SHEAR-DEFORMABLE BENDING SOLUTIONS FOR NONUNIFORM BEAMS AND PLATES WITH ELASTIC END RESTRAINTS FROM CLASSICAL-SOLUTIONS

The relationships of bending solutions between Timoshenko beams and Eu ler-Bernoulli beams are derived for uniform and non-uniform beams with elastic rotationally restrained ends. Extensions of these relationshi ps for the cylindrical bending of Mindlin and Kirchhoff plates and for the bending of symmetrically laminated beams are also discussed. The new set of general relationships is useful because the more complex Ti moshenko beam and Mindlin plate solutions may be readily obtained from their simpler Euler-Bernoulli beam and Kirchhoff plate solutions resp ectively, without much tedious mathematics.