Numerical modelling of single component tests

This section validates the numerical model of cladding connections for horizontal concrete panels by quasi-static cyclic and dynamic single component tests (presented in Chapter 3).

The scheme of a simple model is shown in Figure 5.9. Each connection is represented by a zeroLength Element, whose response in the horizontal direction is described with a combination of material models presented in Section 5.1. To model the vertical supports, two ENT (Elastic-No Tension) materials were added that ensure the stability of the model and are used to simulate lifting of the panel. Note that the lifting of the panel and the rotations are relatively small and not significant for the overall response because the cladding connections and panel response is predominantly translational (please see discussion in Sections 3.3.5 and 4.2.4). The rigid panel was modelled with elasticBeamColumn elements.

Figure 5.9: Schematic presentation of the numerical model for the single connection tests: (a) top connections, (b) complete fastening system and (c) ENT material model

Slika 5.9: Shematski prikaz numeričnega modela testov na fasadnih stikih: (a) zgornji stiki, (b) celoten sistem stikov, (c) ENT materialni model

The material parameters as recommended in Tables 5.1 and 5.2 were used for the simulation of the single component test. Because the position of the connections during single connection tests was almost ideal in the centre of the available space in the panel, the connection gaps were the same in both directions:

𝑑_{𝑔𝑎𝑝,𝑡𝑜𝑝}= ±4 𝑐𝑚 (5.6)

𝑑_{𝑔𝑎𝑝,𝑏𝑜𝑡𝑡𝑜𝑚}= ±4.5 𝑐𝑚 (5.7)

The friction force at the top connection was gradually reduced after each test due to the deformations and loosening of the bolt (see also Section 3.3.5). The values used for numerical modelling are provided in Table 5.3. The force–displacement relationships of the numerical models used for the simulation of the complete fastening system are schematically presented in Figure 5.10.

Table 5.3: Friction forces in the top connections Preglednica 5.3: Sila trenja v zgornjih stikih

Test Rfr,top [kN] Test Rfr,top [kN]

Tc1 5 Cc1 5

Tc2 5 Cc2 6

Td1 5 - 5 - 5 - 3 - 0 Cd1 8 - 6 - 4 - 3 - 2

Td2 8 - 6 - 0 Cd2 8 - 5 - 3 - 1 - 1

Td3 8 - 8 - 3 Td4 8 - 5 - 2

Figure 5.10: Schematic envelopes of numerical models: (a) only the top connections, (b) the complete fastening system during the cyclic test and (c) the complete fastening system during the dynamic test Slika 5.10: Shematski prikaz ovojnic numeričnega modela: (a) samo zgornji stiki, (b) celoten s istem stikov med ciklično obtežbo in (c) celoten system stikov med dinamično obtežbo

The experimental and numerical hysteretic responses of the connections are compared in Figures 5.11–5.14. Figures 5.11 and 5.12 present the hysteretic responses of the top connections under the quasi-static cyclic (denoted with ‘Tc’) and dynamic loading (‘Td’), respectively. Figures 5.13 and 5.14 present the response of the complete system under quasi-static cyclic (‘Cc’) and dynamic loading (‘Cd’), respectively. The hysteretic responses that correspond to all the test intensities are shown on each plot. A satisfying match between the experimental and numerical results was achieved with the proposed numerical models. To better evaluate the calibration, some graphs of the accumulated hysteretic energy during the dynamic tests are shown in Figure 5.15.

The numerical models describe the behaviour of the connections with quite high accuracy, although there are some differences in the experimental and numerical hysteretic responses. During the experiments, a small increase in the force during the sliding phase was observed, which was more obvious during the test of the top connections (Figures 5.11 and 5.12). However, this does not have an important influence on the overall response of the connections. As already mentioned, the friction forces activated in the analysed connections are relatively small compared to the forces in the main precast structure (i.e. columns) during the seismic excitation. Thus, this increase of the force was not simulated with the model, which assumes constant friction during the sliding phase.

In general, the match of experimental and numerical envelopes is quite good. The stiffness at the impacts of the top connection is, on average, well estimated. In some cases, it is overestimated for impacts in the positive direction and underestimated for impacts in the negative direction (see, for example, tests Td2 and Td4 in Figure 5.12).

For the simulation of cyclic tests, the impact stiffness of 3·10³ kN/m was used for the bottom connection. This stiffness is somewhat underestimated, which is also shown with the response of connections in positive directions during the test Cc2 (Figure 5.13 b). However, it is possible to

accurately describe the response with higher impact stiffness of 1.5·10⁴ kN/m at the bottom connections (see the simulation of dynamic tests in Figure 5.14). Graphs in Figure 5.15 show a good match of the dissipated energy for the tests of top connections and the complete fastening system.

Figure 5.11: The experimental (black) and numerical (red) hysteretic responses of the top connections during the quasi-static cyclic tests: (a) test Tc1 and (b) test Tc2

Slika 5.11: Ekperimentalni (črna) in numerični (rdeča) histerezni odziv zgornjih stikov med kvazi -statičnimi cikličnimi testi: (a) test Tc1 and (b) test Tc2

Figure 5.12: The experimental (black) and numerical (red) hysteretic responses of the top connections during the dynamic tests: (a) test Td1, (b) test Td2, (c) test Td3 and (d) test Td4

Slika 5.12: Ekperimentalni (črna) in numerični (rdeča) histerezni odziv zgornjih stikov med dinamičnimi testi: (a) test Td1, (b) test Td2, (c) test Td3 and (d) test Td4

Figure 5.13: The experimental (black) and numerical (red) hysteretic responses of the complete fastening system during the quasi-static cyclic tests: (a) test Cc1 and (b) test Cc2

Slika 5.13: Ekperimentalni (črna) in numerični (rdeča) histerezni odziv sistema stikov med kvazi -statičnimi cikličnimi testi: (a) test Cc1 and (b) test Cc2

Figure 5.14: The experimental (black) and numerical (red) hysteretic responses of the complete fastening system connections during the dynamic tests: (a) test Cd1 and (b) test Cd2

Slika 5.14: Ekperimentalni (črna) in numerični (rdeča) histerezni odziv sistema stikov med dinamičnimi testi:

(a) test Cd1 and (b) test Cd2

Figure 5.15: A comparison of the accumulated hysteretic energy during the experiments (black) and

numerical (red) simulation of dynamic tests: (a) Td1, (b) Td2 and (c) Cd1 and (d) Cd2

Slika 5.15: Primerjava akumulirane histrezne energije med dinamičnimi testi (črna) in numerično simulacijo (rdeča): (a) Td1, (b) Td2, (c) Cd1 in (d) Cd2