2. DEFINITION:
AIM OF FINDING THE DEGREE OF
INDETERMINACY IN STRUCTURE:
We Find The Degree Of Indeterminacy To
Check Whether The Structure Is Stable Or
Unstable .There No Use Of Constructing
Any Structure If It Is Stable
Statically indeterminate structures are structures that cannot be analyzed
using statics, or equations of equilibrium only; they require other material
properties. The degree of indeterminacy is the number of unknown reactions
minus the number of equations of equilibrium.
3. TYPES OF THE DEGREE OF INDETERMINACY
1.The degree of static indeterminacy (Ds)
2.The degree of kinematic indeterminacy(Dk)
The Total indeterminacy of structure is given by the sum of the degree of static
indeterminacy and kinematic indeterminacy.
STATIC INDETERMINACY:
When the static equilibrium equations are
insufficient for determining the internal forces
and reactions on that structure.
4. Types of static indeterminacy (Ds)
1.Internal static indeterminacy
2.External total indeterminacy
The total static indeterminacy is given by the sum of external static indeterminacy
(DSe) and internal static indeterminacy (DSi)
Kinematic Indeterminacy:
It is defined as the number of non-zero joints
displacement of the structure. It is also called
the Degree of freedom.
5. Where,
R= no. of unknown reaction
r=3 + (additional equation due to
internal thing if any)
no. of available equation
M= no. of member
J= no. of joints
C= no. of closed loop
According to the above chart, we are going to
calculate the degree of indeterminacy of beam,
frame, and truss.
For each structure, there are the different formula
of static and kinematic indeterminacy.
6. EXAMPLE
1) Find the degree of Kinematic indeterminacy and
Static indeterminacy of the structure as shown in the
figure.
S0LUTION:
We have,
Ds = DSe + DSi [ Let equation——(1)]
By formula,
DSe = (R-3) – (M’-1)
Since there is internal hinge,
We add M’ ( Number of member.)
So, DSe = (5-3) – (2-1)
Again, DSi = 0 For Beam
DS = 1+0 From equation —-(1)
=1
and DK = 4
Hence,
Degree of Kinematic indeterminacy(DK) = 4
and Degree of Static indeterminacy(DS) = 1
