1(a) State St.Venant’s principle.
(4 Marks)

(b) Write a brief note on
properties of engineering materials.(6 Marks)

(c) Deduce a relation between
Young’s modulus and Rigidity modulus. (6 Marks)

(d) A steel press has four
tension members. Each member has a diameter of 16 mm. The largest load to be
resisted by the press is to be 48 kN. Determine axial stress in the tension
members. (4 Marks)

2(a) Prove that normal stress
acting on maximum and minimum shear stress planes is the average of any two
orthogonal normal stresses acting on the point. (8 Marks)

(b) Write a note on construction
of Mohr’s circle. (8 Marks)

(c) A round bar of 30mm diameter
is subjected to an axial compressive force P. Taking the allowable stresses for
the material of the bar as 110 MPa in compression and 50 MPa in shear, determine
the magnitude of maximum value of P which can be applied such that the member
does not fail. (4 Marks)

3(a) The magnitude of bending
moment at a section will be maximum or minimum when the shear force at that
section is zero or changes its sign. Explain. (8 Marks)

(b) A 6m long beam simply
supported its ends is subjected to UDL of 30 kN/m over 2 meters length from LHS
support. Draw the SF and BM diagrams. (8 Marks)

(c) A 6 meters long beam is
simply supported such that there is a over hang of L meters on either support. The
beam is subjected to load W at its either ends. Determine W and L such that
maximum bending moment and maximum shear stress induced in the beam are 30 kN-m
and 15 kN respectively. (4 Marks)

4(a) What are the assumptions
made during the derivation of equations related to theory of pure bending. (6
Marks)

(b) What is section modulus? Find
the section modulus of a hollow circle. (6 Marks)

(c) A beam with I section has two
equal flanges of each 220 mm wide and 12 mm thick. The web has 12 mm thickness
and depth 460 mm. Determine the percentage of moment of resistance shared by
the flanges and web, when the section is subjected to bending moment M. (8
Marks)

5(a) Derive the moment-curvature
relationship for the deflected curve. (8 Marks)

(b) Macauleys method is an
improved version of double integration method which can be used for finding the
deflections of beams subjected to discontinuous loads. Explain. (8 Marks)

(c) A 2 meters long cantilever is
subjected to UDL of 10 kN/m throughout its length and a vertically downward
point load 20 kN at its free end. Taking E=200 GPa and maximum deflection as
0.3 mm, determine the width and depth of rectangular section. Depth of the
section is twice the width. (4 Marks)

6(a) Show that shear stress distribution
in any section of a shaft is directly proportional to the torque applied. (5
Marks)

(b) Explain the terms torsional
rigidity and torsional flexibility. (6 Marks)

(c) Compare the mass of solid
shaft with that of hollow shaft of same length, when they are made of same
material and are to transmit same power at same speed. The outer diameter of
hollow shaft is 1.4 times its inner diameter. Maximum shear stresses induced in
both cases are equal. (5 Marks)

(d) A 1m long wire is hung in
vertical position and disc is attatched at the bottom end. Diameter of the wire
is 2 mm. Material of wire has yield stress in shear of 150 MPa. Determine the
angle through which the disc can be rotated so that the wire does not yield. Take
G= 80 GPa. (4 Marks)

7(a) Develop Euler’s buckling
load formula for the column with both ends hinged. (6 Marks)

(b) Write a note on limitations
of Euler’s formula. (4 Marks)

(c) Derive Rankine-Gordon
formula. (6 Marks)

(d) A column 2.6 meters long with
a square section of side 50 mm is to be replaced by a column with hollow square
section of outer side 70 mm. Determine the wall thickness of the column and
percentage saving in material. Both ends of the column are hinged. (4 Marks)

8(a) Show that the volumetric
strain is the sum of longitudinal strain and twice the circumferential strain.
(6 Marks)

(b) Radial and circumferential
stresses in a thick wall pressure vessel vary parabolically across the section
of the wall, while longitudinal stress is uniform throughout the cylinder. Explain.
(6 Marks)

(c) A pressure vessel with outer
and inner diameters of 400 mm and 320 mm respectively is subjected to an
external pressure 8 MPa. Determine the circumferential stress induced at the
inner and outer surfaces. (4 Marks)

(d) A water pipe with 500 mm
diameter supplies water at 51 meters head. Taking allowable stress for pipe
material as 30 MPa and efficiency of circumferential riveted joint as 80%,
determine the thickness of the pipe. Specific weight of water is 9.81 kN/m

^{3}. (4 Marks)
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