Two aluminum rods (EAl = 10.0 × 106 psi, αAl = 13.3 × 10−6 ◦K−1) and an iron bar (EF e = 28.5 × 106 psi,
αF e = 6.5 × 10−6 ◦K−1) are attached to a rigid support at the left and a cross-bar at the right. The
cross-sectional area of each bar is A = 0.5 in2 and L = 10 in. The normal stresses in the bars are initially
zero. If the temperature is increased by ∆T = 300 ◦K, what are the resulting normal stresses in the three
bars? The deformation of the cross-bar can be neglected.
Question 2
Consider a rocket docked on the ground, not pressurized nor experiencing G’s yet. Assume it to be an akin
to an unrestricted pipe as a first order approximation. The main rocket body is made from titanium with a
coefficient of thermal expansion of 9× 10−6 K−1, a Young’s Modulus of 116 GPa, and yield strength of 240
MPa. What temperature change would fail the structure in tension (longitudinally) assuming no safety
factor, if restricted? You may treat this in a 1D sense. What is the average temperature of rocket launch
(general Googling is fine here, obviously it depends on the size and hence combustion power system, just
cite some reasonable stats/examples)? Would what you found potentially mean your titanium rocket
structure would survive a launch? This is an over-simplified example of why we need thermal coatings on
rockets, and it only gets worse with applied G’s on the system.