The lead engineer on the new Starfinder rocket must determine the force in each member of the inter-stage truss structure. If the load is too high, the first-stage thrust will buckle the truss members.

What is known:

The base ring radius is 1 m.

The top ring radius is 0.75 m.

The base and top ring are 1 m apart.

The total thrust of the first-stage main engine is 2,400 kN (300 kN per joint).

What is the force in each of the truss members of the truss structure between the second- and third-stage rockets when the first-stage main engine is firing?

Approach

Sum all forces at a joint (method of joints).

ΣF =
0

Find the 3D unit vectors for all forces at the joint. Find the unknown magnitudes of the member forces.