Equilibrium of Forces

Whenever a body (static or dynamic) is subjected to external force then it tends to remain in the same state as it was in the former case, so that the algebraic sum of horizontal , vertical forces and moments is equal to zero as a result the condition is termed to be in equilibrium.

Conditions of Equilibrium,

1) The algebraic sum of all the horizontal forces or forces in X direction is equal to zero .i.e, ΣH=0 or ΣX=0

2) The algebraic sum of all the vertical  forces or forces in Y direction is equal to zero .i.e, ΣV=0 or ΣY=0

3) The algebraic sum of all the moments for the system  is equal to zero .i.e, ΣM=0

Note:
ΣH or ΣV = 0 and ΣM_x=0 or ΣM_y=0 (In case of one dimensional system)
ΣH , ΣV = 0 and ΣM_x=0 , ΣM_y=0 (In case of two dimensional system)
ΣH , ΣV, ΣZ = 0 and ΣM_x=0 , ΣM_y=0 ,ΣM_z=0(In case of three dimensional system)

Pure Bending

PURE BENDING

FIGURE  1

FIGURE  2

whenever the structure is applied with some magnitude of load, then there is a resultant of shear force and a couple simultaneously.consider the above figures we can observe that some part of the beam is 

resulted to negligible or zero shear force but at the same part of the structure, the bending moment is maximum or constant.Therefore, pure bending  is the condition of stress where the bending moment is maximum or constant  simultaneously the shear force or the torsional force is zero or negligible.