Torsion Practice Questions

A $3 \mathrm{~m}$ long, horizontal, rigid, uniform beam $\mathrm{PQ}$ has negligible mass. The beam is subjected to a $3 \mathrm{kN}$ concentrated vertically downward force at $1 \mathrm{~m}$ from $P$ , as shown in the figure. The beam is resting on vertical linear springs at the ends $\mathrm{P}$ and $\mathrm{Q}$ . For the spring at the end $P$ , the spring constant $K_{p}=100 \mathrm{kN} /$ $\mathrm{m}$ . If the beam does not rotate under the application of the force and displaces only vertically, the value of the spring constant $\mathrm{K}_{\mathrm{O}}$ (in $\mathrm{kN} / \mathrm{m}$ ) for the spring at the end $\mathrm{Q}$ is

A circular solid shaft of span $L=5 \mathrm{~m}$ is fixed at one end and free at the other end. $A$ torque $T=$ $100 \mathrm{kN} . \mathrm{m}$ is applied at the free end. The shear modulus and polar moment of inertia of the section are denoted as $\mathrm{G}$ and $\mathrm{J}$ , respectively. The torsional rigidity $\mathrm{GJ}$ is $50,000 \mathrm{kN} . \mathrm{m}^2 / \mathrm{rad}$ . The following are reported for this shaft: Statement i) The rotation at the free end is 0.01 $\mathrm{rad}$ Statement ii) The torsional strain energy is 1.0 kN.m With reference to the above statements, which of the following is true?

A solid circular torsional member OPQ is subjected to torsional moments as shown in the figure (not to scale). The yield shear strength of the constituent material is 160 MPa. The absolute maximum shear stress in the member (in MPa, round off to one decimal place) is ________

A closed thin-walled tube has thickness, t, mean enclosed area within the boundary of the centerline of tube's thickness, $A_m$ , and shear stress, $\tau$ . Torsional moment of resistance, T, of the section would be

A plane frame shown in the figure has linear elastic springs at node H. The spring constants are $k_x=k_y=5 \times 10^5kN/m$ and $k_\theta =3 \times 10^5kNm/rad$ . For the externally applied moment of 30 kNm at node F, the rotation (in degrees, round off to 3 decimals) observed in the rotational spring at node H is_____

A solid circular beam with radius of 0.25 m and length of 2 m is subjected to a twisting moment of 20 kNm about the z-axis at the free end, which is the only load acting as shown in the figure. The shear stress component $\tau_{xy}$ at Point 'M' in the cross-section of the beam at a distance of 1 m from the fixed end is

A hollow circular shaft has an outer diameter of 100 mm and inner diameter of 50 mm. If the allowable shear stress is 125 MPa, the maximum torque (in kN-m) that the shaft can resist is____

A solid circular shaft of diameter d and length L is fixed at one end free at the other end. A torque T is applied at the free end. The shear modulus of the material is G. The angle of twist at the free end is

A hollow circular shaft has an outer diameter of 100 mm and a wall thickness of 25 mm. The allowable shear stress in the shaft is 125 MPa. The maximum torque the shaft can transmit is

A thin walled cylindrical pressure vessel having a radius of 0.5 m and wall thickness of 25 mm is subjected to an internal pressure of 700 kPa. The hoop stress developed is

The maximum shear stress in a solid shaft of circular cross-section having diameter d subjected to a subject to a torque T is $\tau$ . If the torque is increased by four times and the diameter of the shaft is increased by two times, the maximum shear stress in the shaft will be

The maximum and minimum shear stresses in a hollow circular shaft of outer diameter 20 mm and thickness 2 mm, subjected to a torque of 92.7 Nm will be

A long shaft of diameter d is subjected to twisting moment T at its ends. The maximum normal stress acting at its cross-section is equal to

A thin-walled long cylindrical tank of inside radius r is subjected simultaneously to internal gas pressure p and axial compressive force F at its ends. In order to produce 'pure shear' state of stress in the wall of the cylinder, F should be equal to

A circular shaft shown in the figure is subjected to torsion T at two point A and B. The torsional rigidity of portions CA and BD is $GJ_{1}$ and that of portion AB is $GJ_{2}$ . The rotations of shaft at points A and B are $\theta_{1}$ and $\theta_{2}$ . The rotation $\theta_{1}$ is

A circular solid shaft of span L = 5 m is fixed at one end and free at other end. A twisting moment T = 100 kN-m is applied at the free end. The torsional rigidity $G_j$ is 50000 kN- $m^{2}$ /rad. Following statements are made for this shaft : I. The maximum rotation is 0.01 rad II. The torsional strain energy is 1 kN-m With reference to the above statements, which of the following applies ?