Torque

By ‘torque’ we mean here what would be measured if we broke the beam and then reconnected it via an inserted a hinge like joint connecting the two parts of the beam. The torque at that point would be the tendency for the hinge to turn.

In n dimensions the forces, or momentum flux, across a point in a beam is composed of a vector force, and a skew-symmetric tensor torque. (In 2D the torque is an axial scalar.) The flux of linear momentum is a vector which does not vary from point to point along the beam. The tensor torque T^ij is the flux of angular momentum and does vary from point to point. It can always be given in the form T^ij = T₀^ij + xⁱf^j − x^jfⁱ where {xⁱ} are the coordinates of the point along the beam and {fⁱ} is some vector force.