NCEES Mechanics of Materials 3 — Questions and Answers
Question 1: A cantilever beam of length L with a point load P at the free end has a maximum bending moment of:
- PL at the fixed end (Correct answer)
- PL/2 at mid-span
- PL/4 at the fixed end
- PL/8 at the free end
Correct answer: PL at the fixed end
For a cantilever with tip load P, the maximum moment M = PL occurs at the fixed support.
Question 2: Two bars made of different materials are connected in parallel (same strain) under an axial load. How is the load shared?
- Proportional to each bar's axial stiffness (AE/L) (Correct answer)
- Equally between the two bars
- Proportional to cross-sectional area only
- Proportional to elastic modulus only
Correct answer: Proportional to each bar's axial stiffness (AE/L)
In a parallel assembly with equal deformation, load is distributed proportional to each member's stiffness k = AE/L.
Question 3: A simply supported beam of span 6 m carries a uniformly distributed load of 10 kN/m. What is the maximum bending moment?
- 45 kN·m (Correct answer)
- 90 kN·m
- 30 kN·m
- 60 kN·m
Correct answer: 45 kN·m
M_max = wL²/8 = 10 × 6² / 8 = 45 kN·m, occurring at mid-span.
Question 4: The modulus of resilience for a material is best defined as:
- The strain energy per unit volume at the yield point (Correct answer)
- The total area under the stress-strain curve to fracture
- The elastic modulus divided by the yield strength
- The slope of the plastic region of the stress-strain curve
Correct answer: The strain energy per unit volume at the yield point
Modulus of resilience = Sy²/(2E), representing the energy stored per unit volume at yielding.
Question 5: A solid circular shaft of diameter 50 mm transmits a torque of 2 kN·m. What is the maximum shear stress?
- approximately 81.5 MPa (Correct answer)
- approximately 40.7 MPa
- approximately 163 MPa
- approximately 20.4 MPa
Correct answer: approximately 81.5 MPa
τ = Tc/J = 2000 × 0.025 / (π × 0.05⁴/32) = 2000 × 0.025 / 6.136×10⁻⁷ ≈ 81.5 MPa.
Question 6: Plane stress conditions are characterized by:
- All stress components on one plane being zero (σ_z = τ_xz = τ_yz = 0) (Correct answer)
- Equal normal stresses in all directions
- Zero shear stress on all planes
- All strain components being zero in one direction
Correct answer: All stress components on one plane being zero (σ_z = τ_xz = τ_yz = 0)
In plane stress, stresses normal to one face (typically z) vanish: σ_z = τ_xz = τ_yz = 0.
Question 7: For a statically indeterminate axial member problem, which additional condition is needed beyond equilibrium?
- Compatibility (geometric constraint on deformation) (Correct answer)
- The material's ultimate strength
- The cross-sectional shape
- The applied load direction
Correct answer: Compatibility (geometric constraint on deformation)
Indeterminate problems require a compatibility equation relating deformations to ensure geometric consistency.
NCEES Mechanics of Materials 3
A cantilever beam of length L with a point load P at the free end has a maximum bending moment of: