What is Statics?
Statics is the branch of mechanics that studies bodies at rest or moving at constant velocity, where all forces and moments acting on the body are perfectly balanced. It underlies the design of bridges, buildings, cranes and any structure that must not move.
Statics analyzes rigid bodies in equilibrium: the vector sum of all forces is zero (ΣF = 0) and the sum of all moments about any point is zero (ΣM = 0).
- 1↓Draw the free-body diagramIsolate the body and sketch every external force and reaction acting on it.
- 2↓Resolve forces into componentsBreak each force into x and y (and z if needed) components.
- 3↓Apply ΣF = 0Sum forces in each direction and set the total equal to zero.
- 4↓Apply ΣM = 0Sum moments about a convenient point and set the total equal to zero.
- 5Solve for unknownsUse the equilibrium equations to find unknown forces, reactions or angles.
Try it: interactive calculator
Step-by-step worked examples
A bracket is pulled by a horizontal force of 300 N and a vertical force of 400 N. Find the resultant force.
R = √(Fx² + Fy²) R = √(300² + 400²) = √(90000 + 160000) R = √250000 = 500 N
A 5 m ladder rests against a frictionless wall, with its base on the ground 3 m from the wall. If the ladder weighs 200 N acting at its center, find the horizontal reaction at the wall using ΣM = 0 about the base.
Height on wall: h = √(5² − 3²) = 4 m ΣM(base) = 0: Wall force × 4 − Weight × (3/2) = 0 Fwall × 4 = 200 × 1.5 = 300 Fwall = 300 / 4 = 75 N
A simply supported beam 6 m long carries a single point load of 900 N at its midpoint (3 m from each support). Find each support reaction.
By symmetry the load splits equally between both supports ΣFy = 0: R1 + R2 = 900 N R1 = R2 = 900 / 2 = 450 N
Flashcards
Quick quiz
Q1.In statics, what must be true of the net force on a body?
Q2.Two perpendicular forces of 300 N and 400 N act on a bracket. What is the resultant?
Q3.What does ΣM = 0 represent?
Q4.A body in statics can be:
The full card deck, worked steps and AI-tutor support for “What is Statics?” are in Notek — study by hand before your exam.
Common mistakes
Assuming statics only applies to stationary objects. — Correct: Statics applies to zero net acceleration — including constant-velocity motion, not just objects at rest.
Forgetting to include support reactions in the free-body diagram. — Correct: Every external force, including reactions at supports and pins, must appear on the FBD.
Summing moments about a point that leaves multiple unknowns. — Correct: Choose a moment point where an unknown force acts, so that force drops out and the equation is solvable directly.
Mixing up force equilibrium with moment equilibrium. — Correct: Both ΣF = 0 and ΣM = 0 are needed independently — satisfying one does not guarantee the other.
FAQ
What is statics?
Statics is the mechanics branch studying rigid bodies in equilibrium, where all forces and moments balance to zero net effect.
What is the statics formula for a resultant force?
For two perpendicular components, R = √(Fx² + Fy²), found using the Pythagorean theorem.
What are some statics examples?
Bridges under load, ladders leaning on walls, beams with point loads, and cranes holding stationary weights.
How do you calculate statics problems?
Draw a free-body diagram, resolve forces into components, then apply ΣF = 0 and ΣM = 0 to solve for the unknowns.