Problem $1.$ The beam shown below is acted upon by the service loads indicated. Find:

a$)$ Reactions, shear force and bending moment diagrams $($including points of inflection$)$ using service loads. Find $V_{\text{m}\text{a}\text{x}}$ and $M_{\text{m}\text{a}\text{x}}.$

b$)$ Reactions, shear force and bending moment diagrams $($including points of inflection$)$ using design loads. Find $V_{\text{m}\text{a}\text{x}}$ and $M_{\text{m}\text{a}\text{x}}.$