What is the Torsion Constant?

December 5, 2013 by Bernie Roseke, P.Eng., PMP 6 Comments

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 mm⁴ or inches⁴.

Equation

The bending resistance formula, in which the torsional constant is used, is:

$\theta = \frac{T\cdot L}{G\cdot J}$
Where:
θ = Angle of Twist
T = Applied Torque (N·m or lb·ft)
L = Length of Beam (mm or in)
J = Torsional Constant (mm⁴ or in⁴)
G = Modulus of Rigidity (GPa or psi)

Values of J for various shapes

Shape	Torsional Constant
	$J = \frac{1}{2}\pi r^4$
	$J = \frac{\pi a^3\cdot b^3}{a^2 + b^2}$
	$J = 2.25a^4$
	$J = \frac{2bt^3 + d$ $d$
	$J = \frac{2b$ $b$ $d$
	$J = \frac{(b$ $b$ $d$
	$J = \frac{bt^3 + d$ $d$
	$J = \frac{b_1 t_1^3 + b_2 t_2^3 + d$ $d$

Standard Shapes

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

About Bernie Roseke, P.Eng., PMP

Bernie Roseke, P.Eng., PMP, is the president of Roseke Engineering. As a bridge engineer and project manager, he manages projects ranging from small, local bridges to multi-million dollar projects. He is also the technical brains behind ProjectEngineer, the online project management system for engineers. He is a licensed professional engineer, certified project manager, and six sigma black belt. He lives in Lethbridge, Alberta, Canada, with his wife and two kids.

Comments

Dilip Biswas says
July 10, 2014 at 8:25 am

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.

Reply
- Bernie Roseke, P.Eng., PMP says
  July 14, 2014 at 7:42 pm
  
  Thanks Dilip. It has been updated.
  
  Reply
masoud says
November 12, 2014 at 2:57 am

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

Reply
Craig says
July 7, 2015 at 1:38 am

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

Reply
asad says
December 5, 2015 at 7:25 am

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 ?

Reply
Waris Ali Waris says
February 13, 2017 at 4:21 am

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

Reply