TASK $1($of $2)$

Reconsider task $7\mathrm{.}1.$ You are doing such a great job for ODOT, your supervisor would like you

continue your analysis of the proposed highway signage on I$-75.$ The beam shown below is part of

contractor proposal. The beam is supported by a pin at A and a cable at $B.$ The weight of the beam

and sign is $2\mathrm{.}83kN.$ The ODOT needs to hang a sign at point B that will cause a total tension force

in the cable of $5\mathrm{.}0kN($this includes the aforementioned $2\mathrm{.}83kN$ above$).$ Assume the cable has a

circular cross section. The proposal recommends $1cm$ radius for the cable $BC.$ The pin at point $A$

can be built using an assembly that allows for either single or double shear. The allowable pin

radius shall be chosen from the following list: $[0\mathrm{.}25,0\mathrm{.}35,0\mathrm{.}45,0\mathrm{.}50,0\mathrm{.}70]cm.$

Determine the design stress in the cable in newtons per meter squared $(\frac{N}{m^{{?}^{{?}^{?}}}}2).$

The yield stress for the cable is reported to be $16$MPa. Determines the factor of safety and

comment on the designed margin.

Your supervisor has let you know that an industry best practice is to use a factor of safety of

at least $1\mathrm{.}5.$ Recalculate the minimum radius of the cable based on this new information.

For the pin design at point A$,$ calculate the shear stress for both single and double shear

with the allowable pin radius list provided above. Show a sample calculation for single and

double shear in your solution and then use Excel for the rest of the calculations and just

include the answers in your PPM solution $($you do not need to submit the Excel file$).$

Finally, your supervisor has asked you to identify which pin sizes can be selected such that

the shear stress does not exceed $100$MPa. Which pin diameters is this true for when in

Single Shear? and when in Double Shear?