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Prestressed slab with tendons at the centroid - flexural capacity
2

Prestressed slab with tendons at the centroid - flexural capacity

Prestressed slab with tendons at the centroid - flexural capacity

(OP)
I'm designing a slab with prestressing strands running through the centre with no additional reinforcing. Common sense dictates the max moment capacity occurs when stress at the extreme tension fiber is zero, and the strain diagram is a triangle (P/A=M/S). However, per the code, you would end up with a rectangular stress distribution, leaving negligible moment capacity. Can anyone point in the right direction, as clearly the slab has some capacity?

RE: Prestressed slab with tendons at the centroid - flexural capacity

or whatever your code permits as concrete tensile capacity.

Dik

RE: Prestressed slab with tendons at the centroid - flexural capacity

Quote (canwesteng)

Common sense dictates the max moment capacity occurs when stress at the extreme tension fiber is zero

No, you are confusing elastic stresses with ultimate flexural moment capacity. Such a calc would be called the 'decompression moment' - nothing to do with ultimate moment capacity.

Go back to the typical rectangular stress block, your strain diagram assuming εc=0.002, check your strain in the strand (account for all the strains), assume a neutral axis location, sum the internal forces to be equal (so iterate once or twice), then sum forces (about say top fiber) to calc moment capacity.

Any pesky secondary moments (hyperstatic) to include?

RE: Prestressed slab with tendons at the centroid - flexural capacity

Ingenuity, εc=0.003 correct? Not 0.002?

RE: Prestressed slab with tendons at the centroid - flexural capacity

(OP)
It's 0.0035 for my code, the exact number is irrelevant in any case. There are no secondary moments occurring from restraint at supports if that's what is meant by hyperstatic. The problem is, with the strand at the centre of the section, and compressive stress block effectively at the centre of the section, the decompression moment is much larger than the moment otherwise if I take moments about the centroid of the section. Are you suggesting I take moments about the netural axis, which in this case is the extreme fiber?

RE: Prestressed slab with tendons at the centroid - flexural capacity

Quote (canwesteng)

The problem is, with the strand at the centre of the section, and compressive stress block effectively at the centre of the section

I don't think so. Under ultimate flexural conditions, your compression block is still rectangular and up top as usual. This is similar to Ingenuity's comment I believe.

Quote (canwesteng)

Are you suggesting I take moments about the netural axis, which in this case is the extreme fiber?

Like with a concrete column, I think that the natural place to take moments is about the centroid of the compression block with the compression block including the pre-compression.

With your prestress at the centroid of the cross section, and presumably no mild reinforcement, the thing to keep a close eye on is flexural crack widths at the service load level.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

RE: Prestressed slab with tendons at the centroid - flexural capacity

(OP)
Ok, I guess the conventional approach is the only way to go. I just got a bit muddied in my own thoughts. Thanks for the help all

RE: Prestressed slab with tendons at the centroid - flexural capacity

Quote (sticksandtriagles)

Ingenuity, εc=0.003 correct? Not 0.002?

Sorry, should have been 0.003 (or what ever the Canucks are doing these days!).

In my defense, my reply was too early in the morning...and before the mandatory coffee smile

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