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

Third Semester

Civil Engineering

CE2201 — MECHANICS OF SOLIDS

(Regulation 2008)

Time: Three hours Maximum: 100 Marks

Answer ALL Questions

PART A — (10 × 2 = 20 Marks)

1. Define longitudinal strain and lateral strain.

2. Write down the relation between modulus of elasticity and modulus of rigidity.3. Give the methods used to analyze frames.

4. What do you mean by thin cylinder?

5. List any four types of beams.

6. What is the maximum bending moment for a simply supported beam subjected

to uniformly distributed load and where it occurs?

7. Write down the formula used to find the deflection of beam by Moment-Area

method.

8. Define shear stress.

9. 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 SQUARE

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

PART B — (5 × 16 = 80 Marks)

11. (a) A tensile test was conducted on a mild steel bar. The following data wasobtained 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

(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 =

5 2

1.3×10 N/mm , for zinc =

5 2

1×10 N/mm and for

aluminium =

5 2

0.8×10 N/mm .

12. (a) Determine the forces in the truss shown in Fig.(1) which is subjected to

inclined loads.

Fig.(1)

Or

(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

2

3 N/mm . Also calculate the increase in length,

diameter and volume of vessel. Take E =

5 2

2×10 N/mm and =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.

Fig.(2)

Or

(b) (i) Derive an expression for

R

E

I Y

M

= =

σ

. (8)

(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

2

120N/mm . Take

6 4

I=8×10 mm . (8)

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.

Take E = 2 10 N/mm ,

5 2

× I =

6 4

85×10 mm .

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

2

12 N/mm and maximum shearing stress is

2

1N/mm , find the ratio of the span to the depth. (8)

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(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)

Fig (3)

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 =

4 2

8.16×10 N/mm .

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