Reg. No.
Question Paper Code :X10277
B.E./B.Tech. DEGREE EXAMINATIONS – NOV / DEC 2020
THIRD SEMESTER
Chemical Engineering
CH8302 – Solid Mechanics for Technologists
(Regulations 2017)
Time: 3 Hours
Answer ALL Questions
Max. Marks 100
PART- A (10 x 2 = 20 Marks)
1.
State Hooke’s law.
2.
Define poisson’s ratio.
3.
Explain the overhanging and cantilever beams with support conditions.
4.
Define point load and distributed load.
5.
Define double integration method.
6.
Define Macaulay’s method.
7.
State the assumptions in the theory of simple bending.
8.
What is the shear stress distribution value of flange portion of the I-section?
9.
State the assumptions in the theory of pure torsion.
10. State the assumptions in the Euler’s column theory.
PART- B (5 x 13 = 65 Marks)
11.
a)
A short steel tube of external diameter 70mm and internal diameter 40mm is
surrounded by a brass tube of same length and external diameter 90mm and
internal diameter 80mm. The tubes are rigidly fixed and an axial load of 20
kN is placed on the tubes. Find the load carried in each tube and shortening
of each tube. Take L=30cm, modulus of elasticity of steel is 2.1 x 105 N/mm2
and modulus of elasticity of brass is 1.1 x 105 N/mm2.
(13)
OR
b) A steel tube of 50mm external diameter and 30mm internal diameter
encloses a copper rod of 25mm diameter. The tube is closed at each end by
rigid plates of negligible of stress. Calculate the stresses in the rod and tube
when temperature is raised to 200°C.
(13)
2
2
Take
Es = 200 GN/m
Ec = 100 GN/m
αs = 12 x 10-6/ ° C
αs = 18 x10-6/ °C
12.
a)
Abeam is freely supported over a span of 6m. It carries a UDL of 3kN/m
over 1.5m from the left-hand support and also from the center up to the righthand support. It has, besides two-point loads of 2 and 5 kN and 4.5m from
left hand support. Construct SF and BM diagrams.
(13)
OR
b) A beam of 5m length is hinged at one end and freely supported at a distance
of 3.5m from the hinge. It carries a uniformly distributed load of 2.5kN/m
between hinged end and support and a point load of 9kN at the free end.
Construct the SF and BM diagrams. Find out the maximum bending moment
and location of point of contra flexure.
(13)
13.
a)
A simply supported beam of length 8m long supported at its ends is carrying
a point load of 5 kN at 2 m from its right support, Calculate the slope and
deflection at each point by the following methods
i)
Macaulay’s method
(7)
ii)
Double integration
(6)
OR
b) A cantilever projecting 3m from a wall carries a UDL of 12 kN/m for a
length of 2m from the fixed end and a point load of 1.5 kN at the free end.
Find the deflection at the free end. Take E= 2x 105 N/mm2 and I = 1 x 108
(13)
mm4.
14.
a)
Derive the theory of simple bending.
(13)
OR
b) A I section beam 350mm x 200mm has a web thickness of 12.5 mm and a
flange thickness of 25mm. It carries a shearing force of 20 tonnes at a
section. Sketch the shear stress distribution across the section.
(13)
15.
a)
A composite shaft length of 4.5m consist of a steel rod 75mm diameter
surrounded by a closely fitting tube of brass. A torque of 1200 N-m is
applied to the composite shaft and will be shared equally by the two
materials. If modulus of rigidity of steel is 0.9 x 105 N/mm2 and modulus of
rigidity of brass is 0.5 x 105 N/mm2, find
i)
Outside diameter of the brass tube
(4)
ii)
Maximum shear stress in each material
(4)
iii)
Angle of twist
(5)
OR
b) A slender column is built-in at one end and an eccentric load is applied at the
free end. Working from the first principles find the expression for the
maximum length of column such that the deflection of the free end does not
exceed the eccentricity of loading.
(13)
PART- C (1 x 15 = 15 Marks)
16.
a)
A beam AB, 20m long is supported at the right-hand end b at an intermediate
point C, 4m from A so that BC = 16m. It carries two concentrated loads, one
of 4.8kN at A and another of 8kN E which is at distance of 4m from B. In
addition, the beam carries a UDL of 16kN/m run over its entire length and
also another of 10kN/m run over the length CD, where CD= 6m and
BD=10m. Draw the diagram of BM and SF for the beam.
(15)
OR
b) A shaft PQR of 0.6m length and 0.050m external diameter is bored, for a part
of its length PQ, to a 0.025m diameter and for the remaining length QR to a
0.035m diameter bore. If the shear stress is not to exceed 70N/mm2, find the
maximum power that the shaft can transmit at a speed of 150rpm.
If the angle of twist in the length of 0.025m diameter bore is equal to that in
the 0.035m diameter bore, find the length of the shaft that has been bored to
0.025m and 0.035m diameters.