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RE: More confusion with concrete

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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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