x2-

f NEd + Asfyd -£cu2EsAs ^

x-

f £cu2EsAsd' ^

= 0

f ßl bfcd )

f ß1 bfcd )

The equation, written in synthesis x2-( **) x-( ***) = 0 has the solution r**\2 , /* *

The a's stress is now known and adds up to as' = Es£cu2 f 1- —

and the moment resistance about the centroidal level is:

MRd = Asfyd (h - d') + AsOs'(h - d') + Pix b fcd (h - P2x)

As both reinforcements are yielded, Ned is exclusively supported by concrete. The equilibrium equation is:

Ned = NRd = pib x fcd , so that the depth of the neutral axis is:

With the above-determined x value, the moment resistance is: MRd=Asfyd(d-d')+p1x b fcd (0,5h- P2x)

The equation of equilibrium to shifting is:

As the reinforcement As is in elastic field, as = EsSs e ss is given by (6.2) Replacing and developing it results:

' ^cu2EsAsd"

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