Wrong (?) moment of inertia equation

[flyforever85]

Hi all,
this is a very simple question because either I'm wrong of the book I'm using is.

The formula reported in this book for a moment of inertia of a rectangle with length=a (in) and height= c (in) is and weight=W (lbs) is:

I=[W x (a^2 + c^2)] / (12 x 386.4) my problem is the 12. It should represents in/ft but feet don't appear in this formula so why would I need that coefficient?

Let me know your thoughts. I can take a pic of the book as well.

Thanks!

 

[hydtools]

The 12 does not represent in./ft. It is non-dimensional.

Ted

 

[handleman]

Why do you think the 12 comes from in/ft?

 

[kjoiner]

Hello,

Can you add a picture of the book? For a rectangle, I've always seen I= b(h^3)/12. The result is in^4.

Kyle

 

[rb1957]

bd^3/12 is I for a rectangle.

your equation is in inches, because 386.4 is "g" in in/sec^2

what sort of moment of inertia are you calculating ? is "length" = "width" ? (so that the cross section is b*c ??)

is "W" the weight of the beam, or the weight per linear foot ??

show us the source please.

another day in paradise, or is paradise one day closer ?

 

[hydtools]

Do not confuse area moment with mass moment of inertia. The OP question is about mass moment of inertia.
The mass will be in imperial units. W/g = W/386.4. 386.4 = 12in/ft x 32.2ft/s^2
Ted

 

[rb1957]

so, from Engineer's toolbox …

Rectangular Plane
Moments of Inertia for a rectangular plane with axis through center can be expressed as
I = 1/12 m (a^2 + b^2) (5)
where a, b = short and long sides
and m = mass = W/g.





another day in paradise, or is paradise one day closer ?

 

[flyforever85]

rb1957 you got it! I was stuck with the idea that the general second moment of inertia was mass x length^2 so I assumed wrongly 12 was a conversion factor.

sorry about the confusion!

 

[rb1957]

to be fair, Ted (Hydtools) got it.

another day in paradise, or is paradise one day closer ?

 

[kjoiner]

Hello,

Hydtools - you are correct. After I posted it, I said oops, mass moment of inertia. Sorry for the confusion. I'll blame it on Friday.


Kyle

 

[electricpete]

fwiw, attached is derivation of the result in rb1957's post.
I used b and h instead of a and c for the cross section dimensions.

Edit - I probably didn't treat the variable L (length) properly. The original integral should be multiplied by L to give total moment about centerline (summed along the length). The factor m/(b*h*rho) should be m/(L*b*h*rho). Those "errors" cancel out.


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(2B)+(2B)' ?