# Formula of shear stress

1. Jul 21, 2016

1. The problem statement, all variables and given/known data
in the old thread , i was told that
The formula for calculating the shear stress is a beam is $τ = \frac{V ⋅ Q}{I ⋅ t}$

τ - shear stress
V - shear force
Q - first moment of area above the location where the shear stress is calculated.
I - second moment of area for the entire beam about the N.A.
t - width of the beam where the shear stress is calculated
But , how to change the $τ = \frac{V ⋅ Q}{I ⋅ t}$ into V and A only ?
just like below ?

2. Relevant equations

3. The attempt at a solution
The V represent shear force , it's not volume , am i right ?

2. Jul 21, 2016

sorry , i left out something in post # 1 , so continue here :
as we can see shear stress of various shape is in terms of V and A ,
The V represent shear force , it's not volume , am i right ?

How to change shear stress = (V)(Q)/ (It) into in terms of V and A ?

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3. Jul 21, 2016

### PhanthomJay

V is the conventional designation for shear (in force units). Clearly it doesn't stand for Volume here, right?
V/A is average shear stress, whereas VQ/It is maximum shear stress which usually is at the neutral axis. You cannot generalize a relationship between them since it depends on the cross section shape. For example for the rectangle, max shear stress is 3/2 avg shear stress, and for the circle, max shear stress is 4/3 avg shear stress. Note that for certain shapes like I beams, the area of the web and not the entire shape is used to determine A when computing avg shear stress, because the shear stresses mostly are in the web.

4. Jul 21, 2016