Determine the maximum hoop - conical shells, Mechanical Engineering

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.

1174_Determine the maximum hoop.png

 Figure  

Solution

Apex angle, α= tan - 1 ( 0.5 /2) = 14.036o

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 14.036o / 4 × 29 × cos 14.036o

= 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 14.036o/29 × cos 14.036o)

= 78.995 N/mm2

Posted Date: 1/21/2013 2:13:04 AM | Location : United States







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