(Solved): Consider a beam shown in the figure. The bending and shear stiffnesses of this beam are constant. Th ...

Consider a beam shown in the figure. The bending and shear stiffnesses of this beam are constant. The left end of the beam is fixed supported and the right third is sitting on a Winkler’s elastic foundation with modulus of the foundation as k. A distributed load q is applied to the left two thirds of the beam, as shown in the figure. Find the deflection of the beam
a) using classical beam theory;
b) using Timoshenko’s beam theory.
(To simplify your formulation, the portion of the beam on the elastic foundation can be modeled as a half infinite beam. If you are unable to determine all coefficients, please write all the conditions needed to determine these coefficients).???????