MACHINE DESIGN
MACHINE DESIGN
(OBJECTIVE)
CONTENTS
Unit Chapters Page No.
1 Static Loading 2 - 15
2 Fatigue Loading 16 -22
3 Bolted, Riveted and Welded Joints 23-25
4 Brakes 26-29
5 Bearings 30-37
6 Clutches 38-40
7 Gears 41-45
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Published at : Ascent Gate Academy
“Shraddha Saburi”, Near Gayatri Vidyapeeth,
Rajnandgaon (Chhattisgarh) Mob. 9993336391
© Copyright : Ascent Gate Academy 1
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MECHANICAL ENGINEERING
1(A) STATIC LOADING
1. If the load & diagram of an axillary loaded member becomes double, the value of FOS :
a) Remains save b) becomes double c) Becomes half d) Becomes Triple
2. Two pices of steel are welded along a plane inclined at 300 as shown in figure to form a rectagle bar of c/s area 2500
mm2. If the normal & shear stress are not to exceed 60 & 40 MPa respect. Determine the maximum safe load that can
be corved by the bar :
< <
300
a) 600 KN b) 235 KN c) 230 KN d) 590 KN
3. A weight of W is suspended as shown in figure. The rods AC and BCare of different sizes & made with different
materials as shown fig. Determine the safe weight the rods can withstand 112233445566778899001122
a) 20 KN A = 200mm2 < < A = 100mm2
b) 14 KN σ = 60 NPa
c) 21 KN per σ = 100 NPa
d) 13.5 KN per
600 300
C
W
4. Shown in figure. The rods AC & BC are of same size & made of material with a permissible stress of 100 NPs. The size
of the rod is. 11223344551111166222227733333 111111122222223344556677
a) 6 mm
b) 8 mm 450
c) 7 mm 450
d) 10 mm
5. A hole is to be purnched in a M.S. plate of 10 mm thickness with the help of punch. The allowalbe crushing stress
for the punch is 4 times. The allowable shear stress of the plate. The dia. of the smallest hole that can be punched
in the palge is
a) 20 mm b) 10mm c) 5 mm d) none
6. A steel bar of rectangle c/s carries a load P & is attached to a suppoert by means of round pin of dia. 16mm as shown
in fig. Determine maximum safe load that bar can withstand if σt = 140 MPa & τs (permissible shear stress)
11223344556677889900112233445566778899 11223344556677889900112233445566778899
= 70 MPa.
d = c6
Ans : 1-?, 2-b, 3-d, 4-?, 5-b, 6-?. > >t = 12.5 mm b = 50 mm
*************** >>
p
>
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MACHINE DESIGN
1 (B) COMBINE STRESSESANDTHEORIES OFFAILURE
1. A solid shaft can resist a bending moment of 3.0 kNm and a twisting moment of 4.0 kNm together
, then the maximum torque that can be applied is. (G-96)
(a) 7.0 kNm (b) 3.5 kNm (c) 4.5 kNm (d) 5.0 kNm.
2. A small element at the critical section of a component is in a bi-axial state of stress with the two
principalstresses being 360 MPa and 140 MPa. The maximum working stress according to
Distortion Energy Theory is . (G-97)
(a) 220 MPa (b) 110 MPa (c) 314 MPa (d) 330 MPa.
3. A solid shaft can resist a B.M fo 3 kN-m & T.M of 4 kN-m together. Then Maximum torque.
that can be applied is.
(a) 7 kN-m (b) 3.5 kN-m (c) 4.5 kN-m (d) 5 kN-m
4. A shaft is subjected to maximum bending stress 80 MPa & maximum shear stress 30 MPa at a
particular section of yield point in tension of material is 280 MPa & MSST is used. The FOS
obtained will be.
(a) 2.5 (b) 2.8 (c) 3 (d) 3.5
5. A circular solid shaft is subjected to . a B.M of 400 kN-m & T.M of 300 kN-m. On the basis of
MPST the direct stress is σ & according to MSST, shear stress is τ. The ratio of σ/τis
(a) 1/5 (b) 3/9 (c) 9/5 (d) 11/6
6. The Mohr circle of plane stress for a point in a body is shown in fig. The design is to be done as
the basis of MSST for yielding. the yielding just begins if thedesigner choses a ductile mt whose
yield strength is. ↓↓
(a) 45 MPa -100MPa ↓τmax -10MPa
(b) 50 MPa ←←
(c) 90 MPa σ MPa ↓
(d) 100 MPa
7. For the state of stress as shown in fig, which of the following, theories of failure should be used.
(a) MPST ó
(b) MSST ó
(c) MDET
óó
(d) both b & c. óó ó
8. (a) MPST ó ← ←ó
(b) MSST ó
(c) MDET
(d) All of the above.
9. According to MSST, permissible T.M in a circular shaft is T. The permissible T.M. in same shaft
according to MPST will be :-
(a) T/2 (b) T (c) √2 T (d) 2 T
10. According to MPST, Mper = M, what will be Mper according to MSST:-
(a) M (b) 2M (c) M/2 (d) √2M
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MECHANICAL ENGINEERING
11. State of stress in a system is described by :-
σ1= 200 MPa,σ2 = 90 MPa,σ3 = 160 MPa.
If a Material, of tensile yield strength of 400 MPa is used in the system, The FOS by MSST &
MDET are respectively:-
12. A component in an aircraft flap actuator can be adequately modelled as a cylindrical bar subjected
to an axial force of 8.0 kN, a bending moment of 55 Nm and a torsional moment of 30 Nm.
A 20mm diameter solid bar of 7075 - T 6 aluminium having Sut = 591MPa ,Syp = 542 MPa and
Syp = 271MPa is recommended for its use. Determine the factor of safety available as per
maximum shear stress theory . (G-97)
13. For the component loaded with a force F as shown in the fig., the axial stress at the corner point
P is .(G-08) ↓↓
(a) F (3L - b) / 4b3
PF
(b) F (3L + b) / 4b3 L→ →
(c) F (3L + 4b) / 4b3 L-b ↓
↓
L→
→
2b
(d) F (3L +2b) / 4b3 2b
14. A solid circular shaft of diameter 100 mm is subjected to an axial stress of 50 MPa. It is further
subjected to a torque of 10 kNm. The maximum principal stress experienced on the shaft is
closest to. (G-08)
(a) 41 MPa (b) 82 MPa (c) 164 MPa (d) 204 MPa.
15. An axial residual compressive stress due to a manufacturing process is present on the 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 . (G-08)
(a) decreased
(b) increased or decreased, depending on the external bending load.
(c) neither decreased nor increased . (d) increased .
16T
πd3 M2 + T2
16. 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
is (GATE 2009 ME)
a) Ultimate tensile strength (Su)
b) Tensile yield strength (Sy)
c) Torsional yield strength (Sxy)
d) Endurance strength (Se)
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MACHINE DESIGN
17. A component used in the Mars path finder can be idealized as a circular bar clamped at its ends.
The barshould withstand a torque of 1000 Nm.The component is assembeled on earth when the
temp.is 30oC. Temp. on Mars at the site of landing is - 70oC. The material of the bar has an
allowable shear stress of 300 MPa and its Young’s Modulus is 200 GPa. Design the diameter
of the bar taking a factor of safety of 1.5 and assuming a coefficient of thermal expansion for the
material of the bar as 12 x 10-6 / oC. (G-98)
18. A concentrated force, F, is applied (perpendicular to the plane of the figure) on the tip of
the bent bar shown in Fig.1.7. The equivalent load at a section close to the fixed end is.
(G-99)
→L →
↓
L
F↓
→L→
(a) Force F (b) Force F and bending moment FL
(c) Force F and twisting moment FL.
(d) Force Fbending moment FL, and twisting moment
19. A column of square section 40mm x 40mm, fixed to the ground carries an eccentric load P of
1600N as shown in the fig.
..................................................eP
........................A111111111111222222222222333333333333444444444444555555555555666666666666e777777777777888888888888999999999999000000000000D 40mm
C
B
40mm
If the stress developed along the edge CD is -1.2 N/mm2, the stress along the edge AB will be.
(a) -1.2 N/mm2 (b) +1.2 N/mm2
(c) + 0.8 N/mm2 (d) -0.8 N/mm2
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MECHANICAL ENGINEERING
Data for Linked answer questions 20 and 21
A machine frame shown in the figure below is subjected to a horizontal force of 600 N parallel to
z-direction (GATE 2007 ME)
y
500 mm
→350 mm
111111111111111111111111222222222222222222222222333333333333333333333333z444444444444444444444444555555555555555555555555666666666666666666666666777777777777777777777777888888888888888888888888999999999999999999999999000000000000000000000000111111111111111111111111222222222222222222222222P333333333333333333333333444444444444444444444444555555555555555555555555666666666666666666666666777777777777777777777777888888888888888888888888999999999999999999999999000000000000000000000000φ111111111111111111111111K22222222222222222222222233333333333333333333333330444444444444444444444444mm→ →
600 N
20. The normal and shear stress in MPa at point P are respectively
a) 67.9 and 56.6 b)56.6 and 57.9
c) 57.9 and 0.0 d) 0.0 and 56.6
21. The maximum principal stress in MPa and the orientation of the corresponding principal plane in
degress are respectively
a) -32.0 and -29.52 b) 100.0 and 60.48
c) -32.0 and 60.48 d) 100.0 and -29.52
************************
1 (B) COMBINE STRESSESANDTHEORIES OFFAILURE
1-d, 2-c, 3-d, 4-b, 5-c, 6-c, 7-a, 8-d, 9-d, 10-a, 11-sol, 12-- max stress; 102.85
MPa, factor of safety = 5.27, 13-d, 14-b, 15-d, 16-a, 17-( d = 3cm, 169 cm)
18-c, 19-d, 20-a, 21-c.
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MACHINE DESIGN
PRACTICE SET - 1
One Mark Quesions :
1. In the design of shafts made of ductile materials subjected to twisting moment and bending moment, the
recommended theory of failure is [GATT-ME-88]
a) maximum principal stress theory b) maximum principal strain theory
c) Maximum shear stress theory d) maximum strain-energy theory
2. Strength to weight ratio for a circular shaft transmitting power is directly proportional to the [GATE-ME-91]
a) square root of the diameter b) diameter
c) square of the diameter d) cube of the diameter
3. A large uniform plate containing a rivet hole subjected to uniform uniaxial tension of 95 MPa. The maximum stress
in the plate is [GATE-ME-92]
a) 100 MPa
b) 285 MPa 10 cm 5 mm 95 MPa
<>
95 MPa
c) 190 MPa
d) indeterminate
4. The outside diameter of a hollow shaft is twice its inside diameter the ratio of its troque carrying capacity to that of
a solid shaft of the same material and the same out side diameter is [GATE-ME-93]
a) 15/16 b) 3/4 c) 1/2 d) 1/16
5. 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 [GATE-ME-94]
a) 1/2 b) 1/4 c) 1/8 d) 1/16
6. A solid shaft can resist a bending moment of 3.0 KNm and a twisting moment of 4.0 KNm together, then the maximum
torque that can be applied is [GATE-ME-96]
a) 7.0 KNM b) 3.5 KNM d) 4.5 KNm d) 5.0 KNm
7. Which theory of failure will you use for aluminium components under steady loading is [GATE-ME98]
a) principal stress theory b) principal strain theory
c) strain energy theroy d) maximum shear stress theory
8. Match the following criteria of material failure, under biaxial stress σ1 and σ2 and yield stress σ with their
y
corresponding graphic representations: [GATE-ME-11]
σ2>>
σ
y
P. Maximum normal stress criterion L. −σ > σ1
Q. Maximum distortion energy criterion y σ
y
−σ
y
σ2
σ
y
M. > σ1
−σ σ
y
y
−σ
y
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MECHANICAL ENGINEERING >
σ2
σ
y
R. Maximum shear stress criterion N. −σ > σ1
y σ
y
−σ
y
a) P-M, Q-L, R-N b) P-N, Q-M, R-L c) P-M, Q-N, R-L d) P-N, Q-L, R-M
Two Marks Quesions :
1. A small element at the critical section of a component in bi-axial state of stress with the two principal stresses being
360 MPa and 140 MPa. The maximum working stress according to distortion energy theory is[GATE-ME-97]
a) 220 MPa b) 110 MPa c) 314 MPa d) 330 MPa
2. The homogeneous state of stress for a metal part undergoing plastic deformation is
10 5 0
T = 5 20 0
-10
00
Where the stress component values are in MPa. Using von Mises yield criterion, the value of estimated shear yield
stress, in MPa is [GATE-ME-12]
a) 9.50 b) 16.07 c) 28.52 d) 49.41
3. 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. [GATE-ME-12]
a) 8 b) 16 c) 24 d) 32
*****************
“The pursuit of perfection, then,
is the pursuit of sweetness and light”
1. STATIC LOADING
One Mark Quesions :
1-c, 2-b, 3-a, 4-a, 5-c, 6-c, 7-d, 8-c
Two Marks Quesions :
1-c, 2-b, 3-b.
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MACHINE DESIGN
PRACTICE SET - 2 (COMBINE STRESSESAND THEORIES OFFAILURE )
1 Permissible bending moment in a circular shaft under pure bending is M according to maximum
principal stress theory of failure the permissible bending moment in the same shaft is.
(a) 1/2 M (b) M
(c)√ M (d) 2M
2 The equivalent bending moment under combined action of bending moment M and torque T is.
(a) M2 + T2 (b) 1 / 2 M2 + T2
(c) M + M2 + T2 (d) 1 / 2 ( M + √M2 + T2)
3 If shaft made from ductile material is subjects to combined bending and twisting moments
calculations based on which one of the following failure theories would give the most conservative
value ?
(a) Maximum principal stress theory. (b) Maximum shear stress theory.
(c) Maximum strain energy theory. (d) Maximum distortion energy theory.
4 Match List-I (Failure theories) with List - II (Figures representing boundaries of these theories)
and select the correct answer using codes given below the lists: (IES-97)
List - I
(a) Maximum Principal stress theory. (b) Maximum shear stress theory
(c) Maximum octahedral shear stress theory (d) Maximum shear strain energy theory.
List - II σ2 σ2
1. 2.
σ1 σ1
σ2 σ2
3.
4.
σ1 σ1
5 According to the maximum shear stress theory of failure, permissible twisting moment in a
circular shaft is ‘T’ the permissible twisting moment in the same shaft as per the maximum
principal stress theory of failure will be.
(a) T / 2 (b) T
(c) √2T (d) 2T
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MECHANICAL ENGINEERING
6 Which one of the following fig. represents the maximum shear stress Theory or TRESCA
criterion ? σ2 σyp σ2 σyp
(a) (b)
σ1 σyp σ1 σyp
σ2 σyp (d) σ2 σyp
(c)
σ1 σyp
σ1 σyp
7 A member is subjected to the combined action of bending moment 400 Nm and torque 300 Nm
What, respectively are the equivalent bending moment and equivalent torque ?
(a) 450 Nm and 500 Nm (b) 900 Nm and 350 Nm.
(c) 900 Nm and 500 Nm (d) 400 Nm and 500 Nm
8 The maximum distortion energy theory of failure is suitable to predict the failure of which one of
the following types of materials?
(a) Brittle materials (b) Ductile materials
(c) Plastics (d) Composite materials
9 A solid circular shaft is subjected to a bending moment M and twisting moment T.What is the
equivalent twisting moment Te which will produce the same maximum shear stress as the above
combination?
(a) M2 + T2 (b) M + T
(c) √ M2 + T2 (d) M - T
10. A shaft is subjected to combined twisting moment T and bending moment M. What is the
equivalent bending moment?
1{ }(a) (b) M2 + T2
2 M2 + T2
{ }1 (d) M + M2 + T2
(c) 2 M +
M2 + T2
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MACHINE DESIGN
11 Who postulated the maximum distortion energy theory ?
(a) Tresca (b) Rankine
(c) St. Venant (d) Mises-Henky
12 For obtaining the maximum shear stress induced in the shaft shown in the given fig. the torque should
be equal to.
Wt. of shaft w Gear (Torque
per Unit length Acting : T)
L
..........................................
l ......
(b) Wl+T
(a) T
(c) 2 ½ { }(d) 2 ½
+ T2
(Wl)2+ wL Wl +wL2
2 2
13 A circular solid shaft is subjected to bending moment of 400 kN-m and a twisting moment of
300 kN-m. One the basis of the maximum principal stress theory, the direct stress is σ and
according to the maximum shear stress theory, the shear stress is τ . The ratioσ /τ is
(a) 1 / 5 (b) 3 / 9
(c) 9 / 5 (d) 11 / 16
14. A thin cylindrical pressure vessel with mean diameter 10m and wall thickness 20mm is sub jected to
an internal fluid pressure of 0.4 MPa . if the Y.S. of the material of the cylinder is 200 MPa ,the
factor of safety according to max. shear stress theory ( neglecting radial stress ) is.
(a) 0.5 (b) 1
(c) 1.5 (d) 2 DRDO-08
15. Consider the following statements:
I. Experiments have shown that the D.E.T gives an accurate Prediction about failure of a ductile
component than any other theory of failure.
II According to the D.E.T, the yield strength in shear is less than the Y.S in tension. (IAS -07)
Which of the statements given above is are correct ?
(a) 1only ( b) 2 only
(c) both1& 2 (d)Neither 1 nor 2
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MECHANICAL ENGINEERING
16. For ó1 ≠ ó2 and ó3 = 0 What is the physical boundary for Rankine failure theory ?
(a) A rectangle (b)An ellipse
(c) A Square (d) A parabole
17. Given that the principal stresses ó1 > ó2 > ó3 , and óe is the elastic limit stress in simple tension;
which one of the following must be satisfied such that the elastic failure does not occur
accordance with the max. principal strain theory ?
(a) óe < ó1 - µó2 - µó3 (b) óe > ó1 - µó2 - µó3
E EE E E EE E
(c) óe > ó1 + µó2 + µó3 (d) óe < ó1 + µó2 - µó3
E EE E E EE E
18. Consider the following statements;
(i) Distortion energy theory is in better agreement for predicting the failure of ductile materials.
(ii) Max. Normal stress theory gives good prediction for the failure of brittle materials .
(iii Moduli of elasticity in tension and compression are assure to be different in the stress analysis
of curved beams.
Which of these statements is are correct ? (IAS-03)
(a) 1,2 and 3 ( b) 1,and 2
(c) 3 only (d) 1 and 3
19. A rectangle block shown in fig is subjected to stress ó and ó as shown. The material of block
12
has yield stress 100MPa .To avoid Yielding of block then what will be the value of ó1 if designer
applies st. venant’s T.O.F
(a) ó must be less than 100 MPa. ó ← ←←ó2
1 1
←ó1
(b) ó1 may be smaller or greater than 100 MPa.
(c) ó1 + ó1 must be less than 100 MPa. ó2
2
(d) ó1 - ó1 must be less than 100 MPa
20. According to von- mises D.E.T, the D.E under 3D stress state is represented by
(a) 1 ó21 + ó22 + ó 2 - 2ì (ó1 ó2+ó2ó3+ ó1ó3 )
2E
3
(b) 1- 2ì ó2 + ó2 + ó2 +2ì (ó ó +ó ó +ó ó )
12 3 12 23 13
6E
(c) 1+ì ó21 + ó22 + ó 2 - (ó1ó2+ó2ó3+ó1ó3)
3E
3
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MACHINE DESIGN
21. The area enclosed by the failure locus on the plot of Practical stresses based on.
(a) D.E.T (b) MSST (c)M.P.S.T
(A) a>c>b (B) ) b>a>c
(C) c>b>a (D) ) c>a>b
22. In a M/C component the state of stress at a criticalregion is given below. the y.s os 300MPa,
Sut = 400MPa & ì = 0.28 for the material . compare the factor of safety based on the follow
failure theorem.
(a) M.P.S.T (b) MSST (c) MDET
(A) a=b=c (B) ) a=b<c
(C) a<b<c (D) ) a<b=c
23. At a critical section in a shaft, the follows stresses are induced: bend stress = 60MPa , show
stress = 40MPa Across to MSST, N=?
(a) 2 (b) 2.5
(c) 3 (d) 3.5
24. The state of stress in an Element’s is shown below. The von -mises stress is.
100MPa
100MPa 100MPa
100MPa
(a) 100MPa (b) 200MPa
(c)144MPa (d) 173MPa
25. The state of stress in a component is shown by the Mohr’s circle given below According the
MSST and based on yielding, the yield strength of the material is
(a) 200MPa (b) 300MPa
(c)400MPa (d) 500MPa
26. Match List - I with List -II and select the correct answer using the codes given below the lists:
List-I List-II
P. Shear strain energy theory - 1. Square
Q. Principal stress Theory - 2. Hexagon
R. Max shear stress Theory - 3. Rhombus
S. Max.Principal strain Theory - 4. Ellipse
(a) P- 4 , Q- 2 , R- 1, S -3 (b) P- 4 , Q- 1 , R- 2, S -3
(c) P- 3 , Q- 2 , R- 1, S - 4 (d) P- 3 , Q- 1 , R- 2, S -4
27. A shaft is subjected to twisting moment of 1500N-m and Bending Moment of 1000N-m .The
design shear stress is 45 MPa.
The equivalent torque according to MSST is
(a) 1200N-m (b) 1400N-m
(c)1600N-m (d)1800N-m
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MECHANICAL ENGINEERING
28. The diameter of the shaft is
(a) 59mm (b) 65mm
(c)73mm (d)87mm
29. For a component subjected to complex Loading ,the dimensions obtained from different theories
of failures are arranged in descending order . Which of the following statement is true?
(a) Von Mises > Tresca >Rankine.
(b) Tresca > Von Mises >Rankine.
(c) Rankine > Von Mises>Tresca.
(d) Von Mises > Tresca >Tresca.
30. The complex state of stress in a machine element is shown by the Mohr’s circle in fig. the yield
strength of the material, considering yielding in the machine element according to Distortion
energy theory is.
50 250 σ
(MPa)
(a) 127MPa (b) 148Mpa
(c)187MPa (d)229MPa.
31. The percentage increase in shear yield strength according to Von-Mises theory as compared to
Tresca’s (or Guest’s) theory is .
(a) 12.4 (b) 15.4
(c)18.4 (d) 25.4
The state of stress at a heavily stressed region a component is given by ó1= 250MPa and ó2= -
200MPa. The material has an tensile yield sterength of 500MPa in yielding and the ultimate stress
of 515 MPa in tension .
32 The factor of safety based on MPST
(a) 2 (b) 1.11
(c) 1.125 (d)1.28
33 The factor of safety based on MSST
(a) 2 (b) 1.11
(c) 1.125 (d)1.28
34. The factor of safety based on MDET
(a) 2 (b) 1.11
(c) 1.125 (d)1.28
35.. A component is subjected to biaxial state of stress ó1= - 300MPa , ó2= -300MPa . Is yield
strength in tension and in compression is same and equal to 300MPa .Match the following .
Failure Theory Factor of Safety
a. MDET 1. 1.0
b. MSST 2. -
c. MPST 3. 0.9
(A) a - 1, b - 1, c - 1 (B) a - 3, b - 2, c - 1
(C) a - 3, b - 3, c - 1 (D) a - 3, b - 2, c - 3.
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MACHINE DESIGN
36. The state of stress in a component at the most heavily stressed region are ó1= 200MPa:. The
factor of safety based on.
(a) M.P.S.T (b) MSST (c) MDET
(A) c>b>a (B) ) a=b>c
(C) a>c>b (D) ) c<b=a
37. A component is Subjected to an axial stress of 250MPa and a shear stress of 150MPa . The
yield strength of the material is 400MPa and ultimate strength of the material is 600MPa .The
F.O.S based on DET is.
(a) 1.6 (b) 2.4 (c)1.1 (d) 1.0
38. A component is to be designed with brittle material the appropriate theory of failure is.
(a) MPST (b) MSST (c) MP strain theory (c) MDET
39. A ductile component is in biaxial state fo stress with ó1= 300MPa , ó2= -100MPa,
Syt = 400MPa The factor of safety using MSST is.
(a) 1.333 (b) 1 (c)1.25 (d) 0.15
40. A shaft can carry a torque of 5kN-m and a bending load of 5 Kn-m with a factor of safety of
2. If the shaft is subjected to a torque of 8.5kN-m and a bending load of 1.5 KN-m . The factor
of safey is.
(a) 2 (b)1.8 (c)1.6 (d) 1.4
41.. A component is subjected to the principal stresses ó1= 300MPa; ó2= -
100MPa. Yield strength
of the material in tension is 300MPa . The factor safety based on MPST and MSST are
respectively.
(a) 1 & 1.5 (b)1 & 1.33 (c)1 & 0.75 (d) 1.5 & 0.75
42. A component is subjected to biaxial state fo stress óx= 400MPa; óy= 0; Txy = 200MPa .If the
Y.S in tension is 500MPa and Sut = 500MPa The F.O.S as for DET is
(a) 0.7 (b) 1.44 (c)1.04 (d) 0.96
43. A circular beam is subjected to and axial ;oad causing a stress fo 200MPa and also to bends
load inducing a stress of 200MPa. the VON-Mises stress in the beam is .
(a) 400MPa (b)282.84MPa (c) 0 (d) 565.68MPa.
44. A shaft of uniform circular section is subjected to pure torsion. The ratio of requisite diameters
according to MSST & MPST is given by
(a) 1.26 (b)0.79 (c)1 (d) 1.5
45. A cold rolled steel shaft is designed on the basis of MSST. The Principal stresses induced at its
critical section are 60MPa and -60MPa respectively. If the Syt for the shaft material is
360MPa, The F.O.S of the design is.
(a) 2 (b) 3 (c) 4 (d) 6
PRACTICE SET - 2 (COMBINE STRESSESAND THEORIES OF FAILURE ) (Ans.)
1 - b, 2 - d, 3 - b, 4 - d, 5 - b, 6 - c, 7 - a, 8 - b, 9 - c, 10 - c, 11 - d, 12 - d, 13 - c, 14 - d, 15 - a, 16
- c, 17 - b, 18 - sol, 19 - a, 20 - c, 21 - d, 22 - b, 23 - c, 24 - d, 25 - c, 26 - b, 27 - d, 28 - a, 29 - b,
30 - b, 31 - b, 32 - a, 33 - b, 34 - d, 35 - a, 36 - c, 37 - c, 38 - a, 39 - b, 40 - c, 41 - c, 42 - d, 43 - a,
44 - a, 45 - b.
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MECHANICAL ENGINEERING
2. FATIGUE LOADING
One Mark Questions :
1. Stress concentration in a machine component of a ductile material is not so harmful as it is in a brittle material
because [GATE-ME-89]
a) in ductile material local yielding may distribute stress concentration.
b) ductile material has larger young’s material.
c) Poisson’s ratio is larger in ductile materials.
d) Modulus of rigidity is larger in ductile materials.
2. The process of shot peening increases the fatigue life of steel springs mainly because it results in [GATE-ME-90]
a) surface hardening b) increased stiffness of the material
c) structurarl changes in the material d) residual compression at the surface
3. In a shaft with a transverse hole, as the hole of the shaft diameter ratio .................. (increase / decreases), the
torsional stress concentration factor ............. (increases / decreases) [GATE-ME-91]
4. Fatigue strength of rod subjected to cyclic axial force is less than that of a rotating beam of the same dimensions
subjected to steady lateral force because [GATE-ME-92]
a) axial stiffness is less than bending stiffness
b) of absence of centrifugal effects in the rod
c) the number of discontinuities vulnerable to fatigue are more in the rod
d) at a particular time the rod has only one type of stress whereas the beam has both the tensile and compressive
stresses.
5. The yield strength of a steel shaft is twice its endurance limit. Which of the following torque fluctuations represent
the most critical situation according to soderberg criterion ? [GATE-ME-93]
a) -T to +T b) -T/2 to +T c) 0 to + T d) +T/2 to +T
6. A static load is mounted at the centre of a shaft rotating at uniform angular velocity. This shaft will be designed for
[GATE-ME-02]
a) the maximum compressive stress (static) b) the maximum tensile stress (static)
c) the maximum bending moment (static) d) fatigue loading
7. In terms of theoretical stress concentration factor (Kt) and fatigue stress concentration factor (kf), for the notch
sensitivity ‘q’ is expressed as [GATE-ME-03]
a) (k - 1)/(k - 1) b) (k - 1)/(k + 1) c) (k - 1)/(k - 1) d) (k + 1)/(k + 1)
ff ff tf ff
8. The S-N curve for steel becomes asymptotic nearly at [GATE-ME-03]
a) 103 cycles b) 104 cycles c) 106 cycles d) 109 cycles
Two Marks Questions :
9. A rotating beam test specimen when loaded to a stress of 900 Mpa gives a life of 1000 load cycles. When loaded to
500 MPa withstands 106 cycles. If the required life of the component is 50000 cycles, what maximum stress it can
be loaded
a) 645 Mpa b) 831.56 MPa c) 600 MPa d) 700 MPa
10. A ductile material having an endurance limit of 196 N/mm2 and the yield point at 294 N/mm2 is stressed under
variable load. The maximum and minimum stresses are 147N/mm2 and 49N/mm2. The fatigue stress concentration
factor is 1.32. The available factor of safety for this loading is [GATE-ME-87]
a) 3.0 b) 1.5 c) 1.33 d) 4.0
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MACHINE DESIGN
11. A thin spherical pressure vessesl 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 600,800,400 MPa
respectively. The factor of safety as per Goodman’s relation is [GATE-ME-07]
a) 2.0 b) 1.6 c) 1.4 d) 1.2
12. Repeat above question by using soderberg relation.
13. 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 (S ), yield (S ) and corrected endurance (S ) strengths of steep
Uy e
material are 600 Mpa, 420 MPa and 240 MPa respectively. The factor of safety against fatigue endurance as per
Soderberg’s criteerion is [GATE-ME-09]
a) 1.26 b) 1.37 c) 1.45 d) 2.00
14.. A cylindrical shaft is subjected to an alternating stress of 100MPa. Fatigue strength to sustain 1000 cycles is
490 MPa. If the corrected endurance strength is 70MPa, estimated shaft life will be [GATE-ME-06]
a) 1071 cycles b) 15000 cycles c) 281914 cycles d) 928643 cycles
15. A component is subject to fluctuation normal stress of 100 + 150 MPa. If Sut = 600 MPa, E.L. = 200 MPa. The FOs
based on Goodman crtitation is :
16. If kt = 2 & notch sensitivity index is 0-9, then fatigue strength decreased by ---------- times
17. For the loading shown in fig. determine the thickness of the plate. If sut = 300 MPa & Syt = 200 MPA, FOs = 2,
Kt = 2 & q = 0.9 <>
<>
+ 10 KN = 10 P > 100 <> 5>
+P
< t >
d) None
a) 4 mm b) 5 mm c) 6 mm
18. Design the m11111111111111e22222222222222m3333333333333344444444444444ber for the loading condition as shown in fig.
2d
d + 1 KN
critical section
<>
>
< >< >
500 500
If - yt = 200 MPa & E.L. (under reversed bending ) = 150 MPa, kf = 1.5 & FOS = 2
19. Determine maximum load that the shaft can withstand such that it can have infinite life if FOS = 2,Sut = 300 MPa
a) 3.5 KN b) 4 KN c) 5 KN d) None
> Φ = 50 mn
w=?>
<>
1m
2. FATIGUE ***************
One Mark Quesions : 1-a, 2-d, 3- increases, decreases, 4-c, 5-a, 6-d, 7-a, 8-c.
Two Marks Quesions : 9-a, 10-b, 11-b, 13-a, 14-c © Copyright : Ascent Gate Academy 17
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MECHANICAL ENGINEERING
Practice Questions :
1. Endurance limit of a component
a) increases as the surface roughness increases
b) decreases as the surface roughness increases
c) initially increases with the increase in surface roughness and then decreases.
d) does not depend upon the surface roughness.
2. For Non- Fe materials the S-N curve
a) becomes asymptopic at 106 cycles.
b) becomes asymptopic at 610 cycles.
c) becomes asymptopic at 108 cycles.
d) slopes gradually even beyond 106 cycles.
3. A M.S component is subjected to a completely reversed bends stress of 100MPa. It has a depth of 5mm and surface
is perfectly polished and has a no stress concentration effects. It has to serve for unlimited life with 50% reliability
for mild steels Sut = 400MPa and Syt = 250 MPa. Its N= ? d) 4.
a) 2 b) 2.5 c) 1.25
4. In a M/c element, at a critical section, the Kt = 2, q = 0.5 ; then Kf is.
a) 1.25 b) 1.5 c) 1.75 d) 2.0
5. A plate made of steel is subjected to a completely reversed axial load of 30 kN q = 0.8 Kt = 2.5; σ e = 220 MPa.
Kload = 0.67 ; Ksize = 0.67 ; Kreliability = 0.897 ; N = 2 ; t = ?
a) 4.7 mm b) 11.3 mm c) 19.2 mm d) 29.5 mm
<>50mm +30KN
10mm
<>
6. The endurance strength of a component made of alloy steels depends on
a) diameter of the component
b) Method of Manufacturing
c) Ultimate tensile strength of the material
d) all of the above.
7. A component has A rotating beam test specimen when loaded to a stress of 900 MPa gives a life of 1000 load
cycles.when loaded to 500 MPa with stands 106 cycles . If the required life of the component is 50,000 cycles. What
is the max. stress it can be loaded.
a) 645 MPa b) 831.56 MPa c) 600MPa d) 700 MPa
8. A steel component has a theorectical stress concentration factor of 2.1 and a notch sensitivity of 0.5 . Its effect on
the endurance strength is
a) reduced by 35.5% b) reduced by 53% c) reduced by 36.36% d) reduced by 5.23%
9. A steel component hasthe following data :
Sut = 600 MPa, Sγt = 400 MPa, Surface finish factor = 0.8, size factor = 0.75, relialivility factor = 0.8, fartigue stress
concentration factor is 1.6. The endurance strength of the component is
a) 144 MPa b) 60 MPa c) 154 MPa d) 90 MPa
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MACHINE DESIGN
10. A component is subjected to a fluctuating normal stress of 100 + 150 MPA. If sut = 600 MPa and Se = 200 MPa. The
factor of safety based on soderberg critervion is
a) 0.92 b) 1.05 c) 1.45 d) 1.235
11. In the above problem the factor of safety based on Goodman criterion is
a) 0.92 b) 1.09 c) 1.05 d) 0.95
12. A component is subjected to a fluctuating stress. IF the F.O.S. based on the following critervions are arranged in
ascending order
1) soderling 2) Gerbar 3) Goodman
a) 1,2,3 b) 1,3,2 c) 3,2,1 d) 3,1,2
13. A component of made of steel (Sut = 600 MPa, Syt = 400 MPa) is to be designed for fatigue loading the componenet
is to be machined and has a surface linish factor it 0.8 of has a rauave cross of 6 mm side, expected reliability is 50%.
The fatigue stress concentration factor is .25. Its endurance strength in shear is
a) 64 MPa b) 125 MPa c) 100 MPa d) 96 MPa
14. The endurance strength of
a. machined componenet b. Rolled component
c. Forgedcomponenet d. Polished component
A) d>c>b>a B) a>b>c>d C) b<c<a<d D) c<b<a<d
15. It the component is subjected to a completely revevred
bending stress of magnitude 250 MPa. Its life will be (in
no. of reveloution), Sut = 380 MPa
a) 40 thousand b) 65 thousand
c) 1 million d) 0.5 million
16. A component to be used in space shuttle Ind space - 01 is to designed to with stand a complex fluctuating state of
stress, which can be reduced to the von miles stress of 25+25 MPa. The material used is special steel
(Sut = 667 MPa, Syt = 333 MPa) the component is to be polished and its diameter is 4.5 mm and has no stress
concentration. It has to with stand temperature flctuations so the temperature factor can be taken of 0.75. The
Reability is maximum possible to the reliability factor is 0.5 . The component has to with stand infinite load cycles.
A) What is the endurance / fatigue strength of the conponent in MPa is
a) 125 b) 166.75 c) 62.44 d) 93.75
B) The factor of rorlety for the componenet based on modified Goodman criterion is
a) 3.8 b) 4.2 c) 2.46 d) 3.465
17. A rod of circular cross section is subjected to an alternating tensile force, varying from 20 KN to 70 KN,
Su = 1000MPa, factor of sasfety = 2.0 (Neglect stress concentration effect and other correction factors)
A) The diameter of the rod according to Gerber’s Theory is (approx)
a) 8 mm b) 10 mm c) 12 mm d) 15 mm
B) The diameter at teh rod according to Goodman’s Theory is (approx)
a) 8 mm b) 10 mm c) 12 mm d) 15 mm
C) The diameter of the rod according to Soderberg Theory is (approx)
a) 10 mm b) 12 mm c) 15 mm d) 18 mm
18. An infinitely long plate has a small circular hole in the middle. The maximum stress concentration near the hole is
a) about 0 b) 1.5 c) 2.0 d) 3.0
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MECHANICAL ENGINEERING
19. A component with stands on no. of cycles of load without failure it is said to have minite life
a) 1 million b) 10 million c) 100 million d) 1000 million
20. Generally the low cycle fatigue refer to
a) up to 106 cycles b) up to 1000 cycles
c) 1000 cycles to 106 cycles d) >106 cycles
21. For the long bar shown in fig. the stress in the section A - A is 90 MPa uniform throughout. The maximum stress in
the section B - 13 near the hole. 90 MPa←111111222222 5mm B---------- ^ A
a) 274 MPa
b) 135 MPa B 50mm ←
c) 300 MPa
d) 150 MPa v A
22. A component is subjected to a dynamic stress given by 200 + 100 MPa. The material is ductile and has the following
properties Sut = 600 MPa, Syt = 400 MPa, Se = 100 MPa. The factor of ssfety based on Goodman’s & Sodeberg’s
criteria re respectilvely
a) 1.0 & 1.0 b) 0.75 & 0.75 c) 0.67 & 1.05 d) 0.75 & 0.67
23. Under fatigue load the life of a component is 0.3 million cycles under the load σ it life is 0.9 million cycles under the
1
load σ2. The component completes 0.1 million revolutions under load σ and then the load is reduced to σ . What
1 2
will be the expected life left in millions at revolutions is
a) 0.45 b) 0.6 c) 0.8 d) 0.75
24. Following the design of a shaft the theoretical stress concertration factor is found to be 1.4 from the charts. The
notch sensitiveity factor is found to be 0.75. The fatigue stress concerntration factor will be
a) 1.05 b) 1.86 c) 2.15 d) 1.3
25. A component made of steel subjected to completely reverred bending stress
Ultimate stress = 700 MPa Yield stress = 450 MPa and Fatigue strength is 200 MPa
A) If the component is no with stand 75,000 cyles as load. The maximum stress taht can be incluced in the
componenet is
a) 350 MPa b) 185 MPa c) 400 MPa d) 307 MPa
B) If the component is subjected to a completely reversed stress at 400 MPa the expected life is
a) 15000 cycles b) 35000 cycles c) 10000 cycles d) 80000 cycles
26. Which of the following is not a desirable property for shaft material
a) High strength
b) High stillness
c) High notch sensitivly
d) High wear residance
27. A key-way in a shaft reduces the strength by about
a) 10% b) 15% c) 25% d) 50%
28. In a cantilever beam the theovertical stress concentration beam 151.42 the theovertical notch sensitivity is 0.9 . The
tafigue strength reduction factors is
a) 1.24 b) 1.38 c) 1.45 d) 1.49
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MACHINE DESIGN
A
29. A loaded semi-infinite shaft plate having an elliptical hole ( = 2) in the middle as shown in the above fig. The
B
stress concentration factor at points either X or Y is [IES - 2K]
↓↓↓
a) 1 ( )
b) 3 ) (
( B)
) (
c) 5 ( A )
d) 7
↓↓↓
30. In designing a shaft for variabele loads, the S - N diagram cdan be drawn by [IES 2K7]
a) Joining the Sut at ‘0’ cycles and Se at 106 cycles by a straight line on a log S - log N graph.
b) Joining the 0.9 Sut at 1000 cycles and Se at 106 cycles by a straight line on a log S - log N graph.
c) Joining the 0.95 Sut at 1000 cycles and Se at 106 cycles by a straight line on a S - N graph.
d) Joining the Sut at ‘0’ cycles and Se at 103 cycles by a straight line on a log S - log N graph.
31. The design calculations for members subjected to fluctuating loads with the same factor of safety yield the most
conservative estimate when using [IES - 95]
a) Gerber relation b) Soderberg relation c) Goodman relation d) None of the above
32. If the size of a standard specification for fatigue testing machine is increasd, then the endurance limit for the
material will
a) Have the same value as that of standard specimen b) Increases
c) Decreases d) None of these
33. Stress concentration in a machine component of ductile materials not so harmful as it is in brittle material because
. (G - 89)
a) In ductile material local yielding may distribute stress concentration .
b) Ductile Material have large young’s modulus.
c) Poisson’s ratio is Larger in ductile materials.
d) Modulus of rigidity is larger in ductile materials.
34. Increase in radius of fillets
a) Improves the appearance of M/c part. b) reduce the strength of the part.
c) reduces stress concentration factor. d) Increases the notch sensitivity index.
35. Effect of stress raiser on different material is
a) the same b) indicated by notch sensitivity index.
c) independent of material d) Indicated by stress concentration factor.
36. Maximum stress in the part shown in fig. is induced at the section
a) A - A A 111111111222222222 B
b) B - B A
c) C - C →r C
d) fillets
→
rC
B
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MECHANICAL ENGINEERING
37. The process of shot peening increases the fatigue life of steel springs mainly because it results in. (G - 89)
a) surface hardening b) increased stiffness of the material
c) structural changes in the material d) residual compression at the surface.
38. A rectangular beam of uniform thickness changes from a height ‘H’ to a smaller height ‘h’ with fillet of radius r . the
theoretical stress concentration factor due to the fillet. (G - 90)
a) increases with increase in H / h
b) decreases with increase in H / h
c) increases with increase in H / h up to a value and decreases with further increase in H / h
d) is independent of H / h
39. Which causes fatigue in structures .
1) Max . stress 2) Residual Stress
3) Large No of loading cycles 4) Wide range of stress variation.
a) 1 & 2 b) 3 & 4 c) 2 , 3 & 4 d) 1, 2, 3 & 4
40. The design calculations for members subject to fluctuating loads with the same factor of safety yield the most
conservative estimates when using.
a) Gerber relation b) Soderberg relation c) Goodman relation d) none of the above.
41. The peak bending stress at a critical section of a component varies between and 100 MPa and
300 MPa Sut = 700 MPa ; Syt = 500MPa; E.L. for reversed bending is 350 MPa .find the factor of Safety ?
a) b) c) d)
******************************
“Vision without action is a daydream.
Action without vision is a nightmare”
Practice Question (Ans.)
1 - b, 2 - d, 3 -a, 4 - c,. 5 - d, 6 - d, 7 - a, 8 - a, 9 - d, 10 - a, 11 - b, 12 - b, 13 -d, 14 - d, 15 - a, 16A - a, 16B - b, 17A - b, 17b - d,
17C - d, 18 - c, 19 - a, 20 - b, 21 - c, 22 - d, 23 - b, 24 - d, 25a- d, 26 - c, 27 - c, 28 - c, 29 - c, 30 - b, 31 - b, 32 - c, 33 - a, 34 - c,
35 - b, 36 - d, 37 - d, 38 - a, 39 - b, 40-b, 41-sol.
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MACHINE DESIGN
3. BOLTED, RIVETEDANDWELDED JOINTS
One Mark Questions :
1. Weldments in fabricated steel beams are designed for [GATE-ME-87]
a) bending stresses at the flange
b) shear stresses in transverse plane
c) combination of bending and shear
d) none of these because in fabricated beams welds do not get stressed
2. If the ratio of the diameter of rivet hole of the pitch of rivets is 0.25, then the tearing Efficiency of the joint is
[GATE-ME-96]
a) 0.50 b) 0.75 c) 0.25 d) 0.87
3. The bolts in a rigid flanged coupling connecting two shafts transmitting power are subjected to [GATE-ME-96]
a) shear force and bending moment b) axial force
c) torsion d)torsion and bending moment
4. Bolts in the flanged end of pressure vessel are usually pre-tensioned. Indicate which of the following statements in
not true [GATE-ME-98]
a) Pre-tensioning helps to seal the pressure vessel
b) Pre-tensioning increase the fatigue life of the bolts
c) Pre-tensioning reduces the maximum tensile stress in the bolts
d) Pre-tensioning helps to reduce the effect of pressure pulsations in the pressure vessels
Two Marks Questions :
5. A 60 mm long and 6 mm thick fillet weld carries a steady load of 15 KN along the weld. The shear strength of the weld
material is equal to 200 MPa. The factor of safety is [GATE-ME-06]
a) 2.4 b) 3.4 c) 4.8 d) 6.8
6. A bolted joint in shown below. The maximum shear stress, in MPa, in bolts A and B respectively are
3 holes of M 10 x 1.75 mm bolts [GATE-ME-07]
6mm thick
----
20 F = 10 kN
a) 242.6, 42.5 <>< >< > <>C
b) 42.5, 242.6 ---------- B
c) 42.5, 42.5 ---------------A
d) 2472.6, 242.6 40
---------- ---------
40
----------
20
----
150
STATEMENT FOR LINKEDANSWER QUESTIONS 07AND 08
A steel bar of 10 mm x 50 mm is cantilevered
with two M12 bolts (P and Q) to support PQ 4 kN
a static load of 4 KN as shown in
figure aside -----------------------------------
[GATE-ME-08] 0.4 1.8 m >
< ><
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MECHANICAL ENGINEERING
7. The primary and secondary shear loads on rivet p, respectively are
a) 2 KN, 20 KN b) 20 KN, 2KN c) 20 KN, 0 KN d) 0 KN, 20 KN
8. The resultant shear stress on rivet P is closest to
a) 132 MPa b) 159 MPa c) 178 MPa d) 195 Mpa
9. A bracket shown in fig. is rigidly mounted on wall using four rivets. each rivet is 6 mm in diameter and has an
effective length of 12 mm. < 3 2 >< 3 2 > [GATE-ME-10]
20
100 1000N
---------------------
75
---------------------
25
Direct shear stress in MPa in the most heavily loaded rivet is
a) 4.4 b) 8.8 c) 17.6 d) 35.2
10. 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 30mm. If the allowable shear stress of the weld is 94MPa, considering the minimum throat
area of the weld, the maximum alloable transverse load in kN is [GATE-ME-12]
a) 14.44
b) 17.92 F F
c) 19.93
d) 22.16
***************
3. BOLTED, RIVETEDANDWELDED JOINTS
One Mark Quesions :
1-c, 2-b, 3-a, 4-c.
Two Marks Quesions :
5-b, 6-a, 7-a, 8-b, 9-b, 10-c.
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MACHINE DESIGN
Riveted Joints (Practice Questions)
1. Tearing efficiency of a double riveted lap joint having a pitch of 60 mm and rivet hole dia. of 18 mm is.
a) 30% b) 35% c) 60% d) 70%
2. Two plates of 1.5 mm thick are connected by a double riveted lap joint with zig-zag rivets. The dia. of rivet hole is
24 mm. the allowable tensile stress of plate is 80MPa and the allowable shear stress of rivet is 80MPa. the pitch of the
joints.
a) 50mm b) 60mm c) 70mm d) 80mm.
3. A double riveted bolt joint is shown below pitch of the joint is 120 mm, the normal dia. of rivet is 22 mm and thickness
of plate = 10mm σ = 420 MPa ; Ts = 350 MPa. the rivet hole dia. is 1.5mm more than rivet dia.
t
A). The tear strength of the plate in the outer row is;
a) 202 kN
b) 405 kN
c) 675 kN
d) 825 kN p
B). The η of joint
a) 42%
b) 60%
c) 80%
d) 95%
4. In a riveted joints, the dia. of rivet hole is 20mm. the pitch of the joint is 3.5 times the dia. of rivet hole. The efficiency
of the joint is.
a) 50% b) 60% c) 70% d) 80%
5. The diameter of a lancashire boiler is 2.5m. the pressure of steam is 1 MPa. If the efficiency of the longitudunal joint
is 80% and the maximum tensile stress is limited to 80 MPa, the necessary thickness of the plate is.
a) 14.5mm b) 19.5mm c) 25.5mm d) 28.5mm
6. The efficiency of single riveted lap joint having a rivet hole diameter of 30mm pitch 80 mm and plate thickness of 12mm
is.
a) 62% b) 75% c) 82 % d) 85%
7. A riveted joint has been designed to support an eccentric load P. The load generates value of F1 equal to 4kN and F2
equal to 3kN. the cross sectional area of each rivet is 500mm2 consider the following statements .
1. The stress in the rivet is 10 MPa. F2 p
2. The value of eccentricity is 1 F1 L
Answer Key:- F2
1 - d, 2 - c, 3A - b, 3B - c, 4 - c, 5 - b, 6 - a, 7 - ? F1
“It is easier to do a job right than to explain why you didn’t”
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MECHANICAL ENGINEERING
4. BRAKES
Two Marks Questions :
1. In a band brake the ratio of tight side band tension to the tension to the tension on the slack side is 3. If the angle
of band on the drum is 1800 the coefficient of friction required between drum and the band is [GATE-ME-03]
a) 0.20 b) 0.25 c) 0.30 d) 0.35
Statement for linked answer questions 02 and 03 200 mm
A band brake consists of a lever attached to one end of the band.
The other end of band is fixed to the ground. The wheel has a radius
of 200 mm and the wrap angle of band is 2700. The braking force
applied to the lever is limited to 100 N and the coefficient of friction 111111 100 mm
between the and and the wheel is 0.5. No other information is given. 1m
1m
[GATE-ME-05]
2. The maximum tension that can be generated in the band during braking is
a) 1200 N b) 2110 N c) 3224 N d) 4420
3. The maximum wheel torque that can be completely braked is
a) 200 N-m b) 382 N-m c) 604 N-m c) 844 N-m
4. A block brake shows below has a face width of 300 mm and a mean coefficient of friction of 0.25. For an activating
force of 400 N, the braking torque in N-m is [GATE-ME-07]
200 mm 400 mm P
400 N
----- 4 5-0- - - ------------------ 300 mm
150 mm
----------------------
a) 30 b) 40 c) 45 d) 60
5. A band brake having hand width of 80 mm, drum diameter of 250 mm, coefficient of friction 0.25 and angle of wrap
of 270 degrees is required to exert a friction torque of 1000 N-m. The maximum tension (in kN) developed in the band
is [GATE-ME-10]
a) 1.88 b) 3.56 c) 6.12 d) 11.56
6. A force of 400 N is applied to the brake drum of 0.5m diameter in a -----------------
band - brake system as shown in the figure, where the wrapping 400 N
11111112222222
angle is 1800. If the coefficient of friction between the drum and the
band is 0.25, the braking torque applied, in N.m is ----------------------
[GATE-ME-12] ^
a) 100.6 b) 54.4
c) 22.1 d) 15.7
*************
4. BRAKES
Two Marks Quesions : 1-d, 2-b, 3-b, 4-c, 5-d, 6-b.
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MACHINE DESIGN
Brakes (Practice Questions)
1. A 250 mm radius brake drum contacts a single shoe as shown R=250mm
in fig. and sustains a toque of 300N-m at 500 rpm. coefficient N F
120N
of friction is 0.3. force F required for braking in the case of 40 300
1000
counter CW rotation of the brake drum is.
a) 1152 N. b) 1248 N
c) 4000N d) 2000 N
2. The hand brake as shown in fig is applied to a shaft carrying 100 320
a FW of mass 450 kg. The drum diameter is 250 mm and the 450
coefficient of friction is 0.25. the torque applied on the
drum is.
a) 80N-m
b) 120N-m
c) 200N-m
d) 250N-m
3. A band brake shown below absorbs 30 kw when a drum
rotates at 500 rpm. the dia. of drum is 500mm and µ = 0.3.
the allowable tensile stress of band material is 80 MPa and
band thickness is 3 mm, then the width of the band is. T2 p
a) 13mm 10mm 50mm
b) 18mm
c) 25 mm
d) 34 mm
4. In case of brakes identity the correct statements:-
1) When the self energisation is max. possible; self locking can be avoided.
2) When the self energisation is at lower possibility of ; self locking can be avoided.
3) With out self energisation there is no possibilityof self locking.
4) A single block brake can be designed to have the selflocking for both the directions of rotation of drum by choosing
the pivot property.
a) 2 : 3 b) 2 , 3 , 4 c) 1 , 3, 4 d) 1 , 4
5. A brake has to stop a car with in 10m after the brake are applied. the mass of the car is 500kg and the car travel at
72 kmph before the brakes are applied. what is the energy to be absorbed by the brake.
a) 10 kw b) 158 kw c) 100 kw d) 465 kw.
6. In a band brake shown in fig. if it is designed for the self locking condition with ratio of tensions 2.2, the ratio a/b is
a) 2.2/L b) L/2.22 c) 1/2.2 d) 2.2
7. A band Brake users a V- belt. the pitch dia. of the V- grooved shear µ 500 mm. the groove angle is 450 and the
coefficient of friction is 0.25. the maximum power rating for 300 rev / min is.
a) 5.4 KW b) 10.8 KW c) 8.4 KW d) 12.8 KW
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MECHANICAL ENGINEERING
8. A simple Band Brake has the right side of the band attached to a fixed pivot. the angle of wrap is 280. about a 480 mm
diameter drum. A torque of 170 Nm is surtained at 900 rev / min and the coefficient of friction is 0.2. the right side
tension is.
a) 1000 N b) 1210N c) 1430 N d) 1605 N
9. A Band Brake is lined with 10 wooden blocks each of which subtends an angle of 180 at the center at the Brake drum
if the coefficient friction between the blocks and the wheel is0.36, the ratio of tension is.
a) 2.05 b) 2.5 c) 3.1 d) 4.6
10. A band and block brake having 14 blocks each at which subtends an angle of 150 at the centre is applied to a drum at
90 cm effective diameter. The drum and flywheel mounted on the same shaft have mass at 2000kg and have a
combined radius at gyration at 50 cm. the two ends of the band are attached to pins on opposite sides of the brake
lever at distance at 30 mm and 120 mm from the fulcrum. A force at 200N is applied at a distance at 750 mm from the
fulcrum (µ = 0.25).
A) The maximum Breaking torque is.
a) 2400 N-m b) 3000 N-m c) 4200 N-m d) 6100 N-m
B) The Angular retardation of drum is.
a) 2.8 rad / s2 b) 3.2 rad / s2 c) 4.7 rad / s2 d) 6.4 rad / s2
C) Time taken by the system to come to rest from the rated speed of 360 rpm.
a) 6 sec b) 8 sec c) 10 sec d) 12 sec
11. A 360 mm radius brake drum contacts a single shoe as shown in fig. below and sustain 225 N-m Torque at
500 rev / min. for a coefficient of friction of 0.3 the rate of heat generated is.
a) 11.8 KW
b) 12.4 KW
c) 14.6 KW
d) 18.2 KW
12. Self locking is not possible in case of.
a) Simple block brake
b) Simple band brake .
c) differential band brake
d) interanal expanding shoe brake.
13. For the block brake shown in figure. The braking torque is ____________, if the coefficient of friction is 0.35 and the
drum rotates in clockwise direction.
a) 0.5 kN-m
b) 3 kN-m
c) 0.2 kN-m
d) 1 kN-m
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MACHINE DESIGN
14. For the band brake shown in fig. the drum dia is 50 cm. The co-efficient of friction is 0.25 and the drum rotates at
72 rpm, F = 3 kN.
A) A braking torque for the clock wire rotation of the drum is.
a) 1.375 KN - m b) 5.87 KN - m c) 46.25 KN - m d) 0.92 KN - m
d) 0.92 KN - m
B) The braking torque for CCW rotation of the drum.
a) 1.375 KN - m b) 46.25 KN - m c) 5.87 KN - m
********************
Brakes (Ans.) Practice Questions :
1 - b, 2 - a, 3 - a, 4 - a, 5 - c, 6 - d, 7 - c, 8 - b, 9 - c, 10A - a, 10B- c, 10C- c, 11 - a, 12 - b, 13 - c, 14A- b, 14B - d
“The question is not what you look at, but what you see”
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MECHANICAL ENGINEERING
5. BEARINGS
1. The expected life of a ball bearing subjected to a load of 9800N and working at 10000RPM. is 3000 hours. What is the
expected life of the same bearing for a similar load of 4900 N and a speed of 2000 rpm [GATE-ME-87]
a) Unchanged b) 12,000 hours c) 1,500 hours d) 6,000 hours
2. If the load on a ball bearing is reduced to half, the life of the ball bearing will [GATE-ME-88]
a) increase 8 times b) increase 4 times c) increase 2 times d) not change
3. Match the rolling element bearings with the most appropriate loading condition [GATE-ME-91]
Bearing - typ Loading condition
a) Ball bearing p) Tangential load
b) Roller bearing q) Radial load
c) Needle bearing r) Heavy radial load with impact
d) Taper roller bearing s) Light radial laod with space limitation
t) Heavy radial and axial load
u) Fatigue load
4. Spherical roller bearing are normally used [GATE-ME-92]
a) for increase radial load b) for increased thrust load
c) when there is less radial load d) to compensate for angular misalignment
5. The basic load rating of a ball bearing is [GATE-ME-98]
a) the maximum static radial load that can be applied without causing any plastic deformation of bearing
components
b) the radial load at which 90% of the group of apparently identical bearings run for one million revolutions before
the first evidence of failure
c) the maximum radial load that can be applied during operation without any plastic deformation of bearing
components
d) a combination of radial and axial loads that can be applied without any plastic deformation
6. The dynamic load capacity of 6306 bearing is 22 KN. The maximum radial load it can sustain to operate at 600 rev/
min, for 2000 hours is [GATE-ME-97]
a) 4.16 KN b) 3.60 KN c) 6.25 KN d) 5.29 KN
7. Match the following [GATE-ME-97]
List-I List-II
a) Automobile wheel mounting on axle 1. Magneto bearing
b) High speed grinding spindle 2. Angular contact bearing
c) IC-Engine connecting rod 3. Taper roller bearing
d) Leaf spring eye mounting 4. Hydrodynamic journal bearing
5. Sintered metal bearing
6. Teflon/Nylon bush
8. The life of a ball bearing at a load of 10 KN is 8000 hours. Its life in hours, if the load is increased to 20 KN, keeping
all other conditions same is [GATE-ME-2000]
a) 4000 b) 2000 c) 1000 d) 500
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MACHINE DESIGN
9. A ball bearing operating at a load F has 8000 hours of life. The life of the bearing, in hours, when the load is doubled
to 2F is [GATE-ME-07]
a) 8000 b) 6000 c) 4000 d) 1000
10 Two identical ball bearing P and Q are operating at loads 30kN and 45kN respectively. The ratio of the life of bearing
P to the life of bearing Q is [GATE-ME-11]
a) 81/6 b) 27/8 c) 9/4 d) 3/2
11. Starrting friction is low in [GATE-ME-92]
a) hydrostatic lubrication b) hyddrodynamic lubrication
c) mixed (or semi-fluid) lubrication d) boundary lubrication
12. In thick film hydrodynamic journal bearings, the coefficient of friction [GATE-ME-96]
a) increases with increase in load b) is independent of load
c) decreases with increase in load d) may increase or decrease with increase in load
13. To restore stable operating condition in a hydrodynamic journal bearing, when it encounters higher magnitude
loads. [GATE-ME-97]
a) oil viscosity is to be decreased b) oil viscosity is to be increased
c) oil viscosity index is to be increased d) oil viscosity index is to be decreased
14. Which one of the following is criterion in the design of hydrodynamic journal bearings ? [GATE-ME-05]
a) Sommerfiled number b) Rating life
c) Specific dynamic capacity d) rotation factor
15. A natural feed journal bearing of diameter 50 mm and length 50 mm operating at 20 revolutions/sec carries a load of
2 KN. The lubricant used has a viscosity of 20 mPa/s. The radial clearance is 50µm. The sommerfield number for the
bearing is [GATE-EM07]
a) 0.062 b) 0.125 c) 0.250 d) 0.785
16. A journal bearing has a shaft diameter of 40 mm and a length of 40 mm. The shaft is rotating at 20 rad/s and viscosity
of the lubricant is 20mPa.s. The clearance is 0.020 mm. The loss of the torque due to viscosity of the lubricant is
approximately [GATE-ME-08]
a) 0.040 N m b) 0.252 Nm c) 0.400 Nm d) 0.652 Nm
************
BEARI NGS (ANS.)
1-b, 2-a, 3-a-u b-q c-r d-t, 4-d, 5-b. 6-d, 7-a3 b2 c4 d6, 8-c, 9-d, 10-b, 11-a, 12-c, 13-b, 14-a, 15-b, 16-a.
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MECHANICAL ENGINEERING
Bearings Pracice Questions
1. The performance of a hydrodynamic journal bearing is a function of.
a) Reynolds No. b) Sommer field No. c) speed d) Bearing Modulus
2. When the lubricating oil is forced between the journal and bearing by external pressure, the following is known as
a) zero film bearing b) Boundry lubricated bearing
c) Hydrostatic d) Hydrodynamic bearing
3. Consider the following statements regarding loundary lubrication conditions in hydrodynamic journal bearings
1. It is an undesirable condition. 2. It always occurs duving starting and stopping of the journal
3. It necessiates frequent repair of the journal.
4. This condition can be completely eliminated by using high viscosity lubricant.
Which of the statements given alove are crrect?
a) 1, 2 and 4 b) 2, 3and 4 c) 1and 2 d) 3 and 4
4. A full journal bearing with a journal diameter of 100 mm and a bearing length of 100 mm is subjected to a radial load
of 10000N. the lubricant is SAE40 at 70 has a viscosity of 10 c.p.It has radial clearance of 0.05mm and µ=0.001 .
The journal rotates at 10 yps.whilr the bearing is Stationary.
A. The sommerfield N0.at the operates conditions is
(a) 0.1 b) 0.01 c) 0.001 d) 1.0
B. The rate at which the heat is generated in the bearing in Joules/sec.
a) 31.4 b) 15.7 c) 6.82 d) 3.14
5. A bearing of 50mm in diameter has a shaft speed of 320 rpm and a lubricants oil of viscosity 0.06 kg/ms. the dia.
clearance is 0.15 mm and the bearing pressure is 1.5 MPa . if it is designed for a speed of 320 rpm and pre. is 1.5 MPa,
clearance of 0.12mm, the change made for the viscosity is (in kg/ms).
a) 0.084 b) 0.0184 c) 0.0384 d) 0.0684
6. A ball bearing is operated on a work cycle consists of the parts: a radial load of 3000N at 1440 rpm for one quarter
cycle, a radial load of 5000N at 720 rpm for one half of cycle and a radial load of 2500N at 1440 rpm for the remains cycle.
The expected life of the bearing is 10,000 hrs. the dynamic load carry capacity of the bearing is.
a) 11kN b) 22kN c) 33kN d) 55kN
7. The radial load acts on a ball bearing is 5kN and the expected life for 90% of the bearings is 8000 hr. The dynamic carry
capacity of the bearing, when the shaft rotates at 1450 rpm, is
a) 17.6kN b) 27.4kN c) 35.2kN d) 44.3kN
8. Choose the proper bearing to carry high loads at high speeds
a) Rolling contact bearing b) Hydrodynamic bearing c) Hydrostatic bearing d) Bush bearing
9. In a journal bearing the radial clearance is 0.05mm and the eccentricity ratio is 0.25. Then minimum film thickness is.
a) 0.125mm b) 0.0125mm c) 0.375mm d) 0.2mm
10. A full journal bearing 100mm dia. and 200mm long is supporting a radial load of 25kN.operating at a speed of 960 rpm.
if the resulting coefficient of friction value is 0.003, the power loss in the bearing is.
a) 377 watts b) 300 watts c) 750 watts d) 1.05 kw
11. A ball bearing is subjected to a radial load of 2500N and axial force of 1000N. the catalogue gives the following
data.Radial factor = 0.4, Axial thrust factor = 1.5 , static load rating = 10,000N. Dynamic load rating = 7500N, The
bearing life in millions of revolutions is .
a) 1 b) 9 c) 27 d) 8
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MACHINE DESIGN
12. A ball bearing is subjected to a radial load of 3000N is expected to have a life of 40 million revolutions with a reliability
of 95%. If the desired reliability is 50%, the life of the bearing millions of revolution is.
a) 200 b) 260 c) 320 d) 370
13. The preferred bearing for oscillatory conditions .
a) deep groove ball bearing b) spherical roller bearing
c) needle roller bearing d) tapered roller bearing
14. When the thickness of oil film is of the order of microns, than the lubrication is called.
a) unstable lubrication b) stable lubrication
c)Hydrostatic lubrication d) Elasto hydrodynamic lubrication
15. The type of bearings used, when the radial space is limited to.
a) Deep groove ball bearings b) cylindrical bearings.
c) Needle bearings d) Tapered roller bearings.
16. A shaft running at 900 rev/min is supported by bearings 50 mm in diameter & 75 mm in length. the bearings operate
in still air. the oil used has a viscosity of 0.013kg/ms and the diametrical clearance is 0.05mm. the permissible load
corresponding to the heat generation of 35.8 watts is. [F = 0.326 [ZN/P ] [D/d] + 0.002]
a) 250N b) 350N c) 450 N d) 550N.
17. A ball bearing has a specific dynamically capacity of 40kN. the desired life is 5000hrs for 90% of the bearings. the
equivalent radial load carried by the bearing at 400rev/min is.
a) 7kN b) 8kN c) 9kN d) 10kN
18. Match List - I (bearings) with List- II (Applications) and select the correct answer.
List - I List - II
P. Angular Contact ball bearing. 1. Permit slight axial displacement.
Q. Spherical roller bearing. 2. for combined radial & axial loads.
R. Cylindrical roller bearing. 3. for carrying heavy axial loads.
S. Deep groove ball bearing. 4. self aligning
a) P - 3, Q - 2, R - 1, S - 1. b) P - 4, Q - 3, R - 2, S - 1.
c) P - 3, Q - 4, R - 1, S - 2. d) P - 4, Q - 2, R - 1, S - 3.
Linked Statement
A shaft 150mm in dia. rotates in a bearing at 2000rpm. the length of the bearing is 1.4 times its dia. the bearing
pressure is N/mm2 & the coefficient of friction at the bearing surface is 0.005
19 Load on the bearing is.
a) 31.5 kN b) 42.7 kN c) 53.6 kN d) 67.3 kN
20 Heat generate in the bearing is.
a) 1.03 kw b) 1.74 kw c) 2.47 kw d) 3.52 kw
21. The bearings that are capable of taking considerable misalignment are.
a) cylindrical roller bearings. b) Hellical roller bearings.
c) spherical roller bearings. d) Tapper roller bearings.
22. A bearing has a specific dynamic radial capacity of 40 kN. the desired life is 5000 hrs for 90% of the bearings . the
equivalent radial load at 400 rev/min. is
a) 8.11 kN b) 9.43 kN c) 10.27 kN d) 12.56 kN
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MECHANICAL ENGINEERING
23. The radial load acting on a single row deep groove ball bearing is 30 kN. the bore of the bearing is 50mm. The
coefficient of friction is 0.0015. the friction is torque is.
a) 1.25Nm b) 1.575Nm c) 2.25Nm d) 3.27Nm
Linked Statement
A bearing has a specific dynamic radial capacity of 40 kN.speeds is 400 rev/min. the desired life is 5000 hrs for 90% of
the bearings .
24. The rating life in millions of revolutions is;
a) 120 b) 170 c) 220 d) 340
25. The equivalent radial load is.
a) 4.35 kN b) 5.27 kN c) 7.05 kN d) 8.11 kN
26. Choose;
a) Both (a) and (r) are true and (r) is the correct reason for (a).
b) Both (a) and (r) are true and (r) is not the correct reason for (a).
c) Both (a) and (r) are false. d) (a) is true but (r) is false.
Assention (a):
An important of film lubrication is that once a lubricant film is formed on the making surfaces by running the bearing
with a lubricant having a high degree of oilness it is possible to change to a lubricant with a much lower oilness.
Reason (r):
Lubricants of high oiliness are liable to decompose or oxidize and hence are not suitable for general lubricative
purposes.
27. A journal rotating in clockwise direction at normal speed inside a fluid bearing will be.
a) at the bottom most position of the bearing. b) towards the left side of the bearing.
c) towards the right side of the bearing. d) at the centre of the bearing.
28. The antifriction bearings are -
a) Journal bearings b) Gas lubricated bearings.
c) Ball & roller bearings d) All of the above.
29. The bearing suitable for very high shock load is.
a) Multigroove roller bearings b) Hydrostatic bearings.
c) Hydrodynamic bearings d) Sintered bush bearing.
30. A full journal bearing 100 mm dia. 100m long supports 25kN at an operating speed of 600 rpm. if the coefficient of
friction value is 3 x 10-3 , the power loss is.
a) 2.4 kw b) 0. 24 kw c) 0.85kw d) 0.54 kw
31. A deep groove ball bearing having static load rating of 16,600N and dynamic load rating of 30,700 N is subjected to
an equivalent load of 7742 N. the life of the bearing in millions of revolutions with a reliability of 90% is.
a) 4.32 b) 62.35 c) 9.85 d) 6.32.
III. Linked Statement
A full journal bearing 100 mm dia. and 100 mm long is to support a radial load of 20kN at an operating speed of 600 rpm,
it is to operate at a sommerfield no. of 0.1 & the radial clearance is 0.1 mm and the resulting coefficient of friction value
is 0.004.
32. Viscosity of the oil to be used is.
a) 20 cp b) 40cp c) 80 cp d) 100 cp
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MACHINE DESIGN
33. Frictional power loss is:
a) 0.25 kw b) 0.19 kw c) 0.5 kw d) 0.44 kw
IV. Linked Statement
A ball bearing is anticipated to have a life of 400 million revolutions under an equivalent radial load of 10 kN with a
reliability of 90%.
34. If the load is 22kN the life of the bearing with 90% reliability is.
a) 37.6 mr b) 41.32 mr a) 42.6 mr d) 142 mr
35. With a reliability of 60% under the load 22 kN the expected life is.
a) 600 mr b) 240 mr c) 145 mr d) 180 mr
36. The preferred bearing for oscillatory conditions:
a) Deep groove ball bearing
b) Spherical roller bearing
c) Needle roller bearing
d) Tapered roller bearing.
37. The preferred bearing for heavy shock loads.
a) Hydrostatic bearing
b) Hydrodynamic bearing.
c) Tilted pad thrust bearing
d) Collar bearing.
38. At high speeds the load carrying capacity of the following bearing.
a) Hydrostatic bearings b) Hydrodynamic bearings.
c) Antifriction bearing d) Jewel bearings.
A) a>b>c>d B) b>c>a>d C) c>a>b>d D) d>c>a>b
39. Match the following.
(a) Hydrodynamic bearing. 1. low speeds & high thrust loads.
(b) Hydrostatic bearing. 2. High speed & shock loads.
(c) Antifriction bearing. 3. Any speed any load.
4. Moderate speed & Moderate loads.
A) a - 2, b - 1, c - 4 B) a - 1, b - 2, c - 3 C) a - 2, b - 3, c - 4 D) a - 3, b - 2, c - 4
40. The dimensions of a hydrostatic thrust bearing with a square oil groove are shown in the fig. The pressure
distribution can be assumed to be varying lineraly from supply pressure of 10 MPa at the inner edge to atmospheric
pressure at the outer edge. what is its load carrying capacity.
a) 37.5 kN b) 25 kN c) 62.5 kN d) 50 kN
41. A tapered roller bearing has a static load rating of 10 kN and a dynamic load rating of 15 kN. it is subjected to a static
axial load of 2 kN and a thrust load of 1 kN. the axial load factor is 0.9 and thrust load factor is 1.2 . its life in millions
of revolutions is.
a) 125 b) 213.75 c) 10.08 d) 55.33.
42. Bearing characteristic number for the following cases:
a) Thick film lubrication at moderate speeds. b) Thick film lubrication at high speeds.
c) Thin film lubrication. d) partial film lubrication.
A) d < c < b < a B) c < d < b < a C) c < d < a < b D) a < b < d < c
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MECHANICAL ENGINEERING
43. Choose:-
A) Both (a) & (r) are true & (r) is the correct reason for (a).
B) Both (a) & (r) are true but (r) is not the correct reason for (a).
C) Both (a) & (r) are false.
D) (a) is true but (r) is false.
Assention (a) :
In a journal bearing the bearing pressure is inversely proportional to the bearing diameter.
Reason (r) :
Bearing pressure is proportional to the bearing length.
44. Match the Following :-
a) Tapered roller bearing. 1. Hydraulic turbines
b) Hydrodynamic bearings. 2. Bowl Mills.
c) Hydrostatic bearings. 3. Rail coaches
d) Needle roller bearings. 4. Scooter suspension
5. High speed gas tubines.
a) a - 3,b - 2,c - 1,d - 4 b) a - 4,b - 5,c - 3,d - 2. c) a - 2,b - 1,c - 4,d - 5. d) a - 3,b - 4,c - 5,d - 1.
V. Linked statement:-
A full journal bearing 100mm in diameter & 100 mm long has to support a radial load of 10 kN at an operating speed of
600 rpm. the radial clearance is 0.2 mm & the eccentric ratio is 0.25. the resulting coefficient of friction value is 0.005.
the vis cosity of the oil is used is 25c poise.
45. The sommerfield number is.
a) 0.03125 b) 0.08 c) 0.193359 d) 0.05
46. The frictional powerloss is.
a) 0.05 kw b) 0.157kw c) 0.546 kw d) 1.05 kw .
47. The minimum film thickness is.
a) 0.05 mm b) 1.25 mm c) 0.15 mm d) 0.8 mm.
VI. Linked statement:-
A full journal bearing of dia. 200 mm & length 200 mm carries a steady radial load of 40kN at a speed of 300 rpm. the
radial clearance is 0.3mm & the viscosity of the oil is used30 Cpoise.
48. The equivalent coefficient value based on pelroff’s equation is.
a) 0.1 b) 0.01 c) 0.001 d) 0.0001
49. The frictional powerloss in kw.
a) 0.1256 b) 1.256 c) 12.56 d) 0.01256 .
50. For the following three bearings, which of the statements are correct. (IES-08)
SKF 2015, 3115 and 4215
a) bore is common but width is increasing.
b) outer dia. is common but bore is increasing.
c) width is common but outer dia. is decreasing.
d) bore is common but outer dia. is decreasing.
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MACHINE DESIGN
51. A journal bearing with hydrodynamic lubrication is running steadily with a certain amount of minimum film thickness.
when the load and speed are doubled, how does the minimum film thickness very? (IES-08)
a) remains unchanged b) gets doubled
c) gets reduced to one fourth of original value. d) gets reduced to half of original value.
52. Which one of the following is correct ? (IES-08)
A hydrodynamic slider bearing develops load bearing capacity mainly because of.
a) slider velocity b) wedge shaped oil film.
c) oil compressibility. d) oil viscosity.
53. Increase in values of which of the following results in an increase of the coefficient of friction in a hydrodynamic
bearing ? (IES-07)
1. viscocity of the oil
2. clearance between shaft and bearing.
3. shaft speed .
select the correct the answer using the code given below:
a) 1 & 2 only b) 1 & 3 only c) 2 & 3 only d) 1, 2 & 3.
Consider the following statements:
54. For a journal rotating in a bearing under film lubrication conditions, the frictional resistance is.
1. proportional to the area of contact.
2. proportional to the viscosity of lubricant.
3. proportional to the speed of rotation.
4. Independent of the pressure.
Which of the statements given above are correct?
a) 1, 2, 3 and 4 b) 1 & 4 only c) 2 ,3,and 4 only d) 2 and 3 only.
55. Satisfactory hydrodynamic film in a journal bearing is formed when.
a) journal speed is low, unit pressure on bearing is high and viscosity of lubricant used is low.
b) journal speed is low, unit pressure on the bearing is low and viscosity of lubricant used is low.
c) journal speed is high, unit pressure on the bearing is high and viscosity of lubricant used is high.
d) appropriate combination of journal speed , unit pressure on bearing and lubricant viscosity exists resulting in low
coefficient of friction.
56. It is seen from the curve that there is a minimum value of the coefficient of friction for a particular value of the bearing
characteristic no. denoted by a. what is this value of thebearing characteristic no. called ? (IES-04)
a) Mckee’s number. b) Reynold’s number. c) Bearing modulus. d) sommerfield number.
57. A journal bearing has a shaft dia. of 40mm and a length of 40 mm. the shaft is rotating at 20 rad/s and the viscosity of
the lubricant is 20MPa-s. the clearance is 0.02mm.the loss of torque due to the viscosity of the lubricant is approxi
mately. (G-08)
a) 0.04N-m b) 0.252N-m c) 0.4N-m d) 0.652N-m.
Bearings (Ans.) ************
1-d, 2-c, 3-?, 4-c, 5-c, 6-c, 7-d, 8-b, 9-c, 10-a, 11-c, 12-d, 13-c. 14- a, 15 - c, 16 - ?, 17 - ?, 18 - c, 19 -a, 20 - c, 21 - b, 22 - a,
23 - a, 24 - a, 25 - d, 26 - c, 27 - b, 28 - c, 29 - c, 30 - b, 31 - b, 32 - c, 33 - a, 34 - a, 35 - c, 36 - c, 37 - b, 38 - b, 39 - ?, 40 - ?,
41- ?, 42-c, 43 - d, 44- a, 45 - a, 46 - b, 47 - c, 48 - c, 49- a, 50 -a, 51 -a, 52 - b, 53 - b, 54 - d, 55 - c, 56 - c, 57 - a.
“It is not length of life, but depth of life”
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MECHANICAL ENGINEERING
6. CLUTCHES
One Mark Questions :
1. Axial operation claw clutches having self-locking tooth profile [GATE-ME-87]
a) can be disengaged at any speed b) can be disengaged only when unloaded
c) can be engaged only when unloaded d) can work only with load
Two Marks Questions :
2. A disk clutch is required to transmit 5KW at 2000 rpm the disk has a friction lining with Coefficient of friction equal
to 0.25. Bore radius of friction lining is equal to 25mm. Assume uniform contact pressure of 1 MPa. The value of
outside radius of the friction lining is [GATE-ME-06]
a) 39.4 mm b) 49.5 mm c) 97.9 mm d) 142.9 mm
3. A clutch has outer and inner diameters 100 mm and 40 mm respectively. Assuming a uniform pressure of 2 MPa and
coefficient of inner 0.4, the torque carrying capacity of the clutch is [GATE-ME-08]
a) 148 Nm b) 196 Nm c) 372 Nm d) 490 Nm.
**************
CLUTCHES (PRACTICE QUESTIONS)
1. A S.P.C with both the both sides effective is used to run a m/c through a shaft rotation at a uniform speed of 240 rpm.
µ = 0.25 ; Rt = 120 ; Ro = 240 ; Pmax = 120kPa ; I=7kg-m2 Assume uniform wear theory. the time to attain the full speed
by the m/c is
a) 0.45 b) 1sec c) 1.45 d) 2.65
2. The torque transmission capacity of a cone clutches 300N-m .the mean dia is 250mm and semi cone angleis
12o30’.the µ = 0.25, p at the mean radius is 0.14 MPa . (Assume uniform pre). the width of the contact surface is.
a) 87mm b) 115mm c) 187mm d) 252mm
3. In a plate clutch the presure between the plates during the operation depends on.
a) Axial force b) coefficient of friction c) plate dimensions d) all of the above.
4. A plate clutch consists of a pair of contacting surface the inner and outer radius of the friction disc are 100mm and
200 mm respectively. the coefficient of friction is 0.25 and the permissible intensity of pressure is 1MPa. Assuming
uniform intensity of pressure is 1MPa. Assuming \uniform wear criterion calculate the axial force required to transmit
max. power.
a) 31.4kN b) 62.8kN c) 15.7kN d) None of the above
5. A plate clutch consists of two pairs of contacting surfaces with coeffcient of friction 0.2 has a torque transmitting
capacity of 600N-m. the inner and outer diameter of the plates is 200 mm and 100 mm, what is the axial force required
to avoid slip between the plates. Assume uniform pressure theory.
a) 77 kN b) 38.6 kN c) 100 kN d) 17.3 kN
6. In the above problem if the uniform wear theory is adopted, the axial force is .
a) 40kN b) 80kN c) 60kN d) 60kN.
7. In a centrifugal clutch the radius of C.G. of the shoes is 80 mm and mass of each shoe is 2kg. if the engagement starts
at 300 rpm , the spring force is.
a)158N b) 642.5N c) 60N d) 2.5kN.
8. In a cone clutch with coefficient of friction equal to 0.25, the preferable semi cone angle with.
a) 12.50 b) 14.250 c)22.50 d)300 .
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MACHINE DESIGN
9. In a single plate disk clutch the outer diameter is twice the inner diameter the ratio of torque transmitted assuming
uniform pressure theory to uniform wear theory is.
a) 2/3 b) 4/3 c) 28/29 d) 3/4.
10. A multiple disk clutch and cone clutch have the same mean diameter, operate at the same speed and same axial load
isexerted in both clutches. the co-efficient of friction is same for both the clutches. the multiple disk clutch has 4 steel
disks and 3 bronte disks. the total cone angle of the cone clutch is 200 . the ratio of power transmitting capacities of
two clutches, considering uniform wear is.
a) 1.04 b) 2.02 c) 1.73 d) 2.54
11. A soft surface cone clutch must handle 200N-m of torque at 1250 rev/min. the larger diameter at the clutch is 350mm,
the cone pitch angle is 6.250, the face width is 65mm and the co-efficient of friction is 0.2.
A) The mean radius of the clutch is :-
a) 165mm b) 171mm c) 175mm d)185mm
B) The axial force required to transmit the torque is :-
a) 435N b) 635N c)745N d) 825N
12. In a cone clutch with co-efficient of friction equal to 0.25 the preferable semi cone angle will be:
a) 12.50 b) 14.250 c)22.50 d)300 .
13. In case of single plate disk clutch with inner radius equal to half the outer radius at a velocity of 1rad/sec.
The magnitude of
a) The torque transmitted based on uniform pressure theory.
b) The Power transmitted based on uniform pressure theory.
c) The torque transmitted based on uniform wear theory.
d) The Power transmitted based on uniform wear theory.
A. a = c > b = d B. a = b > c = d C. d = c > b = a D. b = c < a = d
14. In a single plate clutch and ID and OD at the friction disks are 200 mm & 400mm respectively. the friction coefficient
is 0.25. the springs exert a pull of 5kN on the movable disk. the brave transmitted by the clutch. Assuming wear theory
is .
a) 187.5N-m b)185.5 kN-m c) 276.5 kN-m d) 276.5N-m.
15. Consider the following statements:
A) In a single plate disk clutch by keeping all the other variables unchanged and reducing the qinner diameter power
transmitted by the clutch will increase.
B) In a hydrostatic bearing by increasing the film thickness the coefficient friction will decrease and hence the note
power 10µ will be reduced .
a) a & b are always true
b) a & b are sometime true.
c) a is always true and b is sometimes true
d) a is sometimes true and b is always true.
16. A cone clutch has semi cone angle 200 and coefficient of friction is 82.5% of maximum permissible for this angle. the
outer diameter and inner diameter are 300mm and 280 mm respectively. the springs exert an axial force of 5 kN. the
drives shaft rotates at 360rpm.
A). The power transmitted based on uniform pressure theory.
a) 28KW b) 30KW c) 22.5KW d) 24KW
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MECHANICAL ENGINEERING
B).The power transmitted based on uniform wear theory.
a) 28KW b) 30KW c) 22.5KW d) 24KW
17. A plate clutch is subjected to an axial force of 4000N. The inside radius of contact is 50 mm and the outside radius is
100 mm. the maximum pressure considering the uniform wear is .
a) 150 kPa b) 175 kPa c) 255 kPa d) 295 kPa
18. A soft surface cone clutch handle 200Nm of torque at 1250 rev/min. the large diameter at the clutch is 350mm. the cone
pitch angle is 61/40, the face width is 65mm and the coefficient of friction is 0.20. Assume uniform wear. the axial force
required to transmit the brave is ;
a) 237N b) 437N c)537N d) 637N
****************
“The whole world steps aside for the man
who knows where he is going”
6. CLUTCHES
One Mark Quesions : 1-a
Two Marks Quesions : 2-a, 3-b.
Clutches (Ans.) Practice Quetsions :
1 - c, 2 - a, 3 - d, 4 - b, 5 -a , 6 - b, 7 - a, 8 - b, 9 - c, 10 - a, 11(A) - a, 11(B) - b, 12 - b, 13 - b, 14 - a, 15 - b, 16(A) - d, 16(B) - d,
17 - b, 18 - d.
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MACHINE DESIGN
7. GEARS
One Mark Quesions :
1. For full depth of involute spur gears, minimum nuber of teeth of pinion to avoid interference depends upon
[GATE-ME-88]
a) presurre angle b) speed ratio c) circular pitch d) pitch diameter
2. Modern gear tooth profile is given involute shape because [GATE-ME-89]
a) this a very easy curve for manufacturing
b) sliding does not take place anywhere on meshing teeth
c) involute is the only profile that gives conjugate action
d) change in the centre distance does not change gear into
3. For a pinion of 15 teeth, under cutting ............................ (increase / decrease) with .................... (increase / decrease)
of pressure angle. [GATE-ME-91]
4. Interference in a pair of gears is avaoided, if the addendum circules of both the gears intersect common tangent to
the base circles with in the points of tangency. [GATE-ME-95]
a) True b) False
5. Match the following : [GATE-ME-95]
List - I (Grear Types) - List II (Applications)
A) Worm gears - 1. Parallel shaft
B) Cross helical gears - 2. Non-parallel, interescting shafts
C) Bevel gears - 3. Non-parallel, non-interescting shafts
D) Spur gears - 4. Large speed ratios
6. In spur gears, the circle on which the involute is generated is called the [GATE-ME-96]
a) pitch circle b) clearance angle c) base circle d) addendum circle
7. To make a worm drive reversible, it is necessary to increase [GATE-ME-97]
a) centre distance b) worm diameter factor c) number of starts d) reduction ratio
8. A 1.5 KW motor is running at 1440 rev/min. It is to be connected to a strirrer running at 36 rrev/min. the gearing
arrangement suitable for this application is [GATE-ME-2000]
a) differential gear b) heilical grear c) spur gear d) worm gear
9. Large speed reductions (greater than 20) in one stage of a gear train are possible through [GATE-ME-02]
a) spur gearing b) worm gearing c) Bevel gearing d) Helical gearing
10. The minimum number of teeth on the pinion to operate without interference in standard full height involute teeth
gear mechanism with 200 pressure is [GATE-ME-02]
a) 14 b) 12 c) 18 d) 32
11. Two mating spur gears have 40 and 120 teeth respectively. The pinion rotates at 1200 rpm and transmits a torque of
20N.m. The torque transmitted by gear is [GATE-ME-04]
a) 6.6 Nm b) 20 Nm c) 40 Nm d) 60 Nm
12. Tooth interference in an external involute spur gear pair can be reduced by [GATE-ME-10]
a) decreasing center distance between gears b) decreasing module
c) decreasing pressure angle d) incresing number of teeth
Two Marks Quesions :
1. In order to test the efficiency of reducer gear train 1 KW input was given at the input end at a speed of 1440 RPM
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MECHANICAL ENGINEERING
and at the output end the measured torque was 56.36N.m. If the ratio of speed reduction in this unit is 10:1, the
efficiency is about [GATE-ME-89]
a) 78% b) 85% c) 63% d) 96%
2. Twenty degree full depth involute profiled 19-tooth pinion and 37-tooth gear are in mesh.
If the module is 5 mm, the center distance between the gear pair will be [GATE-ME-06]
a) 140 mm b) 150 mm c) 280 mm d) 300 mm
Statement for Linked answer questions 03 and 05
A gear set has a pinion with 20 teeth and a gear with 40 teeth. The pinion runs at 30 rev/s and transmits a power of
20KW. The teeth are on the 200 full-depth system and have a module of 5 mm. The length of the line of action is
19 mm. [GATE-ME-07]
3. The center distance for the above gear set is mm is
a) 140 b) 150 c) 160 d) 170
4. The contact ratio of the contacting tooth is
a) 1.21 b) 1.25 c) 1.29 d) 1.33
5. The resultant force on the contacting gear tooth is N is
a) 77.23 b) 212.20 c) 2258.1 d) 289.43
6. A spur gate has a module of 3mm, number of teeth 16, a face width of 36 mm and a pressure angle of 200. It is
transmitting a power of 3KW at 20rev/s. Taking a velocity factor of 1.5 and a form factor of 0.3, the stress in the gear
tooth is about [GATE-ME-08]
7. Match the type of gears with their most appropriate description [GATE-ME-08]
Type of gear Description
P) Helical 1. Axes non parallel and non intersecting
Q) Spiral Bevel 2. Axes parallel and teeth are inclined to the axis
R) Hypid 3. Axes parallel and teeth are parallel to the axis
S) Rack and pinion 4. Axes are perpendicular and intersecting and teeth are inclined to the axis
5. Axes are perpendicular and used for large speed reduction
6. Axes parallel and one of the gears has infinite radius
a) P-2, Q-4, R-1, S-6 b) P-1, Q-4, R-5, S-6 c) P-2, Q-6, R-4, S-2 d) P-6, Q-3, R-1, S-5
8. One tooth of gear having 4 module and 32 teeth is shown in the figure.
Assume that the gear tooth and the corresponding tooth space make < a>
equal intercepts on the pitch circumference. [GATE-ME-08]
a) 6.08 mm, 4 mm Pitch circle <>b
b) 6.48 mm, 4.2 mm
c) 6.28 mm, 4.3 mm
d) 6.28 mm, 4.1 mm
Statement for Linked answer questions 09 and 10
A 200 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. [GATE-ME-09]
9. The tangential force transmitted (in N) is
a) 3552 b) 2611 c) 1776 d) 1305
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MACHINE DESIGN
10. Given that the tooth geometry factor is 0.32 and the combined effect of dynamic load and allied factors internsifying
the stress is 1.5 ; the minimum allowable stress (in MPa) for the gear material is
a) 242.0 b) 166.5 c) 121.0 d) 74.0
GEARS (PRACTICE QUESTIONS)
1. Match List-I with List-II and select the correct answer using the code given below the lists:
List-I List-II
(Gear Drive) (Function in M/c Tools)
A. Helical Gear 1. To obtain high velocity ratio.
B. Bevel Gear 2. To get rectilinear Motion.
C. Worm and Worm wheel 3. To run smoothly and quietly.
D. Rack and Pinion 4. For Shafts whose axes intersect.
Code:
A BCD
a 2 413
b3 142
c 2 143
d3 412
2 In a spur gear the beam strength is found tobe 150kN for a Module of 6mm.By Keeping all other values as it is it the
module is reduced to 5mm. The beam strength will is.
a) 180kN b) 125kN c) 137kN d) 104kN
3. A spur gear of pitch diameter 200mm,Face width 40mm and 40 teeth with 200. Pressure angle is made of steel with a
permissible bending stress 150MPa. The beam strength of the gear tooth is; (the form factor is 0.3333)
a) 10kN b) 12.5kN c) 8.96kN (d) 7.45kN
4. A gear wheel has a beam strength of 12kN . It is to be used under the condition where the service factor is 1.5 and the
velocity factor is 0.75.What is the maximum power it can transmit at a velocity of 50rad/sec. The module is 5mm and
number of teeth are 40
a) 30KW b) 120KW c) 60KW d) 40KW
5 In a pair of spur gears with 20 teeth each, the ratio factor is 1 and the load stress factor is 1.5,Module is 5 mm, face
width is 40 mm. The wear strength is
a) 30kN b) 6kN c) 18kN d) 0.3kN
6. The wear strength of a spur gear is proporional to ( Ep & Eg are young modulus of pinion and gear materials is)
Ep + Eg Ep . Eg Ep - Eg d) ( Ep/ Eg ) +1
a) Ep . Eg b) Ep + Eg
c)
Ep Eg
7. Interference in the involute spur gears;
a) 200 full depth system b) 250 full depth system. c) 250 Composite system d) 250 Stub.
A).a>b>d>c B).a>c>b>d
C).c>d>b>a D).b>a>c>d
8. Two standard gear wheels are in mesh. The addendium & deendium of the gear wheels are respectively 5mm & 6mm
the clearance of the gear wheel is.
a) 0.5mm b) 0.6mm c) 1mm d) 2mm
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MECHANICAL ENGINEERING
9. In a spur gear, the module is 5mm & the number of teeth is 20. the base circle radius in mm is (Pressure angle = 200)
a) 50cos 200 b) 50sin 200 c) 100cos 200 d) 100sin 200
10. A spur pinion of 100mm pitch diameter drives a 300 mm gear. the pinion shaft has 60 Nm of torque applied , and the
pressure angle is 200.The separating force is.
a) 4370 N b) 5240 N c)6740 N d) 8320 N.
11. A straight sided cutter having standard addendum of one module is required to generate in volute teeth on a gear
wheel having 18 teeth. if the module is 8mm, the smallest pressure angle that can be used to avoid under cutting is.
a) 180 b) 18.50 c) 19.30 d) 21.20
12. The pressure angle of an involute spur gear is 200 .The INV 200 is .
a) 0.00 Irad b)0.00S rad c)0.0I0 rad d)0.00IS rad.
I linked Question.
In a spur gear train gear A recieves 5kw at 500rev/min through its shaft and rotates counter clockwise. gear B is an idler
and gear C is the driven gear. The teeth are 200 full depth form.
40 teeth 70 teeth
35 teeth
13. The torque on the driver & driven gear shaft is.
a) 80NM & 90NM b) 85NM & 97NM c) 95NM & 109NM d) 105NM & 125NM
14. The tangential force on each gear is.
a) 909N,0,0 b) 909N,909N,909N c) 909N,909N,0 d) 909N,0,909N .
15. Spur gears with low pressure angle.
a) Have stronger tooth b) Have weaker tooth . c) Have no effect d) Have high radial reactions.
16. If both Pinion & gear are made of the same material the loadtransmission capacity is decided by.
a) The pinion b) Gear c) Both & pinion Gear d) Either. pinion or gear both being the
17. Lewis Equation in gears is used to find the.
a) Contact Stress b) wear strength c) Endurance strength d) Bending stress.
18. In a spur gear the beam strength is found to be 150 MPa for a module of 6mm. by keeping all other values as it is if the
module is reduced to 5mm. The beam strength will be .
a) 180MPa b) 125MPa c) 137MPa d) 104MPa
19. A spur Pinion rotating at 20rad/sec and having 20teeth transmits 20 kw to a gear wheel. The pressure angle is 200 and
module is 20mm .the reaction exerted by the pinion at the centre of the shaft is .
a) 10kN b) 20kN c) 5.32kN d) 6.4kN
20. For a spur gear having 20teeth the form factor is given as γ = π(0.154 − 0.912/t) where t is the no. of teeth . it has a
module of 5mm & face width of 55mm .The ratio of beam strenth to the allowable bending stress is.
a) 94mm2 b) 108mm2 c) 66.7mm2 d)84mm2
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MACHINE DESIGN
II Linked Question:
A 200 spur gear pinion having 16 teeth of module 5mm is carried by a shaft at one end whose other end is firmly
supported in a rigid bearing.the pinion transmits 6kw @ 600rpm .the shaft can be asssumed as a cantilever length 20cm.
21. Face width of the gear is 300mm & lewis form factor is 0.295 the bending stress in the gear tooth is.
a) 108MPa b) 54MPa c) 40MPa d)112MPa
22. The equivalent torque on the shaft is.
a) 1kN-m b)1.5kN-m c) 0.375kN-m d) 0.5kN-m
23. In a pair of spur gears the arc of contact is 6πmm & the contact ratio the module(in mm)is.
a) 2 b) 3 c) 4 d) 5
24. A pinion of 30 teeth of 10 mm module meshes with a rack of 200 pressure angle . the addendum (if it is to be same for
each)
a) 4.5mm b) 8.5m c)12.5mm d) 17.5mm
25. In a spur gear drive, the strength factor is 7.425, the velocity factor is 0.396, the tangential tooth load is 3275 and. the
face width is 12m(where m is module in mm).
a) 3.2mm b) 4.3 mm c) 5.4mm d) 6.2mm
26. If a standard addendum of one module is used in a rack and pinion arrangement , then least pressure angle
corresponding to 8 teeth on pinion is.
a) 141/2 b) 200 c) 250 d) 300
27. The wear strength of a spur gear is proportional to (Ep & Eg as young modulus of pinion & gear materials).
a)(Ep + Eg)/ (Ep .Eg) b)(Ep. Eg)/ (Ep +Eg) c)(Ep - Eg)/ (Ep .Eg) d)(Ep/ Eg)+ 1
28. Interface in the invoute spur gears.
a) 200 full depth system b) 250 full depth system c) 250 composite system d) 250 stub.
A)a>b>d>c B)a>c>b>d C) c>d>b>a D) b>a>c>d
29. A spur gear has a module of 3mm no of teeth16, a face width of 36mm and pressure angle of 200. it is transmitting a
power of 3kwa 20 rps .Taking a velocity factor of 1.5 and a form factor of 0.3, the stress in the gear tooth is about
a) 32MPa b) 46MPa c)58MPa d)70MPa
30. The beam strength of a shear gear tooth cannot be increased by increasing the .
a) face width b) module c) surface hardness d) No. of teeth.
31. Shaft ‘a’ in the fig. has a power input of 60kw at a speed of 16 rps in ccw divition
and drives shaft ‘c’ through the idler gear 3 mounted on shaft ‘b’. the gears have a 64 T
module of 5mm and a pre. angle of 200 .All the gears are on llel shafts of spains
4
400mm between the bearing and mounted at mid-spans. The equivalent torque on the c
shaft ‘b’ carrying the wheel ‘3’ is ------ (Assume the transmission efficiency is 100%) 32 T
7. GEARS 3
One Mark Quesions :
***************** b 16 T
2
a
1-a, 2-d, 3-decrease, increase, 4-True, 5-A4 B3 C2 A1, 6-c, 7-c, 8-d, 9-b, 10-c, 11-d, 12-d.
Two Marks Quesions : 1-b, 2-a, 3-b, 4-c, 5-c, 6-b, 7-a, 8-d, 9-a, 10-b.
Practice Questions
1 - ? , 2 - b, 3 - a, 4 - a, 5 - b, 6 - a, 7 - a, 8 - c, 9 - a,
10 - a, 11 - c, 12 - d, 13 - c, 14 - b, 15-b, 16-a, 17 - ?, 18 - b, 19-c, 20 - a, 21- b, 22 - d, 23-b,
24-d, 25 - c, 26 - d, 27 - a, 28 - a, 29 - b, 30 - c, 31 - a.
“One of the rarest things that a man ever does, is to do the best he can”
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