Abstract:
Analysis of the beams responses has been the subject of many theories including Bernoulli's theory which neglects the shear deformation and the Timoshenko theory where these deformations are taken into account.
This work aims to modeling and analyzing the behavior of a beam taking into consideration several parameters, mainly the slenderness of the beam, the support condition (Pined-pined beam, cantilever beam, pinned-fixed beam, Fixed-fixed beam) and the Young's modulus and their effects on displacement - rotations as well as the locking phenomenon due to shear.
The modeling was done using the ANSYS software, and the obtained results were validated by comparison with those obtained from the beams theories (Timoshenko theory, Bernoulli theory, Friedman and Kosmatka theory) and those obtained by the analytical expressions of the strength of materials.
Comparative parametric study was conducted. Many parameters were analyzed by different methods including modeling by ANSYS. It was observed that the displacements and rotations curves increase with the increase of the ratio (L / h). The curves obtained by Bernoulli’s theory, Friedman and Kosmatka and those of modeling by ANSYS are nearly the coincident with the analytical curve of RDM, except Timoshenko curve which is often different.
Changes in the displacements - rotations values appear from (L / h = 4).
The beam of Timoshenko gave results that coincide with other theories for (L / h ≤4); beyond this value, results become different with those of the other theories. It is the shear effect of thick beams. However, Bernoulli's theory is satisfactory for the slender beams.
