Section Shear Area

[jtjc23eng]

Hello,

I wanted to ask regarding section shear area. From school and other sources, I learned that the shear area for a rectangular section is often taken as 5/6 the gross area. Does anyone know where this comes from? Is there a reference?

I would be interested to see if the reference would have guidance on other sections as well such as circular sections.

Thanks!

 

[ProgrammingPE]

Just checking since there has been some confusion in the past, but since you are suggesting 5/6, then I believe by "shear area" you are referring to a factor that is used to calculate the deflection due to shear. (If you are instead referring to a factor that can be used to design for maximum shear stress using the average shear stress, then it should be 2/3 which is from v = VQ/Ib = 1.5*V/A. See this thread.)

The formula is k = integral of Q² A/(I² b²) dA. For a rectangle, Q = b/2*(h²/4 - y²). This will simplify to k = 6/5. (References aren't consistent with this term's location in the deflection formulas so sometimes the inverse of k is used instead, so 5/6). Those links will give you values for some other shapes like circles, hollow circles, and wide flanges.

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