Validation of the equivalent model of the structure and the calculation scheme

This section validates the numerical model and procedure used to analyse precast structures with horizontal panels with two typical examples. A structure with a tributary mass of 60 t at the top of the column and a height of 9 m (denoted with m60H9) was analysed. Results are compared with the three-dimensional models of the complete structure. Two ground plan configurations were evaluated, corresponding to the ratio factors k = 2 and k = 1.3 (see Figure 6.15).

Figure 6.15: Precast structure m60H9 with: (a) ratio factor k = 2 and (b) ratio factor k = 1.3 Slika 6.15: Montažna stavba m60H9: (a) s faktorjem k = 2 in (b) s faktorjem k = 1.3

The nonlinear model of columns was defined as presented in Section 6.2.1, with the following parameters: Φcr = 1.2·10^-3/m, Φy = 8.4·10^-3/m, Φu = 165·10^-3/m, Mcr = 232 kNm, My = 836 kNm and Mu = 885 kNm. Cladding connections were modelled as described in Section 6.2.2. All the panels were connected to columns by centrally positioned connections (gaps in the connections were the same at both sides of the connection). The Elastic model was used to simulate the response of silicone sealant because of its simplicity. Structures were subjected to ground motion record number 14 (see Appendix A) at ag = 0.675 g.

The results of equivalent and complete structure models are compared in the following sections. As presented, internal forces and deformations obtained with the equivalent model are a good match with the full three-dimensional model.

Structure m60H9 with ratio k = 2

This section presents the results of the numerical analysis of structure m60H9 with the ratio factor k = 2 (Figure 6.16). The structure has 12 columns; four columns in the analysed direction and three columns in the transverse direction. Altogether, 30 panels (six in the ground plan and five along the column height) are mounted at the two external sides of the structure.

Figure 6.16: Precast structure m60H9 with ratio factor k = 2 Slika 6.16: Montažna stavba m60H9 s faktorjem k = 2

Figures 6.17-6.22 compare the internal forces and deformations obtained by different models. As presented, results obtained with equivalent models are in relatively good agreement with the results of the full three-dimensional model.

Figure 6.17 presents the maximum displacements of the column along its height and displacement response history at the top of the column. As shown, the maximum displacements at the top of the column are practically the same.

Figure 6.18 presents the maximum slips and forces that occur in connections along the structure’s height. Figures 6.19 and 6.20 compare the displacement and force response histories for cladding connections of the panel at the top of the structure. The match of the results is ver y good.

Figure 6.17: Displacements of the column (m60H9, k = 2): (a) displacement envelope along the column height and (b) displacement response history at the top of the column

Slika 6.17: Pomiki stebra (m60H9, k = 2): (a) ovojnica pomikov po višini stebra in (b) časovni potek pomikov na vrhu stebra

Figure 6.18: Maximum response of the connections (m60H9, k = 2): (a) slips and (b) forces in connections Slika 6.18: Maksimalni odziv stikov (m60H9, k = 2): (a) zdrsi in (b) sile v stikih

Figure 6.19: Displacement response histories at top and bottom connections of the top panel (m60H9, k = 2) Slika 6.19: Časovni potek zdrsov v zgornjem in spodnjem stiku vrhnjega panela (m60H9, k = 2)

Figure 6.20: Force response histories at top and bottom connections of the top panel (m60H9, k = 2) Slika 6.20: Časovni potek sil v zgornjem in spodnjem stiku vrhnjega panela (m60H9, k = 2)

Figure 6.21 presents the maximum shear force, moment and curvature along the column height. The response of the column at its base is compared in Figure 6.22, where the moment–curvature hysteretic response and response histories are presented. There is only a small discrepancy in the results, which is acceptable given the simplification of the model.

Figure 6.21: Maximum (a) shear forces, (b) moments and (c) curvature along the column height (m60H9, k = 2)

Slika 6.21: Maksimalna (a) strižna sila, (b) momenti in (c) ukrivljenost po višini stebra (m60H9, k = 2)

Figure 6.22: Response of the column at its base (m60H9, k = 2): (a) moment–curvature hysteretic response, (b) moment response history and (c) curvature response history

Slika 6.22: Odziv stebra ob vpetju (m60H9, k = 2): (a) histerezni odziv moment–ukrivljenost, (b) časovni potek momentov in (c) časovni potek ukrivljenosti

Structure m60H9 with ratio k = 1.3

The results of numerical analyses of structure m60H9 with the ratio factor k = 1.3 (Figure 6.23) are presented in this section. The structure has eight columns; four columns in the analysed direction and two columns in the transverse direction. As for the previous case, 30 panels (six in the ground plan and five along the column height) are mounted at two external sides of the structure.

Figure 6.23: Precast structure m60H9 with ratio factor k = 1.3 Slika 6.23: Montažna stavba m60H9 s faktorjem k = 1.3

Figure 6.24 presents the maximum displacements of the column along its height and displacement response history at the top of the column. Results obtained with the equivalent model are in good agreement with the results of the full three-dimensional model.

Figure 6.25-6.27 compare the response of the connections. Maximum slips and forces along the structure’s height and response histories for the connections of the panel at the top are shown. The match of these results is also very good.

Figure 6.24: Displacements of the column (m60H9, k = 1.3): (a) displacement envelope along the column height and (b) displacement response history at the top of the column

Slika 6.24: Pomiki stebra (m60H9, k = 1.3): (a) ovojnica pomikov po višini stebra in (b) časovni potek pomikov na vrhu stebra

Figure 6.25: Maximum response of the connections (m60H9, k = 1.3): (a) slips and (b) forces in connections Slika 6.25: Maksimalni odziv stikov (m60H9, k = 1.3): (a) zdrsi in (b) sile v stikih

Figure 6.26: Displacement response histories at top and bottom connections of the top panel (m60H9, k = 1.3) Slika 6.26: Časovni potek zdrsov v zgornjem in spodnjem stiku vrhnjega panela (m60H9, k = 1.3)

Figure 6.27: Force response histories at top and bottom connections of the top panel (m60H9, k = 1.3) Slika 6.27: Časovni potek sil v zgornjem in spodnjem stiku vrhnjega panela (m60H9, k = 1.3)

Figure 6.28 presents the maximum shear force, moment and curvature along the column height, respectively. The response of the column at its base is compared in Figure 6.29, where the moment–

curvature hysteretic response and response histories are presented. In general, the match of all the results is very good.

Figure 6.28: Maximum (a) shear forces, (b) moments and (c) curvatures along the column height (m60H9, k = 1.3)

Slika 6.28: Maksimalna (a) strižna sila, (b) momenti in (c) ukrivljenost po višini stebra (m60H9, k = 1.3)

Figure 6.29: Response of the column at its base (m60H9, k = 1.3): (a) moment–curvature hysteretic response, (b) moment response history and (c) curvature response history

Slika 6.29: Odziv stebra ob vpetju (m60H9, k = 1.3): (a) histerezni odziv moment–ukrivljenost, (b) časovni potek momentov in (c) časovni potek ukrivljenosti