EM 319 - Cylindrical Pressure Vessel Example

EM 319 - Cylindrical Pressure Vessel Example - (in plane):...

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A pressurized steel tank is constructed with a helical weld that makes an angle α = 55˚ with the longitudinal axis (see figure). The tank has radius r = 1.8 m, thickness t = 20 mm, and internal pressure p = 800 kPa. The steel has Young’s modulus E = 200 GPa and Poison’s ratio 3 . 0 = ν . I. Stresses Circumferential and Longitudinal stresses: Longitudinal stress: Circumferential stress: (Shear stress: ) The corresponding stress element is shown below. Construct the Mohr’s circle : Read coordinates for point A and B : ) 0 , 36 ( A and ) 0 , 72 ( B , plot them on stress plane. Find the midpoint C , whose coordinate is ). 0 , 54 ( C Use C as center, AC (or BC ) as radius, draw Mohr’s circle. Find radius: Find the stresses perpendicular and parallel , respectively, to the weld line: Rotate = θ 2 from point A on the circle, find point A . = + = = 1 1 1 x y x y x σ = 1 1 y x τ Principal stresses : = = 2 1 p p = = = 2 1 Note: All units are in MPa. Cylindrical pressure vessel α A B A B C S 1 S 2 1 x 1 1 y x R 2
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Maximum shear stresses
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Unformatted text preview: (in plane): = = 2 1 s s = = max II. Strains Circumferential and Longitudinal stresses: Longitudinal strain: ( ) = = c E l l 1 Circumferential strain: ( ) = = l c c E 1 Shear strain: . ) 1 ( 2 + = = = E G G xy xy Find the strains at an angle: . 35 = Method I: Strain transformation (equations or Mohrs circle) . 149 10 149 70 cos 2 306 72 2 306 72 2 sin 2 2 cos 2 2 6 1 = = + + = + + + = xy y x y x x . 229 10 229 6 1 1 = = + = x y x y . 110 10 127 70 sin 2 306 72 2 sin 2 2 6 1 1 = = = = y x y x 220 1 1 = y x . Method II: Hookes law ( ) = = 1 1 1 1 y x x E ( ) = = 1 1 1 1 x y y E = = G y x y x 1 1 1 1...
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This note was uploaded on 09/18/2011 for the course EM 319 taught by Professor Staff during the Spring '11 term at Oklahoma State.

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EM 319 - Cylindrical Pressure Vessel Example - (in plane):...

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