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I have a mat foundation that is 3 m thick (44 story building), I know how to design the upper layer and bottom layer but since at the top layer the reinforcement is too dense I want to make a third layer of reinforcement but my problem is I don't know how to design the third layer.

If for example in total in the top layer I need 55.8 cm2/m so I place T25@15 cm (32.8 cm2/m)in the top layer, for the remaining reinforcement area need I want to place them in a different layer just below the top layer bearing in mind that the effective depth will change so I can't just say 55.8-32.8 = 23 cm2/m and place them.

How can I calculate the remaining reinforcement needed ?

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Actually, you can just subtract the area from the top layer to calculate the subsequent layers. Obviously this is an approximation, since you're losing effective depth in the other layers, but it's a good start.

To check that the approximation is valid, calculate the center of gravity of the total steel in each face and then calculate the requisite steel area. If it is lower than your adopted value, you're fine.

So, for example, if you need 55.8 cm2/m, you can adopt one layer of $\phi20/10$ (31.42 cm2/m) and another $\phi25/20$ (24.54 cm2/m), for a total of 55.96 cm2/m.

Assuming a concrete cover of 2 cm and a distance of 3 cm between rebar faces, your CoG moves from 3 cm (2 cm cover plus half the diameter of the $\phi20$ rebar) to

$$2 + \frac{\frac{2}{2}\cdot31.42 + \left(3 + \frac{2.5}{2}\right)\cdot24.54}{55.96} = 4.425\text{ cm}$$

You can then recalculate your mat adopting the new effective depth. If the required steel area remains below 55.96 cm2/m, you're fine. If it goes above it, just repeat the process. This works for any (reasonable) number of layers.

In this particular case, where you have a mat that's three meters thick, you'll be fine: the change in the effective depth (of 1.425 cm) will be little more than a rounding error.

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  • $\begingroup$ So basically the same way that you design a beam with a double row of bars. $\endgroup$ – hazzey Jun 6 '17 at 14:26
  • $\begingroup$ @wasabi that was very helpful, I was thinking since in my case I have to make two layers of reinforcement at !! the site !! is it easier to have two layers 3 cm apart (as you stated) or do I need to make them further apart (say like 10 cm or even more) ? another question I was wondering if shrinkage reinforcement at the middle of the mat is it the same ratio need for a drop beam (skin reinforcement) ? I don't know if the shrinkage reinforcement at the middle is required by the code basically the minimum reinforcement is provided but 3 m thickness is a lot and needs shrinkage reinforcement $\endgroup$ – J.Daou Jun 6 '17 at 14:47

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