# Shear area and first moment of area to calculate shear stress

QUESTION
For a rectangular cross-section, the shear area is 0.833 times the cross-section area.
Can this shear area be used to calculate the transverse shear stress [approach 1]?
Usually, the transverse shear stress is calculated using the formula VQ/It where Q is the first moment of area [approach 2]

Is there any link between these two approaches?

REPLIES

steve
The term ‘shear area’ seems to mean different things to different people. When I was taught, it related to elastic shear deflection of beams. Shear deflection is usually negligible compared to the flexural deflection so everyone forgets it upon graduation (including me).

There’s probably some relation between shear area and shear stress distribution but I couldn’t say what it is.

From memory, shear deflection is something like the integral of (shear force divided by shear stiffness) over the length of the beam. Shear stiffness = shear modulus of the material multiplied by shear area of the section and is analogous to EI for flexural stiffness.

Your value of 0.833*gross area matches this definition of shear area.

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