PROBLEM $1$

A $6-$kip force is applied to the machine element $AB$ as shown. Knowing that the uniform thickness of the element is $0\mathrm{.}8$ in $.,$ determine the normal and shearing stresses at $($a$)$ point $a,(b)$ point $b,(c)$ point $c.$

$\backslash$table$[[,$PROBLEM $2],[,$A ${?}^{10}10$ rolled$-$steel beam supports a load $P$ as shown. Knowing that $P=45$kips,$a=10in.,$ and ${}_{\text{a}\text{l}\text{l}}=18$ksi, determine $($a$)$ the maximum value of the normal stress ${?}^{{}_m}$ in the beam, $(b)$ the maximum value of the principal stress ${?}^{{}_{\text{m}\text{a}\text{x}}}$ at the junction of the flange and web, $($c$)$ whether the specified shape is acceptable as far as these two stresses are concerned.$]]$

$\backslash$table$[[,$PROBLEM $3],[,($a$)$ Knowing that ${}_{\text{a}\text{l}\text{l}}=24$ksi and ${}_{\text{a}\text{l}\text{l}}=14\mathrm{.}5$ksi, select the most economical wide$-$flange shape that should be used to support the loading shown. $($b$)$ Determine the values to be expected for ${}_m,{}_m,$ and the principal stress ${?}_{\text{m}\text{a}\text{x}}$ at the junction of a flange and the web of the selected beam.$]]$

PROBLEM $4$

Neglecting the effects of fillets and of stress concentrations, determine the smallest permissible diameters of the solid rods $AB$ and $BD.$ Use ${}_{\text{a}\text{l}\text{l}}=8$ksi.