The application of a shear [[Force|force]] necessarily causes the propagation of [[Shear Stress|shear stress]] through the beam in the form of $\tau_{xy}$ and $\tau_{yx}$. Average shear stress through a horizontal strip of a beam cross-section can be calculated as follows:
$\tau_{avg}=\dfrac{VQ}{It}$
With the following definitions:
- $V$: Shear force
- $Q$: [[First Moment of Area|First moment of the area]] from the top/bottom of the beam to the strip in question
- $I$: [[Second Moment of Inertia|Second moment of inertia]] of the cross-section
- $t$: Thickness of cross-section strip in question
By applying the above equation to a beam a general shear stress distribution can be found, allowing analysis of the beam design relative to the maximum shear stress.
![[beam_shear_stress.png|center|400]]
Typically beams will be made of thin members, the typical I-beam as an example. In the case of thin members where shear stress can not flow along the shear force line of action the beam requires more analysis. Examples of this case include I-beams and C-beams, where the shear can not flow vertically in the flanges of the beam and must therefore flow horizontally along the flanges. The shear flow, $q$, can be calculated by the following:
$q=\dfrac{VQ}{I}$
![[Ibeam.png|center|200]]
When calculating the shear stress flowing through a section not aligned with the shear force ($\tau_{xz}$) the shear flow should be used in tandem with the thickness of the section which the shear flows through.
$\tau=\dfrac{q}{t}$
The shear stress through the web of a beam can be approximated by the following:
$\tau_{web}\approx \dfrac{V}{A_{web}}$