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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 17:52:53 -0400 (EDT)
Elias, Take another look at ACI 318's definition of Av0...you are missing a part of it below. Av0 is defined as the "projected area for a single anchor in a deep member and remote from the edge in the direction perpendicular to the shear force." It is _NOT_ "unaffected by edge distance" but rather unaffected by edge distance perpendicular to the applied force. Regards, Scott Adrian, MI On Wed, 8 Jun 2005, Elias Hahn wrote: > I was hoping I was doing something wrong, and not at the limits of the > equation. I'm trying to use an 18" footing, with 1.5" anchor bolts, and I'm > running into the limits of this equation at about 10" edge distance (for a > corner condition, c1=c2). > > Plus, you all have to admit, the commentary is poorly worded when talking > about Avo as representing the failure prism of an anchor "unaffected by edge > distance" when, in fact, it is a function solely of edge distance. Seems > like it should be more a function of diameter an embedment depth... > > -----Original Message----- > From: Arvel L. Williams, P.E. [mailto:awilliams(--nospam--at)gwsquared.com] > Sent: Wednesday, June 08, 2005 10:44 AM > To: seaint(--nospam--at)seaint.org > Subject: RE: More confusion with concrete > > Elias, > > The problem is the boundary conditions that this equation will work in. > > Try looking at some of the theoretical ranges from the original equation > development. I expect that somewhere there is a published range of value > that this equation is valid. > > Taking any working empirical equation to near the boundary will result in > erroneous results. > > Arvel > > -----Original Message----- > From: Elias Hahn [mailto:ehahn(--nospam--at)eepdx.com] > Sent: Wednesday, June 08, 2005 12:35 PM > To: seaint(--nospam--at)seaint.org > Subject: RE: More confusion with concrete > > > 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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