Chapter14

Chapter14 - Mechanics Materials 1 Chapter 14 Chapter...

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- FAMU FSU College of Engineering Department of Mechanical Engineering Chapter 14 Chapter 14 Combined Loadings Combined Loadings
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Thin Walled Pressure Vessels Thin Walled Pressure Vessels • Cylindrical or spherical pressure vessels are used in industry as tanks, boilers or containers. • When under pressure the material is subjected to loadings in all directions. • In general thin wall refers to an inner radius to wall thickness ratio r i /t 10, in most cases it is actually > 50. • If the vessels wall is thin, the stress distribution through the thickness can be assumed to be uniform or constant.
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Cylindrical Pressure Vessels Cylindrical Pressure Vessels • Consider tubes with an internal pressure and closed ends σ xx b axial stress due to the pressure on the end walls σ θθ b “Hoop” stress due to the pressure acting on the curved surface. • P is the internal pressure • Look at a FBD of the axial section
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Axial Stress • Consider the axial equilibrium on this structure. • Which gives the equation for Axial Stress: ( 29 2 2 2 * 2 0 r P rt rt r P F xx xx x π σ = + - = = t xx 2 Pr 2 = = Cylindrical Pressure Vessels: Cylindrical Pressure Vessels: Axial Stress Axial Stress
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Look now at a FBD of the circumferential section • Equating the forces vertically gives: • Which simplifies to give the equation for Hoop Stress: Cylindrical Pressure Vessels: Cylindrical Pressure Vessels: Hoop Stress Hoop Stress t pr = = 1 σ θθ rLP Lt Lt L R P F y 2 ) ( 2 2 * 2 * * 0 = + - = =
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Cylindrical Pressure Vessels • Pressure vessels also have stresses created by the weight of the pressurized fluid inside, its own weight, externally applied loads and by an applied torque. • To analyze this, each loading condition is analyzed individually and the stresses are then combined along their respective axes by the superposition method. • Pressure vessel with ALL possible loading conditions:
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This note was uploaded on 12/11/2011 for the course EML 3011 taught by Professor Schwarz during the Spring '09 term at FSU.

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Chapter14 - Mechanics Materials 1 Chapter 14 Chapter...

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