Exercise $1$: $(2$ points$)$

A beam is to be made of steel that has an allowable

bending stress of ${}_{\text{a}\text{l}\text{l}}=170$MPa and an allowable shear

stress of ${}_{\text{a}\text{l}\text{l}}=100$MPa.

a$)(0\mathrm{.}5$ points$)$ Calculate the maximum moment $M_{\text{m}\text{a}\text{x}}$ and maximum shear $V_{\text{m}\text{a}\text{x}}$

b$)(1$ point$)$ Select an appropriate $W$ shape that will carry the applied loads

c$)(0\mathrm{.}5$ points$)$ Assuming an ultimate normal strength ${}_u=170$MPa, comment on the value of

the factor of safety for normal stresses