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As Jake pointed out, equation D-5 does not account for reinforcing in the
pedestal (see section RD.4.2.1).  Thus, equation D-5 is assuming that the
concrete takes ALL the load.  It does this by way of a failure cone that
is defined by a projected area using a 35 deg angle from the anchor head.

Thus, the "glitch" that you found makes perfect sense to me (unless I am
missing something).

Take the case of a single anchor for simplicity sake.  If the anchor is
not anywhere near the edges, then An will equal An0 and thus the ratio
will be 1.  As you start to deal with edges such than c1 or c2 (edge
distances) are less than 1.5hef, then An will decrease while An0 stays the
same, resulting in the ratio of An/An0 becoming less than 1.  This makes
sense to me as in effect you are now truncating the failure cone, which
means less concrete will be "effective" in resisting the tension force.
Thus, the "anchor capacity" will decrease (assuming that it is controlled
by the concrete rather than the steel).

This is also true for a group of anchors, except to begin with the An/An0
ratio will be slightly larger than 1.  Again, start with edge distances
not being a factor.  To begin with then, An will be larger than
An0 as An includes the area between the anchors (i.e. it is not quite
n*An0 where n is the # of anchors, but is still larger than An0=9*hef^2).
But, as edge distances start to effect things, then again An will become
less than An0.

And, the An/An0 ratio actually over powers the Nb term as the effective
depth increases.  This is because the An0 term increases as a function of
hef^2 while the Nb term increases as a function of hef^1.5 (or hef^5/3).
Thus, equation D-5 will decrease as hef increases IF EDGE DISTANCES EFFECT
THINGS as you end up with hef^1.5/hef^2 or hef^.5.  Note: this comments
does not explore the effects caused by the three modification factors in
sections D.5.2.4 through D.5.2.6 with at least two of those factors
effected by hef).

If, however, edge distances DON'T effect things, then equation D-5 will
increase (as makes sense) as the An/An0 ratio will essentially be 1 or
maybe slighty larger than 1.


Ypsilanti, MI

On Mon, 14 Jul 2003, Chris Banbury wrote:

> Hmmm, that's alarming.  I've used these formulas many times and never detected a glitch here. I've gone back and looked at the equation D-5 and I see that you're right.  The An/Ano term gets smaller and approaches unity (1) as the embedment depth increases. This makes sense though, since at very large depths the projected failure surface would look almost the same for one bolt or eight bolts spaced closely together.  I see, however, that the Nb term (basic concrete breakout strength) increases dramatically with effective embedment depth and overides this effect since it is multiplied by the An/Ano ratio. If you still have trouble give me a call.  I could check your specific case on the spreadsheet I'm developing which implements Appendix D.  Also be sure to apply the limits on An properly and limit projected areas affected by the pedestal.
> Christopher A. Banbury, PE
> Vice President
> Nicholson Engineering Associates, Inc.
> PO Box 12230, Brooksville, FL 34603
> 7468 Horse Lake RD, Brooksville, FL 34601
> (352) 799-0170 (o)         (352) 754-9167 (f)

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