Determine the radial and circumferential stresses, Mechanical Engineering

Determine the radial and circumferential stresses:

The internal & external diameters of a thick hollow cylinder are 80 mm & 120 mm respectively. This is subjected to an external pressure of 40 N/mm2 and an internal pressure of 120 N/mm2. Determine the circumferential stress at the external & internal surfaces and determine the radial & circumferential stresses at the mean radius.

Solution

We know that

σr  =  b /r2 - a r

Thus, at r = 40, σr = 120 N/mm2, and at r = 60, σr = 40 N/mm2. Putting these values, we obtain

120 = (b/402) - a

And 40 =   (b /602) - a

On solving out , we get a = 25 and b = 230400. Circumferential stress is provided by,

σh  = b/r 2  + a

Therefore, at r = 40, σ h  = (230400/402) + 24 = 168 N/mm2

at r = 60,  σ  = (230400 /602 )+ 24 = 88 N/mm2

At the mean radius, i.e. (40 + 60)/2  = 50 mm .

Radial stress = (230400/502 ) - 24 = 68.16 N/mm2 , and

Circumferential stress = (230400/502) + 24 = 116.16 N/mm2 .

Posted Date: 1/21/2013 2:25:28 AM | Location : United States







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