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GATE 2019: Strength of Material Quiz 7

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Question 1

A steel hub of 100 mm internal diameter and uniform thickness of 10 mm was heated to a temperature of 300 °C to shrink-fit it on a shaft. On cooling, a crack developed parallel to the direction of the length of the hub. Consider the following factors in this regard:
1) Tensile hoop stress
2) Tensile radial stress
3) Compressive hoop stress
4) Compressive radial stress
The cause of failure is attributable to

Question 2

Calculate the required wall thickness of the cylinder, considering a factor of safety of 6 for a pressure vessel consists of a cylinder of 1 metre inside diameter and is closed by hemispherical ends. The pressure intensity of the fluid inside the vessel is not to exceed 2.5 N/mm2. The material of the vessel is steel, whose ultimate strength in tension is 432 MPa. Neglect localised effects at the junction of the cylinder and the hemisphere.

Question 3

A water mains 140 cm inner diameter contains water at a pressure head of 200 m. The minimum thickness of the metal shell required for the water mains, given that maximum permissible stress in the metal is 400 kg/cm2, will be ___ mm.

Question 4

A thin cylindrical pressure vessel is subjected to an internal pressure of 3 MPa having diameter and thickness of the cylinder vessel is 600mm and 12 mm respectively. Find the percentage change in volume of the cylinder under given condition if modulus of elasticity is E=200 GPa and poisson's ratio is 0.21.

Question 5

A thin cylinder of internal dameter 60 mm and will thickness 2mm is subjected to an internal pressure of 1.25 N/mm2. The cylinder is also subjected to a torque of 60 Nm, the axis of the torque coinciding with that of the cylinder . The minor principal stress is MPa.

Question 6

The shell of a boiler is 2 m in diameter and the plates are 2 cm thick. By how much % the working pressure will be reduced if the efficiency of the joint is 80% as compared to 100% efficiency
[Assume safe working stress for the shell plates as 70 MPa]
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