PSI - Issue 64

Maria Teresa De Risi et al. / Procedia Structural Integrity 64 (2024) 959–967 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

961

3

Table 1. Shear resistance of beam/column elements according to European and American codes. V R,EC8 =V R,BIS = γ 1 el [V N +k(V c +V w )] V N = h 2 − L x s min(N; 0.55A c f c ) V c = 0.16max(0.5; 100ρ tot ) [1 − 0.16min (5; L s h )]√f c A c V w = A sw f yw s 0.9d V R,VIT =min(V Rc ;V Rs )=min(α c ν̅f c bd ∙ tanθ +1 cotθ ; A sw f yw s 0.9d cotθ) V R,ASCE =V R,SEZ =k(V c +V w ) DM 2018 EC 8 - 2005

(1)

(2)

(3)

(4)

(5)

(6)

V c =( 0.5√f c L s d √1+ 0.5√ N f

c A c )0.8A c

(7)

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2.2. Investigated beam-column joint shear capacity models

According to EN 1998-3 (2005), the shear capacity of the joints is evaluated as for ex-novo buildings, limiting the shear demand V j (eq. 8). Moreover, an additional safety check is required to limit the maximum tensile principal stress, (eq. 9). The same approach is prescribed by the Italian Code for not fully confined joints, except than the adopted principal stress limitations (eqs. 10-11). European and Italian codes in Table 2 have been reformulated in terms of joint shear stress τ j =V j /A j , similarly to American prescription (see eq. 12). The latter defines a shear capacity as a function of a γ coefficient, which depends on the joint configuration (i.e., interior, exterior, or knee joint), presence/absence of transverse beams, and presence/absence of conforming transverse reinforcement. It should be noted that European prescriptions show a capacity variation with axial load, in contrast with American guidelines.

Table 2 Shear resistance of beam/column joints according to European and American codes.

j c   − →  −   j j c f 1 V f 1 A 

v

(8)

f

c

2

j     V A

(9)

A f

j     − →  + + ct j ct f 1 f

sh y

v

EC 8 - 2005

b h f

f

f

j jw ct

c

ct

2

2

   

j V          + j   

N N



(10)

0.5f  → 

0.5f 1

 = +

−

v

jC

c

j

c

2A 2A A

0.5f

j

j

c

2

2

   

j V          + j   

N N



( ) c

1/2

0.3 f

0.3 f

1

 = −



→ 

+

v

(11)

jT

c

j

( ) c

DM 2018

1/2

2A 2A A

0.3 f

j

j

( ) 1/2

j c 0.083 f   

(12)

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3. Case-study buildings Two case-study buildings have been selected: 2- and 4- story RC residential buildings designed according to technical regulations in force in Italy until 1970 (Royal Decree, R.D. 1939), to withstand only gravity loads (GLD). They have the same floor area, are symmetric in both perpendicular directions (X and Y), and both rely on a Moment Resisting Frame (MRF) system consisting of parallel 2D resisting frames in the longitudinal (X) direction only (see Figure 1a), with no beams connecting columns in the transverse (Y) direction (apart from along the exterior perimeter). The floors are 20 cm thick, and the inter-story height is 3 meters (Figure 3b). The cross-sectional dimensions and reinforcement details are based on a simulated design (Verderame et al., 2010; De Risi et al., 2022) in tune with the Italian code in force during the construction period (R.D., 1939), considering a maximum allowable stress of 5 or 6