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Cylinder under external load

I am currently having trouble designing a reel winder in work, picture included below to help with the explanation.

 

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If you can imagine the wire coming off the bottom of the barrel and attached to a pipeline thus, putting the wire in tension. The tension in the wire creates a compressive stress in the barrel (hoop stress).

 

From here I have used to Hoop stress (also known as the circumferential stress) to find the external pressure using Lame’s equation, which is shown in the attached *.pdf.

 

From the solve block the external pressure seems acceptable, but the resultant tangential stress seems excessive.

 

Can anyone confirm if my Maths or logic is correct? I have been told that this could be calculated using the principle stress theory or a method out of Roarks, any ideas?

 

Mike


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