A boundary condition correction for the clamped constraint of elastic plate/beam theory

The finite rotational stiffness within the support is determined by applying a distributed load (statically equivalent to a couple moment) to such a constrained infinite elastic strip. The displacement profile is determined analytically and approximated by a straight line. The ratio of the applied moment to the slope of this line provides the rotational stiffness. Examples are given for a cantilever and a clamped-clamped plate/beam as well as for a clamped circular plate. For a beam we use Timoshenko beam theory, while for a plate Reissner-Mindlin is used. For each of these cases the correction due to the effect of rotational compliance is often greater than the correction due to shear deformation. Finite element analyzes, using two-dimensional elasticity, of these configurations show excellent agreement with the analytical results of this modified plate/beam theory.