Dimensions, loading $(P_1$ and $P_2)$ and cross$-$section of a beam are given in the figure.

a$)$ If $P_1=4kN$ and $P_2=0,$ draw the internal force diagrams of the beam $(T$ and $M)$ and check the safety of the beam.

b$)$ If $P_1=4kN$ and $P_2=72kN,$ draw the internal force diagrams of the beam. Determine the maximum and minimum normal stress $({}_{\text{m}\text{a}\text{x}}$ and ${}_{\text{m}\text{i}\text{n}})$ at the mid$-$span section. Draw a sketch of maximum and minimum normal stress distribution at the mid$-$span section.

${}_{\text{a}\text{l}\text{l}}=1k\frac{N}{c}{m}^2,{}_{\text{a}\text{l}\text{l}}=0\mathrm{.}1k\frac{N}{c}{m}^2,E=1000k\frac{N}{c}{m}^2$