Statics Flashcards

Varignon's theorem states that the moment of a resultant force about a point equals:

Answer: The sum of moments of the component forces about the same point

Varignon's theorem states that M_resultant = ΣM_components about the same point, simplifying moment calculations.

The centroid of a composite area is found by:

Answer: ΣAᵢx̄ᵢ / ΣAᵢ

The x-coordinate of the centroid of a composite area is x̄ = ΣAᵢx̄ᵢ / ΣAᵢ, the area-weighted average of component centroids.

A particle is in equilibrium under the action of three concurrent forces. If two forces are 40 N and 30 N at right angles to each other, what is the magnitude of the third force?

Answer: 50 N

The resultant of 40 N and 30 N is √(40² + 30²) = √2500 = 50 N; for equilibrium the third force must be 50 N in the opposite direction.

The parallel axis theorem states that I = Ī + Ad². Here, Ī is the:

Answer: Centroidal moment of inertia

In the parallel axis theorem, Ī is the moment of inertia about the centroidal axis parallel to the axis of interest.

A 10 kN force acts along the line from A(0,0,0) to B(3,4,0) m. What is the unit vector along AB?

Answer: (0.6i + 0.8j)

|AB| = √(3² + 4²) = 5 m; unit vector = (3i + 4j)/5 = 0.6i + 0.8j.

In a statically determinate beam, the number of unknowns must equal the number of available equilibrium equations. For a 2D beam, how many equilibrium equations are available?

Answer: 3

In 2D statics, three equilibrium equations are available: ΣFx = 0, ΣFy = 0, and ΣM = 0.

A cable supports a 500 N load and makes angles of 30° and 45° with the horizontal on its two segments. What is the tension in the 30° segment?

Answer: 366 N

At the junction: T1 sin30° + T2 sin45° = 500 and T1 cos30° = T2 cos45°; solving: T1 = 500 cos45°/(sin30° cos45° + sin45° cos30°) = 500(0.707)/(0.5×0.707 + 0.707×0.866) = 353.5/(0.354 + 0.612) = 353.5/0.966 ≈ 366 N.