ME6503 - DESIGN OF MACHINE ELEMENTS UNIT - I NOTES

R.M.K COLLEGE OF ENGG AND TECH / AQ / R2013/ ME6503 / V / MECH / JUNE 2016 – NOV 2016
ME6503 – DESIGN OF MACHINE ELEMENTS QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 3
UNIT – I – STEADY STRESSES AND VARIABLE STRESSES IN
MACHINE ELEMENTS
PART - A
1.1) Define CAD.
1.2) What are the advantages of CAD?
1.3) What are the factors to be considered in the selection of materials for a machine
element?
1.4) What is an adaptive design? [AU, Apr / May – 2015, May / Jun – 2016]
1.5) What is adaptive design? Where it is used? Give examples.
[AU, Nov / Dec – 2012]
1.6) How are materials classified?
1.7) What are the common materials used in mechanical engineering design?
[AU, Nov / Dec – 2015]
1.8) What are the mechanical properties to be considered in selecting a material for
engineering applications?
1.9) What are the mechanical properties of metals? List any four mechanical
prosperities. [AU, May / Jun - 2012]
1.10) What is meant by interchangeability?
1.11) What are the steps in machine design process? [AU, Apr / May – 2010]
1.12) How will you account for stress concentration in design of the machine parts .
[AU, Apr / May – 2010]
1.13) What do you mean by Optimum design? [AU, Nov / Dec –2011]
1.14) What are the methods to reduce stress concentration? [AU, Nov / Dec –2008]
1.15) Define nominal, basic and actual size.
1.16) What is meant by tolerance?
1.17) Define limits of size.
1.18) Define limits and fits. [AU, Apr / May – 2015, May / Jun – 2016]
1.19) Define fits, clearance and interference.
1.20) What are the types of fits? [AU, Nov / Dec– 2008]
1.21) Write short notes on clearance fit and interference fit.
1.22) Explain transition fit.

1.23) What are unilateral and bilateral tolerances? [AU, May / Jun - 2013]
1.24) Using the table for tolerances, find the types of fit, maximum and minimum
clearance of interference for 150 G7 – e8 combination.
1.25) The fit between a hole and a shaft is defined by  70 H9F7. Find the allowance.
1.26) What is hole basis system?
1.27) What is shaft basis system?
1.28) Define preferred numbers.
1.29) What is meant by standardization?
1.30) Mention some standard codes of specification of steels. [AU, Nov / Dec– 2008]
1.31) Define load. What are the different types of loads that can act on machine
components?
1.32) What are the factors that govern selection of materials while designing a machine
component? [AU, Nov / Dec– 2010]
1.33) What is steady and variable load?
1.34) What is impact load? [AU, Nov / Dec – 2015]
1.35) What is an impact load? Give example. [AU, May / Jun - 2012]
1.36) What is meant by shock and impact load?
1.37) What are the methods used to improve fatigue strength? [AU, Nov / Dec –2013]
1.38) List at least two methods to improve the fatigue strength. [AU, Nov / Dec –2014]
1.39) Define stress and strain.
1.40) Define Poisson’s ratio. [AU, Apr / May – 2011]
1.41) Explain the normal stress theory and its limitations [AU, Apr / May – 2010]
1.42) Which theory of failure is suitable for the design of brittle materials?
[AU, Nov / Dec – 2015]
1.43) Explain the different types of stresses.
1.44) What is meant by double shear? Give an example.
1.45) Define resilience [AU, Nov / Dec –2009]
1.46) Define proof resilience and modulus of resilience.
1.47) What in meant by modulus of rigidity?
1.48) Explain factor of safety. [AU, Apr / May – 2010]
1.49) Define factor of safety. [AU, Nov / Dec –2012, 2015]

1.50) List the important factors that influence the magnitude of factor of safety.
[AU, Nov / Dec –2011]
1.51) Explain stress - strain diagram with an example.
1.52) What is the yield point of the material?
1.53) Define ultimate and breaking stress.
1.54) Explain working stresses.
1.55) Differentiate the stress distribution in a bar subjected to an axial force and beam
subjected to bending [AU, Apr / May – 2010]
1.56) What is factor of safety for brittle materials? [AU, Apr / May – 2011]
1.57) Discuss the factors affecting the selection of factor of safety.
1.58) Define Poisson's ratio and bulk modulus.
1.59) Give the relation between bulk modulus and Young's modulus.
1.60) Give the relation between Young's modulus and modulus of rigidity.
1.61) Calculate the force required to punch a circular blank of 60 mm diameter in a plate
of 5 mm thick. The ultimate shear stress of the plate is 350 N/mm2.
1.62) Determine the force required to punch a hole of 20mm diameter in a 5mm thick
plate with ultimate shear strength of 250 MPa? [AU, Nov / Dec –2014]
1.63) A mild steel bar of 12mm diameter is subjected to an axial load of 50 KN in
tension. Find the magnitude of the induced stress.
1.64) A M.S. bar of diameter 12 mm and length 1 m is subjected to an axial load of 50
KN in tension and modulus of elasticity is 2 x 105MPa. Find the elongation of
the bar.
1.65) Steel flat 10 mm wide and 12 mm thick is bent into a circular arc of radius 12 m.
Find the maximum intensity of stress induced in the cross section.
1.66) How is the allowable stress estimated in ductile and brittle materials?
1.67) Define the term principal planes and principal stress
1.68) State the various theories of failure.
1.69) What are the various theories of failure? [AU, May / Jun - 2013]
1.70) What is the maximum principal strain theory (Saint Vennant's theory)?
[AU, Nov / Dec – 2009]
1.71) State the maximum strain energy theory (Haigh's theory)

1.72) State the difference between straight beams and curved beams.
[AU, Nov / Dec –2012]
1.73) What is eccentric loading?
1.74) Define stress concentration. [AU, May / Jun – 2012, 2016]
1.75) What is meant by stress concentration?
[AU, May / Jun - 2009, Nov / Dec –2011]
1.76) Give one method of reducing stress concentration in key slots.
[AU, May / Jun - 2012]
1.77) What are the sources of stress concentration in machine elements?
1.78) Define stress concentration factor.
1.79) Define stress concentration and stress concentration factor.
[AU, May / Jun – 2014]
1.80) How to avoid stress concentration? [AU, Nov / Dec –2012]
1.81) What are the methods of reducing stress concentration?
[AU, May / Jun - 2009]
1.82) What are the factors to be considered while designing machine parts to avoid
fatigue failure?
1.83) Define fatigue stress concentration factor.
1.84) Define (a) stiffness and (b) resilience [AU, May / Jun - 2009]
1.85) Describe the material properties of hardness, stiffness and resilience.
[AU, Nov / Dec –2013, May / Jun – 2016]
1.86) Differentiate between hardness and toughness of materials.
[AU, May / Jun – 2014]
1.87) What are the types and modes of fracture?
1.88) Explain soderberg and Goodman lines in details.
1.89) What is Geber theory [AU, Nov / Dec – 2009]
1.90) Write Soderberg equation for a machine component subjected to
(a)Combination of mean and variable torques
(b) Combination of mean and variable bending moments
[AU, Nov / Dec – 2010]

PART –B
1.91) Discuss in detail about the factors influencing machine design.
[AU, May / Jun - 2012]
1.92) What are the factors influencing machine design? Explain it.
[AU, May / Jun – 2014]
1.93) Explain various phases in Design using a flow diagram and enumerate the factors
influencing the machine design. [AU, May / Jun - 2013]
1.94) What is factor of safety? List the factors to be considered while deciding the factor
of safety. [AU, May / Jun – 2014]
1.95) Write short notes on preferred numbers, fits and types of fits.
[AU, May / Jun - 2012]
1.96) What is meant by hole basis system and shaft basis system? Which one is
preferred and why? [AU, May / Jun - 2013]
1.97) Explain the maximum normal stress theory of failure (Rankine's theory)
1.98) Explain the maximum shear theory of failure (Guest's theory)
1.99) Explain distortion energy theory of failure (Hencky and Von Mises theory)
1.100) What is the difference between Gerber curve and soderberg and Goodman
lines? [AU, May / Jun - 2013]
1.101) Explain notch sensitivity. What are the factors that affect notch sensitivity?
1.102) Explain in detail the maximum shear stress theory [AU, Nov / Dec – 2009]
1.103) Explain soderberg and Goodman lines in details. [AU, Nov / Dec – 2009]
1.104) Discuss in detail about CAD and optimum design. State their relevance in
designing mechanical elements. [AU, Nov / Dec – 2008]
1.105) Write short notes on the following: [AU, May / Jun – 2014]
 Interchangeability
 Tolerance
 Allowance
1.106) Define Stress concentration. Give some methods of reducing stress
concentration. [AU, Nov / Dec –2011]
1.107) The dimensions of mating parts, according to basic hole system are given as
follows:
Hole: 25mm Shaft: 24.97mm

25.02mm 24.95mm
Find the hole tolerance, shaft tolerance and allowance.
1.108) The following results were obtained in a tensile test on a mild steel specimen
of original diameter of 20 mm and guage length 40 mm. At the limit of
proportionality, the load was 80000 N and extension is 0.048 mm. The specimen
yielded at a load of 85000 N and the maximum load was 150000 N. When two
parts are fitted together after being broken, the guage length was found to be 55.6
mm and the diameter at neck was 15.8 mm. Calculate the Young’s modulus, stress
at the limit of proportionality, yield stress, ultimate stress, percentage elongation
and reduction and working stress. Take factor of safety = 2
1.109) Consider two aluminum rods and one steel rod combined as one unit which
supports a weight of 1000 kg. If the area of cross section of aluminum and steel
rods is 2 cm2
each and strains are equal, find the stresses acting on aluminum and
steel rods.
2626
/10x1.2/10x7.0 cmkgfEcmkgfE steelAl 
1.110) An unknown weights falls through 10mm onto a collar which is rigidly attached
to the lower end of a vertical bar 3 m long and 600 mm2
cross section. The
maximum instantaneous extension is 2mm. What is the corresponding stress and
the value of the weight? Take E = 200 kN/mm2
. [AU, Nov / Dec –2014, 2015]
1.111) A flat bar 32 mm wide and 12 mm thick is loaded by a steady tensile load of 85
kN. The material is mild steel with yield point stress of 315 N/mm2
. Find the factor
of safety based on the yield point. [AU, Nov / Dec – 2008]
1.112) A flat plate of width 60 mm has a central hole of 10 mm diameter. If the plate
is subjected to an axial tensile load of 10 kN, determine the thickness of the plate.
Assume yield point stress 300 MPa and factor of safety as 2.5.
[AU, Nov / Dec – 2008]
1.113) A shaft is transmitting 100 KW at 160 rpm. Find the suitable diameter of the
shaft if the maximum torque transmitted exceeds the mean by 25%. Take the
maximum allowable shear stress as 70 MPa.
1.114) A cast iron pulley transmits 10kW at 400rpm. The diameter of the pulley is
1.2m and it has four straight arms of elliptical cross section in which the major

axis is twice of the minor axis. Determine the dimension of the arm if the
allowable bending stress is 15MPa. [AU, May / Jun - 2009]
1.115) A shaft is supported in bearings, the distance between their centers being 1 m.
It carries a pulley in the centre and it weighs 1 KN. Find the diameter of the shaft,
if the permissible bending stress for the shaft material is 40 N/mm
2
.
1.116) Determine the diameter of circular rod made of ductile material with endurance
limit is 265MPa and tensile yield strength of 350MPa. The member is subjected
to a varying axial load form – 300kN to 700kN and has a stress concentration
factor is 1.8. The factor of safety as 2. [AU, May / Jun - 2009]
1.117) Two rods made of plain carbon steel 40C8 (Syt= 380 N/mm2
) are connected by
means of cotter joint. The diameter of each rod is 50mm and the cotter is made
of steel plate of 15mm thickness. Calculate the dimension of the socket end
making the following assumptions. (i) the yield strength in compression is twice
of the tensile yield strength and (ii) the yield strength in shear is 50% of the
tensile yield strength. Factor of safety is 6. [AU, Nov / Dec – 2009]
1.118) It is desired to bend a strip of 6 mm thick and 20 mm wide of spring steel into
a loop with the end overlapping and riveted. Find the minimum radius of the loop
if the stresses due to bending are limited to 100 MPa. Also determine the bending
moment required to bend the strip. Take Young’s modulus .10x1.2 5
MPaE 
1.119) A rod of linkage mechanism made up of steel 40Crl (Sut = 550N/mm2
) is
subjected to completely reversed axial load of 100kN. The rod is machined on
the lathe and 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. [AU, Nov / Dec – 2009]
1.120) A shaft transmits 20 KW power and rotates at 500 rpm. The material of shaft
is 50 C4 and the factor of safety is 2.
 Determine the diameter of the shaft on the basis of its shear strength
Determine the diameter of shaft on the basis of its torsional rigidity, if the
permissible angle of twist is 30
per meter length and the modulus of
rigidity of the shaft material is 79300 N/mm2
. [AU, May / June – 2007]

1.121) Design a suitable diameter for a circular shaft required to transmit 90 KW at
120 rpm. The shear stress for the shaft is not to exceed 70 N/mm2
and the
maximum torque exceeds the mean by 40 %.
1.122) The shaft of an overhang crank is subjected to a force F of 2kN as shown in
figure. The shaft is made of 30Mn2 steel having an allowable shear strength equal
to 100N/mm2
. Determine the diameter of the shaft.
[AU, Apr / May – 2015, May / Jun – 2016]
1.123) A weight W falls 10mm on a collar rigidity attached to the lower end of vertical
part 6m long 400mm2
in cross section. The maximum instantaneous extension is
found to be 2mm. Take Young’s modulus 2 * 105
N/mm2
. Find the value W and
impact stress induced
1.124) A bolt is subjected to a direct tensile load of 25kN and shear load of 15kN.
Considering various theories of failure, determine the suitable size of bolt if the
yield stress in tension is 250N/mm2
. Take FOS as 2 and Poisson’s ratio as 0.3
[AU, Nov / Dec – 2008]
1.125) An I-section beam of depth 250 mm is supported at two points 4 m apart. It is
loaded by a weight of 4 KN falling through a height h and striking the beam at
mid span. The moment of inertia of the section is 8 x 107
mm4
; E = 210 KN/ mm2
.
Determine h if the stress is 120 N/mm2
.
1.126) A man weighing 60 kg jumps from a height of 50 cm on a diving board of
rectangular cross - section having 30 cm width and 2 m long. If the maximum
induced stress is limited to 400 kg/cm2 and the modulus of elasticity of the board
is 1 x 105kg/cm2, find the thickness of the diving board.

1.127) A cantilever beam of span 800mm carries a uniformly distributed load of
12kN/m. the yield value of material of cantilever is 400MPa. Factor of safety is
2.5 find the economical section of cantilever among (i) circular cross section of
diameter ‘d’ (ii)rectangular cross section of depth ‘d’ and width ‘w’ d/w= 2.5 (iii)
‘I’ section of total depth 7t width 5t where ‘t’ is thickness. Find the dimension
and cross sectional area of the economic section [AU, Apr / May – 2010]
1.128) A vertical pillar of 50 mm diameter is subjected to a vertical load of 1 kN acting
eccentrically at a distance of 30 mm from the axis. Calculate the maximum stress
in the pillar and locate it.
1.129) A shaft of diameter 40 mm is used to transmit the power of 30 KW at 710 rpm
and is supported in bearings 500 mm apart. A load of 10 KN is concentrated at
the centre of shaft vertically. Calculate the maximum principle stress and shear
stress.
1.130) A hollow shaft is required to transmit 600 kW at 110 rpm, the maximum torque
being 20% greater than the mean. The shear stress is not to exceed 63 Mpa and
twist in a length of 3 meter not to exceed 1.4 degrees. Find the external diameter
of the shaft, if the internal diameter to the external diameter is 3/8. Take modulus
of rigidity as 84 Gpa. [AU, Apr / May 2011]
1.131) Determine the diameter of a steel bar, which is of ductile nature subjected to
an axial tensile of 60kN and torsional moment of 1600N-m. Use the factor of
safety of 2.5, E= 200GPa [AU, Apr / May – 2010]
1.132) A shaft as shown in figure is subjected to a bending load of 3kN, pure torque
of 1000 N-m and an axial pulling force of 15kN. Calculate the stress at A and B
[AU, Apr / May – 2010, May / Jun – 2016]

1.133) A cantilever beam made of cold drawn carbon steel of circular cross section
as shown in fig ., is subjected to a load which varies from –F to 3 F. Determine
the maximum load that this member can withstand for an indefinite life using a
factor of safety as 2. The theoretical stress concentration factor is 1.42 and the
notch sensitivity is 0.9.
Assume the following values:
Ultimate stress =550 Mpa
Yield stress = 470 Mpa
Endurance limit = 275 Mpa
Size factor = 0.85
Surface finish factor = 0.89. [AU, Apr / May – 2011]
1.134) A simply supported beam has concentrated load at the centre which fluctuates
a value from P to 4P. The span of the beam is 500 mm and its cross section is
circular with a diameter of 60 mm. Beam material is cold drawn 0.2% carbon
steel. Calculate the maximum permissible value of P for a factor of safety of 1.3.
Beam surface is ground [AU, Nov / Dec – 2010]
1.135) The C frame of 100kN capacity press is shown in fig. the material of the frame
is grey cast iron an d the factor of safety is 3 determine the dimensions of the
frame [AU, Apr / May – 2010]

1.136) The frame of a punch press is shown in fig. Find the stresses at the Inner and
outer surface at section X-X of the frame, if W = 5000 N.
[AU, May / Jun – 2014]
1.137) A bracket as shown in figure is bolted to the frame - work of a machine which
carries a load P. The cross - section of the bracket is rectangle with 30 mm wide
and 60 mm deep. If the maximum stress is limited to 30 N/mm2, find the value of
P. [AU, Apr / May – 2011]

1.138) A mild steel bracket is shown in figure. It is subjected to a pull of 6000 N acting
at 450
to the horizontal axis. The bracket has a rectangular section whose depth
is twice the thickness. Find the cross sectional dimensions of the bracket if the
permissible stress in the material is 60MPa [AU, Nov / Dec – 2012]
1.139) A cast-iron link, as shown in figure, is to carry a load of 20 kN. If the tensile and
compressive stresses in the link are not to exceed 25 MPa and 80 MPa
respectively, obtain the dimensions of the cross- section of the Link at the middle
of its length. [AU, Nov / Dec –2013]
1.140) A mild steel bracket is shown in figure. It is subjected to a pull of 5000 N acting
at 450
to the horizontal axis. The bracket has a rectangular section whose depth
is twice the thickness. Find the cross sectional dimensions of the bracket if the
permissible stress in the material is 50 N/mm2
[AU, Nov / Dec – 2005, 2007]
1.141) The crank hook carries a load of 20KN as shown in figure. The section at X –X
is rectangular whose horizontal side is 100 mm. Find the stresses in the inner and
outer fibers at the given section

1.142) A C-clamp is subjected to a maximum load of W, as shown in figure. If the
maximum tensile stress in the clamp is limited to 140 MPa., find the value of the
load W. [AU, Nov / Dec –2012]
1.143) Determine the maximum shear stress induced in the member loaded as shown in
figure.

1.144) A cylindrical bar of 50 mm diameter and 250 mm long is fixed at one end. At the
free end it is loaded as shown in figure with axial load of 15 KN, a downward
transverse load of 5KN and a torque of 2 KNm. Calculate the maximum stress at
point A of the bar.
1.145) A bolt is subjected to a direct load of 25 KN and a shear load of 15 KN.
Considering the various theories of failure, determine a suitable size of the bolt,
if the material of the bolt is C15 having 200 N/mm2
yield strength.
[AU, May / June – 2007]
1.146) A shaft of diameter 50 mm is subjected to a bending moment of 20 Nm and torque
15 Nm and the yield stress is 200 N/mm2
. Find the factor of safety according to
all theories of failure.
1.147) A steel member is subjected to a 3 dimensional stress system and the resulting
principal stresses are 120 N/mm2
tension, 80 N/mm2
and 40 N/mm2
compression.
If the proportional limit of the material in simple tension is 280 N/mm2
and its
Poisson’s ratio is 0.3, determine the factor of safety according to
(a) Maximum principal stress theory
(b) Maximum principal strain theory
(c) Maximum shear stress theory.
1.148) A machine part is statically loaded and has a yield point strength of 350 N/mm2
.
If the principal stresses are 70 N/mm2
and 35 N/mm2
, both tensile, find the factor of
safety for the following cases. [AU, Nov / Dec – 2015]

(i) Maximum normal stress theory
(ii) Maximum shear stress theory and
(iii) Distortion energy theory.
1.149) A bolt is subjected to an axial pull of10 kN and a transverse shear force of 5 kN.
The yield strength of the bolt material is 300 MPa. Considering a factor of safety of
2.5. Determine the diameter of the bolt, using (i) maximum normal stress theory, (ii)
maximum shear stress theory, and (iii) maximum principal strain theory. Take
Poisson's ratio as 0.2. [AU, Nov / Dec – 2015]
1.150) A compound bar of 3m length made up of copper having E = 105GN/m2
and the
other of steel having = 210GN/m2
. Each bar is 25mm broad and 12.5mm thick. This
component bar is stretched by a load of 50kN. Find the increase in length of the
compound bar and the stress produced in the steel and copper. The length of copper
as well as of steel bar is 3m each. [AU, Nov / Dec - 2011]
1.151) A tie - bar has to carry a load of 100 KN. What must be the thickness of bar of
110 mm width, if there is a rivet hole of 22 mm diameter on its, centre line? Working
stress for the tie bar is 75MPa
1.152) A stepped shaft of diameters D and d is subjected to a variable axial load P which
cyclically varies between 0 and 10 KN. The shaft is made of C20 steel, mirror
polished with Su= 500 N/mm2 and Sy = 260 N/mm2. Determine the diameters D
and d with D/d = 1.5, factor of safety = 2, notch sensitivity factor = 0.8 and r/d =
0.2 where r is the shoulder radius.

1.153) A steel rod of yield strength 350N/mm2
and endurance limit of 265 N/mm2
is
subjected to axial load of which varies from -300kN to 700kN and has a stress
concentration factor 1.8. Assume FOS as 2. Calculate the diameter of steel rod
[AU, Apr / May – 2011]
1.154) Determine the thickness of a 120mm wide uniform plate for safe continuous
operation if the plate is to be subjected to a tensile load that has maximum value
of 250kN and a minimum values 100kN. The properties of the plate as follows.
Endurance limit stress = 225MPa and yield pint stress 300MPa. The factor of
safety based on yield point may be taken as 1.5. [AU, Nov / Dec - 2011]
1.155) A hot rolled steel shaft of 40mm diameter is subjected to a torsional moment that
varies from 330 Nm to – 110 Nm and an applied bending moment which rises
from 440 Nm to –220 Nm. The material of the shaft has an ultimate strength of
550 MN/m2
and yield strength of 410 MN/m2
. Find the approximate factor of
safety using soderberg equation allowing endurance limit to be half the ultimate
strength and size factor and surface finish factor to be 0.85 and 0.62 respectively.
[AU, Nov / Dec – 2008]
1.156) A hot rolled steel shaft is subjected to a torsional moment that varies from 330
Nm clockwise to 110 Nm counter clockwise and an applied bending moment at
a critical section varies from 440 Nm to -220 Nm The shaft is of uniform cross-
section and no keyway is present at the critical section. Determine the required
shaft diameter. The material has an ultimate strength of 550 MPa and yield
strength of410 MPa. Take the endurance limit as half the ultimate strength, factor
of safety of 2, size factor of 0.85 and a surface finish factor of 0.62.
[AU, Nov / Dec –2013]
1.157) A plate of 12 mm thick, with two holes as indicated in figure below is subjected
to a tensile load of 20 KN. Calculate the stresses at both the holes.
[AU, Nov/Dec – 2004]

1.158) A medium force fit on a 50 mm shaft requires a hole tolerance of 0.025 mm and
a shaft tolerance of 0.016 mm. The maximum interference is to be 0.042 mm.
How will you dimension the hole and the shaft, if hole deviation is H?
[AU, Nov / Dec – 2010]
1.159) A plate of uniform thickness t has two width 45 mm and 30 mm with a fillet
radius of 5 mm. The smaller width portion has a transverse hole of 15 mm
diameter for plate material. The ultimate strength is 200 N/mm2
. Consider stress
concentration factor and assume F.S = 2.5. Find the thickness of the plate for
maximum tensile load of 5 KN. [AU, Nov / Dec – 2006]
1.160) Determine the maximum stress involved in the following cases taking stress
concentration into account.
Case
i) A rectangular plate with a hole under an axial load of 10 KN.
ii) A circular shaft with a step under an axial load of 10 KN.
iii) A shaft under a bending moment of 50 Nm.
iv) A shaft under a twisting moment of 50 Nm.
1.161) A machine component is subjected to a flexural stress which fluctuates between
+300 MN/m2and -150 MN/mm2. Determine the value of minimum ultimate
strength according to
i) Gerber relation
ii) Modified Goodman relation
iii) Soderberg relation
Take yield strength = 0.55 ultimate strength; endurance strength = 0.5 ultimate
strength; factor of safety = 2.
1.162) A machine component is subjected to fluctuating stress that varies from 40 to
100 N/mm2
. The corrected endurance limit stress for the machine component is
270 N/mm2
. The ultimate tensile strength and yield strength of material are 600
and 450 N/mm2
respectively. Find the factor of safety using:
(1) Gerber theory
(2) Soderberg line

(3) Goodman line and
(4) Also, find factor of safety against static failure.
[AU, May / Jun - 2013]
1.163) A cantilever rod of circular section is subjected to a cyclic transverse load
varying from -100N to +300 N as shown in figure. Determine the diameter d of
the rod by
i) Goodman method ii) Soderberg method.
Using the following data :
Factor of safety = 2; theoretical stress concentration factor = 1.4; notch
sensitivity factor = 0.9; ultimate strength = 550 MPa ; endurance strength = 275
MPa; size correction factor = 0.85 surface correction factor = 0.9 ; yield strength
= 320 MPa
1.164) A cantilever rod of length 120 mm with circular section is subjected to a cyclic
transverse load; varying from -100 N to 300 N at its free end. Determine the
diameter ‘d’ of the rod, by (i) Goodman method and (ii) Soderberg method using
the following data. Factor of safety = 2; Theoretical stress concentration factor =
1.4; Notch sensitivity factor = 0.9; Ultimate strength= 550 MPa; Yield strength =
320 MPa; Endurance limit = 275 MPa; Size correction factor = 0.85; Surface
correction factor= 0.9. [AU, Nov / Dec – 2015]
1.165) Determine the cross - section of C frame shown in figure to withstand a
maximum load of 25KN. Permissible stress in tension is 100 N/mm2. Find also
the stresses at X - X. Assume h = 2b

1.166) A cylindrical shaft made of steel of yield strength 700 MPa is subjected to static
loads consisting of bending moment 10 KN-m and a torsional moment 30 KN-m.
Determine the diameter of the shaft using two different theories of failure and
assuming a factor of safety of 2. Take E = 210 GPa and Poisson's ratio = 0.25.
[AU, Nov / Dec – 2012]
1.167) A shaft is subjected to a bending moment varying from - 200 Nm to 500 Nm and
a twisting moment varying from 50 Nm to 175 Nm. The material used has SU =
600 MPa ; Se = 300 MPa; Ka = 0.76; Kb = 0.85; Kc = 0.897; Kt = 1.85 and q =
0.95. Find the diameter of the shaft by Von Misses Hencky theory. Factor of
safety is 1.5 [AU, Nov / Dec – 2003]
1.168) In an elastic material, principal stresses are tensile and compressive and the ratio
being 4 : 1. Determine the limiting stress according to different theories of failure
if the tension test gives the elastic limit of the material as 400 N/mm2. Assume
Poisson's ratio as 0.3.
1.169) A hot rolled steel shaft is subjected to a torsional load varying from 300 Nm
clockwise to 150 Nm counter clockwise and to a bending moment at a critical
section varying from 400 Nm positive to 200 Nm negative. The shaft has uniform
cross - section and no keyway is present at the critical section. Determine the
required shaft diameter assuming σu = 500 N/mm2, σy = 400 N/mm2 and n = 2

1.170) A rod of a linkage mechanism made of steel 40Crl(σut = 550 N/mm2
) is subjected
to a completely reversed axial load of 100 kN. The rod is machined on lathe 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.
[AU, Nov / Dec – 2009]
1.171) Determine the diameter of a circular rod made of ductile material with a
endurance limit is 265 MPa and a tensile yield strength of 350 MPa. The member
is subjected to a varying axial load from – 300 kN to 700 kN and has a stress
concentration factor is 1.8. Take factor of safety as 2. [AU, May / June - 2009]
1.172) A shaft of diameter 'd' is subjected to a torque varying between 900 Nm to 1800
Nm. Assuming a factor of safety 2 and a stress concentration factor of 1.2, find
the diameter of the shaft.Take σu = 650 N/mm2
σy = 480 N/mm2
, Size factor B
= 0.85 and surface finish factor C = 0.5. [AU, Nov / Dec –2014]
1.173) A cast iron pulley transmits 10 kW at 400 rpm. The diameter of the pulley is 1.2
metre and it has four straight arms of elliptical cross-section, in which the major
axis is twice the minor axis. Determine the dimensions of the arm if the allowable
bending stress is 15 MPa. [AU, May / June - 2009]
1.174) A Cast iron pulley transmits 10 kW at 400 rpm. The diameter of the pulley is 1.2
m and it has four straight arms of elliptical cross-section, in which the major axis
is twice the minor axis. Determine the dimensions of the arm if the allowable
bending stress is 15 MPa. [AU, Nov / Dec –2011]
1.175) A circular bar of length 600mm is supported at its ends. It is acted upon by a
concentrated cyclic load at its centre which varies from 20 KN to 50 KN. If the
factor of safety is 1.5, surface finish factor is 0.9 and the size effect is 0.85. Find
the diameter of the bar. The ultimate strength of the bar is 650 N/mm2, yield
strength is 500 N/mm2 and endurance strength is 350 N/mm2.

1.176) A 50 mm diameter shaft is made from carbon steel having an ultimate tensile
strength of 630 MPa. It is subjected to a torque, which fluctuates between 2000
Nm to – 800 Nm. Using Soderberg methods, calculate the factor of safety.
1.177) A simply supported beam has a concentrated load at the center which fluctuates
from a value of P to 4P. The span of the beam is 500 mm and its cross section is
circular with a diameter of 60 mm. Taking for the beam material an ultimate
stress of 700 MPa, a yield stress of 500 MPa, endurance limit of 330 MPa for
reversed bending, and a factor of safety 1.3, calculate the maximum value of P.
Take a size factor of 0.85 and a surface finish factor of 0.9.
[AU, Nov / Dec – 2007]
1.178) A steel cantilever is 200 mm long. It is subjected to an axial load, which varies
from 150 N (compression) to 450 N (tension) and also a transverse load at its free
end, which varies from 80 N up to120 N down. The cantilever is of circular
cross section. It is of diameter 2d for the first 50 mm and of diameter d for the
remaining length. Determine its diameter taking a factor of safety 2 Assume the
following values: [AU, May / Jun – 2016]
Yield stress = 330 MPa
Endurance limit in reversed loading = 300 MPa
Correction factors = 0.7 in reversed axial loading
= 1.0 in reversed bending
Stress concentration factor = 1.44 for bending
= 1.64 for axial loading
Size effect factor = 0.85
Surface effect factor = 0.90
Notch sensitivity index = 0.90
1.179) A pulley is keyed to a shaft midway between two antifriction bearings. The
bending moment at the pulley varies from – 170 Nm to 510 Nm as the torsional
moment in the shaft varies from 55 Nm to 165 Nm. The frequency of the variation
of the load is the same as the shaft speed. The shaft is made of cold drawn steel
having an ultimate strength of 538 MPa and yield strength of 400 MPa.

Determine the required diameter for an indefinite life. The stress concentration
factor for the keyway in bending and torsion may be taken as 1.6 and 1.3
respectively. Correction factor A = 1 (for bending) A = 0.6 (for torsion) B = 0.85,
C = 0.88. Use a design factor N = 1.5[AU, April / May – 2004, May / Jun - 2012]
1.180) A pulley is keyed to a shaft midway between two antifriction bearings. The
bending moment at the pulley varies from – 160 Nm to 500 Nm as the torsional
moment in the shaft varies from 60 Nm to 160 Nm. The frequency of the variation
of the load is the same as the shaft speed. The shaft is made of cold drawn steel
having an ultimate strength of 540 MPa and yield strength of 400 MPa.
Determine the required diameter for an indefinite life. The stress concentration
factor for the keyway in bending and torsion may be taken as 1.6 and 1.3
respectively. The factor of safety is 1.5, size factor = 0.80 and surface finish factor
= 0.85 [AU, May / Jun - 2012]
1.181) A pulley is keyed to a shaft midway between two bearings. The shaft is made of
cold drawn steel for which the ultimate strength is 550MPa and the yield strength
is 400MPa. The bending moment at the pulley varies from -150 N-m to 400 N-m
as the torque on the shaft varies from -50N-m to 150N-m. Obtain the diameter of
the shaft for an indefinite life. The stress concentration factors for the keyway at
the pulley in bending and in torsion are 1.6 and 1.3 respectively. Take the
following values: Factor of safety = 1.5; load correction factors = 1.0 in bending
and 0.6 in torsion; Size factor = 0.85; Surface effect factor = 0.88.
[AU, Nov / Dec –2012]
1.182) A transmission shaft made of C 45 steel is subjected to a fluctuating torque
varying from –100 Nm to + 500 Nm. Also, a fluctuating BM acts on the shaft,
which varies from +500 Nm to – 500 Nm. Kt = 2. FS = 1.5. Determine the
required diameter of the shaft. [AU, Nov / Dec – 2005]
1.183) A transmission shaft made of C45 steel is subjected to a fluctuating torque
varying from -100N-m to +500N-m. Also a fluctuating bending moment acts on
the shaft, which varies from +500N-m to -500N-m. Let the stress concentration
factor be 2. The shaft is machined for a FOS 1.5. Determine the required diameter
of the shaft. [AU, April / May – 2010]

1.184) A steel bar is subjected to a reverse axial load of 180kN. Find the diameter of
the bar for a design factor of 2. Ultimate tensile strength 1070N/mm2
, yield
strength 910N/mm2
. Endurance limit in bending is half of ultimate strength. Use
the following data. Load factor = 0.7, surface finish factor = 0.85 and stress
concentration factor 1 [AU, May / Jun - 2012]
1.185) A bar of circular cross section is subjected to alternating tensile forces varying
from a minimum of 200 KN to a maximum of 500 KN. It is to be manufactured
of a material with an ultimate tensile strength of 900 MPa and an endurance limit
of 700 MPa. Determine the diameter of the bar using safety factors of 3.5 related
to ultimate tensile strength and 4 related to endurance limit and a stress
concentration factor of 1.65 for fatigue load. Use Goodman straight line as basis
for design.
1.186) A circular bar of 500 mm length is supported freely at its two ends. It is acted
upon by a central concentrated cyclic load having a minimum value of 20 kN and
a maximum value of 50 kN. Determine the diameter of bar by taking a factor of
safety of 1.5, size effect of 0.85, surface finish factor of 0.9. The material
properties of bar are given by, ultimate strength of 650 MPa, Yield strength of
500 MPa and Endurance strength of 350 MPa. [AU, Nov / Dec –2011]

ME6503 - DESIGN OF MACHINE ELEMENTS UNIT - I NOTES

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