In this paper, single variable beam theories taking into account effect of transverse shear deformation are developed
and applied for the bending, buckling and free vibration analysis of thick isotropic beams. The most important
feature of the present beam theories is that unlike any other higher order theory, the proposed class of theories
contains only one unknown variable and does not require shear correction factor. The displacement field of the
present theories is built upon the classical beam theory. The theories account for parabolic distribution of transverse
shear stress using constitutive relations, satisfying the traction free conditions at top and bottom surfaces of the
beam. Governing differential equation and boundary conditions of these theories are obtained using the principle
of virtual work. Results obtained for the displacements, stresses, fundamental frequencies and critical buckling
loads of simply supported isotropic solid beams are compared with those obtained by other theories to validate the
accuracy of the present theories