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:

$latex \theta = \frac{T\cdot L}{G\cdot J}&s=2$

*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

## Standard Shapes

Standard structural steel shapes, including the Torsional Constant, J, are found in the AISC Steel Construction Manual, section 1.

Dilip Biswas says

Torsional Constant (J) for an I-section, 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 says

Thanks Dilip. It has been updated.

masoud says

hi

as i searched the websites i didn’t found any formula ,calculating torsion constant…..how can i calculate is?(without software)

Craig says

how will the equation differ if we assume the action of a fully welded plate at the top flange?

asad says

How 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

how we can calculate torsion constant for a long thin wire of copper?