Frame $AB$ is fixed at $"A"$ and supported by a roller at $"B".$ It has a constant symmetrical cross$-$

sectional area $"A"$ and a constant flexural rigidity EI$.$

Using Castigliano's second theorem and neglecting the effect of shear forces:

a$)$ Determine the support reaction at $"$B$"RB$:$-\frac{8AF{L}^{{?}^{?}}2}{31+8A{L}^{{?}^{{?}^{?}}}2}$

b$)$ Determine the horizontal deflection at $"$B$".2F\frac{L}{AE}+2L^{{?}^{{?}^{?}}}3\frac{P-RB}{EI}$