Analysed parameters and summary of performed analyses

The selection of parameters for the analysis was made with regard to real precast structures that can be found in practice. The following parameters were varied and analysed:

- interaction between adjacent panels, that is, presence of the silicone sealant between panels, - construction imperfections, that is, different initial positions of the connections,

- connection of bottom panels to the foundation,

- and different structural configurations, that is, different ratios between the number of all columns of the structure and the number of panels in the ground plan in the analysed direction.

Interaction of adjacent panels

Slots and ribs typically connect adjacent panels, and joints between the panels are afterwards filled with silicone strips. Usually, the silicone sealant is placed at both (external and internal) sides of the panels with a width-to-depth ratio of ts:bs = 2:1 (Figure 2.8 b).

The silicone connection causes a certain interaction between adjacent panels, so its influence on the response of panels and precast columns was analysed. The study considered silicone with a width of 30 mm and a depth of 15 mm, and a total length of silicone at both sides of the panel ls was evaluated.

Construction imperfections

The connections present vital parts of precast structures and might have an important influence on the response of the overall structure. Because of imperfections during the casting and mounting of structures, different initial positions of the connections occur regularly in construction practice.

Initial positions of bolts at the top and cantilevers at the bottom connections are important. If the connections are centrally mounted, larger relative displacements between the column and panel are possible before activating significant forces. In this situation, the panel can slide almost freely (friction is very small) up to the relative displacements of 4 cm and 4.5 cm at the top and bottom connections, respectively. However, if the bolt and cantilever are shifted to the edge of the box at the top and opening at the bottom of the panel, relatively high forces activate in the connections even at small relative displacements between the column and panel in that direction. The resistance of the top and bottom connections is 55 kN and 179 kN, respectively. A top-connection displacement capacity of 3.5 cm after the gap in that connection is depleted was used in the analyses.

To account for different construction imperfections, different positions of the bolt (at the top connection) and cantilever (at the bottom connection) within the connection gap were considered:

a centrally mounted bolt and cantilever equidistant from the opening edges in the panel (denoted with M-middle), and an extremely eccentrically positioned bolt and cantilever within the opening in the panel (L-left and R-right) with no gap available on one side.

The position of the top and bottom connections can be different for different panels in the structure.

Within the parametric study, only three extreme position combinations (see Figure 6.3) were analysed:

- middle position of both top and bottom connections (MM),

- left position of both the top and bottom connections (LL),

- left position of top connection and right position of the bottom connection (LR).

It was assumed that all the top connections are mounted the same way and that all the bottom connections are mounted the same way, respectively.

Figure 6.3: Different positions of (a) top and (b) bottom connections Slika 6.3: Različne pozicije (a) zgornjih in (b) spodnjih stikov

Connection of bottom panels to the foundation

Different versions of the connection between the bottom panel and the foundation can be found in practice. The bottom panel is often attached to the foundation with steel anchors hammered into the façade panel and inserted into pre-drilled holes in the foundation (Figure 2.8 a). Afterwards, the connection is grouted by mortar. Under these conditions, the bottom panel is considered fixed to the foundation, which caused concern about the possible occurrence of the short-column effect.

For this reason, two possible connections of the bottom panel to the foundation were considered.

The panel was either fully fixed to the foundation (F-fixed) or connected to the column as all the other panels (C-connection). In the latter case, the connection between the panel and foundation is provided only by the silicone sealant.

Ground plan configuration

Precast structures of different ground plan configurations can be found in practice. Floor plans of regular shape can be square or rectangular, with the same or a different number of columns in two orthogonal directions. The number of internal columns may also vary from structure to structure.

Therefore, depending on the floor plan configurations, structures have different ratios between the number of columns and the number of cladding panels attached to the external columns, which can also be different in transversal and longitudinal directions. A higher number of panels compared to the number of columns might have a larger influence on the response of the precast system.

A k factor was introduced to account for different ground plan configurations of the structure and investigate the influence of the ratio between the number of columns and the number of panels/connections on the structures’ seismic response. The coefficient presents the ratio between the number of all columns within the structure ncol and the number of panels in ground plan npan in the direction parallel to excitation (see Equation 6.3). Figure 6.4 presents an example for k factor equal to 2 (two columns per panel, as marked with the dotted line in Figure 6.4 a).

Equation 6.3 shows the calculation for one direction; however, both directions were examined in the parametric study, that is, all expected ratios in real structures.

𝑘_𝑥= ^{𝑛𝑐𝑜𝑙}

𝑛_𝑝𝑎𝑛=^{𝑛𝑐𝑜𝑙,𝑥∙𝑛𝑐𝑜𝑙,𝑦}

2∙𝑛_{𝑠𝑝𝑎𝑛,𝑥} =^{𝑛𝑐𝑜𝑙,𝑥∙𝑛𝑐𝑜𝑙,𝑦}

2∙(𝑛_{𝑐𝑜𝑙,𝑥}−1) (6.3)

Figure 6.4: Typical example of a precast structure with ratio factor k = 2: (a) distribution of connections influence on the global response, (b) corner, inner and outer column of the structure

Slika 6.4: Krakteristični primer kontrukcije s faktorjem razmerja med stebri in paneli k = 2: (a) porazdelitev vpliva stikov na globalni odziv konstruckije, (b) vogalni, notranji in zunanji steber konstruckije

Some examples of different ground plan configurations and corresponding k factors are shown in Figure 6.5. Values of k are expected to be between 1 and 10 in real structures and implicitly take into account the ground plan configuration of the structure. A higher value of the k factor means a

larger number of columns compared to the number of panels/connections. For example, a structure wider in the direction perpendicular to excitation with many inner columns and fewer perimeter columns with panels has a larger k factor, whereas a structure longer in the direction of excitation has a lower k factor.

Figure 6.5: Different plans of the precast structures and corresponding k factors in the longitudinal direction Slika 6.5: Različni tlorisi montažnih hal s pripadajočim faktorjem k v vzdolžni smeri

Summary of performed analyses

The parametric analyses were performed in several sets. Each set consisted of dynamic analyses of 15 one-storey RC precast structures subjected to 30 selected ground motions at three different intensities. Within each set of numerical analyses, the parameters were carefully selected and modified, as described in the following points. The test matrix is presented in Figure 6.6 and summarised in Table 3.3.

1. The first set of parametric analyses considered the following properties of precast structures: centrally positioned connections (MM), no silicone sealant (N), bottom panel fixed to the foundation (F) and ratio factor equal to 2.

2. Because the joints between adjacent panels are commonly filled with silicone, two sets of analyses were performed, taking into account the interaction between the panels. Both proposed models of silicone sealant were analysed and compared: Pinching (P) and Elastic (E). Other parameters were not changed.

The results of the first and second sets of analyses were compared to examine the influence of interaction between panels on the response.

3. Next, two sets of analyses were performed to investigate the influence of construction imperfections on the response. The presence of silicone sealant represents a realistic situation in practice. Therefore, the following parameters were selected: eccentrically

positioned connections (LL and LR), silicone-sealed joints (P), bottom panel fixed to the foundation (F) and ratio factor equal to 2.

To analyse the influence of construction imperfections on the response of panels and main precast structure, the results of the third set of analyses were compared (both 3.1 and 3.2 in Figure 6.6) with the results of the second set (2.1 in Figure 6.6). Therefore, in all analyses, joints were sealed with silicone (P), the bottom panel was fixed to the foundation (F), and the ratio factor was equal to 2, while the position of connections was varied (MM, LL and LR).

4. For the fourth set of analyses, the central position of connection was assumed (MM), silicone sealant was modelled (P), and a ratio factor of 2 was considered. However, the bottom panel was not fixed to the foundation but instead connected to the column as all the other panels (C). Results of these analyses were compared to the second set with a different connection of the bottom panel to the foundation.

5. The following analyses were performed to analyse the effect of geometry. Ten sets of analyses were performed to cover the complete range of ratio factors between the number of columns and the number of panels expected in real structures. The ratio factor k varied from 1 to 10 with a step of 1, while all the other parameters were fixed: the central position of the connections (MM), silicone-sealed joints (P) and bottom panel fixed to the foundation (F). Results were compared to investigate the influence of ground plan configuration on the structure’s response.

Figure 6.6: Test matrix of analyses performed within the parametric study Slika 6.6: Matrika analiz izvedenih v okviru parametrične študije

Table 6.3: Matrix of performed analyses Preglednica 6.3: MAtrika narejenih analiz No. of analyses 2700 2700 4050 2700 13500 Legend:MM: central position of connection, LL / LR: eccentrically positioned connections, N: no silicone modelled, P: Pinching silicone model, E: Elastic silicone model, F: bottom panel fixed to foundation, C: bottom panel connected to column

No. of intensities 3 3 3 3 3

No. of accelerograms 30 30 30 30 30

No. of structures 15 15 15 15 15

Ratio factor 2 2 2 2 1 : 1 : 10

Connection of bottom panel to foundation F F F F / C F

Silicone model N / P P / E P P P

Position of the connections MM MM MM / LL / LR MM MM

Parameter analysed Interaction of panels Silicone models Construction imperfections Connection of bottom panel to foundation Ground plan configuration