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I have been solving problems involving pre stress concrete, i want to clarify why is the top fiber always considered as under compressive force, in my understanding the concrete would bend positively to due pre stressing and thus top fiber would be in tension and not compression. Although due to the service loads, the top fiber would then be in compression this time. If an allowable compressive stress is given, is it safe to assume that we can base on the service loads? And not on the pre stressing force?

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  • $\begingroup$ You need to draw a diagram, but a beam suspended by its ends and loaded on top will have tension below and compression above the centreline. $\endgroup$
    – Solar Mike
    Commented Feb 10 at 14:33

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The stress profile of a prestressed beam depends on the layout of the prestressing cables.

It's important to remember these cables don't just apply bending moment, but simple compression, too. Indeed, the cables themselves apply compression, it's their position relative to the central axis that defines the bending moment.

So, indeed, if you have a large beam with cables all the way at the bottom, those cables will apply uniform compression to the beam AND a bending-moment stress profile, with additional compression at the bottom and tension at the top.

The stress on the top fiber is therefore equal to:

$$\sigma_t = \dfrac{My}{I} - \dfrac{F}{A}$$

If the compressive force is sufficient, it will overwhelm the bending-moment-induced tension on the top fiber and leave the top fiber in overall compression.


It's also worth noting that it is common to decide that the top fiber must be under continuous compression (usually after including deadloads). That is, the engineer figures out a cable layout that will ensure the top fiber is under compression, even if a simpler layout would also "work" but leave the top fiber in tension.

This is chosen in order to improve the beam's service life: concrete under tension will crack. Cracks lead to oxidation of the rebar, which eventually expands, expelling the surrounding concrete, which accelerates oxidation... and eventually the beam/structure needs to be replaced/reinforced.

Meanwhile, concrete under compression doesn't crack (or well, drastically less so). Therefore, the rebar takes much longer to oxidize and the beam/structure can operate for longer. And it usually isn't too hard to find a layout which satisfies the "top fiber must be under compression" constraint, and it usually isn't meaningfully more expensive than other alternative layouts.

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