EIT Mechanics of Materials 3 — Questions and Answers
Question 1: The modulus of resilience of a material is defined as:
- The area under the entire stress-strain curve
- The stress at fracture divided by the strain at fracture
- The strain energy per unit volume stored up to the proportional limit (Correct answer)
- The ultimate strength minus the yield strength
Correct answer: The strain energy per unit volume stored up to the proportional limit
Modulus of resilience = σ_y²/(2E), representing elastic strain energy stored per unit volume up to yielding.
Question 2: A thin-walled pressure vessel (sphere) has radius r and wall thickness t. The hoop stress is:
- pr/t
- pr/(2t) (Correct answer)
- 2pr/t
- pr/(4t)
Correct answer: pr/(2t)
For a spherical pressure vessel, hoop stress = pr/(2t) due to biaxial symmetry (both principal stresses are equal).
Question 3: Which of the following boundary conditions applies to a pin support in beam analysis?
- Deflection = 0, slope = 0
- Deflection = 0, moment = 0 (Correct answer)
- Moment = 0, shear = 0
- Slope = 0, shear = 0
Correct answer: Deflection = 0, moment = 0
A pin (simple support) prevents translation (δ = 0) but allows rotation, so bending moment M = 0 there.
Question 4: Shear flow q in a thin-walled open section beam is defined as:
- q = VQ/I
- q = τ × t
- Both A and B are equivalent definitions (Correct answer)
- q = M/S
Correct answer: Both A and B are equivalent definitions
Shear flow q = VQ/I (from shear formula) and also equals τ × t (shear stress × wall thickness), so both are correct.
Question 5: A 200 mm long, 10 mm diameter aluminum rod (α = 23 × 10⁻⁶/°C, E = 70 GPa) is fixed at both ends. If the temperature rises 50°C, what is the thermal stress?
- 40.25 MPa
- 80.5 MPa (Correct answer)
- 20.1 MPa
- 160.5 MPa
Correct answer: 80.5 MPa
σ = αEΔT = 23×10⁻⁶ × 70×10⁹ × 50 = 80.5 MPa (compressive) in a fully restrained member.
Question 6: On a Mohr's circle, the radius represents:
- The maximum normal stress
- The maximum in-plane shear stress (Correct answer)
- The hydrostatic stress
- The principal stress difference
Correct answer: The maximum in-plane shear stress
The radius of Mohr's circle equals the maximum in-plane shear stress τ_max = (σ₁ − σ₂)/2.
Question 7: For a beam in pure bending, the neutral axis is located at:
- The top fiber
- The bottom fiber
- The centroid of the cross-section (Correct answer)
- The point of maximum shear stress
Correct answer: The centroid of the cross-section
In pure bending, the neutral axis passes through the centroid of the cross-section where normal stress is zero.
EIT Mechanics of Materials 3
The modulus of resilience of a material is defined as: