EXCEL
Institute of Engineering Studies
NADEEM Sir
(8421034449)
question bank
BENDING STRESSE IN BEAMS
Type 1: basic concept
Q1: A steel plate of width 120 mm and of thickness 20 mm is
bent into circular arc of radius 10 m. Determine the maximum stress induced and
the corresponding bending moment.
Q2: Calculate the maximum stress induced in cast iron pipe
of external diameter 40 mm, internal diameter 20 mm and of length 4 m. The pipe
is supported at its ends and carries a point load of 80 N at its center.
Q3: A cantilever of length 2 m fails when a load of 2 kN is
implied at its free end if the section of beam is 40 mm × 60 mm find the stress
at the failure.
Q4: A rectangular beam 200mm deep and 300mm wide is simply
supported over span of 8m. It carries a UDL of 3.2 N/m over entire length.
Calculate maximum bending moment induced.
Q5: a rectangular beam 300mm deep is simply supported over
span of 4m .determine UDL per meter which the beam may carry if the bending
stress is not to exceed 120N/mm2. Take M.I =8×106 mm4.
Q6: A beam is simply supported and carries a UDL of40 kN/m
run over whole span. He section of beam is rectangular having depth 500 mm. if
maximum stress in material of beam is 120 N/mm2 and M.I. of section
is 7×108mm4, find span of beam.
Q7: A timber beam of rectangular section is to support a
load of 20 kN uniformly distributed over 3.6m of the entire beam. The beam is
simply supported and the maximum allowable stress is 7 N/mm2. If
depth of the section is to be twice the breadth find the dimensions of cross
section.
Q8: Replace UDL by point load of 20 kN at the center of beam
in above question.
Q9: A symmetrical section 200mm deep has M.I of 2.25 ×10-5m4
about neutral axis. Determine longest span over which, when simply supported,
the beam would carry a UDL of 4kN/m if bending stress is not to exceed 125MN/m2.
Q10: A hollow circular bar having outside diameter twice the
inside diameter is used as beam. From the bending moment diagram it is found
that beam is subjected to bending moment of 40kNm. If bending stress is limited
to 100MN/m2 find diameters.
Q11: A cast iron main 12m long of 500mm inside diameter and
25mm wall thickness runs full of water and is supported at its ends. Calculate
maximum stress if density of cast iron is 7200 kg/m3 and that of
water of 1000kg/m3.
Q12: Determine dimensions of cross section of timber of span
8m to carry a brick wall 200mm thick and 5 m high, if density of brick is
1850kg/m3 and maximum permissible stress is limited to 7.5 N/m2.
The depth of sections twice the breadth.
Type 2: c/s SYMMETRICAL about horizontal neutral axis
Q13: A rolled steel beam of I-section has dimensions as
shown in figure. This beam carry a UDL of 40 kN/m run on span of 10 m.
Calculate max. Bending stress.
Q14: Channel section 100mm×40mm×100mm as shown in figure, is used as cantilever of span
0.82m with a point load acting at its free end. If maximum permissible bending
stress is 160 MPa find magnitude of point load.
Q15: An
I-section beam shown is used as cantilever carries a UDL 3kN/m throughout the
span of 3m. calculate maximum bending stress induced. Also calculate its
section modulus.
Q16: An
I-section shown in figure is simply supported over span of 12m. If maximum
bending stress is 80N/mm2, what point load can be carried at the
distance 4m from one support.
TYPE 3: c/s
UNSYMMETRICAL about horizontal neutral axis
Q17: A cast iron bracket subjected to bending has cross
section of I with unequal flanges. The dimensions of section are shown inn
figure. Find position of neutral axis and M.I. if permissible bending moment is
40 MN.mm, determine maximum bending stress and state its nature.
Q18: A cast iron beam as shown in figure is of T-section the
beam is simply supported on of span of 8m. the beam carries a UDL of 1.5kN/m on
entire span. Determine maximum tensile
and maximum compressive stresses.
Q19: A simply supported beam of length 3m carries a point
load of 12kN at a distance of 2m from left support. The C/S of beam is shown in
figure. Determine maximum tensile and compressive stresses at x-x .
Q20: Figure shows a cast iron bracket of I-section find
position of N.A. and M.I. also find maximum bending moment that should be
imposed on this section if tensile stress of top flange is not to exceed 40MN/m2
also find maximum compressive stress.
Q21: A horizontal beam of section shown is 4m and is simply
supported at ends calculate maximum UDL it can carry if maximum tensile and
compressive stresses are not to exceed 25MN/m2and 45MN/m2
respectively.
Q22: Figure shows cross section of cast iron beam . this beam is subjected to a
bending moment, the tensile stresses at bottom edge is 30MN/m2.
Calculate bending moment and compressive stress at top.
Q23: A beam simply supported at ends and having cross
section as shown in figure. It is loaded with UDL over whole of its span. If
the beam is 8m long find the UDL. Take maximum tensile stress = 30MN/m2
and maximum compressive stress =45MN/m2 also, what are the actual
bending stresses setup in the section.
Q24: A cast iron beam of I-section as shown in figure is
simply supported over span of 5m. If tensile stress is not to exceed 20N/mm2.
Find safe UDL of beam. Also find maximum compressive stress.
Q25: Channel section as shown in figure is of span”L”m and
is simply supported at ends. It carries a UDL of 1kN/m. if maximum stress is
not to exceed 160MPa what should be span of beam.
Q26: A simply supported cast iron beam 2m long has c/s as
shown in figure if intensity of load on beam is 30kN/m. determine the maximum
compressive stress in the beam density of material = 7245kg/m3
COMBINED (direct & bending) stresses (question bank)
Q1: A rectangular column of width 200 mm and thickness 150
mm carries a point load of 240 kN at eccentricity of 10 mm as shown. Determine
maximum and minimum stresses.
Q2: A rectangular column of width 100 mm and thickness 75 mm
carries a point load of 120 kN. If minimum stress is zero find eccentricity of
load along horizontal neutral axis. Also calculate maximum stress induced in
the section.
Q3: A rectangular column of width 200 mm and thickness 150
mm carries a point load of 240 kN at an eccentricity of 50 mm. find max. stress
& min. stress . also plot stresses along width of section.
Q4:Calculate the eccentricity of a point load acting on a
column of circular cross section and diameter 20cm.if ther is zero compression
at one side of cross section .take p=240kN ,b=250mm,d=120 mm .
Q5: A short column of external diameter 40 cm and internal
diameter 20 cm carries a n eccentric load of 80 kN.find the greatest
eccentricity which the load can have without producing tension on the c/s.
Q6: A short column of do=40 cm and di=
20cm carries a point load on 80 kN at an eccentricity of 150 mm. find extreme
stresses.
Q7: A short column of hollow cylindrical section (do=25cm
and di= 15cm) carries a vertical load of 400 kN along one of
diameter plane 10 cm away from the axis of column . find extreme stresses
,their nature and plot stress diagram.
Q8: A hollow rectangular masonry pier is 1.2m ×0.8m over all, the wall
thickness is 0.15 m. a vertical load of 100 kN is transmitted in a vertical
plane bisecting 1.2m side at an eccentricity of 0.1m from geometric axis of
section. Calculate max. and min stresses.
Q9: A hollow
rectangular column of external depth 1m and external with 0.8 m is 10 cm thick.
If vertical load of 200kN is acting with eccentricity of 15cm as shown
calculate max. and min. stresses.
CHIMNEY
Q10: A masonry chimney 24 m high, of uniform circular
section, 3.5 m external diameter and 2 m internal diameter, is subjected to
horizontal wind pressure of 1 kN/m2 of projected area. Find the max.
and min. intensities of stresses at the base if specific weight of masonry is
22 kN/m3.
Q11: A cylindrical chimney 22m high, of uniform circular c/s
has 4 m external dia and 2 m internal diameter. The intensity of horizontal
wind pressure is 1.2 kN/m2.
Find the intensities of stresses if the specific weight of masonry is 22 kN/m3.
Q12: A square chimney 24m high has an opening 1.25m inside.
The external dimensions are 2.5m×2.5
m. the horizontal intensity of wind pressure is 1.3kN/m3 and
specific weight of masonry is 22kN/m3. Calculate the max. and min.
intensities of stresses at the base of chimney.
Q13: A long rectangular wall is 2.5m wide. If the max. wind
pressure on the face of wall is 1.1kN/m2, find the max. height of
wall so that there is no tension in the base of wall. The specific weight of
masonry is 22 kN/m3.
Q14: A chimney has external and internal dimensions of 2m×2m and 1m×1m respectively. The
height of chimney is 14m. Find the max. and min. stress intensities at the base
when it is subjected to horizontal wind pressure of 1.4kN/m2 in the
direction of one of the diagonals of the chimney. Specific weight of masonry is
22kN/m3.
LOAD ECCENTRIC TO BOTH AXES
Q15:A masonry pipe of 3m×4m supports a load of 40kN as shown in fig.
(1)Find stresses developed at each
corner of the pier.
(2)What additional load should be
placed at the Centre of the pier, so that there is no tension anywhere in the
pier section?
(3)What are the stresses at the
corners with the additional load in the center?
Q16: A short column of rectangular cross section 80mm by
60mm carries a load of 40 kN at a point 20mm from the longer side 35mm from the
shorter side. Determine the maximum compressive and tensile stresses in the
section.
Q17:A masonry pier of 3m×4m supports a vertical load of 80 kN as shown in
figure,
(1)Find stresses developed at each
corner of the pier.
(2)What additional load should be
placed at the center of pier, so that there is no tension in anywhere in the
pier section.
Q18: The line of thrust, in a compression testing specimen
15mm dia, is parallel to the axis of specimen but is displaced from it.
Calculate the distance of the line of thrust from the axis when the maximum
stress is 20% greater than the mean stress on a normal section.
Q19: A short column of 20cm external diameter and 15 cm
internal diameter when subjected to a load, the stresses varies from 150MN/m2
compressive at one end to 25MN/m2 tensile on other end. Estimate
load and its intensity.
Q20: A short column of I-section 25cm×20cm has c/s area of 52cm2and maximum
radius of gyration 10.7cm. a vertical load of ‘W’ kN acts through centroid of
section together with a parallel load of ‘W/4’ kN acting through a point on
center line of web distant 6cm from center line. Calculate value of W if
maximum stress is not to exceed 65MN/m2. Also find minimum stress.
Elastic Constant
Q1: Determine the changes in length, breadth and thickness
of a steel bar which is 4 m long, 30 mm wide and 20 mm thick and is subjected
to an axial pull of 30 kN in the direction of its length. Take 
.
.
Q2: Determine the value of Young’s
modulus and Poisson’s ratio of a metallic bar of length 30 cm, breadth 4 cm and
depth 4 cm when the bar is subjected to compressive load of 400 kN. The
decrease in length is given as 0.075 cm and increase in breadth is 0.003 cm.
Q3: Determine the volumetric strain and final volume of a
steel bar which is 4 m long, 30 mm wide and 20 mm thick and is subjected to an
axial pull of 30 kN in the direction of its length. 
.
.
Q4: A steel bar 300 mm long, 50 mm wide
and 40 mm thick is subjected to apull of 300 kN in the direction of its length.
Determine the change in the volume. Take
.
.
Q5: A steel rod 5 m long
and 30 mm in diameter is subjected to an tensile load of 50 kN.
Determine the change in length, diameter and volume of the rod. Take 
.
.
Q6: An elastic member has hollow circular c/s. the internal
diameter is 40 mm and thickness is 4 mm. length of the member is 1.6 m. an
axial pull of 52 kN is applied to the member. If E= 210 GPa and 1/m=0.28.Find
change in length, change in internal diameter and change in external diameter.
Q7: A metallic bar 300mm × 100mm × 40mm is subjected to aforce
of 5 kN (tensile), 6 kN (tensile) and 4 KN (tensile) in x, y and z directions
respectively. Determine change in volume of the block. Take 
Q8: A metallic bar 250mm ×
100mm ×
50mm is loaded as shown in figure. Find the change in volume. Take .
.
Also
find the change that should take place in the 4 MN load, in order that there
should be no change in the volume of the bar.
Q9: A C.I. flat, 300 long and of 30mm ×
50mm uniform section, is acted upon by the following forces uniformly
distributed over the respective cross section; 25 kN in the direction of length
(tensile); 250 kN in the direction of width (compressive) and 200 kN in the
direction of thickness (tensile). Determine the change in volume of the flat. 
.
.
Q10: A bar of steel is 60mm ×
60mm in section and 180 mm long. It is subjecte to a tensile load of 300 kN
along the longitudinal axis and tensile loads of 750 kN and 600 kN on the
lateral faces. Find the change in the dimensions of the bar and the change in
volume.
Take
; 
.
; .
Q11: For a material, Young’s modulus is given as 1.2 × 105
N/mm2 and Poisson’s ratio ¼. Calculate the Bulk modulus.
Q12: A bar of 30 mm diameter is subjected to a pull of 60
kN. The measured extension on guage length of 200 mm is 0.1 mm and change in
diameter is 0.004 mm. Calculate (1)
Young’s modulus, (2) Poisson’s
ratio and (3) Bulk modulus.
Q13: For a given material, Young’s modulus is 110 GN/m2
and shear modulus is 42 GN/m2. Find the Bulk modulus and lateral
contraction of a round bar of 37.5 mm diameter and 2.4 m length when stretched
2.5 mm.
Q14: The following data related to a bar subjected to a
tensile test ;
Diameter = 30mm
Tensile load = 54 kN
Guage length = 300 mm
Extension of bar = 0.112 mm
Change in diameter = 0.00366 mm
Calculate;
Poisson’s ratio
Modulus of elasticity
Bulk modulus
Rigidity modulus
STRAIN ENERGY
Q1: A tensile load of 60 kN is gradually applied to a
circular bar of 4 cm diameter and 5 m long. If the value of 
, determine (1) stretch
in rod,(2) stress in rod and (3)strain energy absorbed by rod.
, determine (1) stretch
in rod,(2) stress in rod and (3)strain energy absorbed by rod.
Q2: Replace load in above question by
load of 60 kN suddenly applied.
Q3: Calculate instantaneous stress
produced in a bar 10 cm2 in area and 3 m long by sudden application
of tensile load of unknown magnitude, if the extension of the bar due to
suddenly applied load is 1.5 mm. also determine the suddenly applied load.
Q4: A steel rod is 2 m long and 50 mm in
dia. axial pull of 100 kN is suddenly applied to the rod. Calculate
instantaneous stress induced and also the instantaneous elongation produced in
the rod.
Q5: A uniform metal bar has c/s area of
700 mm2and length of 1.5 m. If the stress at the elastic limit is
160 N/mm2 , what will be its proof resilience. Determine also the
maximum value of suddenly applied load without exceeding the elastic limit.
Calculate the value of gradually applied load which will produce the same
extension as that produced by suddenly applied load as above.
Q6: A steel bar 4 cm by
4 cm in section , 3m long is subjected to an axial pull of 128 kN .
taking calculate th alteration in length of bar.
Calculate also the amount of energy stored in the bar during the extension.
calculate th alteration in length of bar.
Calculate also the amount of energy stored in the bar during the extension.
Q7: A steel specimen 1.5 cm2in c/s stretches 0.05
mm over 5 cm gauges length under an axial load of 30 kN. Calculate the strain
energy stored in the specimen at this point. If the load at the elastic limit
for specimen is 50 kN, calculate the elongation at the elastic limit and the
resilience.
Q8: A tension bar 5 m long made up of 2 parts, 3m of its
length has c/s area of 10 cm2 while remaining 2 m has c/s area of 20
cm2. An axial load of 80 kN is applied gradually. Find the total
strain energy produced in the bar. Also compare this value with that obtained
in a uniform bar of same length and having the same volume when under the same
load. Take
Q9: The maximum stress produced by a pull
in a bar of length 1 m is 150 N/mm2. The area of c/s and the length
are as shown in figure. Calculate strain energy stored in the bar if
Q10: A bar 100 cm in length is subjected
to an axial pull, such that the maximum stress is 150 MN/m2. Its
area of c/s is 2 cm2over the length of 95 cm and for the middle 5 cm
length it is only 1cm2. If 
, calculate the strain
energy stored in the bar.
, calculate the strain
energy stored in the bar.
Q11: A weight of 10 kN falls by 30 mm on a collar rigidly
attached to a vertical bar 4 m long and 1000 mm2 in section. Find
the instantaneous expansion of the bar. Take .
.
Q12: A load of 100N falls through a
height of 2cm on to a collar rigidly attached to the lower end of a vertical
bar of 1.5 m long and 1.5 cm2
c/s area. The upper end of the vertical bar is fixed. Determine max. stress
induced, max. strain and strain energy stored.
Q13: The maximum instantaneous extension,
produced by an unknown falling weight through a height of 4 cm in a vertical
bar of length 3 m and of c/s area of 5 cm2, is 2.1 mm. calculate
instantaneous stress and value of unknown weight.
Q14: An unknown weight falls through a height of 10 mm on a
collar rigidly attached to the lower end of the vertical bar 500 cm long and
600 mm2 in section. If the maximum extension of the bar is to be 2
mm, what is the corresponding stress and the magnitude of the unknown weight?
Take .
.
Q15: A bar 12 mm diameter gets stretched
by 3 mm under steady load of 8000 N. what stress would be produced in the same
bar by a weight of 800 N, which falls vertically through a distance of 8 cm on
to a rigid collar attached at its end? The bar is initially unstressed. Take .
.
Q16: A rod 12.5 mm in diameter is stretched 3.2 mm under a
steady load of 10 kN. What stress would be produced in a bar by a weight of 700
N, falling through 75 mm before commencing to stretch. Take 
.
.
Q17: An object of 100 N weight falls by
gravity a vertical distance of 5 m, where it is suddenly stopped by a collar at
the end of a vertical rod of length 10 m and diameter 20 mm. the top of the bar
is rigidly fixed. Calculate the maximum stress and strain induced in the bar
due to impact. Take .
.
Q18: A bar 1.2 cm diameter gets stretched by 0.3. cm under a steady load
of 8 kN. What stress would be produced in the same bar by a weight of 0.8 N
which falls freely vertically through a distance of 8 cm on a collar rigidly
attached at its end? Take
Q19: A bar 50 cm long has c/s area of 1.5
cm2 for 30 cm of its length 1 cm2 for remaining length.
If a load of 50 N falls on the collar which is provided at one end of the rod,
the other end being fixed, from a height of 3 cm, find the maximum stress
induced in the bar. Take .
.
Q20: A vertical round steel rod 1.82 m long is securely held
at its upper end. A weight can slide freely on the rod and its fall is rested
by a stop provided at the lower end of the rod. When the weight falls from a
height of 30 mm above the stop the maximum stress reached in the rod is
estimated to be 157 N/mm2. Determine the stress in the rod if the
load had been applied gradually and also the minimum stress if the load had
fallen from the height of 47.5 mm. Take .
.
Q21: A vertical compound tie member fixed
rigidly at its upper end, consist of a steel rod 2.5 m long and 20 mm in
diameter, placed within an equally long brass tube 21 mm in internal diameter
and 30 mm external diameter. The rod and the tube are fixed together at ends.
The compound member is then suddenly loaded in tension by a weight of 10 kN
falling through a height of 3 mm on to a flenge fixed to its lower end.
Calculate the max. stresses in steel and brass assuming 
and 
.
and .
Q22: A vertical bar 4 m long and of 2000
mm2 c/s area is fixed at the upper end and has a collar at the lower
end. Determine the max. stress induced when weight of (1) 3000 N falls through
a height of 20 cm on the collar, (2) 30 kN falls through a height of 2 cm of
the column. Take .
.
Q23: A crain chain whose sectional area
is 6.25 cm2 carries a load of 10 kN. As it is being lowered at
uniform rate of 40 m/min, the chain gets jammed suddenly, at which time the
length of chain unwound is 10 m. estimate the stress induced in the chain due
to the sudden stoppage. Neglect weight of chain. Take .
.
Q24: A cage weighing 60 kN is attached to
the end of the steel wire rope. It is lowered down a mine shaft with a constant
velocity of 1 m/s. what is the maximum stress produced in rope when its
supporting drum is suddenly jammed. The free length of the rope at the moment
of jamming is 15 m, its net c/s area is 25 cm2 and Take .
.
thin cylinders &
spheres
TYPE
(1): DESIGN OF THIN CYLINDERS
Q1: A thin cylinder
of internal diameter 1.25 m contains a fluid at an internal pressure of 2 N/mm2.
Determine the maximum thickness of cylinder if longitudinal stress is not to
exceed 30N/mm2.
Q2: A thin cylinder of internal diameter 1.25 m contains a
fluid at an pressure of 2 N/mm2. Determine the maximum thickness of
cylinder if circumferential (hoop’s stress) not to exceed 45 N/mm2.
Q3: A cylindrical pipe of diameter 1.5 m and thickness 1.5
cm is subjected to an internal fluid pressure of 1.2N/mm2. Determine
1)
Longitudinal stress developed in pipe,
2)
Circumferential stress, and
3)
Shear stress developed in pipe
Q4: A cylinder of internal diameter 2.5m and thickness 5 cm
contains a gas. If the tensile stress in material not to exceed 80 N/mm2,
determine the internal pressure of gas.
Q5: A cylinder of internal diameter 0.5m contains air at
pressure of 7 N/mm2, if the maximum permissible stress induced in
the material is 80 N/mm2, find the thickness of the cylinder.
Q6: Calculate the bursting
pressure for cold drawn seamless steel tubing of 60mm inside diameter with 2 mm
wall thickness. The ultimate strength of steel is 380MN/m2 .
Q7: Calculate the thickness of the
material required for cast iron main 800 mm in diameter for water at a pressure
head of 100 m if the permissible tensile stress is 20 MN/m2 and
weight of water is 10kN/m3.
Q8: Calculate the thickness of the
material required for cast iron main 800mm in diameter for water at a pressure
head of 100 m, if the permissible tensile stress is 20 N/mm2 and
mass of water 980 kg/m3.
TYPE
(2): CHANGE IN DIMENSIONS OF THIN CYLINDER
Q9: Calculate,
1-
The change in diameter,
2-
Change in length and
3-
Change in volume
of a thin cylindrical shell 100 cm diameter, 1 cm thick and
5 m long when subjected to internal
pressure of 3 N/mm2. Take the value of 
and Poison’s ratio 
.
and Poison’s ratio .
Q10: A cylindrical thin drum 80 cm in
diameter and 3 m long has a shell thickness of 1 cm. if the drum is subjected
to an internal pressure of 2.5 N/mm2, determine
1-
Change in length and
2-
Change in volume. Take 
and 
.
and .
Q11: A cylindrical vessel is 1.5 m n diameter and 4 m long
is closed at ends by rigid plates. It is subjected to an internal pressure of 3
N/mm2. If the maximum principal stress is not to exceed 150 N/mm2,
find the thickness of the shell. Also find changes in diameter, length and
volume of the shell.
and 
.
and .
Q12: A closed cylindrical vessel made of
steel plates 4mm thick with plane ends, carries fluid under pressure of 3N/mm2.
The diameter of cylinder is 25 cm and length is 75 cm, calculate longitudinal
and Hoop’s stress in the cylinder wall and determine change in diameter, length
and volume of the cylinder. 
and 
.
and .
Q13: A cylindrical vessel whose ends are
closed by means of rigid flange plates is made of steel plate 3 mm thick. The
internal length and diameter of vessel are 50 cm and 25 cm respectively.
Determine the longitudinal and circumferential stresses in the cylinder shell
due to internal pressure of 3 N/mm2. Also calculate increase in
length, diameter and volume of vessel. 
and .
and .
Q14: A cylindrical shell 3 m long which
is closed at the ends has an internal diameter of 1 m and a wall thickness of
15 mm. calculate the circumferential and longitudinal stresses induced and also
changes in dimensions of the shell if it is subjected to an internal pressure
of 1.5 MN/m2. and .
and .
Q15: A cylindrical shell 90 cm long 20 cm
internal diameter having thickness of metal as 8 mm is filled with a fluid at
atmospheric pressure. If an additional 20 cm3 fluid is pumped into
the cylinder, find
1-
Pressure exerted by the fluid on the
cylinder,
2-
Hoop’s stress. 
and 
.
and .
Q16: A copper cylinder 90 cm long 40 cm,
external diameter and wall thickness of 6 mm has its both ends closed by rigid
blank flanges. It is initially full of oil at atmospheric pressure. Calculate
additional volume of oil which must be pumped into it in order to raise the oil
pressure 5 MN/m2 above atmospheric pressure. For copper 
and 
. Take 
and . Take
Q17: A cylindrical shell with following
dimensions is filled with liquid at atmospheric pressure; length=1.2 m,
external diameter = 20 cm, thickness of metal = 8 mm. find the value of the
pressure exerted by the liquid on the wall of cylinder and the Hoop’s stress
induced if an additional 20 cm3 is pumped into the cylinder. and .
and .
Q17: A hollow cylindrical drum 600 mm in
diameter, 3 m long has shell thickness of 10 mm. if the drum is subjected to
internal pressure of 3N/mm2, determine the increase in its volume. 
and .
and .
TORSION IN SHAFTS
TYPE (1) “TORQUE”
Q1: A solid shaft of150mm dia. is used to transmit torque.
Find max. Torque transmitted by shaft if max. shear stress induced in shaft is
45N/mm2.
Q2: The shearing stress in a solid shaft is not to exceed
40N/mm2 when the torque transmitted is 20,000 Nm. Determine minimum
diameter of shaft.
Q3: In a hollow circular shaft of outer and inner diameter
of 20cm and 10cm respectively. The shear stress is not to exceed 40N/mm2,
find max. Torque that shaft can transmit.
Q4: A hollow shaft of external diameter 120mm transmits
300kW power @ 200 rpm. Determine internal diameter if shear stress is not to
exceed 60N/mm2.
Q5) Find the shear stress induced in a solid shaft of dia.
15cm when the shaft transmits 150kW @ 180rpm.
TYPE (2) “COMPARISON OF SHAFTS”
Q6: Two shafts of same material and same length are
subjected to same torque, if first shaft is of solid cylindrical section and
second is of hollow cylindrical section whose inner dia. is 2/3rd of
external dia.The stress developed in each shaft is same, compare weight of
shafts.
Q7: (same question as above, take di= ¾ do )
TYPE (3) “% SAVING IN MATERIAL”
Q8: A solid cylindrical shaft is to transmit 300kW power @
100rpm.
(a) If
shear stress is not to exceed 80N/mm2 , find it’s diameter.
(b) What %
saving would be obtained in weight if this shaft is replaced by hollow shaft whose inner dia. is 60% of
outer diameter. The length, material and shear stress being the same.
Q9: A hollow
shaft having an inside diameter 70% of its outer diameter, is to replace a
solid shaft transmitting same power at same speed. Calculate the % saving in
material.
Q10: A solid shaft is to be replaced by a hollow shaft whose
outer diameter exceeds the inner diameter by 25%. Calculate the % saving in
material if power transmitted is same @ at same speed for both shafts.
TYPE (4) “TORSIONAL EQUATION”
Q11: What must be the length of 5mm diameter aluminum wire
so that it can be twisted through one complete revolution without exceeding the
shear stress of 42MN/m2?
Q12: Determine the diameter of solid steel shaft which will
transmit 90kW @ 160rpm. Also determine length of shaft if the twist must not
exceed 1o over entire length. The maximum shear stress is limited to
60N/mm2. Take c=8×104 N/mm2.
Q13: Determine the diameter of a solid shaft which transmits
300kW of power @ 250rpm. The maximum shear stress should not exceed 30N/mm2
and twist should not exceed 10 in shaft of length 2m. Take c=1×105
N/mm2.
Q14: A solid circular shaft transmits 75kW @ 200rpm.
Calculated diameter if twist is not to exceed 10 in 2m length &
shear stress is limited to 50N/mm2. Take c=105N/mm2.
Q15: A hollow circular shaft transmits 294kW @ 200rpm.
Determine the diameter of shaft if shear strain due to torsion is not to exceed
8.6×10-4 and inner diameter is 63% of outer diameter. C=80GN/m2.
Q16: A solid steel shaft is subjected to torque of 45 kNm.
If angle of twist per meter length of shaft is 0.50 and shear stress
allowed is 90N/mm2. Find (a)Diameter of shaft (b)Shear stress induced and angle of twist(c)Maximum
shear strain.
Take C=80×103 N/mm2.
TYPE (5) “MEAN TORQUE”
Q17: A solid steel shaft has to transmit 75 kW at 200 r.p.m.
taking allowable shear stress as 70 N/mm2, find suitable diameter
for the shaft, if the maximum torque transmitted at each revolution exceeds the
mean torque by 30%.
Q18: A hollow shaft is to transmit 300 kW power at 80 r.p.m.
if the shear stress is not to exceed 60N/mm2 and internal diameter
is 0.6 of external diameter, find the external and internal diameter assuming
maximum torque is 1.4 times the mean.
Q19: A hollow shaft of diameter ratio 
(internal diameter to outer diameter) is to
transmit 375kW power at 100 r.p.m. the maximum torque beam 20% greater than
mean torque. The shear stress is not to exceed 60 N/mm2 and twist in
a length of 4m not to exceed 20 . Calculate its internal and
external diameter which would satisfy both the above condition assume modulus
of rigidity C=0.85 ×105 N/mm2.
(internal diameter to outer diameter) is to
transmit 375kW power at 100 r.p.m. the maximum torque beam 20% greater than
mean torque. The shear stress is not to exceed 60 N/mm2 and twist in
a length of 4m not to exceed 20 . Calculate its internal and
external diameter which would satisfy both the above condition assume modulus
of rigidity C=0.85 ×105 N/mm2.
Q20: A hollow shaft, having an internal
diameter 40% of its external diameter, transmits 562.5kW at 100 r.p.m. .
Determine external diameter of shaft if shear stress not to exceed 6oN/mm2
and twist in length of 2.5 m should not exceed 1.30 . Assume Tmax=1.25
Tmean. And C=9×104 N/mm2.
Q21:A solid steel shaft has to transmit
75kW at 200 r.p.m. . Taking allowable shear stress as 70 MN/m2.find
suitable diameter of shaft if maximum torque transmitted at each revolution
exceeds the mean by 30%.
Q22: A hollow shaft is to transmit 300 kW
at 80 rpm. if shear stress is not to exceed 60 MN/m2 and internal
diameter is 0.6 of outer diameter assuming that max. Torque is 1.4 times mean.
Q23: A hollow shaft of diameter ratio 
is required to transmit 600 kW at 110 rpm, the
maximum torque beam is 20% greater than mean shear stress is not to exceed 63
MN/m2 and the twist in a length of 3 m not to exceed 1.40.calculate
maximum outer diameter satisfying these condition.
is required to transmit 600 kW at 110 rpm, the
maximum torque beam is 20% greater than mean shear stress is not to exceed 63
MN/m2 and the twist in a length of 3 m not to exceed 1.40.calculate
maximum outer diameter satisfying these condition.
Take C=84GN/m2.
TYPE (6) “VARYING C/S”
Q24: A shaft ABC of 500 mm length and 40 mm ext. diameter is
bored, for a part of its length AB, to a 20 mm diameter and for remaining
length BC to 30 mm diameter bore. If the shear stress is not to exceed 80 N/mm2,
find maximum power, the shaft can transmit at 200 rpm.
If the
angle of twist in the length of 20 mm diameter bore is equal to that of 30 mm
dia. bore. Find the length of shaft that has been bored to 20 mm and 30 mm
diameter.
Q25: a steel shaft ABCD having a total length of 2.4m
consist of 3 lengths having different sections as follows,
AB is
hollow having outside and inside diameters of 80mm and 50mm respectively & BC
and CD are solid, BC having dia. of 80mm and CD a dia. of 70 mm. if the angle
of twist is same for each section, determine the length of each section and
total angle of twist if the maximum shear stress in hollow portion is 50 N/mm2.take
C=8.2×104 N/mm2.
Q26: A hollow shaft is 1m long and has external dia. 50mmit
has 20mm internal diameter for a part of length and 30 mm internal diameter for
rest of length. If max. Shear stress in it is not to exceed 80N/mm2,
determine the max. power transmitted by it at a speed of 300 rpm. If the twist
produce in two portions of the shafts are equal, find length of two portions.
TYPE (7) “COMPOSITE
SHAFTS”
Q27:A composite shafts consists of a steel rod 60 mm
diameter surrounded by a closely fitting tube of brass. Find the outside dia.
of the tube so that when a torque of 1000Nm is applied to the composite shaft,
it will be shared equally by the two materials.
Take Cs=8.4
×104 N/mm, CB=4.2×104N/mm2
Find also
the maximum shear stress in each material and common angle of twist in the
length of 4m.
Q28: A composite shaft consist of steel rod 60 mm in
diameter surrounded by a closely fitted tube of brass fix to it. Find external
diameter of tube so that when torque is applied to composite shaft, it is
equally shared by by the two materials.If torque is 10000 N.m. find max. shear
stress induced in each shaft and the angle of twist. Take C = 4.2
