Radial Displacement Thin-wall Section (Internal and External Pressure)

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Tags: Hoop Stress       

 

pv radial displacement 2

Radial Displacement Thin-wall Section (Internal and External Pressure) Formula

\(\large{ \Delta_r = \frac{ 1 \;-\; \mu }{ \lambda } \;      \frac{ \left( p_i \;r_i^2 \;-\; p_e \;r_e^2 \right) \; r }{ r_e^2 \;-\; r_i^2 }        \;+\;                        \frac{ 1 \;+\; \mu }{ \lambda } \;     \frac{ \left( p_i \;-\; p_e \right) \; r_e^2 \; r_i^2 }{  \left( r_e^2 \;-\; r_i^2 \right) \; r }  }\) 
Symbol English Metric
\(\large{ \Delta_r }\) = radius change \(\large{ in }\) \(\large{ mm }\)
\(\large{ \lambda }\)  (Greek symbol lambda) = elastic modulus \(\large{\frac{lbf}{in^2}}\) \(\large{Pa}\)
\(\large{ \mu }\)  (Greek symbol mu) = Poisson's Ratio \(\large{ dimensionless }\)
\(\large{ p_e }\) = external pressure \(\large{\frac{lbf}{in^2}}\) \(\large{Pa}\)
\(\large{ p_i }\) = internal pressure \(\large{\frac{lbf}{in^2}}\) \(\large{Pa}\)
\(\large{ p }\) = pressure under consideration \(\large{\frac{lbf}{in^2}}\) \(\large{Pa}\)
\(\large{ r }\) = radius to point of intrest \(\large{ in }\) \(\large{ mm }\)
\(\large{ r_e }\) = external radius \(\large{ in }\) \(\large{ mm }\)
\(\large{ r_i }\) = internal radius \(\large{ in }\) \(\large{ mm }\)

 

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Tags: Hoop Stress