# GATE Questions & Answers of Machine Design Mechanical Engineering

#### Machine Design 60 Question(s) | Weightage 07 (Marks)

If the wire diameter of a compressive helical spring is increased by 2%, the change in spring stiffness (in %) is _____ (correct to two decimal places).

A self-aligning ball bearing has a basic dynamic load rating ($C_{10}$, for $10^6$ revolutions) of 35 kN. If the equivalent radial load on the bearing is 45 kN, the expected life (in $10^6$ revolutions) is

The schematic of an external drum rotating clockwise engaging with a short shoe is shown in the figure. The shoe is mounted at point Y on a rigid lever XYZ hinged at point X. A force $F=100\;N$ is applied at the free end of the lever as shown. Given that the coefficient of friction between the shoe and the drum is 0.3, the braking torque (in Nm ) applied on the drum is _______ (correct to two decimal places)

Pre-tensioning of a bolted joint is used to

Fatigue life of a material for a fully reversed loading condition is estimated from

$\sigma_a=1100\;N^{-0.15}$ ,

where $\sigma_a$ a is the stress amplitude in MPa and $N$ is the failure life in cycles. The maximum allowable stress amplitude (in MPa) for a life of $1\times10^5$ cycles under the same loading condition is ________ (correct to two decimal places).

A bar is subjected to a combination of a steady load of 60 kN and a load fluctuating between -10 kN and 90 kN. The corrected endurance limit of the bar is 150 MPa, the yield strength of the material is 480 MPa and the ultimate strength of the material is 600 MPa. The bar cross-section is square with side $a$. If the factor of safety is 2, the value of $a$ (in mm), according to the modified Goodman’s criterion, is ________ (correct to two decimal places).

A motor driving a solid circulr steel shaft transmits 40 kW of power at 500 rpm. If the diameter of the shaft is 400 mm, the maximum shear stress in the shaft is _________ MPa.

Consider the schematic of a riveted lap joint subjected to tensile load F , as shown below. Let d be the diameter of the rivets, and Sf be the maximum permissible tensile stress in the plates. What should be the minimum value for the thickness of the plates to guard against tensile failure of the plates? Assume the plates to be identical.

A machine element has an ultimate strength $\style{font-family:'Times New Roman'}{\left(\sigma_u\right)}$ of 600 N/mm2, and endurance limit $\style{font-family:'Times New Roman'}{\left(\sigma_{en}\right)}$ of 250 N/mm2. The fatigue curve for the element on a log-log plot is shown below. If the element is to be designed for a finite life of 10000 cycles, the maximum amplitude of a completely reversed operating stress is ____________ N/mm2.

A machine component made of a ductile material is subject to a variable loading with ${\sigma }_{min}=-50$ MPa and ${\sigma }_{max}=50$ MPa. If the corrected endurance limit and the yield strength for the material are ${\sigma }_{e}^{\text{'}}$  $=100$ MPa and ${\sigma }_{y}=300$ MPa, respectively,  the factor of safety is___________

A helical compression spring made of a wire of circular cross-section is subjected to a compressive load. The maximum shear stress induced in the cross-section of the wire is 24 MPa. For the same compressive load, if both the wire diameter and the mean coil diameter are doubled, the maximum shear stress (in MPa) induced in the cross-section of the wire is___________

Three masses are connected to a rotating shaft supported on bearings A and B as shown in figure. The system is in space where the gravitation effect is absent. Neglect the mass of shaft and rods connecting the masses. For m= 10 kg, m= 5 kg and m= 2.5 kg and for a shaft angular speed of 1000 radian/s, the magnitude of the bearing reaction (in N) at location B is_________

A steel plate, connected to a fixed channel using three identical bolts A, B and C, carries a load of 6 kN as shown in the figure. Considering the effect of direct load and moment, the magnitude of resultant shear force (in kN) on bolt C is

A single-plate clutch has a friction disc with inner and outer radii of 20 mm and 40 mm, respectively. The friction lining in the disc is made in such a way that the coefficient of friction $\mu$ various radially as $\mu =0.01r$ . Where r is in mm. The clutch needs to transmit a friction torque of 18.85 kN mm. As per uniform pressure theory, the pressure (in MPa) on the disc is___________

The principle stresses at a point in a critical section of a machine component are ${\sigma }_{1}$=60 MPa, ${\sigma }_{2}$=5 MPa and ${\sigma }_{3}$=-40 MPa. For the material of the component, the tensile yield strength is ${\sigma }_{y}$=200 MPa. According to the maximum shear theory, the factor of safety is

The principal stresses at a point inside a solid object are $\sigma_1=100\;\mathrm{MPa}$ $\sigma_2=100\;\mathrm{MPa}$ and $\sigma_3=0\;\mathrm{MPa}$. The yield strength of the material is 200 MPa. The factor of safety calculated using Tresca (maximum shear stress) theory is $n_T$ and the factor of safety calculated using von Mises (maximum distortional energy) theory is $n_V$. Which one of the following relations is TRUE?

In a structural member under fatigue loading, the minimum and maximum stresses developed at the critical point are 50 MPa and 150 MPa, respectively. The endurance, yield, and the ultimate strengths of the material are 200 MPa, 300 MPa and 400 MPa, respectively. The factor of safety using modified Goodman criterion is

Which of the bearings given below SHOULD NOT be subjected to a thrust load?

A bolted joint has four bolts arranged as shown in figure. The cross sectional area of each bolt is 25 mm2. A torque T = 200 N-m is acting on the joint. Neglecting friction due to clamping force,maximum shear stress in a bolt is ______ MPa.

Which one of the following is the most conservative fatigue failure criterion?

A machine element is subjected to the following bi-axial state of stress: ; ; .If the shear strength of the material is 100 MPa, the factor of safety as per Tresca’s maximum shear stress theory is

A horizontal plate has been joined to a vertical post using four rivets arranged as shown in the figure. The magnitude of the load on the worst loaded rivet (in N) is_________.

The uniaxial yield stress of a material is 300 MPa. According to Von Mises criterion, the shear yield stress (in MPa) of the material is ______.

A hollow shaft ($d_0=2d_i$ where $d_0$ and $d_i$ are the outer and inner diameters respectively) needs to transmit 20 kW power at 3000 RPM. If the maximum permissible shear stress is 30 MPA, $d_0$ is

For ball bearings, the fatigue life L measured in number of revolutions and the radial load F are related by FL1/3=K, where K is a constant. It withstands a radial load of 2 kN for a life of 540 million revolutions. The load (in kN) for a life of one million revolution is__________

A cantilever bracket is bolted to a column using three M12 × 1.75 bolts, P, Q and R. The value of maximum shear stress developed in the bolt P (in MPa) is _______.

A hydrodynamic journal bearing is subject to 2000 N load at a rotational speed of 2000 rpm. Both bearing bore diameter and length are 40 mm. If radial clearance is 20 μm and bearing is lubricated with an oil having viscosity 0.03 Pa.s, the Sommerfeld number of the bearing is _______

In a structure subjected to fatigue loading, the minimum and maximum stresses developed in a cycle are 200 MPa and 400 MPa respectively. The value of stress amplitude (in MPa) is _______

For the three bolt system shown in the figure, the bolt material has shear yield strength of 200 MPa. For a factor of safety of 2, the minimum metric specification required for the bolt is

A disc clutch with a single friction surface has coefficient of friction equal to 0.3. The maximum pressure which can be imposed on the friction material is 1.5 MPa. The outer diameter of the clutch plate is 200 mm and its internal diameter is 100 mm. Assuming uniform wear theory for the clutch plate, the maximum torque (in N.m) that can be transmitted is _______

A rotating steel shaft is supported at the ends. It is subjected to a point load at the center. The maximum bending stress developed is 100 MPa. If the yield, ultimate and corrected endurance strength of the shaft material are 300 MPa, 500 MPa and 200 MPa, respectively, then the factor of safety for the shaft is _______

Which one of following is NOT correct?

A drum brake is shown in the figure. The drum is rotating in anticlockwise direction. The coefficient of friction between drum and shoe is 0.2. The dimensions shown in the figure are in mm. The braking torque (in N.m) for the brake shoe is _______

A four-wheel vehicle of mass 1000 kg moves uniformly in a straight line with the wheels revolving at 10 rad/s. The wheels are identical, each with a radius of 0.2 m. Then a constant braking torque is applied to all the wheels and the vehicle experiences a uniform deceleration. For the vehicle to stop in 10 s, the braking torque (in N.m) on each wheel is _______

Ball bearings are rated by a manufacturer for a life of 106 revolutions. The catalogue rating of a particular bearing is 16 kN. If the design load is 2 kN, the life of the bearing will be p× 106 revolutions, where p is equal to ______

A shaft is subjected to pure torsional moment. The maximum shear stress developed in the shaft is 100 MPa. The yield and ultimate strengths of the shaft material in tension are 300 MPa and 450 MPa, respectively. The factor of safety using maximum distortion energy (von-Mises) theory is _______

A bolt of major diameter 12 mm is required to clamp two steel plates. Cross sectional area of the threaded portion of the bolt is 84.3 mm2. The length of the threaded portion in grip is 30 mm, while the length of the unthreaded portion in grip is 8 mm. Young's modulus of material is 200 GPa. The effective stiffness (in MN/m) of the bolt in the clamped zone is _______

A bar is subjected to fluctuating tensile load from 20 kN to 100 kN. The material has yield strength of 240 MPa and endurance limit in reversed bending is 160 MPa. According to the Soderberg principle, the area of cross-section in mm2 of the bar for a factor of safety of 2 is

A single riveted lap joint of two similar plates as shown in the figure below has the following geometrical and material details.

width of the plate w = 200 mm, thickness of the plate t = 5 mm, number of rivets n = 3, diameter of the rivet dr = 10 mm, diameter of the rivet hole dh = 11 mm, allowable tensile stress of the plate σp = 200 MPa, allowable shear stress of the rivet σs = 100 MPa and allowable bearing stress of the rivet σc = 150 MPa.

If the rivets are to be designed to avoid crushing failure, the maximum permissible load P in kN is

A single riveted lap joint of two similar plates as shown in the figure below has the following geometrical and material details.

width of the plate w = 200 mm, thickness of the plate t = 5 mm, number of rivets n = 3, diameter of the rivet dr = 10 mm, diameter of the rivet hole dh = 11 mm, allowable tensile stress of the plate σp = 200 MPa, allowable shear stress of the rivet σs = 100 MPa and allowable bearing stress of the rivet σc = 150 MPa.

If the plates are to be designed to avoid tearing failure, the maximum permissible load P in kN is

A fillet welded joint is subjected to transverse loading F as shown in the figure. Both legs of the fillets are of 10 mm size and the weld length is 30 mm. If the allowable shear stress of the weld is 94 MPa, considering the minimum throat area of the weld, the maximum allowable transverse load in kN is

A solid circular shaft needs to be designed to transmit a torque of 50 N.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

Match the following criteria of material failure, under biaxial stresses ${\sigma }_{1}$ and ${\sigma }_{2}$ and yield stress ${\sigma }_{y}$, with their corresponding graphic representations :

Two identical ball bearings P and Q are operating at loads 30 kN and 45 kN respectively. The ratio of the life of bearing P to the life of bearing Q is

A band brake having band-width of 80mm, drum diameter of 250mm, coefficient of friction of 0.25 and angle of wrap of 270 degrees is required to exert a friction torque of 1000N-m. The maximum tension (in kN) developed in the band is

A bracket (shown in figure) is rigidly mounted on wall using four rivets. Each rivet is 6mm in diameter and has an effective length of 12mm.

Direct shear stress (in MPa) in the most heavily loaded rivet 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 $\frac{16}{\pi {d}^{3}}\sqrt{{M}^{2}+{T}^{2}}$ is

A forged steel link with uniform diameter of 30 mm at the centre is subjected to an axial force that varies from 40 kN in compression to 160 kN in tension. The tensile (Su), yield (Sy) and corrected endurance (Se) strengths of the steel material are 600 MPa, 420 MPa and 240 MPa respectively. The factor of safety against fatigue endurance as per Soderberg’s criterion is

A 20º full depth involute spur pinion of 4mm module and 21 teeth is to transmit 15 kW at 960 rpm. Its face width is 25 mm.

The tangential force transmitted (in N) is

A 20º full depth involute spur pinion of 4mm module and 21 teeth is to transmit 15 kW at 960 rpm. Its face width is 25 mm.

Given that the tooth geometry factor is 0.32 and the combined effect of dynamic load and allied in factors intensifying the stress is 1.5; the minimum allowable stress (in MPa) for the gear material is

An axial residual compressive stress due to a manufacturing process is present on the outer surface of a rotating shaft subjected to bending. Under a given bending load, the fatigue life of the shaft in the presence of the residual compressive stress is

A clutch has outer and inner diameters 100mm and 40 mm respectively. Assuming a uniform pressure of 2 MPa and coefficient of friction of liner material 0.4, the torque carrying capacity of the clutch is

A spur gear has a module of 3 mm, number of teeth 16, a face width of 36 mm and a pressure angle of 20°. It is transmitting a power of 3 kW at 20 rev/s. Taking a velocity factor of 1.5, and a form factor of 0.3, the stress in the gear tooth is about

A steel bar of 10 × 50 mm is cantilevered with two M 12 bolts (P and Q) to support a static load of 4 kN as shown in the figure

The primary and secondary shear loads on bolt P, respectively, are

A steel bar of 10 × 50 mm is cantilevered with two M 12 bolts (P and Q) to support a static load of 4 kN as shown in the figure

The resultant shear stress on bolt P is closest to

A thin spherical pressure vessel of 200 mm diameter and 1 mm thickness is subjected to an internal pressure varying from 4 to 8 MPa. Assume that the yield, ultimate, and endurance strength of material are 600, 800 and 400 MPa respectively. The factor of safety as per Goodman’s relation is

A natural feed journal bearing of diameter 50 mm and length 50 mm operating at 20 revolution/second carries a load of 2.0 k N. The lubricant used has a viscosity of 20 mPa s. The radial clearance is 50 μm. The Sommerfeld number for the bearing is

A bolted joint is shown below. The maximum shear stress, in MPa, in the bolts at A and B, respectively are