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# RE: More confusion with concrete

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• To: seaint(--nospam--at)seaint.org
• 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
> > >
> > >
> > >
> > >
> >
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