# Pure torque position

I understand that a pure torque does not have a point of application. Also, I can replace a pure torque with a force couple in opposite directions like a lug wrench. However, force couple position effects the stress distribution on the body that the torque is being applied to. How is it possible?

Normally one first studies rotational motion in the context of rigid bodies, which by definition have no internal stresses. The only possible motions of a (free) rigid body are (a) translation of the center of mass and (b) rotation about the center of mass. In that context, the angular acceleration is determined by the moment of inertia and the net torque, regardless of how the forces that produce the net torque are applied.

For more a realistic treatment, you can take into account the internal stresses in a body. Then, there are more possible motions, such as deforming the body. Then the distribution of forces on the surface of an object generally does matter; if you have a bowl of jello, applying a torque to the the bowl itself will lead to a different outcome than applying a torque directly to the jello.

In other words, your statement "I can replace a pure torque with a force couple in opposite directions like a lug wrench" is true of rigid bodies, for which there are no internal stresses, but not true in general. In particular you cannot use a rigid body approximation to address your question about the stress distribution within the body.

• If i apply off-center torque on a rigid body by using a lug-wrench, will it rotate around the rigid bodies center of mass? Commented Jan 5, 2023 at 15:58
• I'm not sure what an "off-center torque" means. But, if the net force on the object is zero, and if there are no pivot points holding the object in place, then the only motion it will undergo is rotation about the center of mass. Commented Jan 5, 2023 at 16:13

A pure torque or moment (force couple) is considered a free moment vector, but only with respect to equilibrium requirements and the motion of a rigid body, and therefore can be located at any point on a rigid body without effecting those requirements. But it cannot be located at any point with respect to determining the location of the bending stresses and deformations of a deformable body.

For example, consider the simply supported beam below which is subjected only to force couple (pure moment or torque) $$M_C$$. In terms of determining the reactions at A and B, the location of the couple is irrelevant as the reactions are based only on the sum of the vertical forces. In this case, the reactions are equal in magnitude but opposite in direction. The couple causes the beam to pull up at A (thus the reaction is opposite the direction shown) and bear down at B. The magnitude of the reactions is determined by the magnitude of the couple and the length of the beam.

The shear $$V$$ and moment $$M$$ diagrams below show that the shear force between supports is constant and independent of the location of the couple, but the moment (and thus bending stress) is not, with the maximum bending stress (and associated deformation) occurring at the location of the couple.

Hope this helps.

• How do you apply Mc? let's say with a screwdriver (or a double force). applying torque with a screw driver in the center bends the beam in a different way than putting it on B. Commented Jan 5, 2023 at 19:56
• Check here please: physics.stackexchange.com/questions/744044/… Commented Jan 5, 2023 at 20:08
• See my answer to you linked post. Commented Jan 5, 2023 at 20:34