PSI - Issue 44

Ernesto Grande et al. / Procedia Structural Integrity 44 (2023) 582–589 Grande et al. / Structural Integrity Procedia 00 (2022) 000–000

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characterizing the experimental response of beam-column joints: joint first cracking condition ( τ 1 - γ 1 ); pre-peak phase ( τ 2 - γ 2 ); attainment of the peak strength ( τ 3 - γ 3 ); softening phase with the residual strength ( τ 4 - γ 4 ). Beside the validation of the backbone constitutive law carried out by monotonic nonlinear static analyses performed on a set of 15 experimental tests collected from the literature, the Authors proposed a new formula for estimating the maximum shear strength ( τ 3 = τ max ). This formula was calibrated on the basis of a multivariate linear regression analysis, considering the concrete compressive strength (f c ) and the beam reinforcement index (BI) as the main parameters affecting the shear strength of the exterior unreinforced joints. Then, according to the approach proposed by Grande et al. (2021a), the shear strength corresponding to the joint first cracking ( τ 1 ) is computed according to the formula proposed by Uzumeri (1977), while the pre-peak strength ( τ 2 ) and the residual strength ( τ 4 ) are assumed equal to 0.85 τ max and 0.3 τ max respectively, according to most of the proposals presented in the literature (De Risi et al. 2016, Sharma et al. 2011, Shin and LaFave 2004). A sensitivity analysis was carried out for evaluating the corresponding values of the shear strains, which are affected by a greater uncertainty. The four couples (τ j - γ j ) representing the parameters of the backbone curve are summarized in Table 1. Moreover, the modelling approach was further improved by setting the parameters governing the strength and stiffness degradation and the hysteretic behavior of the joints. However, the cyclic behavior of the exterior joints is not discussed in this paper, since the seismic assessment of the case study frame is carried out only through nonlinear static analyses.

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Figure 1. (a) scheme of the “scissors model”; (b) multilinear law τ - γ (or M- θ ) assigned to the joint shear spring.

Table 1. Shear stress and strain parameters of the proposed constitutive law. backbone point Shear stress,τ j Shear strain, γ j 1 τ 1 = 0.29 � f c � 1 + 0.29 σ j 1 = 0.001087 2 τ 2 = 0.85 ∙ τ 2 = 0.003273 3 τ = 0.569 ∙ ( ) 0 . 445 ∙ ( ) 0 . 783 3 = 0.008733 4 τ 4 = 0.3 ∙ τ 4 = 0.048820

3. Numerical modelling of the RC frame 3.1 Building description To properly assess the calibrated model in the seismic performance of poorly-detailed RC frame structures, a case study is here selected from literature (Del Vecchio et al., 2016) and reported in Figure 2.