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Re: IBC concrete anchor design

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Rick,

For the half pyramid that they are talking about, try to envision this for
a single anchor:

Take the location of the anchor at the top surface as one point of the
"half pyramid".  From that point, draw two lines that are at a 35 deg
angle (using the edge of the concrete as the reference) out to the edge.
This should result in a triangle on the surface of the concrete that has a
height of c1 (the edge distance) and a base of 3*c1 (1.5c1 in each
direction from center of anchor where it crosses the surface).  Now, on
the edge surface, draw a line 1.5*c1 down from the top surface edge that
is parallel to the base of that triangle (which is also the top surface
edge).  This should create a rectangle shape the is 3*c1 wide and 1.5*c1
high on the edge surface.  Now, connect the lower right hand corner of the
rectangle to the original point on the surface (where the anchor is) and
do the same for the lower left hand corner.  That is you failure "cone".

To describe it another way using a 3D coord system...assign the location
of the anchor as it intersects the top surface as the origin (0,0,0).
Make the x-axis parallel to the edge of the concrete surface and the
y-axis perpendicular to the axis (with positive going from anchor to edge)
and the z-axis paraller (same) as the axis of the anchor (positive going
from anchor down into concrete).  The failure cone would then be defined
by the following points: (0,0,0), (1.5*c1,c1,0), (-1.5*c1,c1,0),
(1.5*c1,c1,1.5*c1), and (-1.5*c1,c1,1.5*c1).

That above failure cone assumes that the anchor is far enough away from a
second side (i.e. not at a corner where c2 is the distance to the second
edge and c2 would be less than 1.5*c1) or third side.  It also assumes
that the thickness of the concrete is greater than 1.5*c1.  And it also
assumes only one anchor.  The resulting projected surface on the edge (the
rectangle) is Av0 which equals 4.5*c1^2, which would equal Av _IF_ the
above conditions are meant.

If the conditions vary, then the projected surface would change and Av
would no longer equal Av0 (it would be smaller), except if strictly
dealing with multiple anchors.  If multiple anchors are present (in a line
parallel to the edge), then the single point described above becomes to
points connected by a line of length equal to the spacing (thus, the base
of the now trapazoid rather than triangle is increases by that same
distance...i.e. the base becomes 1.5*c1+x*s1+1.5*c1, where s1 is the
anchor spacing and x is the number of anchors minus one).

Thus, Av is the actual projected rectangle on the edge surface when
factoring the edge conditions and spacings, while Av0 is the projected
rectangle on the edge surface without other edges being to too close.  So,
again, if the other edges don't affect the anchor, then Av will be the
same as Av0.

This is all show quite well in Fig. RD.6.2.1 of Appendix D of ACI 318-02.
So if the above verbal description doesn't do it for you, then I suggest
that you attempt to get a look at that figure.

HTH,

Scott
Ypsilanti, MI


On Fri, 6 Dec 2002, Rick Burch wrote:

> In section 1913.6.2.1 of the 2000 IBC, there is a factor Av used for
> checking the concrete breakout strength in shear.  Item 4 in this
> section says:
>
> "Av is the projected area of the failure surface on the side of the
> concrete member at its edge for a single anchor or group of anchors. It
> shall be permitted to evaluate this area as the base of a truncated half
> pyramid projected on the side face of the member where the top of the
> half pyramid is given by the axis of the anchor row selected as
> critical. The value of C1 shall be taken as the distance from the edge
> to this axis."
>
> I have no idea what they are trying to say here - I can't tell how wide
> or deep this pyramid base is.
>
> Can someone clarify this? I believe this section is being dropped from
> the IBC in an upcoming ammendment, in favor of referencing of ACI
> 318-02. So, ACI 318-02 may explain this better, but I don't have a
> copy.  Any help would be appreciated.
>
> Rick Burch
> Columbia, SC
>
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