$4\mathrm{.}1$

Problem Statement: You are designing a truss system to support the Raptor $3$ thruster, which produces $2\mathrm{.}75$

MN $($Mega Newtons$)$ of thurst. The truss members you decide to use will be made of

stainless steel, which has a modulus of elasticity of $200$ GPa $.$ The rocket will be supported

by three truss members that are axisymmetrically spaced, as shown below. The bolts

holding these truss members have a yielding shear stress of $200$ MPa $.$

Problem Queries:

$5$ pts$.$

$20$ pts$.$

$25$ pts$.$

$20$ pts$.$

$10$ pts$.$

$20$ pts$.$

a$)$ Will the members be in compression or tension?

b$)$ Draw the free body diagram of JUST member $AB$ below. Provide the length and height of

the member in the FBD$.$

c$)$ Given that the total thrust is $2\mathrm{.}75$ MN $,$ determine the reactions at A and $B.$

d$)$ What diameter bolt is needed to support the thrust if a factor of safety of two is desired?

e$)$ Draw a cross$-$section of the relevant area for the bearing stress in member $AB$ at $B.$

f$)$ Given that the support of $AB$ is shown below, and using the bolt diameter found above,

what is the bearing stress of member $AB$ at $B.$

Known Parameters: