# Calculating shear stress in a beam?

The equation for shear stress as I know it is VQ/It where V is the shear force, Q is the first moment of area(?), I is moment of inertia and t is the length of the section in question.
My question is, is there a general formula for Q? In my Solid Mechanics notes I've written that Q = ∫y.dA but for some reason this isn't giving me the answers I get from the equation τ= F. (A.ybar/I.t)
Could someone write down the general formula for Q?

## Answers and Replies

SteamKing
Staff Emeritus
Homework Helper
The equation for shear stress as I know it is VQ/It where V is the shear force, Q is the first moment of area(?), I is moment of inertia and t is the length of the section in question.
My question is, is there a general formula for Q? In my Solid Mechanics notes I've written that Q = ∫y.dA but for some reason this isn't giving me the answers I get from the equation τ= F. (A.ybar/I.t)
Could someone write down the general formula for Q?
There is no general formula for Q. Q represents the first moment of area of the cross section from the point at which you wish to calculate the shear stress to the outermost edge of the section. Q does have to be calculated with reference to the centroid of the section, however.

The quantity t represents the thickness, not the length of the material in way of the shear stress location.

As to your formulas for calculation, VQ / I t is just a re-statement of F (A*y-bar) / I t, where the quantity A*y-bar = Q and F = V. In my experience, VQ / I t seems to be preferred in the US, whereas the other formula was used quite a lot in older texts written in the UK.

A book on strength of materials should illustrate how to treat the calculation of Q for specific examples of different cross sections.

If you have a particular case where you need to analyze the shear stress, please feel free to post this information and we'll be glad to discuss it with you.