Questions: Equilibrium of Rigid Bodies

Question 1

A simply supported beam carries a single vertical load. You write ΣFx = 0, ΣFy = 0, and ΣM_A = 0 for the three equilibrium equations. How many unknown support reactions can this system of equations solve?

• A. 1
• B. 2
• C. 3
• D. 4

Answer: (C)

In 2D, three independent equilibrium equations are available (ΣFx = 0, ΣFy = 0, ΣM = 0). A simply supported beam has exactly three unknown reactions (one horizontal pin component and two vertical supports), making it statically determinate — three equations solve three unknowns. Choosing four unknowns would make the system indeterminate.

Question 2

When summing moments for a rigid body in equilibrium, the moment reference point should be located at the body's center of mass.

• T. True
• F. False

Answer: False

The moment equilibrium condition ΣM_O = 0 holds for any reference point O when the body is in static equilibrium. The choice of reference point is a mathematical convenience, not a physical requirement. Strategically placing the reference point at the intersection of two or more unknown forces eliminates those unknowns from the moment equation, simplifying the algebra significantly.

Question 3

Explain the strategy for choosing an optimal moment reference point when solving a rigid body equilibrium problem.

Model answer: Choose the moment reference point at the location where the most unknown forces intersect (i.e., pass through). A force passing through the moment point contributes zero moment (zero moment arm), so it drops out of the equation, leaving fewer unknowns to solve simultaneously.

Moment = Force × perpendicular distance. If the reference point lies on the line of action of an unknown force, the perpendicular distance is zero and that unknown does not appear in the moment equation. By choosing the point where the maximum number of unknowns intersect, you can often reduce the moment equation to a single unknown, which can be solved directly without simultaneous equations.