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# ACI Code EQ. 11-9 Shear Strength from Precast members

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## ACI Code EQ. 11-9 Shear Strength from Precast members

(OP)
First post, but I have been a lurker here for a while. I enjoy viewing the posts.

My question involves the equation for calculating Vc of a prestressed section.
A typical example found in a textbook or PCI handbook might be a 200mm hollowcore plank with a 65mm topping slab. To calculate the shear capacity of the concrete the example would use the equations in ACI 318-08: 11-10, 11-11, and 11-12. Alternatively the simplified equation 11-9 can be used. In the textbook example the section is considered prestressed and depth, dp, is calculated from the extreme compression fiber to the centroid of the prestressed tendons. In this example the tendons are 45mm up from the bottom so dp=220mm. The example will use the equation 11-9 and Vc is calculated assuming the moments and shears are known along the beam in question, and we also abide by the stipulations that Vc not be higher than xxxx and not be taken greater than yyyy. If this is a prestressed concrete equation why does it include the non prestressed topping in the calculation of shear? I would say that the topping is fully in compression after the concrete has cured due to dead load and the overall new section is in compression due to the prestressing.

So my real question is if you added another topping slab onto the example above lets say another 200mm, so now we have 200mm hollow core beam+65mm topping+200 additional topping,(assume surface is roughened) h = 465, dp = 420mm can we still utilize equation 11-9 to calculate Vc. I want to say it does not apply because part of that upper topping slab is not going to be in compression, but tension and it is certainly not precompressed.

Thanks for reading and any feedback is certainly appreciated

### RE: ACI Code EQ. 11-9 Shear Strength from Precast members

First of all the shear provisions are some of the least precise provisions in the code and are very much open to debate. The hope was that they were at least conservative.
More recent research shows that they are not always conservative, particularly with deep unreinforced slabs, and hollowcore on flexible supports.

The prestress shear provisions attempt to account for the effect the prestress has on the shear strength at the point of cracking. For flexural shear failure, Vci, the prestress is accounted for at the tensile extremity of the section where the flexural crack would start. For web shear failure, Vcw, the prestress is accounted for at the centroid (approximately) of the section where an inclined web crack would start. The compression at the top of the section at ultimate failure (for positive bending) is a given whether the section is prestressed or not. In your example of the additional topping, the centroid would now lie in the topping and it would be prudent to consider the section unprestressed. Using the prestressed provisions but taking the web prestress as zero would get you back to the maximum unprestressed provisions (i.e. 3.5 sqrt(f'c)bd).

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