Question

Give brief understanding of degree of static indeterminancy and kinematic indeterminancy. Explain it with more number of examples

Answer 1

Please go through the videos on Review of Basic Structural Analysis I and II. Several examples will show up, and you will gain a better understanding. You may also look up the NPTEL course material on "Structural Analysis", and the textbook authored by me (published by Narosa), in which this topic is discussed in great detail.

Please note that this understanding is a pre-requisite for this course on "Advanced Structural Analysis".

Answer 2

Statical Indeterminacy
*Degree of static indeterminacy (S.I) = No.of unknown forces - equations  of  equilibrium
Let
m = No. of members
r = No. of reactions
j = No. of joints
............................................
Type of structure     DOF
.............................................
Fixed                           0
Hinge                          1
Roller                          2
Free                             3
.............................................
            Formulas for (S.I)
Plane Truss(2D):
m+r-2j
• Space Truss (3D):
m+r-3j
• Plane Frame(2D):
3m+r-3j
• Space Frame(3D):
6m+r-6j

                                 Kinematic indeterminacy
*Kinematic indeterminacy(K.I) is the minimum number of independent displacement quantities that we require to know the displaced geometry of the structure.
K.I = Unrestrained kinematic indeterminacy(U.K.I) – total no. of restraints.
U.K.I = No. of joints* D.O.F(degree of freedom)
.......................................................................
Support      No. of restraints           D.O.F
.......................................................................
Roller                   1                              2
Hinge                   2                              1
Fixed                    3                              0
.......................................................................

For explanation through examples please see the NPTEL videos on Introduction to structural analysis.