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Total degree of indeterminacy (both internal and external) of the plane frame shown in the given figure is
The degree of indeterminacy,
Number of external reactions = re
= 3 + 3 + 3 + 3 = 12
Number of rigid joints,
Number of joints at which releases are located,
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, rr = 3.
If there are m unknown member forces, r unknown reaction components and j number of joints, then the degree of static indeterminacy of a pin-jointed plane frame is given by
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
Degree of kinematic indeterminacy of a pin jointed plane frame is given by where j is number of joints and r is reaction components.
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.
A pin-jointed plane frame is unstable if where m is number of members r is reaction components and j is number of joints
The degree of static indeterminacy of a pin- jointed space frame is given by
The degree of kinematic indeterminacy of a pin-jointed space frame is given by
The degree of static indeterminacy of the pin- jointed plane frame shown in figure is
No, of members, m = 21
Number of joints, j = 11
The portal frame as shown in the given frame is statically indeterminate to the
m=3; r= 3+3 =6 ; j=4
Ds = 3m+r-3j = 3(3) + 6 -3(4) = 3
A perfect plane frame having n number of members and j number of joints should satisfy the relation
A perfect plane frame means a determinate structure, so
Neglecting axial deformation, the kinematic indeterminacy of the structure shown in the figure below is
j = 11; r=8; m=11
Dk = 3j-r-no. of inextensible members = 3(11) – 8 -11 = 14