NCEES Mechanics of Materials 4 — Questions and Answers
Question 1: A steel bolt (E = 200 GPa, α = 12 × 10⁻⁶ /°C) is constrained between two rigid walls. If temperature drops by 50°C, what thermal stress develops?
- 120 MPa tension (Correct answer)
- 120 MPa compression
- 60 MPa tension
- 240 MPa compression
Correct answer: 120 MPa tension
σ = EαΔT = 200×10⁹ × 12×10⁻⁶ × 50 = 120 MPa; a temperature drop in a constrained member induces tension.
Question 2: On Mohr's circle for a 2D stress state, the radius of the circle represents:
- The maximum in-plane shear stress (Correct answer)
- The average normal stress
- The principal stress difference
- The hydrostatic stress
Correct answer: The maximum in-plane shear stress
The radius of Mohr's circle equals τ_max (in-plane) = √[(σx−σy)²/4 + τxy²].
Question 3: A simply supported beam with overhang can have an inflection point where:
- The bending moment changes sign (crosses zero) (Correct answer)
- Shear force is maximum
- Deflection is maximum
- Normal stress is maximum
Correct answer: The bending moment changes sign (crosses zero)
An inflection point is where the bending moment equals zero and changes sign, meaning curvature reverses.
Question 4: The shear flow q in a thin-walled open cross-section is defined as:
- q = VQ/I (force per unit length)
- q = τt (shear stress times thickness)
- q = VA/I (load per area)
- Both A and B are equivalent definitions (Correct answer)
Correct answer: Both A and B are equivalent definitions
Shear flow q = VQ/I has units of force/length and also equals the product of shear stress and wall thickness (q = τt).
Question 5: What is the significance of the slenderness ratio (KL/r) in column design?
- It determines whether Euler or inelastic buckling governs (Correct answer)
- It defines the yield strength of the column material
- It gives the ratio of axial load to shear load
- It is used only for short compression blocks
Correct answer: It determines whether Euler or inelastic buckling governs
A high slenderness ratio (KL/r) indicates elastic (Euler) buckling; a low ratio indicates inelastic (Johnson) buckling governs.
Question 6: The angle of twist θ of a circular shaft subjected to torque T over length L is given by:
- θ = TL/(GJ) (Correct answer)
- θ = TL/(EJ)
- θ = TJ/(GL)
- θ = GL/(TJ)
Correct answer: θ = TL/(GJ)
The angle of twist formula is θ = TL/(GJ), where G is the shear modulus and J is the polar moment of inertia.
Question 7: A rectangular bar (20 mm × 40 mm) is subjected to a bending moment of 500 N·m about the strong axis. What is the maximum bending stress?
- 93.75 MPa (Correct answer)
- 46.9 MPa
- 187.5 MPa
- 62.5 MPa
Correct answer: 93.75 MPa
S = bh²/6 = 0.02 × 0.04²/6 = 5.33×10⁻⁶ m³; σ = M/S = 500/5.33×10⁻⁶ ≈ 93.75 MPa.
NCEES Mechanics of Materials 4
A steel bolt (E = 200 GPa, α = 12 × 10⁻⁶ /°C) is constrained between two rigid walls.
If temperature drops by 50°C, what thermal stress develops?