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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) = 14.036o
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
Calculate and draw the Shear force and Bending moment diagrams for the loaded beam and determine the maximum moment M and its location x from left end.
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