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The second moment of area is an important aspect of beam theory and allows for all bending equations to be valid for any shape of beam!
δ/y=M/I=Eκ
In this equation, the I represents the second moment of area
It can also be used to the the flexural rigidity and bending stiffness of a beam
I is a geometrically determined value and is found by integrating a beam's
height across its cross-section
Although this isn't something which you would actually need to remember, all
you need to know is how to calculate it for common shapes and what it used for
Second moments of area for common beam shape
o For solid rectangular cross-section:
I=(bh
3
)/12
o For solid circular cross-section:
I=(πr
)/4=(πd
4
4
)/64
o For semi-circular cross-section:
I≈0.110r
4
o For circular tube:
I≈πr
3
t , where t is the tube thickness
o For rectangular tube:
I=(h
3
/6)(1+3(b/h))
o For an I-beam:
I=(T(H−2T
^3)/12+(BT(H−T)^2)/4)
)^3/12+2((BT
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