Question

Determine the degree of static and kinematic indeterminacy of the rigid-jointed plane frame shown below.

• A. 6, 26
• B. 36, 24
• C. 42,28
• D. 3,30

Answer 1

The correct option is C 42,28

$D_{SI}=3\times 12=36;D_{Se}=6;D_s=36+6=42$

Possible displacements considering inextensibility of the members are


$\Delta X_1=\Delta X_2=\Delta X_3=\Delta X_4$

$\Delta X_5=\Delta X_6=\Delta X_7=\Delta X_8$

$\Delta X_9=\Delta X_{10}=\Delta X_{11}=\Delta X_{12}$

$\Delta X_{13}=\Delta X_{14}=\Delta X_{15}=\Delta X_{16}$

$\Delta X_{17}=\Delta X_{18}=\Delta X_{19}=\Delta X_{20}$

$\Delta X_{23}$

${\theta }_1,{\theta }_2,{\theta }_3,$ ${\theta }_4$, ${\theta }_5$,${\theta }_6$,${\theta }_7$,${\theta }_8$,${\theta }_9$,${\theta }_{10}$,${\theta }_{11}$,${\theta }_{12}$,${\theta }_{13}$,${\theta }_{14}$,${\theta }_{15}$,${\theta }_{16}$,${\theta }_{17}$,${\theta }_{18}$,${\theta }_{19}$,${\theta }_{20}$,${\theta }_{21}$,${\theta }_{22}$,${\theta }_{23}$

$Hence{D}_k=28$