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 = wh²  tan α / 4t cos α

 Unit weight of water, w = 9.81 × 10^{- 3}  N/mm³

Thickness, t = 29 mm.

∴ Maximum hoop stress =

9.81 × 10^{- 3} × 2000² × tan 14.036^o / 4 × 29 × cos 14.036^o

= 105.25 N/mm²

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} × 2000² × tan 14.036^o/29 × cos 14.036^o)

= 78.995 N/mm²