Yp is just a parameter meant to represent the yield line mechanism. That way, no matter the bolt arrangement, you can always write the end plate yielding limit state capacity as:
Phi*Mnp = Phi*Fyp*Yp*tp^2
The Yp values vary based on the actual bolt arrangement and geometry of the plate. But, this allows the equation for the failure mode to look the same.
Just a way of simplifying the concept so that it can be more easily applied by a practicing engineer (as opposed to a PhD researcher).
thank you could I ask you another question in this formula (Phi*Mnp = Phi*Fyp*Yp*tp^2)>>I know that yield strength of the plate multiply by plastic section modulus but where (4) had gone? (plastic section modulus =(1)*tp^2/4)
We're not using this equation to calculate the plastic section modulus of the plate. Rather, we are using this equation to calculate the moment capacity of the overall connection.
In the derivation of the the derivation of the Yp values you do start with a plastic moment of plate per unit width (Fyp*tp^2)/4. But, they are eventually all wrapped up in that Yp value.
If you're interested in the original derivation of those yield lines there is a PhD thesis by Emmet Sumner titled "Unified Design of Extended End-Plate Moment Connections Subject to Cyclic Loading" which forms the basis for much of those AISC design guides. I'm sure there are other references as well, but that one seemed to be the most detailed to me as far as the derivation of the yield lines.
