Calculating Shear Stress in Beams: V and A Formula

[chetzread]

Homework Statement

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 ?

Homework Equations

The Attempt at a Solution

The V represent shear force , it's not volume , am i right ?

 

[chetzread]

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 ?

 

[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.

 

[chetzread]

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.

so , shear stress is VQ/It for beam , and for the other shape , it's function of V and A ..There's no way to derive he shear stress of other shape from VQ/It ?

 

[PhanthomJay]

I think you misunderstood. repeat: For the rectangle, max shear stress VQ/It is 3/2(V/A), or 3/2 times the avg shear stress in the rectangle. For the circle, max shear stress VQ/It is 4/3 (V/A), or 4/3 times the average shear stress in the circle.