For the load and the beam shown, determine a$)$ slope @ point b$,$ b$)$ deflection @ point b$,$ c$)$ slope @ point c$,$ and d$)$ deflection @ point c using virtual work method.

For the load and the beam shown, determine a$)$ slope @ point b$,$ b$)$ deflection @ point b$,$ c$)$ slope @ point c$\text{'},$ and d$)$ deflection @ point c using Castigliano's method.