post-tensioned beams: secondary forces and "concordance"

[hippo11]

Does anyone have any experience with concordance? Or know of any case studies...

Basically concordance is the strategic positioning of your PT strands to eliminate secondary forces...

Thanks

 

[hippo11]

this applies to indeterminate structures only, by the way...there are no secondary forces in a determinate structure, such as a simple-span precast bm...

thanks

 

[Taro]

Is this an academic exercise or a practical design problem? The only time I have ever spent on concordant tendon profiles was in school many years ago. Nilson's textbook says this about concordant tendons...

"Although use of a concordant tendon in a given instance offers the possibility of simplified analysis, there is little practical advantage in terms of structural behavior. The most economical design in a given case is usually obtained with the steel centroid as high as possible over the supports, and as low as possible near midspan, an arrangement that will not generally result in a concordant tendon."

 

[rapt]

hippo11

Taro has it right. There is no need to try to achieve concordance. There is no problem with inducing secondary prestress reactions, in fact they are often benificial, and using the full drape available in controlling spans normally results in the most economical design.

 

[hippo11]

Interesting...thanks guys.

But say you have a two-span PT beam with a parabolic drape in each span---you get a big secondary POSITIVE moment at your midspans--this is additive to your dead and live moments at midspan. So it's not worth trying condcordance there? I guess if you did get concordance you would be eliminating your secondary moments but then your resulting drape would not be effective in resisting applied gravity loads?

 

[rapt]

hippo11,

You applied load bending moemnts in that case are

negative - wl2/8
positive - wl2/14

The prestress has basically the same capacity at both faces, so the positive secondard moments are reducing the very high negative moment and increasing the low positive moment. Helps both ways and makes the prestress more efficient.

The only problem comes in when some idiot with flanged beams assumes an unrealisticly wide effective flange width which by calculation creates unrealistically high secondary moments and makes the design very unconservative. Some computer programs widely used in America used to and may still do this.