Engineering Mechanics: Equilibrium and Stress

Study Notes

A body is in equilibrium when no net force acts on it.
All forces acting on the body must add up to zero.
Equilibrium can occur when a body is at rest or moving at a constant speed without changing direction.
Both conditions must be met simultaneously for equilibrium to exist.
Structures experience external forces (weights, wind, etc.) that are balanced by reactions at support points.
The loads and reactions form a system of forces in equilibrium governed by the laws of statics.
Loads are forces applied by active agents (gravity, wind).
Reactions are forces applied by a resisting medium (ground).

Stress is the resistive force developed in a body per unit area when a force is applied.
Stress is related to the magnitude of forces causing deformation, defined as force per unit area.
Stress is a measure of the force required to cause deformation.

Shear stress is a resistive force developed per unit area due to an applied shear force.
Shear force causes shape changes without affecting the volume of the body.
Shear strength is the ability of a material to resist shear load until failure.
Shear strength is a property of the material, while shear stress varies with the applied load.

A moment is the turning effect of a force around a pivot point.
A moment (also called torque) is the tendency for a force to rotate a body.
The principle of moments, or Varignon's theorem, states that the moment of a force about a point is equal to the sum of moments of its components about the same point.
The moment is calculated by multiplying the force magnitude by the perpendicular distance from the force's point of application to the pivot point.
Varignon's theorem helps analyze complex force systems in a two-dimensional plane.