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As I know, a thinner mat may be possible by providing a nominal amount of vertical reinforcement as compared to a mat without vertical reinforcement, the vertical reinforcement is used to resist punching shear at d/2 from columns or shear walls at foundation level.

Now my question is to what distance (or offset) from the column to stop placing these vertical reinforcement is it at a distance d/2 ?

Please if possible provide reference in ACI Code.

critical section outside slab shear reinforcement

What i need is the critical section outside slab shear reinforcement from which distance from the column ?

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For a more complete discussion see: ACI 421.1R-08 - Guide to Shear Reinforcement for Slabs.

But in principle you need to continue to provide punching shear reinforcement until the shear capacity of the slab is sufficient to prevent punching shear at that perimeter.

From ACI 421.1R-08 this means:

You need to check at $d/2$ from the column face to determine if shear reinforcement is required. If it is then you need to continue to check perimeters at a distance of $\alpha d$ from the column face until you find that (in SI units) $$\frac{\nu_u}{\phi} \leq \frac{0.17\lambda\sqrt{{f'}_c}}{2}$$

Then the outermost perimeter of shear reinforcement must be at least $\alpha d - \frac{d}{2}$ from the column face.

$\nu_u$ is maximum shear stress due to factored forces. $\phi$ is the strength reduction factor = 0.75. ${f'}_c$ is the specified concrete compressive strength. $\lambda$ is the modification factor for the reduced mechanical properties of lightweight concrete (=1 for normal weight concrete). $d$ is the effective depth of slab.

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