On parameters affecting the racking stiffness of timberglass walls
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Abstract
An extensive parametric numerical study was performed after completed experimental campaign of timberglass hybrid walls (TGW and TGWE). 36 timberglass models (TG) with different outer dimensions were built and analysed with a goal to capture the basic response of mechanically tested timberglass walls and to determine the racking stiffness of the calculated numerical models. Timber frame was modelled using linear beam elements with hinges in all four corners, an IGU was modelled as a multilayer shell and finally a layer of adhesive was modelled with linear and nonlinear springs, which were distributed circumferentially around the edge of IGU and connected onto a timber frame. Normal and shear stiffness coefficients for linearelastic springs were calculated, while for nonlinear springs a special series of mechanical tests on polyurethane (PU) adhesive was performed since a lack of data available in addition to the desired amount of information needed for the numerical analysis. Uniaxial tension, compression and shear tests were made to obtain the results in form of the loaddisplacement curve, which presented a direct input for nonlinear normal and shear springs of the mathematical model. For each compression and tension mechanical test three specimens were prepared and tested up to rupture, while a doublelap shear test was conducted using two specimens giving two results each. PU adhesive specimens of the first series had dimensions of 50 mm \(\times \) 50 mm and thickness of 5.0 mm. Mechanical tests were repeated for two additional thicknesses of PU adhesive, namely 7.0 mm and 9.0 mm. After completed experimental investigation on PU adhesive joint, together 108 numerical models with different external dimensions were analysed in commercial code SAP2000. Having the correct information about the stiffness of the single TG shear wall one can calculate the stiffness of the entire timberglass building built with such walls.
Keywords
Timberglass walls Hybrid structures Adhesive joint FEA Springs Linearelastic Nonlinear1 Introduction
The field of hybrid structural elements made of glass and timber are a subject of research for quite some time. In the last ten years many different types of structural elements were developed, namely timberglass beams, shear walls (Winter et al. 2010; Blyberg et al. 2014; Ber et al. 2014; Kozłowski et al. 2015; Niklisch et al. 2015) and finally lifesize timberglass buildings (Premrov et al. 2017).
1.1 Background and previous work on timberglass walls
The presented research is focused on the structural interaction between timber and glass. Some important findings from previous research on timberglass walls are used in further parametric numerical analysis. One of the most suitable materials for bonding timber and glass together is a polyurethane adhesive (PU), which is elastic enough to withstand static as well as dynamic loads (Ber et al. 2014, 2015; Štrukelj et al. 2015). A bond line made from PU adhesive has one primary function (i.e. loadbearing) and multiple positive side effects: (i) It presents a soft bedding, which prevents an insulating glass unit (IGU) from damage and (ii) air tightness of the circumferential bond line, which is mandatory in reallife construction. From previous research it is also known that only the inner two layers of the threelayer IGU have a loadbearing function, mainly because of the specific detail of installation (Ber et al. 2016), which can be seen on Fig. 1—Detail A. From our previous studies (Ber et al. 2016; Frangež et al. 2016) the results for TGWE and TGW were used. Figure 1 shows their external dimensions (length/height) which were \(240\hbox { cm} \times 240\hbox { cm}\) and \(120\hbox { cm} \times 240\hbox { cm}\). The difference between them is also in the width and thickness \((\hbox {w}_{\mathrm{a}} \times \hbox {t}_{\mathrm{a}})\) of the adhesive joint, which was 50 mm \(\times \) 5.0 mm for TGWE models and \(28\hbox { mm} \times ~5.07.0\hbox { mm}\) for TGW models, as shown on Fig. 1. Although, the first “test sample” of timberglass wall in TGW test group had the same detail of installation as TGWE models: threelayer IGU and a PU adhesive joint of 50 mm \(\times \) 5.0 mm.
Frangež et al. (2016) came to a conclusion that there is practically no difference in loadbearing capacity and racking stiffness between a threelayer and a twolayer IGU, or in their case between 50 and 28 mm wide adhesive joint, respectively. The main reason is in the specific installation detail, where an IGU is located at the edge of the timber frame where the strains in adhesive are soon exceeded. Consequently the outermost glass pane of an IGU is sheared away and racking load is transferred to remaining two glass panes. Figure 2 presents this failure mechanism, which began to show early in tensileloaded corners at approximately 15–25 kN of the horizontal racking load. However, when the racking load reached approximately 30–40 kN, which is close to a 40% of the maximum racking load reached, the outermost glass pane detachment was evident (Fig. 2b, c).

External dimensions of TG walls;

Thickness of PU adhesive.
The matrix of TG models with varying parameters: (i) height of the wall (H), (ii) width of the wall (L) and (iii) thickness of the adhesive joint (\(t_{a}\))
Height of the wall H (cm)  Thickness of the adhesive \(\hbox {t}_{\mathrm{a}}\) (mm)  Width of the wall  L (cm)  

120  140  160  180  200  220  240  260  280  
240  5.0  1(E)  2  3  4  5  6  7(E)  8  9 
7.0  10  11  12  13  14  15  16  17  18  
9.0  19  20  21  22  23  24  25  26  27  
250  5.0  28  29  30  31  32  33  34  35  36 
7.0  37  38  39  40  41  42  43  44  45  
9.0  46  47  48  49  50  51  52  53  54  
270  5.0  55  56  57  58  59  60  61  62  63 
7.0  64  65  66  67  68  69  70  71  72  
9.0  73  74  75  76  77  78  79  80  81  
290  5.0  82  83  84  85  86  87  88  89  90 
7.0  91  92  93  94  95  96  97  98  99  
9.0  100  101  102  103  104  105  106  107  108 
2 Methods
2.1 Description of the timberglass wall mathematical model
Numerical models of TG walls were built using frame elements for the timber frame and a multilayer shell for an IGU to assure the proper thickness of spacers for a gas cavity. Thus the expected load transfer from the timber frame via PU adhesive to an IGU in evenly distributed to glass panes. The phenomena of loadsharing in IGUs is in depth analysed in Bedon and Amadio (2018).
Normal and shear springs were used in the model, which were distributed circumferentially around the edge of an IGU and connected onto a timber frame. They represent an adhesive joint between timber and glass and can behave both: (i) linearelastic, as well as (ii) nonlinear. Similar equivalent springs were used by Bedon and Amadio (2016) to simulate the adhesive joint for a glasssteel connection.
The behavior of the TG wall element is thus composed from linear elastic behavior, followed by a nonlinear plastic behavior. Initially, a shear flow along the circumference of the glass is present, but when the adhesive starts yielding, a tension field and a compression diagonal are formed as it is schematically presented on Fig. 3a.
2.2 Calculation of coefficients for a linear elastic analysis

A stiffness normal to the surface \(A\,(K_{1})\) in z direction,

A stiffness collinear with a surface A and parallel to a horizontal load \(F_{h}\,(K_{2})\) in x direction and

A stiffness collinear with a surface A and orthogonal to a horizontal load \(F_{h}\,(K_{3})\) in y direction.
2.3 Uniaxial laboratory tests on polyurethane adhesive
Since relatively few data were available in addition to the desired amount of information needed for the numerical analysis, additional laboratory tests on PU adhesive were conducted. As it is impossible to assess the behavior of the chosen adhesive based on a very limited data given by manufacturers, additional experiments became a common practise of many researchers in this field (Huveners et al. 2007; Blyberg et al. 2012; Weller et al. 2013; Ber et al. 2015). The process of data collection necessary for further numerical study is described and analysed in the following sections.
In order to avoid the unfavorable material characteristics of glass and timber, and to focus only on the properties of the adhesive, a mechanical device for physical simulation of the adhesive joint was designed and built, as seen on Fig. 5. A device is composed of parts made from structural steel with the grade of S235. Using steel instead of glass and timber parts, the machine is universal and easy to clean, prepare and use repeatedly. As the cohesive fracture of the adhesive is expected, it is not relevant what kind of adherent is used in the experiment.
Three different tests on adhesive joint can be performed with the same mechanical device, namely uniaxial compression, tension and shear test. A \(50\hbox { mm} \times 50\hbox { mm} \times 20\hbox { mm}\) steel plate was used for compression and tension (Fig. 5), while for the shear test two steel plates with the same dimensions were placed vertical forming a double lap shear test setup. Therefore, a possible negative effect of eccentricity was eliminated. All models were subjected to a uniform load at a speed of 10 mm per minute. The effect of different loading rates plays an important role. However, it is expected that a higher loading rate yields an increased stiffness of the tested bond line (Blyberg et al. 2012).
2.3.1 Compression and tension test
2.3.2 Double lap shear test
2.3.3 Testing the specimens
In total three specimens were prepared for compression and three for tension test. For the double lap shear test two specimens were prepared yielding four results. All specimens were tested on Zwick Z010 universal testing machine in three different manners, namely tension, compression and pure shear. Load capacity of the machine is 10 kN. Each specimen was equipped with two laser displacement transducers on one side, and a force transducer on the other side. The entire composition was fixed into the jaws of the testing machine and the measuring instruments were connected to the measurement amplifier and computer, where we monitored two diagrams in realtime, namely time versus displacement and time versus force plot. The model was loaded up to yielding of the adhesive joint, while the measuring continued up to 50% decrease of the maximum force.
2.3.4 Results of compression, tension and shear tests and their implementation
Basic input data of chosen materials
Timber frame GL24h  Glass panel  PU adhesive  

Standard/manufacturer  EN 1194  EN 12150  Kömmerling/Ködiglaze P  
E (MPa)  \(\Vert 11600\)  \(\bot 720\)  70000  1.0 
\(\upnu \) (−)  \(\Vert 0.25\)  \(\bot 0.45\)  0.23  0.49 
G (MPa)  \(\Vert 720\)  \(\bot 35\)  0.45  1,3 
ϱ\( \,(\hbox {kg}/\hbox {m}^{3})\)  380  2500  1170  
\(\hbox {f}_{\mathrm{t}}\) (MPa)  \(\Vert 14 \)  \(\bot 0.5\)  45  2.0 
\(\hbox {f}_{\mathrm{c}}\) (MPa)  \(\Vert 14 \)  \(\bot 0.5\)  500  – 
It can be noticed that “FEA input” values of presented load versus displacement diagrams on Fig. 9 are lower than those obtained from lab tests on PU adhesive joint, because of the known fact that the actual loadbearing part of the adhesive joint is 2/3 of \(w_{a}\) (for explanation see Sect. 1.1).
2.4 Numerical parametric analysis of timberglass wall elements
A commercial code SAP2000 was used for a linearelastic as well as nonlinear analysis of TG walls. Advanced analytical techniques in SAP2000 allow for systematic large deformation analysis, Eigen and Ritz analyses based on stiffness of nonlinear cases, material nonlinear analysis with springs and a multilayered nonlinear shell element.
When preparing a numerical model in SAP2000 a frame function was used to draw a timber frame, while a multilayer shell was used for IGU. Springs are link elements that are used to elastically connect joints between elements and can be linear or nonlinear in nature.
In nonlinear analysis, the exact values from laboratory tests were used as input for nonlinear link elements in form of load versus displacement relation for compression, tension and shear (Fig. 9).
Material characteristics of timber and glass, as well as basic manufacturer’s information on polyurethane are summarized in Table 2.
The mathematical model from SAP2000 is shown on Fig. 10a. At a distance of 50 mm springs connect each node of the shell and the timber frame circumferentially. On Fig. 10b different influence area of springs can be seen, i.e. 25 mm in corners and 50 mm elsewhere around the perimeter of the bond line.
The matrix of numerical TG models with experimentally determined (E) and calculated horizontal loadbearing capacity, \(F_{{ max}}\)
Height—H (cm)  Width—L (cm)  

Horizontal loadbearing capacity—\(F_{{ max}}\) (kN)  
120  140  160  180  200  220  240  260  280  
240  23.52 (E)  33.26  43.01  52.76  62.51  72.25  83.5 (E)  91.75  101.50 
250  22.58  31.93  41.29  50.65  60.01  69.36  78.72  88.08  97.44 
270  20.91  29.56  38.23  46.89  55.57  64.22  72.89  81.56  90.22 
290  19.47  27.53  35.60  43.66  51.73  59.79  67.86  75.93  84.00 
The first logical step when testing a behaviour or response of a numerical model is to apply material data within its elastic range. A linearelastic analysis is fast and usually gives satisfying results within a linearelastic domain of the used adhesive. Therefore, coefficients for normal \((K_{1})\) and shear springs \((K_{2}=K_{3})\) were calculated and used to simulate linearelastic behaviour of PU adhesive. Values of E and G were taken from Table 2.
However, it is impossible to assess an elastic limit of the used adhesive, which is important when setting an ultimate limit state. As the behaviour of PU adhesive is not linearelastic in nature, we expect a more accurate result with nonlinear spring elements, which are defined by the stressstrain constitutive law derived from smallscale experiments. Such an assumption is correct yet does not offer the possibility to check that relative deformations of the glass panel, compared to the timber frame, are reliable and possible misleading penetrations are fully prevented. A past FE investigation of Amadio and Bedon (2016) proved that additional contact mechanisms, i.e. compressive crushing at the glass panel edges once the available glasstoframe gap is closed, have a key role for the estimation of local stress peaks, as well as on the overall deformed shape of glass layers.
3 Results and discussion
Results of the linearelastic and nonlinear parametric numerical analysis for each wall height are presented on the following pages.
Because our main interest was to obtain the response of TG numerical models, the stiffness of each one was calculated between 20 and 40% of \(F_{{ max}}\). From the set of numerical results, the racking stiffness (R) of individual TG wall is extracted and bar diagrams with summing tables are thus formed and shown on Fig. 12. Racking stiffness bar diagrams show values of R for various widths (L) of the TG model. Each of four diagrams presents results for different height (H) of a TG wall, namely 240 cm (Fig. 12a), 250 cm (Fig. 12b), 270 cm (Fig. 12c) and 290 cm (Fig. 12d). For comparison with experimentally investigated TGW and TGWE, their stiffness is given on a diagram in Fig. 12a.
While the racking stiffness values of models with 5.0 mm and 7.0 mm thick bond line are fairly close together, models with 9.0 mm thick bond line show approximately 2/3 lower values. Such results were expected after performed laboratory tests on a PU adhesive where a great difference can be seen (Fig. 9), which reflects on the global response of numerical models.
4 Conclusions
An extensive numerical study of timberglass models was performed using a commercial code SAP2000. Polyurethane adhesive, which bonds insulating glass unit and timber frame into a loadbearing composite shear wall, was modelled with linearelastic as well as nonlinear springs at a distance of 50 mm. Models were well built and simplified enough for a swift calculation, which took approximately 5.0–30 s. Comparing to FEA of timberglass walls using solid finite elements (Ber et al. 2016), where a single calculation lasted a few hours, a great progress is made allowing more calculations with less computational resources.
While for a linearelastic analysis existing manufacturer data were applied, a straightforward procedure was used to acquire a nonlinear response of the PU bond line. A universal apparatus was designed especially for testing a \(50\hbox { mm} \times 50\hbox { mm} \times t_{a}\) portion of the bond line, which is equal to an influence area of an individual spring used in a FE model. Apparatus proved to be easy to handle and it allowed for a quick change of samples. However, curing of samples, especially those 9.0 mm thick, was tough since a stable environment had to be assured by means of temperature and relative humidity. Uniform curing was ensured by raising the temperature and humidity within the permitted limits given by the manufacturer. Results of the uniaxial laboratory tests on PU show disproportionate reduction of stiffness at increased thickness of the bond line, especially between 7.0 and 9.0 mm. At first, we suspected insufficient curing of thicker samples, but after a bond line failed cohesively the interior was checked showing no signs of the latter.
Taking into account the simplicity of numerical models and the use of highly nonlinear materials such as timber and PU adhesive, presented results are satisfying. Calculated values of stiffness are in good agreement with experimental results. Overall, linearelastic analysis underestimates the response of TG walls, while nonlinear analysis overestimates it by a few percent.

Thickness of 7.0 mm presents an optimum value, while a 5.0 mm thick bond line is physically hard to perform in practise;

With 9.0 mm thick bond line models exhibit flexible behaviour, reaching serviceability limit state at early stage.
For a future work a variation of other parameters should be done, e.g. thickness of the glass pane, number of glass panes forming an IGU, etc. It would be sensible to include more adhesives with different E modulus. In this way design curves covering as many of mentioned parameters as possible could become widelyused in practise. Moreover, an effect of loadsharing in IGUs should be analysed and considered in future numerical investigations.
Notes
Acknowledgements
The investment is cofinanced by the Republic of Slovenia and the European Union under the European Regional Development Fund.
References
 Amadio, C., Bedon, C.: Effect of circumferential sealant joints and metal supporting frames on the buckling behavior of glass panels subjected to inplane shear loads. Glass Struct. Eng. (2016). https://doi.org/10.1007/s4094001500012 Google Scholar
 Bedon, C., Amadio, C.: A unified approach for the shear buckling design of structural glass walls with nonideal restrains. Am. J. Eng. Appl. Sci. (2016). https://doi.org/10.3844/ajeassp.2016 Google Scholar
 Bedon, C., Amadio, C.: Buckling analysis and design proposal for 2side supported double insulated glass units (IGUs) in compression. Eng. Struct. (2018). https://doi.org/10.1016/j.engstruct.2018.04.055 Google Scholar
 Ber, B., Premrov, M., Štrukelj, A., Kuhta, M.: Experimental investigations of timberglass composite wall panels. Constr. Build. Mater. (2014). https://doi.org/10.1016/j.conbuildmat.2014.05.044 Google Scholar
 Ber, B., Šušteršič, I., Premrov, M., Štrukelj, A., Dujič, B.: Testing of timberglass composite walls. Proc. Inst. Civ. Eng. Struct. Build. (2015). https://doi.org/10.1680/stbu.13.00105 Google Scholar
 Ber, B., Premrov, M., Štrukelj, A.: Finite element analysis of timberglass walls. Glass Struct. Eng. (2016). https://doi.org/10.1007/s4094001600154 Google Scholar
 Blyberg, L., Serrano, E., Enquist, B., Sterley, M.: Adhesive joint for structural timber/glass applications: experimental testing and evaluation methods. Int. J. Adhes. Adhes. (2012). https://doi.org/10.1016/j.ijadhadh.2012.02.008 Google Scholar
 Blyberg, L., Lang, M., Lundstedt, K., Schander, M., Serrano, E., Silfverheilm, M., Stalhandske, C.: Glass, timber and adhesive joints: innovative load bearing building components. Constr. Build. Mater. (2014). https://doi.org/10.1016/j.conbuildmat.2014.01.045 Google Scholar
 Frangež, R., Ber, B., Premrov, M.: Experimental and numerical investigations of timberglass shear walls. In: Proceedings of the World Conference on Timber Engineering, Vienna, Austria (2016)Google Scholar
 Hochhauser, W.: A contribution to the calculation and sizing of glued and embedded timberglass composite panes. Ph.D. Thesis. Vienna University of Technology, Austria (2011)Google Scholar
 Huveners, E.M.P., van Herwijnen, F., Soetens, F., Hofmeyer, H.: Mechanical shear properties of adhesives. In: Proceedings of Glass Performance Days, Tampere, Finland (2007)Google Scholar
 Huveners, E.M.P.: Circumferentially adhesive bonded glass panes for bracing steel frames in facades. Ph.D. Thesis. University of Technology Eindhoven, Netherlands (2009)Google Scholar
 Kozłowski, M., Dorn, M., Serrano, E.: Experimental testing of loadbearing timberglass composite shear walls and beams. Wood Mater. Sci. Eng. (2015). https://doi.org/10.1080/17480272.2015.1061595 Google Scholar
 Niklisch, F., Hernandez Maetschl, S., Schlehlein, M., Weller, B.: Development of loadbearing timberglass composite shear wall elements. In: Proceedings of Glass Performance Days, Tampere, Finland (2015)Google Scholar
 Premrov, M., Žegarac Leskovar, V., Mihalič, K.: Influence of the building shape on the energy performance of timberglass buildings in different climatic conditions. Energy (2016). https://doi.org/10.1016/j.energy.2015.05.027 Google Scholar
 Premrov, M., Ber, B., Štrukelj, A.: Cyclic and shakingtable tests of timberglass buildings. Int. J. Comput. Methods Exp. Meas. (2017). https://doi.org/10.2495/CMEMV5N6928939 Google Scholar
 Štrukelj, A., Ber, B., Premrov, M.: Racking resistance of timberglass elements using different types of adhesives. Constr. Build. Mater. (2015). https://doi.org/10.1016/j.conbuildmat.2015.05.112 Google Scholar
 Weller, B., Aßmus, E., Niklisch, F.: Assessment of the suitability of adhesives for loadbearing timberglass composite elements. In: Proceedings of Glass Performance Days, Tampere, Finland (2013)Google Scholar
 Winter, W., Hochhauser, W., Kreher, K.: Load bearing and stiffening timberglasscomposites (TGC). In: Proceedings of the World Conference on Timber Engineering (2010)Google Scholar