Torsion (Circle Section)

Written by Jerry Ratzlaff on . Posted in Classical Mechanics

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Torsion, abbreviated as T, is the stress of twisting of an object due to applied torque.

 

 

 

 

 

torsion constant circle 1Torsion (Circle section) FORMULA

\(\large{ T = \frac{ J \; \tau }{ \rho } }\)  
\(\large{ \tau = \frac{ T \; \rho }{ J } }\)  
\(\large{ k = \frac{ G \; J }{ l } }\)  
\(\large{ \mu = \frac{ T^2 \; l }{ 2 \; G \; J } }\)  
\(\large{ f = \frac{ l }{ G \; J } }\)  
\(\large{ \theta = \frac{ T \; l }{ G \; J } }\)  

Where:

\(\large{ T }\) = applied torque or moment of torsion

\(\large{ \theta }\)  (Greek symbol theta) = angle

\(\large{ \rho }\)  (Greek symbol rho) = distance between the rotational axis and the farthest point in the section

\(\large{ l }\) = length

\(\large{ \tau }\) (Greek symbol tau) = maximum shear stress at the outer surface

\(\large{ G }\) = shear modulus

\(\large{ \mu }\)  (Greek symbol mu) = strain energy

\(\large{ J }\) = torsion constant (polar momentum of inertia)

\(\large{ f }\) = torsional flexibility

\(\large{ k }\) = torsional stiffness

 

Tags: Equations for Strain and Stress Equations for Structural Steel