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P.T.O.

Total No. of Questions12] [Total No. of Printed Pages8+4

Seat

No. [4262]-119

S.E. (Mechanical) (II Sem.) EXAMINATION, 2012

STRENGTH OF MACHINE ELEMENT

[Common to Mech. S/W of Sem. I and Mech. Branch Sem. II]

(2008 PATTERN)

Time : Three Hours Maximum Marks : 100

N.B. : (i) Answer three questions from Section I and three questions

from Section II.

(ii) Answers to the two Sections should be written in separate

answer-books.

(iii) Neat diagrams must be drawn wherever necessary.

(iv) Figures to the right indicate full marks.

(v) Use of logarithmic tables, slide rule, Mollier charts, electronic

pocket calculator and steam tables is allowed.

(vi) Assume suitable data, if necessary.

SECTION I

Unit 1

1. (a) Define and explain the following terms : [4]

(i) Modulus of rigidity

(ii) Lateral strain.

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(b) Show that E = 2G(1 + ) with usual notations. [4]

(c) A solid steel bar 500 mm long and 70 mm diameter is placed

inside an aluminium tube having 75 mm inside diameter and

100 mm outside diameter. The aluminium tube is 0.15 mm

longer than the steel bar. An axial load of 600 kN is applied

to the bar and the cylinder through rigid cover plate from

both ends. Find the stresses developed in the steel bar and

the aluminium tube.

Use Es = 220 kN/mm2 and Ea = 70 kN/mm

2. [8]

Or

2. (a) A hollow steel tube of 30 mm in diameter and 5 mm thickness

encloses centrally a solid copper bar of 15 mm diameter to

which it is rigidly connected at each ends. If, at a temperature

of 10C there is no longitudinal stress. Find the stresses in

each metal when heated to 200C. The value of coefficient

of linear expansion for steel and copper is 11 106 per C

and 18 106 per C respectively. Take Es = 2.1 105 MPa

and Ec = 1 105 MPa. [8]

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(b) A bar LMNP, fixed at L and P is subjected to axial forces

as shown in Fig. 1. Determine : [8]

(i) Forces in portion LM, MN and NP.

(ii) Displacement of points M and N.

Take E = 200 GN/m2.

Fig. 1

Unit 2

3. (a) A simply supported beam of length 10 m long carries a uniformly

distributed load and two point loads as shown in Fig. 2. Draw

the shear force and bending moment diagram, also calculate

maximum bending moment. [12]

Fig. 2

22

2

50 kN 100 kN

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(b) Show that for a simply supported beam of length L subjected

to a central concentrated Load of W, deflected at mid span

is given by y = WL3/48EI Downward. Use double integration

method. [6]

Or

4. (a) A cantilever AE of 5 m long is subjected to forces as shown

in figure. Draw the shear force and bending moment diagram

for the beam shown in Fig. 3. [10]

Fig. 3

(b) A cantilever of 3 m length and uniform rectangular cross-section

150 mm wide and 300 mm deep is loaded with 30 kN

load at its free end. In addition to this it carries a uniformly

distributed load of 20 kN per meter run over its entire length,

calculate :

(i) The maximum slope and deflection

(ii) The slope and deflection at 2 m from fixed end. [8]

2.5 kN1 kN/m

3 kN

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Unit 3

5. (a) An element in plane stress is subjected to stresses

x = 70 MP Tensile, y = 35 MPa Compressive and

xy = 35 MPa as shown in Fig. 4. Determine the principal

stresses and their planes, also determine maximum shear stress

and planes on which it acts. [8]

Fig. 4

(b) Derive an expression for principal stresses and maximum shear

stress for a shaft subjected to combined bending and twisting

moment. [8]

Or

6. (a) On a mild steel plate, a circle of diameter 50 mm is drawn

before the plate is stressed as shown in Fig. 5. Find the length

y

x

xy

xy

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of major and minor axes of an ellipse formed as a result

of the deformation of the circle marked. Take E = 200 GPa,

Poissons ratio = 0.25. [8]

Fig. 5

(b) Write short notes on any two of the following : [8]

(i) Maximum Distortion energy

(ii) Maximum principal stress theory

(iii) Maximum shear stress theory.

20 N/mm2

40 N/mm2

80 N/mm2

40 N/mm2

40 N/mm2

20 N/mm2

40 N/mm2

80 N/mm2

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SECTION II

Unit 4

7. (a) Derive the following expression :

M E

.I Ry

= = [8]

(b) A beam of the cross-section shown in Fig. 6 is bent about

a horizontal axis. If the bending moment is 8 kN-m, determine

the total force action on the top flange. [8]

Fig. 6

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Or

8. (a) For a hollow circular section whose external diameter is twice

the internal diameter, find the ratio of maximum shear stress

to average shear stress. [6]

(b) A beam AB of length L and rectangular cross-section carries

a uniformly distributed load W and is supported as shown

in Fig. 7 :

(i) Show that the ratio of the maximum values of the shearing

and normal stresses of the beam is equal to 2

L

h, where

h and L are respectively the depth and the length of

beam.

(ii) Determine the depth h and width b of the beam knowing

that L = 5 m, W = 8 kN/m, Zm = 1.08 MPa and

m = 12 MPa. [10]

Fig. 7

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Unit 5

9. (a) Derive Eulers formula for buckling load for column with hinged

ends. Also state the limitations of Eulers formula. [8]

(b) A hollow shaft is 1 m long and has external diameter 50 mm.

It has 20 mm internal diameter for a part of length and

30 mm internal diameter for the rest of length. If the maximum

shear stress is not to exceed 80 N/mm2, determine the maximum

power transmitted by it at a speed of 300 rpm. If the twists

produced in the two portions of the shaft are equal, find the

lengths of the two portions. Refer Fig. 8. [8]

Fig. 8

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Or

10. (a) Derive the following expression :

T G

.J L

z

r

= = [8]

(b) Two brass rods used as compression member, each of

3 m effective length, have the cross-sections as shown

in Fig. 9 : [8]

(i) Determine the wall thickness of the hollow square rod

for which the rods have the same cross-sectional area.

(ii) Using E = 105 GPa, determine the critical load of each

rod.

Fig. 9

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Unit 6

11. (a) Write a short note on Preferred Size. [4]

(b) Explain various steps in the process of designing machine

components. [6]

(c) A knuckle joint is subjected to an axial load of 100 kN. Determine

the diameter of knuckle pin considering the load to be uniformly

distributed over the pin in the eye and uniformly varying over

the portion of pin in fork.

Allowable tensile and compressive stress for pin is 600 N/mm2

Allowable shear stress for pin is 300 N/mm2

Allowable bearing pressure for pin is 200 N/mm2

Thickness of eye is 1.5 d where d is pin diameter. [8]

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Or

12. (a) A C frame subjected to a load of 10 kN is as shown in

Fig. 10. It is made of gray cast iron with allowable normal

stress of 120 N/mm2. Determine the dimensions of the cross-

section of the frame. [6]

Fig. 10

(b) Write a short note on design for environment. [6]

(c) Explain the term design synthesis. [6]

5t

t

7.5t

10 kN

10 kN