# Shear Stress Formula

Could anyone tell me what the variables in this formula are?

$$\tau=\frac{S\;a\; \bar{v}}{I\; t}$$

I believe it is used for shear stress and that $I$ is moment of inertia but unsure on the other variables.

• This is the formula for shear flow – atom44 Apr 27 '17 at 12:19
• @Conor:I tried to open your link, but the picture contains errors & cannot be opened – Fred Apr 27 '17 at 13:09
• @Fred it works fine in for me in two different browsers - including Firefox. If you are using something else, try that instead. – alephzero Apr 27 '17 at 14:20
• @Fred Hi sorry for that, its τ = (S * a * v) / (I * t) and there is a bar over the v. – Conor Apr 27 '17 at 15:20

The sign convention I currently use is as shown ($x$ "out of the display" towards you, $y$ to the left, $z$ down) The way I was taught the formula is: $$\tau=\frac{V_z\cdot Q_y}{I_y \cdot t}$$
$V_z$ … shear force at position $x$ in $z$-direction
$Q_y$ … first moment of area ($\int zdA$) of the blue area wrt neutral axis
$I_z$ … second moment of area of ($\int z^2dA$) entire cross section wrt neutral axis
$t$ … thickness of cross section at point where $\tau$ has to be determined
$Q_y$ can also be written as $A\bar{z}$, where $A$ is the blue area and $\bar{z}$ the $z$-coordinate of its centroid.