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MECHANICAL ENGINEERING DESIGN TUTORIAL 4 –15: PRESSURE VESSEL DESIGN | Mechanical Engineering Design Tutorial 4 -15 Pressure Vessel Design Pressure Vessel Design Models for Cylinders 1. Thick-walled Cylinders 2. Thin-walled Cylinders Thick-wall Theory Thick-wall theory is developed from the Theory of Elasticity which yields the state of stress as a continuous function of radius over the pressure vessel wall. The state of stress is defined relative to a convenient cylindrical coordinate system 1. yt Tangential Stress 2. dr Radial Stress 3. 7l Longitudinal Stress Stresses in a cylindrical pressure vessel depend upon the ratio of the inner radius to the outer radius ro ri rather than the size of the cylinder. Principal Stresses 71 72 73 1. Determined without computation of Mohr s Circle 2. Equivalent to cylindrical stresses o 7r 7l Applicable for any wall thickness-to-radius ratio. Cylinder under Pressure Consider a cylinder with capped ends subjected to an internal pressure p and an external pressure p FIGURE T4-15-1 ro Text Eq. refers to Mechanical Engineering Design 7th edition text by Joseph Edward Shigley Charles R. Mischke and Richard G. Budynas equations and figures with the prefix T refer to the present tutorial. The cylinder geometry is defined by the inside radius r the outside radius ro and the cylinder length l. In general the stresses in the cylindrical pressure vessel ot 7r 7l can be computed at any radial coordinate value r within the wall thickness bounded by r and ro and will be characterized by the ratio of radii Z ro r These cylindrical stresses represent the principal stresses and can be computed directly using Eq. 4-50 and 4-52. Thus we do not need to use Mohr s circle to assess the principal stresses. Tangential Stress t 2 2 2 2 2 Pr - Poro - r ro Po - Pi r r r2 for r r ro Text Eq. 4-50 Radial Stress r 2 2 22 x 2 Piri -Poro r ro Po-Pi Vr ro2 ri2 for r r ro Text Eq. 4-50 Longitudinal Stress Applicable to cases where the cylinder carries the longitudinal load such as capped ends. Only valid far away from end caps .
