EIT Statics, Dynamics & Mechanics of Materials 5 — Questions and Answers
Question 1: Which stress state describes pure shear on an element rotated 45° from the principal planes?
- Equal biaxial tension
- Zero normal stress with maximum shear stress (Correct answer)
- Maximum normal stress with zero shear
- Hydrostatic stress
Correct answer: Zero normal stress with maximum shear stress
At 45° from principal planes, normal stresses are zero and shear stress is at its maximum value τ_max = (σ₁–σ₂)/2.
Question 2: The centroid of a triangle with base b and height h is located at what distance from its base?
- h/4
- h/3 (Correct answer)
- h/2
- 2h/3
Correct answer: h/3
The centroid of a triangle is at h/3 from the base (or 2h/3 from the apex), a standard result in statics.
Question 3: A vehicle travels around a circular curve of radius 100 m at 20 m/s. What is its centripetal acceleration?
- 0.2 m/s²
- 2.0 m/s²
- 4.0 m/s² (Correct answer)
- 200 m/s²
Correct answer: 4.0 m/s²
Centripetal acceleration aₙ = v²/r = (20)²/100 = 400/100 = 4.0 m/s².
Question 4: Thermal stress in a fully restrained bar with temperature increase ΔT, coefficient α, and modulus E is:
- EαΔT (tension)
- EαΔT (compression) (Correct answer)
- αΔT/E
- E/(αΔT)
Correct answer: EαΔT (compression)
When a bar is fully restrained and temperature rises, it wants to expand but cannot, creating compressive thermal stress σ = –EαΔT.
Question 5: The parallel-axis theorem states that I = Ī + Ad², where d is the distance between:
- The centroidal axis and any parallel axis (Correct answer)
- Two non-centroidal axes
- The neutral axis and outer fiber
- Two perpendicular axes
Correct answer: The centroidal axis and any parallel axis
The parallel-axis theorem transfers moment of inertia from the centroidal axis Ī to any parallel axis at distance d: I = Ī + Ad².
Question 6: In dynamics, the coefficient of restitution e = 1 describes a:
- Perfectly plastic collision
- Partially elastic collision
- Perfectly elastic collision (Correct answer)
- Inelastic collision with energy loss
Correct answer: Perfectly elastic collision
e = 1 means the relative velocity of separation equals the relative velocity of approach — a perfectly elastic collision with no kinetic energy loss.
Question 7: The flexure formula σ = Mc/I applies when:
- Shear forces dominate over bending moments
- The beam material is homogeneous, linearly elastic, and symmetric about the bending axis (Correct answer)
- The cross-section is circular only
- Large deformations occur
Correct answer: The beam material is homogeneous, linearly elastic, and symmetric about the bending axis
The flexure formula assumes homogeneous, linearly elastic material with a symmetric cross-section and plane sections remaining plane (small deformation).
EIT Statics, Dynamics & Mechanics of Materials 5
Which stress state describes pure shear on an element rotated 45° from the principal planes?