In structural steel design, the Torsion Constant, J, represents the ability of the steel beam to resist torsion, i.e. twisting. It’s units are mm^{4} or inches^{4}.
Equation
The bending resistance formula, in which the torsional constant is used, is:
Where:
θ = Angle of Twist
T = Applied Torque (N·m or lb·ft)
L = Length of Beam (mm or in)
J = Torsional Constant (mm^{4} or in^{4})
G = Modulus of Rigidity (GPa or psi)
Values of J for various shapes
Shape  Torsional Constant 



Standard Shapes
Standard structural steel shapes, including the Torsional Constant, J, are found in the AISC Steel Construction Manual, section 1.
Dilip Biswas says
July 10, 2014 at 8:25 amTorsional Constant (J) for an Isection, multiplier 2 is missing from the first term of the numerator. The formula should have been, J = (2bt^3+d’w^3)/3.
Bernie Roseke, P.Eng., PMP says
July 14, 2014 at 7:42 pmThanks Dilip. It has been updated.
masoud says
November 12, 2014 at 2:57 amhi
as i searched the websites i didn’t found any formula ,calculating torsion constant…..how can i calculate is?(without software)
Craig says
July 7, 2015 at 1:38 amhow will the equation differ if we assume the action of a fully welded plate at the top flange?
asad says
December 5, 2015 at 7:25 amHow can you use Length (L) in mm or inch and multiply it with value of Torque which is in Meters ? and with J which is in mm^4 ?
and use Angle without mentioning if it is Degree or Radians ?
Waris Ali Waris says
February 13, 2017 at 4:21 amhow we can calculate torsion constant for a long thin wire of copper?