Showing papers on "Timoshenko beam theory published in 1976"
TL;DR: Within the framework of classical beam theory it was shown that a strain independent surface stress has no effect on the natural frequency of a thin cantilever beam as discussed by the authors, therefore, the experimental results of Lagowski, Gatos, and Sproles must have a different explanation.
Abstract: Within the framework of classical beam theory it is shown that a strain‐independent surface stress has no effect on the natural frequency of a thin cantilever beam Therefore, the experimental results of Lagowski, Gatos, and Sproles must have a different explanation
172 citations
TL;DR: In this paper, the dynamics of pipes conveying fluid is described by means of the Timoshenko beam theory, and the equations of motion are derived and solved by a finite-difference technique, and by a variational method.
Abstract: The dynamics of pipes conveying fluid is described by means of the Timoshenko beam theory. The equations of motion are derived and solved (a) by a finite-difference technique, and (b) by a variational method. It is shown that the latter is the more efficient method.The eigenfrequencies of the system and its stability characteristics are compared with results obtained previously using the Euler-Bernoulli beam theory, and it is shown that in certain cases (e.g. short pipes) the two sets of results diverge. Experiments indicate that the present theory is more successful in predicting the observed behaviour. Furthermore, the present theory shows that, in some cases, cantilevered pipes may lose stability by buckling, whereas previous theories indicate that the system always loses stability by flutter.
55 citations
45 citations
TL;DR: In this paper, an idealized model of the double cantilever problem was developed within the framework of the geometric simplifications and the two dimensional elastostatic theory of plane.
37 citations
TL;DR: In this article, a finite element model is developed for the stability analysis of a Timoshenko beam subjected to periodic axial loads, and the effect of shear deformation on the static buckling loads is studied by finite element method.
Abstract: A Finite Element model is developed for the stability analysis of Timoshenko beam subjected to periodic axial loads. The effect of the shear deformation on the static buckling loads is studied by finite element method. The results obtained show excellent agreement with those obtained by other analytical methods for the first three buckling loads. The effect of shear deformation and for the first time the effect of rotary inertia on the regions of dynamic instability are investigated. The elastic stiffness, geometric stiffness, and inertia matrices are developed and presented in this paper for a Timoshenko beam. The matrix equation for the dynamic stability analysis is derived and solved for hinged-hinged and cantilevered Timoshenko beams and the results are presented. Values of critical loads for beams with various shear parameters are presented in a graphical form. First four regions of dynamic instability for different values of rotary inertia parameters are presented. As the rotary inertia parameter increases the regions of instability get closer to each other and the width of the regions increases thus making the beam more sensitive to periodic forces.
32 citations
TL;DR: In this paper, the first five natural frequencies of marine drilling risers are compared with frequencies obtained using an approximate method based on classical, uniformly tensioned beam equations, and an example calculation is given.
Abstract: This paper presents data relating the first five natural frequencies of marine drilling risers to typical riser and drilling parameters. The riser is idealized as a vertical flexible beam with pinned supports. Variable tension and fluid environment make the mathematics different from classical beam theory, leading to a differential equation that perhaps is unique to the oil industry. Exact natural frequencies or eigenvalues are compared with frequencies obtained using an approximate method based on classical, uniformly tensioned beam equations. An example calculation is given.
30 citations
TL;DR: Theoretical and experimental studies were made in obtaining the natural frequencies of cantilever sandwich beams subjected to only gravity forces as discussed by the authors, and the method of minimizing the total energy of the system was used for determining the frequencies.
15 citations
TL;DR: In this paper, the use of a reduced width of flange as a means of allowing for shear lag effects in wide shallow composite box girders with an overhanging top flange is examined.
Abstract: The use of a reduced width of flange as a means of allowing for shear lag effects in wide shallow composite box girders with an overhanging top flange is examined. Equivalent widths with beam theory leads to a gross underestimation of the maximum stresses and deflections for girders with short spans and gives no significant improvement over the results obtained by beam theory alone for girders with long spans. Thus, equivalent widths do not provide an acceptable method of dealing with shear lag effects in wide-flange shallow box girders; simple beam theory without equivalent widths gives a satisfactory estimate of maximum longitudinal stresses and deflections for girders in which the span-to-width ratio is greater than 12 for the overhanging portion and greater than 5 for the central portion of a flange between two webs; and a more rigorous theory such as folded plate analysis should be used for girders in which the foregoing span-width ratios are not satisfied.
10 citations
TL;DR: In this article, the effect of shear deformation on a layered composite being heated to a prescribed temperature is analyzed according to a recently developed theory for unsymmetric laminated plates.
Abstract: The effect of shear deformation on a layered composite being heated to a prescribed temperature is analyzed according to a recently developed theory for unsymmetric laminated plates. Expanding the fundamental solutions of thermal stress and warping into a power series form, the first approximation gives us familiar formulas of classical plate theory. The second approximation leads to an equivalent Timoshenko’s plate equation. In addition to Timoshenko’s shear correction factor, a thermal shear correction parameter has to be introduced for thermal expansion problems.
9 citations
8 citations
TL;DR: In this article, the in-plane and transverse motion of box beams is analyzed using the finite element displacement method and the results compared with the predictions of Euler and Timoshenko beam theories.
TL;DR: In this paper, a finite element method for analysis of asymmetric multi-storey buildings with varying cross-section is presented, where the basic structural component is a rectangular thin panel bounded between floors and vertical edges.
TL;DR: In this article, the vibration characteristics of turbine blade profiles were modeled by a Timoshenko beam with idealized boundary conditions permitting the system dynamics to be simulated by differential equations, resulting in an optimization problem in a finite number of variables.
TL;DR: In this paper, it is shown how those effects may be allowed for in the analysis of symmetric response, that they do not alter the form of the more rudimentary analysis and that the response lends itself to a convenient matrix formulation.
TL;DR: In this paper, an improved beam theory considering the effects of shearing deformation and rotatory inertia is applied to a bending motion of the bars, and the results obtained from the improved theory are compared with those from the elementary one.
Abstract: This paper deals with a transient response problem of connected bars excited by the impact loads at rigid joints. In the analysis, an improved beam theory considering the effects of shearing deformation and rotatory inertia is applied to a bending motion of the bars. As a numerical example, we examine the dynamic response of an L-Bar to a step-function load to clarify the influence of the angle between its legs and slenderness ratio on the dynamic behaviors of the bar. The free vibration of the bar is also treated, and the results obtained from the improved theory are compared with those from the elementary one.
01 Jan 1976
TL;DR: In contrast with the inequality constraint which controls the minimum cross-section, the present inequality constraint leads to more meaningful designs as mentioned in this paper, which leads to a more meaningful design for the Euler-Bernoulli or Timoshenko beam of a specified constant volume.
Abstract: The fundamental frequency of vibration of an Euler-Bernoulli or a Timoshenko beam of a specified constant volume is maximized subject to the constraint that under a prescribed loading the maximum stress or maximum deflection at any point along the beam axis will not exceed a specified value. In contrast with the inequality constraint which controls the minimum cross-section, the present inequality constraints lead to more meaningful designs. The inequality constraint on stresses is as easily implemented as the minimum cross-section constraint but the inequality constraint on deflection uses a treatment which is an extension of the matrix partitioning technique of prescribing displacements in finite element analysis.
01 Jan 1976
TL;DR: In this article, a rational procedure for the dimensioning of subsea pipelines is described, which consists of a computer program which determines pipe diameter and wall thickness for given quantities of flow rate, depth of water, bottom current velocity and towing capacity of the lay barge.
Abstract: A rational procedure for the dimensioning of subsea pipelines is described. It consists of a computer program which determines pipe diameter and wall thickness for given quantities of flow rate, depth of water, bottom current velocity and towing capacity of the lay barge. Steel quality, out-of-roundnees of pipe and characteristics of the concrete coating are also taken into account. The paper explains in detail the bending/ buckling criteria used in determining the steel pipe wall thickness. An analytical expression is derived for the maximum combined stress of a pipe subjected to constant external pressure and an external bending moment, allowing for initial cut-of-roundness. The concrete coating dimensions are determined in such a way that sufficient negative buoyancy of the air-filled pipe in water is maintained to counteract the lift originating from bottom currents. The bending moment is calculated with the help of large-deflection beam theory, solving the non-linear differential equation by means of finite-beam-element techniques. Sample applications of the design technique are given and checked against model tests and full scale data.
01 Jan 1976
TL;DR: In this article, an approximate solution for a system of two differential equations with linear partial derivatives of the second order was developed by using Galerkin's variational method, which corresponds to the physical model known in the literature as the Timoshenko Beam.
Abstract: By using Galerkin's variational method an approximate solution is developed for a system of two differential equations with linear partial derivatives of the second order. This system of differential equations corresponds to the physical model, known in the literature as the Timoshenko Beam. The results obtained are applied to two particular cases representing respectively: the case of a beam with a rectangular section, with a constant height and a basis with a linear variation; and the case of a beam with a constant basis and a height with cubic variation.