DEGREE OF FREEDOM

The degree of freedom (DOF) is defined as the set of independent displacements/

rotations that describe the deformed shape of the structure with respect to 

its initial position.

In simple terms, the DOF of the structure is the number of directions in the 

the structure can be moved freely without any restrainment.

As in the case of two-dimensional structures; each joint will have the 3 possible

 degrees of freedom. i.e., one in the horizontal direction, one in the vertical 

direction and one in rotation. 

But as in the case of a 3-dimensional structure; each joint will have 

the 6 possible degrees of freedom. i.e., 2 in the horizontal direction,2 

 in the vertical direction and 2 rotations.

The model number and mode type are the two important factors on which to depend.

 Since every possible mode has to fit with the respective moving direction of the structural element. Therefore structure with more has more complicated modes.

Example: The train moving freely on the rail. This means the train can move

 freely along the rail in only one direction itself. Therefore the DOF for the 

above case will be 1.

The human head has 6 degrees of freedom

DOF is calculated as

DOF=R-S

Where R= 3, .i.e, Conditions of Equilibrium

S= No of Reaction forces of the support required to resist the External load acting.

Degree of freedom for various support conditions

For Simple support

R = 3; S = 1 (i.e vertical direction)

Therefore, Dof = 2 (1 Horizontal direction and 1 rotation)

For Hinged support

R = 3; S = 2 (i.e vertical direction and 1 Horizontal direction)

Therefore, Dof = 1 (  1 rotation)

For Roller support

R = 3 ; S = 1 (i.eVertical direction)

Therefore, Dof = 2 (1 Horizontal direction and 1 rotation)

For Fixed support

R = 3; S = 3 (i.e Vertical direction, 1 Horizontal direction and 1 rotation)

Therefore, Dof = 0

Er. SP.ASWINPALANIAPPAN., M.E.,(Strut/.,)

Structural Engineer

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