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INPUT   DATA

♥ EXAMPLE Of Input/Output

Title

Mean Radius, r		m
Thickness, t		m
Modulus of elasticity, E		109N/m2
Poisson's ratio, υ
Internal pressure, p		106N/m2

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OUTPUT   VARIABLES   &   GRAPHS

SPHERE	Values	Units
♦ Stress, σsph		N/m2
♦ Increase in radius, Δr		m
♦ Increase in volume, ΔV		m3

CYLINDER	Values	Units
♦ Axial Stress, σaxial		N/m2
♦ Hoop Stress, σhoop		N/m2
♦ Increase in radius, Δr		m
♦ Volume increase per length, ΔV/L		m3/m

Pressure Loading of Thin-walled Vessels

A thin-walled vessel (such as a hollow cylinder or sphere) is one where the thickness of the wall is no greater than one-tenth of the radius. Consider such a vessel subjected to an internal pressure above atmospheric pressure. The resulting stresses and expansion of the vessels are described by the following equations:

where
     σ_sphere = stress at any point in the wall of the sphere
     σ_hoop = circumferential stress within the material of the cylinder
     σ_axial = logitudinal stress within the material of the cylinder
     p = uniform internal pressure
     r = radius
     t = wall thickness
     E = modulus of elasticity of the material
     υ = Poisson's ratio of the material
     Δr = increase in radius due to p
     ΔV = increase in volume of sphere
     ΔV/L = increase in volume per unit length of cylinder

Tips

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

BIBLIOGRAPHY

• 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.
• Nash WA; Theory and Problems of Statics and Mechanics of Materials; Schaum's Outline Series, McGraw Hill, New York, 1992, Chapter 10.
• Brown TH; Marks' Calculations for Machine Design; McGraw Hill, New York, 2005, Chapter 2.
• Hicks TG; Mechanical Engineering Formulas, Pocket Guide; McGraw Hill, New York, 2003, Section 3.