Design against fluctuating load procedure.ppt

Design Procedure

1. STRESS CONCENTRATION:
X
Y
Z
In design of machine elements, the following three fundamental
equations are used,
The above equations are called elementary equations. These
equations are based on a number of assumptions. One of the
assumptions is that there are no discontinuities in the cross-section
of the component.
However, in practice, discontinuities and abrupt changes in cross-
section are unavoidable due to certain features of the component
such as oil holes and grooves, keyways and splines, screw threads
and shoulders. Therefore, it cannot be assumed that the cross-
section of the machine component is uniform. Under these
circumstances, the ‘elementary’ equations do not give correct
results.

2. STRESS CONCENTRATION:
X
Y
Z
A plate with a small circular hole, subjected to tensile stress is
shown in Fig. 5.1. The distribution of stresses near the hole can
be observed by using the Photo-elasticity technique. In this
method, an identical model of the plate is made of epoxy resin.
The model is placed in a circular polariscope and loaded at the
edges. It is observed that there is a sudden rise in the magnitude
of stresses in the vicinity of the hole. The localized stresses in the
neighbourhood of the hole are far greater than the stresses
obtained by elementary equations.

3. X
Y
Z
Stress concentration is defined as the localization of high stresses
due to the irregularities present in the component and abrupt
changes of the cross-section. In order to consider the effect of
stress concentration and find out localized stresses, a factor
called stress concentration factor is used. It is denoted by K
t

and defined as,

4. X
Y
Z

5. STRESS CONCENTRATION:
X
Y
Z

6. STRESS CONCENTRATION:
X
Y
Z
The causes of stress concentration are as follows:
(ii) Load Application
Machine components are subjected to forces. These forces act
either at a point or over a small area on the component. Since
the area is small, the pressure at these points is excessive. This
results in stress concentration. The examples of these load
applications are as follows:
(a)Contact between the meshing teeth of the driving and the driven
gear
(b)Contact between the cam and the follower
(c)Contact between the balls and the races of ball bearing
(d)Contact between the rail and the wheel
(e)Contact between the crane hook and the chain
In all these cases, the concentrated load is applied over a very
small area resulting in stress concentration.

7. STRESS CONCENTRATION:
X
Y
Z
The causes of stress concentration are as follows:
(iii) Abrupt Changes in Section
In order to mount gears, sprockets, pulleys and ball bearings on a
transmission shaft, steps are cut on the shaft and shoulders are
provided from assembly considerations. Although these features
are essential, they create change of the cross-section of the shaft.
This results in stress concentration at these cross-sections.
(iv)Discontinuities in the Component
Certain features of machine components such as oil holes or oil
grooves, keyways and splines, and screw threads result in
discontinuities in the cross-section of the component. There is
stress concentration in the vicinity of these discontinuities.
(v) Machining Scratches
Machining scratches, stamp marks or inspection marks are surface
irregularities, which cause stress concentration.

8. STRESS CONCENTRATION FACTORS:
X
Y
Z

9. STRESS CONCENTRATION FACTORS:
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Y
Z

10. STRESS CONCENTRATION FACTORS:
X
Y
Z

11. STRESS CONCENTRATION FACTORS:
X
Y
Z

12. STRESS CONCENTRATION FACTORS:
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Y
Z

13. STRESS CONCENTRATION FACTORS:
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Y
Z

14. STRESS CONCENTRATION FACTORS:
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Y
Z
The nominal stresses in these three cases are as follows:
(i) Tensile Force
(ii) Bending Moment
(iii) Torsional Moment

15. STRESS CONCENTRATION FACTORS:
X
Y
Z
In practice, there are a number of geometric shapes and
conditions of loading. A separate chart for the stress
concentration factor should be used for each case. It is
possible to find out the stress concentration factor for some
simple geometric shapes using the Theory of elasticity. A
flat plate with an elliptical hole and subjected to tensile
force, is shown in Fig. 5.7. It can be proved using the Theory
of elasticity that the theoretical stress concentration factor
at the edge of hole is given by,

16. STRESS CONCENTRATION FACTORS:
X
Y
Z

17. REDUCTION IN STRESS
CONCENTRATION:
X
Y
Z
Although it is not possible to completely eliminate the effect of
stress concentration, there are methods to reduce stress
concentrations. This is achieved by providing a specific geometric
shape to the component. In order to know what happens at the
abrupt change of cross-section or at the discontinuity and reduce
the stress concentration, understanding of flow analogy is useful.
There is a similarity between velocity distribution in fluid flow in
a channel and the stress distribution in an axially loaded plate
shown in Fig. 5.8. The equations of flow potential in fluid
mechanics and stress potential in solid mechanics are same.
Therefore, it is perfectly logical to use fluid analogy to understand
the phenomena of stress concentration

18. REDUCTION IN STRESS
CONCENTRATION:
X
Y
Z
When the cross-section of a channel has uniform dimensions
throughout, the velocities are uniform and the streamlines are
equally spaced. The flow at any cross-section within the
channel is given by,
When the cross-section of the plate has the same dimensions
throughout, the stresses are uniform and stress lines are
equally spaced. The stress at any section is given by,

19. REDUCTION IN STRESS
CONCENTRATION:
X
Y
Z
When the cross-section of the channel is suddenly reduced, the
velocity increases in order to maintain the same flow and the
streamlines become narrower and narrower and crowd
together. A similar phenomenon is observed in a stressed
plate. In order to transmit the same force, the stress lines
come closer and closer as the cross-section is reduced. At the
change of cross-section, the streamlines as well as stress lines
bend. When there is sudden change in cross-section, bending
of stress lines is very sharp and severe resulting in stress
concentration. Therefore, stress concentration can be greatly
reduced by reducing the bending by rounding the corners.
Streamlined shapes are used in channels to reduce turbulence
and resistance to flow. Streamlining, or rounding the counters
of mechanical components, has similar beneficial effects in
reducing stress concentration. There are different methods to
reduce the bending of the stress lines at the junction and
reduce the stress concentration.

20. REDUCTION IN STRESS
CONCENTRATION:
X
Y
Z
In practice, reduction of stress concentration is achieved by
the following methods:
(i) Additional Notches and Holes in Tension Member A flat plate
with a V-notch subjected to tensile force is shown in Fig.
5.9(a). It is observed that a single notch results in a high
degree of stress concentration. The severity of stress
concentration is reduced by three methods:
(a) use of multiple notches;
(b) drilling additional holes; and
(c) removal of undesired material.
These methods are illustrated in Fig. 5.9(b), (c) and (d)
respectively. The method of removing undesired material is
called the principle of minimization of the material. In these
three methods, the sharp bending of a force fl ow line is
reduced and it follows a smooth curve

21. REDUCTION IN STRESS
CONCENTRATION:
X
Y
Z

22. REDUCTION IN STRESS
CONCENTRATION:
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Y
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In practice, reduction of stress concentration is achieved by the
following methods:
(ii) Fillet Radius, Undercutting and Notch for Member in Bending
A bar of circular cross-section with a shoulder and subjected to
bending moment is shown in Fig. 5.10(a). Ball bearings, gears
or pulleys are seated against this shoulder. The shoulder
creates a change in cross-section of the shaft, which results in
stress concentration. There are three methods to reduce stress
concentration at the base of this shoulder. Figure 5.10(b) shows
the shoulder with a fillet radius r. This results in gradual
transition from small diameter to a large diameter. The fillet
radius should be as large as possible in order to reduce stress
concentration. In practice, the fillet radius is limited by the
design of mating components. The fillet radius can be increased
by undercutting the shoulder as illustrated in Fig. 5.10(c). A
notch results in stress concentration. Surprisingly, cutting an
additional notch is an effective way to reduce stress
concentration. This is illustrated in Fig. 5.10(d).

23. X
Y
Z
In practice, reduction of stress concentration is achieved by
the following methods:

24. REDUCTION IN STRESS
CONCENTRATION:
X
Y
Z
In practice, reduction of stress concentration is achieved by
the following methods:

(iii) Drilling Additional Holes for Shaft A transmission shaft
with a keyway is shown in Fig. 5.11(a). The keyway is a
discontinuity and results in stress concentration at the corners
of the keyway and reduces torsional shear strength. An
empirical relationship developed
by HF Moore for the ratio C of
torsional strength of a shaft
having a keyway to torsional
strength of a same sized shaft
without a keyway is given by

25. REDUCTION IN STRESS
CONCENTRATION:
X
Y
Z
where w and h are width and height dimensions of the keyway
respectively and d is the shaft diameter. The four corners of the
keyway, viz., m
1, m
2, n
1 and n
2 are shown in Fig. 5.11(c). It has
been observed that torsional shear stresses at two points, viz.
m
1
and m
2
are negligibly small in practice and theoretically
equal to zero. On the other hand, the torsional shear stresses at
two points, viz., n
1
and n
2
are excessive and theoretically
infinite which means even a small torque will produce a
permanent set at these points. Rounding corners at two points,
viz., n
1 and n
2 by means of a fillet radius can reduce the stress
concentration. A stress concentration factor K
t
= 3 should be
used when a shaft with a keyway is subjected to combined
bending and torsional moments. In addition to giving fillet
radius at the inner corners of the keyway, there is another
method of drilling two symmetrical holes on the sides of the
keyway. These holes press the force flow lines and minimise
their bending in the vicinity of the keyway. This method is
illustrated in Fig. 5.11(b).

26. REDUCTION IN STRESS
CONCENTRATION:
X
Y
Z

(iv) Reduction of Stress Concentration in Threaded Members A
threaded component is shown in Fig. 5.12 (a). It is observed
that the force flow line is bent as it passes from the shank
portion to threaded portion of the component. This results in
stress concentration in the transition plane. In Fig. 5.12(b), a
small undercut is taken between the shank and the threaded
portion of the component and a fillet radius is provided for this
undercut. This reduces bending of the force flow line and
consequently reduces stress concentration. An ideal method to
reduce stress concentration is illustrated in Fig. 5.12(c), where
the shank diameter is reduced and made equal to the core
diameter of the thread. In this case, the force flow line is
almost straight and there is no stress concentration.

27. REDUCTION IN STRESS
CONCENTRATION:
X
Y
Z

28. REDUCTION IN STRESS
CONCENTRATION:
X
Y
Z
Problem 1: A flat plate subjected to a tensile force of 5
kN is shown in Figure. The plate material is grey cast
iron FG 200 and the factor of safety is 2.5. Determine
the thickness of the plate.

29. REDUCTION IN STRESS
CONCENTRATION:
X
Y
Z
Problem 1:.

30. REDUCTION IN STRESS
CONCENTRATION:
X
Y
Z
Problem 1:.

31. REDUCTION IN STRESS
CONCENTRATION:
X
Y
Z
Problem 2: A non-rotating shaft supporting a load of 2.5
kN is shown in Fig. 5.14. The shaft is made of brittle
material, with an ultimate tensile strength of 300
N/mm
2
. The factor of safety is 3. Determine the
dimensions of the shaft.

32. REDUCTION IN STRESS
CONCENTRATION:
X
Y
Z
Problem 2:

33. REDUCTION IN STRESS
CONCENTRATION:
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Y
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Problem 2:

34. REDUCTION IN STRESS
CONCENTRATION:
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Y
Z
Problem 2:

35. X
Y
Z
In many applications, the components are subjected to
forces, which are not static, but vary in magnitude with
respect to time. The stresses induced due to such forces
are called fluctuating stresses.
It is observed that about 80% of failures of mechanical
components are due to ‘fatigue failure’ resulting from
fluctuating stresses.
In practice, the pattern of stress variation is irregular
and unpredictable, as in case of stresses due to
vibrations.
For the purpose of design analysis, simple models for
stress–time relationships are used. The most popular
model for stress–time relationship is the sine curve.

36. X
Y
Z
There are three types of mathematical models for cyclic stresses—
fluctuating or alternating stresses, repeated stresses and reversed stresses.
Stress–time relationships for these models are illustrated in Fig.

37. FLUCTUATING STRESSES:
X
Y
Z
The fluctuating or alternating stress varies in a sinusoidal manner
with respect to time. It has some mean value as well as amplitude
value. It fluctuates between two limits—maximum and minimum
stress. The stress can be tensile or compressive or partly tensile and
partly compressive.
The repeated stress varies in a sinusoidal manner with respect to
time, but the variation is from zero to some maximum value. The
minimum stress is zero in this case and therefore, amplitude stress
and mean stress are equal.
The reversed stress varies in a sinusoidal manner with respect to
time, but it has zero mean stress. In this case, half portion of the
cycle consists of tensile stress and the remaining half of
compressive stress. There is a complete reversal from tension to
compression between these two halves and therefore, the mean
stress is zero.

38. FLUCTUATING STRESSES:
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Y
Z

39. FATIGUE FAILURE :
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Y
Z
It has been observed that materials fail under fluctuating stresses
at a stress magnitude which is lower than the ultimate tensile
strength of the material. Sometimes, the magnitude is even lower
than the yield strength. Further, it has been found that the
magnitude of the stress causing fatigue failure decreases as the
number of stress cycles increase. This phenomenon of decreased
resistance of the materials to fluctuating stresses is the main
characteristic of fatigue failure.
Let us examine a phenomenon we have experienced in our
childhood. Suppose, there is a wire of 2 to 3 mm diameter and we
want to cut it into two pieces without any device like a hacksaw.
One method is to shear the wire by applying equal and opposite
forces P1 and P2 by left and right hands.

40. FATIGUE FAILURE :
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Y
Z

41. FATIGUE FAILURE :
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Y
Z
There is a basic difference between failure due to static load and
that due to fatigue. The failure due to static load is illustrated by
the simple tension test. In this case, the load is gradually applied
and there is sufficient time for the elongation of fibres. In ductile
materials, there is considerable plastic flow prior to fracture. This
results in a silky fibrous structure due to the stretching of crystals
at the fractured surface.
On the other hand, fatigue failure begins with a crack at some
point in the material. The crack is more likely to occur in the
following regions:
(i)Regions of discontinuity, such as oil holes, keyways, screw
threads, etc.
(ii)Regions of irregularities in machining operations, such as
scratches on the surface, stamp mark, inspection marks, etc.
(iii)Internal cracks due to defects in materials like blow holes

42. ENDURANCE LIMIT :
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Y
Z

43. ENDURANCE LIMIT :
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Y
Z

44. ENDURANCE LIMIT :
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Y
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The principle of a rotating beam is illustrated in Fig. 5.18.

45. ENDURANCE LIMIT :
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Y
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46. ENDURANCE LIMIT :
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Y
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47. ENDURANCE LIMIT :
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Y
Z
The amplitude can be increased or decreased by increasing or
decreasing the bending moment respectively.
A schematic diagram of a rotating beam fatigue testing machine
is shown in Fig. 5.19. The specimen acts as a ‘rotating beam’
subjected to a bending moment. Therefore, it is subjected to a
completely reversed stress cycle.

48. ENDURANCE LIMIT :
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Y
Z

49. ENDURANCE LIMIT :
X
Y
Z

50. ENDURANCE LIMIT :
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Y
Z

51. X
Y
Z

52. LOW-CYCLE AND HIGH-CYCLE
FATIGUE :
X
Y
Z
Components subjected to high-cycle fatigue are designed on the basis of
endurance limit stress. S–N curves, Soderberg lines, Gerber lines or
Goodman diagrams are used in the design of such components.

53. NOTCH SENSITIVITY :
X
Y
Z

54. NOTCH SENSITIVITY :
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Y
Z

55. NOTCH SENSITIVITY :
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Y
Z

56. NOTCH SENSITIVITY :
X
Y
Z

57. NOTCH SENSITIVITY :
X
Y
Z

58. ENDURANCE LIMIT— APPROXIMATE
ESTIMATION:
X
Y
Z

59. ENDURANCE LIMIT— APPROXIMATE
ESTIMATION:
X
Y
Z

60. ENDURANCE LIMIT— APPROXIMATE
ESTIMATION:
X
Y
Z
The endurance limit of a component is different from the endurance
limit of a rotating beam specimen due to a number of factors. The
difference arises due to the fact that there are standard
specifications and working conditions for the rotating beam
specimen, while the actual components have different specifications
and work under different conditions. Different modifying factors are
used in practice to account for this difference. These factors are,
sometimes, called derating factors. The purpose of derating factors
is to ‘derate’ or reduce the endurance limit of a rotating beam
specimen to suit the actual component.

61. ENDURANCE LIMIT— APPROXIMATE
ESTIMATION:
X
Y
Z
(i) Surface finish Factor: The surface of the rotating beam
specimen is polished to mirror finish. The final polishing is carried
out in the axial direction to smooth out any circumferential scratches.
This makes the specimen almost free from surface scratches and
imperfections. It is impractical to provide such an expensive surface
finish for the actual component. The actual component may not even
require such a surface finish. When the surface finish is poor, there
are scratches and geometric irregularities on the surface. These
surface scratches serve as stress raisers and result in stress
concentration. The endurance limit is reduced due to introduction of
stress concentration at these scratches. The surface finish factor
takes into account the reduction in endurance limit due to the
variation in the surface finish between the specimen and the actual
component. Figure 5.24 shows the surface finish factor for steel
components4. It should be noted that ultimate tensile strength is also
a parameter affecting the surface finish factor. High strength
materials are more sensitive to stress concentration introduced by
surface irregularities. Therefore, as the ultimate tensile strength
increases, the surface finish factor decreases.

62. ENDURANCE LIMIT— APPROXIMATE
ESTIMATION:
X
Y
Z

63. ENDURANCE LIMIT— APPROXIMATE
ESTIMATION:
X
Y
Z

64. ENDURANCE LIMIT— APPROXIMATE
ESTIMATION:
X
Y
Z
The above mentioned values of surface finish factors are developed
only for steel components. They should not be applied to components
made of other ductile materials like aluminium alloys. The surface
finish factor for ordinary grey cast iron components is taken as 1,
irrespective of their surface finish. It is observed that even mirror
finished samples of grey cast iron parts have surface discontinuities
because of graphite flakes in the cast iron matrix. Adding some
more surface scratches does not make any difference. Therefore,
whatever is the machining method; the value of surface finish factor
for cast iron parts is always taken as 1.

65. ENDURANCE LIMIT— APPROXIMATE
ESTIMATION:
X
Y
Z

66. ENDURANCE LIMIT— APPROXIMATE
ESTIMATION:
X
Y
Z

67. ENDURANCE LIMIT— APPROXIMATE
ESTIMATION:
X
Y
Z
Table 5.2 as well as Eqs (5.19) and (5.20) can be used only for
cylindrical components. It is diffi cult to determine the size factor for
components having a non-circular cross-section. However, since the
endurance limit is reduced in such components, it is necessary to
defi ne effective diameter based on an equivalent circular cross-
section. In this case, Kuguel’s equality is widely used. This equality
is based on the concept that fatigue failure is related to the
probability of high stress interacting with a discontinuity. When the
volume of material subjected to high stress is large, the probability
of fatigue failure originating from any flaw in that volume is more.
Kuguel assumes a volume of material that is stressed to 95% of the
maximum stress or above as high stress volume. According to
Kuguel’s equality, the effective diameter is obtained by equating the
volume of the material stressed at and above 95% of the maximum
stress to the equivalent volume in the rotating beam specimen.
When these two volumes are equated, the lengths of the component
and specimen cancel out and only areas need be considered.

68. ENDURANCE LIMIT— APPROXIMATE
ESTIMATION:
X
Y
Z

69. ENDURANCE LIMIT— APPROXIMATE
ESTIMATION:
X
Y
Z

70. ENDURANCE LIMIT— APPROXIMATE
ESTIMATION:
X
Y
Z

71. ENDURANCE LIMIT— APPROXIMATE
ESTIMATION:
X
Y
Z

72. ENDURANCE LIMIT— APPROXIMATE
ESTIMATION:
X
Y
Z

73. ENDURANCE LIMIT— APPROXIMATE
ESTIMATION:
X
Y
Z

74. ENDURANCE LIMIT— APPROXIMATE
ESTIMATION:
X
Y
Z

75. ENDURANCE LIMIT— APPROXIMATE
ESTIMATION:
X
Y
Z

76. XYZ

77. XYZ

78. P
r
o
f
.
D
i
g
v
i
j
a
y

G
.

B
h
o
s
a
l
e
XYZ

79. XYZ

80. XYZ

81. XYZ

82. XYZ

83. Problem: A rod of a robot linkage mechanism made of steel 40Cr1 (S
ut =
550 N/mm
2
) is subjected to a completely reversed axial load of 100 kN.
The rod is machined on a CNC and the expected reliability is 95%. There is
no stress concentration. Determine the diameter of the rod using a factor of
safety of 2 for an infinite life condition.
XYZ

84. XYZ

85. 
Problem: A component of robot arm is machined from a plate made of steel
45C8 (S
ut = 630 N/mm
2
) is shown in Figure. It is subjected to a completely
reversed axial force of 50 kN. The expected reliability is 90% and the factor
of safety is 2. The size factor is 0.85. Determine the plate thickness t for
infinite life, if the notch sensitivity factor is 0.8.
XYZ

86. XYZ

87. XYZ

88. XYZ

89. Finite-life Problems (Reversed Load)
Problem: A rotating bar made of steel 45C8 (S
ut = 630 N/mm
2
) is
subjected to a completely reversed bending stress. The corrected endurance limit
of the bar is 315 N/mm
2
. Calculate the fatigue strength of the bar for a life of
90,000 cycles.
XYZ

90. XYZ

91. Problem: A forged steel bar, 50 mm in diameter, is subjected to
a reversed bending stress of 250 N/mm
2
. The bar is made of
steel 40C8 (S
ut = 600 N/mm
2
). Calculate the life of the bar for a
reliability of 90%.
XYZ

92. XYZ

93. XYZ

94. XYZ

95. Problem: A rotating shaft, subjected to a nonrotating force of 5
kN and simply supported between two bearings A and E is
shown in Figure. The shaft is machined from plain carbon
steel 30C8 (S
ut = 500 N/mm
2
) and the expected reliability
is 90%. The equivalent notch radius at the fillet section can
be taken as 3 mm. What is the life of the shaft?
XYZ

96. XYZ

97. XYZ

98. XYZ

99. XYZ

100. Problem: A cantilever beam made of cold drawn steel 20C8 (S
ut =
540 N/mm
2
) is subjected to a completely reversed load of 1000
N as shown in Figure. The notch sensitivity factor q at the fillet can
be taken as 0.85 and the expected reliability is 90%. Determine the
diameter d of the beam for a life of 10000 cycles.
XYZ

101. XYZ

102. XYZ

103. XYZ

104. XYZ

105. XYZ

106. CUMULATIVE DAMAGE IN FATIGUE
XYZ

107. Problem: The work cycle of a mechanical component subjected to
completely reversed bending stresses consists of the following three
elements:
(i)± 350 N/mm
2 for 85% of time
(ii)± 400 N/mm
2 for 12% of time
(iii)± 500 N/mm
2 for 3% of time
The material for the component is 50C4 (S
ut = 660 N/mm
2 ) and the corrected
endurance limit of the component is 280 N/mm
2 . Determine the life of
the component.
XYZ

108. CUMULATIVE DAMAGE IN FATIGUE
Problem : The work cycle of a mechanical component subjected to
completely reversed bending stresses consists of the following three
elements:
(i)± 350 N/mm
2 for 85% of time
(ii)± 400 N/mm
2 for 12% of time
(iii)± 500 N/mm
2 for 3% of time
The material for the component is 50C4 (S
ut = 660 N/mm
2 ) and the
corrected endurance limit of the component is 280 N/mm
2 . Determine
the life of the component.
XYZ

109. CUMULATIVE DAMAGE IN FATIGUE
P
r
o
f
.
D
i
g
v
i
j
a
y

G
.

B
h
o
s
a
l
e
Problem:
XYZ

110. CUMULATIVE DAMAGE IN FATIGUE
Problem:
XYZ

111. XYZ

112. SODERBERG AND GOODMAN LINES
XYZ

113. XYZ

114. SODERBERG AND GOODMAN LINES
XYZ

115. SODERBERG AND GOODMAN LINES
XYZ

116. SODERBERG AND GOODMAN LINES
XYZ

117. XYZ

118. MODIFIED GOODMAN DIAGRAMS
XYZ

119. XYZ

120. MODIFIED GOODMAN DIAGRAMS
XYZ

121. MODIFIED GOODMAN DIAGRAMS
XYZ

122. MODIFIED GOODMAN DIAGRAMS
XYZ

123. MODIFIED GOODMAN DIAGRAMS
XYZ

124. MODIFIED GOODMAN DIAGRAMS
XYZ

125. MODIFIED GOODMAN DIAGRAMS
XYZ

126. MODIFIED GOODMAN DIAGRAMS
Problem 12 :
XYZ

127. MODIFIED GOODMAN DIAGRAMS
Problem 12 :
XYZ

128. MODIFIED GOODMAN DIAGRAMS
Problem 12 :
XYZ

129. MODIFIED GOODMAN DIAGRAMS
Problem 12 :
XYZ

130. MODIFIED GOODMAN DIAGRAMS
Problem 12 :
XYZ

131. MODIFIED GOODMAN DIAGRAMS
Problem 13 : A transmission shaft of cold drawn steel
27Mn2 (S
ut=500N/mm
2
and
S
yt
=300N/mm2)is
subjected to a fluctuating torque which varies from – 100
N-m to + 400 N-m. The factor of safety is 2 and the
expected reliability is 90%. Neglecting the effect of
stress concentration, determine the diameter of the
shaft. Assume the distortion energy theory of failure.
XYZ

132. MODIFIED GOODMAN DIAGRAMS
Problem 13 :
XYZ

133. MODIFIED GOODMAN DIAGRAMS
Problem 13 :
XYZ

134. MODIFIED GOODMAN DIAGRAMS
Problem 13 :
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135. MODIFIED GOODMAN DIAGRAMS
Problem 14 : A spherical pressure vessel, with a 500 mm
inner diameter, is welded from steel plates. The welded
joints are sufficiently strong and do not weaken the
vessel. The plates are made from cold drawn steel 20C8
(S
ut = 440 N/mm2 and S
yt = 242 N/mm
2
). The vessel is
subjected to internal pressure, which varies from zero
to 6 N/mm
2
. The expected reliability is 50% and the
factor of safety is 3.5. The size factor is 0.85. The vessel
is expected to withstand infinite number of stress
cycles. Calculate the thickness of the plates.
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136. MODIFIED GOODMAN DIAGRAMS
Problem 14 :
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137. MODIFIED GOODMAN DIAGRAMS
Problem 14 :
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138. MODIFIED GOODMAN DIAGRAMS
Problem 14 :
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139. MODIFIED GOODMAN DIAGRAMS
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140. MODIFIED GOODMAN DIAGRAMS
Finite-life Problems (Fluctuating Load)
Problem 15 :
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141. MODIFIED GOODMAN DIAGRAMS
Finite-life Problems (Fluctuating Load)
Problem 15 :
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142. MODIFIED GOODMAN DIAGRAMS
Finite-life Problems (Fluctuating Load)
Problem 15 :
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143. MODIFIED GOODMAN DIAGRAMS
Finite-life Problems (Fluctuating Load)
Problem 15 :
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144. MODIFIED GOODMAN DIAGRAMS
Finite-life Problems (Fluctuating Load)
Problem 15 :
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145. MODIFIED GOODMAN DIAGRAMS
Finite-life Problems (Fluctuating Load)
Problem 15 :
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146. MODIFIED GOODMAN DIAGRAMS
Finite-life Problems (Fluctuating Load)
Problem 16 : A polished steel bar is subjected to axial tensile
force that varies from zero to P
max. It has a groove 2 mm
deep and having a radius of 3 mm. The theoretical stress
concentration factor and notch sensitivity factor at the
groove are 1.8 and 0.95 respectively. The outer diameter of
the bar is 30 mm. The ultimate tensile strength of the bar is
1250 MPa. The endurance limit in reversed bending is 600 MPa.
Find the maximum force that the bar can carry for 10 5 cycles
with 90% reliability.
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147. MODIFIED GOODMAN DIAGRAMS
Finite-life Problems (Fluctuating Load)
Problem 16 :
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148. MODIFIED GOODMAN DIAGRAMS
P
r
o
f
.
D
i
g
v
i
j
a
y

G
.

B
h
o
s
a
l
e
Finite-life Problems (Fluctuating Load)
Problem 16 :
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149. MODIFIED GOODMAN DIAGRAMS
Finite-life Problems (Fluctuating Load)
Problem 16 :
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150. MODIFIED GOODMAN DIAGRAMS
Finite-life Problems (Fluctuating Load)
Problem 16 :
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151. MODIFIED GOODMAN DIAGRAMS
Finite-life Problems (Fluctuating Load)
Problem 16 :
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152. MODIFIED GOODMAN DIAGRAMS
Finite-life Problems (Fluctuating Load)
Problem 16 :
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153. GERBER EQUATION
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154. GERBER EQUATION
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155. GERBER EQUATION
Problem 17 : A machine component is subjected to
fluctuating stress that varies from 40 to 100 N/mm
2
.
The corrected endurance limit stress for the
machine component is 270 N/mm
2
. The ultimate
tensile strength and yield strength of the
material are 600 and 450 N/mm
2
respectively. Find
the factor of safety using (i) Gerber theory (ii)
Soderberg line (iii) Goodman line Also, find the factor
of safety against static failure.
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156. GERBER EQUATION
Problem 17 :
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157. GERBER EQUATION
Problem 17 :
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158. FATIGUE DESIGN UNDER COMBINED STRESSES
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159. FATIGUE DESIGN UNDER COMBINED STRESSES
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160. FATIGUE DESIGN UNDER COMBINED STRESSES
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