Self-Assessment Quiz: Structures and Materials

Twenty questions to check your grasp of launch loads, primary and secondary structure, materials, stress and strain, the factor of safety, mass budgets, and the Starship steel decision. Answer each before opening the key. Aim for 16 or more. Use $g_0 = 9.81\ \text{m/s}^2$.

Question 1

Which launch load usually reaches its peak near the end of a stage's burn rather than at lift-off?

A) acoustic loading B) pyroshock C) quasi-static (steady) axial acceleration D) random vibration

Question 2

A sound-pressure level of $140\ \text{dB}$ (typical inside a fairing) corresponds to an RMS fluctuating pressure of about:

A) $2\ \text{Pa}$ B) $200\ \text{Pa}$ C) $20{,}000\ \text{Pa}$ D) $101{,}000\ \text{Pa}$

Question 3

Pyrotechnic shock (from stage or payload separation) is best described as:

A) a slow, steady push lasting minutes B) a very brief, very-high-frequency, very-high-peak transient C) the same as acoustic loading D) the dominant load on heavy primary structure

Question 4

On most launch vehicles, the primary structure is usually:

A) the payload fairing B) the avionics mounting brackets C) the propellant tank walls and thrust structure D) the thermal blankets

Question 5

A "load path" is:

A) the trajectory the rocket flies B) the continuous route a force takes through the structure to where it is finally reacted C) the wiring harness routing D) the sequence of staging events

Question 6

For a mass-limited vehicle, the correct figure of merit when choosing a material is:

A) raw ultimate strength B) density alone C) specific strength (strength ÷ density) and specific stiffness ($E/\rho$) D) melting point

Question 7

At room temperature, which material has the highest specific strength?

A) stainless steel (annealed) B) aluminum C) carbon-fiber composite D) titanium

Question 8

Comparing specific stiffness $E/\rho$ for aluminum, titanium, and steel, you find:

A) steel is far lower (it is too heavy) B) they are all nearly the same ($\approx 2.5\times10^{7}\ \text{m}^2/\text{s}^2$) C) titanium is 10× the others D) aluminum is far higher than the rest

Question 9

A composite (CFRP) carries load primarily through:

A) the polymer matrix B) the carbon fibers, aligned along the load C) internal air pockets D) a metal core

Question 10

Stress is defined as:

A) $\sigma = F/A$ (force per unit area) B) $\sigma = \Delta L / L$ C) $\sigma = m a$ D) $\sigma = p V$

Question 11

Strain is:

A) the force applied to a material B) the fractional deformation $\Delta L / L$ (dimensionless) C) the same as stress D) measured in pascals

Question 12

In a thin pressurized cylinder, the hoop stress $\sigma_{\text{hoop}} = pr/t$ compared with the longitudinal stress is:

A) equal to it B) half of it C) twice it D) unrelated to it

Question 13

A typical ultimate factor of safety for metallic launch-vehicle structure is about:

A) 1.05 B) 1.4 C) 3 D) 10

Question 14

Aerospace uses the lowest factors of safety in engineering primarily because:

A) rockets never fail B) every increment of safety factor is mass, taxed exponentially by the rocket equation C) materials in space are stronger D) regulations forbid high factors

Question 15 (True/False, justify)

"A part with a margin of safety of $+1.5$ ($+150\%$) is exactly what a mass-optimized rocket wants." True or false? Justify in one sentence.

Question 16 (True/False, justify)

"On an upper stage with mass ratio $5$, adding $1\ \text{kg}$ of structure adds only $1\ \text{kg}$ to the fueled stage." True or false? Explain.

Question 17 (True/False, justify)

"A well-run program carries a large mass margin at concept and a small one at launch." True or false? Say why.

Question 18 (True/False, justify)

"SpaceX chose stainless steel for Starship because steel has the best specific strength of any material at room temperature." True or false? Correct it if false.

Question 19 (Short answer)

Name the two thermal properties of stainless steel — one at cold temperature, one at high temperature — that help justify its use for Starship.

Question 20 (Short answer)

A tank has radius $r = 1.2\ \text{m}$, wall thickness $t = 2.5\ \text{mm}$, and internal pressure $p = 3\ \text{bar}$. Compute the hoop stress $pr/t$ in MPa.

Answer Key

Q Ans Note
1 C Thrust ~constant while mass falls, so $a = F/m$ peaks near burnout (often forcing a throttle-down).
2 B $p = 2\times10^{-5}\times10^{140/20} = 2\times10^{-5}\times10^{7} = 200\ \text{Pa}$.
3 B Pyroshock: milliseconds long, very high frequency/peak; barely moves heavy structure, murders brittle parts.
4 C The tank is the primary (monocoque) structure; its failure loses the vehicle.
5 B Every load needs a continuous path to ground (the engines/thrust); structure provides it.
6 C Specific strength and stiffness — per-kilogram figures — decide a mass-limited design, not raw values.
7 C CFRP (~375) beats titanium (~214), aluminum (~174), and steel (~71 annealed).
8 B $E/\rho$ is nearly identical for Al, Ti, and steel — only composites break the metals' ceiling.
9 B Aligned carbon fibers carry the load; the epoxy matrix binds them and transfers load between them.
10 A $\sigma = F/A$, in Pa (usually MPa).
11 B $\varepsilon = \Delta L/L$, dimensionless (Hooke: $\sigma = E\varepsilon$).
12 C Hoop is twice longitudinal ($pr/t$ vs $pr/2t$) — vessels split lengthwise.
13 B ~1.4 ultimate (1.25 yield) for metallic launch structure — the lowest in engineering.
14 B Margin is mass, and mass is taxed exponentially; aerospace buys down uncertainty instead.
15 False $+150\%$ means the part is grossly overbuilt (dragging mass); the target is a small positive MS at the required FoS.
16 False To hold the mass ratio, fueled mass rises by $R\times1 = 5\ \text{kg}$ (1 kg structure + 4 kg propellant).
17 True Estimates are uncertain early (cover the ~25–30% historical growth) and firm up by launch, so margin is consumed on purpose.
18 False Steel has the worst room-temperature specific strength; it was chosen for cryo-strengthening, heat tolerance, cost, and weldability — a systems decision.
19 — Cold: 300-series austenitic stainless strengthens at cryogenic temperature (and stays tough). Hot: it retains strength to ~800 °C, cutting the heat-shield mass for re-entry.
20 — $\sigma_{\text{hoop}} = pr/t = 3\times10^{5}\times1.2/0.0025 = 3\times10^{5}\times480 = 1.44\times10^{8}\ \text{Pa} = 144\ \text{MPa}$.

Topics to review by question

Questions Topic Section
1, 2, 3 Launch loads (acceleration, acoustic, shock) §23.1
4, 5 Primary vs. secondary structure & load paths §23.2
6, 7, 8, 9 Materials, specific strength/stiffness, composites §23.3
10, 11, 12, 20 Stress, strain, Hooke's law, hoop stress §23.4
13, 14, 15 Factor of safety and margin of safety §23.4
16, 17 Mass budgets and mass growth §23.5
18, 19 The Starship stainless-steel decision §23.6