The three-dimensional state of stress at a point is given by
$$\sigma = \begin{pmatrix}
10 & 0 & 0 \\
0 & 40 & 0 \\
0 & 0 & 0
\end{pmatrix} \text{ MPa.}$$
The maximum shear stress at the point is
Find the correct match between the plane stress states and the Mohr’s circles.
A homogeneous shaft PQR with fixed supports at both ends is subjected to a torsional moment T at point Q, as shown in the figure. The polar moments of inertia of the portions PQ and QR of the shaft with circular cross-sections are $J_1$ and $J_2$, respectively. The torsional moment reactions at the supports P and R are $T_P$ and $T_R$, respectively.
If $T_P/T_R = 4$ and $J_1/J_2 = 2$, the ratio of the lengths $L_1/L_2$ is:
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.
If the axial deformations are neglected, the degree of kinematic indeterminacy is _________ (in integer).