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Glass Structures & Engineering

, Volume 4, Issue 1, pp 69–82 | Cite as

On parameters affecting the racking stiffness of timber-glass walls

  • Boštjan BerEmail author
  • Gregor Finžgar
  • Miroslav Premrov
  • Andrej Štrukelj
SI: Challenging Glass paper
  • 100 Downloads

Abstract

An extensive parametric numerical study was performed after completed experimental campaign of timber-glass hybrid walls (TGW and TGWE). 36 timber-glass models (TG) with different outer dimensions were built and analysed with a goal to capture the basic response of mechanically tested timber-glass 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 linear-elastic 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 load-displacement 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 double-lap 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 timber-glass building built with such walls.

Keywords

Timber-glass walls Hybrid structures Adhesive joint FEA Springs Linear-elastic Nonlinear 

1 Introduction

Due to the growing awareness of people regarding a healthy lifestyle, sustainability and energy efficiency, contemporary buildings have to offer all of mentioned attributes as well as high level of comfort. Timber together with glass comprise all the desired requirements. But why combining those two rather different materials? Glass for transparency and timber due to the alive structure of the building. However, transparency and openness of the building is conditioned with the increased amount of glass surfaces and optimized amount of timber.
Fig. 1

Outer dimensions of mechanically tested timber-glass walls with a detail of the horizontal cross-section

When dealing with timber-glass hybrid structures some important design aspects are to be taken into account: (i) structural design, (ii) proper detailing and (iii) building physics; the aim of presented paper is to describe the first two design aspects. The latter associated with appropriate shape and orientation of the building together with an optimal proportion of the glazed envelope to gain heat from solar radiation is in-depth analysed and well described by Premrov et al. (2016).
Fig. 2

TGWE during a mechanical racking test (a) with a detailed bottom left corner, where a glass pane detachment can be observed (b, c)

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 timber-glass 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 life-size timber-glass buildings (Premrov et al. 2017).

1.1 Background and previous work on timber-glass walls

The presented research is focused on the structural interaction between timber and glass. Some important findings from previous research on timber-glass 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. load-bearing) 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 real-life construction. From previous research it is also known that only the inner two layers of the three-layer IGU have a load-bearing function, mainly because of the specific detail of installation (Ber et al. 2016), which can be seen on Fig. 1Detail 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 \(28\hbox { mm} \times ~5.0-7.0\hbox { mm}\) for TGW models, as shown on Fig. 1. Although, the first “test sample” of timber-glass wall in TGW test group had the same detail of installation as TGWE models: three-layer 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 load-bearing capacity and racking stiffness between a three-layer and a two-layer 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 tensile-loaded 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).

The parametric numerical analysis is based on the above mentioned findings and limitations. The main aim of the presented research is to determine the stiffness of the TG walls while varying two basic parameters:
  • External dimensions of TG walls;

  • Thickness of PU adhesive.

First, a group of 240 cm high models was expanded to different widths and numerical models of TG walls were calibrated with experimentally investigated TGW and TGWE. Further, three additional groups with commonly used heights were added. However, the expected result of the research is to find the correlation between the geometry of a TG wall and its racking stiffness in form of a function. The summary table of numerically investigated timber-glass models is shown in Table 1.
Table 1

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

Experimentally investigated models are marked with (E)

2 Methods

2.1 Description of the timber-glass 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 load-sharing 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) linear-elastic, as well as (ii) nonlinear. Similar equivalent springs were used by Bedon and Amadio (2016) to simulate the adhesive joint for a glass-steel 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.

Since numerical models with volume finite elements were proven to be quite time consuming and thus inappropriate for a large element problem, numerical models with springs were used in our parametric analysis. Similar spring models can be found in Huveners (2009) and Hochhauser (2011), while the principle of the mathematical model is shown on Fig. 3b.
Fig. 3

a Response of a TG wall subjected to horizontal racking load and b spring model of a timber-glass wall proposed by Kreuzinger (Hochhauser 2011)

2.2 Calculation of coefficients for a linear elastic analysis

Figure 4a represents a shear deformation of adhesive joint. When subjected to a force \(F_{h}\), the joint deforms at the angle \(\Theta \). The deviation from the starting position is \(\Delta x\), while A represents the base surface.
Fig. 4

An infinitesimal piece of adhesive joint subjected to a horizontal load \(F_{h}\) (a) and geometric parameters of adhesive joint connecting IGU and a timber frame (b)

The shear modulus G is defined as the ratio between the shear stress and the specific deformation:
$$\begin{aligned} G=\frac{\tau _{xy}}{\varepsilon _{xy}} \end{aligned}$$
(1)
wherein the shear stress and the specific deformation in x direction are defined by:
$$\begin{aligned} \tau _{xy}= & {} \frac{F}{A} \end{aligned}$$
(2)
$$\begin{aligned} \varepsilon _{xy}= & {} \frac{\varDelta x}{l} \end{aligned}$$
(3)
If the latter equations are combined, we get:
$$\begin{aligned} G=\frac{\tau _{xy}}{\varepsilon _{xy}}=\frac{\frac{F}{A}}{\frac{\varDelta x}{l}}=\frac{F\cdot l}{A\cdot \Delta x} \end{aligned}$$
(4)
The shear spring stiffness can be now calculated as:
$$\begin{aligned} K_2= & {} \frac{F}{\Delta x}=\frac{G\cdot A}{l} \end{aligned}$$
(5)
$$\begin{aligned} K_2= & {} \frac{G_a \cdot A_a }{t_a }=\frac{G_a \cdot (w_a \cdot l_a )}{t_a}=K_3 \end{aligned}$$
(6)
where \(l_{a}\) represents the unit length and is therefore 1,0 mm, \(w_{a}\) represents the width of the adhesive and \(t_{a}\) designates the thickness of the adhesive layer, as seen on Fig. 4b. While a shear deformation in y direction is physically possible, a \(K_{3}\) shear component was also taken into account.
Fig. 5

Mechanical device for uniaxial shear test (left) and compression/tension test (right)

Thus, the normal spring stiffness is obtained by the same procedure, except that the normal stress acting in z direction is used instead of the shear stress, and the shear modulus, \(G_{a}\) is replaced by the elastic modulus, \(E_{a}\).
$$\begin{aligned}&E=\frac{\sigma _{xy} }{\varepsilon _{xy}} \end{aligned}$$
(7)
$$\begin{aligned}&K_1 =\frac{E_a \cdot A_a }{t_a }=\frac{E_a \cdot (w_a \cdot l_a )}{t_a} \end{aligned}$$
(8)
The adhesive joint possess three linear stiffnesses in three-dimensional space:
  • 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.

As calculated values of \(K_{2}\) and \(K_{3}\) are the same, only directions are perpendicular, we will assume \(K_{2}=K_{3}\). Two coefficients, namely \(K_{1}\) and \(K_{2}\) are therefore used for linear-elastic analysis, while for a nonlinear analysis we had to collect the results from laboratory tests.

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

The setup for compression and tension test is a composition of several steel parts connected by screws. The load-bearing part is represented by three parallel ribs \(6,0\hbox { mm} \times 50\hbox { mm}\), which simulates an edge of the IGU, as seen on Fig. 6a, b. The base of the device, representing IGU, is a \(50\hbox { mm} \times 50\hbox { mm} \times 20\hbox { mm}\) steel plate with two grooves \(16\hbox { mm} \times 1.5\hbox { mm}\). Grooves represent spacers of the IGU which do not have a load bearing function in real life. Therefore, when performing a physical test, the groove is covered with a self-adhesive tape acting as a separation layer (Fig. 6c).
Fig. 6

Outer edge of the insulating glass unit (a) and preparation of specimens for the compression/tension uniaxial test (b, c)

2.3.2 Double lap shear test

For a double lap shear test a more complex composition was used made of several steel plates and connected with screws. A base steel plate with dimensions of \(108\hbox { mm} \times 50\hbox { mm} \times 16\hbox { mm}\) has two \(16\hbox { mm} \times 1.5\hbox { mm}\) grooves on both sides. Thus, the model has double lap shear adhesive joint yielding two results from a single shear test. The model is assembled with PU and treated with excessive humidification at room temperature \(23~^{\circ }\hbox {C}\). The preparation of the shear test model is shown on Fig. 7.
Fig. 7

Multiple stages of preparing a specimen for the uniaxial double lap shear test: a applying the first layer PU adhesive, b installation of the steel plate which simulates an IGU and c applying the second layer of PU adhesive and closing with an outer steel plate

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 real-time, 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

The experimental analysis was performed to observe the behaviour of PU adhesive joint in three situations, i.e. compression, tension, and shear, as it is shown on Fig. 8. The situation simulates the actual behaviour of load-bearing IGU in a timber frame. The measured characteristic values served for determination of adhesive joint properties in the numerical model.
Fig. 8

Uniaxial a compression, b tension and c double lap shear laboratory test

Experimental results were obtained from the measuring devices, processed and set in the final form. Processing was necessary, since the results of specimens in each group had to be averaged. Average load-displacement curves obtained from compression, tension and shear tests are shown on Fig. 9. Those exact load-displacement relations were used as input for the normal \((K_{1})\) and shear \((K_{2}=K_{3})\) components of nonlinear springs used in the numerical model.
Fig. 9

Load versus displacement diagrams obtained from uniaxial compression/tension (a, b, c) and double lap shear tests (d, e, f), which were performed for 5.0 mm, 7.0 mm and 9.0 mm thick layer of PU adhesive

Table 2

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 load-bearing part of the adhesive joint is 2/3 of \(w_{a}\) (for explanation see Sect. 1.1).

2.4 Numerical parametric analysis of timber-glass wall elements

A commercial code SAP2000 was used for a linear-elastic 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 multi-layered 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.

Supports were placed according to the width of the frame at two, three or four evenly distant nodes on the bottom girder of the timber frame. The model was subjected to a horizontal racking load in the upper left edge of the timber frame. Besides the considered self-weight, each upper corner was loaded with additional vertical point load representing dead load, imposed load and snow load. Additional vertical load was estimated to \(25\hbox { kN}/\hbox {m}^{1}\), which was multiplied by length of the wall and divided by two corners.
Fig. 10

Static system of the numerical model including loads and boundary conditions (a) with enlarged upper left corner where springs and loads are clearly visible (b)

Horizontal racking load was increased in each step by 5.0 kN up to calculated or experimentally determined horizontal load-bearing capacity \(F_{{ max}}\). Values of \(F_{{ max}}\) for each numerical model were interpolated between 23.52 (TGW) and 83.50 kN (TGWE). For the remaining two models (\(L = 260\hbox { cm}\) and \(L = 280\hbox { cm}\)) values of \(F_{{ max}}\) were extrapolated. Those values are listed in Table 3.
Table 3

The matrix of numerical TG models with experimentally determined (E) and calculated horizontal load-bearing capacity, \(F_{{ max}}\)

Height—H (cm)

Width—L (cm)

Horizontal load-bearing 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 linear-elastic analysis is fast and usually gives satisfying results within a linear-elastic domain of the used adhesive. Therefore, coefficients for normal \((K_{1})\) and shear springs \((K_{2}=K_{3})\) were calculated and used to simulate linear-elastic 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 linear-elastic in nature, we expect a more accurate result with nonlinear spring elements, which are defined by the stress-strain constitutive law derived from small-scale 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 glass-to-frame 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 linear-elastic and nonlinear parametric numerical analysis for each wall height are presented on the following pages.

Figure 11 shows load versus displacement master curves for two experimentally investigated walls, namely TGW and TGWE, together with the response of calibrated nonlinear numerical models with the same geometrical and material properties. Fitting of numerical curves is fairly good in both cases, although no pronounced plastification can be observed.
Fig. 11

Diagram of horizontal load vs. horizontal displacement for two mechanically investigated testing groups of timber-glass walls, namely a TGW and b TGWE

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.

In addition to the results of the nonlinear analysis, Fig. 12 also shows the results of the linear-elastic numerical analysis. These are shown only for the bond line thickness of 5.0 mm. Due to poor matching with the actual results of experimental investigations, linear-elastic analysis for the remaining thicknesses (7,0 mm and 9.0 mm) was not further investigated.
Fig. 12

Racking stiffness versus width (L) diagram of four different heights: a\(H = 240\hbox { cm}\), b\(H = 250\hbox { cm}\), c\(H = 270\hbox { cm}\) and d\(H = 290\hbox { cm}\)

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.

The racking stiffness functions of TG models are presented on Fig. 13, which comprise results of the entire parametric numerical investigation. Functions are in form of height-to-width ratio (r) versus racking stiffness (R). Again, a great difference can be observed between upper two functions and the lower one, representing a 9.0 mm bond line.
Fig. 13

Exponential design curves for 5.0 mm, 7.0 mm and 9.0 mm thick layer of adhesive approximating dependency between the racking stiffness and height-width ratio of TGW

4 Conclusions

An extensive numerical study of timber-glass models was performed using a commercial code SAP2000. Polyurethane adhesive, which bonds insulating glass unit and timber frame into a load-bearing composite shear wall, was modelled with linear-elastic 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 timber-glass 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 linear-elastic 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, linear-elastic analysis underestimates the response of TG walls, while nonlinear analysis overestimates it by a few percent.

A great difference between 7.0 and 9.0 mm thick bond line indicates the following:
  • 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.

Having the correct information about the stiffness of the single TG wall one is able to calculate the stiffness of the entire timber-glass building. For this reason, racking stiffness design curves were made to easily pick the calculated stiffness based on (i) thickness of the bond line and (ii) a height-to-width ratio of a TG wall.

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 widely-used in practise. Moreover, an effect of load-sharing in IGUs should be analysed and considered in future numerical investigations.

Notes

Acknowledgements

The investment is co-financed by the Republic of Slovenia and the European Union under the European Regional Development Fund.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Boštjan Ber
    • 1
    • 2
    Email author
  • Gregor Finžgar
    • 3
  • Miroslav Premrov
    • 1
  • Andrej Štrukelj
    • 1
  1. 1.Faculty of Civil Engineering, Transportation Engineering and ArchitectureUniversity of MariborMariborSlovenia
  2. 2.Jelovica hiše d.o.o.PreddvorSlovenia
  3. 3.Kager hiša d.o.o.PtujSlovenia

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