A $7/8-$in$.-$diameter bolt, having a diameter at the root of the threads of $0\mathrm{.}731in.,$ is used to fasten two timbers together as shown. The nut is tightened to cause a tensile stress of $18$ksi in the bolt. Compute the shearing stress in the head of the bolt and in the threads. Also, determine the outside diameter of the washers if their inside diameter is $\frac{9}{8}$ in$.$ and the bearing stress is limited to $800$ psi.

Given:

Diameter of bolt $=\frac{7}{8}$ inch

Diameter at the root of the thread $($bolt$)=0\mathrm{.}731$ incl

Inside diameter of washer $=\frac{9}{8}$ inch

Tensile stress in the nut $=18$ksi

Bearing stress $=800$

Required:

Shearing stress in the head of the bolt

Shearing stress in threads of the bolt

Outside diameter of the washer

a$.$ Shearing stress in the head of the bolt

Given:

Diameter of bolt $=\frac{7}{8}$ inch

Diameter at the root of the thread $($bolt$)=0\mathrm{.}731$ inch

Inside diameter of washer $=\frac{9}{8}$ inch

Tensile stress in the nut $=18$ksi

Bearing stress $=800$