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# Re: POST-TENSIONED: Calculating Friction Losses

• To: seaint(--nospam--at)seaint.org
• Subject: Re: POST-TENSIONED: Calculating Friction Losses
• From: Scott Maxwell <smaxwell(--nospam--at)engin.umich.edu>
• Date: Sun, 28 Nov 2004 04:00:33 -0500 (EST)

Bill:

First, the "obvious" thing that you are likely already aware of...but just
to be on the safe side...

Alpha is to be an angle in radians.  I only mention it cause you state
"...be Ninety Degrees...".

Now as to determining alpha, let's deal with a "simple" case.  Take a
simply supported beam with a parabolic shaped "simple" profile.  At one
end (left end) of the beam, there will be a negative angle
(relatively small/shallow in most cases) relative to the zero degree point
(using stadard polar coordinate stuff...zero degree is the due "east"
line, 90 degree due "north", 180 degree due "west", etc).  At the other
end (right end) of the beam, there will be a positve angle, again
small/shallow in most cases, relative to the 180 degree point.  Alpha is
then the change in angle (in radians) from the left point to the right
point.  In otherwords, draw a tangent to the left point and a tangent to
the right point, then alpha is the angle between those two tangents (this
is for friction loses over the whole length of the beam from the jacking
end to the anchored end).

If you have a more complex profile (i.e. a combination of straight and/or
curved segments), the "...losses may be calculated progressively, starting
at the jacking end." (to quote Nilson's Design of Prestressed Concrete).

HTH,

Scott

On Sat, 27 Nov 2004, Bill Polhemus wrote:

> I have never had occasion to calculate/estimate prestress losses due to
> Friction/Wobble/Anchor Seating, all of which are typically concerns for
> Post-Tensioned Concrete only.
>
> The governing equations are defined in ACI 318 Section 18.6.2. However,
> I'm not absolutely sure I "get" how to apply this.
>
> For example, my typical detail for PT slab design shows a tendon
> trajectory in the slab beams that is an "S-curve" specified to occur for
> a distance of two times the beam depth. Now, it seems to me that the
> "alpha" term in ACI 318 Eqs. 18-1 & 18-2 would "always" be Ninety
> Degrees in such a case. But that's a qualitative assessment on my part,
> because I'm not sure if I completely understand the definition of "alpha."
>
> So, I'm asking for some guidance from anyone out there who does--or has
> done--post-tensioned concrete design: How have you typically gone about
> computing the loss due to friction as defined in ACI 318 Sec. 18.6.2?
>
> [N.B. Sorry for the rambling missive. I very often find that I can't
> really phrase my question until I've stumbled around a bit, gathering my
> thoughts...]
>
> Happy Thanksgiving, Everyone.
>
>
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