Derivation of bolt group moment of inertia
Derivation of bolt group moment of inertia
(OP)
Hello everyone,
I have a formula that I can not seem to derive. The moment of inertia for a bolt group is given about the x axis (at C.G. of bolt group) as:
Ix = 1/12*[nb^2*(n^2-1)] where n = rows of bolts, b = spacing between bolts
I tried assuming the bolt group had a unit width with a height = (n-1)*b, but I still do not come up with this formula. Does anyone know where this comes from or how to derive it?
Thanks
I have a formula that I can not seem to derive. The moment of inertia for a bolt group is given about the x axis (at C.G. of bolt group) as:
Ix = 1/12*[nb^2*(n^2-1)] where n = rows of bolts, b = spacing between bolts
I tried assuming the bolt group had a unit width with a height = (n-1)*b, but I still do not come up with this formula. Does anyone know where this comes from or how to derive it?
Thanks






RE: Derivation of bolt group moment of inertia
Typically the moment of inertia of a bolt group is the sum of the D^2 terms where D is the distance from the centroid to each bolt.
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RE: Derivation of bolt group moment of inertia
For multiple columns you multiply by the number of columns (provided they have the same number of bolt rows). There is a similar expression for Iy as follows:
Iy = 1/12*mD^2*(m^2-1) where m = number of bolt columns, and D is the spacing between the bolt columns.
I have used the formulas before, I just don't know how to derive them and was curious.
RE: Derivation of bolt group moment of inertia
DaveAtkins
RE: Derivation of bolt group moment of inertia
I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.
RE: Derivation of bolt group moment of inertia
https://res.cloudinary.com/engineering-com/image/upload/v1456328358/tips/Scan-to-Me_from_172.31.22.80_2016-02-24_103350_vnyjzu.pdf
RE: Derivation of bolt group moment of inertia
I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.
RE: Derivation of bolt group moment of inertia
RE: Derivation of bolt group moment of inertia
you can work from each fastener or you can (if you have a simple pattern, say 4 rows with n fasteners per row) generalise ... locate the centroid (in the example it's at the middle), calc the offset for each row (the inner rows are p/2 from the centroid, the outer rows are 3p/2) and calc ... I = 2*(9p^2/4*nA+p^2/4*nA) ... how does that fit with your equation ?
another day in paradise, or is paradise one day closer ?
RE: Derivation of bolt group moment of inertia
Ibot = Ab.b2[1 + 22 + 32....+ (n-1)2]
Icg = Ibot - n.Ab.[(n-1)b/2]2
If n = 5, Ibot = Ab.b2[1 + 4 + 9 + 16] = 30Ab.b2
Icg = Ibot - 5Ab.4b2 = Ab.b2(30 - 20) = 10Ab.b2
BA