$($b$)$ A beam shown in Figure $2$ is to be made of steel that has an allowable bending stress of ${}_{\text{a}\text{l}\text{o}\text{w}}=205$MPa and an allowable shear stress of ${}_{\text{a}\text{l}\text{l}\text{o}\text{w}}=120$MPa. Propose an appropriate W shape beam based on the table given in Appendix. Prove if the beam can safely support the loadings and justify the beam design selection.

$(15$ Marks$)$