PSI - Issue 44

Vanni Nicoletti et al. / Procedia Structural Integrity 44 (2023) 371–377

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Vanni Nicoletti et al. / Structural Integrity Procedia 00 (2022) 000 – 000

bottom rebars of the beam. Alternatively, the Approach 2 consists in verifying the following equations, for interior and exterior joints, respectively: ℎ ≥ ( 1 + 2 ) (1 − 0.8 ) (7a) ℎ ≥ 2 (1 − 0.8 ) (7b) Differently from the concrete compressive bearing capacity verification, in Eq.s 7a ν d is calculated considering the axial force ( N Ed ) acting on the column above the joint, whilst for Eq. 7b on the column below the joint. In Eq.s 7, f ywd and f yd represent the design value of the yield strength of the hoops and beam rebars, respectively. The NTC18 prescribes very similar B-CJ verifications, with minor differences that do not change the verification outcomes. For example, the overstrength factor γ Rd adopted to calculate the shear demand is assumed equal to 1.2 and 1.1 for high (CDA) and medium (CDB) ductility classes, respectively, while the EC8 leaves the designer free to decide its value (not lower than 1.2). Moreover, for the concrete compressive bearing capacity (Eq. 2), the coefficient η is differently calculated for exterior and interior joints, adopting the following equation: = (1 − 250 ) (8) where α j is equal to 0.6 and 0.48 for interior and exterior joints, respectively. Nevertheless, the calculation of the concrete compressive bearing capacity does not change between the two codes because the EC8 foresees the reduction of the 20% of the resistance in case of exterior joints, which is equal to the reduction of α j in the calculation of the η coefficient provided by the NTC18 for the same type of joint. The NTC18 and, in particular, its explanatory Circular (Circ. 19) add an important concept that is not reported in the EC8. Indeed, the Italian code suggests using the same approach (Approach 1 or 2) for confinement verifications of the B-CJ in the two orthogonal directions since the adoption of both approaches for the same B-CJ seems to be incompatible (e.g. the onset of cracking in one of the two orthogonal joint directions is not compatible with the hypothesis of intact node in the other one). 3. Nomograms for the B-CJ assessment The nomograms are simple practical and graphical tools for supporting the B-CJ design of RC structures even from the earliest stages of the structural design process. They are charts representing graphically the code verifications and they essentially constitute a strategy that provides the characteristics of the B-CJs, in terms of size and shear reinforcement amount, necessary to satisfy the verifications required by EC8. To construct a nomogram, verification expressions proposed by EC8 are considered in this work, and suitably manipulated to generate resisting domains in the σ - τ stress plane. At first, the normal ( σ Ed ) and shear ( τ Ed ) design stresses are defined as: = (9a) = ℎ ℎ (9b) Then, the three expressions provided by the EC8 for the B-CJ verifications (Eq. 2, Eq. 6 and Eq.s. 7) are re-written in terms of stresses as follows, considering the limit case in which the demand matches the capacity: = √1 − | | (10)