<p>The simplified kinematics in the theory of shear elastic beams usually lead to shear stress distributions that are not statically admissible, i.e. they violate local equilibrium and/or boundary conditions. This paper deals with a general formulation to obtain admissible shear stress distributions in cross-sections of arbitrary geometry and arbitrary variations of material parameters, such as FGM. The method is applied to loadings of warping torsion as well as transverse shear-force bending. From a finite element solution of a boundary value problem over the section area, appropriate measures of shearing stiffness are defined for bending and torsion. Within a variational formulation the effect of admissible stresses is represented through the introduction of suitable shear correction factors. The approach is supported by numerical results showing accurate distributions of shear stresses for different FGM type cross-sections, which closely correspond to three-dimensional reference solutions by finite elements.</p>