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The degree of kinematic indeterminacy of a plane structure shown in the figure neglecting axial strain, is

The degree of kinematic indeterminacy of a plane structure shown in the figure neglecting axial strain, is Correct Answer 7

Concept:

Kinematic indeterminacy (DK ) also known as degree of freedom.

Kinematic indeterminacy: The number of unknown joint displacement is called the degree of freedom.

Type of joint

 

Degree of freedom

 

Rigid Joint of plane frame

3 (δ x , δ y , θ )

 

Rigid joint of a space frame

 

6 (3 rotation θ xy , θ yz , θ xz

3 translations δ x , δ y , δ z )

Pin joint of a plane frame (2D Truss)

 

2 (δ x , δ y )

 

Pin joint of a space frame (3 D Truss)

3 (δ x , δ y , δ z )

Hinge joint

 

1 (θ )

Roller joint

 

2 (δ x , θ )

Fixed joint

 

0

NOTE:  Neglecting axial strain.

When Axial deformations are neglected then 

Dk = total degree of freedom -  number of members

Calculation:

For the given 2D frame

Number of members = 6.

Number of rigid joints = 4, One fixed joint, and One hinge joint.

∴ DK = 4 × (3) + 1 × (1) + 1 × (0)

 = 13

This is the total degree of freedom but the question asked is to neglect axial constraints

So our Dk = total degree of freedom -  number of members.

= 13 – 6  = 7.

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