B.E./B.Tech. DEGREE EXAMINATION, APRIL/MAY 2010.
CE2201 — MECHANICS OF SOLIDS
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
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 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
(1) The Young’s modulus
(2) The stress at elastic limit
(3) The percentage of elongation
(4) The percentage decrease in area.
(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
1.3×10 N/mm , for zinc =
1×10 N/mm and for
0.8×10 N/mm .
12. (a) Determine the forces in the truss shown in Fig.(1) which is subjected to
(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
3 N/mm . Also calculate the increase in length,
diameter and volume of vessel. Take E =
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
(b) (i) Derive an expression for
(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/mm . Take
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 ,
× I =
85×10 mm .
(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
12 N/mm and maximum shearing stress is
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)
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.
(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 =
8.16×10 N/mm .