Stresses in cylinderical shells

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Information about Stresses in cylinderical shells

Published on August 10, 2009

Author: baher


Slide 1: Hoop and Axial stress in a cylindrical shell Slide 2: Consider the forces acting on the Shell from Pressure From pressure Force = Pressure x Area = PLD F = P x L x D Area = D x L Here is the pressure Slide 3: This is resisted by the internal stress Force = Stress x Area Stress S F = S x L x t x 2 = 2SLt Area = 2 x t x L Stress S Slide 4: For equilibrium - Forces must be Equal From pressure : F = PDL From internal stress: F = 2SLt Equating therefore : PDL = 2SLt This is known as the HOOP STRESS Sh Slide 5: Consider now the Axial or Longitudinal Stress Force = Pressure x Area Pressure Slide 6: Consider now the Axial or Longitudinal Stress Force = Stress x Area This is kown as the Axial or Longitudinal Stress Stress Slide 7: Comparison of Hoop and Longitudinal Stress What is the relationship between SL and Sh ? Sh is twice SL or Sh = 2.SL Slide 8: True Stress - Lame Theorem We have assumed the stress is like this: In reality it is like this: Slide 9: According to the Lame Theorem (Thick Cylinder Theory) S S > Sh (simple theory) Slide 10: We now have three formulae for Hoop Stress Let us now look at the ASME Division 1 Equation We now have two formulae for the hoop stress Slide 11: This is how the three formulae look ---- Lame (Accurate) ---- ASME (Less Accurate) ---- Simple (Very Inaccurate) Slide 12: Simple versus ASME formulae Slide 13: Consider the cylinder - ASME Code This is the formula per UG-27 in the code: P = Pressure psi R = Radius inches S = Design Stress psi E = Welded Joint Efficiency Calculations are done the the CORRODED condition Slide 14: Effect of the Corrosion Allowance All calculations are performed in the CORRODED state Slide 15: Effect of the Corrosion Allowance Equation becomes: Finally:

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