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Strength of Materials Or Solid Mechanics
Centroid and Moment of InertiaTorsionPure BendingShear Stress In BeamsStrain Energy MethodColumns and StrutsComplex StressDeflection of BeamsThin CylinderSimple StressesShear Force and Bending MomentPropped Cantilever Beam
Torsion
Practice Questions
Marks 1
1

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.

GATE CE 2024 Set 2 Strength of Materials Or Solid Mechanics - Torsion Question 2 English

Qualitatively, the shear center of the section lies at

GATE CE 2024 Set 2
2

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?

GATE CE 2023 Set 2
3

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

GATE CE 2022 Set 1
4
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
GATE CE 2006
Marks 2
1

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.

GATE CE 2024 Set 1 Strength of Materials Or Solid Mechanics - Torsion Question 3 English

If $T_P/T_R = 4$ and $J_1/J_2 = 2$, the ratio of the lengths $L_1/L_2$ is:

GATE CE 2024 Set 1
2
A hollow circular shaft has an outer diameter of $$100$$ $$mm$$ and inner diameter of $$50mm.$$ If the allowable shear stress is $$125$$ $$MPa$$, the maximum torque (in $$kN$$-$$m$$) that the shaft can resist is ___________
GATE CE 2017 Set 2
3
For the cantilever bracket, $$PQRS,$$ loaded as shown in the adjoining figure $$(PQ=RS=L,$$ and $$QR=2L),$$ which of the following statements is FALSE ? GATE CE 2011 Strength of Materials Or Solid Mechanics - Torsion Question 5 English
GATE CE 2011
4
A solid circular shaft of diameter d and length $$L$$ is fixed at one end and 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 three free ends is
GATE CE 2010
5
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
GATE CE 2009
6
The maximum shear stress in a solid shaft of circular cross-section having diameter subjected 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
GATE CE 2008
7
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 $$92.7$$ $$N.m$$ will be
GATE CE 2007
8
A circular shaft shown in the figure is subject to torsion $$T$$ at two points $$A$$ and $$B.$$ The torsional rigidity of portions $$CA$$ and $$BD$$ is $$G{J_1}$$ and that portion $$AB$$ is $$G{J_2}$$. The rotations of shaft at points $$A$$ and $$B$$ are $${\theta _1}$$ and $${\theta _2}$$. The rotation $${\theta _1}$$ is GATE CE 2005 Strength of Materials Or Solid Mechanics - Torsion Question 11 English
GATE CE 2005
9
A circular solid shaft of span $$L=5m$$ is fixed at one end and free at the other end. A twisting moment $$T=100$$ $$kN$$-$$m$$ is applied at the free end. The torsional rigidity $$GJ$$ per unit angular twist is $$50000$$ $$kN$$-$${m^2}/rad.$$ Following statements are made for this shaft:

$$1.$$ 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?

GATE CE 2004