Statics
Statics is the branch of mechanics that studies bodies at rest or moving at constant velocity, where all forces and moments balance. Its governing conditions are that the sum of forces equals zero and the sum of moments equals zero.
Statics deals with equilibrium. A body is in equilibrium when it has no acceleration, which by Newton's second law requires that the net force acting on it be zero. For a rigid body, a second condition is needed: the net moment about any point must also be zero, otherwise the body would rotate even with balanced forces. Written out, the conditions are ΣF = 0 and ΣM = 0. In two dimensions this gives three independent equations — ΣFx = 0, ΣFy = 0, and ΣM = 0 — and in three dimensions it gives six. Statics is the counterpart of dynamics, which handles bodies that are accelerating.
The practical tool for applying these conditions is the free body diagram. You isolate the body of interest, replace every support and connection with the forces and moments it exerts, add the applied loads and the weight, then write the equilibrium equations. Choosing the moment axis through a point where several unknown forces act eliminates those unknowns and often solves a problem in one step. A structure with no more unknown reactions than available equations is statically determinate; one with more is statically indeterminate and requires deformation compatibility from mechanics of materials.
Standard applications include trusses, analyzed by the method of joints or sections; frames and machines; beams with distributed loads and their shear and moment diagrams; friction problems; and centroids and moments of inertia for cross sections. Fluid statics applies the same reasoning to fluids at rest, giving the hydrostatic pressure relation p = ρgh and the buoyancy results used for submerged and floating bodies.
Statics is a named subject area on the FE Civil and FE Mechanical exams, and it underpins later topics on both — mechanics of materials, structural analysis, and machine design all begin from equilibrium. The MCAT covers a related equilibrium topic in electrostatics, where charges at rest exert forces described by Coulomb's law.
Key takeaways
- Statics studies bodies in equilibrium — at rest or moving at constant velocity with zero net force and zero net moment.
- The governing conditions are ΣF = 0 and ΣM = 0, giving three equations in 2D and six in 3D.
- Free body diagrams are the standard method for setting up equilibrium problems.
- A structure is statically determinate when unknown reactions do not exceed the available equilibrium equations.
- Fluid statics extends the same reasoning to fluids at rest, yielding hydrostatic pressure and buoyancy relationships.