Showing papers on "Timoshenko beam theory published in 1985"
996 citations
TL;DR: In this paper, the beam theory derived from variational principles is based on the sole kinematic assumption that each section is infinitely rigid in its own plane, but free to warp out of plane.
Abstract: Beam theory plays an important role in structural analysis. The basic assumption is that initially plane sections remain plane after deformation, neglecting out-of-plane warpings. Predictions based on these assumptions are accurate for slender, solid, cross-sectional beams made out of isotropic materials. The beam theory derived in this paper from variational principles is based on the sole kinematic assumption that each section is infinitely rigid in its own plane, but free to warp out of plane. After a short review of the Bernoulli and Saint-Venant approaches to beam theory, a set of orthonormal eigenwarpings is derived. Improved solutions can be obtained by expanding the axial displacements or axial stress distribution in series of eigenwarpings and using energy principles to derive the governing equations. The improved Saint-Venant approach leads to fast converging solutions and accurate results are obtained considering only a few eigenwarping terms.
156 citations
TL;DR: In this paper, the frequency equation for the whole system is obtained in terms of the eigenvalues, or their natural logarithms, of the transfer matrix for a single periodic subsystem.
107 citations
TL;DR: In this article, a stress analysis of orthotropic beams subjected to concentrated loads is performed, within the framework of the classical theory of elasticity, on both three-point and four-point bending.
71 citations
41 citations
TL;DR: Following the generalized coordinate method of Vlasov, simple beam theory has been extended to treat torsional, distortional, and shear lag effects in straight, thin-walled box beams as mentioned in this paper.
Abstract: Following the generalized coordinate method of Vlasov, simple beam theory has been extended to treat torsional, distortional, and shear lag effects in straight, thin-walled box beams of uniform sec...
34 citations
TL;DR: In this article, the authors extended a previous study of electromagnetic radiation from a finite train of electron pulses to an infinite train of such pulses, where the electrons are assumed to follow an idealized helical path through a space plasma in such a manner as to retain their respective position within the beam.
31 citations
TL;DR: In this article, a comparative study of the shear deformation theory with a higher order model is presented, of which Timoshenko's model is a special case, and it is shown that there are considerable discrepancies in the information it gives regarding the mode shapes and dynamic response, and there is a need to consider higher order models for the dynamical analysis of flexure of beams.
30 citations
TL;DR: In this article, the vibration force of a poutre de Timoshenko anisotrope and viscoelastique is investigated in extremites libres, in the context of poutres de bois.
Abstract: Etude theorique et experimentale de la vibration forcee d'une poutre de Timoshenko anisotrope et viscoelastique, aux extremites libres. Les experiences sont faites sur des poutres de bois. Calcul et mesure du module de Young dynamique et de la tangente de perte en fonction de la forme de la poutre et de la frequence
29 citations
TL;DR: In this article, an approximate theory of the bending of cross-ply fiber-reinforced composites that is simpler than the exact theory of elasticity but is capable of accommodating any given displacement boundary conditions and arbi trarily varying side loads is presented.
Abstract: The Saint-Venant theory of beams cannot account for constraints against cross- sectional warping, and for this reason it gives results that are inaccurate near fixed ends and at points where the warping changes abruptly, as under concentrated side loads. In highly anisotropic materials such as fiber-reinforced composites, the cumulative effect of such inaccuracies may be significant in some circumstances.In the present paper we present an approximate theory of the bending of cross-ply fiber-reinforced composites that is simpler than the exact theory of elasticity but is capable of accommodating any given displacement boundary conditions and arbi trarily varying side loads. As an illustration, the theory is applied to the problem of a tip-loaded cantilever with a fixed end. In this problem the theoretical results agree with elementary beam theory (with a particular choice of the shear correction factor) except in a relatively long end-effect region near the clamped end.To test the theory, cantilever specim...
27 citations
TL;DR: In this paper, the authors present theoretical expressions for the displacement response of an axially loaded Timoshenko beam subjected to concentrated or distributed random loads having stationary and ergodic properties, illustrated by its application to investigate the effects of axial force on the random response of a simply supported beam acted upon by an ideal white noise.
TL;DR: In this paper, a general-purpose beam model is described with particular emphasis being given to experimental justification, comparison with similar computing methods, and design applications of the model, and restrictions in the use of the beam model which are dependent on external dimensions of connected parts and their basic form.
Abstract: The behaviour of bolt connections is illustrated by an example of eccentrically loaded plate strip, examined on a FE model with a description of the beam model of this connection. The development of a general‐purpose beam model is described with particular emphasis being given to experimental justification, comparison with similar computing methods, and design applications of the model. The restrictions in the use of the model which are dependent on external dimensions of connected parts and their basic form are also mentioned.
01 Jan 1985
TL;DR: In this paper, the authors derived equivalent stiffnesses for an extended Timoshenko beam used to represent truss beams using a typical substructure of a truss, and compared the solutions with the full-scale finite element solutions.
Abstract: Procedures for deriving equivalent stiffnesses for an extended Timoshenko beam used to represent truss beams are presented. A typical substructure of a truss is used to calculate these equivalent properties. Free vibration of asymmetric trusses is studied by using the equivalent Timoshenko beam model, and the solutions are compared with the full-scale finite element solutions. A method is presented for extracting the truss member load from the Timoshenko beam solution. Forced vibration of a symmetric truss is used as an evaluative example. In general, the extended Timoshenko beam model is excellent in predicting natural frequencies, mode shapes, and loads in truss members.
TL;DR: Theoretical predictions of the natural frequencies and mode shapes of beams depend on the choice of beam theory (Bernoulli-Euler [1, Timoshenko [1], Vlasov [2, 3], Wagner-Kappus [4]) adopted in the mathematical model as discussed by the authors.
TL;DR: In this paper, an incremental variational equation for non-linear motions of multilayer beams composed of n stiff layers and (n - 1) soft cores is derived from the dynamic virtual work equation by an appropriate integration procedure.
01 Jan 1985
TL;DR: In this paper, the free vibration of symmetrically-laminated, composite, rectangular plates which may have orthotropic or anisotropic properties was examined by means of the Rayleigh-Ritz method and shear deformation plate theory.
Abstract: A study is made of the free vibration of symmetrically-laminated, composite, rectangular plates which may have orthotropic or anisotropic properties. The problem is examined by means of the Rayleigh—Ritz method and shear deformation plate theory is employed rather than the classical plate theory. Trial functions for the lateral deflection and the two cross-sectional rotations are expressed as series of products of Timoshenko beam functions. Results for plates having various boundary conditions are presented in numerical and graphical form, and these reveal the very significant effect that shear deformation can sometimes have on calculated natural frequencies.
TL;DR: In this article, a finite element model for thin, laminated, orthotropic beams is presented, where each segment of the section can have different number of orthotropic material layers, with each layer having its unique orthotropic axes relative to beam coordinates.
TL;DR: In this paper, a theory for anisotropic materials which relates the deflection of a beam to the stress pattern is considered, which allows the calculation of corrections to the natural frequencies derived by standard beam theory.
TL;DR: In this article, the effects of load rate and beam-end restraint on direct shear failure in reinforced concrete slabs were investigated using elastic beam action and wave-action models.
Abstract: Direct shear failure in reinforced concrete slabs under impulsive loads is relatively undocumented because of the paucity of data showing failure characteristics. The combined effects of beam action and wave action are likely to be important in developing models to understand the dynamic direct shear phenomenon. The research summarized in this paper makes an initial attempt to understand this phenomenon by considering elastic beam action to describe incipient direct shear failure conditions. The effects of load rate and beam‐end restraint are investigated. Failure curves developed from elastic Timoshenko beam models are compared with experimental data on one‐way slabs which failed in direct shear.
TL;DR: In this paper, stress relief holes at the root of a cantilever beam were found to increase the flexural strength of the beam by 1 4 to 1 3, compared to conventional cantilevers.
TL;DR: In this paper, the dynamic contact problem of a rigid, smooth striker impacting an elastically supported beam is solved using the superposition of an elastic layer solution together with an elementary beam theory solution that incorporates the dynamic effects.
TL;DR: In this paper, a finite element model for thin, laminated, orthotropic beams is presented, where each segment of the section can have different number of orthotropic material layers, with each layer having its unique orthotropic axes relative to beam coordinates.
TL;DR: In this article, the Ritz finite element approach is used to study the nonlinear free vibrations of a beam considering shear deformation and rotary inertia effects, and the governing nonlinear equations are derived using Lagrange equations at the point of reversal of motion.
Abstract: The Ritz finite element approach is used to study the nonlinear free vibrations of a beam considering shear deformation and rotary inertia effects. The governing nonlinear equations are derived using Lagrange equations at the point of reversal of motion. The nonlinear strain-displacement relations include the curvature terms based on three-dimensional incremental deformations, as used in Trefftz theory. A simple and efficient beam element, with three independent degrees-of-freedom at each node, and with linear polynomial distributions within the element, is made use of. The reduced integration technique is adopted on the shear related matrix to eliminate spurious constraints occurring when exact integration is used for the same in the case of slender beams. The governing equations are solved using a direct iteration scheme. Numerical results are presented in the form of tables for hinged-hinged immovable beam. When the present results are compared with the available ones wherever possible, good agreement is in general, found.
TL;DR: In this article, the hierarchical Timoshenko beam finite element is transformed into modal co-ordinates, where the degrees of freedom of the new element are the deflection and cross section rotation at the two nodes together with an arbitrary number of coefficients of the elements clamped-clamped modes.
TL;DR: In this paper, a new formulation of the governing equations for the finite displacement beam theory is presented, which considerably simplifies the derivations through the principle of virtual work, and can be easily obtained even for the exact theory under beam assumptions.
Abstract: The governing equations for the finite displacement beam theory are often formulated through the principle of virtual work by introducing the pertinent kinematic field with displacement components defined in terms of the coordinates fixed in space. However, this formulation can hardly be applied for the theory of space beam without any restrictions on the magnitude of displacements, since the kinematic field becomes highly nonlinear largely due to the finite rotations in space.This paper presents a new formulation which considerably simplifies the derivations through the principle of virtual work. By the formulation, the governing equations can be easily obtained even for the exact theory under beam assumptions.
TL;DR: In this article, an analysis of a long edge-cracked beam resting on an elastic foundation and with rotational and translational restraints at the ends is presented, and the bending moment redistribution caused by the crack growth is analyzed and graphically illustrated.
TL;DR: In this article, the Timoshenko beam theory is applied to study the failure of one-way slabs by assessing the importance of the shear deformations and importance of support constraint.
Abstract: Recent experimental evidence shows that the roof elements of reinforced concrete box-like structures fail in a direct shear mode when subjected to transverse, uniformly distributed, near impulsive pressures. These failures are typically characterized by excessive shear deformations near the roof supports. The Timoshenko beam theory is applied to study the failure of these one-way slabs by assessing the importance of the shear deformations and the importance of the support constraint. The Timoshenko equations are altered to account for variable rotational end constraint and the resulting normal mode solution is illustrated with a numerical example.
TL;DR: In this article, the Timoshenko beam theory is used to deal with the vibration and stability of multi-span beams elastically supported against translation and rotation at several intermediate points as well as both ends.