As well known, the stress intensity factor Kj is connected with the strain energy release rate Qj through the following expression:
e, - % m in which E is the Young's Modulus of concrete.
Furthermore, by means of an energy balance approach, one can demonstrate the equivalence between Qj and the total potential energy W released during the formation of a unitary increment of the crack surface A:
By applying Betti's theorem (from which \PM — ^ M P ) a n d Clapeyron's theorem, the total potential energy of the beam element takes the form:
W = - \ \ p P P 2 + \ P M P M - l - \ M M M 2 (9)
Finally, the expressions of the localized compliances are achieved through the integration of eq.(8) and by equating the result to the right-hand side of eq.(9):
Hence, by making use of a proper congruence condition, one can obtain the unknown reaction P in the different situations of loading and unloading, ac companied by crack propagation, steel yielding and/or slippage between steel and concrete.