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In prestressed concrete, we add a tensioned steel cable at the bottom half of the beam to balance out the tensile forces resulting from the applied load. But before the load is added, doesn't the beam deflect upwards and cause tensile cracks now at the top of the beam (situation 5 in the above picture)? Let's say we tension the cable and cast the concrete and then release the cables into compressive stress. I don't see how in practice we can immediately apply the designed load to balance the situation before the beam bows upwards and cracks at the top.

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Note that the pretension $P$, besides causing a bending moment $(M=P\cdot e$, where $e$ is the eccentricity) to counteract the expected loads, also inflicts a normal (compressive) force ($N=-P$).

Usually, a stress analysis needs to be made for the different loading setups to confirm that tensile stresses either do not occur or exceed a certain value. This can be achieved by applying the following equation: $$\sigma_x=\frac{N_x}{A}+\frac{M_y}{I_y}z$$ The equation uses the right-hand-rule, where the $x$-Axis points from left ro right, $y$ into the plain and $z$ upwards. Furthermore, tensile forces/stresses are positive.

So, for no tensile stress to occur, the compressive stress caused by applying the compressive force $P$ must exceed the tensile stress caused by the moment $P\cdot e$.

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Because there are rebars designed for this exact task on the top layer of the beam rebars.

These are in addition to other rebars required for other loads, such as negative moment rebars at the supports. the codes allow certain bars to share loads.

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  • $\begingroup$ So there are rebars? But doesn't that defeat the whole purpose of using prestressed concrete? Doesn't the concrete crack around those rebars just like in normal reinforced concrete and therefore make the prestressing process useless? $\endgroup$ – S. Rotos Jan 18 at 18:16
  • $\begingroup$ A-those rebars have no prestressed tension. So they give somewhat to accommodate the concrete. B- The way prestress works it squeezes the lower part of the beam shifting the neutral axis down. effectively putting a much larger part of the beam's concrete section to carry compression versus before, they used to just sit there. because they where below neutral axis. $\endgroup$ – kamran Jan 18 at 18:47
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For starters, what makes you think the concrete doesn't crack at the top?

Let's assume for a second that it does crack. Well, if we were dealing with a pure concrete beam, that'd be a big problem since the crack would propagate down the height of the beam until it falls apart.

Thankfully, prestressed concrete beams aren't just concrete and a prestressing cable. They are also given some light longitudinal rebar (usually just the minimum required by the relevant code on each face). So if the beam starts to crack, it'll activate the rebar which will impede the beam's collapse.

And is this a big deal? Well, no, not really. After all, the beam will soon be under the expected load, at which point the downwards forces will counteract the camber, the top face will go under compression and those cracks will all seal up. No harm, no foul.

So, even if the concrete were to crack a bit on the top, it's honestly not the end of the world (assuming all safety requirements are met, of course).

But does the concrete crack?

Well, not necessarily. And I'd say it usually doesn't.

The reason has already been mentioned in @Andrew's answer: prestress doesn't just generate a bending moment, but also a compressive force. So the prestress doesn't simply generate the exact reverse of the expected bending moment so that they cancel out: it generates the reverse of a fraction of the bending moment and then leaves the rest to be canceled out by simple compression.

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