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Due to a question asked by one of our clients regarding the punching shear verifications in CEDRUS, we thought it would be interesting to write this article in order to give some clarifications that might be rather useful for the users.

The question is about the effects that the introduction of prestressing in CEDRUS may have on the punching shear verification of a slab. To explain it, we will look at two fundamental effects that we can consider in the punching shear verifications when there is prestressing: the favourable effect of precompression and the reduction of the punching load due to the vertical load on the supports due to the prestressing.

**- Favourable effect of precompression:**

CEDRUS does not directly take into account the term of the contribution of precompression in the increase of punching shear strength. This term is the famous **+0.1σcp**, which is added (summing) to the equation used to obtain VRd (value of the dimensioning of the punching shear strength). What it does have is the possibility of introducing that effect in the dialog box of the punching object, giving an additional strength value **VRd+:**

This factor, which will correct the value of the strength, is available for any punching shear calculation model that we select.

The typical application is the correction by compressive stresses caused by the existence of prestressing tendons. Entering this value, which has to be calculated manually, CEDRUS will include it in the calculation of the punching shear strength. If we look at, for example, the function for the obtention of VRd, which is given in the CEDRUS manual, in case of selecting a model as ‘Critical perimeter (standard)’, we see how we have the term VRd+ summing.

**- Redistribution of the reactions on the support (hyperstatic effect)**

A redistribution of the reactions on the supports of the slab will occur because of the existence of prestressing:

PRESTRESSING:

ULS WITHOUT PRESTRESSING:

ULS WITH PRESTRESSING (ULS without PS + 0.9PS):

438.23+0.9*(-69.972)=375.26 -> **OK**

**- Vertical load on the support zone due to the hyperstatic effect of prestressing**

If the prestressing load, with the deviation forces, is included in the specification of the surroundings for the punching shear check, the influence of the load to support by punching will be taken into account automatically and it will not be necessary to apply any correction due to this phenomenon. However, if, apart from the effect of the vertical load due to the prestressing we also want to consider the decompression in the punching shear strength calculation, we will have to introduce a value of **VRd+.**

Let’s look at an example:

On a slab **without prestressing**, the punching shear strength of its interior pillar is:

We can see that there is a reaction on the column of 754.36 kN and a load on the punching shear area of -37.48 kN, which gives a punching load of (754.36-37.48)*1.15=824.41kN, meeting the verification requirements since it is lower than the value in comparison, 884.87 kN.

**If we now introduce a tendon** that goes just above the column and we consider a value VRd+ (10 kN for example):

We can observe the two effects mentioned before. On the one hand the increase of VRd of 10 kN, going through a punching shear strength of 884.87 and 894.87 kN and, on the other, the variation of the values of the reaction and the load over the punching area, resulting in this case in a punching load of (758.48-46.85)*1.15=818.37kN, value which is lower than the one we obtained without prestressing.

Another way of understanding the favourable effect would be realising that the reaction, when introducing the prestress, increases 4.12 kN but the load inside the critical perimeter, which we have to deduct from the reaction because it will not affect the punching shear since it descends directly through the support, increases 9.37 kN (more than the reaction), thus making the effect favourable.

It is also easy to understand by visualising the equivalent prestressing forces, which are some linear positive and negative forces that ‘displace the slab up and down’. This equivalent forces have greater values closer to the supports, that is why it is common for them to stay inside the critical perimeter and to deduct more than what the reaction has increased.

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