Determine the normal stress in a ball, which has an outside diameter of 160 mm and a wall thickness of 3.8 mm, when the ball is inflated to a gage pressure of 78 kPa.

The normal stress is 0.7821 MPa

Explanation:

The external diameter D = 160 mm

The thickness t = 3.8 mm = 3.8 x 10^-3 m

gauge pressure P = 78 kPa = 78 x 10^3 Pa

The maximum shear stress τmax = ?

The external radius of the shell from the external surface R = D/2 = 160/2 = 80 mm

The internal radius of the shell r = R - t

==> 80 - 3.8 = 76.2 mm

Therefore the internal diameter d = 2r = 2 x 76.2 = 152.4 mm

==> d = 152.4 x 10^-3 m

The normal stress σ = = = 782052.63 Pa

==>  σ = 0.7821 MPa

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