Problem $1(50$ points$)$:

The following structure has a steel link $BC$ with a

thickness of $15$ mm and ultimate tensile strength of

$450$ MPa $.($a$)$ What should be the width $w$ of link $BC$ if

the structure shown is being designed to support a

$30-kN$ load $P$ with a factor of safety $5.($b$)$ If the

modulus of elasticity of steel is $200$ GPa $,$ find the

change in the length of link $BC.$