Question

The plane frame shown in the figure has fixed support at joint A, hinge support at joint F, and roller support at joint I. In the figure, A to I indicate joints of the frame. \includegraphics[width=0.5\linewidth]{45image.png} \ If the axial deformations are neglected, the degree of kinematic indeterminacy is \_\_\_\_\_\_ \textit{(in integer).}

Hint:

For plane frames, the kinematic indeterminacy is calculated as \( 3J - R \), considering three possible displacements per joint (translation in x, translation in y, and rotation).

Answer 1

Step 1: Formula for kinematic indeterminacy: \[ \text{Kinematic Indeterminacy (K.I.)} = 3J - R \] where: \( J \) = Number of joints \( R \) = Number of support reactions Step 2: Counting the joints and reactions: \[ J = 9 \quad \text{(A to I)} \] Support conditions: Joint A (Fixed support) provides 3 reactions. Joint F (Hinge support) provides 2 reactions. Joint I (Roller support) provides 1 reaction. \[ R = 3 + 2 + 1 = 6 \] Step 3: Calculation of kinematic indeterminacy: \[ \text{K.I.} = (3 \times 9) - 6 = 27 - 18 = 9 \] Conclusion: The degree of kinematic indeterminacy is: \[ \text{9} \]