AKTU Mechanics of Solids Problems 1
2002-2003 (ME303)
1. Show that if E is assumed correct, an error of 1% in the determination of G 6
will involve an error of about 5% in the calculation of Poisson's ratio when its
correct value is 0.25.
2004-2005 (ME303)
1. While testing on a metallic rod, it is observed that the diameter of rod is re- 6
duced by 0.0025 mm under an axial pull of 20 KN. The original diameter of
the rod is 15 mm. If rigidity modulus for the rod metal be 50 KN/mm 2. Find
the Young's modulus and Bulk modulus.
2005-2006 (TME303)
1. What are the factors that have to be considered while designing members for 10
dynamic loads? Discuss the effect of shape, stress distribution and elastic con-
stants.
2006-2007 (TME303)
1. Write short notes of the following: 7
(i) Equilibrium equations and its applications
(ii) Airy's stress function.
2006-2007 (ME405)
1. At a point in a body, the displacement field is linear and is given by the follow- 6
ing expressions. Find all the strains.
u = 0.06x + 0.05y + 0.01z
v = 0.01y 0.03x
w = 0.02x + 0.01z
2. Write brief notes on the following: 4
i) St. Venant's principle,
ii) Airy's stress function.
2007-2008 (TME303)
1. State the generalized Hook's law and prove for an anisotropic elastic material 6
the maximum number of elastic constants is 21 only. Also show that for iso-
tropic materials it is 2.
2. Derive the equation of equilibrium in z-direction, by considering the equilib- 6
rium of an infinitesimal rectangular element of size dx dy dz in the Cartesian
co-ordinate system as
z xz yz
Z 0
z x y
3. At a point in a body, the displacement field is linear and is given by the follow- 6
ing expressions. Find all the strains:
u = 0.07x + 0.05y + 0.01z
v = 0.01y 0.04x
w = 0.02x + 0.02z
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Brij Bhooshan Asst. Professor B.S.A College of Engg. & Technology, Mathura (India)
Copyright by Brij Bhooshan @ 2010
2 Introduction & Review
2008-2009 (TME303)
1. What is significance of strain compatibility equations? Write down these com- 5
patibility equations.
2009-2010 (EME302)
1. Write short notes on: 7
(i) Compatibility equations,
(ii) Three dimensional stresses.
2009-2010 (TME303 COP)
1. Derive compatibility equations in Cartesian co-ordinates. 10
2010-2011 (TME303 COP)
1. A vertical rod 2 m long, fixed at the upper end, is 13 cm2 in area for 1 m and 10
20 cm2 in area for 1 m. A collar is attached to the free end. Through what
height can a load of 100 kg fall on to the collar to cause a maximum stress of
50 N/mm2? E = 2,00,000 N/mm2.
2012-2013 (EME302)
1. A weight W = 5 kN attached to the end of a steel wire rope moves downward 10
with constant velocity 1 m/s. What stresses are produced in the rope when its
upper end is suddenly stripped? The free length of rope at the moment of im-
pact is 20 m, its net cross-sectional area is 10 sq cm. and E = 2 × 105 N/mm2.
2012-2013 (EME302 MTU)
1. Explain Impact load and impact stress. 5
2012-2013 (TME303 COP)
1. Describe the applications of Airy's stress function. 5
2. Draw and explain stress-strain diagram for ductile material. 5
2013-2014 (EME302)
1. What are complementary shear stresses? Explain with diagram. 5
2. The modulus of rigidity of material is 39 GPa. A 10 mm diameter rod of the 5
material is subjected to an axial tensile force of 5 kN and the change in its di-
ameter is 0.002 mm. Calculate the Poisson's ratio of the material.
2013-2014 (ME304 MTU)
1. Explain complementary shear stress. 2
2. Derive an expression for deformation of conical bar hung to a ceiling having 10
diameter „D‟ and height „L‟, weight density of bar and Young‟s modulus is E.
3. Show that if E is assumed correct an error of 1% in the determination of G will 10
involve an error of about 5% in the calculation of Poisson‟s ratio when its cor-
rect value is 0.25.
For more information log on www.brijbhooshan.in or www.brijrbedu.org
Brij Bhooshan Asst. Professor B.S.A College of Engg. & Technology, Mathura (India)
Copyright by Brij Bhooshan @ 2010
AKTU Mechanics of Solids Problems 3
2013-2014 (CE302 MTU)
1. Draw the stress - strain diagram for ductile and brittle materials. 2
2. Write down the generalized Hook's Law. 2
3. A steel bar of 25 mm diameter is acted upon by forces shown in Fig. 1. Deter- 5
mine the total elongation of the bar. Take E = 200 kN/mm2.
4. If a bar is stretched in such a manner that all the lateral strain is prevented, 5
what is the value of the modified modulus of elasticity and modified Poisson's
ratio? Take as the Poisson's ratio.
5. A steel rod 2 m long is heated through a temperature of 100°C. Find the 5
stresses induced in the rod, if coefficient of linear expansion 0.000012/°C. Take
E = 2 × 106 kg/cm2.
2014-2015 (NME302)
1. Derive the expression for extension in the vertically suspended bar due to self 5
weight.
2014-2015 (NME302 SCOP)
1. Write down the generalized Hook' law. 2
2. A square steel rod 20 mm × 20 mm in section is to carry an axial load (com- 2
pressive) of 100 kN. Calculate the shortening in length of 50 mm. E = 2.14 ×
108 kN/m2.
3. A vertical circular bar 20 mm diameter, 3 m long carries a tensile load of 150 5
kN. Calculate:
i) Elongation;
ii) Decrease in diameter; and
iii) Volumetric strain.
2014-2015 (EME302 COP)
1. State the generalized Hook's law and prove for an anisotropic elastic material 10
the maximum number of elastic constant is 21 only. Also show for isotropic
material it is 2.
2014-2015 (ME304 MTU COP)
1. If the ratio G/K = 0.3, then what is the value of Poisson's ratio? Where E is 2
the Modulus of Elasticity? G is the Modulus of Rigidity and K is bulk Modulus.
2. A rod consists of two parts that are made of steel and copper as shown in fig- 10
ure below. The elastic modulus and coefficient of thermal expansion for steel
are 200 GPa and 11.7 × 10 6 per °C respectively and for copper 70 GPa and
21.6 × 10 6 per °C respectively. If the temperature of the rod is raised by 50°C,
For more information log on www.brijbhooshan.in or www.brijrbedu.org
Brij Bhooshan Asst. Professor B.S.A College of Engg. & Technology, Mathura (India)
Copyright by Brij Bhooshan @ 2010
4 Introduction & Review
determine the forces and stresses acting on the steel rod and copper rod.
3. A flat bar of section 50 mm × 10 mm is subjected to an axial pull of 130 kN. 10
One side of the bar is polished and lines are ruled on it to form a square of 30
mm side, one diagonal of the square being along the middle line of the pol-
ished side. If E = 200 GPa and Poisson's ratio is 0.25 .Calculate the change in
the angles and sides of the square.
2014-2015 (CE302 MTU COP)
1. State the generalized Hook's law and prove for an anisotropic elastic material 5
the maximum number of elastic constants is 21 only Also show that for iso-
tropic materials it is 2.
2. The modulus of rigidity for a material is 0.5 × 105 N/mm2. A 12 mm diameter 5
rod of material was subjected to axial pull of 14 kN and change in diameter
was observed 3.6 × 10 3 mm. Calculate Poisson‟s ratio and modulus of elastic-
ity
2015-2016 (NME302)
1. Why stresses are called tensor? 2
2. State the generalized Hook's law and prove for an anisotropic elastic material 10
the maximum number of elastic constants is 21 only. Also show that for iso-
tropic materials it is 2.
3. Draw the Stress - Strain diagram for mild steel under tensile load. 5
2015-2016 (EME302 COP)
1. Define and explain stress at a point. 2
2. Derive the expression for Three dimensional stress equilibrium equation 10
(Generalised hook's Low).
2016-2017 (NME302)
1. What is Hook's law? Explain. 2
2. What are thermal stress and thermal strain. 2
3. Determine the poisson's ratio and bulk modulus of a material, for which 5
young's modulus is 120 GPa and modulus of rigidity 4.8 Mpa.
4. Derive the expression for elongation of a uniform bar due to its self-weight. 5
5. Derive the expression for elongation of a conical bar due to its self-weight. 5
6. A steel rod of 3 cm diameter is enclosed centrally in a hallow copper tube of 5
external diameter 5 cm and internal diameter 4 cm. The composite bar is then
For more information log on www.brijbhooshan.in or www.brijrbedu.org
Brij Bhooshan Asst. Professor B.S.A College of Engg. & Technology, Mathura (India)
Copyright by Brij Bhooshan @ 2010
AKTU Mechanics of Solids Problems 5
subjected to an axial pull of 45000 N. If the length of each bar is equal to 15
cm.
Determine:
i) The stresses in the rod and the tube,
ii) Load carried by each load.
E for steel = 200 GPa and for Copper = 100 GPa.
2017-2018 (NME302 COP)
1. Define principal of superposition. 2
2. Explain briefly the term 'shear stress' and 'complimentary stress' with proper 2
illustrations.
3. A steel rod 15 mm in diameter and 2 m long is heated from 20°C to 120°C, E = 2
200 GPa and = 12 × 10 6 per °C. If the rod is not free to expand, find the
thermal stress developed in steel rod?
4. If the value of Poisson's ratio is zero, then it means that 2
(a) The material is rigid.
(b) The material is perfectly plastic.
(c) There is no longitudinal strain in the material.
(d) The longitudinal strain in the material is infinite.
5. The figure 1. Below shows a steel rod of 25 mm2 cross sectional area. It is 10
loaded at four points, K, L, M and N. Assume Esteel = 200 GPa. Calculate the
total change in length of the rod due to loading.
Figure 1
2017-2018 (EME302 COP)
1. Derive the expression for extension in the vertically suspended bar due to self 2
weight.
2. Derive the equation of equilibrium in z-direction by considering the equilib- 2
rium of an infinitesimal rectangular element of size dx dy dz in the Cartesian
co-ordinate system.
3. A brass bar having a cross sectional area of 1000 mm2 is subjected to axial 10
forces as shown in fig. Find the total change in length of the bar. Take Es = 105
GN/m2.
4. A rigid bar is supported by three rods in the same vertical plane and equidis- 10
tant. The outer rods are of brass and of the length 600 mm and diameter 30
mm. The central rod is of steel of 900 mm length and of 37.5 mm diameter.
For more information log on www.brijbhooshan.in or www.brijrbedu.org
Brij Bhooshan Asst. Professor B.S.A College of Engg. & Technology, Mathura (India)
Copyright by Brij Bhooshan @ 2010
6 Introduction & Review
Calculate the force in the bar due to an applied force 100 kN, Take Es = 2 Eb.
2018-2019 (RME303)
1. The load to be carried by a lift may be dropped 10 cm on to the floor. The cage 7
itself weighs 100 kg and is supported by 25 m of wire rope weighing 0.9 kg/m,
consisting of 49 wires each 1.6 mm diameter. The maximum stress in the wire
is limited to 90 N/mm2 and E for the rope is 70000 N/mm2. Find the maximum
load which can be carried.
2. A steel tube of 24 mm external diameter and 18 mm internal diameter en- 7
closes a copper rod 15 mm diameter to which it is rigidly attached at each end.
If, at a temperature of 10C there is no longitudinal stress, calculate the
stresses in the tube and rod when the temperature is raised to 200C.
Esteel = 210 kN/mm2, Ecopper = 210 kN/mm2,
Coefficients of linear expansion: steel = 11 × 10 6 /C, copper = 11 × 10 6 /C.
2018-2019 (NME302 COP)
1. Briefly explain about types of stresses? 2
2. What is Hooke‟s law? 2
2018-2019 (EME302 COP)
1. Explain Poisson‟s ratio and its importance. 2
2. Explain Hooke‟s law and differentiate between Young‟s modulus and modulus 2
of rigidity.
3. A steel rod 20 mm in diameter passes centrally through a steel tube of 25 mm 5
internal diameter and 30 mm external diameter. The tube is 800 mm long and
is closed by rigid washers of negligible thickness which are fastened by nuts
threaded on the rod. The nuts are tightened until the compressive load on the
tube is 20 kN. Calculate the stresses in the tube and the rod.
Find the increase in these stresses when one nut is tightened by onequarter of
a turn relative to the other. There are 4 threads per 10 mm. Take E = 2 × 105
N/mm2.
4. A load of 2 kN falls through 25 mm on to a stop at the end of a vertical bar 4 m 5
long, 600 mm2 cross-sectional area and rigidly fixed at its other end. Deter-
mine the instantaneous stress and elongation of the bar. E = 200 GN/m2.
2019-2020 (RME303 COP)
1. What do you understand by Three dimensional state of stress and strain. 2
2. What is meant by the term “Volumetric Strain”. 2
3. Define Poisson‟s Ratio. 2
4. Write short notes on: Compatibility equations &-Three-dimensional stress. 7
2019-2020 (NME302 COP)
1. What do you understand by hydrostatic stress? Give one example of it. 2
2. Explain Hooke‟s law and differentiate between Young‟s modulus and modulus 2
of rigidity.
3. A steel tube of 24 mm external diameter and 18 mm internal diameter en- 10
For more information log on www.brijbhooshan.in or www.brijrbedu.org
Brij Bhooshan Asst. Professor B.S.A College of Engg. & Technology, Mathura (India)
Copyright by Brij Bhooshan @ 2010
AKTU Mechanics of Solids Problems 7
closes a copper rod 15 mm diameter to which it is rigidly attached at each end.
If, at a temperature of 10C there is no longitudinal stress, calculate the
stresses in the tube and rod when the temperature is raised to 200C.
Esteel = 210 kN/mm2, Ecopper = 210 kN/mm2,
Coefficients of linear expansion: steel = 11 × 10 6 /C, copper = 11 × 10 6 /C.
4. A steel rod 20 mm in diameter passes centrally through a steel tube of 25 mm 10
internal diameter and 30 mm external diameter. The tube is 800 mm long and
is closed by rigid washers of negligible thickness which are fastened by nuts
threaded on the rod. The nuts are tightened until the compressive load on the
tube is 20 kN. Calculate the stresses in the tube and the rod.
Find the increase in these stresses when one nut is tightened by onequarter of
a turn relative to the other. There are 4 threads per 10 mm. Take E = 2 × 10
N/mm2.
2019-2020 (EME302 COP)
1. Explain Hooke‟s law and differentiate between Young‟s modulus and modulus 2
of rigidity.
2. A steel rod 20 mm in diameter passes centrally through a steel tube of 25 mm 10
internal diameter and 30 mm external diameter. The tube is 800 mm long and
is closed by rigid washers of negligible thickness which are fastened by nuts
threaded on the rod. The nuts are tightened until the compressive load on the
tube is 20 kN. Calculate the stresses in the tube and the rod.
Find the increase in these stresses when one nut is tightened by onequarter of
a turn relative to the other. There are 4 threads per 10 mm. Take E = 2 × 10
N/mm2.
For more information log on www.brijbhooshan.in or www.brijrbedu.org
Brij Bhooshan Asst. Professor B.S.A College of Engg. & Technology, Mathura (India)
Copyright by Brij Bhooshan @ 2010
