# Re: Balanced Moment vs PT Moment

• To: seaint(--nospam--at)seaint.org
• Subject: Re: Balanced Moment vs PT Moment
• From: Scott Maxwell <smaxwell(--nospam--at)engin.umich.edu>
• Date: Tue, 31 May 2005 20:26:07 -0400 (EDT)
```The short answer is "yes".

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
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

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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