Question

The degree of static indeterminacy, $N_s$ and the degree of kinematic indeterminacy, $N_k$ for the plane frame shown below, assuming axial deformations to be negligible, are given by:

• A. $N_s=4$ & $N_k=6$
• B. $N_s=6$ & $N_k=6$
• C. $N_s=4$ & $N_k=4$
• D. $N_s=6$ & $N_k=11$

Answer 1

The correct option is A $N_s=4$ & $N_k=6$


$N_s\to 3C-R^{\prime }\to$ for plane frames
C $\to$ no. of cuts to make structure
determinate.
R' = no. of restraints applied to make all joints rigid.
C = 2
R' = 2
$\therefore N_s=3\times 2-2=4.$
$N_k=3J-r-m\to$ rigid jointed plane frame
J $\to$ no. of joints = 6
r $\to$ no. of reactions =7
m' = no. of inextensible member = 5
$N_K=3\times 6-7-5=6.$