1(a) A semi- infinite elastic
medium is subjected to a normal pressure of intensity ‘P’ distributed over a
circular area of radius ‘a’ at x=0. Determine the stress distribution by using Fourier
integral method. (8 Marks)

(b) A cantilever beam of
rectangular cross-section 40 mm wide and 60 mm thick is 800 mm in length. It
carries a load of 500 N at the free end. Determine the stresses in the
cantilever at mid-length. (6 Marks)

(c) Determine the stress and
displacement fields in an infinite medium due to equal and opposite point
forces acting at different points along their common line of action. (6 Marks)

2(a) What are general solution to
Biharmonic equation. (6 Marks)

(b) What is Winkler’s theory?
Explain. (8 Marks)

(c) A circular disc of 8 cm
diameter and 5 mm thick is subjected to diametral compression. If the applied
load is 800 N, determine the stress distribution in the disc at the centre. (6
Marks)

3(a) An infinite plate contains
an elliptical hole, with major and minor axes a and b. If the plate is under
all round tension and the hole is unstressed, determine the hoop stress around
the hole and show that the stress concentration factors at the ends of the
major and minor axes are 2a/b and 2b/a respectively. (6 Marks)

(b) Explain St.Venant’s theory. (5
Marks)

(c) An elliptical shaft of semi
axes a=0.05 m, b=0.025 m, and G=80 GPa is subjected to a twisting moment of
1200 π N.m. Determine the maximum shearing stress and the angle of twist per
unit length. (4 Marks)

(d) Derive Bredt’s formula for
the rate of twist in terms of the shear-stress distribution for the torsion of
thin-walled sections. (5 Marks)

4(a) An 150 mm × 100 mm × 12 mm
unequal angle bar is placed with the long leg vertical and used as a beam
supported at each end, the span being 3 m. If load of 6500 N is placed at the
mid length of the bar, determine the maximum stress due to bending. (6 Marks)

(b) Derive the generalized
flexure formula. (5 Marks)

(c) A prismatic bar of 2a × 2b
cross-section is bent by two equal and opposite couples. Determine the
equations for the bent shape of the prismatic bar. (5 Marks)

(d) A point force of 500 N is
applied normal to a semi-infinite solid. Determine the stress distribution at a
depth of 50 mm and angular location of 15

^{0}with the line of action of the force. (4 Marks)
5(a) Describe membrane analogy
for the bending of thin plates. How this analogy can be used to determine the
deflection of a plate? (6 Marks)

(b) Derive Navier’s equations for
the bending of a circular plate. What are the assumptions made? (10 Marks)

(c) A circular plate 50 mm
diameter is clamped at the edge. Its deflection at the centre is limited to 1
mm when a pressure of 1 MPa is applied. Calculate the thickness of the plate
and the maximum stress developed in it. E = 200 GPa, v=0.3. (4 Marks)

6(a) By neglecting bending
stresses, derive the equations of equilibrium for shells of revolution. (8
Marks)

(b) A long circular pipe of
radius 300 mm and wall thickness 10 mm is subjected to a uniform bending moment
of 10 N-m and a shear force of 1600 N at one end. Determine the maximum
deflection of the pipe. (4 Marks)

(c) What are different types of
elastic foundations? Derive the differential equation for the elastic line of a
beam resting on an elastic foundation. (8 Marks)

7(a) State and prove the
Maxwell-Betti reciprocal theorem. (8 Marks)

(b) What are the various types of
elements used for plane stress analysis. (4 Marks)

(c) What do you understand by
interpolation function or shape function for an element? (4 Marks)

(d) A beam column of circular
cross-section is 50 mm in diameter and 2 m long. It is simply supported at the
ends and carries an axial compressive load of 3.5 kN. If a couple of 15 N-m is
applied at the right end in the anti-clockwise direction, determine the
deflection and maximum stress developed in the column at mid-span. Take E=2×10

^{5}N/mm^{2}. (4 Marks)
8(a) Derive an expression for the
deflection of a thin circular plate of radius ‘a’ heated on the lateral
surface. (6 Marks)

(b) The temperature rise of a
solid conductor of radius ‘b’ due to a uniform heat source is given by the
formula T = λ (b

^{2 }- r^{2}), where λ is a constant. If there are no external forces resisting longitudinal or radial expansion, determine the stress distribution in the conductor. (6 Marks)
(c) A 500 mm radius wheel
supporting a 200 kN load rests on a rail 100 mm radius. The material of both is
steel with E=2×10

^{3}N/mm^{2}and v=0.3. Determine the maximum contact pressure and the total contact area. (4 Marks)
(d) Distinguish between
stress-concentration factor and strain-concentration factor. (4 Marks)

Material science and engineering-
Model question paper for B.E/B.Tech Engineering

1(a)

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