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RE: More confusion with concrete

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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
> >
> >
> >
> >
>
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