# CE 2201 MECHANICS OF SOLIDS

Mechanics

Oct 30, 2013 (5 years and 3 months ago)

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CE 2201

MECHANICS OF SOLIDS

UNIT

I

STRESS STRAIN & DEFORMATION OF SOLIDS, STATES OF
STRESS

Part

A

1.

What do you mean by stiffness? (May / June

2012)

2.

With a simple sketch explain lateral strain. (May / June

2012)

3.

Write the relation between
Elastic constants. (May / June

2011)

4.

Define Thermal stress. (May / June

2011)

5.

What is meant by ‘Limit of proportionality’? (Nov /Dec

2010) (April / May

2010) (Nov / Dec

2008) (Nov /Dec

2011)

6.

Define principal plane & principal stress (Nov /Dec

2010) (April /May

2010)
Nov /Dec

2007)

7.

Define modulus of Elasticity (April / May

2010)
(
Nov

/ Dec

2009) (April /
May

2010)

8.

Write down the relation between young’s modulus Bulk modulus. (Nov / Dec

2009) (April / May

2008)

9.

State Hookes l
aw. (Nov /Dec

2009)

10.

How the thermal stress is induced? (Nov /Dec

2009)

11.

Define : (i) Poisson’s ratio (ii) Shear Modulus
(April / May

2008) (Nov / Dec

2007)

12.

Express the relationship among the three elastic constants (Nov / Dec

2007)

13.

In a Mohn’s Circle of stresses, What represents the maximum shear stress? (Nov
/Dec

2007)

14.

Define Hookis Law (Nov /Dec

2012) Nov /Dec

2011)

15.

Compare the stress strain curve for mild steal (May /June

2007)

Part

B

1.

(i)
A steel of
cross
-
sectional area 2000 mm
2

and two brass rods each of cross

sectional area of 1200 mm
2

together support a load of 500 KN. Find the stresses in
the rods. Take E for steel = 2x10
5

N/mm
2

and E for brass = 1x10
5

N/mm
2
.
(November / December
-
2012)

(ii)

A steel bolt 650 mm
2

cross

sectional area passes centrally through a
copper tube of 1200 mm
2

cross sectional area. The tube is 500 mm long and
is closed by rigid washers, which are fastened by the threads on the steel
bolt. The nut is now tightened by ¼ of a turn. Find the stress in the bolt and
the tube if the pitch of the thread is 3mm. Take E
s

= 2.05x10
5

N/mm
2

and
E
c
=1x10
5

N/mm
2
. (November / December
-
2012)

2.

A rectangular block 250 mmx100 mmx80 is subjected to axial loads as follows.

480 KN tensile in X
-
direction 1000 KN compressive force in Z
-
direction and 900
KN tensile force in Y
-
direction
. Assuming Poission’s ratio as 0.25, find in terms
of modulus of elasicity of the material E, the strains in the direction of each force.
If E=2x10
5

N/mm
2
, find the values of the modulus o rigidity and bulk modulus
for material of the block. Also calcula
te the change in volume of the block due to
-
2012)

3.

(i) Derive a relation for change in length of a bar hanging freely under its own
weight.

(ii) Draw stress

strain curve for a mild steel rod subjected to tension and explain
about the salient points on it.

(May / June
-
2012)

4.

(i) Derive the relationship between bulk modulus and young modulus.

(ii)

Derive relations for normal and shear stres
ses acting on an inclined plane at a
point a stained material subjected to two mutually perpendicular direct stresses.

(May / June
-
2012)

5.

(a) A member formed by connecting a steel bar to an aluminium bar is shown in
figure assuming that the bars are prev
ented from buckling, calculate the magnitude
of force P that will cause the total length of the member to decrease by 0.25 mm.
The values of elastic modules for steel and aluminium are 2.1 x 10
5

N/mm
2

and
7x10
4

N/mm
2

respectively.

(November / December
-
2011)

(b) Deter mine the value of young’s modulus and Pisson’s ratio of a metallic bar
of length 30 cm, breadth 40 mm and depth 40 mm when the bar is subjected to an
axial compressive load of 400 KN. The decrease in length is given as 0.075 cm
and incre
ase in breadth is 0.003 cm.

(November / December
-
2011)

6.

(a) A compound tube consists of a steels tube with 140 mm internal diameter and
160 mm external diameter and an outer brass tube with 160 mm internal diameter
and 180 mm external diameter. The two t
ubes are of same length. The compound
tube carries an axial load of 900 KN. Find the stresses and the load carried by each
tube. Length of each tube is 140 mm. Take E=2x10
5

N/mm
2

for steel and 1x10
5

N/mm
2

for brass.

(November / December
-
2011)

(b) At a p
oint in a strained material, the stresses on tow planes, at right angles to
each other are 20 N/mm
2

and 10 N/mm
2

both tensile. They are of accompanied by
a shear stress of magnitude 10 N/mm
2
. Find the location of principal planes and
evaluate the principal

stresses.

(November / December
-
2011)

7.

a) Derive the relationship between the modulus of Elasticity and shear modulus .

b) A railway track is laid so that there is no stress in the rails at 10°C Calculate.

(i) the stress on the rails at 60°C if there is

no allowance for expansion.

(ii) the stress in the rails at 60°C if there is expansion allowance 10mm per rail.

(iii) the expansion allowance if the stress in the rail is to be zero when the
temperature is 60 °C. The rails are 30m long. Take α=12x10
-
6

per

°C and E =
2x10
5
N/mm
2
. (May /June

2011)

8.

An element in a stressed material has tensile stress of 500 N/mm
2

and a
compressive stress of 350 N/mm
2

acting on two mutually perpendicular planes and
equal shear stress of 100 N/mm2 on these planes. Find t
he Principal stresses and
their planes. Find also maximum shear stress and the normal stress on the plane of
maximum shear stress.
(May /June

2011)

9.

(a) Prove that Poisson’s ratio

[

]

where

K is the Bulk modulus and C is the shear modulus.

(b) A compound tube Consists of a steel tube 150 mm internal diameter and 10
mm thickness and outer brass tube 170 mm internal diameter and 10 mm
thickness. The two tubes are of the same length. The compound tube carries an
axial load o 1000 kN. Find the
stresses and the load carried by each tube and the
amount it shortens. Length of each tube is 150 mm. Take Es = 2x10
6

N/mm
2

and
Eb = 1x10
5

N/mm
2
. (November / December
-
2012)

10.

At a certain point in a strained material, the horizontal tensile stress is 80
MPa
and vertical compressive stress is 140 Mpa. The shear stress is 40 Mpa. Find the
principal stresses and locate the principal planes. Also find the maximum shear
stress and locate the planes of maximum shear stress. (November / December
-
2010)

11.

A steel

tube of 30 mm external diameter and 20 mm internal diameter encloses a
copper rod of 15mm diameter to which it is rigidly joined at each end. If, at a
temperature of 10°C there is no longitudinal stress, calculate the stresses in the rod
and tube when the

temperature is raised to 200°C. Take E = 2.1 x10
5

N/mmm
2

and
E
c

= 1x10
5

N/mm
2
. The value of coefficient of linear expansion for steel and
copper is given as 11x10
-
6

per °C and 18x10
-
6

per °C respectively. (April / May

2010)

12.

The intensity of resultant

stress on a plane AB fig 1 at a point in a material under
stress is 800 N/Cm
2
and it is inclined at 30° to the normal to that plane. The
normal component of stress on another plane BC at night angles to plane AB is
600 N/Cm
2

Determine the following :

a)

The

resultant stress on the plane BC

b)

The principal stresses and their directions

c)

The maximum shear stresses and their planes.

(April / May

2010)

13.

a) A composite bar of brass (length = 500mm, dia. = 40 mm) and (length = 750
mm, dia. = 25mm) is held between two supports. There are stress free at 30°C.
What will be the stresses induced temperature is lowered to 15°C when

(i) the supports are unyieldin
g and

(ii) the supports yield by 0.08mm E
b

= 85 GN/ m
2
, α
b

= 19x10 E
c

= 110 GN /m
2

,
α
c

= 17.5 x 106 /° C?

(April / May

2010)

14.

Find graphically and otherwise the magnitude and direction principal stresses and
maximum shear stress at a point in
a when subjected to two mutually
perpendicular stresses of 150 MN (tensile) and 500 MN/m
2

(Compressive) and
shear stress of intex 100 MN /m
2
.

(April / May

2010)

15.

A steel rod 5m long and 30 mm in diameter

is subjected to an axial tensile load
of 50kN.D
etermine the change in length, diameter and volume of the rod. Take
E=2x105 N/mm2 and poisson’s ratio

16

A steel rod 5 m long and 30 mm in diameter is subjected to an axial tensile load of
50 kN. Determine the change in length, diameter and volume of the ro
d. Take
E=2xl0
5

N/mm
2
and Poisson's ratio = 0.25. November / December
-
2010

17

At a point in a strained material, the principal stresses are 100 N/mm
2

tensile and
40 N/mm
2

compressive. Determine the resultant stress in magnitude and direction
on a plane inclined at 60
° to the axis of the major principal stress. What is the
maximum intensity of shear stress in the material at the point?
(
November /
December
-
2010
)

18

Two verti
cal rods, one of steel and other of bronze are suspended from a
horizontal ceiling, the horizontal distance between being 80 mm. Each rod is 2.5
m
long and 12.5 mm in diameter. A horizontal cross piece connects the lower end of
the bar. Where should a load

of 10 kN be placed on the cross piece so that it
remains horizontal after being loaded? Calculate the stresses in each rod. Assume
Es = 200 KN/mm
2

and Eb= 110 kN/mm
2
. Neglect any bending in the cross piece.
(
November / December
-
2009
)

19

At a certain point

in a strained material, there is a tensile stress of 85 N/mm
2

upon
the horizontal plane and a tensile stress of 40 N/mm
2
upon the vertical plane.
There is also a shear stress of 50 N/mm
2

upon each of this planes determine
graphically or otherwise (i) the
principal stresses (ii) the maximum shear stress
(iii) the principal planes.
(
November / December
-
2009
)

20

A bar of steel 60 mm x 60 mm in section and 180 mm long. It is subjected

to a tensile load of 300 kW along the longitudinal axis and tensile load of

7
50 kW and 600 kW as the lateral forces in z and y directions

respectively. Find the resulting change in dimensions and the volume of

the bar. E=200GN/m
2
/
u=0.30.
(
May/June

2009
)

21

An element in a stressed material has tensile stress of 500 N/mm
2

and a

compressive stress of 350 N/mm
2

acting on two mutually perpendicular

planes and equal shear stresses of 100 N/mm
2

on these planes. Find the

principal stresses and its planes. Find the plane of maximum shear

stress and its plane. May/June

2009.

22

A 2m lon
g steel bar is having uniform diameter of 40 mm for a length of 1
m, in the next 0.5 m, its diameter gradually reduces to 'd' mm and for the
remaining 0.5 m. length, diameter remains 'd' mm uniform. When a load of
300 KN was applied, the extension observed

is equal to 5.78 mm. Determine
the diameter 'd' of the bar if E = 2 x 10
5

N/mm
2
.
.
(
April/May
-
2008.
)

23

At a certain point in a piece of elastic material, there are normal tensile
stresses of magnitude 120 MPa and
60
MPa acting orthogonal to each other.
In a
ddition, there is a shearing stress of 80 MPa acting normal to the normal
stresses. Determine.

(i)

The magnitude and direction of the principal stresses,

(ii)

Maximum shearing stress.

(
April/May
-
2008.
)

24.

(a) A compound tube consists of a steel tube 170mm exter
nal diameter and 10mm
thickness and an outer brass tube 190mm external diameter and 10mm thickness.
The two tubes are of the same length. The compound tube carries an axial load of
1 MN. Find the stresses and the load carried by each tube and the amount

by
which it shortens. Length of each tube is 200 mm.
E steel = 200 GN/m
2

and E
brass = 100 GN/ m
2
.(Nov /Dec
-
2008)

25.

Two mutually perpendicular planes of an element of material are subjected to
direct stresses of 60 N/mm
2

(tensile) and 20 N/mm
2

(Compressive) and shear
stress of 20 N/mm
2
. Find

(i)

the principal stresses and orientation of principal planes.

(ii)

find the maximum shear stress, The orientation of the plane of
maximum shear stress and the normal stress on the plane of
maximum shear stress.

(Nov /Dec
-
2008)

26.

A steel flat 24 mm x 6 mm in section riveted between two aluminium flats of same
size at a temperature of 288 K is shown in fig. 2 If this assembly is subjected to a
compressive force of 35 kN, find the stresses developed in each material
. To what
temperature the assembly can be rised that the stresses in the material due to the
load are nullified. Es = EA1 = 210 GPa. α
s

= 12 x 10
-
6
/K and
α
Al

= 23 x 10
-
6
/K.
(Nov /Dec
-
2007)

Fig. 2 (Qn. 11(a))

27.

A.M.S Bar of 50 mm square in size and
150 mm long is subjected to an axial
thrust of 200 kN. Half the lateral strain is prevented by the application of uniform
external pressure of certain intensity. If E = 200 GPa and Poisson’s ratio 0.3,
calculate the change in the length of the bar.

(Nov
/Dec
-
2007)

28.

A copper rod of 40 mm diameter is surrounded by a cast iron tube of 80 mm
external diameter. The ends being firmly fastened together. When put to a
compressive load of 35 kN, what load will be shared by each? Also determine the
amount by whi
ch the compound bar shortens if its initial length is 2.5 m. E
C.I

=
175 GN/m
2

E
C

= 75 GN/m
2
. (Nov /Dec
-
2007)

29.

(i) Find maximum shear plane and maximum shear stress for an element with state
of stress shown in Fig. 5. (Nov /Dec
-
2007)

Fig. 5 Q.No.
12(b) (i)

(ii) Derive the relationship between Young’s modulus and Bulk modulus.

30.

A compound tube consists of steel tube 170 mm external diameter and 100 mm
thickness and a outer brass tube 190 mm extended diameter and 10 mm thickness.
The two tubes are
of the same length. The compound tube carries an axial tensile
load of 1000 kN. Find the stresses and the loads carried by each tube and the
amount by which it shortens. Length of each tube is 150 mm. Assume the
modulus of elasticity of steel and that
of brass as 200 kN/mm
2

and 100 kN/mm
2

respectively. (May / June

2006)

31.

(i) Determine the Poisson’s ratio and bulk modulus of a material for which
modulus of elasticity is 120 kN/mm
2

and modulus of rigidity is 45 kN/mm
2
.
(May / June

2006)

(ii) Fig.
(2) shows the state of stress at a point in a strained body. Calculate the
magnitude of the principal stress and orientation of the principal planes. (May /
June

2006)

Fig. (2)

32.

(a) A 32 m steel rod is concentrically fixed in a brass tube which has th
e inside
and outside diameters as 34 mm and 48 mm respectively. The length being equal
to 400 mm for both, the assembly is held between two stoppers exactly at 400 mm
apart. If the temperature of the assembly is raised by 60
o
C, find the stresses
develope
d in the two materials, if

(i)

the distance between the stoppers remains constant and

(ii)

increased by 0.25 mm. Also find

(iii)

the increase in the distance between the stoppers if a force of 80 kN
is exerted between them. E
s

= 2 x 10
5

MPa, E
b

= 0.9 x 10
5

MPa,
α
s

=
12

x 10
-
6

/
o
C and
α
b

= 21 x 10
-
6 /
o
C

(May / June

2007)

33.

At a certain material under stress, the intensity of resultant stress on a plane in 65
MPa (tensile) inclined at 30
o

to the normal to that plane. The stress on a plane at
right angle to this plane has a normal component of intensity 40 MPa (tensile).
Find

(i)

the resultant stress on the second plane

(ii)

the principal stresses and their planes of action and

(iii)

critical shear

(May

/ June

2007)

UNIT

II

ANALYSIS OF PLANE TRUSS, THIN CYLINDERS / SHELLS

Part

A

1.

What are the advantages of trusses over beams? (May / June

2012)

2.

Define ‘tension coefficient’. (May / June

2012 ) (April / May

2010) (April /
May

2008)

3.

When is the method of sections preferred for analysis of trusses? (May / June

2011)

4.

Write the expression for circumferential stress in case of spherical shell
(May /
June

2011)

5.

What is the condition to be satisfied for a perfect frame? (Nov /Dec
-
2010)

6.

When a thin cylinder is subjected to internal fluid pressure. What are the stresses
developed in its wall? (Nov /Dec

2010) (May /June

2009)

7.

What are the
assumptions made in finding out the in a frame? (April / May

2010) (Nov /Dec

2009) (May /June

2006)

8.

Write down the expression for the change in volume of a thin cylindrical shell
subjected to internal fluid pressure. (April / May

2010)

9.

Define thi
n cylinder . (Nov /Dec

2009) (Nov /Dec

2008)

10.

What is a redundant fram
e

(May /June

2009) (Nov /Dec
-
2008) (Nov /Dec

2012)

11.

When do you adopt method of sections. (April / May

2008)

12.

What are
the two types of trusses with respect to their joints?
(Nov /Dec
-
2007)

13.

How to increase the strength of a thin cylinder? (Nov /Dec

2007)

14.

What is a plane frame? Sketch any two types of truss? (Nov /Dec
-
2007)

15.

What is meant by perfect frame
. Deficient frame? (Nov /Dec

2012)

Part

B

1.

(a)
A truss is
located as in Fig. Determine the force in all the members of the
truss. (November / December
-
2012)

(b)
A seamless spherical shell is of 0.8 m internal diameter and 4 mm
thickness. It is filled with fluid under pressure until is volume increases by 50
cubic centimeters. Determine the fluid pressure taking E=2x10
5

N/mm
2

and
Poisson’s ratio = 0.3. (November / December
-
2012)

2.

(a) Determine the forces in all the members of the frame shown in fig Q 12a.
Use method of joints. (May / June
-
2012)

(b) Derive

relations for change in length, thickness and volume of a thin
cylinder subjected to an internal pressure. Also explain the failure of thin
cylinders. (May / June
-
2012)

3.

(a) A truss of span 5 m is loaded as shown in Figure Find the reactions and
forces i
n the members of the truss.

(November / December
-
2011)

4.

(a) A thin cylindrical vessel with following dimensions is filled with liquid at
atmospheric pressure: Length = 1.2.m. External diameter = 200mm. Thickness
= 8.mm. Find the value of pressure
exerted by the liquid on the walls of the
cylinder and hoop stress induced if an additional volume of 25cm
3

of liquid is
pumped into the cylinder. Take E=2.1 x 105 N/mm
2

and Poisson’s ratio = 0.33.

(November / December
-
2011)

(b) A spherical shell of int
ernal diameter 0.9m and thickness 10 mm is
subjected to an internal pressure of 1.4M/mm
2
. Determine the increase in
diameter and increase in volume. Take E=2.1 x 105 N/mm
2

and Poisson’s ratio
= 1/3.

(November / December
-
2011)

5.

Find the forces in all the

members of the truss shown in fig by method of
section.

6.

A cylindrical shell 3 meter long has 1 meter internal diameter and 15 mm
thickness. Calculate the circumferential and longitudinal stresses induced and
also the changes in the dimension of the
shell if it is subjected to an internal
pressure of 1.5 N/mm
2
. Take E=2x10
5

N/mm
2

and Poission’s ration = 0.3.

7.

A truss of span 8 meters is loaded as shown in fig. Find out the forces in all the
members of the truss using method of joints. (November / D
ecember
-
2010)

8.

A cylindrical shell 1000 mm long and 200 mm internal diameter having a
thickness of metal 6 mm in filled with fluid at atmospheric pressure. If an
3

of fluid is pumped into the cylinder, find the pressure
exerted by the

fluid on the cylinder, hoop stress and the longitudinal stress
induced. Assure E = 2x10
5

N/mm
2

and Poisson’s ratio as 0.3. (November /
December
-
2010)

9.

A truss of span 9m is loaded as shown in Fig 2. Find the reactions and forces in
the members marked 1,
2 and 3 using method of section.

(April / May

2010)

10.

A Cylindrical vessel whose ends are closed by means by rigid flange plates, is
made of steel plate 3 mm thick. The length and the internal diameter of the
vessel are 50 cm and 25cm respectively.
Determine the longitudinal and hoop
stresses in the cylindrical shell due to an internal fluid pressure of 3N/mm
2
.
Also calculate the increase in length, diameter and volume of the vessel. Take
E =2x10
5

N/mm
2

and µ= 0.3

(April / May

2010)

11.

Find the forc
es in the members of the truss shown in Figure 1.

(April / May

2010)

12.

A closed cylindrical vessel made of steel plate 5mm thick is 50 cm long and its
internal diameter is 20cm. Determine the longitudinal and hoops stresses in the
cylindrical shell due

to an internal fluid pressure 3N/mm
2
. Also calculate the
change in length, diameter and volume of the vessel . Take E = 2x105 N /mm
2

and 1/m = 0.3 (April / May

2010)

13.

Determine the forces in all the members of truss shown in fig. (1) by method of
joint
s. November / December
-
2010

14.

A closed cylindrical vessel made of steel plates 4 mm thick with plane ends,
carries fluid under a pressure of 3 N/mm
2
. The diameter of cylinder is 25 cm
and the length is 75 cm. Calculate the longitudinal and hoop stresses
in the
cylinder wall and determine the change in diameter, length and volume of the
cylinder. Take E = 2.1 x 10
5

N/mm
2

and
µ

= 0.286.

November / December
-
2010

15.

(a) Analyse the truss shown in fig.Q.12 (a) using method of joints and verify
the force in the member BC by the method of section.

November / December
-
2009

Fig. Q. 12(a)

16.

A cylindrical shell 3 m long, which is closed at the ends has an internal
diame
ter of 1 m and a wall thickness of 15 mm. It is subjected to internal
pressure of 1.5 N/mm
2
. Compute the following.

(i) The circumferential and longitudinal stresses.

(ii) The change in internal diameter and length.

(iii) The change in volume. Ass
ume Es = 120 kN/mm
2

and poisons ratio is

0.3. November / December
-
2009

17.

(a) For the truss shown in Fig. 2 find the forces in members CD, CB, BD and
AE by method of joints. May/June

2009

18.

A thin cylinder 5 cm internal diameter and 0.1 cm
wall thickness is closed at its
ends and subjected to an internal pressure of 100 N/cm
2
. If the cylinder is
subjected to a torque of 5000 Ncm, the axis which coincides with the axis of
the cylinder. Calculate the principle stress and maximum shear stress f
or a
point on the outer surface of the cylinder.

19.

(a) Find the forces in the members of the truss shown in Fig. 1 April/May
-
2008.

Fig. 1

20.

Find the forces in the members AB, BF, BC and FE of the truss shown in
Fig.2 April/May
-
2008.

Fig. 2

21.

(a) A tr
uss of 10 m span is loaded as shown in Fig.1, find the forces in the
members of the truss using method of section. (Nov /Dec
-
2008)

Fig. 1

22.

Calculate (i) the change in diameter (ii) change in length and (iii) change in
volume of a thin cylindrical shell

of 1 m diameter, 10 mm thick and 5 m long
when subjected to an internal pressure of 3 N/mm
2
.

Take the value of E = 2 x 10
5

N/mm
2

and Poisson’s ratio = 0.3.

(Nov /Dec
-
2008)

23.

(a) Find the forces in the members of the truss shown in fig. 3.

(Nov /Dec
-
20
07)

Fig. 3. (Qn. 12(a))

24.

A steel cylinder with flat ends in 2 m long and 1m diameter with metal
thickness 10 mm. It is filled with water at atmospheric pressure. The pressure
has been increased to 2 MPa by pumping more water. An amount of 2.9 x 10
6

mm
3

of water has been collected at the outlet after releasing the pressure. If E =
2 x 10
5

MPa and Poison’s ratio 0.3, find out the bulk modules. (Nov /Dec
-
2007)

25.

(a) Find the forces members of the truss shown in Figure 3 by method of joints.
(Nov /Dec
-
2
007)

Fig. 3 Q. No. 11(a)

Or

26.

For the truss shown in Figure 4, find the forces in members BC, BD and DC
by method of sections. (Nov /Dec
-
2007)

Fig. 4 Q. No. 11 (b)

27.

Determine the forces in all the members of the truss shown in fig. (1) by
method of
joints. (May / June

2006)

Fig. (1)

28.

(a) Find the forces in the members of the Warren truss built of equilateral
triangles as shown in fig.2. (May / June

2007)

Fig. 2

29.

A shell 3.25 m long, 1 m dia, is under an internal pressure of 1 MPa. If the
thickness of th shell is 10 mm, find

(May / June

2007)

(i)

hoop and longitudinal stresses

(ii)

maximum shear stress and

(iii)

change in the dimensions. E = 2 x 10
5

MPa and poison’s ratio 0.3.

UNIT

III

Part

A

1.

Derive the relationship between bending moment & (Nov /Dec

2007)

(
Nov/Dec

2008) (May / June

2012) Nov/Dec

2010) (May/June
-
2009)
(April/May

2008)

2.

What is meant by section modulus? (May /June

2012)

3.

State the assumption made in the theory of simple bending. ( May /June

2011)

4.

What is meant by point of contra flexure? (May/June

2011)

5.

W
rite the sending equations? (Nov/Dec

2010)

6.

Write are the types of loads acting on beams? (April/May
-
2010)

7.

What

is point of
inflection
? (April/May
-
2010)

8.

Write down the simple bending equations? (April/May
-
2010)

9.

Define bending moment diagram? (Nov/Dec
-
2011)

10.

What do you mean by ‘pure bending’? (Nov/Dec
-
2009)

11.

Write any two assumptions made in simple beam theory?

(Nov/Dec
-
2011)
(April/May
-
2008) (Nov/Dec
-
2013)

12.

What is meant by moment of resistance of a beam? (Nov /Dec

2008)

13.

What are guided supports? (Nov/Dec
-
2007)

Part

B

1.

(a) Draw the shear force and bending moment diagrams for the beam shown in
Fig. Indicate the numerical values at all important points.

(November / December
-
2012)

2.

(i)
What are the types of supports in beams and explain any two types?

(ii)
A beam 5
00 mm deep of a symmetrical section has I=1x10
8

mm
4

and is
simply supported over a span of 10 metres. Calculate.

(1)

The uniformly distributed load it can carry if the maximum bending
stress is not to exceed 150 N/mm
2
.

(2)

The maximum bending stress if the beam ca
rries a central point load of
25 KN.

(November / December
-
2012)

3.

(a) Draw shear force and bending moment diagram f
or the beam given in fig.
(May / June
-
2012)

4.

State the assumptions made in the theory of simple bending and derive the
bending formula.
(May / June
-
2012)

5.

A cantilever beam of length 5m is loaded as shown in figure Draw the shear
force and bending moment diagrams.

(November / December
-
2011)

6.

Draw the shear force and bending moment diagrams for the beam which is
ure. (November / December
-
2011)

7.

A steel beam of I
-
section is simply supported at its ends. It is 250 mm deep and
150mm wide, the flanges being 20 mm thick and web 15mm. It carries a load of
40kN at the middle of the span. Find the length of span if the
maximum bending
stress is 120 N/mm2. Calculate how much more steel will be required if, with
the same value of maximum stress, the I
-
beam is replaced by a rectangular
beam having depth twice the width.

(May /June

2011)

8.

A simply supported beam 10m span is subjected to a point load of 15 KN at 3 m
from the left support and a uniformly distributed load of 10k/N/m over the right
half span. Using Macaulay’s method, find the slopes at the support points and
the deflection unde
r the point load in terms of the flexural rigidity EI.
(May
/June

2011)

9.

For the beam shown in Fig. draw the bending moment diagram and shear force
diagram. What is the maximum bending moment in the beam? (November /
December
-
2010)

10.

A timber beam of
depth 300 mm and symmetrical section is simply supported
over a span of 10 m. What uniformly distributed load including its own weight
can it carry if the maximum permissible bending stress is 7.5 N/mm
2
. The
moment of inertia of the section of the beam is
450x10
6
mm4. Find the
maximum bending stress and radius o f curvature at a section 1 m from a
support. E for timber = 12.6 x 103 N/mm
2
. (November / December
-
2010)
(November /December
-
2010)

11.

Draw the shear force and bending moment diagrams for the overha
nging beam
carrying uniformly distributed load of 2KN/m over the entrie length as shown in
fig.3. Also locate the point of contra flexure.

(April / May

2010)

12.

A case iron beam is of T
-
Section as shown in Fig
-
4 The beam is simply
supported on a span of

8m. The beam carries a uniformly distributed load of
1.5kN/m length on the entire span. Determine the maximum tensile and
compressive stress.

(April / May

2010)

13.

Draw the shear force and bending moment diagram indicating salient points for
the beam s
hown in Figure.2

(April / May

2010)

14.

Draw the bending stress distribution across the cross

section of the simply
supported beam of span 5m shown in Figure 3. The tensile stress is not to
exceed 40 N/mm
2

and the compressive stress is not to exceed 100
N/mm
2
. Find
the uniformly distributed load carrying capacity if the region above the neutral
axis is in tension. (April / May

2010)

15.

A simply supported beam of length 10 m, carries the uniformly distributed load
and two point loads as shown in fig.
(2). Draw the S.F. and B.M. diagram for
the beam. Also calculate the maximum bending moment. November /
December
-
2010

16.

A timber beam of rectangular section is to support a load of 20 kN uniformly
distributed over a span of 3.6 m when beam is simply
supported. If the depth of
section is to be twice the breadth, and the stress in timber is not to exceed 7
N/mm
2
, find the dimensions of the cross
-
section. How would you modify the
cross section of the beam, if it carries a concentrated load of 20 kN place
d at the
centre with the same ratio of breadth to depth? November / December
-
2010.

17.

(a) A beam of span 10 m is simply supported at its ends and carries point loads
of 5 kN each at a distance 3 m and 7 m from the left support and also a
uniformly distribut
ed load of 1 kN/m between the point loads. Draw the shear
force and bending moment diagrams and determine the maximum bending
moment. November / December
-
2009.

18.

A beam is simply supported at its ends and carries a uniformly distributed
run over the whole span. The section of the beam is
rectangular having depth as 500 mm. If the maximum stress . OuV induced in
the material of the beam is 120 N/mm
2

and the moment of inertia of the cross
section is 7 x 10
8

mm
4
. Find the span of the beam. N
ovember / December
-
2009.

19.

For the over hanging beam shown in Fig. 3. draw SFD and BMD.

Indicate the maximum
-
ve and +ve B.M. May/June

2009.

Fig. 3

20.

(i)

What is meant by 'beam of uniform strength'?

(ii)

A cantilever of span 'L' is loaded at free end wi
Find the expression for width keeping the depth constant.

(iii)

A symmetrical T section 200 mm deep has a moment of inertia

2.26xl0"
5
m
4

about its neutral axis. Determine the longest span

over which when simply supported, the beam
would carry a UDL of 4
kN/m, when the bending stress is limited to 125 N/mm
2
. May/June

2009.

21.

(a) Draw the shear force and bending moment diagrams for the beam loaded as
shown in Fig.3 April/May

2008.

Fig. 3

22.

Determine the dimensions of a timber
beam of span 8 m, which carries a brick
wall of 200 mm thick and 5 m high and whose density is 18.5 kN/m
3
. The
maximum permissible stress is limited to 7.5 N/mm
2
. Assume depth of beam as
twice its width. April/May
-
2008.

23.

An overhanging beam ABC is simply
supported at A and B over a span of 6 m
and BC overhangs by 3 m. If the supported span AB carries central
concentrated load of 8 kN and overhanging span BC carries 2 kN/m completely,
draw shear force and bending moment diagrams indicating salient points.
(Nov
/Dec
-
2008)

24.

The outer diameter of a tubular section beam is 120 mm and inner diameter is
80mm. What single concentrated load shall it be able to carry at mid point of a
simply supported span of 3m if bending stress is not to exceed 135 N/mm
2
.
Find

the dia of a solid circular beam by which this tubular section beam can be
replaced. (Nov /Dec
-
2008)

25.

(a) A beam of uniform section 10 m long carries a UDL of 10 kN/m for the
entire length and a concentrated load of 10 kN at the right end. The beam is
freely supported at the left end. Find the position of the second support so that
the maximum bending moment in the beam is as minimum as possible. Also
compute the maximum bending moment. (Nov /Dec
-
2007)

26.

Two wooden planks 50 mm x 150 mm in section is
used to form a Tee section
as shown in fig. 4. If a bending moment of 3400 Nm is applied with respect to
the neutral axis, find the extreme fibre stresses and the total tensile force. (Nov
/Dec
-
2007)

Fig. 4 (Qn. 13(b))

27.

(a) Draw BMD and SFD for the
beam shown in Figure 6. Indicate the
maximum SF, maximum BM and other salient points. (Nov /Dec
-
2007)

Fig. 6 Q.No. 13 (a)

28.

For the beam shown in Fig. 7 draw BMD, SFD. Indicate maximum SF, BM.
(Nov /Dec
-
2007)

Fig. 7 Q.No. 13 (b)

29.

(a) Draw the shear force and bending moment diagrams for the loaded beam
shown in Fig. (3) and calculate the maximum bending moment and locate the
point of contraflexure. (May / June

2006)

Fig. (3)

30.

A water line of 1.2 m internal diameter and 12 mm
thickness is running full. If
the bending stress is not to exceed 56 N/mm
2
. Find the greatest span on which
the pipe may be freely supported. Assume the unit weight of material of the
pipe and water as 76.8 kN/m
3

and 10 kN/m
3

respectively (May / June

2006)

31.

(a) A simply supported beam of span 9 m carries a UDL of 1.8 kN/m over a
length of 4 m from one end. Draw the shear force and bending moment
diagrams indicating the maximum and maximum values. (May / June

2007)

32.

A cast iron beam is a symmetric
al I section having 80 x 20 mm top flange, 160
x 40 mm bottom flange and 20 mm thick web. The depth of the beam is 260
mm. The beam is simply supported over a span of 5 m. If the tensile stress is
limited to 20 MPa, find the safe UDL it can take and the

corresponding
compressive stress. (May / June

2007)

UNIT

IV

DEFLECTION OF BEAMS & SHEAR STRESSES

Part

A

1.

What is meant by shear can be? (May /June
-
2012)

2.

How do you determine the maximum deflection in a simply supported beam?
(May/June
-
2012)

3.

To find slope & deflection of beams which method is suitable for single load &
which method is suitable for several loads? (May/June
-
2011)

4.

Sketch the shear stress distribution diagram for a T
-
section (May/June
-
2011)

5.

Sketch the shear stress distribution f
or a circular section (Nov/Dec
-
2010)
(May/June

2009) (April/May
-
2008)

6.

A cantilever beam of length L is subjected to a point load w at the free end. What
is the deflection at the free end? (Nov/Dec
-
2010) (May/June
-
2009)

7.

What is ‘Principle of complementa
ry shear? (April/May
-
2010)

8.

State ‘mohr’s theorems’ for finding the slope & deflection of beams. (April/May

2010) Nov/Dec
-
2011)

9.

Draw the shear stress distribution for an angle section (or L
-
section &
(Nov/Dec
-
2012) (April/May
-
2010)

10.

What is slope at the

supports of a simply supported beam carrying a point load at
the central? (Nov/Dec
-
2009)

11.

What is the maximum shear stress at the neutral axis for a circular section?
(Nov/Dec
-
2009) (Nov/Dec
-
2011)

12.

Sketch the shear stress distribution for symmetrical I

section (Nov/Dec
-
2009)
(Nov/Dec
-
2008) (May/June
-
2007)

13.

State any four methods to evaluate the slope & deflection of determinate beams.
(Nov/Dec
-
2009)

14.

State the moment area theorems. (April / May
-
20
08)

15.

What is a conjugate
beams? (Nov/Dec
-
2007)

Part

B

1.

(a) A beam simply supported at ends A and B is loaded with two point loads of 30
KN each a distance of 2 m and 3 m respectively from end A. Determine the
position the and magnitude of the maximum
deflection. Take E=2x105 M/mm
2

and I=7200 cm
4
. (November / December
-
2012)

2.

(i) A 300 mm x 150 mm I section has 12 mm thick flanges and 8 mm thick web.
It is subjected to a shear force of 150 KN at a particular section. Find the ratio of
maximum shear
stress to minimum shear stress in the web. What is the maximum
shear stress in the flange? (November / December
-
2012)

(ii) The cross section of a joist is a T
-
section 120 mm x 200 mm x 12 mm, with
120 mm side horizontal. Sketch the shear stress distrib
ution and find the maximum
shear stress if it has to resist a shear force of 200 KN.

(November / December
-
2012)

3.

(a) Determine the slope at the supports and maximum deflection for the beam
given in Fig use Macaulary’s method.

E=2 x 10
5

N/mm
2

I = 20 x10
6

mm
4

(May / June
-
2012)

4.

(b) The cross section of a T
-
beam is as follows: flange thickness = 10 mm; width
of flange = 100 mm; thickness of web = 10 mm; depth of web = 120 mm. If a
shear force of 2KN is acting at a particular section of the beam. Draw the shear
stress distribution
across the cross secting.

(May / June
-
2012)

5.

A beam of length 6 m is simply supported at its ends and carries two point loads of
48 KN and 40kN at a distance of 1m and 3m respectively from the left support.
Find the deflection under each load. Take E=2x1
0
5
N/mm
2

and 1=85x10
6

mm
4
.

(November / December
-
2011)

6.

A simply supported beam of length 4 m carries a point load of 3kN at n distance of
1 m from each end. If E = 2x 10
5

N/mm
2

and I=10
8

mm
4

for the beam, using
conjugate beam method determine (a) slope at each end and under each load (b)
deflection under each end.

(November / December
-
2011)

7.

A laminated wooden beam 120mm wide and 180mm deep is made of three 120
mm x 60 mm planks glued toge
ther to resist longitudinal shear. The beam is
simply supported over a span of 2.5 m. If the allowable shearing stress in the glued
joint is 0.6 N/mm
2
, find the safe uniformly distributed load the beam can carry.

8.

(a) A cantilever of span I is carrying un
iformly distributed load of w per unit run
on a length ‘a’ from the fixed end. Determine the slope and deflection at the free
end. Use conjugate beam method.

9.

(b) A laminated wooden beam 120 mm wide and 180mm deep is made of three
120 mm x 60 mm planks glu
ed together to resist longitudinal shear. The beam is
simply supported over a span of 2.5 m. If the allowable shearing stress in the glued
joint is 0.6 N/mm2, find the safe uniformly distributed load the beam can carry.

10.

A hollow shaft of 55 mm external d
iameter and 35 mm internal diameter is
subjected to a torque of 2.5 kNM to produce and angular twist of 0.6° measured
over a length of 0.3m of shaft. Calculate the value of modulus of rigidity.
Calculate also the maximum power which could be transmitted by

the shaft at
2000 rpm, if the maximum allowable shearing stress is 70 N/mm
2
.

11.

A Simply supported beam AB of span l carrying a uniformly distributed load of w
per unit run over the whole span. Find the maximum deflection and slope at the
end ‘A’ using doub
le integration method.

(November /December
-
2010)

12.

A beam of channel section 120 mmx 60mm has a uniform thickness of 20mm.
Draw the distribution of shear stress for a vertical section where shearing force is
kN. Find the ratio between maximum and mean s
tress.

(November /December
-
2010)
]

13.

A simply supported beam of length 4m carries a point load of 3KN at a distance of
1m from each end . If E=2x105 N/mm2 and I = 108 mm4 for the beam, then using
conjugate beam method, determine

a)

slope at each end and

b)

Deflection at the centre

(April / May

2010)

14.

The shear force acting on a section of a beam is 50 KN. The section of the beam
is of T
-
shaped as shown in Fig.4 Calculate the shear stress at the neu
tral axis and
at the junction

of the web and the flange.

(April / May

2010)

15.

a) A beam 10m long is subjected to a clockwise couple of intensity 200 kNm at
the mid span and a point load of intensity 50kN acts at a distance of 6m from the
left support. Find the maximum deflection an
d the deflection at the point of
application of the couple. EI = 80 MNm
2
. Use macaulay’s method.

(April / May

2010)

16.

b) Using conjugate beam method find the slope and deflection at C and D for the
beam shown in Figure 4. (April / May

2010)

17.

a) A holl
ow shaft is required to transmit 1000kw at 300rpm maximum torgue
being 40% greater than the mean. The shear not to exceed 150 N/mm
2

and the
angle of twist is not to exceed calculate the maximum external diameter of the
shaft satisfying conditions G = 80 GN

/m
2
.

(April / May

2010)

18.

A close

coiled helical spring is t carry a load of 150 N. The spring made of 8mm
dia meter steel wires and has 20 coils each of 15 mean diameter G = 80 GN /m
2

calculate the

(i)

Max. shear stress produced

(ii)

Deflection

(iii)

Stiffness and

(iv)

Strain energy stored

(April / May

2010)

19.

A beam of length 6 m is simply supported at its ends and carries two point loads
of 48 kN and 40 kN at a distance of 1 m and 3 m respectively from the left
support. Find :

(a)

(b)

Maximum
deflection and

(c)

The point at which maximum deflection occurs. Given
E = 2 x 10
5

N/mm
2

and I = 85 x 10
6

mm
4
.

November / December
-
2010

20.

An I section beam 350 mm x 150 mm has a web thickness of 10 mm and a flange
thickness of 20 mm. If the shear force acting
on the section is 40 kN, find the
maximum shear developed in the I section. Also, sketch the shear stress
distribution showing the stress values at the salient points, across the section.
November / December
-
2010.

21.

(a) A simply supported beam of span 10 m

carries two point loads 100 kN

and 60 kN at a distance of 2 m and 5 m from the left support. Calculate

the slope and deflection under each load. Assume EI= 2.15 x 10
5
kN
-
m
2
.

November / December
-
2009.

22.

A T section beam of flange 200 mm
x 20 mm and web 250 mm x 25 mm is
subjected to a shear force of 50 kN. Find the shear stress at (i) the

junction of flange and web (ii) the neutral axis. Also sketch the shear

stress distribution across the section.

23.

(a) For the beam shown in Fig. 4 show t
hat the deflection at free end is

Use
Macaulay's method. May/June
-

2009

Fig. 4.

24.

A beam of channel section 120 mm x 60 mm has a uniform thickness of

15 mm.
Draw the shear stress distribution for a vertical section where the shear

force is 50 kN. Find the ratio between the maximum and mean shear stress.
May/June

2009.

25.

(a) A simply suported beam has a span of 6 m. It carries two concentrated loads of
40 kN and l0 kN at distances of 2 m and 4 m from the left support. Find the

deflection under the 40kN load. Take EI = 8000 kNm
2
. Use Macanlay's method.
April/May
-
2008.

26.

(b) If a hollow circular bearry whose external diameter is twice the internal

diameter is subjected to a shear force, show that the maximum shear stress is 1
.866

times the average shear stress. April/May
-
2008.

27.

(a) A beam AB of 4 meters span is simply supported at the ends and is loaded as
shown in Fig. 2. Determine (i) Deflection at D (ii) Slope at the end A. Take E =
200 x 10
6

kN/m
2

and I = 20 x 10
-
6

m
4
.
(Nov /Dec
-
2008)

Fig. 2

28.

(b) A T

shaped cross

section of a beam shown in Fig. 3 is subjected to a
vertical shear force of 45 kN. Calculate the shear stress at neutral axis and at the
junction of the web and flange. (Nov /Dec
-
2008)

Fig. 3

29.

(a)

Obtain the deflection under the greater load for the beam shown in fig. 5 using
the conjugate beam method. (Nov /Dec
-
2007)

30.

(b) Three planks of each 50 x 200 mm timber are built up to a symmetrical I
section for a beam. The maximum shear force over
the beam is 4 kN. Propose an
alternate rectangular section of the same material so that the maximum shear stress
developed is same in both sections. Assume the width of the section to be 2/3 of
the depth. (Nov /Dec
-
2007)

31.

(a) (i) Derive the simple bend
ing equation

= E/R.

(ii) A cantilever beam of span 2m is subjected to a concentrated load at free end,
10 kN. The cross section of beam “T” with 10 x 2 cm flange and 2 x 8 cm web.
Draw the shear stress distribution. (Nov /Dec
-
2007)

32.

(b) A cantil
ever beam 2.5 m long carries a UDL of 30 kN/m. The width of the
beam remains constant and in 100 mm. Determine the depth of the section at the
middle of the length and at fixed end if the shear stress remains same throughout
and equal to 120 MN/m
2
. (Nov
/Dec
-
2007)

33.

(a) A beam of span 8 m and of uniform flexural rigidity EI = 40 x 10
3

kN
-
m
2

is
simply supported at its ends. It carries a uniformly distributed load of 15 kN/m
over the entire span. It is also subjected to a clockwise moment of 160 kN/m at a
distance of 3 m from the left support. Calculate the slope and deflection at the
point
of application of the moment. (May / June

2006)

34.

(b) For the loaded beam shown in Fig. (4) determine (i) the slope at the left
support (ii) the slope and deflection under 100 kN load. Assume EI = 2 x 10
4

kN
-
m
2
. Use moment area method. (May / June

200
6)

Fig. (4)

35.

(a) Using conjugate beam method, obtain the slope and deflections at A, B, C and
D of the beam shown fig. 3. Take E = 200 GPa and I = 2 x 10
-
2

m
4
. (
May /
June

2007)

Fig. 3

36.

(b) A simple beam of span 10 m carries a UDL of 3 kN/m. The
section of the
beam is a T having a flange of 125 x 25 mm and web 25 x 175 mm. For the
critical section obtain the shear stress at the Neutral axis and at the junction of
flange and the web. Also draw the shear stress distribution across the section.
(Ma
y / June

2007)

UNIT

V

TORSION & SPRINGS

Part

A

1.

What are the user of leaf springs? (May / June

2012) (May/June
-
2011)

2.

Define the term ‘for que’ (May/June

2011)

3.

Define
: stiffness of spring &

spring index. (Nov/Dec
-
2010) (May/June
-
2009)
(Nov/Dec

2007)

4.

What are the advantages of hollow shaft over
solid

shaft? (Nov
-
Dec
-
2010)

5.

What is a spring? Name the two important types of spring. (April/May
-
2010)

6.

Write down the expression for torque
inter
ms of polar moment of inertia.
(April/May
-
2010)

7.

Give the torsion equations. (April/May

2010)

8.

Define helical springs. Name the two important types of helical springs.
(Nov/Dec
-
2009) (Nov/Dec
-
2008)

9.

Write down the
relation between torque polar moment of inertia & shear stress.
(Nov/Dec
-
2009)

10.

What are the main uses of springs? (Nov/Dec
-
2009)

11.

What is a leaf spring? & applications? (April/May
-
2008) (Nov/Dec
-
2007)
(Nov/Dec
-
2011)

12.

Define the term: Tensional rigidity.
(Nov/Dec
-
2008)

13.

How does the

shear stress vary across a soli
d shaft? (Nov/Dec
-
2007)

14.

Write the expression for power transmitted by a circular shaft. (Nov/Dec
-
2007)

15.

Write the torsion formula for a solid

circular bar of uniform diameter (
Nov/Dec
-
2012)

16.

Stat
e the difference between torsion spring & bending spring (Nov/Dec
-
2012)

17.

Define the polar modulus of a circular section? (May/June
-
2006)
(Nov/Dec
-
2011)

18.

What is a stepped shaft?
(May/June
-
2007)

Part

B

1.

(a) A hollow steel shaft 5 m long is to 160 kW of

power at 120 r.p.m. The total
angle of twist is not exceed 2° in this length and the allowable shear stress is 50
N/mm
2
. Determine the inside and outside diametres of the shaft, taking N=

0.8

x

10
5

N/mm
2
.

(November / December
-
2012)

2.

(b) A close

coiled
helical compression spring is made of 10 mm steel wire
closely coiled to a mean diameter of 100 mm with 20 coils. A weight of 100 N is
dropped on to the spring. If the maximum instantaneous compression is 60 mm,
calculate the height of the drop. Take N = 0
.85 x 10
5

N/mm
2
.

(November / December
-
2012)

3.

(a) Derive Torsional formula. Also explain how do you analyse the shafts fixed at
both ends.

(May / June
-
2012)

4.

(b) Derive expressions for the deflection bending stress and shear stress induced in
an open
coiled helical spring subjected to an axial load ‘w’.

(May / June
-
2012)

5.

(a) A close coiled helical spring of 100 mm mean diameter is made of 10mm
diameter rod and has 120 complete turns. The spring carries and axial load of
200N. Determine the maximum sh
ear stress. Take the modulus of rigidity as
8.4x104 N/mm2. Also determine the deflection, stiffness of the spring and
frequency of the vibrations for a mass hanging from it.

(November / December
-
2011)

6.

(b) A laminated spring I m long is made up of plates

each 50 mm wide and 10 mm
thick. If the bending stress in the plate is limited to 100 N/mm2, how many plates
would be required to enable the spring to carry a central
is the deflection under the load? Take E=2.1x105 N/mm2.

(Novembe
r / December
-
2011)

7.

Two solid shafts AB and BC of aluminum and steel
respectively are rigidly
fastened together at B and attached to two rigid supports at A and C. Shaft AB is
75 mm in diameter and 2 m in legth. Shaft BC is 55 mm in diameter and 1 m in
length. A torque of 20000N
-
cm is applied at the junction B. Compute the
maximum shearing stresses in each material. What is the angle of twist at the
junction? Take modulus of rigidity of the materials as C
aluminium

=0.3x105 N/mm2
and C
steel

= 0.9x105 N/mm2.

(November / December
-
2011)

8.

(a) A solid steel shaft 6 m long is se
curely fixed at each end. A torque of 1500 NM
is applied to the shaft at a section 2.4m from one end. What is the fixing torques
set up at the ends the shaft?

9.

(b) A close coiled helical spring 100 mm mean diameter is made up of 20 turns of
10 mm diameter
steel wire. If the maximum shear stress is not to exceed 90 Mpa,
calculate the maximum axial load the spring can take and the stiffness of the
spring. What is the strain energy stored at the maximum load? Take rigidity
modulus as 0.8 x 105 MPa.

10.

A hollow
shaft of diameter ratio 3/8 is required to transmit 588kW at 110 rpm, the
maximum torque being 20% greater than the mean the shear stress is not to
exceed 63 MN/m
2

and angle of twist ina length of 3 meters not to exceed 1.4
degree. Calculate the external

diameter of the shaft which would satisfy these
condition. Rigidity modulus is 84 GN /m
2
.

(November /December
-
2010)

11.

a) Derive the torsion equation
τ
/R

= C
θ

/L

b) A close

coiled helical spring is made out of 10mm diameter steel rod. The coil
consists of 10 complete turns with a mean diameter of 120mm. The spring carries
an axial pull of 220N. Find the maximum shear stress induced in the section of the
rod. If C 80 GN /m
2
, find the deflection of the spring, the stiffness and strain
energy store
d in spring.

(November /December
-
2010)

12.

Determine the diameter of a solid steel shaft which will transmit 90 KW at 160
r.p.m Also
determine the length of the sha
f
t

if the twist must not exceed 1° over
the entire length. The
maximum shear stress is
limited to 60 N/mm
2

Take C =
8x10
4

N/mm
2
.

(April / May

2010)

13.

A close coiled helical spring of 10 cm mean diameter is made up of 1 cm
diameter rod and has 20 turns. The spring carries an axial load of 200 N .
Determine the shearing stress. Taking the
va
lue of modulus of rigidity C =8.4
x10
4
N/mm
2
, determine the deflection when carrying this load. Also calculate the
stiffness of the spring.

(April / May

2010)

14.

A solid circular shaft transmits 75 kW power at 200 r.p.m. Calculate the shaft
diameter, if
the twist is not to exceed 1
° in 2 m length of shaft and shear stress is
limited to 50 N/mm
2
. Take C = 1 x 10
5

N/mm
2
.
November / December
-
2010

15.

The stiffness of a close
-
coiled helical spring is 1.5 N/mm of compression under a
maximum load of 60N. The maxi
mum shearing stress produced in the wire of the
spring is 125 N/mm
2
. The solid length of the spring (when the coils are touching)
is given as 5 cm. Find

(a)

Diameter of wire

(b)

Mean diameter of the coils and

(c)

Number of coils required. Take C = 4.5 x 10" N/mm
2

November / December
-
2010

16.

(a) A steel shaft is transmitting 150 kW power at 75 rpm. If the allowable

shear stress in the shaft is not to exceed 100 N/mm
2

and the allowable

twist is not to exceed 3 degrees per meter length of the shaft, find the

minimum di
ameter of the shaft. Assume shear modulus of the steel has

80 kN/mm
2
. November / December
-
2009.

17.

(b) Design a closed coil helical spring which when put a load of 400 N may

deflect 80 mm. The diameter of each coil is to be 10 times that of the wire of the

spring and the maximum shear stress is not to exceed 55 N/mm
2
. Assume the
shear modulus of the spring material as 75 kN/mm
2
.

November / December
-
2009.

18.

(a) (i) Derive the torsion equation for a circular shaft of diameter 'd'

subjected to torque T'.

(ii) Find the torque that can be transmitted by a thin tube 6 cm mean diameter
and wall thickness 1 mm. The permissible shear stress is 6000 N/cm
2
.

May/June
-

2009

19.

A close coiled helical spring is made of a round wire having 'n' turns and the mean
coil ra
dius R is 5 times the wire diameter. Show that the stiffness of the spring =
2.05 R/n. If the above spring is to support a load of 1.2 kN with 120 mm
compression calculate mean radius of the coil and Number of turns assuming G =
8200 N/mm
2

and permissible
shear stress,
ƛ
allowable

= 250 M/mm
2
. May/June
-

2009

20.

(a) A solid circular shaft transmits 294 kN at 300 rpm. If the maximum shear
stress should be less than 42 MPa and the angle of twist in a length of 3 m should
not exceed 1
°, find the diameter of the
shaft. Take G = 80 G Pa. April/May
-
2008.

21.

(b) A close coiled helical spring of 100 mm mean diameter is made up of 10 mm
diameter rod and has 20 turns. The spring carries an axial load of 200 N.
Determine the shearing stress and the deflection developed in the spring. Also find
the stiffness of the

spring. Take G = 84 G Pa.
April/May
-
2008.

22.

(a) A steel shaft ABCD having a total length of 2400 mm is contributed by three
different sections as follows. The portion AB is hollow having outside and inside
diameters 80 mm and 50 mm respectively, BC is
solid and 80 mm diameter. CD
is also solid and 70 mm in diameter. If the angle of twist is same for each section,
determine the length of each portion and the total angle of twist. Maximum
permissible shear stress is 50 MPa and shear modules 0.82 x 10
5

MPa. (Nov /Dec
-
2007)

23.

(b) It is required to design a close coiled helical spring which shall deflect 1 mm
under an axial load of 100 N at a shear stress of 90 MPa. The spring is to be made
of round wire having shear modules of 0.8 x 10
5

MPa. The mean di
ameter of the
coil is 10 times that of the coil wire. Find the diameter and length of the wire.
(Nov /Dec
-
2007)

24.

(a) (i) Derive the torsion equation T/J =

(ii) A closely coiled helical spring carries a load of 500 N. Its mean coil diameter
is equal to 10 times the diameter of the coil. Calculate the diameters if the
maximum shear stress is 80 MN/m
2
.
(Nov /Dec
-
2007)

25.

(b) A circular shaft has to transmit a power of 75 kW. The rpm is 180. If the
maximum shear stress is limited to 50 N/mm
2

and the angle a twist 1
o

for a shaft
length of 2 m is permissible. Find the diameter of the shaft G = 0.8 x 10
5

N/mm
2
.
(Nov /Dec
-
2007)

26.

(a) A steel shaft is to transmit 300 kW at 100 r.p.m. If the shear stress is not to
exceed 80 N/mm
2
, find the diamete
r of the shaft. What percent saving in weight
would be obtained if this shaft were replaced by a hollow one whose internal
diameter equals 0.6 of the external diameter, the length, material and maximum
shear stress being the same? (May / June

2006)

27.

(b)

A helical spring, in which the mean diameter of the coils is 8 times the wire
diameter, is to be designed to absorb 200 N
-
m of energy with an extension of 100
mm. The maximum shear stress is not to exceed 125 N/mm
2
. Determine the
mean diameter of the he
lix, diameter of the wire and the number of turns. Also,
find the load with which an extension of 40 mm could be produced in the spring.
Assume the modulus of rigidity of the spring’s material as 84 kN/mm
2
.

(May /
June

2006)

28.

(a) A hollow shaft of di
ameter ratio 2/3 has to be designed to transmit 500 HP at
250 rpm. The allowable shear stress is 45 MPa and the T
max

is 30% more than the
T
mean
. Find size of the hollow section. If the hollow one is to be replaced by a
solid shaft of same material, find

the diamater solid one. If the q
max

is same for
both, how much more material is required for the solid shaft. (May / June

2007)

29.

(b) An open coiled spring is made up of 15 mm dia. steel rod to a mean coil
diameter of 100 mm with 12 coils. If the angle o
f helix is 12
o

what is the
deflection due to an axial load of 300 kN and the intensity of direct and the shear
stresses. If the axial load is replaced by an axial torque of 8 Nm, obtain the angle
of rotation about the coil axis and the axial deflection.

E = 2 x 10
5

MPa and N = 0.84 x 10
5

MPa. (May / June

2007)