PSI - Issue 47

Luciano Feo et al. / Procedia Structural Integrity 47 (2023) 800–811 Author name / Structural Integrity Procedia 00 (2019) 000–000

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Figure1 . Kinematic of Cracked-Hinge model. Adapted from Martinelli et al. (2020).

3.2 Constitutive laws According to the Fib Bulletin No. 42 (2008), when the concrete is in compression (Figure 2), the stress-strain relationship can be evaluated as follows: � � �� ∙ ∙ � � 1 �� � 2 � ∙ (8) where �� (MPa) is the concrete compressive strength, while the plasticity number, , and the quantity are calculated as: � � �� � � � �� �� � (9) � � �� (10) �� � 1.60 ∙ � �� 10 � � . �� (11) � � 22000 ∙ � �� 10 � � . � (12) In addition, � (MPa) and �� (MPa) are the elastic modulus in compression and the secant modulus from the origin to the peak compressive stress, respectively. Instead, based on the fictitious crack model proposed by Hillerborg (1991), the tensile behavior of the concrete can be evaluated as follows: until the section is uncracked, a bilinear stress-strain relationship is assumed as in Eq.13; when the tensile strain of the k-th strip, � , reaches a conventional value of 0.00015 , the residual tensile stress, �� , depend on the crack opening displacement, , as in Eq.14: