Chapter14

# Chapter14 - Mechanics Materials 1 Chapter 14 Chapter...

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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.
Cylindrical Pressure Vessels Cylindrical Pressure Vessels Consider tubes with an internal pressure and closed ends σ xx barb2right axial stress due to the pressure on the end walls σ θθ barb2right “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 π σ σ π π = + - = = t xx 2 Pr 2 = = σ σ Cylindrical Pressure Vessels: Cylindrical Pressure Vessels: Axial Stress Axial Stress
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 σ θθ rLP Lt Lt L R P F y 2 ) ( 2 2 * 2 * * 0 = + - = = θθ θθ σ σ

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Cylindrical Pressure Vessels 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.
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