Pretension force distributed into concrete beam - strain and load distribution.

[geopat69]

Hi All.

In regard to a simply supported pretensioned beam (with straight horizontal and fully bonded strands for the purposes of this discussion)...this does appear to be a fundamental question, but is in fact a little more complex…with an understanding of strand strain and concrete strain at transfer required.

When the strands are pulled, there is a steel strain induced in the strands which results in a constant tension (which I know and is easily calculated). At transfer, the strand is released and wants to transmit load to the concrete. Obviously the strand does not transmit load discretely at the end points, and the compressing load is realistically distributed along the interface of the strand/ concrete.

Just prior to transfer a strand will have uniform strain and therefore uniform tension for the entire length. But also note that the strand extension at ends is highest and the extension at midspan is zero. At transfer, the strand will want to return to its original length but is now uniformly restrained by the concrete.

The question: (which relates strain and the distribution of load to the concrete)… how can the transmission of force to the concrete be confined to the end ( 1 or 2 meters ) of the beam when clearly the strain in the steel is existent for the the entire length. In other words, wouldn’t the concrete force reach maximum compression at the mid span rather than near the ends (by virtue of strain comparability).?

 

[geopat69]

Forgot to mention… for the sake of this discussion and simplification, ignore elastic shortening effect.

 

[Retrograde]

Obviously the strand does not transmit load discretely at the end points

That is exactly what happens

 

[IDS]

That is exactly what happens

??

That's not even approximately what happens.

There is a significant length at the ends of the strands where the strand slips relative to the concrete, so that some of the tension is released, but some is transferred to the concrete. At the end of the transition zones there is sufficient compression in the concrete that force equilibrium is maintained without further transfer of stress across the interface, and the concrete and the strand have the same compressive strain, relative to the strain immediately before transfer.

You can't ignore the elastic shortening effect if you want to consider how it works. It would be like explaining why things fall if you remove whatever is supporting them, without considering gravity.


Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[Retrograde]

Actually I was wrong - I missed the fully bonded bit and was thinking of a post-tensioned system with anchorages. I should read more carefully in the future...

 

[ProgrammingPE]

When the concrete is cured, every part of the strand is positioned where it needs to be to have a constant tension. If the strand does not move at all, then it will remain in constant tension. When the tension is released from the jacks, if bond stress at the very end of the beam was capable of transferring all of the compression to the concrete at the very end, then it would, and there would be no change in the strand's position at any point. This is not possible through bond stress, though, so the strand will slip some at the ends. The tension in the strand and the compression in the concrete at the very edge of the beam will be 0, but both of these will increase linearly based on the maximum possible bond stress until the strand reaches the tension that was initially applied. The tension in the strand from the point of maximum tension to the center of the beam will be constant and every part of the strand will remain in the same position it was before the jacks were released.

(It may be easier to think of this as a strand attached to a rigid support at the midspan of the beam, which you can do because of symmetry. Then you can see that nothing changes (compression in concrete, tension in strand, and position of strand) from the support to the point of maximum tension so it does not matter that there's slipping at the ends.)

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[geopat69]

hi and thanks to all that contributed. Particularly ProgrammingPE.. your first paragraph explained it really well - so thank you.

To reiterate, I think the mention of the slip is the key!!

Upon jack release, if there is no slip(unrealistic case)...ALL the load is transferred at the discrete end points (AND there is no strand movement anywhere along the length)<- this is what i conceptually forgot!. But with minor slip, the load is "distributed: in an end zone and eventually transferred to the concrete.

 

[Ingenuity]

Keep in mind, for PRE-tensioned elements (where strands are stressed with a jack then fully 'supported' by the prestressing bed or end buttresses), how the pre-tensioning force is released (slow vs sudden) has a significant effect on the magnitude of strand end-slip.

 

[BridgeSmith]

It may be convenient (although not completely correct) to remember that the tension force in the strand is not lost, but is transferred to the concrete. So, thinking about it that way, whether it transfers the force instantaneously at the ends, or over the entire length to midspan, (neither of which is actually the case) the overall effect on the concrete is the same. Only the local effects on the concrete vary.

In reality, the strain compatibility dictates that the transfer of force to the concrete only goes to zero at midspan. Due to slipping above a certain level of force and the non-linear nature of the materials (mostly the concrete), the distribution of force transfer is also non-linear. However, the force transfer doesn't end at the end of the so-called transfer length; it just drops to a level that doesn't require special consideration to keep the concrete intact, and it's low enough to approximate that all the force has been transferred to the concrete for the purposes of modeling the stresses in the beam.

Rod Smith, P.E., The artist formerly known as HotRod10