For a skeletal frame shown in the figure Static and kinematic in

SOLUTION

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 beam & 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:

Static Indeterminacy, 

D_se = r – S = 6 - 3 = 3

D_si = 3 × 2 = 6

D_s = 6 + 3 = 9

Kinematic Indeterminacy,

Dk = 3J - r = 3 × 9 – 6 = 21

Dk = 21 - 10 = 11 (For rigid members)