# Stresses

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Science-Technology

Published on November 6, 2008

Author: aSGuest2692

Source: authorstream.com

Stresses in Pressurized Cylinders : Stresses in Pressurized Cylinders Cylindrical pressure vessels, hydraulic cylinders, shafts with components mounted on (gears, pulleys, and bearings), gun barrels, pipes carrying fluids at high pressure,….. develop tangential, longitudinal, and radial stresses. Wall thickness t Stresses in a Thin-Walled Pressurized Cylinders : Stresses in a Thin-Walled Pressurized Cylinders In a thin-walled pressurized cylinder the radial stress is much smaller than the tangential stress and can be neglected. (l) /4 [ (do)2 – (di)2] = ( p ) /4 (di)2 Internal pressure, p (l) [ (di + 2t)2 – (di)2] = ( p ) (di)2 4t2 is very small, (l) (4di t) = ( p ) (di)2 Stresses in a Thin-Walled Pressurized Cylinders : Stresses in a Thin-Walled Pressurized Cylinders Tangential (hoop) stress Stresses in a Thick-Walled Pressurized Cylinders : Stresses in a Thick-Walled Pressurized Cylinders In case of thick-walled pressurized cylinders, the radial stress, r , cannot be neglected. Assumption – longitudinal elongation is constant around the plane of cross section, there is very little warping of the cross section, εl = constant 2(θ)(dr)(l) + r (2rl) – (r + dr) [2(r + dr)l] = 0 (dr) (dr) is very small compared to other terms ≈ 0 Stresses in a Thick-Walled Pressurized Cylinders : Stresses in a Thick-Walled Pressurized Cylinders Deformation in the longitudinal direction Stresses in a Thick-Walled Pressurized Cylinders : Stresses in a Thick-Walled Pressurized Cylinders Boundary conditions r = - pi at r = ri Stresses in a Thick-Walled Pressurized Cylinders : Stresses in a Thick-Walled Pressurized Cylinders Special case, po (external pressure) = 0 Press and Shrink Fits : Press and Shrink Fits ds (shaft) > dh (hub) Inner member Outer member p (contact pressure) = pressure at the outer surface of the inner member or pressure at the inner surface of the outer member. Press and Shrink Fits : Press and Shrink Fits Consider the outer member at the interface po = 0 pi = p o = increase in the inner radius of the outer member i = decrease in the outer radius of the inner member Press and Shrink Fits : Press and Shrink Fits Tangential strain at the outer radius of the inner member εit = i R – Radial interference,  = o – i

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