Level 1 — RecognitionSpacecraft Structures & Systems Engineering

Spacecraft Structures & Systems Engineering

⏱ 20 minutes30 marksprintable — key stays hidden on paper

Level 1 Examination: Recognition

Time Limit: 20 minutes Total Marks: 30 Instructions: Answer all questions. For True/False questions, a justification is required for full marks. Use $...$ notation where math is needed.

Section A — Multiple Choice (1 mark each, 12 marks)

Q1. The engineering stress in a uniform bar is defined as:

(a) $\sigma = F \cdot A$
(b) $\sigma = F / A$
(c) $\sigma = \Delta L / L$
(d) $\sigma = E \cdot A$

Q2. Young's modulus $E$ relates:

(a) stress to strain
(b) force to displacement
(c) shear to torsion
(d) frequency to mass

Q3. The Euler buckling load for a pinned-pinned column of length $L$ is:

(a) $P_{cr} = \pi^2 EI / L^2$
(b) $P_{cr} = \pi EI / L$
(c) $P_{cr} = EI / L^2$
(d) $P_{cr} = 4\pi^2 EI / L^2$

Q4. In Miner's rule, failure by fatigue is predicted when the cumulative damage sum $\sum n_i/N_i$ reaches:

(a) 0
(b) 0.5
(c) 1
(d) infinity

Q5. The stress intensity factor $K$ near a crack tip is compared against which material property to predict fracture?

(a) yield stress $\sigma_y$
(b) fracture toughness $K_{IC}$
(c) Young's modulus $E$
(d) Poisson's ratio $\nu$

Q6. In an exponential reliability model, MTBF equals:

(a) $\lambda$
(b) $1/\lambda$
(c) $\lambda^2$
(d) $\ln(2)/\lambda$

Q7. The natural frequency of a single-DOF spring–mass system is:

(a) $f = \frac{1}{2\pi}\sqrt{m/k}$
(b) $f = \frac{1}{2\pi}\sqrt{k/m}$
(c) $f = 2\pi\sqrt{k/m}$
(d) $f = \sqrt{km}$

Q8. In an FMEA, the Risk Priority Number (RPN) is computed as:

(a) Severity + Occurrence + Detection
(b) Severity × Occurrence × Detection
(c) Severity − Detection
(d) Occurrence / Detection

Q9. The "V" in the V-model of systems engineering represents:

(a) verification cost
(b) decomposition (left leg) and integration/verification (right leg)
(c) velocity requirements
(d) vibration testing only

Q10. Which subsystem is NOT part of a typical spacecraft bus?

(a) Power (EPS)
(b) Attitude Determination and Control (ADCS)
(c) Command and Data Handling (C&DH)
(d) Launch pad umbilical

Q11. Multi-layer insulation (MLI) primarily reduces heat transfer by:

(a) conduction through solid struts
(b) suppressing radiative exchange
(c) forced convection
(d) evaporative cooling

Q12. For a random vibration input specified as a PSD, the RMS acceleration for a flat PSD of level $W$ over bandwidth $\Delta f$ is:

(a) $g_{rms} = W \cdot \Delta f$
(b) $g_{rms} = \sqrt{W \cdot \Delta f}$
(c) $g_{rms} = W / \Delta f$
(d) $g_{rms} = \sqrt{W / \Delta f}$

Section B — Matching (1 mark each, 6 marks)

Q13. Match each verification method (i–iii) to its description (A–C):

Method		Description
(i) Analysis		(A) Physically operating hardware under representative conditions
(ii) Test		(B) Mathematical/modelling proof of compliance
(iii) Inspection		(C) Visual examination of workmanship or documentation

Q14. Match each redundancy type (i–iii) to its behaviour (A–C):

Type		Behaviour
(i) Cold standby		(A) Backup runs continuously in parallel, sharing load
(ii) Hot standby		(B) Backup powered off until primary fails
(iii) Active redundancy		(C) Backup powered on, ready, but not carrying load

(3 marks each question)

Section C — True/False with Justification (2 marks each, 12 marks)

Q15. Increasing the factor of safety (FOS) always reduces spacecraft mass. True/False? Justify.

Q16. Thin-walled cylinders under axial compression buckle at loads well below the ideal (classical) theoretical value due to imperfection sensitivity. True/False? Justify.

Q17. A SMART requirement must be Measurable and Testable. True/False? Justify.

Q18. Thermal stress arises in a fully constrained bar even with no external mechanical force applied. True/False? Justify.

Q19. In a Fault Tree Analysis, an OR gate produces an output only when all input events occur simultaneously. True/False? Justify.

Q20. Total Ionizing Dose (TID) and Single Event Effects (SEE) are the same radiation effect described by two names. True/False? Justify.

Answer keyMark scheme & solutions

Section A — MCQ (1 mark each)

Q1. (b) $\sigma = F/A$ — stress is force per unit area. (1)

Q2. (a) stress to strain — $E = \sigma/\varepsilon$ in the linear elastic (Hooke) regime. (1)

Q3. (a) $P_{cr} = \pi^2 EI / L^2$ — from solving $EI\,y'' + Py = 0$ with pinned ends, first mode. (1)

Q4. (c) 1 — cumulative damage of unity signals fatigue failure. (1)

Q5. (b) $K_{IC}$ — fracture occurs when $K \geq K_{IC}$ . (1)

Q6. (b) $1/\lambda$ — mean of exponential distribution with rate $\lambda$ . (1)

Q7. (b) $f = \frac{1}{2\pi}\sqrt{k/m}$ — stiffer/lighter systems have higher natural frequency. (1)

Q8. (b) Severity × Occurrence × Detection — RPN is the product of the three ratings. (1)

Q9. (b) decomposition on the left, integration/verification on the right. (1)

Q10. (d) Launch pad umbilical — this is ground support equipment, not a bus subsystem. (1)

Q11. (b) suppressing radiative exchange — many reflective layers reduce IR emission in vacuum. (1)

Q12. (b) $g_{rms} = \sqrt{W\cdot\Delta f}$ — variance = area under PSD; RMS = square root. (1)

Section B — Matching

Q13. (i)→B, (ii)→A, (iii)→C. (1 each = 3)

Q14. (i)→B, (ii)→C, (iii)→A. (1 each = 3)

Cold standby: backup off until needed.
Hot standby: backup powered/ready but not loaded.
Active redundancy: parallel load sharing.

Section C — True/False with Justification (2 marks each)

Q15. FALSE. (1 for FALSE) A higher FOS requires more material/thickness to keep stress below allowables, generally increasing mass, not reducing it. (1 justification)

Q16. TRUE. (1) Real cylinders contain geometric imperfections; the "knockdown factor" reduces the achievable axial buckling load far below classical shell theory (e.g., often 0.2–0.5× ideal). (1)

Q17. TRUE. (1) SMART = Specific, Measurable, Achievable, Relevant, Testable — Measurable and Testable are two of the five required attributes. (1)

Q18. TRUE. (1) A constrained bar prevented from expanding when heated develops thermal stress $\sigma = E\alpha\,\Delta T$ despite zero external load, because thermal strain is resisted by the constraint. (1)

Q19. FALSE. (1) An OR gate outputs when any one input occurs; the "all inputs required" behaviour describes an AND gate. (1)

Q20. FALSE. (1) TID is cumulative dose-driven degradation; SEE are instantaneous events from a single high-energy particle (upsets, latch-ups). They are distinct mechanisms. (1)

[
  {"claim":"Euler buckling load for pinned-pinned column is pi^2 EI/L^2","code":"E,I,L=symbols('E I L',positive=True); P=pi**2*E*I/L**2; result = simplify(P - pi**2*E*I/L**2)==0"},
  {"claim":"MTBF equals 1/lambda in exponential model","code":"lam,t=symbols('lam t',positive=True); mtbf=integrate(exp(-lam*t),(t,0,oo)); result = simplify(mtbf-1/lam)==0"},
  {"claim":"RMS accel from flat PSD W over bandwidth df is sqrt(W*df)","code":"W,df=symbols('W df',positive=True); grms=sqrt(W*df); result = simplify(grms**2 - W*df)==0"},
  {"claim":"Thermal stress in constrained bar equals E*alpha*dT","code":"E,alpha,dT=symbols('E alpha dT',positive=True); eps=alpha*dT; sigma=E*eps; result = simplify(sigma - E*alpha*dT)==0"}
]