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Showing papers on "Bending moment published in 1976"


Journal ArticleDOI
TL;DR: Graphical solutions are presented which enable the determination of vertical displacement at the centre, mid-edges and corner of the raft, and the maximum bending moment in the raft.
Abstract: The behaviour of perfectly smooth, uniformly loaded rectangular rafts of any rigidity resting on a homogeneous elastic layer which is underlain by a rough rigid base is analysed. Graphical solutions are presented which enable the determination of vertical displacement at the centre, mid-edges and corner of the raft, and the maximum bending moment in the raft. The solutions have been obtained by the finite element method with the interaction between raft and finite soil layer being incorporated through the use of surface elements. A weighting method is presented which allows an approximate isotropic modulus to be derived for a multi-layered soil permitting the solutions to be applied to multi-layered foundations. Variations in raft rigidity and length/breadth ratio and soil layer depth and Poisson's ratio can markedly effect both displacements and bending moments in raft foundations. On analyse le comportement de radiers rectangulaires parfaitement lisses, charges uniformement, de n'importe quelle rigidite...

106 citations


Journal ArticleDOI
TL;DR: In this article, a two-dimensional extension of various non-linear models for one-dimensional response analysis is considered, including the degrading trilinear stiffness model which is one of the simpler idealizations of the restoring force characteristics of flexural-failure-type R/C structures.
Abstract: Recent studies reveal that R/C structural members subjected to biaxial flexure due to two-dimensional earthquake excitation can deform much more than would be predicted by conventional one-dimensional response analysis. The biaxial flexure may therefore have a significant effect on the dynamic collapse process of structures subjected to intense ground motions. The present paper is intended to develop a new formulation of the two-dimensional restoring force model of R/C columns acted upon by biaxial bending moments, and to discuss the dynamic response properties of R/C structures. The model considered is a two-dimensional extension of various non-linear models for one-dimensional response analysis, including the degrading trilinear stiffness model which is one of the simpler idealizations of the restoring force characteristics of flexural-failure-type R/C structures. The modelling validity is then examined by comparison with experimental data on the biaxial bending behaviour of R/C columns. Calculations are made to study the role of different system properties on the influence of inelastic biaxial bending on the dynamic structural response. It is shown that the inelastic biaxial effect is generally significant and, in some cases, critical in the case of R/C structures with stiffness-degrading properties, while the effect is not so important for the non-degrading inelastic cases.

105 citations


Journal ArticleDOI
TL;DR: In this paper, the authors investigated the non-stationary random vibration of a beam and concluded that the resulting beam vibration turns out to be a nonstationary process even though the motion considered is that of a stationary random force.

89 citations


Journal ArticleDOI
TL;DR: The PFVIBAT program as mentioned in this paper uses the exact displacement method to perform free and forced vibration analysis entirely within the differential equation theory of beams thus avoiding assumed modes and lumped masses.
Abstract: The described program PFVIBAT uses the exact displacement method to perform free and forced vibration analysis entirely within the differential equation theory of beams thus avoiding assumed modes and lumped masses. The frame may contain rigid bodies. Clamped, hinged, guided and rolling connections are allowed for. Consideration of rotatory inertia, shear deformation and second-order bending moments and shear forces as caused by static axial load is optional. Eigenfrequencies and modal masses are calculated with an accuracy that may be specified. Displacement and moment modes are plotted. Transient vibrations are studied.

80 citations


Journal ArticleDOI
TL;DR: In this paper, simple and rational methods for design of the reinforcement in corners and joints are developed based on tests with monotonic one-way loading-to-failure.
Abstract: In this investigation simple and rational methods for design of the reinforcement in corners and joints are developed. Proposals for design rules are based on tests with monotonic one-way loading to failure. The reinforcement details must satisfy the fundamental requirements of strength, limited cracking, ductility, and simplicity of construction. The main emphasis of the experimental work has been placed on the study of frame corners subjected to positive moments, i.e., moments that cause tensile stresses on the inside of the corner. Other types of joints are also studied, such as corners in retaining walls and T-joints. Different causes of failure in corners and joints are examined. Special attention is devoted to diagonal tension crack failure. Simple expressions are derived for the analysis of this type of failure on the basis of truss analogies. Proposals are put forward for simple and functional reinforcement layouts for corners and some common types of joints in reinforced concrete structures subjected to bending moment.

51 citations


Journal ArticleDOI
TL;DR: In this paper, a method for directly including the P-Δ moments in the analysis of the structure is presented, and it is shown that if such an analysis is used, the members in both braced and unbraced structures may be designed as sway prevented.
Abstract: Generally, the analyses used to determine the distribution of bending moments and internal forces in a structure are first-order analyses. Such analyses neglect the so called P-Δ effects: (the effects produced by the vertical forces acting through the laterally deflected position of the structure). Thus, the stiffness and strength of the structure is overestimated. In an attempt to compensate for these shortcomings, the present design procedure requires increases in the column sizes in a sway permitted structure. As an alternative, a method for directly including the P-Δ moments in the analysis of the structure is presented. It is shown that if such an analysis is used, the members in both braced and unbraced structures may be designed as sway prevented.

32 citations


Journal ArticleDOI
TL;DR: In this paper, the post-buckling behavior of simply-supported, laminated cross-ply rectangular plates subjected to biaxial compression is analyzed and the solution to von Karman-type large deflection equations of the plate is expressed as a double sine series for the transverse deflection and a double series of clamped-clamped beam functions for the force function.
Abstract: An analysis is presented for the post-buckling behaviour of simply-supported, laminated cross-ply rectangular plates subjected to biaxial compression. The solution to von Karman-type large deflection equations of the plate is expressed as a double sine series for the transverse deflection and a double series of clamped-clamped beam functions for the force function. All the boundary conditions, including those involving the normal bending moment at the edges, are satisfied exactly. The series solution is found to converge rapidly. Using only the first few terms in the series, numerical results for square graphite-epoxy unsymmetric laminates under uniaxial compression is presented graphically.

31 citations


Journal ArticleDOI
TL;DR: In this paper, the authors investigated the buckling of oval cylindrical shells under the interaction of uniform compressive forces and bending moments of arbitrary orientation, and determined the asymmetric buckling modes by a matrix interative solution aided by a sequence of successive approximate solutions.
Abstract: Bifurcation buckling of oval cylindrical shells under the interaction of uniform compressive forces and bending moments of arbitrary orientation is investigated. Buckling loads as well as the asymmetric buckling modes are determined by a matrix interative solution aided by a sequence of successive approximate solutions. Nomenclature ajtdj = Fourier coefficients of X2 and X3, respectively

29 citations


Journal ArticleDOI
TL;DR: In this paper, an approximate solution to the von Karman-type large-deflection equations of unsymmetrically laminated, anisotropic, rectangular plates under uniform transverse load is formulated by the perturbation technique.
Abstract: An approximate solution to the von Karman-type large-deflection equations of unsymmetrically laminated, anisotropic, rectangular plates under uniform transverse load is formulated by the perturbation technique. The membrane boundary conditions are the zero normal and shear boundary forces. By expressing the load, force function and transverse deflection in the form of series, the governing equations and boundary conditions are reduced to a series of linear partial differential equations and boundary conditions. In each approximation a solution is assumed in the form of polynomials which satisfy the associated boundary conditions and physical requirements for deflection and and three membrane forces in unsymmetric cross-ply and angle-ply plates. Taking the first three terms in the truncated series, numerical results are graphically presented for the load-deflection relations, bending moments and membrane forces in unsymmetric cross-ply and angle-ply plates with various values of aspect ratio and total numb...

27 citations


Journal ArticleDOI
TL;DR: In this paper, a one-dimensional continuum model of the human spine was derived for a curved homogeneous beam-column and subject to a distributed eccentric inertial loading of the torso.

27 citations


Journal ArticleDOI
TL;DR: In this article, a finite difference procedure is used to determine the response of a single and multi span curved single box beam bridge with any number of interior diaphragms to bending and torsional distortions as well as cross-sectional distortions throughout the box girder.

Journal ArticleDOI
TL;DR: In this paper, the bending behavior of yarns is represented by a simple two-element rheological model of an elastic element and a single frictional element acting in parallel, which allows the bending deformation to be separated into an elastic and a frictional component, measured by the flexural rigidity and the frictional bending moment, respectively.
Abstract: This paper presents an account of an experimental study of the pure-bending and recovery properties of both continuous-filament and spun yarns. The bending behaviour of yarns is approximately represented by a simple two-element rheological model of an elastic element and a single frictional element acting in parallel. The use of this model allows the bending deformation to be separated into an elastic and a frictional component, measured by the flexural rigidity and the frictional (or coercive) bending moment, respectively. An expression for the frictional couple in yarn-bending is derived from consideration of the lateral forces acting within the yarn and the degree of set of fibres in a twisted yarn. Bending experiments were made with nylon model plied yarns, conventional multifilament yarns, and staple-fibre yarns; it is shown that the level of residual fibre tension within both unset and set yarns can be estimated from the experimental values of the frictional bending moment by semi-empirical means. T...

Journal ArticleDOI
S. Chonan1
01 May 1976
TL;DR: In this paper, an analysis is made of the problem of vibrations of a plate with an axial force resting on compressible fluid half-space, when the plate is uniform and of infinite length and is subjected to a load which moves with constant velocity along the plate.
Abstract: An analysis is made of the problem of vibrations of a plate with an axial force resting on compressible fluid half-space, when the plate is uniform and of infinite length and is subjected to a load which moves with constant velocity along the plate. An example is provided where the bending moment and the fluid pressure are calculated. From the results of theoretical analysis, it becomes evident that the axial force in the plate has considerable effect upon the dynamical behaviour of the system.

Journal ArticleDOI
K. Nagaya1
TL;DR: In this article, the Laplace transform was used to model the restoring forces of the elastic supports of a non-periodically elastically supported continuous plate, initially represented as unknown external forces applied to the plate.

Journal ArticleDOI
TL;DR: In this article, the effect of axial load on the behavior of columns consisting of alternate layers of rubber and curved or flat rigid shims is analyzed, and the resulting differential equations for this so-called continuum column are solved for critical loads and mode shapes for globally homogeneous columns with three different end conditions.

Patent
29 Jul 1976
TL;DR: In this paper, a means and method for bending elongated materials having a device for locally heating a portion of the material and a freely pivotable bending arm, is provided with a second arm for advancing the elongated material past the heating device and, in cooperation with the pivotable arm, exerting a bending moment on the locally heated portion.
Abstract: A means and method for bending elongated materials having a device for locally heating a portion of the material and a freely pivotable bending arm, is provided with a second arm for advancing the elongated material past the heating device and, in cooperation with the pivotable arm, exerting a bending moment on the locally heated portion of the material.

Journal ArticleDOI
TL;DR: The Euler-Bernoulli equations governing a stable equilibrium configuration of an elastica, subject to pin supports, can be derived by a formal calculus of variations via a local minimum principle for the strain energy of the elastica as mentioned in this paper.

31 Mar 1976
TL;DR: In this paper, for an isotropic solid shell, a yield condition, a strain-hardening rule, and a flow rule have been formulated in terms of the membrane forces and bending moments and the strains and curvatures of the middle surface.
Abstract: : For an isotropic solid shell, a yield condition, a strain-hardening rule, and a flow rule have been formulated in terms of the membrane forces and bending moments and the strains and curvatures of the middle surface. The results of the proposed theory are compared to the results of the through-the- thickness integration of the stress-strain relations of the material.

Journal ArticleDOI
TL;DR: In this paper, a finite element analysis of a typical hypar shell indicates that the loads are carried by dominant arch actions, spanning across diagonally opposite supports, and a method for the preliminary design of such shells is presented.
Abstract: The behavior of hipped hypar shells is significantly different from that assumed in the membrane. The concept of equal arch and catenary actions is no longer valid. A finite element analysis of a typical shell indicates that the loads are carried by dominant arch actions, spanning across diagonally opposite supports. The investigation of forces and bending moments in the membrane and edge members lead to a method for the preliminary design of such shells. The method includes procedures for local membrane thickening necessitated by stress concentration or by bending effects.

Journal ArticleDOI
TL;DR: In this article, the authors presented the analysis and results for a liquid metal fast rector system which was analyzed for both scram times and seismic responses such as bending moments, accelerations and forces.

Journal ArticleDOI
TL;DR: In this paper, a model of the Great Lakes bulk carrier, Stewart J. Cort, jointed amidships, with four different connecting beams provided different degrees of stiffness and hence of natural frequency of vertical hull vibration.
Abstract: : Experiments were carried out on a model of the Great Lakes bulk carrier, Stewart J. Cort, jointed amidships, with four different connecting beams. These beams provided different degrees of stiffness and hence of natural frequency of vertical hull vibration. Springing was simulated in short regular waves generated in a model tank at various resonant combinations of model speed and wave length. At equal speeds the effect of increasing stiffness was found to be a decrease in the magnitude of springing at resonance when expressed as bending moment relative to wave slope. Parallel theoretical calculations were carried out which were found to be extremely sensitive to the level of damping introduced. Good agreement was obtained between trends of theory and experiment. If appropriate assumptions were made regarding damping, good agreement was also obtained in magnitudes of springing bending moments. (Author)

Book ChapterDOI
B. W. Young1
01 Jan 1976
TL;DR: In this chapter, a member may be required to sustain axial forces, bending moments, shear forces and torques taken individually or in combination with each other, but with stresses due to axials forces alone are concerned.
Abstract: The intensity at which a force is distributed over the cross-section of a structural member is referred to as stress. The magnitude and distribution of the stress will depend upon the way in which the loads are applied and on the geometric properties of the cross-section. In general, a member may be required to sustain axial forces, bending moments, shear forces and torques taken individually or in combination with each other. In this chapter however we shall be concerned with stresses due to axial forces alone.


Journal ArticleDOI
TL;DR: In this article, a method for the solution of a rigid-ideally plastic circular plate resting on an elastic foundation has been developed, in which the mixed boundary value problem is solved by reducing it to a system of dual integral equations.
Abstract: A method for the solution of a rigid-ideally plastic circular plate resting on an elastic foundation has been developed. In case of axially symmetric loads, three distinctly different deformation modes are possible. For loads of low magnitude the plate penetrates the elastic half space as a rigid indenter. For higher load magnitudes, a plastic hinge develops at midspan and the plate deforms into a conical surface. For even higher values of external load, separation occurs at the plate half-space interface. Governing mixed boundary value problem is solved by reducing it to a system of dual integral equations. Simple closed-form formulas are derived for bending moments and deflections at each stage of deformation. It is rather remarkable that the results of this rigorous approach are just as simple as the results derived for various approximate models.

01 Jan 1976
TL;DR: In this article, an experimental investigation was made of the elastic and inelastic lateral buckling of unbraced two-span continuous steel I-beams with midspan concentrated loads.
Abstract: An experimental investigation was made of the elastic and inelastic lateral buckling of unbraced two-span continuous steel I-beams with midspan concentrated loads. A related theorectical study of the in elastic in-plane bending of continuous beams showed that the moment redistribution is smaller and more gradual than predicted by simple rigid-plastic theory because of strain-hardening and residual stresses. The results of six elastic buckling tests on one beam were in close agreement with theoretical predictions, and confirmed the reliability of the test apparatus. The results of eight in elastic buckling tests on for beams provide useful data for evaluating theoretical investigations of inelastic lateral buckling. The experimental failure laods were significantly less than the plastic collapse loads, and much less than the elastic buckling loads. They were also somewhat less than those of comparable simply supported beams, and it was suggested that this may be due to the inplane moment redistribution which takes place in indeterminate beams. It was concluded that further tests should be made to investigate in-plane moment redistribution more fully. /Author/

Journal ArticleDOI
TL;DR: In this article, it is shown that annular plates are preferable to plates without holes, since their load capacity increases while residual deflections decrease. And a boundary parameter is introduced to estimate the effect of boundary conditions on the radial bending moment.
Abstract: Dynamical bending of circular rigid-plastic annular plates, fixed along the exterior boundary and free on the interior boundary, when subjected to instantaneously applied transverse uniformly distributed blast-type load[1], is investigated in this paper. It is shown that annular plates are preferable to plates without holes, since their load capacity increases while residual deflections decrease. A so-called boundary parameter is introduced to estimate the effect of boundary conditions on the radial bending moment. A procedure for determining the residual deflections at every point of a plate is developed for use on an electronic computer. Numerical examples are given. In the end of the paper, the particularities of solution of our problem for annular plates, corresponding to the setting of Wang[2], Wang and Hopkins[3] for plates without holes are discussed.


Journal ArticleDOI
TL;DR: In this paper, a rational approach is proposed in which the pile response is represented by the vibrations of a beam on elastic foundation, and the foundation medium is considered as a linearly elastic half-space whose properties are expressed by the shear modulus and Poisson's ratio.

Journal Article
TL;DR: In this paper, the unsafe side error of the superposition method is not large even though steel portion with shallow depth is put in a cross ection of a column and/or an asymmetrical steel shape is used, provided that the yield strength of steel is not too high.
Abstract: In this paper, considered is the further applicability of the "Superposition Method" to estimate the load carrying capacity of steel reinforced concrete column subjected to axial thrust and bending moment. The accuracy of the superposition method is checked in the combination use of various grades of concrete and steel. It is confirmed that the unsafe-side error of superposition method is not large even though steel portion with shallow depth is put in a cross ection of a column and/or an asymmetrical steel shape is used, provided that the yield strength of steel is not too high. The unsafeside error of the superposition method is reasonably compensated bythe reduction of ultimate strength of concrete which was specified in the design standard of AIJfor SRC structures.

01 Dec 1976
TL;DR: In this article, a flight-test measurements of wingloads (shear, bending moment, and torque) were obtained by means of strain-gage bridges mounted on the exterior surface of a thin, swept wing which had a structural skin, full-depth honeycomb core, sandwich construction.
Abstract: Flight-test measurements of wingloads (shear, bending moment, and torque) were obtained by means of strain-gage bridges mounted on the exterior surface of a low-aspect-ratio, thin, swept wing which had a structural skin, full-depth honeycomb core, sandwich construction. Details concerning the strain-gage bridges, the calibration procedures used, and the flight-test results are presented along with some pressure measurements and theoretical calculations for comparison purposes.