NCEES Mechanics of Materials 2 — Questions and Answers
Question 1: A hollow circular shaft has outer diameter 60 mm and inner diameter 40 mm. What is the polar moment of inertia J?
- approximately 1.02 × 10⁻⁶ m⁴ (Correct answer)
- approximately 2.04 × 10⁻⁶ m⁴
- approximately 0.51 × 10⁻⁶ m⁴
- approximately 3.14 × 10⁻⁶ m⁴
Correct answer: approximately 1.02 × 10⁻⁶ m⁴
J = π(do⁴ − di⁴)/32 = π(0.06⁴ − 0.04⁴)/32 ≈ 1.02 × 10⁻⁶ m⁴.
Question 2: A steel rod (E = 200 GPa) of 20 mm diameter and 2 m length is subjected to a tensile load of 50 kN. What is the elongation?
- 1.59 mm (Correct answer)
- 0.80 mm
- 3.18 mm
- 0.40 mm
Correct answer: 1.59 mm
δ = PL/(AE) = 50000 × 2 / (π/4 × 0.02² × 200×10⁹) ≈ 1.59 mm.
Question 3: A beam with a rectangular cross-section (width b, height h) is subjected to bending. Where does the maximum shear stress occur?
- At the neutral axis (Correct answer)
- At the top fiber
- At the bottom fiber
- At h/4 from neutral axis
Correct answer: At the neutral axis
For a rectangular section, the shear stress distribution is parabolic, peaking at the neutral axis where τ_max = 3V/(2A).
Question 4: Which failure theory is most appropriate for ductile materials under static multiaxial loading?
- Von Mises (distortion energy) theory (Correct answer)
- Maximum normal stress theory
- Coulomb-Mohr theory
- Fracture mechanics (K_IC) criterion
Correct answer: Von Mises (distortion energy) theory
The von Mises (distortion energy) criterion best predicts yielding in ductile materials under multiaxial stress states.
Question 5: A column with both ends pinned has a length of 3 m and a cross-sectional area moment of inertia I = 8 × 10⁻⁶ m⁴. If E = 200 GPa, what is the Euler critical buckling load?
- approximately 1,754 kN (Correct answer)
- approximately 877 kN
- approximately 438 kN
- approximately 3,508 kN
Correct answer: approximately 1,754 kN
P_cr = π²EI/L² = π² × 200×10⁹ × 8×10⁻⁶ / 3² ≈ 1,754 kN.
Question 6: A thin-walled pressure vessel (sphere) has radius 0.5 m, wall thickness 10 mm, and internal pressure 2 MPa. What is the hoop stress?
- 50 MPa (Correct answer)
- 100 MPa
- 25 MPa
- 200 MPa
Correct answer: 50 MPa
For a spherical vessel, σ = pr/(2t) = 2×10⁶ × 0.5 / (2 × 0.01) = 50 MPa.
Question 7: A material has yield strength Sy = 250 MPa and ultimate strength Su = 400 MPa. The percent elongation at fracture is 35%. This material is best classified as:
- Ductile (Correct answer)
- Brittle
- Elastic
- Viscoelastic
Correct answer: Ductile
A percent elongation greater than 5% (here 35%) and a clearly defined yield point indicate a ductile material.
NCEES Mechanics of Materials 2
A hollow circular shaft has outer diameter 60 mm and inner diameter 40 mm.
What is the polar moment of inertia J?