The maximum fictitious shear stress calculated by the torsion formula by using the experimentally found maximum torque (ultimate torque) required to rupture a shaft.

If, τ_{r} = Modulus of rupture in torsion (Also called computed ultimate twisting strength)

T_{u} = Ultimate torque at failure

R = Outer radius of the shaft

Then, T_{u}/J = τ_{r} /R

The above expression for Ä_{r} gives fictitious value of shear stress at the ultimate torque because the torsion formula T/J = τ/R is not applicable beyond the limit of proportionality.

The actual shear stress at the ultimate torque is quite different from the shearing modulus of rupture because the shear stress does not vary linearly from zero to maximum but it is uniformly distributed at the ultimate torque.