Determine the maximum pressure applied inside the shell, Mechanical Engineering

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Determine the maximum pressure applied inside the shell:

A thin spherical shell of 1.5 m diameter is built by joining steel plates of 8 mm thickness by riveting. The efficiency of joint is given to be 75%. Determine the maximum pressure that may be applied inside the shell. Take permissible tensile stress as 140 N/mm2.

The efficiency of the joints influences the stresses induced. For a seamless shell, that means a shell having not joints, efficiency is 100%. For decreased efficiency, stresses are enhanced. Therefore, if η is the efficiency of the joints in the shell, then the hoop stress is provided by σh  = pd/4t η

Solution

In this example, this is given

Diameter, d = 1.5 m = 1500 mm.

Thickness, t = 8 mm.

Permissible hoop stress = 140 N/mm2.

Efficiency = 75% = 0.75.

 Therefore, we have

140 = p × 1500 / 4 × 8 × 0.75

∴ p = 2.24 N/mm2


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