ME or MEng Master of Engineering Structural Analysis and Materials Science 1 — Questions and Answers
Question 1: Hooke's Law states that stress is proportional to strain within the:
- Plastic zone
- Elastic limit (Correct answer)
- Ultimate tensile strength
- Fracture point
Correct answer: Elastic limit
Hooke's Law (σ = Eε) holds only within the elastic limit, where deformation is fully recoverable upon load removal.
Question 2: The moment of inertia of a rectangular cross-section (width b, height h) about its centroidal axis is:
- bh³/12 (Correct answer)
- bh²/6
- bh³/3
- b³h/12
Correct answer: bh³/12
The second moment of area for a rectangle about its centroidal axis is I = bh³/12, used in beam bending calculations.
Question 3: In beam theory, the neutral axis is the location where:
- Shear stress is maximum
- Bending stress is zero (Correct answer)
- Deflection is maximum
- Normal stress is maximum
Correct answer: Bending stress is zero
The neutral axis is the centroidal axis of the cross-section where bending stress is zero; material above and below carries tension or compression.
Question 4: Poisson's ratio for a material is defined as:
- Axial stress divided by axial strain
- Negative ratio of lateral strain to axial strain (Correct answer)
- Shear stress divided by shear strain
- Ratio of volume change to original volume
Correct answer: Negative ratio of lateral strain to axial strain
Poisson's ratio ν = −ε_lateral/ε_axial describes the lateral contraction that accompanies axial elongation in an elastic material.
Question 5: Euler's critical buckling load formula for a column is P_cr =:
- π²EI / (KL)² (Correct answer)
- σ_y × A
- EI / L²
- 2EI / L
Correct answer: π²EI / (KL)²
Euler's formula P_cr = π²EI/(KL)² gives the axial load at which a slender column buckles, where KL is the effective length.
Question 6: The von Mises yield criterion predicts yielding when:
- Maximum principal stress exceeds yield stress
- Maximum shear stress exceeds half the yield stress
- The effective (von Mises) stress equals the uniaxial yield stress (Correct answer)
- Hydrostatic pressure exceeds the bulk modulus
Correct answer: The effective (von Mises) stress equals the uniaxial yield stress
Von Mises criterion states yielding occurs when the distortion energy per unit volume equals that at uniaxial yield, expressed as σ_vm = σ_y.
ME or MEng Master of Engineering Structural Analysis and Materials Science 1
Hooke's Law states that stress is proportional to strain within the: