AN IMPROVED METHOD OF CALCULATING BEAM DEFORMATION CONSIDERING TRANSVERSE SHEAR STRAIN
Keywords:Euler–Bernoulli beam theory, Timoshenko beam theory, Transverse shear strain, Shear locking
In 1921, Timoshenko improved upon the Euler‒Bernoulli beam theory by adding the effect of transverse shear strains. In the Euler–Bernoulli beam theory, transverse shear strains are neglected, and cross- sections remain plane and perpendicular to the neutral axis. In the Timoshenko beam theory, cross-sections still remain plane but are no longer perpendicular to the neutral axis. Although the transverse shear strain approaches zero, the Timoshenko beam theory does not converge on the Euler‒Bernoulli beam theory due to the shear locking. Many authors have attempted to overcome this problem and although they have brought acceptable results, these still have theoretical limitations. Therefore, in this paper, the author presents an improved method of calculating the beam considering transverse shear strain to overcome the theoretical limitations of previous authors. The problem is addressed by the use of numerical methods which achieve convergence and avoid the issue of shear locking.