PSI - Issue 44

Vanni Nicoletti et al. / Procedia Structural Integrity 44 (2023) 371–377 Vanni Nicoletti et al. / Structural Integrity Procedia 00 (2022) 000 – 000

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2. EC8 verification formulas and differences with the Italian technical code The RC B-CJ verifications are treated in EN1998-1-1, which focuses on the earthquake resistant design of framed structures. These verifications are based on the principle that the demand acting on the B-CJ must be lower, or at least equal, to the joint capacity. The demand, expressed in terms of horizontal shear acting on the joint, is expressed by the following formulas proposed in the code: ℎ = ( 1 + 2 ) − (1a) ℎ = 1 − (1b) With reference to plane frames, Eq. 1a is suitable for interior joints, namely when two beams frame into the joint, while Eq.1b must be adopted for exterior joints, i.e., when only one beam frame into the joint. In Eqs.1, A s1 and A s2 represent the area of the reinforcement bars at the top and bottom of beams, respectively, V C is the seismic shear force acting in the column above the joint, and γ Rd is the overstrength factor, assumed not less than 1.2. As for the joint capacity, two main resisting mechanisms can be accounted for: the concrete compressive bearing capacity and the joint confinement provided by the steel hoops. Starting from the former, the EC8 prescribes that the where ν d is the normalized design axial force in the column above the joint, calculated as: = ⁄ (3) while η is a coefficient accounting for the concrete cracked in shear in which f ck must be expressed in MPa: = 0.6 (1 − 250 ) (4) For exterior joints, the right-hand-side of Eq.2 must be reduced of 20%. In Eq. 2 the product b j h jc is the horizontal effective joint area, and b j and h jc are the effective joint width and the distance between the extreme layers of column reinforcement, respectively. In detail, b j is calculated as follows: = { ; ( + 0.5ℎ )} if > (5a) = { ; ( + 0.5ℎ )} if < (5b) In Eq.s 5, b c is the gross cross-sectional dimension of the column normal to the longitudinal axis of the beams, h c is the gross cross-sectional dimension of the column parallel to the longitudinal axis of the beams, and b w is the beam web width. Considering the joint confinement, two different and alternative approaches to perform the verifications are proposed by EC8: the Approach 1, which foresees to limit the maximum diagonal tensile stress within the joint core avoiding the concrete cracking, and the Approach 2, which assumes that the joint shear capacity is entirely entrusted by hoops since the concrete is considered already cracked. The Approach 1 is verified if: ℎ ℎ ≥ ( ℎ ℎ ) 2 + − (6) The left-hand-side of Eq. 6 represents the resistant contribution of the hoops within the joint ( A sh f ywd ), which must be greater (or at least equal) to the shear acting on the joint ( V jhd ) reduced by the concrete tensile resistance ( f ctd ). In Eq. 6 the joint lateral area is expressed by the product b j h jw , where h jw is the clear distance between the top and the joint integrity is satisfied if: ℎ ≤ √1 − ℎ (2)