Stress in Circumferential Direction - Hoop Stress

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Jul 24, 2020, 6:28:07 PM

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Jul 19, 2014, 1:20:12 PM

$theta_c = (( p_i * r_i ^2)-( p_o * r_o ^2))/(( r_o ^2)-( r_i ^2))-(( r_i ^2)*( r_o ^2)*( p_o - p_i ))/(( r ^2)*( r_o ^2- r_i ^2))$

$"internal pressure in the tube or cylinder (MPa, psi)"$

$"internal radius of tube or cylinder (mm, in)"$

$"external pressure in the tube or cylinder (MPa, psi)"$

$"external radius of tube or cylinder (mm, in)"$

$"radius to point in tube or cylinder wall (mm, in)"$

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The stress in circumferential direction - hoop stress - at a point in the tube or cylinder wall can be expressed as:

σc = [(pi ri2 - po ro2) / (ro2 - ri2)] - [ri2 ro2 (po - pi) / (r2 (ro2 - ri2))]

where

σc = stress in circumferential direction (MPa, psi)
r = radius to point in tube or cylinder wall (mm, in) (ri < r < ro) maximum stress when r = ri (inside pipe or cylinder)
pi = internal pressure in the tube or cylinder (MPa, psi)
ri = internal radius of tube or cylinder (mm, in)
po = external pressure in the tube or cylinder (MPa, psi)
ro=external radius of tube or cylinder (mm, in)

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