static force analysis

STATIC FORCE ANALYSIS

STATIC EQUILIBRIUM

• A body or group of bodies is said to be in equilibrium if all the forces exerted on the system are in balancé.

• In other words, a body is in static equilibrium if it remains in its state of rest or motion.

• If the body is at rest, it tends to remain at rest and if it is in motion, it tends to keep the motion.

Condition for static equilibrium (Equations of equilibrium):

The necessary and sufficient conditions for the static equilibrium of a body are:

1. The vector sum of all the external forces acting upon it is zero.

Mathematically, ΣF = 0, which is known as force law of equilibrium.

2. The vector sum of the moments of all forces acting about any arbitrary axis is zero. 

Mathematically, ΣM = 0, which is known as momentum law of equilibrium.

• Mathematically, these two conditions are expressed as

The above expression is also known as equations of equilibrium. In a planar system, it is convenient to resolve the forces along two mutually perpendicular directions x and y. Then the equation of equilibrium (10.1) can be written as