Fundamentals of Engineering FE Knowledge 5 — Questions and Answers
Question 1: Which failure theory is most appropriate for ductile materials under static loading?
- Maximum normal stress theory
- Maximum shear stress (Tresca) theory (Correct answer)
- Mohr's rupture theory
- Maximum principal strain theory
Correct answer: Maximum shear stress (Tresca) theory
The Tresca (maximum shear stress) criterion is commonly used and conservative for ductile materials under static loads.
Question 2: For a second-order linear ODE with characteristic roots r = −2 ± 3i, the general solution is:
- e^(2t)(C₁cos3t + C₂sin3t)
- e^(-2t)(C₁cos3t + C₂sin3t) (Correct answer)
- C₁e^(-2t) + C₂e^(3t)
- C₁cos2t + C₂sin3t
Correct answer: e^(-2t)(C₁cos3t + C₂sin3t)
Complex roots α ± βi give the solution e^(αt)(C₁cosβt + C₂sinβt); here α = −2, β = 3.
Question 3: In Mohr's Circle for plane stress, the radius of the circle represents:
- The maximum normal stress
- The average normal stress
- The maximum in-plane shear stress (Correct answer)
- The hydrostatic stress
Correct answer: The maximum in-plane shear stress
The radius of Mohr's Circle equals the maximum in-plane shear stress τ_max.
Question 4: Darcy-Weisbach equation is used to calculate:
- Velocity distribution in laminar pipe flow
- Head loss due to friction in a pipe (Correct answer)
- Pressure recovery in a diffuser
- Flow rate over a sharp-crested weir
Correct answer: Head loss due to friction in a pipe
The Darcy-Weisbach equation h_f = f(L/D)(V²/2g) computes frictional head loss in a pipe.
Question 5: A capacitor of 100 μF is charged to 50 V. How much energy is stored?
- 0.125 J (Correct answer)
- 0.25 J
- 2.5 J
- 5.0 J
Correct answer: 0.125 J
Energy W = ½CV² = ½ × 100×10⁻⁶ × 50² = ½ × 100×10⁻⁶ × 2500 = 0.125 J.
Question 6: Which of the following correctly describes a statically indeterminate structure?
- One where equilibrium equations alone are sufficient to find all reactions
- One where the number of unknowns exceeds the number of equilibrium equations (Correct answer)
- One that is unstable under any loading
- One with no internal forces
Correct answer: One where the number of unknowns exceeds the number of equilibrium equations
A statically indeterminate structure has more unknown reactions or member forces than available equilibrium equations.
Question 7: The standard deviation of the data set {4, 8, 6, 5, 7} is closest to:
- 1.14
- 1.41 (Correct answer)
- 1.67
- 2.00
Correct answer: 1.41
Mean = 6; squared deviations: 4,4,0,1,1 → variance = 10/5 = 2; σ = √2 ≈ 1.41.
Fundamentals of Engineering FE Knowledge 5
Which failure theory is most appropriate for ductile materials under static loading?