# Set No. 1

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30 Οκτ 2013 (πριν από 4 χρόνια και 8 μήνες)

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Code No: RR220304

Set No. 1

II B.Tech Supplimentary Examinations, Aug/Sep 2008

MECHANICS OF SOLIDS

( Common to Mechanical Engineering, Production Engineering and

Automobile Engineering)

Time: 3 hours

Max Marks: 80

tions

All Questions carry equal marks

⋆⋆⋆⋆⋆

1. (a) The piston of a steam engine is 40 cm in diameter while the piston rod is 6

cm in diameter. The pressure of the steam acting is 1.05 N/mm
2
. Find the

stress in the piston rod and its elongation, if the piston rod is 75 cm long. E

= 205 kN/mm
2

when the piston is on in the instroke.

(b) A reinforced concrete column 50 cm in diameter has four 30 mm diameter steel

rods embedded, and carries an axial load of 850 kN. Calculate the stresses in

each of the two materials. E for steel = 2.04×10
5
N/mm
2

an
d E for concrete

= 0.136×10
5
N/mm
2
. What is the adhesive force between steel and concrete.

[8]

2. (a) De
ﬁne Factor of safety, Poisson’s ratio and strain energy.

(b) Show that the volumetric strain of a body is the algebraic sum of the linear

strains in three mutually perpendicular directions.

3. Sketch the shear force and bending moment diagrams showing the

salient values for the loaded beam shown in the ﬁgure 3 below.

Figure 3

4. (a) State the assumptions involved in the theory of simple bending.

(b) Derive the Bending equation from ﬁst principle.

5. (a) What is moment area method? Explain the t
wo Mohr’s theorems, as applica
-

ble to the slope and deﬂection of a beam.

(b) A cantilever of uniform cross
-
section of length l carries two point loads, W at

the free end and 2W at a distance a from the free end. Find the maximum

deﬂection due to this loa
ding.

[10]

6. (a) Enumerate the di

erences between longitudinal stress and circumferential

stress in a cylindrical shell subjected to an internal pressure.

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Code No: RR220304

Set No. 1

(b) A thin cylindrical pressur
e vessel of inside diameter 350 mm is subjected to an

internal pressure of 500 kPa. Determine the thickness of the cylindrical wall

assuming joint factor to be 0.85 and corrosion allowance 1 mm. The allowable

stress for the cylindrical material is 160 N/mm
2
.

7. At a point in material under stress, the intensity of resultant stress on a certain

plane is 60 N/mm
2

(tensile) inclined 30
0

to normal of that plane. The stress on a

plane at right angles to this has a normal tensile component of intensity 40 N/mm
2
.

Find fully

(a) The resultant stress on the second plane

(b) The principal planes and stresses

(c) The plane of maximum shear and its intensity.

8. A propeller shaft, 160mm external diameter, 80mm internal diameter, transmits

450kW at 4/3 Hz. There is, a
t the same time, a bending moment of 30kN
-
m and

an end thrust of 250kN. Find

(a) the maximum principal stresses and their planes

(b) the maximum shear stress and its plane

(c) the stress, which acting alone, will produce the same maximum strain. Take

poi
sson’s ratio = 0.3

⋆⋆⋆⋆⋆

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Code No: RR220304

Set No. 2

II B.Tech Supplimentary Examinations, Aug/Sep 2008

MECHANICS OF SOLIDS

( Common to Mechanical Engineering, Production Engineering
and

Automobile Engineering)

Time: 3 hours

Max Marks: 80

All Questions carry equal marks

⋆⋆⋆⋆⋆

1. (a) Derive the relation between Bulk modulus and Modulus of rigidity.

(b) A rigid bar AB 9 m long is suspended by two vertical r
ods at its ends A and

B and hangs in horizontal position by its own weight. The rod at A is brass,

3m long, 1000mm
2

area and E is 10
5

N/mm
2
. The rod at B is steel, 5m long,

450 mm
2

area and E is 2
×
10
5
N/mm
2
. At what distance

d

from A may a

= 5 kN be applied if the bar is to remain horizontal even after

[10]

2. Prove that Poisson

s ratio for the material of a body is 0.5, if its volume does not

change when stressed. Prove also that Poisson

s ratio is zero when there
is no

lateral deformation when a member is axially stressed.

3. (a) De

ne shear force and bending moment.

(b) A horizontal beam AB of length 4m in hinged at A and supported on rollers

at B. the beam carries inclined loads of 100N, 200N and 300N incised to
wards

the roller support at 60
0
, 45
0

and 30
0

Respectively to the horizontal, at 1m,

2m and 3m respectively from A. draw the SF and BM diagrams.

4. (a) A rectangular beam 300mm wide and 460mm deep is simply supported over

a span of 8.5m. what u.d.l the bea
m may carry if the bending stress is not to

exceed 150MPa.

(b) A horizontal beam is of the section shown in Figure4b is 6.5m long and is

simply supported at its ends. Calculate the maximum u.d.l it can carry if

the tensile and compressive stresses are not
to exceed 45 MPa and 68MPa,

respectively.

Figure 4b

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Code No: RR220304

Set No. 2

5. (a) What is moment area method? Explain the two Mohr

s theorems, as applica
-

ble to the slope and de

ection of a beam.

(b) A

cantilever of uniform cross
-
section of length l carries two point loads, W at

the free end and 2W at a distance a from the free end. Find the maximum

de

[10]

6. (a) Derive the expression for the change of diameter and lengt
h of a thin cylindrical

shell subjected to an internal pressure.

(b) A cylindrical shell 2.4 m long 0.6 m in diameter is made up of 12 mm thick

plate. Find the changes in the length and diameter, when the shell is subjected

to an internal pressure of 2 N/m
m
2
.

7. The principal stresses at a point in a material are 120 N/mm
2

and 60 N/mm
2
,

the third principal stress being zero. Both the stresses are tensile. Find by the

circular diagram of stress, or otherwise, the magnitude and direction of the resultant

str
ess on a plane inclined at 30
0

to the direction of the smaller principal stress and

perpendicular to the plane across which the stresses are zero.

From the same diagram, or otherwise,

nd also the plane on which the resultant

stress is the most oblique and

the value of this resultant stress and it

s maximum

obliquity.

[16]

8. A propeller shaft, 160mm external diameter, 80mm internal diameter, transmits

450kW at 4/3 Hz. There is, at the same time, a bending moment of 30kN
-
m and

an end thrust of 250kN. Fi
nd

(a) the maximum principal stresses and their planes

(b) the maximum shear stress and its plane

(c) the stress, which acting alone, will produce the same maximum strain. Take

poisson

s ratio = 0.3

⋆⋆⋆⋆⋆

2 of 2

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Code No: RR220304

Set No. 3

II B.Tech Supplimentary Examinations, Aug/Sep 2008

MECHANICS OF SOLIDS

( Common to Mechanical Engineering, Production Engineering and

Automobile Engineering)

Time
: 3 hours

Max Marks: 80

All Questions carry equal marks

⋆⋆⋆⋆⋆

1. A rigid bar is supported by three rods, the outer one of steel and the central one

of copper. The cross sectional area of each steel rod is 300 mm
2

and of the co
pper

rod is 1000 mm
2
. The three rods are equally spaced and the loads of 50 kN are

each applied midway between the rods. Determine the forces in each of the vertical

bars if the rigid bar remains horizontal after the loads have been applied. Neglect

the we
ight of the rigid bar. Take Es = 205 kN/mm
2

and Ec = 110 kN/mm
2
. [16]

2. (a) Draw stress
-
strain diagram for mild steel specimen tested under uni
-
axial ten
-

sion till fracture and mark all the salient points.

(b) A metallic rod of 1 cm diameter, when teste
d under an axial pull of 10 kN was

found to reduce its diameter by 0.0003 cm. The modulus of rigidity for the

rod is 51 kN/mm
2
. Find the Poisson

s ratio, modulus of elasticity and Bulk

Modulus.

[8]

3. (a) How do you classify loads? Give examples.

(b) A

simply supported beam of length 5m carries a uniformly increasing load of

800 N/m run at one end to 1600 N/m run at the other end. Draw the S.F.

and B.M. diagrams for the beam.

4. (a) State the assumptions involved in the theory of simple bending.

(b) De
rive the Bending equation from

st principle.

5. A beam of uniform section, 10 meters long, is simply supported at the ends. It

carries point loads of 110 kN and 60 kN at distances of 2m and 5m respectively from

the left end. Calculate: The de

ection unde
r each load and maximum de

ection

Given : E = 200
×
10
6
N/m
2

and I = 118
×
10

4
m
4
.

6. (a) Derive the expression for the change of diameter and length of a thin cylindrical

shell subjected to an internal pressure.

(b) A cylindrical shell 2.4 m long 0.6 m in d
iameter is made up of 12 mm thick

plate. Find the changes in the length and diameter, when the shell is subjected

to an internal pressure of 2 N/mm
2
.

7. Derive an expression for the major and minor principal stresses on an oblique

plane, when the body is
subjected to direct stresses in two mutually perpendicular

directions accompanied by a shear stress.

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Code No: RR220304

Set No. 3

8. An open coiled helical spring is made out of 10 mm diameter steel rod, the coils

havi
ng 10 complete turns, and a mean diameter 80 mm, the angle of helix 15
0
.

Calculate the de

ection under an axial load of 250 N and the maximum intensities

of direct and shear stresses induced in the section of the wire. If the axial load of

250 N is replace
d by an axial torque of 6 N.m, calculate the angle of rotation about

axis of the coil and actual de

ection. N=0.85
×
10
5
N/mm
2

and E=2.5
×
10
5
N/mm
2
.

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Code No: RR220304

Se
t No. 4

II B.Tech Supplimentary Examinations, Aug/Sep 2008

MECHANICS OF SOLIDS

( Common to Mechanical Engineering, Production Engineering and

Automobile Engineering)

Time: 3 hours

Max Marks: 80

All Questions carry equal mark
s

⋆⋆⋆⋆⋆

1. (a) Derive the relationship between Modulus of Elasticity and Modulus of Rigidity.

[8]

(b) A steel rod 600 mm long is of 20 mm diameter in the

rst 200 mm and 16

mm diameter in the second 200 mm and 12 mm diameter in the remaining

length. It is
subjected to a tensile load of (axial) of 50 kN. Determine the

strain energy stored in the rod. Take E = 210 kN/mm
2
.

2. (a) Derive the relationship between the three moduli of elasticity.

(b) Show that in a prismatic bar, the maximum stress intensity due
to a suddenly

applied load is twice the stress intensity produced by the same load applied

[8]

3. A horizontal beam AB of length 6m is height at A and supported on rollers at B.

The beam carries inclined loads on 75 kN, 100 kN, 125 kN and 10
0 kN inclined

towards the hinged support at 30
0
, 45
0
, 50
0

and 60
0

Respectively to the vertical.

The points of application of the loads are 1m, 2.5m, 4m and 5m respectively form

A. Draw the SFD and BMD.

[16]

4. (a) State the assumptions involved in the
theory of simple bending.

(b) Derive the Bending equation from

st principle.

5. (a) A beam of length L is supported at each end with a couple applied at an in
-

termediate point. Deduce an expression for the de

ection and hence calculate

the de

ection at the point of application of the moment.

(b) A beam of length L
carries a uniformly distributed load w/unit length and

rests on three supports, two at the ends and one in the middle. Find how much

the middle support be lower than the end ones in order that the pressures on

the three supports shall be equal.

6. Derive
the formula for the thickness of the thin cylindrical shell and solve the

following problem. A thin cylindrical shell of 1 m diameter is subjected to an

internal pressure of 1 N/mm
2
. Calculate the suitable thickness of the shell, if the

tensile strength of

the plate is 400 N/mm
2

and factor of safety is 4.

7. Derive an expression for the shear stress produced in a circular shaft which is

subjected to torsion. What are the assumptions made in the above derivation ?

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Code No: RR22
0304

Set No. 4

8. A propeller shaft 300 mm external diameter and 150 mm internal diameter trans
-

mits 1800 kN power at 100 r.p.m. There is at the same time a bending moment of

12 kN.m and an end thrust of 300 kN. Find

(a) The principal stress a
nd their planes

(b) The maximum shear stress

(c) The stress which acting alone will produce the same maximum strain. Take

1/m = 0.3

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