upto mayjune 2010 ce 1201 - mechanics of solids - Tancet Academy

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B.E./B.Tech. DEGREE EXAMINATION, APRIL/MAY 2010

Third Semester

Civil Engineering

CE2201 — MECHANICS OF SOLIDS

(Regulation 2008)

Time: Three hours Maximum: 100Marks

Answer ALL Questions

PART A — (10 x 2 = 20 Marks)

1. Define longitudinal strain and lateral strain.
2. Write down the relation between modulus of elasticity and modulus of rigidity.
3. What do you mean by thin cylinder?
4. List any four types of beams.
5. What is the maximum bending moment for a simply supported beam subjected to uniformly distributed
load and where it occurs?
6. Write down the formula used to find the deflection of beam by Moment-Area method.
7. Define shear stress.
8. A solid shaft of 150 mm diameter is used to transmit torque. Find the maximum torque
transmitted by the shaft if the maximum shear stress induced to the shaft is 45N/mm
2

9. Define springs. What are the different types of springs?

PART B — (5 x 16 = 80 Marks)

11. (a) A tensile test was conducted on a mild steel bar. The following data was obtained from the
test:
(i) Diameter of the steel bar = 3 cm
(ii) Gauge length of the bar = 20cm
(iii) Load at elastic limit = 250 kN
(iv) Extension at a load of 150 kN = 0.21 mm
(v) Maximum load = 380 kN
(vi) Total extension = 60 mm
(vii) Diameter of rod at failure = 2.25 cm

Determine:

(1) The Young's modulus
(2) The stress at elastic limit
(3) The percentage of elongation
(4) The percentage decrease in area.
Or
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(b) Three bars made of copper; zinc and aluminium are of equal length and have cross section 500,
700, and 1000 sq.mm respectively. They are rigidly connected at their ends. If this compound
member is subjected to a longitudinal pull of 250 kN, estimate the proportional of the load
carried on each rod and the induced stresses. Take the value of E for copper = 1.3x10
5
N/mm
2
,
for zinc = 1x10
5
N/mm
2
and for aluminium = 0.8x10
5
N/mm
2
.


12. (a) Determine the forces in the truss shown in Fig.(l) which is subjected to inclined loads.




(b) A cylindrical vessel, whose ends are closed by means of rigid flange plates, is made up of
steel plate 3 mm thick. The length and internal diameter of the vessel are 50 cm and 25 cm
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 vessel. Take E = 2x10
5
N/mm
2
and µ= 0.3.

13. (a) A simply supported beam of length 10m, 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 and also calculate the
maximum bending moment.



(ii) A rectangular beam 300 mm deep is simply supported over the span of 4 m. Determine the
uniformly distributed load per metre which the beam may carry, if the bending stress
should not exceed 120N/mm3.Take I = 8xl06mm4. (8)

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14. (a) 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

(i) Deflection under each load

(ii) Maximum deflection

(iii) The point at which the maximum deflection occurs. TakeE= 2xlO
5
N/mm
2
, 1= 85x10° mm4.

Or
(b) (i) A timber beam of rectangle section is simply supported at the ends
and carries a point load at the center of the beam. The maximum
bending stress is 12N/mm2and maximum shearing stress is
lN/mm2, find the ratio of the span to the depth. (8)

(ii) An I section beam 350 x 150 mm as shown in Fig.(3) 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 stress developed in the
I section. (8)



15. (a) Two shafts of the same material and of same lengths are subjected to a same torque, if the first
shaft is of a solid circular section and the second shaft is of hollow circular section, whose internal
diameter is 2/3 of the outside diameter and the maximum shear stress developed in each shaft is
the same, compare the weights of the shafts.
Or

(b) A closely coiled helical spring made of 10mm diameter steel wire has 15 coils of 100 mm mean
diameter. The spring is subjected to an axial load of 100 N. Calculate
(i) The maximum shear stress induced

(ii) The deflection

(iii) Stiffness of spring. Take modulus of rigidity, C = 8.16xlO4 N/mm2.

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B.E./B.Tech. DEGREE EXAMINATION, APRIL/MAY 2010.

Third Semester

Civil Engineering

CE 1201— MECHANICS OF SOLIDS

(Regulation 2004)

(Common to B.E. (Part-Time) Second Semester Regulation 2005)
Time : Three hours Maximum : 100 marks

Any missing data may be assumed reasonably.

Answer ALL questions.

PART A — (10 x 2 = 20 marks)

1. A material has modulus of rigidity equal to 0.65x10
5
N/mm
2
and Poisson's ratio equal to 0.28. Find
the Young's modulus and the bulk modulus of the material.

2. What is limit of proportionality?

3. A spherical shell of diameter 750 mm and metal thickness 12 mm is completely filled with a fluid at
atmospheric pressure. Find the maximum pressure that can be permitted if efficiency of the joint is
80 % and the permissible stress is 90 N/mm
2
.

4. Define tension coefficient.

5. Determine the cross-section of a rectangular beam of uniform strength for a simply supported beam
of span 5m subjected to a central concentrated load of 30 kN by keeping depth of 250 mm
throughout. Take permissible stress as 10 N/mm
2


6. Write down the simple bending equation.

7. Draw the shear stress distribution for an angle section.

8. A simply supported beam of length 5m is subjected to a udl of intensity 2 kN/m over its left half
span. Draw the conjugate beam for this beam. EI is constant throughout.

9. A leaf spring of span 1 m has 6 numbers of leaves of width 75 mm and thickness 10 mm each. What
maximum load can it take if stress is to be limited to 250 N/mm
2
?

10. Give the torsion equation.


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PART B — (5 x 16 = 80 marks)

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

(i) the supports are unyielding and

(ii) the supports yield by 0.08 mm. Eb= 85 GN/m2, ab= 19 x WVC ; Ec= 110 GN/m2,
α
c
= 17.5 x 106 /°C?

Or

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

12. (a) Find the forces in the members of the truss shown in Figure 1.




(b) A closed cylindrical vessel made of steel plate 5 mm thick is 50 cm long and its internal
diameter is 20 cm. Determine the longitudinal and hoop stresses in the cylindrical shell due to an
internal fluid pressure of 3N/mm2. Also calculate the change in length, diameter and volume of
the vessel. Take E = 2 x 10
5
N/mm
2
and 1/m = 0.3.

13. (a) Draw the shear force and bending moment diagram indicating salient points for the beam
shown in Figure. 2


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(b) Draw the bending stress distribution across the cross-section of the simply supported beam of span
5 m 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.



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

Or

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




15. (a) A hollow shaft is required to transmit 1000 kW at 300 rpm, the maximum torque being 40 %
greater than the mean. The shear stress is not to exceed 150 N/mm
2
and the angle of twist is not to
exceed 1.5 degrees. The outer diameter is 1.9 times the inner diameter.
Calculate the maximum external diameter of the shaft satisfying these conditions. G = 80 GN/m
2
.

Or
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(b) A close-coiled helical spring is to carry a load of 150 N. The spring is made of 8 mm diameter
steel wires and has 20 coils each of 150 mm mean diameter. G = 80 GN/m
2
. Calculate the

(i) Max. shear stress produced . (4)

(ii) Deflection (4)

(iii) Stiffness and (4)

(iv) Strain energy stored. (4)






































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B.E./B.Tech. DEGREE EXAMINATION, APRIL/MAY 2008.

Third Semester
(Regulation 2004)
Civil Engineering

CE 1201 — MECHANICS OF SOLIDS
(Common to B.E. (Part-Time) Second Semester Regulation 2005)

Time: Three hours Maximum : 100 marks
Answer ALL questions.
.
PARTA—(10x2 = 20 marks)

1. Define: (i) Poisson's ration (ii) shear modulus.

2. Write down the relationship between E, K and Poisson's ratio.

3. Define tension coefficient.

4. When do you adopt method of sections?

5. Write any two assumptions made in simple beam theroy?

6. Write down the relationship between intensity of loading, S.F and B.M.

7. State the moment area theorems.

8. Draw the stear stress variation of a circular section.

9. What is a leaf spring?
.
10. For same weight, which shaft will carry more torque, a solid one or a hollow one? Why?

PART B — (5xl6 = 80 marks)

11.(a) A 2m long 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
.

Or

(b) 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 addition, 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.
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12. (a) Find the forces in the members of the truss shown in Fig. 1



(b) Find the forces in the members AB, BF, BC and FE of the truss shown in Fig.2




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




Or

(b) 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.
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14. (a) A simply suported beam has a span of 6 m. It carries two concentrated loads of 40 kN
and lOkN at distances of 2 m and 4 m from the left support. Find the deflection under the
40kN load. Take El = 8000 kNm
2
. Use Macanlay's method.

Or
(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.

15 (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 = 80GPa.

Or
(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 = 84GPa.






























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B.E./B.Tech. DEGREE EXAMINATION, NOVEMBER/DECEMBER 2008

Third Semester

(Regulation 2004)

Civil Engineering

CE 1201 —MECHANICS OF SOLIDS

(Common to B.E. (Part-Time) - Second Semester - Regulation 2005)

Time : Three hours Maximum: 100 marks

Answer ALL questions.
PART A — (10 x 2 = 20 marks)

1. What is meant by 'Limit of Proportionality’?

2. For a material if the modulus of rigidity is 80 GN/m
2
and modulus of Elasticity is
200 GN/m
2
, determine Poisson's ratio.

3. What is the difference between a deficient and a redundant frame?

4. Define thin cylinders. Name the stresses setup in thin cylinder subjected to internal fluid
pressure.

5. State the relationship between load, shear force and bending moment.

6. What is meant by Moment of Resistance of a beam?

7. Using moment area method, find the deflection at the free and of a cantilever beam with a
concentrated load at the free end.


8. Draw the shear stress distribution for an I — Section.

9. Define the term : Torsional rigidity.

10. Define helical springs. Name the two important types of helical springs.

PART B — (5 x 16 = 80 marks)

11.(a) A compound tube consists of a steel tube 170 mm external diameter and
10 mm thickness and an outer brass tube 190 mm external diameter and 10 mm 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.

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Or
(b) Two mutually perpendicular planes of an element of material are subjected to direct stresses
of 60 N/mm2 (tensile) and 20 N/mm2 (Compressive) and shear stress of 20 N/mm2. 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.

12.(a) A truss of 10 m span is loaded as shown in Fig 1, find the forces in the members of the truss
using method of section.



(b) 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 xlO
5
N/mm
2
and Poisson's ratio = 0.3.

13.(a) 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.
Or

(b) The outer diameter of a tubular section beam is 12Q mm and inner diameter is 80 mm. 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.

14.(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/m2 and
I = 20 x 10
-6
m
4
.


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(b) AT- 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.






15.(a) A .solid steel shaft 6 m long is securely fixed at each end. A torque of 1500 NM is applied to
the shall at a section 2.5 m from one end. What are the fixing torques set up at the ends of the
shaft? If the diameter of the shaft is 40 mm what are the maximum shear stresses in the two
portions? Calculate also the angle of twist for the section where the torque is applied. Modulus
of rigidity 84 GN/m
2
.

Or

(b) A close-coiled helical spring is made out of 10 mm diameter steel rod. The coil consists of 10
complete turns with a mean diameter of 120 mm. The spring carries an axial pull of 220 N. Find
the maximum shear stress induced in the section of the rod. If modulus of rigidity = 80 GN/m
2
,
find the deflection in the spring, the stiffness and strain energy stored in the spring.




















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B.E./B.Tech. DEGREE EXAMINATION, NOVEMBER/DECEMBER 2007.

Third Semester

(Regulation 2004)

Civil Engineering

CE 1201 — MECHANICS OF SOLIDS

(Common to B.E. (Part-Time) Second Semester Regulation 2005)

Time : Three hours Maximum : 100 marks

Answer ALL questions.

PART A — (10 x 2 = 20 marks)

1. Express the relationship among the three elastic constants.

2. In a Mohr's circle of stresses, what represents the maximum shear
stress?

3. What are the two types of trusses with respect to their joints?

4. How to increase the strength of a thin cylinder?

5. What are guided supports?

6. Draw the shear force and bending moment diagrams for the beam shown in fig. 1.




7. What is a conjugate beam?

8. Draw the variation of shear stress for a Tee section.

9. How does the shear stress vary across a solid shaft?

10. What are leaf springs?

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PART B — (5 x 16 = 80 marks)

11. (a) 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 materials due to the load are nullified. Es = E
A1
= 210 GPa.
α
s
= 12 x 10
-6
/K and α
Al
= 23 x 10
-6
/K.




(b) 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.

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




Or

(b) A steel cylinder with flat ends is 2m long and lm 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 modulus.

13. (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
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as possible. Also compute the maximum bending moment.

Or

(b) 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.




14. (a) Obtain the deflection under the greater load for the beam shown in fig. 5 using the conjugate
beam method.




(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 section. Assume the
width of the section to be 2/3 of the depth.

15. (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 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 modulus 0.82 x M
5
Mpa.

Or

(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
modulus of 0.8 x 10
5
MPa. The mean diameter of the coil is 10 times that of the coil wire. Find
the diameter and length of the wire.

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B.E./B.Tech. DEGREE EXAMINATION, MAY/JUNE 2007.

Third Semester (Regulation 2004)

Civil Engineering

CE 1201 — MECHANICS OF SOLIDS

(Common to BE Part-Time Second Semester Regulation 2005)

Time : Three hours Maximum : 100
marks
Answer ALL questions.

PART A — (10 x 2 = 20 marks)

1. Compare the stress-strain curve for Mild steel.
2. A structural steel girder of span L has fixed ends. If the temperature increases by 20°C,
what nature of stress will be induced in the girder?
3. What is the basic difference in the skeleton of Pratt and Howe types of trusses?
4. The volumetric strain of a thin spherical shell is -------------------that of the linear strain.
5. Find the value of W for equal reactions on either side for the beam show in fig. 1.

6. Draw the bending stress distribution for a symmetrical I section.
7. Relate the rate of loading, shear force, bending moment, slope and deflection by integral
equations.
8. What is a shear center?
9. What is a stepped shaft?
10. Compare close coiled and open coiled springs under the action of an axial load.

PART B — (5 x 16 = 80 marks)

11. (a) A 32 mm steel rod is concentrically fixed in a brass tube which has the 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°C,
find the stresses developed in the two materials, if

(i) the distance between the stoppers remains constant and
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(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. Es =2x 10
5
MPa, E
b
= 0.9 x 10
5
MPa, αs= 12 x 10
-6
/
0
C and ab = 21 x10-6rc.
Or

(b) At a certain material under stress, the intensity of resultant stress on a plane is 65 MPa (tensile)
inclined
at 30° to the normal to that plane. The stress on a plane at right angles 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.


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




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

(i) hoop and longitudinal stresses

(ii) maximum shear stress and

(iii) change in the dimensions. E=2x 10
5
MPa and poison's ratio 0.3.

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

Or

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(b) A cast iron beam is a symmetrical 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.


14. (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 = 2x 10
-2
m
4
.





Or

(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.

15. (a) A hollow shaft of diameter 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 diameter
solid one. If the q
max
is same for both, how much more material is required for the solid shaft.

Or

(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 of helix is 12° 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 NID,
obtain the angle of rotation about the coil axis and the axial deflection. E=2X 10
5
MPa and
N = 0.84 X 10
5
MPa.











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B.E./B.Tech. DEGREE EXAMINATION, NOVEMBER/DECEMBER 2006.


Third Semester

Civil Engineering

CE 1201 — MECHANICS OF SOLIDS

(Common to B.E. (Part-Time) Second Semester Regulation 2005)

(Regulation 2004)

Time : Three hours Maximum : 100 marks

Answer ALL questions.

PART A — (10 x 2 = 20 marks)

1. A circular steel rod tapers uniformly from 40 mm to 15 mm diameter in a length
of 40 mm. What is the elongation of the bar if the axial pull is 40 kN.

E = 2 x 10
5
N/mm
2
.

2. State Hooke's Law.

3. What is a perfect frame?

4. What is tension coefficient?

5. What is the condition for maximum bending moment in a beam?

6. Write down the bending equation.

7. Give conjugate beam for a simply supported beam and cantilever beam.

8. Draw the variation of shear stresses in T-Section and rectangular section due to

bending.

9. Compute torsional rigidity of a 100 mm diameter, 4 m length shaft
C = 80 kN/mm
2
.

10. Write down the expressions stiffness and shear stress in close coiled helical springs.







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PART B — (5 x 16 = 80 marks)

11. (a) (i) Calculate the modulus of rigidity and bulk modulus of the
cylindrical bar of diameter 25 mm, length 1.5 m if the longitudinal strain is
4 times the lateral strain. E = 1.5 x 10
5
N/mm
2
.



(ii) Determine the total strain in a bar made of 40 mm diameter solid for a length of

80 mm and hollow circular cross section of outer diameter 40 mm and inner
diameter of 20 mm for a length of 120 mm as shown in Fig. Q. 11.
The axial load is 80 kN.
E = 200 kN/mm
2
.



Or

(b) A bar of 30 mm diameter is subjected to a pull of 60 kN. The measured
extension on a gauge length of 200 mm is 0.09 mm and change in
diameter is 0.0039 mm. Calculate Poisson's ratio and three moduli.

12. (a) Find the forces in the members of the truss shown in Fig. Q. 12(a).


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(b) A cylindrical shell 900 mm long, 150 mm internal diameter, 8 mm thick is filled with a
fluid at atmospheric pressure. If an additional 20000 mm
3
of fluid is pumped into the
cylinder find the pressure exerted by the fluid on the cylinder and the hoop stress
induced. E = 2 x 105 N/mm
2
and µ = 0.3

13. (a) Draw the shear force and bending moment diagrams for the beam
shown in Fig. Q. 13(a).


Or

(b) Find the cross section dimensions of a wooden beam of span 4 m and carrying UDL of
10 kN/m over the entire span. The beam is of rectangular cross section. Assume the depth
of the beam is twice the width.

14. (a) Find the maximum deflection using Macaulay's method for the beam shown in
Fig. Q. 14(a). El = 8.6 x 10
10
kN/mm
2




(b) Find the deflection at mid span and slope at the end A using conjugate beam method.
El = 16000 kNm2. The beam is shown in Fig. Q. 14(b).
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15. (a) A hollow shaft with diameter ratio
is required to transmit 450 kW at 120 rpm. The
shearing stress in the shaft must not exceed 60 N/mm
2
and the twist in a length of 2.5 m is
not to exceed 1°. Calculate the minimum external diameter of the shaft.
C = 80 kN/mm
2
.

Or

(b) It is required to design a close coiled helical spring which shall deflect 10 mm under an axial
load at a 100 N at a shear stress of 90 N/mm
2
. The coil mean diameter is 10 times the wire
diameter. Find the diameters and the length of the wire. E = 80 kN/mm
2
.

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