The shear stress, shear, shear or shear is the internal or resulting stress of stresses parallel to the cross section of a mechanical prism such as a beam or a column. It is variously designated as T, V or Q.

This type of stress formed by parallel stresses is directly associated with shear stress. For a prismatic piece it is related to the shear stress through the relationship:.

For a straight beam for which the Euler-Bernoulli theory is valid, there is the following relationship between the components of the shear stress and the bending moment:

The notion of shear stress should not be confused with that of shear stress. The components of the shear stress can be obtained as the resultants of the shear stresses. Given the force resulting from the stresses on a cross section of a prismatic piece, the shear stress is the component of said force that is parallel to a cross section of the prismatic piece:.

where:.

Obviously given that:.

It turns out that equation () is equivalent to ().

The shear stress diagram of a prismatic piece is a function that represents the distribution of shear stresses along its barycentric axis. For a prismatic piece whose barycentric axis is a straight segment, the shear forces are given by:.

Where the sum over i extends to k given by the condition, being the point of application of the strut force. The previous function will be continuous if and only if there are no point forces, since in that case the sum would be null, and since it is a piecewise continuous function, its primitive is a continuous function. If there is a prop load in the position then:.

And therefore the limit on the left and on the right do not coincide, so the function is not continuous. The expression () can be written in single integral form if the generalized Dirac delta function is used:.

where:.

The moment diagram defined by (1) or by (2) turns out to be the derivative (in the sense of distributions) of the bending moment diagram.