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The degree of static indeterminacy NS and the degree of kinematic indeterminacy, NK for the plane frame as shown neglecting axial deformation are given by

The degree of static indeterminacy NS and the degree of kinematic indeterminacy, NK for the plane frame as shown neglecting axial deformation are given by Correct Answer N<span style="position: relative; line-height: 0; vertical-align: baseline; bottom: -0.25em;font-size:10.5px;">S</span> = 4, N<span style="position: relative; line-height: 0; vertical-align: baseline; bottom: -0.25em;font-size:10.5px;">K </span>= 6

Concepts:

The kinematic indeterminacy is given as

 Dk­ = 3j-r-m

j = no of joints

r = no of support reactions

m = no of axially rigid members 

Degree of Static Indeterminacy (Ds):

 Ds = 3×C – R

C = No of cuts required to make stable cantilever frame 

R= No of releases   

Calculations:

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Kinematic Indeterminacy:

No of Joints, j = 6

No of support reactions, r = 7 ( 3 at support A, 2 at each support D and F)

No fo axially rigid members, m = 5

Dk­ = 3j-r-m

Dk = 3 × 6 – 7 – 5

∴ Dk = 6

Static Indeterminacy

 No of cuts = 2

Releases

Moment releases at joint D = 1

Moment releases at joint F = 1

Total Releases, R = 2  

Dsi = 3 × 2 – 2 = 4

Static Indeterminacy, D­s = 4

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