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Unit VI
Q.1. The principal stresses at a point across two perpendicular planes are 80 N/mm2 (tensile)
and 40 N/mm2 (tensile). Find normal, tangential stresses and the resultant stress and the
obliquity on a plane at 20o with the major principal plane.
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Q.2. A bar of cross-section 850 mm2 is acted upon by axial tensile forces of 60 kN applied at
each end of the bar. Determine the normal and shearing stresses on a plane inclined at 30 o to
the direction of loading. Also find maximum shearing stress
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Q.3. At a point in a strained material the normal stresses acting are +50 MPa and -30 MPa at
a plane right angle to each other, with a shear stress of 20 MPa. Determine :
i) Principal stresses and their nature.
ii) Normal and tangential stress on a plane inclined at an angle of 25o with the plane of
50 MPa.
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Q.4. A short metallic column of 500 mm2 cross sectional area carriers an axial compressive
load of 100 kN. for a plane inclined at 60o. with the direction of load, calculate :
1) Normal stress 2) Tangential stress 3) Resultant stress 4) Maximum shear stress
5) Obliquity of the resultant stress
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Q.5. An element in a stresses material has tensile stress of 500 MN/m 2 and a compressive
stress of 350 MN/m2 acting on two mutually perpendicular planes and equal shear stresses of
100 MN/m2 on these planes. Find principal stresses and position of principal planes, also find
shearing stresses.
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Q 6. Draw Mohr’s circle for principal stresses of 80N/mm2 tensile and 50 N/mm2 compressive
and find the resultant stresses on the plane making 22o and 64o with major principal plane.
Find also the normal and tangential stresses on these planes
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Q 7. The principal stress at a point across two perpendicular plane are 80Mpa (tensile) and
40Mpa (compressive) . Find the normal,tangential and resultant stress on a plane inclined at
200 to the axis of major principal plane.(using Mohr’s Circle Method)
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Q 8. At a point in a bracket the normal stresses on two mutually perpendicular planes are of
120 N/mm2 tensile and 60 N/mm2 tensile. The shear stress across these planes 30 N/mm2.
Find using the Mohr’s stress circle, the principal stresses and maximum shear stress at the
point.
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Q. 9. A bolt is subjected to an axial pull of 8kN and a transverse shear force of 3KN.
Determine the diameter of the bolt required based on:
1) Maximum principal stress theory
2) Maximum shear stress theory
3) Maximum strain energy theory
Take elastic limit in simple tension is equal to 270 MPa and Poisson’s ratio = 0.36. Assume
FOS= 3
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Q 10. A square pin is required to resist a pull of 40 kN and shear force at 15 kN. Derive a
suitable section according to strain energy theory. Maximum tensile stress is 350 MPa and
Poisson’s ratio is 0.3. Take FOS = 2.5.
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Q 11. A cylindrical shell of mild steel plate and 1.2 m in diameter is to be subjected to an
internal pressure of 1.5 MN/m2. If the material yields at 200 MN/m2, calculate the thickness of
the plate on the basis of the following three theories, assuming a factor of safety 3 in each
case:
1) Maximum principal stress theory
2) Maximum shear stress theory
3) Maximum shear strain theory
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Q 12. Taking principal stresses in a steam boiler as P, P/2 and 0. Poisson’s ration as 0.25 and
the equivalent stress in a simple tension test as f. Find p in accordance with theories.
1) Maximum principal stress theory
2) Maximum Principal strain theory
3) Maximum shear stress theory
4) Maximum strain energy theory
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Q 13. In a metallic body the principal stresses are +35 MN/mm2 and -95 MN/mm2, the third
principal stress being zero. The elastic limit stress in simple tension as well as in simple
compression is equal and is 220 MN/mm2. Find the factor of safety based on the elastic limit if
the criterion for failure is the maximum principal stress theory.
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Q 14. A hollow mild steel shaft having 100 mm external diameter and 50 mm internal
diameter is subjected to a twisting moment of 8 kNm and a bending moment of 2.5 kNm.
Calculate principal stresses and find direct stress which, acting alone, would produce the
same.
1) Maximum elastic strain energy
2) Maximum elastic shear strain energy, as that produced by the principal stresses
together.
Assume Poisson’s ratio = 0.35
.
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Q 15. The mild steel shaft 120 mm diameter is subjected to a maximum torque of 20 kNm and
a maximum bending moment of 12 kNm at a particular section. Find the factor of safety
according to the maximum shear stress theory if the elastic limit in simple tension is 220
MN/mm2
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Q 16. A shaft is subjected to a maximum torque of 10 kNm and a maximum bending moment
of 7.5 kNm at a particular section. If the allowable equivalent stress in simple tension is 160
find the diameter of the shaft according to the strain energy theory. Take Poisson’s ratio =
0.24
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Q 17. In a material the principal stresses are 60 N/mm2 , 48 N/mm2and -36 N/mm2.
Calculate:- i) Total strain energy
ii) Volumetric strain energy
iii) Shear strain energy
iv) Factor of safety on the total strain energy criterion if the material yields at
120 N/mm2
Take E = 200 GN/mm2 and 1/m= 0.3
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Q 18. A bolt is under an axial thrust of 9.6 kN together with a transverse force of 4.8 kN.
Calculate its diameter according to:
i)
Maximum principal stress theory
ii)
Maximum shear stress theory
Factor of safety = 3, yield strength of material of bolt = 270 120 N/mm2 and
Poisson’s ratio = 0.3
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Q 19. A cylindrical shell made of mild steel plate and 1.2 mm in diameter is to be subjected to
an internal pressure of 1.5 MN/mm2. If the material yields at 200 MN/mm2 , calculate the
thickness of the plate o the basis of the following three theories, assuming factor of safety 3 in
each case:
i)
Maximum principal stress theory
ii)
Maximum shear stress theory
iii)
Maximum shear strain energy theory
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Q 20. In a metallic body the principal stresses are + 35 MN/mm 2 and -95 MN/mm2,the third
principal stress being zero. The elastic limit stress in simple tension as well as in simple
compression is equal and is 220 MN/mm2. Find the factor of safety based on the elastic limit if
the criterion for failure for the material is the maximum principal stress theory.
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Q 21. In a cast iron body the principal stresses are + 40 MN/mm2 and – 100 MN/mm2 the third
principal stress being zero. The elastic limit stresses in simple tension and in simple
compression are 80 MN/mm2 and 400 MN/mm2. Find the factor of safety based on the elastic
limit if criterion of failure is the maximum principal stress theory.
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Q 22. The maximum allowable shear stress in a hollow shaft of external diameter equal to
twice the internal diameter, is 80 N/mm2 Determine the diameter of the shaft if it is subjected
to a torque of 4×106 N-mm and bending moment of 3×106 N-mm.
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Q 23. A solid shaft of diameter 80 mm is subjected to a twisting moment of 8 MN-mm and a
bending moment of 5MN-mm at a point. Determine principal stresses and position of the
plane on which they act.
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Q 24. The tank has an inner radius of 600 mm and a thickness of 12 mm. It is filled to the top
with water having a specific weight of 10 kN/m3. If it is made of steel having a specific weight
of 78 kN/m3, determine the state of stress at point A present on outer surface at distance of 1
m from the top surface . The tank is open at the top.
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Q 25. A shaft section 80 mm in diameter is subjected to a bending moment of 3 kNm and
torque of 8 kNm. Find the maximum normal stresses induced on section and locate the plane
on which it acts. Find also what stress acting alone can produce the same maximum strain.
Take poisson’s ratio = 0.3
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Q 26. A solid shaft of 100 mm diameter transmits 500 kW at 500 rpm and is also subjected to
an axial thrust of 200 kN. If the maximum principal stress is not to exceed 100 MPa, find what
additional bending moment may safely be carried?
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Q 27 A flywheel weighing 4 kN is mounted on a shaft 50 mm diameter, 600 mm long. Shaft is
free to rotate at ends and flywheel is mounted on centre of shaft. If shaft is transmitting 44 kW
at 300 rpm, calculate the principal stress and maximum shear stress in the shaft at the ends
of the horizontal and vertical diameter of cross section close to that of flywheel
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Q 28. A pawl (see figure) is loaded by a force of 320 kg. The diameter of the circular portion at
section DEFC is 50 mm. Determine principal stresses at point D, F and also at intersecting
point of vertical DE and horizontal FC.
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Q 29. At a point in a strained material, the principal stresses are 200 N/mm2 (T) and 60 N/mm2
(C) Determine the direction and magnitude in a plane inclined at 600 to the axis of major
principal stress. What is the maximum intensity of shear stress in the material at the point
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Q 30. A plane element is subjected to stresses as shown in fig. Determine principal stresses
maximum shear stress and their planes. Sketch the planes determined.
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Q 31. A point in a strained material is subjected to tensile stress of 60N/mm2 along horizontal
direction and compressive stress of 40N/mm2 along vertical direction. Draw a Mohr’s circle for
the stress system
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Q 32. A point in a strained material is subjected to tensile stress of 60 N/mm2 along horizontal
direction and compressive stress of 40N/mm2 along vertical direction and shear stress 40
N/mm2 . Draw a Mohr’s circle for the stress system.
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Q 33. A solid circular shaft 120 mm diameter is subjected to a torque of 2000 Nm and a
bending moment of 8000 Nm. Calculate the maximum direct and shear stress and the angle
of the principal plane.
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Q 34. A propeller shaft has a bending stress of 7MPa on the surface.
Torsion produces a shear stress of 5 MPa on same point of the surface.The propeller pushes
and puts a compressive stress of 2 MPa in the shaft.Determine the following.
i) The principal stresses on the surface.
ii) The position of the principal plane.
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Q 35. For a given loading conditions the state of stress in the wall of a cylinder is expressed
as follows:
(a) 85 MN/m2 tensile
(b) 25 MN/m2 tensile at right angles to (a)
(c) Shear stresses of 60 MN/m2 on the planes on which the stresses (a) and (b) act; the
sheer couple acting on planes carrying the 25 MN/m2 stress is clockwise in effect.
Calculate the principal stresses and the planes on which they act. What would be the effect on
these results if owing to a change of loading (a) becomes compressive while stresses (b) and
(c) remain unchanged
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Q 36. A solid shaft of 150 mm diameter transmits 1800kw at 600 rpm and is also subjected to
an axial thrust of 250 kN. If the principal stress is not to exceed 80 N/mm2 find what additional
bending moment may be safely carried? what will be the direction of the maximum principal
stress?
.
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Q. 37 A generator shaft of hollow circular cross section with outside diameter 200 mm and
inside diameter 160 mm is subjected to a torque of 11.1 kNm and axial compressive load of
362 kN. Determine the maximum tensile stress, maximum compressive stress and maximum
shear stress in the shaft
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Q. 38 A simply supported beam of rectangular section is 200 mm wide and 300 mm deep. It
supports uniformly distributed load of 6 KN/m over span of 4 m. Calculate the magnitude and
direction of the principal stresses at a point located 0.5 m from left support and 50 mm above
the neutral axis.
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Q. 39 A torsional pendulum consists of a horizontal disc of mass 100 kg suspended by 4 mm
dia. 2 m long vertical steel wire. Find the maximum angle of rotation so that tensile stress in
the wire does not exceed 100 N/mm2 and maximum shear stress does not exceed 50 N/mm2.
Take C=8 x104 N/mm2.
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Q. 40 At a point in a material under stress, the intensity of the resultant stresses on certain
plane is 50 N/mm2(tensile), inclined at 30 degrees to the normal of that plane. The stress on
the plane right angle to it has a normal tensile component of 30 N/mm2. Find
1. Resultant stress on second plane.
2. Principal plane and stresses.
3. Plane of maximum shear stress and its intensity.