Torsion · Strength of Materials · GATE ME

A motor driving a solid circular steel shaft transmits $$40$$ $$kW$$ of power at $$500$$ $$rpm$$. If the diameter of the shaft is $$40$$ $$mm,$$ the maximum shear stress in the shaft is ________ $$MP$$a.

The cross sections of two hollow bars made of the same material are concentric circles as shown in the figure. It is given that 𝑟₃ > 𝑟₁ and 𝑟₄ > 𝑟₂ , and that the areas of the cross-sections are the same. J₁ and J₂ are the torsional rigidities of the bars on the left and right, respectively. The ratioJ₂/J₁ is

A rope brake dynamometer attached to the crank shaft of an $$I.C.$$ engine measures a brake power of $$10$$ kW when the speed of rotation of the shaft is $$400$$ rad/s. The shaft torque (in N-m) sensed by the dynamometer is ________

Consider a stepped shaft subjected to a twisting moment applied at $$B$$ as shown in the figure. Assume shear modulus, $$G=77$$ GPa. The angle of twist at $$C$$ (in degrees) is ________

Two solid circular shafts of $${{R_1}}$$ and $${{R_2}}$$ are subjected to same torque. The maximum shear stresses developed in the two shafts are $${\tau _1}$$ and $${\tau _2}.$$ If $${{{R_1}} \over {{R_2}}} = 2,$$ then $${{{\tau _1}} \over {{\tau _2}}}$$ is _______.

A solid circular shaft of diameter $$d$$ is subjected to a combined bending moment, $$M$$ and torque, $$T.$$ The material property to be used for designing the shaft using the relation $${{16T} \over {\pi {d^3}}}\sqrt {{M^2} + {T^2}} $$

For a circular shaft of diameter $$'d'$$ subjected to torque $$T,$$ the maximum value of the shear stress is

Maximum shear stress developed on the surface of a solid circular shaft under pure torsion is 240 MPa. If the shaft diameter is doubled then the maximum shear stress developed corresponding to the same torque will be

A cylindrical transmission shaft of length 1.5 m and diameter 100 mm is made of a linear elastic material with a shear modulus of 80 GPa. While operating at 500 rpm, the angle of twist across its length is found to be 0.5 degrees.

The power transmitted by the shaft at this speed is _______kW. (Rounded off to two decimal places)

Take π = 3.14.

A shaft of length L is made of two materials, one in the inner core and the other in the outer rim, and the two are perfectly joined together (no slip at the interface) along the entire length of the shaft. The diameter of the inner core is d; and the external diameter of the rim is d₀, as shown in the figure. The modulus of rigidity of the core and rim materials are G_i and G₀, respectively. It is given that d₀ = 2d_i and G_i = 3G₀. When the shaft is twisted by application of a torque along the shaft axis, the maximum shear stress developed in the outer rim and the inner core turn out to be τ₀ and τ_i, respectively. All the deformations are in the elastic range and stress-strain relations are linear. Then the ratio τ_i/τ₀ is (round off to 2 decimal places).

A rigid horizontal rod of length $$2L$$ is fixed to a circular cylinder of radius $$R$$ as shown in the figure. Vertical forces of magnitude $$P$$ are applied at the two ends as shown in the figure. The shear modulus for the cylinder is $$G$$ and the Young’s modulus is $$E.$$

The vertical deflection at point $$A$$ is

Two circular shafts made of same material, one solid $$(S)$$ and one hollow $$(H)$$, have the same length and polar moment of inertia. Both are subjected to same torque. Here. $${\theta _S}$$ is the twist and $${\tau _S}$$ is the maximum shear stress in the solid shaft, whereas $${\theta _H}$$ is the twist and $${\tau _H}$$ is the maximum shear stress in the hollow shaft. Which one of the following is TRUE?

A hollow shaft of $$1$$ m length is designed to transmit a power of $$30$$ kW at $$700$$ rpm. The maximum permissible angle of twist in the shaft is $${1^0}.$$ The inner diameter of the shaft is $$0.7$$ times the outer diameter. The modulus of rigidity is $$80$$ GPa. The outside diameter (in mm) of the shaft is _______

A solid circular shaft needs to be designed to transmit a torque of 50N.m. If the allowable shear stress of the material is $$140$$MPa, assuming a factor of safety of $$2,$$ the minimum allowable design diameter in mm is

A torque $$T$$ is applied at the free end of a stepped rod of circular cross-sections as shown in the figure. The shear modulus of the material of the rod is $$G.$$ The expressions for diameter to produce an angular twist $$\theta $$ at the free end is

A solid shaft of diameter, $$d$$ and length, $$L$$ is fixed at both the ends. A torque, $${T_0}$$ is applied at a distance, $$L/4$$ from the left end as shown in the figure below.

The maximum shear stress in the shaft is

A machine frame shown in the figure below is subjected to a horizontal force of $$600$$ $$N$$ parallel to $$Z$$-direction.

The maximum principal stresses in $$MP$$a and the orientation of the corresponding principal plane in degrees are respectively

A machine frame shown in the figure below is subjected to a horizontal force of $$600$$ $$N$$ parallel to $$Z$$-direction.

The normal and shear stresses in $$MP$$a at point $$P$$ are respectively

The two shafts $$AB$$ and $$BC$$, of equal length and diameters $$d$$ and $$2d$$, are made of the same material. They are joined at $$B$$ through a shaft coupling, while the ends $$A$$ and $$C$$ are built-in (cantilevered). A twisting moment $$T$$ is applied to the coupling. If $${T_A}$$ and $${T_C}$$ represent the twisting moments at the ends $$A$$ and $$C,$$ respectively, then

A solid circular shaft of $$60$$ mm diameter transmits a torque of $$1600$$ N - m. The value of maximum shear developed is

A torque of $$10$$ $$N-m$$ is transmitted through a stepped shaft as shown in figure. The torsional stiffnesses of individual sections of lengths $$MN, NO$$ and $$OP$$ are $$20$$ $$N-m/rad,$$ $$30$$ $$N-m/rad$$ and $$60$$ $$N-m/rad$$ respectively. The angular deflection between the ends $$M$$ and $$P$$ of the shaft is

Two shafts $$A$$ and $$B$$ are made of the same material. The diameter of shaft $$B$$ is twice that of shaft $$A$$. the ratio of power which can be transmitted by shaft $$A$$ to that of shaft $$B$$ is

A circular rod of diameter $$d$$ and length $$3d$$ is subjected to a compressive force $$F$$ acting at the top point as shown below. Calculate the stress at the bottom-most support point A.

The compound shaft shown is built-in at the two ends. It is subjected to a twisting moment $$T$$ at the middle. What is the ratio of the reaction torques $${{T_1}}$$ and $${{T_2}}$$ at the ends?