Equations of Equilibrium
For a body to be in static equilibrium, the resultant force and resultant moment acting on the body must be zero. The equations are ΣFx = 0, ΣFy = 0, and ΣM = 0. These three equations allow solving for up to three unknown reactions or forces.
Knowledge Check
1.A body has forces of 20 N to the right, 30 N to the left, and 15 N upward. What additional horizontal force is needed for equilibrium?
2.How many independent equilibrium equations exist for a 2D rigid body?
3.A simply supported beam has a 100 N load at its center. The reactions at both supports are:
4.For a 3D rigid body, how many equilibrium equations are there?
5.A cantilever beam of length L has a point load P at its free end. What is the reaction force at the fixed support?
6.A 10 m long beam has a 200 N load at 4 m from the left support. What is the reaction at the left support?
7.What is the sum of moments about any point for a body in equilibrium?
8.A 50 N force acts upward at x=2 m and a 30 N force acts downward at x=5 m on a 6 m beam. What is the required reaction at x=0 to satisfy moment equilibrium?
9.If ΣFx = 0, ΣFy = 0, and ΣM = 0 are satisfied, the body is:
10.A 5 kN force is applied at 45° to a fixed support. What are the horizontal and vertical reaction components?