NCEES Statics 4 — Questions and Answers
Question 1: The parallel axis theorem states I = Ic + Ad², where d is:
- The depth of the section
- The distance from the centroid to the new parallel axis (Correct answer)
- The diameter of the cross-section
- The moment arm of the applied force
Correct answer: The distance from the centroid to the new parallel axis
In the parallel axis theorem, d is the perpendicular distance between the centroidal axis and the new parallel axis.
Question 2: A pin-connected truss has 8 members, 5 joints, and 3 support reactions. Using m + r vs 2j, what is its classification?
- Statically determinate (m + r = 2j)
- Statically indeterminate (m + r > 2j) (Correct answer)
- A mechanism (m + r < 2j)
- Cannot be determined from this information
Correct answer: Statically indeterminate (m + r > 2j)
m + r = 8 + 3 = 11 > 2j = 2(5) = 10, so the truss is statically indeterminate by one degree.
Question 3: Two forces of 100 N each act at 120° apart. What is the magnitude of their resultant?
- 0 N
- 100 N (Correct answer)
- 141 N
- 200 N
Correct answer: 100 N
R = √(F1² + F2² + 2F1F2cos120°) = √(10000 + 10000 − 10000) = √10000 = 100 N.
Question 4: A wrench applies a 40 N force at 0.25 m from a bolt axis. What moment is developed?
- 8 N·m
- 10 N·m (Correct answer)
- 16 N·m
- 40 N·m
Correct answer: 10 N·m
M = F × d = 40 N × 0.25 m = 10 N·m.
Question 5: For a body on an inclined plane of angle θ with static friction coefficient μs, impending slip occurs when:
- θ = arctan(μs) (Correct answer)
- θ = arcsin(μs)
- θ = arccos(μs)
- θ = μs (in radians)
Correct answer: θ = arctan(μs)
At impending slip, the driving force (W sinθ) equals maximum friction (μs W cosθ), giving tan(θ) = μs.
Question 6: Which method is most efficient for finding the force in a single interior member of a large truss?
- Method of joints starting from the nearest support
- Method of sections cutting through that member (Correct answer)
- Graphical force polygon construction
- Influence line construction
Correct answer: Method of sections cutting through that member
The method of sections cuts through the target member and applies three equilibrium equations directly, avoiding sequential joint analysis.
Question 7: A uniform distributed load of 5 kN/m acts over a 4 m span. What is the equivalent concentrated force and its location?
- 10 kN at 2 m from one end
- 20 kN at 2 m from one end (Correct answer)
- 20 kN at 4 m from one end
- 5 kN at 2 m from one end
Correct answer: 20 kN at 2 m from one end
Equivalent force = 5 × 4 = 20 kN, acting at the centroid of the rectangular load distribution (2 m from either end).
NCEES Statics 4
The parallel axis theorem states I = Ic + Ad², where d is: