Showing papers on "Bending moment published in 1974"

Torsion-bending-shear interaction for concrete beams

Abstract: A rational, simple method is presented for analysis of the torsion-bending-shear interaction at failure for reinforced concrete beams. Equilibrium equations are studied for observed failure mechanisms. Three mechanisms can occur depending on where the concrete compression zone is formed: in the top (mode t ), in the bottom (mode b ), or in one vertical side (mode s ). In modes t and b , the torsion-bending and the shear-bending interaction are governed by second-degree parabolas, whereas the torsion-shear interaction is governed by an ellipse. In mode s , the interaction surface is a cylinder with an elliptic base in the torsion-shear plane. The interaction in this mode is not influenced by the value of the bending moment, M . Approximations regarding the lengths of the moment lever arms and regarding the shear-carrying capacity are examined. Some test results are presented to demonstrate the accuracy of the method. The main feature of the method is that the vertical shear forces are considered in a simple but rational way.

An Ultimate Transverse Strength Analysis of Ship Structure

Abstract: There are many deep girders in a ship structure as the main strength members. Under increasing loads, local failures, such as buckling, yielding etc., occur in these members. These phenomena decrease the stiffness of the members and these changes of relative stiffness in the structure induce redistribution of internal forces and the structure finally shows its ultimate strength.A ship structure is composed of so many such members and its behavior to the ultimate strength is highly nonlinear. There are powerful tools to analyze nonlinear behavior, such as the finite element method, finite strip method, etc. However, the analysis by these methods requires enormous computing time for calculation and in the present circumstances it is impossible to apply these methods directly.To overcome these difficulties, an analytical unit of large size and idealization of the highly nonlinear behaviors are developed in this paper. A “Girder Element” is proposed, of which stiffness matrices are derived for indivisual kinematic condition, such as after buckling, at the ultimate strength or plastic strength under compression, bending, and/or shear. Based on these idealized behaviors, a method of ultimate strength analysis is proposed. The result of analysis by this method represents well the detail behavior of example structures, of which simple one well coincides experimental behavior conducted in this study. The computing time is remarkably very short.These nature of the new method promises the validity and possibility of the method to the ultimate strength analysis of structure of large size.

Crack propagation in wedged double cantilevered beam specimens

Abstract: A closed form analytical solution of crack propagation in double cantilevered beam specimens opened at a constant rate has been found. Hamilton's principle for non-conservative systems was applied to describe the crack motion, under the assumption of a Bernoulli-Euler beam. The criterion of crack propagation is a critical bending moment at the crack tip. The calculations of beam motion take into account wave effects in the Bernoulli-Euler theory of elastic beams. The beam shape during the crack motion is found with a similarity transformation and expressed by Fresnel integrals. The boundary conditions satisfied are the fixed ones of zero bending moment and constant beam opening rate at the load end of the specimen and the moving ones of zero deflection and zero slope of the deflected beam at the tip of the moving crack. The fracture represents a moving critical bending moment. The analytical results show that the specific fracture surface energy is a unique function of the ratio of the crack length squared to the time subsequent to loading and this is computed from the recorded time-dependence of the crack length.

Multi-axis load cell

Abstract: A load cell capable of measuring forces along three orthogonal axes as well as bending moments about each of these axes is disclosed which is of simple construction while being capable of measuring accurately a wide range of dynamic working loads. The load cell consists of a housing drivingly connected to a central hub member by means of a cross pattern formed by pairs of compliant cantilever bars, each bar slidable in the housing along its axis so as to not be capable of resisting transverse loads along respective orthogonal axes in the plane transverse to the load cell. Displacements of the hub relative to the housing are measured by four sets of LVDT transducers, each set measuring relative lateral movement parallel to each of the orthogonal axes on opposing points radially displaced from the central axis of the load cell. These displacements are used to generate signals corresponding to the force components along each of the orthogonal axes as well as bending moments about each of these axes.

On numerically accurate finite element

Abstract: A general criterion for testing a mesh with topologically similar repeat units is given, and the analysis shows that only a few conventional element types and arrangements are, or can be made suitable for computations in the fully plastic range. Further, a new variational principle, which can easily and simply be incorporated into an existing finite element program, is presented. This allows accurate computations to be made even for element designs that would not normally be suitable. Numerical results are given for three plane strain problems, namely pure bending of a beam, a thick-walled tube under pressure, and a deep double edge cracked tensile specimen. The effects of various element designs and of the new variational procedure are illustrated. Elastic-plastic computation at finite strain are discussed.

Joint for transferring bending moments

Abstract: A joint for attaching a horizontal beam to a vertical column in either a shear connection or a moment connection A continuous beam is manufactured comprising main beam portions in end-to-end alignment with the opposed ends spaced to define the ends of joint openings A pair of opposed channel members define the sides of each joint opening, the channel members being attached to said main beam portions by moment connections The vertical column extends through the joint opening, and the channel members are bolted to the column (shear connection) or welded to the column (moment connection)

Comparison of ship motion theories with experiments for a container ship

Abstract: Two calculation methods by which the ship motions, shearing forces, etc. in regular waves can be predicted are compared. The first method is analog to the method introduced by Korvin-Kroukovsky and Jacobs, while the second method is analog to the recently developed methods. The results of both methods are compared mutually and with data obtained from model experiments of a large container ship, considering the heave, pitch, roll and the relative motion and all bending moments, shearing forces and the torsional moment. An attempt is made to account for a part of the non linear effects.

Inelastic Analysis of Reinforced Concrete Frames

Abstract: The imposed rotation method for the inelastic analysis of frames rests on the interpretation of the actual bending moment distribution as the superposition of linear elastic moment responses to loads and to unknown plastic rotations regarded as imposed strains. The method given herein is a generalized formulation, covering second-order geometric effects and moment-axial force interaction. Finite element models of frames and piecewise linear moment-rotation laws for critical sections are assumed. Recent algorithms for solving quadratic programming and linear complementarity problems are shown to be efficiently applicable to the analysis of multistory frames. The safety factor with respect to local failure because of “brittle” flexural behavior turns out to be attainable by a suitably modified linear programming procedure.

Program scores--ship structural response in waves

Abstract: : Information necessary for the use of the SCORES digital computer program is given. This program calculates both the vertical and lateral plane motions and applied loads of a ship in waves. Strip theory is used and each ship hull cross-section is assumed to be of Lewis form for the purpose of calculating hydrodynamic forces. The ship can be at any heading, relative to the wave direction. Both regular and irregular wave results can be obtained, including short crested seas (directional wave spectrum). All three primary ship hull loadings are computed, i.e. vertical bending, lateral bending and torsional moments. All the basic equations used in the analysis are given, as well as a description of the overall program structure. The input data requirements and format are specified. Sample input and output are shown. The Appendices include a description of the FORTRAN program organization, together with flowcharts and a complete cross-referenced listing of the source language.

Three-Dimensional Stochastic Response of Offshore Towers to Wave Forces

Abstract: A theory has been developed to calculate the dynamic response of offshore towers to random wave forces. Vibrations are considered simultaneoulsy in the orthogonal horizontal directions and for rotations about a vertical axis. A lumped mass model of the structure is used in the dynamic analysis. Numerical results for seven deep water towers having heights of 475, 675, 875, and 1,075 feet, are presented. These results include standard deviations and mean peak values for displacements, rotations, shear forces and twisting and bending moments. They show that the directional spread of the waves normally has little effect on the rotational response, and that the effect of the rotational response on the overall structural response is small.

Comparison of three methods for calculation of helicopter rotor blade loading and stresses due to stall

Abstract: A comparison is made of the results of three methods for calculating the effects of dynamic stall on the performance, airloads, and blade stresses of a helicopter rotor at high loading. The three dynamic-stall methods considered predict essentially the same performance and trim for the rotor. They give roughly the same mean bending moments, but the peak-to-peak torsion and bending moments differ by 25 to 40 percent, and there are differences in the details of the predicted blade motion and stresses. The latter are due to significant differences in the dynamic stall aerodynamic loads, particularly the aerodynamic pitch moment, predicted by the three methods.

The deformation of disc-shaped particles by a shearing fluid with application to the red blood cell

Abstract: The shear stress distribution at the surface of an oblate spheroid in Couette flow is obtained using the hydrodynamical solutions of Jeffery to the Navier-Stokes creeping flow equations in the presence of ellipsoidal particles. The maximum hydrodynamic compression experienced by the precessing spheroid in a direction perpendicular to the particle's symmetry axis is calculated when the thickness-to-diameter ratio is made extremely small. Euler's differential equation for the bending moments about a column is integrated for a disc-shaped lamina of uniform thickness to obtain the critical diametric loading under which the disc would buckle in a sinusoidal mode. The resulting buckling load is equated to the maximum hydrodynamical compression force and the corresponding shear stress in the fluid obtained. An application of the foregoing principles to the erythrocyte is then discussed.

Large Deflection of a Circular Plate on Elastic Foundation under Symmetrical Load

Abstract: The large deflection of a clamped circular plate on elastic foundation under nonuniform but symmetrical loads has been investigated following Berger's approximate method. The deflections are obtained in the form of an infinite series involving Bessel functions. Graphs are plotted for deflections, bending moments, and bending stresses for various values of foundation modulus and load functions.

Seismic behaviour of above‐ground oil pipelines

Abstract: The dynamic behavior of above-ground oil pipelines which are allowed to slide back and forth on intermediate supports during strong motion earthquakes is studied. This sliding is resisted by friction between the pipe and the top of the support. The main objective of the study is to determine the effect of this non-linear friction on both the static and dynamic stresses in the pipe. The study also considers the influence of other critical parameters such as: pipeline configuration, seismic wave velocity, initial temperature differential and internal pressure, and ground motion characteristics. Results show that the critical bending moments in the pipe occur during the static loading and that with seismic excitation, these moments tend to shake down as the pipe moves to a more stress free configuration. It is shown that the use of sliding friction can be an effective means of dissipating seismic energy and thereby damping the dynamic response of the pipeline even for low values of the coefficient of friction. /Author/

Buckling Stress States of Cylindrical Shells

Abstract: Plexiglass cylindrical shell models with nearly perfect geometry and constant thickness were tested under various combinations of membrane stresses. In cylinders under axial compression alone and axial compression with internal pressure, the buckling procedure was initiated by means of a small dynamic disturbance which reduced the dispersion of the test results. The normal forces and bending moments in the middle of the model were measured. The number of buckling waves observed in the tests agreed quite well with the result of the classical theory for the laterally loaded cylindrical shell. Only the shape, the length, and the depth of the buckling waves changed with the stress state. A buckling criterion and an interaction curve realistic for civil engineering purposes are proposed for checking the stability of cylindrical shells with fixed ends under combined membrane stress states.

Inelastic spatial stability of restrained beam-columns

Abstract: A numerical method for computing the deflections and rotations up to the point of instability of elastically restrained inelastic beam columns is described. The cross section considered is open, thin-walled, and arbitrary in shape. The external forces, applied at ends of the beam column, could include a normal force, two bending moments, two shear forces, or a torsional moment or a combination of these. The restraints are represented by elastic rotational or directional springs, or both, at each end of the beam column. The material considered is ideally elastic-plastic and residual stresses are included in the analysis. The equilibrium equations are written with respect to an arbitrary system of orthogonal coordinate axes. The influence of the shift in the shear center and the shift and rotation of the principal axes of partially plastified sections are thus taken care of automatically in the analysis. The resulting fourth-order nonlinear differential equations are solved using finite differences and the tangent stiffness method.

Principal displacements in a pressurized elliptic cylinder: Theoretical predictions with experimental verification by laser interferometry

Abstract: Equations for principal displacements in a uniformly pressurized thin-walled cylinder having an elliptic median line are developed from a knowledge of the expressions for tension and bending moment (1) at a general position in the cylinder wall. Displacements derived from these equations are compared with the simple expressions presented by Bresse (2) and MacAlpine (3).The results of a detailed experimental study in which displacements were measured by a laser interferometer are used to assess the validity of the new displacement equations and to compare these with the predictions due to Bresse and MacAlpine.It is shown that the equations developed here give good agreement with experimentally measured displacements and furthermore the predictions made in (2) and (3) grossly overestimate the displacement values and are also very much in error when stating that the minor-diameter expansion is of the same order as the major-diameter contraction. In the investigation reported here (ellipse with mean a...

On the thermal bending of a thin elastic simply supported rectangular plate resting on an elastic foundation

Abstract: Deflection and bending moments of a thin isotropic rectangular plate, having its edges simply supported and maintained at zero temperature, have been investigated in this paper. The upper surface is kept at a constant temperature while the lower surface, which is in contact with an elastic foundation, is thermally insulated.

Closure key apparatus

Abstract: A simple key assembly for supporting an end wall structure within a rotary machine such as a turbine or a compressor. A shear key is interposed between the casing of the machine and an end wall closure carried internal the casing. A portion of the shear key is seated within an internal groove formed within the casing and a second portion thereof seated within a recessed shoulder formed in the end wall. A support key is mounted beneath the shear key within the end wall recess which serves to translate radial forces from the wall to the shear key. A pair of raised moment control pads are mounted on the casing contacting surfaces of the shear key, the pads being strategically located in relation to the center of gravity of the shear key to offset the load induced bending moments exerted thereon by the end wall and the support key.

Adjustable-bow bar or roll axle

Abstract: An adjustable-bow bar or roll axle, useful for spreading slit sheets of paper and for other purposes, includes a hollow cylindrical shell. Two tension bolts extend along axes parallel to the centerline of the shell, and interconnect the ends of the bar or axle. One of the bolts lies in a plane of desired curvature of the bar and applies a bending moment to curve the bar in this plane; this bolt may be located inside or outside the shell, depending on the required bending moment. The second bolt may be inside the shell; its angular position is adjustable with respect to that of the first. This bolt is set in the plane of a resultant force applied to the bar by the tension in the sheet, and applies a bending moment to offset this force and prevent curvature of the bar in this plane. A third bolt may be located in a vertical plane to apply a bending moment to prevent curvature of the bar by its weight; or the second bolt may serve this purpose also.