Blodgett's Properties of Weld Treated as Line

[Archie264]

I'm going through Table 5 of Section 7.4 of Blodgett's book and I can understand the derivation of every section property I've examined thus far except one: the circular one. It seems to me it should be thus:

I_w = Πd(d/2)² = (Πd³)/4

S_w = I_w/c = [(Πd³)/4] / (d/2) = (Πd²)/2

However, the book's value is S_w = (Πd²)/4

I'm not prepared to bet against Omer Blodgett so can someone help me understand this? I know it works out to the book's value using I_w = Π(d/2)(d/2)² but that doesn't seem right or consistent with how the values for the other configurations were calculated.

I'm looking at it as though the weld was a circular line, consistent with how the properties for the other configurations seem to have been calculated. It appears the book is looking at it as some sort of two dimensional "area", i.e., Πr instead of Πr². The book's value is more conservative, so I'm fine with it, I'm just curious how it was obtained. Any one know? Or can anyone show me where I've dropped the 1/2 somewhere?

(Π = pi, by the way.)

Thanks.

 

[KootK]

Check out this, oddly similar, recent thread: Link. I get Blodgett's result for Sx but, of course, that's based on an assumed formula for Ix.

On another note, I finally ordered that concrete text by Fling that you've mentioned on occasion (K-factor column design etc). It showed up at my wife's office this morning. Like a mini-Christmas.

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.

 

[Guastavino]

So for a thin ring, Ix=Iy=Pi*d^3*t/8, but we take out the "t" to treat it as a line, therefore Iw=Pi*d^3/8.

Then Sw=Iw/(d/2)=Pi*d^2/4

So the thin ring formula is the difference. Where did you get the Iw formula?

 

[Archie264]

Njlutzwe,

Excellent. Thanks, that explains it. Now I can get on with my life. I had to look in a bunch of books before I found the equation for I for a thin ring. Plenty of books, including the Steel Manual, have formulas for a hollow circle (i.e. annulus ('hope I spelled that right)) but it took a while before I found one for a thin ring, confirming what you wrote.

The formula I used was simply the parallel axis theorem, I = I₁ + Ad² with I₁ set to zero and using the circle's circumference instead of it's area. That approach worked for the straight line section properties I checked.

Kootk,

I think you're going to enjoy that book, I know I have. A benefit of everything going paperless is that libraries are divesting themselves of books so a lot of good ones can be had for a song. I wish it was as simple to absorb the material therein but at least I can have them for a reference when I need them.

 

[wannabeSE]

Archie,
The Steel Construction Manual (page 8-13 in 14th edition) has I for different weld groups. For a circle, I = ΠR³ with R = radius. Blodgett is nice because it has formulas for the elastic section modulus, S. Salmon and Johnson also includes formulas for S.

 

[Archie264]

Whoops, just saw this. WannabeSE, yes, but those values in the steel manual are for Iw, that is, the value obtained by treating the weld as a line. I was trying to derive that value from the value for I with a thickness. To do that I needed the value for I for a thin ring. It was an otherwise trivial exercise, except that I was trying to understand it better. (Oh, alright: understand it.) And I must be the last engineer on earth without Salmon & Johnson's steel book...probably ought to correct that at some point. Anyway, thanks.