NCEES Statics 5 — Questions and Answers
Question 1: Force F = 2i − 3j + 6k kN acts at position r = i + 2j − k m. What is the moment about the origin?
- 9i − 8j − 7k kN·m (Correct answer)
- 9i + 8j + 7k kN·m
- 3i − 8j + 7k kN·m
- −9i + 8j − 7k kN·m
Correct answer: 9i − 8j − 7k kN·m
M = r × F: i(2·6 − (−1)(−3)) − j(1·6 − (−1)·2) + k(1·(−3) − 2·2) = 9i − 8j − 7k kN·m.
Question 2: The centroid y-coordinate of a semicircle of radius R, measured from its flat diameter, is:
- R/2
- R/π
- 4R/(3π) (Correct answer)
- 2R/π
Correct answer: 4R/(3π)
Integration of the semicircular area yields ȳ = 4R/(3π) from the flat (diameter) edge.
Question 3: A cable supports a 200 N weight at a junction, with left segment at 30° and right segment at 45° from horizontal. Which equation set is correct?
- T1cos30° = T2cos45° and T1sin30° + T2sin45° = 200 (Correct answer)
- T1 + T2 = 200 N
- T1cos30° + T2cos45° = 200 and T1sin30° = T2sin45°
- T1 = T2 = 200 N
Correct answer: T1cos30° = T2cos45° and T1sin30° + T2sin45° = 200
ΣFx = 0 gives T1cos30° = T2cos45°; ΣFy = 0 gives T1sin30° + T2sin45° = 200 N.
Question 4: The product of inertia Ixy equals zero for any cross-section that has:
- At least one axis of symmetry (Correct answer)
- A circular shape only
- Equal width and height dimensions
- Its centroid located at the origin
Correct answer: At least one axis of symmetry
When at least one axis of symmetry exists, paired area elements on opposite sides cancel, making Ixy = 0.
Question 5: A rigid body is subjected to a pure couple. Which statement is true about the couple moment?
- It can be balanced by a single force applied at any point
- It produces the same moment value about any reference point (Correct answer)
- Its moment depends on where the two forces are located
- It can be resolved into a single equivalent force
Correct answer: It produces the same moment value about any reference point
A pure couple's moment is a free vector — it has the same magnitude and direction regardless of the reference point chosen.
Question 6: A force of 100 N is directed at 210° from the positive x-axis. What is its y-component?
- +86.6 N
- −86.6 N
- +50 N
- −50 N (Correct answer)
Correct answer: −50 N
Fy = 100 sin(210°) = 100 × (−sin30°) = 100 × (−0.5) = −50 N.
Question 7: In 2D static analysis, how many reaction components does a pin support provide, and why?
- 1 — it allows rotation and translation in one direction
- 2 — it prevents translation in both x and y but allows rotation (Correct answer)
- 3 — it prevents all translation and rotation
- 0 — it is a free joint with no resistance
Correct answer: 2 — it prevents translation in both x and y but allows rotation
A pin prevents translation in both x and y directions (2 reaction forces) but allows free rotation, providing exactly 2 unknowns.
NCEES Statics 5
Force F = 2i − 3j + 6k kN acts at position r = i + 2j − k m.
What is the moment about the origin?