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RE: More confusion with concrete
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- Subject: RE: More confusion with concrete
- From: Scott Maxwell <smaxwell(--nospam--at)engin.umich.edu>
- Date: Wed, 8 Jun 2005 18:46:25 -0400 (EDT)
Elias, What is your particular case (give the specific example with numbers) that you are trying to look at? I believe you gave it before, but I deleted that message. Regards, Scott Adrian, MI On Wed, 8 Jun 2005, Elias Hahn wrote: > Ahhh see, so there it is. I didn't catch/understand/pay attention to the > doubling factor. It still seems a little silly, and for my case with a > relatively big couple of anchors trying to get away with a relatively thin > footing, I'm still losing capacity by increasing my edge distance, which is > not how it should work. Or can I double it because the force is in fact > parallel to an edge? (c1=c2, so either way it is both parallel and > perpendicular to an edge.) > > -----Original Message----- > From: Scott Maxwell [mailto:smaxwell(--nospam--at)engin.umich.edu] > Sent: Wednesday, June 08, 2005 3:27 PM > To: seaint(--nospam--at)seaint.org > Subject: RE: More confusion with concrete > > Elias, > > Yes...you are correct in what you wrote below...but your are forgeting > that there is another c1 in the overall equation for the shear breakout > strength. Remember the overall breakout strength is Av/Av0*(a bunch of > factors depending on either single anchor or group of anchors)*Vb. The > key is that Vb is a function of c1^1.5. > > So, your case of the long beam in the "big" c1 direction...Av will be > (c2+c2)*h (unless you want to consider a REALLY deep beam such that > h>1.5c1). and Av0 will be 4.5*c1^2. Thus, Av/Av0 will nominally be 1/c1^2 > if you consider c2 and h to be negligble compared to c1. But then Vb is > some value*c1^1.5. So, in fact, you end up with Vcb being proportional to > 1/c1^.5. Now, keep in mind that you have some "constant"/value there as > well, so it is not just 1/c1^.5 but rather a/c1^.5. And then beyond that > section (c) of D.6.2.1 states: "for shear force parallel to an edge, Vcb > or Vcbg shall be permitted to be twice the value for shear force > determined from Eq. (D-20) or (D-21), repectively, with psi6 taken equal > to 1"...and your "big" c1 direction is such a case. Thus, the end result > is that I am willing to bet in most cases the Vcb of the "big" c1 > direction will still be bigger than the Vcb of the "small" c1 direction. > > Let's do an example with some numbers. Say it is a 24"x42" concrete beam > that spans 24 ft. Put a 1" dia. anchor in the middle of the beam with an > embedment of say 24". OK. > > For the "big" c1 case: c1 is 144". c2 is 12". h is 42". d0 is 1". > l is 8*d0 or 8". Let's make f'c equal to 3000 psi. psi7 will be the same > for either case. psi6 will be 1. So, Av will be (c2+c2)*h or 1008 sq in. > Av0 will be 4.5c1^2 or 93312 sq in. So, Av/Av0 is .0108. Vb is > 7*(l/d0)^0.2*d0^0.5*f'c^0.5*c1^1.5 or 1004200.4 lbs. So, Vcb will be > 10845.4 lbs (assuming psi7 is 1.0), but section (C) let's us double that > to 21690.7 lbs. > > For the "small" c1 case: c1 is 12". c2 is 144". h is 42". d0 is 1". l > is 8". Using f'c of 3000 psi again. psi6 will be 0.7. So, Av will be > 1.5*c1*(1.5*c1+1.5*c1) or 4.5c1^2. Av0 will be 4.5*c1^2. So, Av/Av0 will > be 1. Vb will be 24157.3 lbs. Vcb will end up being 16910.1 lbs (again > assuming that psi7 is 1.0). > > Thus, here you have a situation that you describe in basics terms but this > time with some specific numbers. You can see that the "big" c1 direction > does produce a higher breakout condition than the "small" c1 direction. > > Now, one could argue that this may still not fit the intuitive sense, > which for me would want to say that the "big" c1 direction should be > SIGNIFICANTLY larger than the "small" c1 direction is such a case and > while it is bigger, I would say not "big enough" to match the intuitive > feel...and I would agree with this arguement. But, from a structural > point of view in checking the anchor, while it might not be completely > accurate, it does produce the expected result of the "small" c1 direction > being the "weak link". > > HTH, > > Scott > Adrian, MI > > > On Wed, 8 Jun 2005, Elias Hahn wrote: > > > Agreed, the problem I have with formulas is that if you increase c1 until > it > > is "big" (ie, 1.5c1 is greater than c2 and/or h), Av/Avo gets small. (or > > conversely, have a thin slab, or a corner condition where c1 is roughly > > equal to c2.) > > > > Ok, now my long hypothetical - feel free to not read: > > The problem in my mind is if you take a long beam, and put an anchor in > it, > > and look at the calculated strength of that anchor (side-face blow out) in > > both directions. Now, in one direction, c1 is "big", much bigger than > > either c2 or h, while in the other direction c1 is "small." Now on the > case > > were c1 is "big" Avo is great, but Av is small, (assume c2 and h are > > negligible in that direction, Av/Avo tends to 1/(3*c1), which makes the > > overall equation roughly (a number less than one)*(Square root(c1)). Now > if > > you look at the other direction, were Av/Avo tends to one, you now end up > > with an overall equation of (a number greater than one)*(c2)^1.5)). It is > > easy to see that the direction without much edge distance could have a > > larger concrete side-face blow out strength... > > > > > > -----Original Message----- > > From: Scott Maxwell [mailto:smaxwell(--nospam--at)engin.umich.edu] > > Sent: Wednesday, June 08, 2005 10:21 AM > > To: seaint(--nospam--at)seaint.org > > Subject: Re: More confusion with concrete > > > > Elias, > > > > First, I would say that you need to be a little clearer about what kind of > > condition you are looking at. The edge distance, the effective thickness > > of the concrete (h), and the number of anchors can affect the "view" of > > things. > > > > Take a simple basic condition...a single anchor in a concrete element that > > is MUCH thicker than the depth of the anchor and is only at a side, not a > > corner. Kind of like what is shown in Fig. RD.6.2.1(a) and RD.6.2.1(c) in > > the 2002 ACI 318. In such a case, c2 and h don't enter the picture. > > > > In such a case, then Av is equal to Av0. Both have a value of 4.5*c1^2. > > Av/Av0 will be 1. > > > > Ok, now make it two anchors that are spaced 3*c1 apart. This will be that > > same as above but Av will be twice as big because the failure surface (Av) > > will still be bottom of two FULL half pyramids with a base of 3*c1 by > > 1.5*c1. This is because you now have two anchors with FULL failure > > surfaces that do not interesect (remember Av is the failure surface for > > the entire group of anchors). So, Av/Av0 will be 2. > > > > OK, now decrease that space of the two anchors. The failure "half > > pyramids" will now overlap. Av will become 1.5*c1 (depth of failure > > plane) times 1.5*c1+s+1.5*c1 where s is less than 3*c1. The result is > > that Av/Av0 will be less than 2 and approaching 1 as s decreases toward > > zero. > > > > I will leave it to you to look at more complitcated, "less perfect" cases > > such as when concrete thickness is not much greater than anchor depth > > (i.e. h<1.5*c1) or corners or multiple rows of anchors parallel to the > > edge. > > > > This is as it should be. Av0 is the shear breakout of ONE anchor assuming > > "perfect" edge conditions (i.e. no other anchors to overlap the failure > > surface, at just a plain edge not corner, and concrete thickness much > > greater than the anchor depth). Av is the shear breakout of the entire > > anchor group, which could in fact be single anchor in the group [if you > > have an isolated anchor] or an actual group of anchors, under potentially > > less than ideal conditions (i.e. close spacing, at a corner, and/or > > concrete thickness less than 1.5*c1). Thus, things like spacing, another > > edge (i.e. at a corner), or "thin" concrete will affect Av. The point is > > that under "perfect" conditions (i.e. spacing greater than 3*c1, edges not > > corners, concrete thickness much greater than anchor depth [i.e. > > h>1.5*c1], anchors all in one parallel row/line that is parallel to the > > edge) Av will be a integer number multiple of Av0, where the integer > > multiple is the number of anchors. This multiple becomes a non-integer > > and less than the number of anchors as the conditions become less than > > perfect. > > > > Now, I can only hope that I am remembering/explaining this right...I > > am little scatter-brained today. > > > > HTH, > > > > Scott > > Adrian, MI > > > > > > On Wed, 8 Jun 2005, Elias Hahn wrote: > > > > > So, I come again to this list with a question stemming primarily from > ACI > > > 318. > > > > > > > > > > > > I'm "designing" some anchor bolts, and I'm confused about the formula > for > > > concrete breakout strength of anchor bolts. Specifically about Av/Avo. > > > Because Avo is a function of 1.5*c1, and Av is a function of 1.5*c1, c2, > > and > > > h - it seems like the larger c1 gets, the smaller Av/Avo gets, which > seems > > > counter-intuitive. > > > > > > > > > > > > The reason it gets so small is because as c1 gets large, 1.5*c1 will be > > much > > > larger than h and c2, so that Av becomes much smaller than Avo. > > > > > > > > > > > > My confusion is why is Avo a function of c1 if it supposed to > approximate > > > the "surface area of full breakout prism. unaffected by edge distance"? > > > > > > > > > > > > Thank you, > > > > > > Elias Hahn > > > > > > Evergreen Engineering, LLC > > > > > > phone 503.502.0698 > > > > > > > > > > > > > > > > ******* ****** ******* ******** ******* ******* ******* *** > > * Read list FAQ at: http://www.seaint.org/list_FAQ.asp > > * > > * This email was sent to you via Structural Engineers > > * Association of Southern California (SEAOSC) server. 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