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.

  • $\begingroup$ This is the formula for shear flow $\endgroup$
    – atom44
    Commented Apr 27, 2017 at 12:19
  • $\begingroup$ @Conor:I tried to open your link, but the picture contains errors & cannot be opened $\endgroup$
    – Fred
    Commented Apr 27, 2017 at 13:09
  • $\begingroup$ @Fred it works fine in for me in two different browsers - including Firefox. If you are using something else, try that instead. $\endgroup$
    – alephzero
    Commented Apr 27, 2017 at 14:20
  • $\begingroup$ @Fred Hi sorry for that, its τ = (S * a * v) / (I * t) and there is a bar over the v. $\endgroup$
    – Conor
    Commented Apr 27, 2017 at 15:20

1 Answer 1


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.

  • $\begingroup$ That's perfect thanks very much for the help. $\endgroup$
    – Conor
    Commented Apr 27, 2017 at 16:30

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