Showing papers on "Timoshenko beam theory published in 1979"
TL;DR: A second order beam theory which takes into account shear curvature, transverse direct stresses and rotatory inertia is presented in this article, where the governing differential equation is similar in form to the Timoshenko beam equation but contains two coefficients, one of which depends on cross-sectional warping just as does Cowper's expression while the second includes terms dependent on the transversal direct stresses.
112 citations
TL;DR: In this paper, the stiffness, mass and gyroscopic matrices of a rotating beam element are developed, a cubic function being used for the transverse displacement, and rotatory inertia effects are included in the energy functional to provide a Timoshenko beam formulation.
53 citations
TL;DR: In this article, the vibration and stability of an elastically supported beam carrying an attached mass and subjected to axial and tangential compressive loads are investigated based on the Timoshenko beam theory and the effects of the attached mass are expressed with Dirac delta functions.
49 citations
TL;DR: In this article, the transient motion of an end-loaded column buckles is studied using a nonlinear Timoshenko beam theory, and the results are compared with those of a previous analysis of the same problem that employed the Euler-Bernoulli beam theory.
Abstract: The transient motion that results when an ended-loaded column buckles is studied using a nonlinear Timoshenko beam theory. The two-time method is used to construct an asymptotic expansion of the solution. The results are then compared with those of a previous analysis of the same problem that employed the Euler-Bernoulli beam theory. Thus, the effects of shear deformations and rotary inertia on the dynamics of the column are explicitly demonstrated.
24 citations
TL;DR: In this paper, a variational methodology for investigating the dynamic stability of frames subjected to a suddenly applied load of constant magnitude and infinite duration is developed and successfully demonstrated through a simple two-bar frame.
Abstract: A variational methodology for investigating the dynamic stability of frames subjected to a suddenly applied load of constant magnitude and infinite duration is developed and successfully demonstrated through a simple two-bar frame. A criterion for dynamic stability is presented on the basis of which dynamic snap-through loads are established. Using Timoshenko's beam theory the individual and coupling effects of various parameters (i.e. cross-sectional shape, loading eccentricity, slenderness ratio and moment of inertia ratio of the two bars) on the dynamic and static snap-through load are fully assessed.
18 citations
TL;DR: In this paper, a solution methodology is presented for studying the stability of a uniform cantilever having a translational and rotational spring at its support, carrying two concentrated masses, one at the support and the other at its tip, subjected to a follower compressive force at its free end.
17 citations
TL;DR: In this paper, the steady state response of an internally damped Timoshenko beam of varying cross-section to a sinusoidally varying point force is determined by use of the spline interpolation technique.
15 citations
TL;DR: In this paper, the state space approach is extended to two dimensional elastodynamic problems and the frequency values are calculated using the Timoshenko beam theory and the present analysis for different values of Poisson's ratio and they are in good agreement.
Abstract: The state space approach is extended to the two dimensional elastodynamic problems The formulation is in a form particularly amenable to consistent reduction to obtain approximate theories of any desired order Free vibration of rectangular beams of arbitrary depth is investigated using this approach The method does not involve the concept of the shear coefficientk It takes into account the vertical normal stress and the transverse shear stress The frequency values are calculated using the Timoshenko beam theory and the present analysis for different values of Poisson's ratio and they are in good agreement Four cases of beams with different end conditions are consideredDie Zustandsraum-Technik wird auf zweidimensionale elastodynamische Probleme ausgedehnt Die Formulierung ist besonders geeignet fur die Aufstellung von Naherungstheorien beliebigen Grades Freie Schwingungen von Rechteckbalken beliebiger Hohe wurden mit Hilfe dieser Technik untersucht Das Verfahren umgeht den Begriff des Schubbeiwertsk Es berucksichtigt die senkrechte Normalbeanspruchung und die Querkraft Die Frequenzwerte werden mit Hilfe der Balkentheorie von Timoshenko und der vorliegenden Analyse berechnet, und zwar fur verschiedene Werte der Querdehnzahl Die berechneten Werte befinden sich in guter Ubereinstimmung Vier Falle von Balken mit verschiedenen Endbedingungen werden untersucht
15 citations
TL;DR: In this article, the authors considered the problem of stress analysis of a pipeline lifted for jointing or repair, in the absence of axial loads, but the analysis is non-trivial because the total length of line lifted from the foundation is unknown.
7 citations
01 Jan 1979
TL;DR: Doshi and Chinubhai as discussed by the authors derived the Timoshenko beam equation in terms of variable "w" where w is the deflection due to the bending of a beam, and the equation is used to analyze an infinite beam loaded with a concentrated transverse load and an impulse.
Abstract: Doshi, Chinubhai S.; M.S., Rochester Institute of Technology, Feb. "79. 'On the Analysis of the Timoshenko Beam Theory With and Without Internal Damping.1 Advisor: R. B. Hetnarski The Timoshenko beam equation in terms of variable 'w ' is derived where 'w is the deflection due to the bending of a beam. D The equation is used to analyze an infinite beam loaded with (i) a concentrated transverse load and (ii) an impulse. It is also shown that the rotatory damping in the equation eliminates the increasing amplitude in the propagation of the bending moment when an impulse is applied to an infinite beam. Also the general procedure for the anlysis of a non-homogeneous equation is explained.
6 citations
TL;DR: In this paper, an approximate method of analysis for dynamic response problems of a Timoshenko beam is presented by adding the solution for bending and rotatory motions and neglecting the inertia force of the shear motion.
Abstract: An approximate method of analysis for dynamic response problems of a Timoshenko beam is presented. The results for the beam are obtained by the addition of the solution for bending and rotatory motions and that for the shear motion by neglecting the inertia force of the shear motion. The result by this analysis compared with both exact results for Timoshenko and Euler–Bernoulli beams. As applications of this study, dynamic response problems of taper beams with moving load are solved by this method.
TL;DR: In this article, the best possible distribution of Young's modulus or the cross-sectional area or both for a cantilevered Timoshenko beam which, for a given volume and end deflection, carries the maximum possible load at its free end was determined.
Abstract: The best possible distributions of Young's modulus or the cross-sectional area or both are determined explicity for a cantilevered Timoshenko beam which, for a given volume and end deflection, carries the maximum possible load at its free end. Closed-form solutions are given for the optimal height, width and/or Young's modulus functions. Numerical results are presented in graphical form. It is found that the inclusion of shear deformation decreases the efficiency of the optimal design, and that optimization with respect to Young's modulus in addition to shape increases the efficiency considerably in comparison with optimization of the shape only.
TL;DR: In this paper, the problem of adjusting the mathematical model of a turbine-rotor system such that the computed natural frequencies coincide with those measured experimentally is considered, where the stiffness diameters are assumed variable, thereby allowing for deficiencies in the model near discontinuous changes of section.
Abstract: This paper is concerned with the problem of adjusting the mathematical model of a system such that the computed natural frequencies coincide with those measured experimentally. The particular system considered is a laboratory turbine-rotor model, modelled mathematically by 42 Timoshenko beam elements and lumped masses. Model adjustments are made by assuming, firstly, Young's modulus and the modulus of rigidity to be variable, a change from standard values representing overall stiffness deficiencies in the mathematical model. In this case, a best fit to the lowest six natural frequencies, as measured experimentally, is made. Secondly, stiffness diameters are assumed variable, thereby allowing for deficiencies in the model near discontinuous changes of section, and in this case, the lowest six natural frequencies are matched exactly, but an overall measure of the differences between the actual and the stiffness diameters is minimized. An analysis for the rates of change of natural frequency with the various...
TL;DR: In this article, the free transverse vibrations of a beam composed of variable thickness layers are studied on the basis of Timoshenko shear theory and the differential equations governing the transverse motion of the beam are solved to determine the frequencies by using the quintic spline collocation technique.
TL;DR: In this paper, one-dimensional beam equations are derived for a rectangular-cross section beam consisting of shear webs and corner stringers with one cross-sectional axis of symmetry, and it is shown that a systematic statement of this problem involves one more equation than elementary theory, with this additional equation involving the concept of crosssectional warping and bi-moment.
Abstract: : One-dimensional beam equations are derived for a rectangular-cross section beam consisting of shear webs and corner stringers with one cross-sectional axis of symmetry. It is shown that a systematic statement of this problem involves one more equation than elementary theory, with this additional equation involving the concept of cross-sectional warping and bi-moment. As an application of the general results of the paper, new conclusions are deduced concerning the location of the center of shear of the beam. (Author)
01 Jul 1979
TL;DR: In this paper, a linear bending moment-curvature relation is derived parallel to the classical beam theory for pure bending of a circular cylinder with the couple-stress theory of linear elasticity.
Abstract: This report presents the solution to the pure-bending of a circular cylinder with the couple-stress theory of linear elasticity. A linear bending moment-curvature relation is derived parallel to the classical beam theory. The section modulus (or the proportional coefficient) associated with the couple-stress theory is always greater than that predicted by the classical theory, and the ratio of the former to the latter increases as the radius of the beam decreases. These aspects clearly agree with the observed behavior of nuclear-grade graphite. Based on the solution, it is further estimated that the characteristic length l/sub 2/ of the couple-stress theory for H-451 graphite ranges from 0.62 to 1.54 mm. This range of l/sub 2/ concurs with the magnitude of the grain size (maximum is 1.57 mm for H-451 graphite) and agrees with an aspect of the couple-stress theory.
TL;DR: In this paper, the load-deformation responses of laminated cantilever beams with the consideration of interlayer slip was analyzed. But the authors did not consider the effect of inter-layer slip on the final state of the beam.
Abstract: This paper deals with the load-deformation responses of laminated cantilever beams with the consideration of interlayer slip. In the analysis, a slip criterion was assumed that slip between the laminae of a beam will occur if the interlayer shear reaches a critical value. An analytical solution was obtained by extending the simple beam theory for which interlayer slip of the beam is permitted. Analysis results indicate that slip deformation not only reduces the bending stiffness of the beam, but also leads to an ultimate state in a manner similar to plastic deformation.
01 Jan 1979
TL;DR: In this article, the multi-axial stress distributions in the three-points flexural test and the influences of various factors such as span/depth ratio and shape of load distribution on beam are analyzed in order to discuss the validity of these fracture strengths and to propose a reasonable testing method.
Abstract: The interlaminar shear strength and the flexural strength are usually determined by means of the three-points flexural test because of its simplicity. These strengths are defined as the maximum stress values predicted by elementary beam theory based on Euler-Bernoulli hypotheses. However, in the three-points flexural test on composite materials, especially with high anisotropy, the stress distribution in the vicinity of central loading point is not so simple as that given by the elementary beam theory. In the present paper, the multi-axial stress distributions in the three-points flexural test and the influences of various factors such as span/depth ratio and shape of load distribution on beam are analysed in order to discuss the validity of these fracture strengths and to propose a reasonable testing method. Consequently, it is found that the local stresses at the maximum bending moment region are very high, and that, in the case of small span/depth ratio, the stress distribution differs extremely from that based on the elementary beam theory. The validity of these analytical results is confirmed by using the finite element method analysis. The initial failure behaviors can be explained by these analytical results.
TL;DR: In this article, the behavior and strength of reinforced concrete beams with shear span to depth ratio = 1.5 were investigated in an experimental program involving eight beams with a constant longitudinal steel ratio.
Abstract: The behavior and the strength of reinforced concrete beams with shear span to depth ratio = 1.5 is investigated in an experimental program involving eight beams with a constant longitudinal steel ratio. The beams were loaded in the common framing situation where the loads and reactions are applied as shear on the sides of the member. For the shear span to depth ratio and reinforcing particulars employed the test results show that the horizontal web reinforcement has no significant effect on the beam strength and behavior. The aggregrate interlock does not have a large effect on the strength of beams with vertical web reinforcement. The vertical web reinforcement decreases the beam deflections and crack movement. After cracking, the simple beam theory is not valid for predicting the strain distribution in the zone where the beam is subjected to bending moments and shearing forces, while it is valid in the zones of pure moment. The measured strain distribution shows a tendency towards the arch action behavior.