3.6.1 · D5Spacecraft Structures & Systems Engineering
Question bank — Structural loads — axial (thrust), bending (wind shear), dynamic (vibration, acoustics, shock)
True or false — justify
True or false: axial compression is largest at the very top of the rocket, right under the payload.
False — axial force is where is the mass above the cut, so it grows toward the base where the most mass presses down.
True or false: the load factor is just the acceleration in disguise, so quoting "6 g" and "6 g of acceleration" mean the same thing.
False — bundles gravity with acceleration, so means the true acceleration is only .
True or false: bending stress is uniform across a cross-section, just like axial stress.
False — bending stress varies linearly with distance from the neutral axis: one side stretches, the opposite side compresses, and the middle sees zero.
True or false: the worst structural moment of the whole launch is at liftoff, when thrust is highest.
False — the sizing peak is usually near max-Q, where axial compression and the wind-shear bending moment stack on the same fiber as .
True or false: a stiffer spacecraft (higher ) is always safer against vibration.
False — stiffness only raises ; that helps only if it moves you away from the excitation band. It can just as easily push into a strong PSD peak. See Modal Analysis & Natural Frequencies.
True or false: higher damping ratio means larger resonant amplification.
False — , so more damping means less amplification. Low (~0.02) is the dangerous case giving .
True or false: shock loads with peak accelerations of thousands of g are the biggest threat to the primary load-bearing shell.
False — shock is high-frequency and tiny-duration, so massive parts barely feel the momentum; it wrecks electronics, relays, and brittle components instead. See Pyrotechnic Separation Systems.
True or false: acoustic loading matters most for the thick, heavy propellant tanks.
False — acoustics dominate large lightweight panels (solar arrays, antennas) whose big area and low mass respond strongly to pressure waves.
True or false: at resonance a small driving force can only ever produce a small deflection.
False — at resonance , so a modest force is amplified by ~10–25×; that is precisely why we avoid it.
Spot the error
"The axial force at a cut is using the rocket's full mass." — what's wrong?
Wrong mass — only the mass above the cut, , is being pushed by the structure at that station; the mass below is carried by lower structure.
"Since , and the rocket coasts in free-fall at , the load factor is ." — spot the error.
In free-fall gives , so — the structure carries no axial load (weightlessness), not .
", so to cut bending stress just make (the radius) smaller." — what's the trap?
Shrinking also shrinks (which scales as ), so the ratio actually gets worse; a fatter tube is stiffer in bending.
"To survive vibration we should design so equals the excitation frequency for a clean match." — error?
Matching frequencies causes resonance, the very thing we avoid. Miles' rule demands stay above the LV minimums, well separated from the excitation.
"Miles' equation shows response falls as rises, so add stiffness to boost ." — spot the two errors.
Response grows with (it's inside the square root, in the numerator), and is set by damping, not stiffness — stiffness moves , not . See Random Vibration & PSD.
"We designed each component to its RMS response, so it's safe." — what's missing?
RMS is the 1σ value; random peaks routinely exceed it, so the design load uses ==== (covering ~99.7% of peaks), not .
"Thrust makes tension in the lower skin because the engine pulls the rocket up." — error?
The engine pushes from below and inertia of the mass above resists, so the lower skin is compressed, not stretched.
Why questions
Why do engineers add axial and bending stresses at the same fiber near max-Q instead of treating them as separate cases?
Because both act simultaneously on the windward/leeward outer fiber; superposition means that one fiber carries , and ignoring the sum underestimates the true worst-case stress.
Why is the natural frequency and not ?
Setting gives , i.e. ; matching forces . Stiffer or lighter → faster oscillation.
Why do we quantify random vibration with a PSD (g²/Hz) instead of a single peak acceleration?
Random vibration has energy spread across many frequencies with no repeating peak, so we describe how much power sits at each frequency; the structure's response depends on where its lands in that spectrum.
Why does wind loading make the rocket behave like a cantilever beam rather than a simply-supported one?
The vehicle is effectively held/driven at one end (engine/base) and free at the other, so a transverse gust bends it exactly like a broomstick pushed in the middle while gripped at one end.
Why does the factor appear in Miles' equation?
It comes from integrating the SDOF resonance response over the effective bandwidth of the peak — the area under the sharp resonance curve — turning a PSD level into a total RMS. See Modal Analysis & Natural Frequencies.
Edge cases
Edge case: what axial load does the structure carry during ballistic coast (engine off, free-fall)?
With , we get , so — the vehicle is weightless and the primary axial compression vanishes.
Edge case: what happens to bending stress at the neutral axis of the cross-section?
It is zero there, since and on the neutral axis; the material there does bending work only in shear, not tension/compression.
Edge case: as damping , what does the amplification do?
— an undamped structure would amplify without bound at resonance; real damping is what keeps deflection finite.
Edge case: a component's sits exactly at an LV minimum (e.g. 25 Hz axial) — is that acceptable?
No — the rule requires to be above the minimum with margin; sitting on the boundary leaves no separation and risks resonant coupling. See Factor of Safety & Margins of Safety.
Edge case: for a thin ring, why is and not (area)?
Because material sits at every angle around the ring, and ; the averaging gives , not . See Beam Bending & Second Moment of Area.
Edge case: what happens to the axial load factor right at first-stage burnout compared to liftoff?
It peaks near burnout because the vehicle is nearly empty (low mass) but thrust is still high, so (and thus ) is largest just before shutdown. See Rocket Equation & Thrust.
Edge case: at exactly zero angle of attack in still air, what is the bending moment from wind?
Essentially zero — no side force means no cantilever bending; bending only appears once a gust or wind-shear layer gives a nonzero angle of attack. See Max-Q and Dynamic Pressure.
Recall One-line self-test
The single sentence that ties axial, bending, and dynamic together at the sizing point? ::: Near max-Q the outer fiber carries statically, and any dynamic input near multiplies deflections by on top — so worst-case = combined static stress with dynamic amplification and a margin.