Moment of Inertia Formula Query

[Iain123]

Hello, this formula was given to me in an exam to find the moment of inertia of an I beam,

https://ibb.co/jY7ZKG

However this formula seems to give a different answer to the standard bd^3/12 method, is the formula in the image wrong ?
Thanks

 

[BvU]

Hello Iain,

Interesting, an exam that provides a formula without explaining what the symbols and their dimensions are and (at least, if $I$ stands for the moment of inertia) gives a formula with the wrong dimension.

I see no images. The link works:

What is this and what is your standard ? (not this one, I suppose)

 

[jack action]

It seems to be a crude approximation of the appropriate way of doing it (see $I_x$, from source):

 

[Dr.D]

if II stands for the moment of inertia) gives a formula with the wrong dimension.

The dimensions of this expression are L^4 which is entirely appropriate for an AREA moment of inertia, a quantity commonly used in the analysis of beams.

 

[BvU]

I kind of realized that. Would have helped if Iain had mentioned it in post #1 ($I$ as moment of inerita is more common for ordinary physicists... ).

Now: wat is your standard?

 

[Iain123]

Thanks for your reply's,
I have attached an image showing my working using both formulas, and also a picture showing the I beam dimensions (web thickness is 20mm).

https://ibb.co/nMDCrw

Using Skyciv's online beam calculator returns an I value of 7.73x10^6 mm^4 , the same as i got on top line. Also this is only concerning the Ixx value and not Iyy , and I is referring to the second moment of area.
I don't understand how the second formula can return a different value and still be correct, i must be missing something :-/
Thanks

 

[Ned Gan]

The answer I = 7733333 mm4 is correct. To make sure, I double checked it with Calcpad:
http://calcpad.net/Spreadsheet/208/double-tee-section

The formula in the exam is correct but it is approximate. It is obtained by taking the web and adding the flanges by the Steiner's theorem:
I = 2t*h³/12 + 2*b*t*(h/2)²
I = t*h³/6 + b*t*h²/2
I = (t*h³/6) + 3*b/h*(t*h³/6)
I = t*h³/6*(1 + 3*b/h)
The problem is that web and flanges overlap, so this formula produces higher values than the exact one.
It can be used only for thin-walled sections where 't' is much smaller than the other dimensions. Then the overlap becomes negligible.