Role of secondary components in the numerical analysis and in-plane seismic performance assessment of glass curtain walls

3.1. Strategy for refined or simplified models

The numerical investigation was carried out in ABAQUS [7] and SAP2000 [8].

As also discussed in [6], the refined model in ABAQUS/Standard (MREF) consisted of three-dimensional solid brick elements (C3D8R type), which were used to reproduce the nominal geometry of primary and secondary façade components. For the purpose of present study, 1/4th of the experimental sample schematized in Fig. 2(a) was taken into account, with appropriate boundaries. Through the modelling phase, a special attention was given to the description of basic façade components (including the realistic reproduction of IGUs [9, 10], pressure plates, frame detailing, etc.), as well as to their possible mechanical interactions under in-plane seismic loads. To this aim, surface-to-surface contacts (with penalty + “hard” normal options) were introduced along all relevant interfaces. An example of model detailing is shown in Fig. 3.

Mesh size was defined to avoid distortion in façade elements, especially its flexible components affected by local deformations under the imposed displacement path. The FE system corresponding to 1/4th of façade consisted of ≈431,000 brick elements and 1.510,000 DOFs. Based on experimental methods described in [3], the typical simulation was defined as a displacement-controlled, Dynamic Implicit step with imposed in-plane deformations (45 mm of maximum displacement, corresponding to ≈1/175 the façade height, in a time interval of 45 seconds).

Fig. 3MREF model (ABAQUS): cross-section of a) glass-to-mullion and b) glass-to-transom interaction. Figures reproduced from [6] with permission

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The geometrically simplified model (MSIMP) was described in SAP2000, and inspired by strategic modelling steps discussed in [3] for the same façade prototype. The typical simulation consisted of nonlinear Direct-Integration time-history analysis, with the same strain rate of MREF (1 mm /sec). Differing from MREF, key features in MSIMP can be summarized as follows [6]:

1) Monolithic 2D shell elements to describe IGUs (with total thickness corresponding to the sum of IGU glass layers), thus disregarding 2-ply laminated sections, cavity, edge spacer connections, pressure plates, etc.

2) 1D frame elements for mullions and transoms (with equivalent geometrical and mechanical properties).

3) a set of “Gap” and “Wen” link joints (Fig. 4(a)), which were used to reproduce the mechanical interaction of IGUs with frame members, especially in the region of setting blocks, and possible contact with frame – along the edges – after clearance closure.

Due to its high computational efficiency, the MSIMP assembly described the whole geometry of the experimental prototype, see Fig. 4(b). The chosen mesh size resulted in ≈450 frame elements, ≈1200 shell elements and ≈1600 joints.

Fig. 4MSIMP model (SAP2000): a) detail of “Gap” and “Wen” links and b) front view. Figures reproduced from [6] with permission

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3.2. Material properties

Input material properties for primary and secondary MREF components were calibrated as in Table 1 [6]. To note that a linear elastic constitutive law was taken into account for most of materials, through the parametric study. In this regard, the post-processing stage was carefully focused on the analysis of stress peaks in all façade elements, to ensure the correctness (for the purpose of present study) of linear elastic material characterization. For aluminium, an elastic-plastic material behaviour (with hardening) was used, with $f_y=$ 120 MPa the yielding stress, $f_u=$ 160 MPa the ultimate stress and $e_{pl}=$ 0.08 the corresponding elongation. For MSIMP, glass and aluminium were successively described as linear elastic, with input from Table 1.

4.1. Load-displacement response

The post-processing analysis was primarily focused on the elaboration of global and local structural behaviours for the façade under in-plane lateral deformations. For both MREF and MSIMP models, this stage included a first comparison of load-displacement response towards the experiment in [3], but also a more accurate analysis of local phenomena, such as (i) stress distribution in components, as a function of the imposed displacement; (ii) analysis of contact forces and reactions in setting blocks; (iii) sensitivity studies (for MREF) in terms of material properties and friction for contacts; (iv) effect of boundaries (for MREF), with respect to the full-size setup in Fig. 1(a). Fig. 5, in this regard, shows the numerical response for the façade subjected to monotonic in-plane displacement (1 mm/sec), as a function of the corresponding reaction force, compared to the experiment in [3]. The numerical results, especially for MREF, have good agreement with the test, for most of the recorded path. The final stiffness / resistance overestimation in MREF derives, at around 40 mm, from local indentation of IGUs in mullions. The MSIMP model, on the other side, tends to underestimate the expected resistance, especially in range of 5-30 mm. Such a global result confirms the key role of an appropriate calibration for model components and for their mechanical interactions, and thus the need of refined computational strategies.

Fig. 5Load-displacement response of MREF (ABAQUS) and MSIMP (SAP2000) models, compared to the reference experiment. Figure adapted from [6] with permission

In Fig. 5, it can also be seen that MREF and MSIMP curves have local discrepancies in the whole load-displacement path, which suggest further investigations. Their variable scatter is maximized especially for (a) the initial phase (i.e., elastic stiffness) and (b) the progressive / ultimate deformation stage, where the MSIMP assembly seems respectively (a) more rigid and (b) less stiff / resistant than MREF. In both cases, the progressive arrangement of IGU panels within the frame members, when subjected to increasing in-plane lateral deformations, has major effects on the façade performance, and still depends on the interaction of glass panels with secondary components.

4.2. Local performance assessment

The analysis of local phenomena further highlights possible consequences for structural safety considerations. Among others, stress peaks in IGUs are of primary interest to verify the possible fracture of glass. Fig. 6, in this regard, shows the typical compressive stress distribution in glass elements at the imposed in-plane lateral displacement of 45 mm.

As it can be noted in Fig. 6(a) for MREF, glass elements approach a peak of ≈30-32 MPa in compression, in the region of setting blocks, with a typical diagonal propagation of stresses which can be also observed in the schematic model of Fig. 1 and agrees with the discussion of experiments reported in [3]. The tensile stress peak was indeed measured at the glass edges, and quantified in ≈38 MPa.

For MSIMP, see Fig. 6(b), the local rotation and translation of glass elements was found mostly uniform in the height and width of the examined full-size façade system, and this evidence further confirms the use of equivalent boundaries for the MREF model.

Most importantly, the compressive stress in glass in Fig. 6(b), at the same imposed displacement of 45 mm, is still located in the region of setting blocks, but hardly achieves a maximum of ≈8-9 MPa, as a major consequence that the mechanical interaction of IGUs with frame members is not sufficiently captured by the simplified numerical assumptions. In this regard, it is important to note that such an intrinsic limit of simplified numerical procedures was also emphasized in [3], where the compression peaks for glass elements close to setting blocks were quantified in ≈5 MPa, at the imposed displacement of 45 mm.

Fig. 6Analysis of compressive stress peaks in the region of setting blocks (legend values in MPa), for MREF (ABAQUS) and MSIMP (SAP2000) numerical models, at an imposed in-plane lateral displacement of 45 mm. Figures reproduced from [6] with permission

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Certainly, it is important to note that – for present simulations – the above stress peaks were found remarkably low, compared to the reference characteristic strength of glass (which is equal to 45 MPa in tension and ≈10 times higher, that is ≈450 MPa in compression, for annealed glass). Also, lack of glass fracture was experimentally observed at the imposed displacement of 45 mm, for the reference test discussed in [3], and this aspect further justifies – for the present numerical investigation – the use of linear elastic material properties according to Table 1.

In any case, the herein discussed numerical investigations highlight that careful consideration should be taken into account in the use of approximate modelling strategies for the structural performance assessment of similar systems, especially in terms of glass-to-frame mechanical interactions. Overall, the MREF model manifested compressive stress peaks in the order of ≈4-5 times higher than MSIMP, which is obviously computationally efficient but not sufficiently accurate and thus realistic for conservative design considerations. In this sense, further efforts will be spent for the optimization of refined numerical strategies, towards the definition / calibration of enhanced / efficient approaches for the description of secondary components in façades.