Internal Redundancy and External Redundancy

Fig.1 Continuous Indeterminate Bridge StructuresGirders 
If,
n = number of members of the truss system
r = number of external restraints or reactions
j = number of joints or nodes,
Truss system is determinate when,
n + r = 2j eq. (1)
Truss system is Indeterminate when,
n + r > 2j eq. (2)
Truss system in Unstable when
n + r < 2j eq. (3)
Internal and External Redundancy
The Internal redundancy is explained in terms of the number of members of the truss or the frame. If I is the degree of internal redundancy, then it is given by
I = m – (2j r) eq. (4)
The condition of fewer members, as in eq. (3), will make the structure to be unstable.
The external indeterminacy is explained in terms of the number of external reactions and the equilibrium equations. If the number of reactions is not equal to the condition equilibrium equation, then the structure is externally indeterminate. The External Indeterminacy E is given by the
E = R – r eq. (5)
Here, E = Degree of External Redundancy
R = Total number of reaction components
r = Total number of condition equations available
The Total Redundancy (T) or the indeterminacy is equal to the sum of external and internal indeterminacies.[ From eq. (4) and eq. (5) ]
T = E + I = [(R – r)] + [m – (2j – r)]