Chapter 10, Problem 10.4.10P

Beam AB has a pin support at A and a roller support at B Joint B is also restrained by a linearly elastic rotational spring with stiffness k_R, which provides a resisting moment M_Bdue to rotation at B. Member AB has flexural rigidity EI. A moment M₀acts counterclockwise at B.

1. Use the method of superposition to solve for all reactions.

Find an expression for joint rotation ${\theta }_A$in terms of spring stiffness k_R. What is ${\theta }_A$when k_R $\to$ 0? What is ${\theta }_A$when k_R— $\infty$ ? What is ${\theta }_A$when k_R= 6EI/L?