Statics and Dynamics

Internal Forces

Forces and moments transmitted between neighboring portions of a body due to external loads.

Normal Force (N)

Force acting along a member's longitudinal axis, producing tension or compression.

Shear Force (V)

Force acting perpendicular to a member's longitudinal axis, causing cut faces to slide.

Bending Moment (M)

Moment that tends to bend the member.

Method of Sections

A technique to find internal forces by cutting a member and isolating one side.

Free-body Diagram

A graphical representation showing all forces acting on a body.

Equilibrium Equations

Mathematical expressions (ΣFx = 0, ΣFy = 0, ΣM = 0) used to analyze static systems.

Positive N (Tension)

Normal force acting away from the cut, representing tension.

Negative N (Compression)

Normal force acting towards the cut, indicating compression.

Shear-Force Diagram

A graphical representation showing how shear force varies along a beam.

Bending-Moment Diagram

A graphical representation showing how bending moment varies along a beam.

Catenary

The shape of an ideal flexible cable carrying a uniform load per unit of its own length.

Parabola (Cable)

Shape produced by a cable under a uniform load per unit horizontal distance.

Resultant of a Distributed Load (FR)

The total force derived from a distributed load, expressed as FR = ∫w(x) dx.

Location of Resultant

The centroid of the load distribution, given by x̄ = ∫xw(x) dx / ∫w(x) dx.

Concentrated Load

A force applied at a single point on a member.

Uniform Distributed Load

A load distributed evenly along a length, usually expressed in N/m.