Torsion · Strength of Materials Or Solid Mechanics · GATE CE

For a thin-walled section shown in the figure, points P, Q, and R are located on the major bending axis X−X of the section. Point Q is located on the web whereas point S is located at the intersection of the web and the top flange of the section.

Qualitatively, the shear center of the section lies at

A circular solid shaft of span L = 5 m is fixed at one end and free at the other end. A torque T = 100 kN.m is applied at the free end. The shear modulus and polar moment of inertia of the section are denoted as G and J, respectively. The torsional rigidity GJ is 50,000 kN.m² /rad. The following are reported for this shaft:

Statement i) The rotation at the free end is 0.01 rad

Statement ii) The torsional strain energy is 1.0 kN.m

With reference to the above statements, which of the following is true?

The hoop stress at a point on the surface of a thin cylindrical pressure vessel is computed to be 30.0 MPa. The value of maximum shear stress at this point is

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:

$$1.$$ The maximum rotation is $$0.01$$ radius
$$2.$$ The torsional strain energy is $$1$$ $$kN$$-$$m.$$

With reference to the above statements, which of the following applies?