Homework Chapter $1$: Do the homework, do not copy the homework.

$1-8$ The steel structure supports uniformly distributed load $\backslash ($ w$=750\backslash$mathrm$\{$~N$\}/\backslash$mathrm$\{$m$\}\backslash ).$ The $\backslash (\backslash$operatorname$\{$rod$\}$ B C $\backslash ),$ pin at $\backslash ($ B $\backslash )$ and $\backslash ($ C $\backslash )$ have diameter of $\backslash (10,7\mathrm{.}5\backslash )$ and $7\mathrm{.}5$ mm $,$ respectively. If the steel has yielding stress of $250$ MPa and yielding shear stress of $125$ MPa $,$ determine the stress in the $\backslash (\backslash$operatorname$\{$rod$\}$ B C $\backslash ),$ pin at $\backslash ($ B $\backslash )$ and $\backslash ($ C $\backslash )$ and the factor of safety.

$1-9$ If the allowable shear stress of the steel pin at $\backslash ($ A$,$ B $\backslash )$ and $\backslash ($ C $\backslash )($having $7\mathrm{.}5$ mm diameter$)$ is $85$ MPa and the allowable normal stress of rod $\backslash ($ B C $\backslash )($having $10$ mm diameter$)$ is $150$ MPa $,$ determine the uniformly distributed load $\backslash ($ w $\backslash ).$

$1-10$ The steel structure supports uniformly distributed load $\backslash ($ w$=1\mathrm{.}0\backslash$mathrm$\{$kN$\}/\backslash$mathrm$\{$m$\}\backslash ).$ If the steel has yielding stress of $250$ MPa and yielding shear stress of $125$ MPa $,$ determine the diameter of the rod $\backslash ($ B C $\backslash ),$ pin at $\backslash ($ B $\backslash )$ and $\backslash ($ C $\backslash ).$ The factor of safety is given as $2\mathrm{.}0.$