Statics Flashcards

The parallel axis theorem states I = Ic + Ad², where d is:

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.

A pin-connected truss has 8 members, 5 joints, and 3 support reactions. Using m + r vs 2j, what is its classification?

Answer: Statically indeterminate (m + r > 2j)

m + r = 8 + 3 = 11 > 2j = 2(5) = 10, so the truss is statically indeterminate by one degree.

Two forces of 100 N each act at 120° apart. What is the magnitude of their resultant?

Answer: 100 N

R = √(F1² + F2² + 2F1F2cos120°) = √(10000 + 10000 − 10000) = √10000 = 100 N.

A wrench applies a 40 N force at 0.25 m from a bolt axis. What moment is developed?

Answer: 10 N·m

M = F × d = 40 N × 0.25 m = 10 N·m.

For a body on an inclined plane of angle θ with static friction coefficient μs, impending slip occurs when:

Answer: θ = arctan(μs)

At impending slip, the driving force (W sinθ) equals maximum friction (μs W cosθ), giving tan(θ) = μs.

Which method is most efficient for finding the force in a single interior member of a large truss?

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.

A uniform distributed load of 5 kN/m acts over a 4 m span. What is the equivalent concentrated force and its location?

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).