Torsion Constant for Ellipse Cross-section

on . Posted in Classical Mechanics

   

torsion constant ellipse 1

Torsion Constant for Ellipse Cross-section formula

\(\large{ J = \frac{ \pi\;a^3\;b^3 }{ a^2\;+\;b^2 }   }\)     (Torsion Constant for Ellipse Cross-section)

\(\large{ a = \sqrt{   \frac{ J \; b^2 }{ \pi \; b^3 \;-\; J }   }   }\)

\(\large{ b = \sqrt{   \frac{ J \; b^2 }{ \pi \; a^3 \;-\; J \; a }   }   }\)

Symbol English Metric
\(\large{ J }\)  (Greek symbol alpha) = torsion constant \(\large{in^4}\) \(\large{mm^4}\)
\(\large{ \pi }\) = Pi \(\large{3.141 592 653 ...}\)
\(\large{ a }\) = semi-major axis of an ellipse \(\large{in}\) \(\large{mm}\)
\(\large{ b }\) = semi-minor axis of an ellipse \(\large{in}\) \(\large{mm}\)

 

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Tags: Strain and Stress Torsion