Lesson 3 of 3
Equilibrium and Free Body Diagrams
Put it all together: solve for unknown reactions using the equations of equilibrium.
The equations of equilibrium
For a body in static equilibrium in 2D, three conditions must hold:
ΣFx = 0
ΣFy = 0
ΣM = 0
That is, all horizontal forces sum to zero, all vertical forces sum to zero, and all moments about any point sum to zero.
Free body diagrams (FBDs)
A free body diagram isolates an object and shows every external force acting on it. Drawing a correct FBD is 80% of solving a statics problem. Steps:
- Isolate the body.
- Draw all applied forces.
- Draw all reaction forces at supports.
- Add a coordinate system.
Worked example
A simply supported beam 4 m long carries a 100 N load at its center. Find the support reactions.
By symmetry, each support carries half:
R_left = R_right = 100 N / 2 = 50 N
Verify with moments about the left support:
ΣM = (100 N · 2 m) - (R_right · 4 m) = 0
R_right = 50 N ✓
Congratulations - you now have the core toolkit of statics. Practice with the Beam Stress Calculator.