Test: Determinacy & Indeterminacy -1 - Civil Engineering (CE) MCQ

The degree of indeterminacy,

Number of external reactions = r_e
= 3 + 3 + 3 + 3 = 12
Number of rigid joints,
j= 10
Number of joints at which releases are located, 
j= 1
Number of members, 
m = 12
As the hinge is located at a point where 4 members meet. Hence it is equivalent to three hinges.
Therefore number of releases, r_r = 3.

Ds for a pin jointed frame = m+r-2j
Ds for a rigid jointed frame = 3m+r -3j
m- No. of members, r- no. of reactions, j- no. of joints

Dk = 2j –r for a pin jointed frame
Dk = 3j –r for a rigid jointed frame
j number of joints and r number of reactions.

- Kinematic indeterminacy refers to the number of possible independent movements of a structure.
- For a pin-jointed space frame, each joint has 3 degrees of freedom (translations in x, y, and z directions).
- Formula: (3j - r), where (j) is the number of joints and (r) is the number of reaction components or constraints.
- This formula accounts for the three-dimensional nature of space frames, unlike planar frames, which have 2 degrees of freedom per joint.

External indeterminacy,

Internal indeterminacy,

No, of members, m = 21
Number of joints, j = 11

m=3; r= 3+3 =6 ; j=4
Ds = 3m+r-3j = 3(3) + 6 -3(4) = 3

A perfect plane frame means a determinate structure, so

j = 11; r=8; m=11
Dk = 3j-r-no. of inextensible members = 3(11) – 8 -11 = 14