Determine the maximum hoop:
A conical water tank of height 2 metres & base radius 500 mm is supported at top and is full of water. The thickness of the wall is refer to 24 mm, determine the maximum hoop and meridional stress.
Figure
Solution
Apex angle, α= tan - 1 ( 0.5 /2) = 14.036^{o}
Maximum hoop stress occurs at h/2 = 2/2 = 1m from the bottom.
Maximum hoop stress = wh^{2} tan α / 4t cos α
Unit weight of water, w = 9.81 × 10^{- 3} N/mm^{3}
Thickness, t = 29 mm.
∴ Maximum hoop stress =
9.81 × 10^{- 3} × 2000^{2} × tan 14.036^{o} / 4 × 29 × cos 14.036^{o}
= 105.25 N/mm^{2}
Similarly, maximum meridional stress occurs at 3h/4 = 3 × (2/4) = 1.5 m from the bottom.
∴ Maximum meridional stress =(3/16)( wh2 tan α / t cos α )
= (3/16) × (9.81 × 10^{- 3} × 2000^{2} × tan 14.036^{o}/29 × cos 14.036^{o})
= 78.995 N/mm^{2}