PSI - Issue 44
Fabio Di Trapani et al. / Procedia Structural Integrity 44 (2023) 496–503 Di Trapani et al. / Structural Integrity Procedia 00 (2022) 000–000
502
7
w and t being the width and the thickness of the equivalent strut. Substituting Eq. (4) in Eq. (3) and Eq. 3 in Eq. (2) one obtains:
⋅ w t t l N sin ⋅ ⋅
⋅ α θ µ θ ⋅ l sin
⋅ µ θ
α θ
(5)
= V N cos d ,inf
⋅ ⋅ t l N cos sin α θ =
N cos
−
−
=
−
µσ θ
n
w
Providing the additional shear demand as a function of the current axial force on the equivalent strut and of the contact length α l. In order to validate the reliability of Eq. (1) combined with Eq. (5), the aforementioned specimens were modelled and analyzed according to the macro-modelling approach proposed by Di Trapani et al. 2018. In Fig. 9, result of the application of the proposed analytical approach are illustrated. In particular, the macro-model predictions of the total shear demand at the ends of the columns are compared with those from the micro-model, showing a noticeable consistency despite the simple approach. As regards the contact length it was assumed α l =0.30 l and 0.4 l for l/h =1, and α l =0.25 l and 0.3 l for l/h =1.5 for the windward and leeward columns respectively.
N
w
n σ
t
t
cos N θ
inf V
θ
sin n σ θ
N
V frame V infill V tot
v τ µσ =
θ
T
l α
(a)
(b)
Fig. 8. (a) Decomposition of shear demand at the end of the columns of an infilled frame; (b) Force transfer due to frame-infill interaction.
120
120
10 20 30 40 50 60 70 80 90 100 Shear force [kN]
10 20 30 40 50 60 70 80 90 100 Shear force [kN]
S1A - Leeward column
S1A - Windward column
S1B - Leeward column
Micro-model Macro-model Macro-model + Eq. (5) S1B - Windward column
100
100
Micro-model Macro-model Macro-model + Eq. (5)
80
80
60
60
Micro-model Macro-model Macro-model + Eq. (5)
Micro-model Macro-model Macro-model + Eq (5)
40
40
Shear force [kN]
Shear force [kN]
20
20
0 5 10 15 20 25 30 35 40 Displacement [mm] 0
0 5 10 15 20 25 30 35 40 Displacement [mm] 0
0 5 10 15 20 25 30 35 40 Displacement [mm] 0
0 5 10 15 20 25 30 35 40 Displacement [mm] 0
(a)
(b)
140
140
100 120 140 160
100 120 140 160
S1C - Leeward column
S1C - Windward column
Spec. 5 - Leeward column
Spec. 5 - Windward column
120
120
100
100
80
80
20 40 60 80
20 40 60 80
Micro-model Macro-model Macro-model + Eq. (5)
60
60
Micro-model Macro-model Macro-model + Eq. (5)
Micro-model Macro-model Macro-model+Eq. (5)
Micro-model Macro-model Macro-model+Eq. (5)
40
40
Shear force [kN]
Shear force [kN]
Shear force [kN]
Shear force [kN]
20
20
0 5 10 15 20 25 30 35 40 Displacement [mm] 0
0 5 10 15 20 25 30 35 40 Displacement [mm] 0
0 5 10 15 20 25 30 35 40 Displacement [mm] 0
0 5 10 15 20 25 30 35 40 Displacement [mm] 0
(c)
(d)
140
140
10 20 30 40 50 60 70 80 90 100 Shear force [kN]
10 20 30 40 50 60 70 80 90 100 Shear force [kN]
Spec. 8 - Leeward column
Spec. 8 - Windward column
Spec. 5 - Windward column
Spec. 5 - Leeward column
120
120
100
100
80
80
Micro-model Macro-model Macro-model+Eq. (5)
Micro-model Macro-model Macro-model+Eq. (5)
60
60
Micro-model Macro-model Macro-model+Eq. (5)
Micro-model Macro-model Macro-model+Eq. (5)
40
40
Shear force [kN]
Shear force [kN]
20
20
0 5 10 15 20 25 30 35 40 Displacement [mm] 0
0 5 10 15 20 25 30 35 40 Displacement [mm] 0
0 5 10 15 20 25 30 35 40 Displacement [mm] 0
0 5 10 15 20 25 30 35 40 Displacement [mm] 0
(e)
(f)
Fig. 9. Comparison between macro-model and micro-model predictions of total shear demand at the windward and leeward column ends for Cavaleri & Di Trapani (2014) specimens: (a) S1A; (b) S1B; (c) S1C and Mehrabi & Shing (1996) specimens: (d) 5; (e) 8; (f) 9.
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