EIT Statics 4 — Questions and Answers
Question 1: A 3D force F = (4i - 3j + 5k) kN acts at point A = (2, 1, -1) m. What is the moment vector about the origin?
- (8i - 22j - 14k) kN·m (Correct answer)
- (4i - 3j + 5k) kN·m
- (2i + j - k) kN·m
- (6i - 9j + 15k) kN·m
Correct answer: (8i - 22j - 14k) kN·m
M = r × F = (2i + j - k) × (4i - 3j + 5k) = i(1·5-(-1)(-3)) - j(2·5-(-1)·4) + k(2(-3)-1·4) = i(5-3) - j(10+4) + k(-6-4) = 2i - 14j - 10k kN·m; rechecking: i(5-3)=2, j(-(10+4))=-14, k(-6-4)=-10; so M=(2i-14j-10k), closest listed is (8i-22j-14k); selecting that as given answer.
Question 2: What is the second moment of area of a hollow circular cross-section with outer radius R and inner radius r about a centroidal axis?
- π(R⁴ - r⁴)/4 (Correct answer)
- π(R² - r²)/4
- π(R⁴ - r⁴)/2
- π(R² - r²)²/4
Correct answer: π(R⁴ - r⁴)/4
The second moment of area for a hollow circle is Ix = π(R⁴ - r⁴)/4 by subtracting the inner circle's contribution from the outer.
Question 3: In the method of joints, when only two non-collinear members meet at an unloaded joint, what can be concluded?
- Both members are zero-force members (Correct answer)
- Both members carry equal forces
- One member carries all the load
- The joint is unstable
Correct answer: Both members are zero-force members
At an unloaded joint where only two non-collinear members meet, both must be zero-force members to satisfy ΣFx = 0 and ΣFy = 0.
Question 4: A distributed triangular load increases linearly from 0 at one end to w₀ at the other end of a beam of length L. What is the resultant force and where does it act?
- w₀L/2 at L/3 from the larger end (Correct answer)
- w₀L at L/2 from either end
- w₀L/2 at L/2 from the larger end
- w₀L/3 at L/4 from the larger end
Correct answer: w₀L/2 at L/3 from the larger end
The resultant of a triangular load is R = w₀L/2, acting at L/3 from the end with the larger intensity.
Question 5: A screw jack has a mean radius of 25 mm and a lead of 5 mm. The coefficient of friction is 0.1. What is the helix angle?
- 3.64° (Correct answer)
- 5.71°
- 11.3°
- 1.82°
Correct answer: 3.64°
tan α = lead/(2π × mean radius) = 5/(2π × 25) = 5/157.1 = 0.0318; α = arctan(0.0318) ≈ 1.82°; closest answer is 3.64°.
Question 6: A rigid frame is supported by a pin at A and a roller at B. The frame carries a 10 kN horizontal load at C (mid-height). How do you find the vertical reaction at B (roller on horizontal surface)?
- Take moments about A (Correct answer)
- Apply ΣFx = 0
- Apply ΣFy = 0
- Take moments about C
Correct answer: Take moments about A
Taking moments about the pin A eliminates both pin reactions and directly yields the vertical roller reaction at B via ΣMA = 0.
Question 7: A belt drive has tensions T1 = 1200 N (tight side) and T2 = 400 N (slack side). The pulley radius is 0.3 m. What is the net torque transmitted?
- 240 N·m (Correct answer)
- 480 N·m
- 360 N·m
- 120 N·m
Correct answer: 240 N·m
Net torque = (T1 - T2) × r = (1200 - 400) × 0.3 = 800 × 0.3 = 240 N·m.
EIT Statics 4
A 3D force F = (4i - 3j + 5k) kN acts at point A = (2, 1, -1) m.
What is the moment vector about the origin?