EIT Statics, Dynamics & Mechanics of Materials 2 — Questions and Answers
Question 1: A uniform beam of weight W is supported by a pin at A and a roller at B. If a concentrated load P acts at the midspan, what is the vertical reaction at B?
- (W + P)/2
- W/2 + P/2
- P/2 + W/2
- All of the above are equivalent (Correct answer)
Correct answer: All of the above are equivalent
All three expressions are mathematically identical, equaling (W+P)/2 by symmetry of a simply supported beam with midspan load.
Question 2: Which condition must be satisfied for a body to be in static equilibrium in 2D?
- ΣFx=0 only
- ΣFx=0 and ΣFy=0 only
- ΣFx=0, ΣFy=0, and ΣM=0 (Correct answer)
- ΣM=0 only
Correct answer: ΣFx=0, ΣFy=0, and ΣM=0
2D static equilibrium requires three independent equations: sum of forces in x, sum of forces in y, and sum of moments about any point all equal zero.
Question 3: A particle moves along a straight line with acceleration a = 4t m/s². If the initial velocity is 2 m/s, what is the velocity at t = 3 s?
- 14 m/s
- 18 m/s
- 20 m/s (Correct answer)
- 38 m/s
Correct answer: 20 m/s
Integrating a=4t gives v = 2t² + C; with v₀=2 m/s, v = 2(9)+2 = 20 m/s at t=3 s.
Question 4: The modulus of resilience is defined as the strain energy per unit volume up to the:
- Ultimate stress
- Fracture point
- Proportional limit
- Yield point (Correct answer)
Correct answer: Yield point
Modulus of resilience is the area under the stress-strain curve up to the yield point, representing elastic energy storage capacity.
Question 5: For a hollow circular shaft in torsion, which parameter most directly increases torsional stiffness?
- Increasing inner diameter only
- Decreasing outer diameter
- Increasing polar moment of inertia J (Correct answer)
- Increasing length L
Correct answer: Increasing polar moment of inertia J
Torsional stiffness = GJ/L; increasing the polar moment of inertia J directly increases stiffness.
Question 6: A 500 N force acts at 30° above the horizontal. What is its horizontal component?
- 250 N
- 433 N (Correct answer)
- 500 N
- 289 N
Correct answer: 433 N
Fx = 500 cos(30°) = 500 × 0.866 = 433 N.
Question 7: Poisson's ratio is the ratio of:
- Axial strain to lateral strain
- Lateral strain to axial strain (Correct answer)
- Shear stress to normal stress
- Normal stress to shear stress
Correct answer: Lateral strain to axial strain
Poisson's ratio ν = –(lateral strain)/(axial strain), measuring how much a material contracts transversely when stretched axially.
EIT Statics, Dynamics & Mechanics of Materials 2
A uniform beam of weight W is supported by a pin at A and a roller at B.
If a concentrated load P acts at the midspan, what is the vertical reaction at B?