EIT Mechanics of Materials 2 — Questions and Answers
Question 1: A hollow circular shaft has outer diameter 80 mm and inner diameter 50 mm. What is its polar moment of inertia (J)?
- 2.66 × 10⁻⁶ m⁴
- 3.59 × 10⁻⁶ m⁴
- 1.81 × 10⁻⁶ m⁴ (Correct answer)
- 4.02 × 10⁻⁶ m⁴
Correct answer: 1.81 × 10⁻⁶ m⁴
J = π/32 × (D⁴ - d⁴) = π/32 × (0.08⁴ - 0.05⁴) ≈ 1.81 × 10⁻⁶ m⁴.
Question 2: A cantilever beam of length L carries a point load P at its free end. What is the maximum bending moment?
- PL/4
- PL/2
- PL (Correct answer)
- 2PL
Correct answer: PL
The maximum bending moment in a cantilever with tip load P occurs at the fixed end and equals PL.
Question 3: Which failure theory is most conservative for a ductile material under biaxial stress?
- Maximum Normal Stress Theory
- Maximum Shear Stress (Tresca) Theory (Correct answer)
- Von Mises (Distortion Energy) Theory
- Coulomb-Mohr Theory
Correct answer: Maximum Shear Stress (Tresca) Theory
The Tresca criterion is more conservative than Von Mises because its yield surface is inscribed within the Von Mises ellipse.
Question 4: A steel bar (E = 200 GPa) of cross-sectional area 500 mm² and length 2 m is subjected to an axial load of 100 kN. What is the axial deformation?
- 0.5 mm
- 1.0 mm (Correct answer)
- 2.0 mm
- 0.25 mm
Correct answer: 1.0 mm
δ = PL/(AE) = (100,000 × 2)/(500×10⁻⁶ × 200×10⁹) = 0.001 m = 1.0 mm.
Question 5: For a simply supported beam with a uniformly distributed load w over its full length L, where does the maximum deflection occur?
- At the supports
- At L/4 from each support
- At midspan (Correct answer)
- At L/3 from each support
Correct answer: At midspan
By symmetry, the maximum deflection of a simply supported beam under UDL occurs at midspan (x = L/2).
Question 6: Poisson's ratio (ν) for an incompressible material is:
- 0
- 0.25
- 0.5 (Correct answer)
- 1.0
Correct answer: 0.5
An incompressible material has zero volumetric strain, which requires ν = 0.5.
Question 7: A 10 mm diameter rod is loaded in tension with 20 kN. What is the average normal stress?
- 127 MPa
- 255 MPa (Correct answer)
- 64 MPa
- 318 MPa
Correct answer: 255 MPa
A = π(0.01)²/4 = 7.854×10⁻⁵ m²; σ = 20,000/7.854×10⁻⁵ ≈ 255 MPa.
EIT Mechanics of Materials 2
A hollow circular shaft has outer diameter 80 mm and inner diameter 50 mm.
What is its polar moment of inertia (J)?