Chapter 10, Problem 10.3.6P

A cantilever beam of a length L and loaded by a uniform load of intensity q has a fixed support at A and spring support at B with rotational stiffness k_R. A rotation ${\theta }_B$ at B results in a reaction moment M_B=k_Rx ${\theta }_B$.

Find rotation ${\theta }_B$ and displacement ${\delta }_B$at end B. Use the second-order differential equation of the deflection curve to solve for displacements at end B.