A continuous beam ABC with span AB = BC = L is shown in the figure. Support A is fixed type, and supports B and C are roller type. The kinematic indeterminacy of the beam is:

A continuous beam ABC with span AB = BC = L is shown in the figure. Support A is fixed type, and supports B and C are roller type. The kinematic indeterminacy of the beam is:

Right Answer is:

4

SOLUTION

Degree of Kinematic Indeterminacy:

The degree of kinematic indeterminacy (Dk) refers to the total number of independent available degrees of freedom of all joints. The degree of kinematic indeterminacy may be defined as the total number of unrestrained displacement components of all joints.

Degree of kinematic indeterminacy for rigid jointed plane frame and beam is given by,

Dk = 3j − re

Where

j = Number of joint = 3
re = Number of external reaction

The hinged joint has one and a roller joint has two degrees of kinematic indeterminacy.

Total number of external reaction = 4 + 1 = 5 (since there are two roller structure)

Calculation:

Degree of kinematic indeterminacy (Dk) = 3j – re

Here, j = 3 and re = 5

Dk = 3 × 3 – 5 = 4

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