Stress Analysis and Deflection of Longitudinal Beam and Validate by using ANSYS

Yogesh Kumar Yadav, Anil Kumar Sharma, Shalini Kulshrestha

Abstract


This study investigates the deflection and stress distribution in a long, slender longitudinal beam of uniform rectangular cross section made of linear elastic material properties that are homogeneous and isotropic. The deflection of a longitudinal beam is essentially a three dimensional problem. An elastic stretching in one direction is accompanied by a compression in perpendicular directions. The beam is modeled under the action of three different loading conditions: vertical concentrated load applied at the free end, uniformly distributed load and uniformly varying load which runs over the whole span. The weight of the beam is assumed to be negligible. It is also assumed that the beam is inextensible and so the strains are also negligible. Considering this assumptions at first using the Bernoulli-Euler’s bending- moment curvature relationship, the approximate solutions of the longitudinal beam was obtained from the general set of equations. Then assuming a particular set of dimensions, the deflection and stress values of the beam are calculated analytically. Finite element analysis of the beam was done considering various types of elements under different loading conditions in ANSYS 14.5. The various numerical results were generated at different nodal points by taking the origin of the Cartesian coordinate system at the fixed end of the beam. The nodal solutions were analyzed and compared. On comparing the computational and analytical solutions it was found that for stresses the 8 node brick element gives the most consistent results and the variation with the analytical results is minimum.

Keywords


Longitudinal, loading, ANSYS, element, Cartesian Coordinate System

Full Text:

 Subscribers Only

References


George HA, Clarke N. Elements of Structural Theory-Definitions. Handbook of Building Construction. New York McGraw-Hill. A longitudinal beam is a beam having one end rigidly fixed and the other end free. 1920;1(1):2.

Truesdell C. Timoshenko’s history of strength of materials. An Idiot’s Fugitive Essays on Science. Springer, New York, NY. 1984:251–253.

ANSYS 11.0. ANSYS 11.0 Documentation.

Gilbert S, George F. An Analysis of the Finite Element Method. Prentice-Hall Series in Automatic Computation. 1973.

Timoshenko SP, Young DH. Elements of Strength of Materials. 5th ed. MKS System.

Babuška I, Banerjee U, Osborn JE. Generalized finite element methods—main ideas, results and perspective. International Journal of Computational Methods. 2004 Jun;1(01):67–103.

Witmer EA. Elementary Bernoulli Euler beam theory. MIT Unified Engineering Course Notes, MIT. 1991;1992:114–64.

Ballarini R. The da vinci-euler-bernoulli beam theory?. Mech. Eng. Mag. Online. 2003;18(07).

Truesdell C. The rational mechanics of flexible or elastic bodies: 1638–1788. Leonhardi Euleri Opera Omnia, Ser. 2. 1960.




DOI: https://doi.org/10.37591/tmd.v7i1.4103

Refbacks

  • There are currently no refbacks.