Jadavpur University 2007 B.E Mechanical Engineering STOF MATARIALS - Question Paper

xi) For the identical pressure, identical diameter and identical material, a spherical vessel needs
only
(a) Half the thickness as that of the cylindrical shell
(b) Quarter the thickness as that of the cylindrical shell
(c) 5 8th the thickness as that of the cylindrical shell
(d) identical thickness as that of the cylindrical shell
xii) The equivalent bending moment of a circular shaft subjected to a torsional
moment T and bending moment M is provided by
(a) (b) (c) (d) None
2 (a) Derive the formula for finding the critical load of a straight column having its one
end fixed and the other end being free.
(b) elaborate the assumptions of derivation in the above ques..
(c) Refer to Fig Q2(c). A horizontal bar AB is supported by a pin-ended column CD.
The Column is a steel bar with E = 200 GPa of square cross-section having its
every side equal to 50 mm. obtain the allowable load Q if factor of safety with
respect to the buckling is n = 3.0 (Note: )
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3(a) A helical spring is set inside a different with the outer spring having its free length 7.0
mm greater than that of the inner spring. The specifications of the springs are as
follows:
Description Outer
Spring
Inner
Spring
Mean Diameter (mm) 30.0 21.0
Wire Diameter (mm) 3.5 -
Number of active turns 12 10
obtain : (i) Load carried by every spring after 150 N load has been applied to the
assembly to deflect the outer spring by 20 mm.
(ii) Maximum shear stress developed in every spring using Wahl’s formula.
(iii) Wire diameter of the inner spring.
Use G = 77.0 GPa for the above computations.
(b) A thin-walled closed cylindrical vessel of internal diameter 900 mm and wall
thickness 20 mm is subjected to a uniform internal pressure ‘p’. If the safe stress in
tension be 150 MPa, obtain the safe value of ‘p’. If the heads of the vessel are
changed to spherical ends, what would be the thickness of the sphere?
4a) Refer to the subsequent figure. The torsional pendulum shown in the figure consists of
a horizontal circular disk of mass M = 50 kg suspended by a vertical steel wire (G =
80 GPa) of length L = 1.0 m and diameter d = four mm. obtain the maximum permissible
angle of rotation ? max of the disk so that the stresses in the wire do not exceed
80MPa in tension or 50 MPa in shear.
b) Show that the ratio of maximum shear stress to the avg. shear stress in a
rectangular cross- part of a beam is 1.5.
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5 a) The shaft ABC as shown in FigQ5a is driven by an electric motor at A which
delivers 30 KW power at a rotational speed of 3Hz. The gears at B and C remove
120 and 180 KW respectively. obtain the needed diameter of the shaft if the
allowable shear stress of the shaft material is 50 MPa and the allowable angle of
twist in the shaft ranging from points A and C is 0.02 radians and G = 75 GPa (1Hz.= 1
cycle/sec)
b) Derive the general relation ranging from the stresses and the internal pressure in case of a
thin pressure vessel
6. A bi-axial stress element is shown beneath in FigQ6. Using Mohr’s circle of stresses,
find:
(i) Maximum and minimum normal stresses and their respective orientations in
the body plane.
(ii) Maximum shear stress and the orientation of this plane in the body.
(iii) Values of normal stress, shear stress and the resulting stress at a plane whose
normal makes an angle of 40° in the clockwise direction with the x-axis.
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7. A beam is supported and loaded as shown in the figure. obtain the deflection of the free
of the beam. Also obtain the maximum deflection and its location. Express your answers of
deflections in terms of the flexural rigidity, EI, of the beam. presume : EI=Constant.
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Earning:   Approval pending.