Mechanical Engineering Basics

The sum of all forces acting on a body must equal zero: ΣF = 0.

The sum of all moments about any point must equal zero: ΣM = 0.

A sketch of a body isolated from its surroundings showing all external forces and moments acting on it.

A structure where all unknown reactions can be found using the equations of equilibrium alone.

A roller provides one reaction force (normal to surface); a pin provides two reaction forces (horizontal and vertical).

M = F × d, where F is the force magnitude and d is the perpendicular distance from the point to the line of action.

Two equal, opposite, and non-collinear forces that produce a pure rotational effect (moment) with no net translational force.

The geometric center of an area or volume; the point where the body would balance perfectly if supported there.

A geometric property I = ∫y² dA that measures a cross-section's resistance to bending.

I = I_c + Ad², where I_c is the moment of inertia about the centroid, A is area, and d is the distance between axes.

A body remains at rest or in uniform motion unless acted upon by a net external force.

The net force on a body equals its mass times acceleration: F = ma.