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A singly-bay single-storeyed portal frame ABCD is fixed at A and D as shown in the figure. If axial deformation is neglected, the kinematic indeterminacy is

A singly-bay single-storeyed portal frame ABCD is fixed at A and D as shown in the figure. If axial deformation is neglected, the kinematic indeterminacy is Correct Answer 3

Concept:

Static Indeterminacy: If the equilibrium equations are enough to analyze for unknown reactions, the structure is said to be statically indeterminate.

Ds = Dse + Dsi

Dse = r – S

Dsi = 3 × Number of closed loop (For portal frame)

Dsi = m- 2j+ 3 (For truss structure)

Kinematic Indeterminacy: It is the total number of possible degree of freedom of all the joints.

Dk = 3J - r (For portal frame)

Dk = 2J-r (For truss structure)

where, Dse = External Indeterminacy, Dsi = Internal Indeterminacy, Dk = Kinematic Indeterminacy, r = No. of unknown reactions, S = No. of equilibrium equation, m = No. of mombers & J = No. of joints

Solution:

∴ Dk = 3j - r = 12 - 6 = 6

For axial deformation is neglected, Dk = 6 - 3 = 3

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