Derivation of bolt group moment of inertia

• Feb 23, 2016

• #2

JAE

Structural

Jun 27, 2000

15,463

So if n is the number of rows of bolts what represents the number of columns of bolts?

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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• Feb 24, 2016

• Thread starter
• #3

Perception

Structural

Feb 4, 2015

34

JAE,

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.

 

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• Feb 24, 2016

• #4

DaveAtkins

Structural

Apr 15, 2002

2,868

If you are talking about the moment of inertia, and not the polar moment of inertia, then I agree with JAE--it is the summation of the number of bolts in each row times the square of the distance of that row from the centroid.

DaveAtkins

 

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• Feb 24, 2016

• #5

KootK

Structural

Oct 16, 2001

18,272

It's a rough approximation that gets tougher as the number of bolts decrease. And I disagree slightly with one of your terms.

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.

 

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• Feb 24, 2016

• Thread starter
• #6

Perception

Structural

Feb 4, 2015

34

KootK I agree with your math, but what is interesting is that all 3 methods produce the same results. An example is shown below.

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• Feb 24, 2016

• #7

KootK

Structural

Oct 16, 2001

18,272

In your method III, I believe that the four ought to be a two. Method III should always provide a lower bound estimate of the true result predicted by method one in my opinion.

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.

 

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• Feb 24, 2016

• #8

Hokie93

Structural

Sep 9, 2007

375

The equation is derived in Chapter 8 of "Design of Steel Structures" (third edition) by Gaylord, Gaylord, and Stallmeyer.

 

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• Feb 24, 2016

• #9

rb1957

Aerospace

Apr 15, 2005

15,754

just consider the fasteners as point area's (ie no self moment of inertia) and work though the calc ...
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 ?

 

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• Feb 26, 2016

• #10

BAretired

Structural

Nov 16, 2008

10,867

Another procedure is to find I about the lowest bolt, then correct for the eccentricity to the c.g. of bolts.

I_bot = A_b.b²[1 + 2² + 3²....+ (n-1)²]

I_cg = I_bot - n.A_b.[(n-1)b/2]²

If n = 5, I_bot = A_b.b²[1 + 4 + 9 + 16] = 30A_b.b²

I_cg = I_bot - 5A_b.4b² = A_b.b²(30 - 20) = 10A_b.b²

BA

 

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