EIT Mechanics of Materials 4 — Questions and Answers
Question 1: A steel column (E = 200 GPa, I = 8 × 10⁻⁶ m⁴) is 4 m long and pin-pin supported. What is the Euler critical load?
- 986 kN (Correct answer)
- 2467 kN
- 3948 kN
- 493 kN
Correct answer: 986 kN
P_cr = π²EI/L² = π²×200×10⁹×8×10⁻⁶/4² ≈ 986 kN for a pin-pin column (K=1).
Question 2: Which stress state exists at the neutral axis of a beam subjected to transverse loading?
- Maximum normal stress, zero shear stress
- Zero normal stress, maximum shear stress (Correct answer)
- Zero normal stress, zero shear stress
- Equal normal and shear stresses
Correct answer: Zero normal stress, maximum shear stress
At the neutral axis, bending normal stress is zero while transverse shear stress is maximum.
Question 3: The flexure formula σ = Mc/I applies only when:
- The material is isotropic and homogeneous
- Plane sections remain plane and the material is linearly elastic (Correct answer)
- The beam has a rectangular cross-section
- The loading is concentrated forces only
Correct answer: Plane sections remain plane and the material is linearly elastic
The flexure formula assumes linear elastic behavior and the Bernoulli-Euler hypothesis that plane sections remain plane.
Question 4: A shaft transmits 50 kW at 500 rpm. What is the torque?
- 477 N·m
- 955 N·m (Correct answer)
- 1910 N·m
- 239 N·m
Correct answer: 955 N·m
T = P/ω = 50,000/(2π×500/60) = 50,000/52.36 ≈ 955 N·m.
Question 5: Plane stress condition assumes which stress components are zero?
- σ_x and σ_y
- τ_xy and τ_yx
- σ_z, τ_xz, and τ_yz (Correct answer)
- σ_x, σ_y, and σ_z
Correct answer: σ_z, τ_xz, and τ_yz
In plane stress, all out-of-plane stress components (σ_z, τ_xz, τ_yz) are zero while in-plane components may exist.
Question 6: The stiffness of a helical coil spring with n active coils, wire diameter d, coil radius R, and shear modulus G is:
- k = Gd/(8nR)
- k = Gd⁴/(64nR³) (Correct answer)
- k = Gd³/(32nR²)
- k = Gd²/(16nR)
Correct answer: k = Gd⁴/(64nR³)
Spring stiffness k = Gd⁴/(64nR³), derived from torsional deflection of the coil wire.
Question 7: Under combined axial and bending loads, the maximum stress in a cross-section is:
- σ_max = P/A only
- σ_max = Mc/I only
- σ_max = P/A + Mc/I (Correct answer)
- σ_max = P/A × Mc/I
Correct answer: σ_max = P/A + Mc/I
By superposition, normal stresses from axial load (P/A) and bending (Mc/I) add algebraically at the extreme fiber.
EIT Mechanics of Materials 4
A steel column (E = 200 GPa, I = 8 × 10⁻⁶ m⁴) is 4 m long and pin-pin supported.
What is the Euler critical load?