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Re: Balanced Moment vs PT Moment

[Subject Prev][Subject Next][Thread Prev][Thread Next] Will,

The Balanced Moment at any point can be calculated directly from the  balanced loads as long as you include all of the loads induced. These include effects from anchorage eccentricity and changes in concrete section (and change in force if you want to get accurate).

In the case of a straight tendon at constant eccentricity, there is a moment equal to P*e at each end due to the eccentricity of the strands where they anchor giving a continuous moment diagram over the length of the strands of Pe. This is assuming no loss in force over the length of the strand which is not really correct as there is a transmission length for pretensioned strands.

In the case of a parabolic tendon profile with end eccentricity there is a UDL from the parabolic profile plus end moments due to the anchorage eccentricity.

It all adds up to P*e at every cross-section along the member if the member is determinant.

At 09:35 PM 1/06/2005, you wrote:



Yes,

I was confusing the "balanced load" (from the load balancing method) with generating a "balanced moment". When apparently the "balanced moment" is just the resulting PT moment and cannot always be derived directly from the "balanced load".

 It would seem more logical just to call it the "PT moment" but it appears as the standard for some reason to refer to it as the "balanced moment".




>From: Scott Maxwell <smaxwell(--nospam--at)engin.umich.edu>
>Reply-To: <seaint(--nospam--at)seaint.org>
>To: seaint(--nospam--at)seaint.org
>Subject: Re: Balanced Moment vs PT Moment
>Date: Tue, 31 May 2005 20:26:07 -0400 (EDT)
>
>The short answer is "yes".
>
>The longer answer...first, I believe you are thinking of "balancing loads"
>not "balancing moments" (but then I may be misunderstanding).  If you are
>using the methodology of "balancing load" that I have seen, then the end
>goal is to produce uniform compressive stresses over the entire cross-section
>of the member over the entire length of the member.  This means that you
>need to find a loading that completely replicates the bending stresses in
>reverse that the prestressing/tendon profile creates.  An example would be
>you have a parabolic tendon profile with the eccentricity of 0 at the
>ends.  A balancing load would be a uniform load (as the moment diagram is
>a parabola).
>
>Now, in practice, this rather difficult to completely do.  Take a simple
>drapped tendon profile (eccentricity 0 at ends, max at midspan and a
>straight line connecting the two points in between).  The balancing load
>would be a point load (creates nice "triangular" moment diagram like the
>tendon profile).  Yet, you would still in reality have a uniform load also
>(the dead weight of the beam itself), so it would not be truly
>"balanced".
>
>Thus, I am used to the concept of "balanced loads" primary use to
>illustrate basics of prestressing and how tendon profiles can be thought
>of in terms of applied loading in "conventional" terms (usually balanced
>loading leads to discussion of "equivalent loads").  This can help people
>new to prestressing get a grasp of how prestressing can induce stresses in
>the members.  I will note that the basic concept of "balanced loads" can
>be useful, even if you completely balance forces created by the tendon
>profile...the closer your are to balanced, the less deflection or camber
>issues to deal worry about and the member should be crack free as it it
>should be largely under uniform or darn close to uniform compression.
>
>HTH,
>
>Scott
>Adrian, MI
>
>
>On Tue, 31 May 2005, Will Haynes wrote:
>
> > Is the "balanced moment" always equal to the moment from the post
> > tensioning?
> >
> > In other words, if I have beam with a straight tendon at a constant
> > eccentricity of 6" and a force of 150 kips, the moment from the post
> > tensioning is a constant 75 ft*kips. Would it be correct to also call
> > this the "balanced moment"?  Even though this is not a parabolic profile?
> >
> >
> > Or, if the same beam has a parabolic tendon profile, but the tendon is
> > eccentrically placed at each end. Would the balanced moment at the beam
> > midspan be the sum of the (eccentric end moment + the moment from the
> > drape), or would it be just the moment from the drape?
> >
> > I am not sure what the definition of "balanced moment" is supposed to be
> > for beams with tendons that are eccentrically placed at the ends.
> >
> >
> >
> >
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Regards  Gil Brock
Prestressed Concrete Design Consultants Pty. Ltd. (ABN 84 003 163 586)
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