Problem C$-2[$Average Normal and Average Shear Stresses$]$

As shown in the figure, member $AB$ and member $BC$ are

connected through a pin joint at $B($i$.$e$.,$ double shear$)$; The

other ends of the members $AB$ and $BC$ are connected to the

walls at points A and $C($i$.$e$.,$ single shear$),$ respectively.

There is a uniform distributed load of $2ki\frac{p}{f}t$ applied to

the member $AB$ in the transverse direction achieving

equilibrium.

Given the cross section of $BC$ is rectangular in shape, with

width $w=1\mathrm{.}5in.$ and thickness $t=0\mathrm{.}25in.$ All the pins $($at

$A,B$ and $C)$ have the same diameters $d=1in.$ The length

of $BC{l}_{BC}=6ft.$ The length of $AB{l}_{AB}=8ft.$

Determine the following:

$(1)$ The average normal stress ${}_{a-a}$ and average shear

stress ${}_{a-a}$ in member $BC$ at the cross$-$section $a-a$;

$(2)$ The average shear stress ${}_A$ in the pin at point $A$

$($assume simple shear$)$