Showing papers on "Bending moment published in 1973"

Crack Propagation Studies in Brittle Materials.

Abstract: An analysis was made of cantilever beam specimens used for crack propagation studies, Included in this analysis were the effects of a plastic zone at the crack tip, beam rotation, and the viscoelastic response of the material. This analysis showed that application of a constant bending moment to the specimen rather than a constant load provides a test in which the strain energy release rate,G, is independent of crack length. Other advantages of this test configuration are that corrections for shear or beam rotation effects are not necessary. Results of this test on both glass and ceramics are reported.

Large-Deflection Spatial Buckling of Thin-Walled Beams and Frames

Abstract: The potential energy expression and the (14 by 14) stiffness matrix of a straight thin-walled beam element of open asymmetric cross section, subjected to initial axial force, initial bending moments, and initial bimoment, are derived. The transformation matrix relating the forces and displacements (including bimoment and warping parameter) at the adjacent end cross section of two elements meeting at an angle is deduced as the limiting case of a transfer matrix of a curved beam. To cope with asymmetric cross sections, some element displacements and forces are referred to the shear center and others to the cross-sectional centroid and the matrix for transformation from shear center to centroid is set up. The incremental larger-displacement analysis is formulated using the Eulerian coordinate approach with updating of the local coordinate systems at each load increment. The deformed beams are imagined to be composed of straight elements. Results of lateral post-buckling analysis of various beams are presented.

Large-deflexion torsion and flexure of initially curved strips

Abstract: General expressions are derived for the large-deflexion relations between bending moment, torque, longitudinal and twisting curvature for initially curved strips of lenticular and constant thickness section. Particular attention is paid to the behaviour under pure moment and pure torque and it is shown that the presence of initial curvatures can introduce some novel forms of instability.

Load Criteria for Ship Structural Design

Abstract: : Consideration is given to the critical loads on ships' hulls, as indicated by possible modes of structural damage and/or failure An ultimate load criterion is then set up involving the following bending moments: quasi- static wave-induced, vertical and lateral combined, still water, including effect of ship's own wave, dynamic loads, including slamming, whipping, and springing, and thermal effects The determination of each of these loads is discussed in detail, and the need for further clarification of dynamic loads is brought out Methods of combining these loads, all expressed in probability terms, are considered A criterion for cyclic loading is discussed, involving the prediction of the expected number of combined loads of different levels, as well as the expected shifts of mean value A criterion for brittle fracture is also discussed Attention is given to estimating an acceptable probability of failure for use in design Finally, calculations of loads are carried out for a typical cargo ship, the SS Wolverine State The loads are then combined in accordance with the proposed ultimate load criterion and compared with the standards under which the ship was designed

Method of pseudosubsurface scoring and cutting glass sheets and sheet cut thereby

Abstract: Pieces of flat glass are cut to desired size without the necessity of grinding to size and polishing. Edges of the piece are cut in accordance with a procedure involving the use of a large diameter scoring wheel at a greater-than-usual applied pressure, to produce a pseudosubsurface score, followed by the application of heat to the score and/or the application of a bending moment about the score to propagate a fracture in the piece of glass. Light seaming of the top and bottom portions of the edges completes the preparation of those edges.

Prestressed Concrete Sections with Cyclic Flexure

Abstract: A theory is presented to determine the moment-curvature characteristics of prestressed concrete sections with bonded tendons subjected to axial load and reversed cycles of bending moment. The analysis is based on expressions for the stress-strain relationships of concrete and prestressing steel under cyclic loading. Provision is included to allow for varying degrees of confinement of the concrete by transverse reinforcement. An idealization is also presented to represent the moment-curvature characteristics of prestressed concrete members under cyclic loading of large amplitude for use in the dynamic analyses of framed structures subject to seismic motions. Both the theory and the idealization are compared with experimental moment-curvature curves for beam and column sections subjected to high intensity cyclic loading. Good correlation is found between theory and experiment. It is shown that substantial ductility can be available from prestressed concrete members but that energy dissipation may not be significant until crushing of the concrete has commenced.

Moment desensitization of load cells

Abstract: A parallelogram beam-type load cell for measuring shear force of static loads. Located at specified positions on the load cell are a plurality of strain gauges connected to form an electrical bridge network. One dimension of the beam is reduced at predetermined beam locations where strain gauges comprising a specified one-half of the bridge network are situated. Such a beam-type load cell is insensitive to bending moments caused by the load. The location and dimensions of the reduced beam portion depend upon the original configuration of the beam and the response characteristics of the strain gauges.

Load cell and flexure means for transferring force thereto

Abstract: A flexure frame includes top, bottom, rear, and front plates secured together to define a generally rectangular shape. The top and bottom plates includes flexure webs adjacent to the rear and front edges of the plates such that the rectangular frame can flex into a parallelogram shape when the rear plate is anchored to a stationary structure to cantilever the frame and a downward force is applied to the top plate adjacent to its front edge. An elongated load cell is secured between the rear and front plates and includes a load cell flexure adjacent to its securement to the front plate so that when a force is applied to distort the flexure frame into a parallelogram shape, the force is transferred as a shear force to the load cell flexure web which in turn translates this shear force into a bending moment on the load cell. Essentially bending and torsion moments resulting from an off center applied force to the top plate are isolated from the load cell so that only the downward vector force itself is measured by the load cell.

Structural Concrete-Biaxial Bending and Compression

Abstract: This note presents a modification of the extended Newton-Raphson method for the study of the moment-curvature characteristics of structural concrete sections subjected to biaxial bending moments and axial load.

Nonlinear Equations for Bending of Rotating Beams with Application to Linear Flap-Lag Stability of Hingeless Rotors

Abstract: The nonlinear partial differential equations for the flapping and lead-lag degrees of freedom of a torisonally rigid, rotating cantilevered beam are derived. These equations are linearized about an equilibrium condition to study the flap-lag stability characteristics of hingeless helicopter rotor blades with zero twist and uniform mass and stiffness in the hovering flight condition. The results indicate that these configurations are stable because the effect of elastic coupling more than compensates for the destabilizing flap-lag Coriolis and aerodynamic coupling. The effect of higher bending modes on the lead-lag damping was found to be small and the common, centrally hinged, spring restrained, rigid blade approximation for elastic rotor blades was shown to be resonably satisfactory for determining flap-lag stability. The effect of pre-cone was generally stabilizing and the effects of rotary inertia were negligible.

Inelastic Bending of Wood Beams

Abstract: The bending stress analysis of wood beams in the plastic range is presented and a new theoretical method of predicting the ultimate load is developed. The method is based on the approach known as the bending theory of beams, but the pattern of stress distribution at failure in the critical cross-sectional area is now mathematically formulated on the basis of the stress-strain diagram obtained by the tests. The validity of the theoretical method is verified by a testing program using three full-size specimens. The test results agreed favorably with the theoretical predictions. The actual ultimate bending moment closely coincides with that obtained by the theory presented, as does the downward shifting of the neutral axis. Wood beams of any species can be computed by this theory if the mathematical equation for the stress-strain diagram is known. This theory is verified through tests on glue laminated beams using wood of the best quality.

Inelastic Lateral Buckling of Restrained Beams

Abstract: An analytical method of the elastic and the inelastic lateral buckling of restrained beams is presented using the transfer matrix method. The field transfer matrix is derived under the assumption that each element is in a uniform bending moment and it is presented that the various restraints against the out of plane deformations at the supports and in the spans can be considered in the analysis using the point transfer matrix. The treatments of the boundary conditions and the effects of the locations of loadings are given. Using this method, the numerical examples are presented for simply supported beams and two-span continuous beams.

Three-Dimensional Interaction of Walls and Frames

Abstract: The three-dimensional interaction of several plane walls, open section walls, and plane frames is studied under the action of horizontal forces. Walls are taken to have infinite shear rigidity while warping effects are considered. Frames are treated as vertical cantilever beams with infinite bending moment rigidities but finite shear stiffnesses. The floor slabs are replaced by an infinite number of diaphragms with no transverse stiffness but infinite in-plane rigidity. The stiffnesses of the walls and frames are assumed constant throughout the height of the building. A system of three differential equations of the third order solves the problem in a way similar to the displacement method. The method is useful in providing a general view of the macroscopic behavior of the structure through the use of a small number of elastic parameters.

On wave-induced stress in a ship executing symmetric motions

Abstract: The equation of motion of a simple beam in head waves is solved in terms of modal responses. Examination of the resulting expression for wave-induced bending moment indicates that at lower wave frequencies large fluctuating stresses are generally associated with 'ship-wave matching', a phenomenon governed by the relative geometry of ship and wave; whereas large stresses in the higher frequency range are the result of 'resonant encounter', during which the encounter frequency of ship with wave corresponds to a natural vibration frequency of the ship as a beam. The contrasting characteristics of these different response mechanisms are shown to provide a rational explanation of the fluctuating stresses induced in large or flexible ships in confused seas.

Solid medium thermal engine

Abstract: A thermal engine apparatus including an elongated cylindrical tube of metal providing a single phase working substance supported to rotate freely about its longitudinal axis while being subjected to continuous bending moment producing stress loads applied intermediate its ends wherein the bending moment causes portions of the tube to alternately pass through states of compression and tension as the tube rotates about its axis. The apparatus further includes structure for positioning the cylindrical tube relative to a source of radiant energy such that the radiant energy strikes that portion of the tube surface which is under compression, transfers thermal energy thereto, and the consequent expansion creates an unbalance of internal forces which causes the body to rotate about its axis.

Stress distribution in beams of varying depth

Abstract: Beams of varying depth are widely used in civil engineering structures, and are particularly suitable for large span prestressed concrete bridges. It is well known that the distribution of shear stress and hence principal tensile stress may be considerably affected by the variation in depth. A review is made of the various elastic analytical methods available, and their assumptions are discussed. The accuracy of each analysis is assessed on a plane wedge under separate application of normal force, shear, and bending moment, for a range of slopes and curvatures. The effect of curvature is shown to be unimportant for the values associated with bridges. The approximate forms of the solutions reached by Boussinesq and Wysiatycki are shown to be identical. These expressions are simple and give good agreement with the exast solution. Photo-elastic and finite element models are used to examine the accuracy of the various analytical methods applied to box-sections. /AUTHOR/

A plastic theory for collapse of plate girders under combined shearing force and bending moment

Abstract: The end panel of a plate girder is analysed for plastic collapse under high shearing load by means of the upper bound theorem. Two possibilities are considered for the behaviour of the web: either (a) it remains unbuckled or (b) it develops a full plastic tension field. Curves are presented showing how the collapse load depends on the dimensions and on a parameter signifying the full plastic bending strength of the flanges in relation to the web strength. In general, the numerous experimental results available in the literature lie between the predictions based on (a) and (b) respectively. The analysis is developed to account for collapse under the action of shearing force and bending moment simultaneously. There is a section on collapse by a mechanism which involves plastic bending in the vertical 'end post', which includes a design method for suppression of this mode. Finally there is a worked example.(a)

Work Bounds and Associated Deformation of Cyclically Loaded Creeping Structures

Abstract: In this paper the deformations of a beam subject to cyclic bending moment and a thick-walled cylinder subject to cyclic internal pressure are investigated for an elastic/time hardening/perfectly plastic material. Bounds [1, 2] are computed on the work done by the applied loads over a cycle when the material has reached a cyclic state of stress. The bounds provide the extreme states when the cycle time is either large or small compared with a characteristic time of the material. It is found that the difference between the bounds is generally very small. This result is discussed in relation to recent work by Williams and Leckie [3].

Creep Analysis of Smooth Curved Pipes under in-plane Bending

Abstract: Theoretical analyses are presented for the behaviour of a smooth circular cross-section thin-walled curved pipe of constant thickness when loaded by in-plane bending moments under isothermal creep conditions. Twin energy analyses, designated type 1 and type 2 respectively, are used in conjunction with an n-power stationary creep constitutive relationship. Approximate solutions are obtained by direct minimization techniques on a computer.Deformation results and stress-concentration factors relevant to the stationary condition based on straight-pipe values are reported for all practical geometries of pipe bends. The influence of the results on design and matters of total deformation and stress redistribution are briefly mentioned.

Pure bending of helical wound composite cylinders

Abstract: In order to simulate the influence of specimen misalignment, we determine the elastic response of a helical wound composite tube under pure bending using an existing general solution for a wide class of boundary value problems. Theoretical results for several composite materials of engineering interest are presented which illustrate the influence of material properties on the stress field.

Strength Analysis of Corner Column-Slap Connections

Abstract: An analytical method is presented for predicting the strength of a corner column-slab connection in a flat plate structure subjected to bending moment or combined bending and axial load through the column stubs. It takes into account the column side to the effective slab depth ratio, r/d , concrete and steel properties, steel configuration near the column-slab interface, and the moment to shear ratio, γ. The validity of the method was checked against the available test data and excellent correlation was obtained. Recommendations for its application and a numerical example are given.

Tests of Flat-Plate Corner Column-Slab Connections

Abstract: The results of the tests on nine corner column-slab connections subjected to either bending moment, or shear, or both are reported. The principal variables were the ratio of column side to effective depth of the slab, \Ir/d\N, the ratio of the bending moment to axial load, \IM/V\N, and the reinforcement configuration. An idealized failure mechanism is defined. Punching was found to be a secondary phenomenon following the destruction of the concrete in compression due to the combined action of flexure and shear. Analysis showed that the proposed ACI (American Concrete Institute) code method is extremely conservative and does not account for the variables considered.

The Vibrations of a Circular Plate with Uniformly Distributed Load around the Outer Periphery

Abstract: The vibrations of a circular plate with uniformly distributed load around the outer periphery are studied. The circular plate has a hole at the center and the profile is of an exponential curve. The frequencies of circular plates with various boundary conditions are also obtained and the deflections, the inclinations, the bending moments and the shearing forces are shown in graphs.

Optimal Plastic Design for Bending and Shear

Abstract: In optimizing flexural systems (such as beams, frames, and grillages) of continuously varying cross section, most authors assume that the specific cost of the member is a function of the bending moment only. However, the Prager-Shield theory of plastic optimal design and its extensions to multiload and multicomponent systems, partially preassigned geometry, and nonconvex cost functions can be applied readily to problems in which the specific cost depends on both bending and shear. In this note, a generalization of Heyman's method is considered but the same technique can be used for an improved optimization of grillages for which only flexure was taken into consideration in previous studies.

Postrcracking 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/