAB SHOULD BE LARGER THAN THE TENSILE CAPACITY OF THE CONCRETE ALONE, (2) SIMPLE SPAN BEAMS LOADED UNDER NEGATIVE MOMENT CONDITIONS ARE SUITABLE TO STUDY THE NEGATIVE MOMENT REGION OF CONTINUOUS COMPOSITE BEAMS, AND (3) AN ACCURATE THEORY IS REQUIRED TO PREDICT THE STRESSES IN CONTINUOUS COMPOSITE BEAMS IN WHICH THERE ARE NO SHEAR CONNECTORS IN THE NEGATIVE MOMENT REGION. /AUTHOR/

Bending Stiffness Factors in Conjugate Fiber Crimp

Abstract: A bending moment induced by differential length changes is the physical basis for crimp in conjugate fibers. There fore, effects of cross-sectional shapes and component distributions on crimp can be estimated from considerations of mechanical principles governing the bending of rods or beams. Indices of these effects are defined as (a) stiffness of components relative to an axis perpendicular to the line between component area centroids and (b) angular deviation of this line from the cross-section principal moment of inertia axis. Regression analysis of experimental data shows these indices are statistically significant factors in bicomponent fiber crimp.

Nonlinear static behavior of a cantilever subjected to an inclined follower force

Abstract: The nonlinear static behavior of a linearly elastic cantilever subjected to a nonconservative force of the follower type is formulated and examined. The formulation allows for finite rotations with small strains (the elastica). Exact solutions are found. The investigation is greatly facilitated by means of a phase plane analysis in which the phase plane variables are related to slope angle and bending moment. Some of the interesting and unusual effects occurring in this system are discussed and illustrated with a set of deflection curves for a typical case.

Phase Transformation Effects on the Bending Stress Distributions in Carburized Steel Components

Abstract: An analytical model has been developed for the elastic and elastoplastic bending of rectangular bars in which the neutral bending plane need not remain in the geometric center of the bar. With this model, distribution of both longitudinal and transverse stress can be computed on the basis of applied bending moment and measured, surface strains. The strain-induced transformation of austenite retained in the case of carburized steel bars of several compositions was found to occur at linear rates whose values depend upon the sign of the stress and the composition of the steel. It was further found to produce pronounced shifts in the neutral bending plane and to have major effects on the magnitude of the transverse bending stresses. The bending fracture characteristics of the carburized steel bars were found to be affected by the inherent toughness of the case, and all factors which influence it, as well as the inherent toughness of the core. In general, the presence of nickel in the steel enhanced the fracture resistance of the steels because of its contribution to the toughness of both case and core.

Precast prestressed sections under axial load and bending

Abstract: Interaction curves for reinforced concrete columns, derived on the basis of Whitney's theory «> , or some variation thereof, can be plotted in dimensionless form for a given shape of column. This procedure is embodied in design handbooks such as that published by the American Concrete Institute( 2 ), and it has been extended to the case of prestressed columns by Zia and Guillermo (3>. When precast, prestressed sections such as single or double tees are used in load-bearing walls, they are subject to axial load and bending moment. Because of the irregular shapes of these members, their interaction curves do not lend themselves to dimensionless plotting. Nevertheless, various devices have been used to achieve the simplicity of the former problem, for example, substitution of an "equivalent" rectangular section with a radius of gyration equal to that of the actual section. It is the writers' contention that such devices are misleading and unnecessary, and that, in fact, the number of assumptions in the design procedure could and should be reduced rather than increased in connection with these members. This is based upon the following points: 1. The interaction curves of members such as prestressed T-sections are unusual in shape and are not well represented by drastic simplifications. In fact, the radius of gyration of the cross-section has no significance at all with respect to the interaction curve at ultimate strength, although it does, of course, affect the magnification factor associated with slenderness of beam-columns. 2. The justification for the use of such members as load-bearing wall panels is that they are massproduced in large numbers in precast plants. Therefore the economic pressure for highly simplified design procedures is reduced. 3. A consequence of Point 2 is that large numbers of cases are likely to be designed in advance for a plant as part of its promotional policy, and the use of a computer is strongly indicated. The need for simplifications is immediately removed. 4. The labor involved in calculating interaction curves, even by hand, is not, in fact, prohibitive if large numbers of members are to be manufactured. 5. Since there is no established

Torsion, bending, and shear in prestressed concrete

Abstract: An ultimate strength interaction criterion for web reinforced, prestressed concrete beams under torsion, bending moment and flexural shear is presented. Principal variables considered are the level of prestress and its eccentricity, torque: bending moment ratio, and flexural shear. Test results for 54 rectangular beams include beam properties, ultimate strength, angle of twist at failure, torque-twist curves and typical crack patterns. Bending moment in moderate amounts increases the torsional strength, but the effect of flexural shear is always detrimental. Within limits, the web reinforcement provides a ductile type behavior with ample rotation capacity at failure. The initial torsional stiffness is not affected by the variables considered. Higher levels of prestress and web reinforcement increase the pure torsional strength. Torsion-bending moment interaction is represented by a second degree parabola, and a three-dimensional curved interaction surface is envisaged when flexural shear is also present. Proposed interaction equations indicate good correlation with test data.