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INPUT   DATA

♥ EXAMPLE Of Input/Output

Title

Inside Radius, ri		m
Outside Radius, ro		m
Modulus of elasticity, E		109N/m2
Poisson's ratio, υ
Internal pressure, pi		106N/m2
External pressure, po		106N/m2

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OUTPUT   VARIABLES   &   GRAPHS

CYLINDER	Values	Units	Graphs:  Stresses Vs Radial Distance
♦  Max Radial Stress, σr		N/m2
♦  Max Hoop Stress, σh		N/m2
♦  Axial Stress, σa		N/m2
♦  Increase in inner radius, Δri		10-6m
♦  Increase in outer radius, Δro		10-6m
♦  Increase in axial length per length, ΔL/L		10-6m/m

Pressure Loading of Thick-walled Cylinderical Tube

A thick-walled cylinder or tube is one where the thickness of the wall is greater than one-tenth of the radius. Consider such a vessel subjected to an internal pressure above atmospheric pressure, and an external pressure associated with the outside radius. The resulting stresses and expansion of the cylinder are described by the following equations:

where
     σ_h = circumferential stress variation within the material of the cylinder
     σ_r = stress variation in the radial direction
     σ_a = logitudinal stress within the material of the cylinder
     p_i = uniform internal pressure
     p_o = uniform external pressure
     r_i = inside radius
     r_o = ouside radius
     E = modulus of elasticity of the material
     υ = Poisson's ratio of the material
     u_r = displacement in the radial direction due to pressurization
     du_a/da = relative increase in length in the axial direction

Tips

    ◊ Use link EXAMPLE Of Input/Output  to demo data entry expectations and results; you may edit & use it as starting point

BIBLIOGRAPHY

• Brown TH; Marks' Calculations for Machine Design; McGraw Hill, New York, 2005, Chapter 3.
• Moulton A, Grosjean J & Owen G; The Moulton Formulae and Methods - directly usable for calculations in mechanical engineering; Professional Engineering Publishing Ltd, London, UK, 2005.
• Hicks TG; Mechanical Engineering Formulas, Pocket Guide; McGraw Hill, New York, 2003, Section 2.
• Exact solution for thick wall pressure vessel; in www.iastate.edu/~e_m.424/thick wall cylinder.pdf , Iowa state University, Ames, Iowa.