Saturday, 24 January 2015

Equilibrium Conditions


Statics deals with forces groups that are in equilibrium, that is, for the affected system in that it does not move, it is static. A fulfillment of the conditions of equilibrium always says that the body or the system is at a resting position.

A planar body is in equilibrium if the following conditions are met:

Fr = 0 And  Ma = 0

This means that the total resultant of all the forces and the resultant moment with respect to an arbitrary point A must be zero.
One can relate these conditions to Cartesian coordinates.
This gives three equilibrium conditions:

Sum of the forces in the x-direction is zero: FRx = ΣH = 0

Sum of the forces in the y-direction is zero: Fry = ΣV = 0

Sum of the moments about a point is zero: MA = ΣMAi = 0

These conditions apply to all directions of force. The moment equilibrium must be met for each point of the system.

As the equilibrium conditions are applied, shall be demonstrated by an example.

At a statically determinate mounted circular disk of radius r, the bearing forces are to be determined by the equilibrium conditions. The disc is loaded by its own weight G, a moment M0 and a force F.

From the sum Horizonatlkrfte follows: FRx = AH + F = 0 (1)

From the sum Vertikalkrfte follows: Fry = AV - BV - G = 0 (2)

Of the sum of the moments follows: MS = AV • r - F • r - M0 = 0 (3)

From (1) follows: AH = -F
From (3) follows: AV = F + M0 / r (4)
From (2) and (4) the following: BV = AV - G = F + M0 / r - G