DEGREE OF FREEDOM

DEGREE OF FREEDOM

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, DOF of the structure is the number of directions the structure can be moved freely without any restrainment.

As in case of two dimensional structures; each joint will have the 3 possible degrees of freedom .i.e., one in horizontal direction, one in vertical direction and one rotation. But as in case of 3 dimensional structure; each joint will have the 6 possible degrees of freedom .i.e., 2 in horizontal direction ,2  in vertical direction and 2 rotation.

Mode number and mode type are the two important factors on which dof depend. Since every possible mode has to fit with the respective moving direction of the structural element. Therefore structure with more dof 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.

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 which 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