set 2 (unit 2)

NRI INSTITUTE OF INFORMATION SCIENCE & TECHNOLOGY BHOPAL (M.P)

COMPILED BY AMIT SINGH 9827740442 ([email protected])

SET 2 OF 2 (UNIT 2)

PROBLEM 1:- A cylindrical pipe of diameter 1.5m and thickness 1.5cm is subjected

to an internal fluid pressure of 1.2N/mm2. Determine:

(i) Longitudinal stress developed in the pipe, and

(ii) Circumferential stress developed in the pipe.

(Answer: -

)

PROBLEM 2:- A cylinder of internal diameter 2.5m and of thickness 5cm contains

a gas. If the tensile stress in the material is not to exceed 80N/mm2. Determine

the internal pressure of the gas.

(Answer: - )

PROBLEM 3:- A cylinder of internal diameter 0.5m contains air at a pressure of

7N/mm2 (gauge). If the maximum permissible stress induced in the material is

80N/mm2. Find the thickness of the cylinder.

(Answer: -t=2.2 cm)

PROBLEM 4:- A thin cylinder of internal diameter 1.25m contains a fluid at an

internal pressure of 2N/mm2. Determine the maximum thickness of the cylinder

if:

(i) The longitudinal stress is not to exceed 30N/mm2.

(ii) The circumferential stress is not to exceed 45N/mm2.

(Answer: -t=2.80cm)

PROBLEM 5:- A gas cylinder of internal diameter 40mm is 5mm thick. If the tensile

stress in the material is not to exceed 30MPa, find the maximum pressure which

can be allowed in the cylinder.

(Answer: - P=7.5MPa)



PROBLEM 6:- A steam boiler of 800mm diameter is made up of 10mm thick

plates. If the boiler is subjected to an internal pressure of 2.5MPa, find the

circumferential and longitudinal stresses induced in the boiler plates.

(Answer: - )

PROBLEM 7:- A cylindrical shell of 1.3m diameter is made up of 18mm thick

plates. Find the circumferential and longitudinal stress in the plates, if the boiler is

subjected to an internal pressure of 2.4MPa. Take efficiency of the joints as 70%.

(Answer: - , )

PROBLEM 8:- A water main 80 cm diameter contains water at a pressure head of

100m. If the weight density of water is 9810N/m3, find the thickness of the metal

required for the water main. The permissible stress is given as 20N/mm2.

(Answer: -t = 2cm)

PROBLEM 9:- Calculate the thickness of the metal required for a cast iron main

800mm in diameter for water at a pressure head of 100m, if the maximum

permissible tensile stress is 20MN/m2 and weight of water is 10kN/m3.

(Answer: - 20mm)

PROBLEM 10:- A thin cylindrical shell of diameter 300mm and wall thickness 6mm

has hemispherical ends. If there is no distortion of the junction under pressure

determine the thickness of hemispherical ends.

Take E=208GN/m2, and Poisson’s ratio=0.3.

(Answer: - t2=2.47mm)

PROBLEM 11:- A boiler is subjected to an internal steam pressure of 2N/mm2. The

thickness of boiler plate is 2.0cm and tensile stress is 120N/mm2. Find out the

maximum diameter, when efficiency of longitudinal joint is 90% and that of

circumferential joint is 40%.



(Answer: -d=192cm)

PROBLEM 12:- A boiler shell is to be made of 15mm thick plate having a limiting

tensile stress of 120N/mm2. If the efficiencies of the longitudinal and

circumferential joints are 70% and 30% respectively determine:

(i) The maximum permissible diameter of the shell for an internal pressure

of 2N/mm2.

(ii) Permissible intensity of internal pressure when the shell diameter is

1.5m.

(Answer: - d = 1080mm, p = 1.44 N/mm2)

PROBLEM 13:- A cylinder of thickness 1.5cm has to withstand maximum internal

pressure of 1.5N/mm2. If the ultimate tensile stress in the material of the cylinder

is 300N/mm2, factor of safety 3.0 and joint efficiency 80%, determine the

diameter of the cylinder.

(Answer: - d=1.6m)

PROBLEM 14:- Calculate:

(i) The change in diameter.

(ii) The change in length.

(iii) The change in volume of a thin cylindrical shell 100cm diameter, 1cm

thick and 5m long when subjected to internal pressure of 3N/mm2. Take

the value of and Poisson’s ratio, μ=0.3.

(Answer: - 0.06375cm, 0.075cm, 5595.96cm3)

PROBLEM 15:- A cylindrical thin drum 80cm in diameter and 3m long has a shell

thickness of 1cm. If the drum is subjected to an internal pressure of 2.5N/mm2,

determine:

(i) Change in diameter.

(ii) Change in length, and



(iii) Change in volume.

Take and Poisson’s ratio, μ=0.25.

(Answer: - 0.035cm, 0.0375cm, 1507.96cm3)

PROBLEM 16:- A cylindrical shell 90cm long 20cm internal diameter has thickness

of metal as 8mm is filled with fluid at atmospheric pressure. If an additional

20cm3 of fluid is pumped into the cylinder, find

(i) The pressure exerted by the fluid on the cylinder and

(ii) The hoop stress induced.

Take and Poisson’s ratio, μ=0.3.

(Answer: - P=5.95N/mm2, )

PROBLEM 17:- A cylindrical vessel, whose ends are closed by means of rigid flange

plates, is made of steel plate 3mm thick. The length and the internal diameter of

the vessel are 50cm and 25cm respectively. Determine the longitudinal and hoop

stresses in the cylindrical shell due to an internal fluid pressure of 3N/mm2. Also

calculate the increase in length, diameter and volume of the vessel.

Take and Poisson’s ratio, μ = 0.3.

(Answer: - ,

)

PROBLEM 18:- A cylindrical vessel is 1.5m diameter and 4m long is closed at ends

by rigid plates. It is subjected to an internal pressure of 3N/mm2. If the maximum

principal stress is not to exceed 150N/mm2, find the thickness of the shell.

Assume and Poisson’s ratio, μ=0.25. Find the changes in

diameter, length and volume of the shell.

(Answer: -15mm, 0.984mm, 0.75mm, 10602875mm3)



PROBLEM 19:- A closed cylindrical vessel made of steel plates 4mm thick with

plane ends, carries fluid under pressure of 3N/mm2. The diameter of the cylinder

is 25cm and length is 75cm, calculate the longitudinal and hoop stresses in the

cylinder wall and determine the change in diameter, length and volume of the

cylinder. Take and Poisson’s ratio, μ=0.286.

(Answer: - 46.875N/mm2, 93.75N/mm2, 0.0956mm, 0.0716mm, 31680mm3)

PROBLEM 20:- A cylindrical shell 3m long which is closed as the ends has an

internal diameter of 1m and a wall thickness of 15mm. Calculate the

circumferential and longitudinal stresses induced and also changes in the

dimensions of the shell, if it is subjected to an internal pressure of 1.5N/mm2.

And Poisson’s ratio, μ = 0.3.

(Answer: - 50N/mm2, 25N/mm2, 0.015cm, 1119.19cm3)

PROBLEM 21:- A hollow cylindrical drum 600mm in diameter and 3m long has a

shell thickness of 10mm. If the drum is subjected to an internal air pressure of

3N/mm2, determine the increase in its volume. Take And

Poisson’s ratio, μ=0.3 for the material.

(Answer: - 655103.5mm3)

PROBLEM 22:- A thin cylindrical shell with following dimensions is filled with a

liquid at atmospheric pressure.

Length=1.2m, External diameter=20cm, Thickness of metal=8mm.

Find the value of the pressure exerted by the liquid on the walls of the cylinder

and the hoop stress induced if an additional volume of 25cm3 of liquid is pumped

into the cylinder. Take And Poisson’s ratio, μ=0.33 for the

material.

(Answer: - 7.77N/mm2, 89.42N/mm2)



PROBLEM 23:- A thin cylindrical tube 80mm internal diameter and 5mm thick, is

closed at the ends and is subjected to an internal pressure of 6N/mm2. A torque

of 2009600Nmm is also applied to the tube. Find the hoop stress, longitudinal

stress; maximum and minimum principal stresses and maximum shear stress.

(Answer: - 48N/mm2, 24N/mm2, 77.7N/mm2 (t), 5.76N/mm2 (c), 41.76N/mm2)

PROBLEM 24:- A copper cylinder, 90 cm long, 40cm external diameter and wall

thickness 6mm has its both ends closed by rigid blank flanges. It is initially full of

oil at atmospheric pressure. Calculate the additional volume of oil which must be

pumped into it in order to raise the oil pressure to 5N/mm2 above atmospheric

pressure. For copper assume And Poisson’s ratio, μ=1/3.

Take bulk modulus of oil as 2.6 .

(Answer: - )

PROBLEM 25:- A thin cylindrical tube of 90-mm internal diameter and 6mm

thickness and closed at the end is subjected to an internal pressure of 8MPa.

Determine the maximum and minimum principal stresses and the maximum shear

stress if a torque of 4000N.m is also applied to the tube.

(Answer: - )

PROBLEM 26:- A cylindrical water tank of height 25m, inside diameter 2.2m,

having vertical axis is open at the top. The tank is made of steel having yield stress

of 210MN/m2. Determine the thickness of steel used when the tank is full of

water.

Efficiency of the longitudinal joint=70%, factor of safety=3

(Answer: - 6mm)

PROBLEM 27:- A cylindrical air drum is 2.25m in diameter with plates 1.2cm thick.

The efficiency of the longitudinal and circumferential joints is 75% and 40%. It the

tensile stress in the plating is to be limited to 120MN/m2. Find the maximum safe

air pressure.



(Answer: - 0.96MN/m2)

PROBLEM 28:- A cylindrical vessel whose ends are closed by means of rigid flange

plates is made of steel plate 3mm thick. The internal length and diameter of

vessel are 50cm and 25cm respectively. Determine the longitudinal and

circumferential stresses in the cylindrical shell due to an internal fluid pressure of

3MN/m2. Also calculate increase in length, diameter and volume of the steel.

Take: E=200GN/m2, and

(Answer: - 125MN/m2, 62.5MN/m2, δd=0.01328cm, δl=0.00625cm, δV=29.15cm3)

PROBLEM 29:- A cylindrical shell 3m long which is closed at the ends has an

internal diameter of 1m and a wall thickness of 15mm. Calculate the

circumferential and longitudinal stresses induced and also change in the

dimensions of the shell if it is subjected to an internal pressure of 1.5MN/m2.

Take: E=200GN/m2, and

(Answer: - 50MN/m2, 25MN/m2, δd=0.2125mm, δl=0.15mm, δ V = 1119.3mm3)

PROBLEM 30:- A built up cylindrical shell of 300mm diameter, 3m long and 6mm

thick is subjected to an internal pressure of 2MN/m2. Calculate the change in

length, diameter and volume of the cylinder under that pressure if the efficiencies

of the longitudinal and circumferential joints are 80% and 50% respectively.

E=200GN/m2; m=3.5.

(Answer: - δd=0.0723mm, δl=0.483mm, δV=136300mm3)

PROBLEM 31:- A copper cylinder, 90cm long, 40cm external diameter and wall

thickness of 6mm has its both ends closed by rigid blank flanges. It is initially full

of oil at atmospheric pressure. Calculate the additional volume of oil which must

be pumped into it in order to raise the oil pressure 5MN/m2 above atmospheric

pressure. For copper, assume E=100GN/m2 and Poisson’s ratio=

. Take bulk

modulus of oil as 2.6GN/m2.



(Answer: - 520.12cm3)

PROBLEM 32:- Calculate the bursting pressure for cold drawn seamless steel

tubing of 60mm inside diameter with 2mm wall thickness. The ultimate strength

of steel is 380MN/m2.

(Answer: - 25.33MN/m2)

PROBLEM 33:- A vessel in the shape of a spherical shell of 1.20m internal

diameter and 12 mm shell thickness is subjected to pressure of 1.6N/mm2.

Determine the stress induced in the material of the vessel.

(Answer: - 40N/mm2)

PROBLEM 34:- A spherical vessel 1.5m diameter is subjected to an internal

pressure of 2N/mm2. Find the thickness of the plate required if maximum stress is

not to exceed 150N/mm2 and joint efficiency is 75%.

(Answer: - 6.67mm)

PROBLEM 35:- A spherical shell of internal diameter 0.9m and of thickness 10mm

is subjected to an internal pressure of 1.4N/mm2. Determine the increase in

diameter and increase in volume.

(Answer: - 0.0945mm, 120236.5mm3)

PROBLEM 36:- Calculate the increase in volume of a spherical shell 1m in

diameter and 1 cm thick when it is subjected to an internal pressure of

1.6MN/m2.

(Answer: - 219.9cm3)



PROBLEM 37:- A thin spherical shell 1m in diameter with its wall of 1.2cm

thickness is filled with a fluid at atmospheric pressure. What intensity of pressure

will be developed in it if 175cm3 more of fluid is pumped into it? Also, calculate

the circumferential stress at that pressure and the increase in diameter.

(Answer: - 0.111m, 31.714MN/m2, 1.522MN/m2)

PROBLEM 38: - The cylindrical shell is shown in figure is 1m long and has diameter

=200mm. The metal thickness is 6mm. It has spherical ends. Calculate the change

in volume, if the internal pressure is raised to 1.5N/mm2, take

.

(Answer: - Total change in volume=8443.03mm3)

PROBLEM 39: - A boiler drum consists of a cylindrical portion 4m long, 1.5m in

diameter and 2.25 cm thick. It is closed by hemispherical ends. In a hydraulic test

to 6MN/m2, how much additional water will be pumped in after initial filling at



atmospheric pressure? The circumferential strain at the junction of the cylinder

and hemisphere may be assumed as same for both.

E=200GN/m2, k (for water) =2.13GN/m2, and 1/m=0.3

(Answer: - 42828.8cm3)

PROBLEM 40:- A cast iron cylinder of 200mm inner diameter and 12.5 mm thick is

closely wound with a layer of 4mm diameter steel wire under a tensile stress of

55 MN/m2. Determine the stresses set up in the cylinder and steel wire if water

under a pressure of 3MN/m2 is admitted in the cylinder. Take Young’s modulus

for cast iron and steel as 100GN/m2 and 200GN/m2, and Poisson’s ratio=0.25.

(Answer: - ( ) ( ) ,( )

( ))

PROBLEM 41:- A cast iron pipe of 300mm internal diameter and 12mm thick is

wound closely with a single layer of circular steel wire of 5mm diameter under a

tension of 60MPa. Find the initial compressive stress in the pipe section. Also find

the stresses set up in the pipe and steel wire, when water under a pressure of

4MPa is admitted into the pipe. Take E for cast iron and steel as 100GPa and

200GPa respectively. Poisson’s ratio=0.3

(Answer: - 13.6MPa, 111.4MPa)

PROBLEM 42:- A cast iron pipe of 240-mm inside diameter and 15-mm thick is

closely wounded with a layer of 6-mm diameter steel wire under a stress of

35MPa. Find the stresses developed in the pipe and the steel wire when water is

admitted into the pipe at a pressure of 3MPa.

For steel E=204GPa

For cast iron E=102GPa; Poisson’s ratio=0.3

(Answer: - )

PROBLEM 43:- A cast iron pipe of 200mm internal diameter and 12mm thick is

wound closely with a single layer of circular steel wire of 5mm diameter, under a



tension of 60N/mm2. Find the initial compressive stress in the pipe section. Also

find the stresses set up in the pipe and steel wire, when water under a pressure of

3.5N/mm2 is admitted into the pipe. Take E for cast iron as and

for steel as . Poisson’s ratio is given as 0.3.

(Answer: - 19.63N/mm2, ( )

( ))

PROBLEM 44:- A gun metal tube of 100mm bore, wall thickness 2.5mm is closely

wounded externally by a steel wire 1mm diameter. Determine the tension under

which the wire must be wound on the tube, if an internal radial pressure of

3MN/m2 is required before the tube is subjected to tensile stress in the

circumferential direction. Take:

For gun metal: E=102GN/m2; 1/m=0.35

For steel: E=210GN/m2

(Answer: - 129.12MN/m2)

PROBLEM 45:- The internal and external diameters of a copper tube are 42mm

and 45mm respectively. It is closely wound with a steel wire of 1mm diameter.

Determine the required tension in the wire so that an internal pressure of 2MPa

produces a tensile circumferential stress of 8MPa in the tube.

(Answer: - Winding tension=10.53N)

PROBLEM 46:- A rim type flywheel is rotating at a speed of 2400r.p.m. If the

mean diameter of the flywheel is 750mm and density of the material of the wheel

is 8000kg/m3, then find the hoop stress produced in the rim due to rotation.

Take E=200GN/m2 then what will be the change in diameter of the flywheel due

to rotation.

(Answer: - 71.061MN/m2, 0.2664mm)



PROBLEM 47:- Find the speed of rotation of a wheel of diameter 750mm, if the

hoop stress is not to exceed 120MN/m2. The wheel has a thin rim and density of

the wheel is 7200kg/m3.

(Answer: - 3287.4rpm)

PROBLEM 48: - A steel tube having a bore of 150mm, wall thickness 2.25mm is

plugged at each end to form a closed cylinder with external length of 450mm. If

the tube is filled with oil and is subjected to a compressive load of 90kN

determine:

(i) The pressure produced on oil.

(ii) The resulting circumferential stress in the tube wall.

Given for oil: K (bulk modulus) = 2800MN/m2;

For steel: E = 210GN/m2, and Poisson’s ratio = 0.28

(Answer: -0.267MN/m2, 8.9MN/m2)

PROBLEM 49: - The ends of a thin cylinder, 180mm internal diameter and wall

thickness 3.0mm are closed by rigid plates and it is then filled with a liquid. When

an axial compressive force of 33.6kN is applied to the cylinder, the pressure of the

liquid rises by 72kN/m2. If E = 200GN/m2 and Poisson’s ratio = 0.3, find the bulk

modulus of the liquid.

(Answer: - K = 3.75GN/m2)

PROBLEM 50: - A cylinder made of bronze 180mm outside diameter and 15mm

thick is strengthened by a single layer of steel wire 2.25mm diameter wound over

it under a constant stress of 75MN/m2. The cylinder is subjected to an internal

pressure of 27MN/m2, with rise in temperature of the cylinder by 1200C.

Assuming the cylinder to be a thin shell with closed ends, determine the final

value of:

(i) The stress in the wire.



(ii) The circumferential stress in the cylinder wall.

(iii) The radial pressure between the wire and the cylinder.

Take: -

For steel:

For brass:

Poisson’s ratio = 0.32

(Answer: - 415MN/m2 (t), 86.62MN/m2 (t), 8.06MN/m2)