A numerical and experimental approach to cold-bent timber-glass composite elements

SI: Challenging Glass paper


The current rise of wooden constructions, which is encouraged by a strong trend towards sustainability of our buildings, also engenders innovation in facade design and materials. Timber-glass composite elements are a novel interpretation of the structural sealant glazing concept aiming at a reduction of the carbon footprint of facades by using materials from renewable resources. Already available facade systems based on the principle of timber-glass composite construction are applied in curtain walls, which is a rather conventional way. This paper assesses the feasibility of cold bended timber-glass composite elements to widen the scope of possible applications to curved or freeform surfaces such as timber grid shells. Cold bending appears an efficient way to adopt the flat element to a non-regularly shaped substructure. The twisting from an initial undeformed to a deflected state leads to permanent stresses in the glass as well as in the adhesive joint, the adapter and the screwed connection. Numerical models of a rectangular and a square-shaped timber-glass composite element help to understand the mechanical reactions in the individual components and the joint. The virtual components are deflected on one corner while the other three remain in plane. The cold bending of such elements is additionally assessed in life-size experiments. Shape and size correlate to those used in the numerical models to enable a validation of the virtual model. The derived stresses and time-depended deformations of the deflected test specimens yield a better understanding of the structural behavior and design of timber-glass composite elements.


Bent glass Timber-glass composite Structural sealant Sustainability Numerical simulation Life-size test 

1 Introduction

1.1 Scope and motivation

Over the last years we have seen a significant increase in construction of wooden multi-storey houses in urban areas (Kaufmann et al. 2017 and Buchanan 2016). Every year another city announces a new record for the tallest or highest timber building in the world. Wooden constructions are clearly on the rise again—encouraged by a strong public and economic trend towards sustainable and resource efficient buildings. This development affects all parts of a building. Timber-glass composite elements could contribute to a more efficient use of materials in facade constructions. One manufacturer specifies the reduction of \(\hbox {CO}_{2}\) emissions by 43 % for the substructure of a timber-glass facade compared to a conventional aluminum stick system (UNIGLAS GmbH 2015). In terms of primary energy consumption, wood has significant advantages over established facade materials such as steel or aluminum.

The research presented within this paper is driven by the idea to adopt the timber-glass composite concept to curved and freeform building envelopes and structures. A complex geometry is the unique feature of many outstanding buildings realized over the last years and planned in the near future. Freeform structural grids are not limited to steel or aluminum. Newly designed structures such as the new headquarters for Swatch and Omega in Biel with a flowing timber grid-shell roof designed by Shigeru Ban Architects (Detail Daily 2012) provide evidence that timber could fulfil high architectural and structural demands. Laufs and Vilkner (2010) describes and evaluates different options to clad curved building surfaces. Facade systems with wet sealing and linear support of the glass pane can be very cost efficient, if quadrangle glass units are deformed to the desired shape by pressing it on the substructure. Hence, cold-bent timber-glass composite elements may be one option to glaze such roofs or curved facade surfaces. This development requires further research due to the absence of evaluation tools and insufficient knowledge about its design.

A short overview of different bending techniques for glass defines the starting point of the presented study. Advantages and limitations of each method are assessed in order to comply with the specific features of timber-glass elements. Those composite elements typically comprise a glass pane and a circumferentially wooden adapter. Glass and adapter are adhesively joined by a structural silicone sealant. The main focus is put on cold bending of the glass to achieve the curved shape. The twisting of one edge of those initially flat units to the free-form geometry strains the glass pane, the adhesive joint and the screwed connection between the adapter and the timber mullions. First, the stress distribution and the deformation behavior of the glass pane is assessed numerically by simplified models. The virtual models differ according to their support conditions. The results of the finite element analysis enable the preliminary design of the glass in order to predefine the glass type, thickness and bending forces. Second, improved results can be derived from a detailed model that takes into account the properties and the geometry of the adhesive joint. Finally, the virtual models need to be validated by life-size experiments.
Fig. 1

Mullion design of two different timber-glass composite facades systems: UNIGLAS\(^{{\textregistered }}\) (left) and FASCO\(^{{\textregistered }}\) (right)

1.2 Basic concept of a timber-glass composite facade

A timber-glass composite facade generally comprises three major components: an insulating glass unit, a slim frame made from wood or another suitable material that is glued on the back of the glass lite and a wooden substructure. The facade design follows the stick-built construction method where individual vertical and horizontal mullions are assembled on site. The framework continuously supports all four edges of the glass unit. Laminated veneer lumber or glulam qualify for the mullions since they provide an improved dimensional stability and a higher load bearing capacity compared to solid wood.

First concepts for a timber-glass composite facade element were developed by Hamm (2001) with the aim to enable an in-plane loading of the glass pane. Initially, the glazing was glued directly on the wooden substructure of the facade. Niedermaier (2005) proposes an additional adapter frame. It enables gluing under factory-controlled conditions as well as an easy removal and exchange of damaged glass panes. This adapter is enhanced by means of a notched shape (Edl 2008). Shifted frames of adjacent elements fit together which lead to slender faces of transom and mullions. It is noteworthy that a similar shape was proposed for an aluminum profile by Eversmann et al. (2016). This profile is adhesively joined using acrylic foam tape to the inner surface of the panes of several cold-bent glass prototypes. Interlocking of adjacent panels and screwing in the central line of the mullion is regarded advantageous.

Two manufacturers already implemented the described construction principle for their facade solutions (Fig. 1). Both systems differ mainly in material and layout of the adapter on the back of the glass unit. The UNIGLAS\(^{{\textregistered }}\) | FACADE (Fig. 1, left) comprises notched adapters made from birch plywood. This wood-based material is made from cross-laminated birch veneers and shows excellent shape stability and reduced tendency of shrinkage. Figure 2 displays a pilot facade project using timber-glass composite elements with a plywood adapter. The FASCO\(^{{\textregistered }}\) Facade System (Fig. 1, right) bases on an overlapping adapter made from glass fiber reinforced plastics (GFRP). In both cases, the slim frame is glued circumferentially to the interior side of the insulating glass unit. The joint in the shown systems is rather flexible since silicones are applied, which are comparable or identical to those in structural sealant glazing systems. All gluing work is done in a shop under controlled conditions (Fig. 2b). After sufficient curing of the adhesive, the prefabricated elements are transported to the site and mounted to the supporting timber structure of the facade by screws. A sealing tape protects the wooden mullions against moisture. In both systems, the minimum width of the mullions is 60 mm. The facade joints are sealed using a PE-cord filler and a compatible single-component silicone.
Fig. 2

Timber-glass composite elements with plywood adapter in use: a facade of a logistic center in Fridolfing, b injecting the silicone adhesive between the glass unit and the adapter c detailed view on the notched shape of the plywood adapter (Photos: OTTOCHEMIE)

Compared to plywood, glass fiber reinforced plastic (GFRP) has an almost identical expansion behavior to glass, both under the influence of temperature and humidity. In addition, its resistance to moisture is very good (Knapp 2013). Disadvantages of the GFRP adapter are the low strength of the hole bearing (Engelsmann et al. 2013) and the overlap of the adapter with the one from the adjacent glazing element. This impedes a quick and cost effective replacement of possibly damaged glazing units during the life-span of the facade.

Under certain conditions these facade elements are able to support horizontal wind loads on buildings. However, a sample calculation by Hochhauser et al. (2013) illustrates that the load-bearing capacity of a silicone joint is only utilized around 30 % when the deformation already reaches critical values in the serviceability limit state. Higher demands on the load-bearing capacity require high-modulus adhesives (Nicklisch 2017). This disadvantage may turn into a positive effect when the glass unit is twisted to the curved shape. The forced deformation leads to significant differential deformations between the glass pane and the substructure. An elastic adhesive such as silicone could be able to compensate those differences.

1.3 Bending techniques and their limits

Flat glass can be transformed into a curved shape by several methods. The key difference is the process temperature and the related state of the glass. Thus, bending methods are classified in hot and cold bending techniques. Hot bending requires an oven where the glass is shaped at a temperature between 550 and 620 \({^{\circ }}\)C (Schuler et al. 2012). At this transition temperature glass starts to become viscous. The hot glass plate sags into a mold under its own dead weight. Slow cooling avoids unwanted residual stresses. Rietbergen (2009) describes different molding techniques which can be divided in point, perimeter, linear and full-surface supported molds. Roller bending is another hot bending method, which is commonly used to produce curved thermally toughened glass. Adjustable rollers shape the glass during the tempering process. In both processes the mold or the rollers respectively touch the glass surface while it is viscous. After hot bending, the glass surface is slightly uneven and produces optical distortions. In addition, molding ties up large personnel, time and financial resources - especially when small batches or various shapes are manufactured.

In contrast, cold-bent glass keeps the high-quality surface because the flat glass is mechanically forced to the specified shape while it remains in a linear elastic state. This avoids local surface imperfections, but, permanent bending stresses have to be taken into account in the structural design. Typically, heat-strengthened or thermally toughened glass are used for cold-bent glazing. The low bending strength, which results from a subcritical crack growth under permanent loads, limits the application of annealed glass. The minimal bending radii of cold-bent glass depend on the glass thickness, the dimensions of the pane and the bending shape. They are generally larger for cold-bent glass when compared to glass curved in a thermal process. The forced deformation uses only a part of the load-bearing capacity since external loads also need to be taken into account. Weber (2009) discusses a maximum value of 60 % of the total load bearing capacity.

Cold-bent glass can be produced either by means of a lamination technique or by pressing the glass onto the substructure which defines the desired shape. Single- or double curvatures are possible. Cold bending involves several advantages. The glass units can be produced flat and do not require expensive molds. The surface and thus the optical quality remain unchanged. Another significant advantages of cold-bent glass panes is the multitude of applicable coatings. Cold-bent glass can be functionalized to the same extent than flat glass. In contrast, many coatings would not withstand the high process temperatures of hot bending (Sastré 2010).

Otto et al. (2012) reports about spherically bent rooflights produced using the lamination method. Prior to lamination, glass and interlayer sheets are forced onto a bending device to achieve the curvilinear shape. The batch remains fixed throughout the autoclave process. Afterwards, clamps are released. The laminated glass maintains the bent shape because of a rigid shear bond in the interlayer. Hence, only shear resistant interlayers such as the ionoplast SentryGlas\(^{{\textregistered }}\) qualify for lamination bending. The standard interlayer material polyvinyl butyral (PVB) exhibit a distinct creep behavior which would cause excessive relaxation and a return to the initial flat shape over time. However, a minor recovery of the imposed deformation has also to be taken into account using stiff interlayers.
Fig. 3

Bending modes of quadrangular plate: a first mode and b second mode (Eekhout and Staaks 2004)

Bending the glass on site during installation on a target geometry is another cold bending technique. The curved surface is generated either by displacing one corner of a quadrangular pane or by precurved members of the substructure which define the shape along the edge of the pane. Different bending shapes ranging from single curved to anti- and synclastically curved are possible (Eversmann et al. 2016). However, cold-bent glass with a pre-set single curvature exhibits also a slight bending in the transverse direction (Bijster et al. 2016). In case of cold bending of laminated glass by this technique PVB is a good choice for the interlayer. The creep behavior enables a time-dependent reduction of bending stresses which initially result from the cold bending process (Bijster et al. 2016). To avoid a recovery of the applied deformation cold-bent glass needs to be permanently fixed to the substructure. This is achieved by mechanical fasteners or adhesives.

Cold bending of insulated glass units (IGU) is also possible using this technique. Warping of the unit causes a permanent shear deformation of the edge seal. This may affect the impermeability of the primary seal which would result in a loss of filling gas or vapor diffusion into the cavity. Both reduce the thermal insulation or even damage the unit severely. Hence, deformation limits apply for the cold bending of insulating glass units. Laufs and Vilkner (2010) recommends a ratio between the length of diagonal (D) and the out-of-plane deformation (dZ) of D/175 to protect the edge seal of the insulating glass units.

The shape of a cold-bent glass surface depends on the support conditions and the out of plane deformation of the displaced corner. Eekhout and Staaks (2004) describes different deformation modes of quadrangular glass panes which are point supported at all four corners. A double-curved surface (Fig. 3a) results from quadrangular glass pane if it is deformed out-of plane at one corner. The diagonals bend in opposite directions. All four edges remain straight. Instability occurs at a certain value of dZ. One of the diagonals buckles due to high compression loads und turns almost in a straight line (Fig. 3b). At the same time, the instability leads to a curvature along the glass edges. The sudden change in the bending shape by instability depends on the relation of the offset dZ and the glass thickness t as well as the aspect ratio of the pane. Based on different numerical models, Staaks (2003) and Eekhout and Staaks (2004) define a critical value of \({ dZ} = 16.8 \times t\) where instability occurs for square plates independently from the absolute size. The value does not depend on the Young’s Modulus but is sensitive to the Poisson’s ratio. Buckling does not actually mean failure but results in a change of deformation mode. This affects the visual appearance of the glass. A third mode of deformation is described by Datsiou and Overend (2016). A further deformation of the buckled glass pane leads to a sinusoidal ripple in the center of the pane which is called cold bending distortion. This phenomenon is regarded to impair the optical quality of the glass pane.

The numerical calculations of Galuppi and Massimiani (2014) on a four-point supported glass pane corroborate those observations. A square glass pane (1800 \(\times \) 1800 mm) is deformed in several steps to derive the critical value where bending becomes predominant along one diagonal. The limit of stability is reported about \(\delta =80\) mm for an 8 mm thick glass pane. Another \(\delta \)/2 has to be added in order to correspond to the configuration where only on corner is displaced out of plane. Hence, this yields to a critical value of \({dZ}=15 \times t\), which is close to the findings by Staaks (2003) and Eekhout and Staaks (2004). Furthermore, Galuppi and Massimiani (2014) concludes an increase of this critical value if the glass pane is glued to a stiff frame. The additional elements force the glass edges to remain straight. This observation seems relevant for timber-glass composite elements, which also feature straight structural members along the edges of the pane.

Table 1 summarizes several recommendations on minimal radii or maximum twist (offset) found in literature. The list is enhanced by project examples of cold-bent glass. The project data is used to specify the actually used figures. The table reveals that all realized projects even if they comprise insulated glass units (IGU) go beyond the limit of D/175 which was initially proposed by Laufs and Vilkner (2010). Thus, the study presented here also aims at curved shapes larger than this limit, but below the critical value for instability. Straight edges are considered to be advantageous so that the elements fit together with the adjacent ones.
Table 1

Overview of minimal bending radii and offset recommended or described in literature


Cold bending technique

Dimensions a \(\times \) b (mm)

Bending radii R (m)







R \(\ge \) 1500 \(\cdot \) t


Rough estimation based on utilization ratio of 50 % strength

Sastré (2010)

Double anticlastic


\(\begin{array}{l} 1500~\times ~1500 \\ 3000~\times ~3000 \\ \end{array}\)

\(\begin{array}{l} \hbox {R }\ge 10.0 \\ \hbox {R }\ge \hbox { }20.0 \\ \end{array}\)


Rough estimation based geometry and size

Sastré (2010)

Double synclastic


\(\begin{array}{l} \emptyset 1500 \\ \emptyset 3000 \\ \end{array}\)

\(\begin{array}{l} \hbox {R }\ge 15.0 \\ \hbox {R }\ge 40.0 \\ \end{array}\)


Rough estimation based geometry and size

Sastré (2010)

Double synclastic


\(\begin{array}{l} \emptyset 1500 \\ \emptyset 2500 \\ \end{array}\)

\(\begin{array}{r} \hbox {R}\approx 15.0 \\ \hbox {R}\approx 25.0 \\ \end{array}\)


Städel Museum, Frankfurt (DE)

Otto et al. (2012)

Double anticlastic

Warping on site


1/175 (0.006)

Recommendation for IGU

Laufs and Vilkner (2010)

Double anticlastic

Warping on site

1500 \(\times \) 3000 (single glazing)


100/3354 (0.030)

Tramstation Zuidpoort, Delft (NL)

Eekhout and Niderehe (2009)

Double anticlastic

Warping on site

900 \(\times \) 2000 (IGU)


40/2193 (0.018)

Town Hall Alphen aan den Rijn (NL)

Eekhout and Niderehe (2009)

Double anticlastic

Warping on site

1200 \(\times \) 1800 (IGU)


70/2169 (0.032)

Van Gogh Museum, Amsterdam (NL)

Bjister 2016


Warping on site

1000 \(\times \) 2000 (single glazing)

R = 6.0



Eversmann et al. (2016)

Double synclastic

Warping on site

1000 \(\times \) 2000 (single glazing)

R = 6.5 (R = 4.0)



Eversmann et al. (2016)

Double anticlastic

Warping on site

1000 \(\times \) 2000 (single glazing)

R = 11.5



Eversmann et al. (2016)

Fig. 4

Cold bending process of a timber-glass composite element

2 Methods and materials

2.1 General approach

The aim of this work is to examine the feasibility of cold-bent timber-glass composite elements both numerically and experimentally. Only vertical facades have been realized using timber-glass composite technology so far. The study approaches the issue by a straightforward strategy to derive the curved shape by displacing one node of quadrangular elements (Fig. 4). Digital prototypes and life-size components are assessed with regard to their deformation behavior and the stress distribution in the glass. Initially flat elements with a plywood adapter that is circumferentially bonded to the inner glass surface cover a broad range of possible sizes (1500 \(\times \) 1500 mm and 1000 \(\times \) 2000 mm) and aspect ratios. The geometry is in line with typical sizes listed in Table 1. The individual elements of the assumed substructure are not curved. Curvature is only achieved in the glass. The straight wooden mullions change their angle at the intersection points of the structural framework. Screws that are mounted after the cold bending process transfer the elastic restoring forces into the wooden frame and hold the glass edges in place.

The study is performed on monolithic glass sheets. This simplification avoids time-dependent behavior due to relaxation of a viscoelastic interlayer. However, application in a real facade, roof or building envelope would require the use of laminated safety glass for post-breakage robustness and retaining of fragments of broken glass especially in overhead configurations. Demands on the thermal performance of the building envelope would further lead to insulated glass.

2.2 Adhesive

The two-part, condensation-curing silicone adhesive OTTOCOLL\({\textregistered }\) S660 is selected for the analysis. The product was specifically developed for timber-glass composite facades since it is used for the facade system shown in Fig. 1 (left). It provides a very good adhesion to the substrate materials involved. The material properties are comparable to other structural silicones for facade applications. Table 2 summarizes the relevant manufacturer data in the context of other commonly used products for Structural Sealant Glazing (SSG) facades. Yet one of the remarkable advantages of OTTOCOLL\({\textregistered }\) S660 is the fast curing. The manufacturer specifies only two days of curing at room temperature until the element can be moved and transported. Volume shrinkage during the curing process is low. Minor differences can be identified in strength and stiffness, but the values range on a similar level than established adhesives. The impact of this small differences on the behavior of the numerical model is regarded negligible. It is assumed that the results also apply to other structural silicone sealants.

In general, silicone adhesives are widely used for facades. Several guidelines already exist for application and testing of silicones in glass constructions. Silicones offer adequate temperature stability and remain highly flexible even at low temperatures. Hence, they qualify for bonding materials of different thermal expansion like glass and aluminium, or glass and wood where swelling and shrinkage have to be compensated. Ageing tests and years of practical experience have proven an excellent durability. Aging tests on timber-glass joints have been performed e.g. by Schober et. al. (2006 and 2007) and Nicklisch et al. (2016). However, allowable stresses are quite low.
Table 2

Material properties of different structural sealants (manufactures data)

Product name

OTTOCOLL\(^{{\textregistered }}\) S660

DC 993/Dowsil\(^{\textsc {TN}}\) 993

Sikasil\(^{{\textregistered }}\) SG-500



Dow Corning\(^{{\textregistered } }\)/\(\hbox {DOW}^{{\textregistered }}\)

Sika\(^{{\textregistered }}\)

Curing time (d)




Tensile strength (MPa)

Characteristic \(\sigma _{k}\)/\(\hbox {R}_{u,5}\)




Design \(\sigma _{d}\)




Design \(\sigma _{d,\infty }\)




Shear strength (MPa)

Characteristic \(\tau _{k}/\hbox {R}_{u,5}\)




Design\(_{ }\tau _{d}\)




Design \(\tau _{d,\infty }\)




Young’s modulus (MPa)




Shear modulus (MPa)





abZ Z-70.1-226\(^\mathrm{a}\)



\(^\mathrm{a}\)abZ—Approval by the German building authorities (allgemeine bauaufsichtliche Zulassung)

\(^\mathrm{b}\)ETA—European Technical Approval/European Technical Assessment

2.3 Glass and timber

Tempered soda-lime glass of 8 mm nominal thickness is used throughout the experimental tests. More glass thicknesses are evaluated by means of numerical models. The choice of glass depends on the expected stresses and the permanent loading of the cold-bent glass. Its higher strength compared to that of standard float glass minimizes the risk of glass failure during testing. Even for large displacements of the twisted node the glass surface remains in compression due to the residual stress state. All four cut edges are ground and chamfered. Glass exhibits an ideal elastic material behavior without any plastic deformability. The German standard about glass in Building DIN 18008-1:2010-12 provides fundamental material characteristics. The numerical calculations presented in this paper involve a Young’s Modulus of \(E_{\mathrm{glass}} = 70,000 \hbox { N/mm}^{2}\) and a Poisson’s Ratio of \(\mu = 0,23\).

Birch plywood, a wood-based material made from cross-laminated birch veneers, was used in the tests. Birch plywood is characterized by its excellent strength, stiffness and creep resistance. It has a high planar shear strength and impact resistance, which makes it especially suitable for heavy duty structures. It relates to the state-of-the-art in timber-glass composite construction, since the adapter frame of a commercially available timber-glass composite facade system (UNIGLAS GmbH 2016) is manufactured from this material. Plywood shows excellent shape stability and reduced tendency of shrinkage.

3 Numerical simulation

3.1 Simplified calculation

The stress distribution and the curved shape is derived in a first approach from simple numerical models using ANSYS Workbench 17.1. The digital prototypes differ in terms of the support conditions of all four edges or all four nodes respectively. The adhesive joint and the plywood adapter are not implemented in these models. Figure 5 shows the three different models for the square shaped glass pane of 1500 \(\times \) 1500 mm. The equivalent models for the rectangular glass pane with a size of 1000 \(\times \) 2000 mm feature the same support conditions. The models of the glass panes are meshed using square shell elements with a size of 25 \(\times \) 25 mm and a thickness of  t = 10 mm.
Fig. 5

Support conditions of the three simplified numerical models

Fig. 6

First principal stress on the upper glass surface derived from the three different numerical models, dZ = 50 mm, t = 10 mm

The general stress distribution in the glass pane is evaluated by means of principal stresses resulting from an offset of dZ = 50 mm. The results shown in Fig. 6 reveal a strong dependency from the support conditions. The continuous supports restrain the free deformation of the glass pane along the edge since the supports are modelled rigid and do not allow any displacement except a rotation around the axis which is parallel to the edge. Maximum tensile stresses concentrate in the glass edges which are tilted downwards (edge 3 and 4) when the displacement is applied.

Model 1 features the least restraint. The maximum stresses are observed in the center of the edges, except from singular stress peaks at the nodes which are point supported. The stress distribution is almost symmetrically in relation to the two central axes. In model 2 the stress contours changes to an unsymmetrical plot due to the modified supports. Still, the maximum stress is located near the center of the free edges of glass pane. The higher restraint along the supported edges leads to higher stress values when compared to model 1. The highest stresses are derived from model 3 where the stress distribution changes again. The peak values occur in close proximity to the nodes C and D where the local distortion of the glass pane is very high. These observations apply for both glass geometries—the squared and the rectangular pane.

Maximum values of the first principal stress are significantly below the ultimate tensile strength of tempered glass for all shown numerical solutions at an offset of dZ = 50 mm. Even if the offset is increased to 100 mm (contour plot is not shown) the maximum tensile stress reaches values around 70 \(\hbox {N/mm}^{2}\) which is less than the characteristic tensile strength of tempered glass. Further parametric studies on the simplified numerical models lead to the expected relation between the thickness and the stress level. The calculated stresses increase with the glass thickness for all three support configurations.
Fig. 7

Element mesh of the detailed numerical model of the 1500 \(\times \) 1500 mm glass pane

The simplified models 1 and 2 are also used to estimate the forces which are required to warp the glass in the experiments. A concentrated load of approximately 0.7 kN is required to deform the free corner of the glass pane (thickness of t = 10 mm) of the point supported model 1 by an offset of 100 mm. The numerical calculation yields to the same load for both glass geometries. The constraint force nearly doubles on Model 2 which exhibit a higher stiffness due to the continuous support along edge 1 and edge 2. The square glass pane measuring 1500 \(\times \) 1500 mm requires a concentrated load of approximately 1.1 kN to be warped to the same extent. The rectangular must be loaded even by approximately 1.3 kN to reach this offset.

Based on the numerical calculations using the simplified models it can be concluded that the behavior of the cold-bent glass pane is very sensitive to the support conditions along the four edges. Hence, a refined numerical model needs a more precise approximation of the adhesive joint and its stiffness. Finally, it was decided to use 8 mm glass sheets for the component testing to reduce the glass stresses and the necessary loading in the experiments. Thus, a thickness of 8 mm was also used throughout the more precise FEA-calculations.

3.2 Detailed computational model

As a next step, we developed a more precise model of the timber-glass composite element. The three-dimensional model comprises the glass pane and the complete adhesive joint, which is based on solid elements. The full mesh and details of important parts are shown in Fig. 7. The generated mesh is coarse in the center and fine along the boundary of the glass pane, where loads are transferred via the bond. The edge length of the small finite elements is fixed to 5 mm while maximum element edge length is set to 50 mm in the inner part of the glass pane.

The fine meshing applies also to the adhesive joint. The bondline is modeled with solid elements and runs at a distance of 10 mm to the glass edges. The cross-section is defined by a width of 12.5 mm and a thickness of 3.2 mm which is the typical size used in timber-glass composite facades and also for the test specimens. All components of the three-dimensional geometry of the adhesive joint are idealized with homogenous structural solids. The contact between the flexible adhesive and the surface of the glass pane is defined as fully composite. On the side of the stiffer glass pane, ANSYS Workbench creates a targe170 element and on the adhesive joint a conta174 element that links the two meshes which initially have no coincident nodes.
Fig. 8

Vertical deformation the glass pane calculated with the detailed numerical model of the twisted timber-glass elements: 1500 \(\times \) 1500 mm (left), 1000 \(\times \) 2000 mm (right), \({ dZ}=50\) mm, \(t=8\) mm

Boundary conditions of the nodes on the bottom of the adhesive joint are set to full restraint. Thus, the substructure including the adapter frame which is connected by screws have an infinite stiffness in the model. This assumption is sufficiently accurate since the stiffness of the adhesive is so low, that the deformations of the joint are much greater than that of the screwed adapter.

Only linear elastic properties are used. In this basic numerical calculation the deformation behavior of the adhesive is idealized by linear elastic material models with a Young’s Modulus of \({E}_{\mathrm{Adh}.}=1.6\hbox { N/mm}^{2}\) and a Poisson’s Ratio of \(\mu =0.49\). The influence of geometric non-linearity in the FEA calculation is taken into account since large deformations occur when the glass pane is twisted towards the curved shape. The large deformations may lead to significant membrane stresses and an enhanced load bearing potential. Similar meshing strategies apply to the rectangular element, which is not shown in Fig. 7.

Figure 8 displays the curved shape resulting from an offset of dZ = 50 mm for both glass geometries. The warping can be clearly read from the plot. The radius of the diagonal between A and B narrows towards the twisted corner node B. Here the contour lines become closer. All edges remain almost straight. Edge 1 and 2 experience only a minor upward deformation. The Uplift is less than 1 mm. The related principal stresses are shown in Figs. 9 and 10. The stress distribution is more homogeneous compared to the results from the simplified model since all edges are supported elastically by the adhesive joint. High stresses develop again along the edges of the glass pane. One maximum is located near the center of each edge. The direction of the first and second principal stress.

In general, the stresses derived from the detailed model are lower than that calculated using the simplified model. Maximum tensile stresses in the contour plots shown in Fig. 9 are around 9 \(\hbox {N/mm}^{2}\). This observation has two reasons. On the one hand this results from the better approximation of the joint which give the nodes along the glass edges the possibility to move. The detailed model contains less points of constraint. Thus, the glass pane is able to bend in a more homogeneous way without being forced in position at certain points like this is the case in the point supported model 1 or the continuously but rigidly supported models 2 and 3. On the other hand the glass pane thickness was changed from 10 mm to 8 mm in the detailed model. The stiffness of the glass pane decreases and lower stresses result if the thinner glass pane is warped with the same curvature. A cross-check calculation which is not shown here using a glass thickness of 8 mm with the simplified model 1 still leads to higher stresses and inhomogeneous distribution of principle stresses than in the detailed model (Fig. 9).
Fig. 9

Principal stresses \(\sigma _{1}\) on the upper and lower surface of the glass pane calculated with the detailed numerical model of the twisted timber-glass elements: 1500 \(\times \) 1500 mm (left), 1000 \(\times \) 2000 mm (right), \({ dZ}=50\) mm, \(t=8\) mm

Fig. 10

Direction of principal stresses calculated with the detailed numerical models: 1500 \(\times \) 1500 mm (left), 1000 \(\times \) 2000 mm (right), \({ dZ}=50\) mm, \(t=8\) mm (red arrow = first principal stress \(\sigma _{1} -\) tension, blue arrow = second principal stress \(\sigma _{2} -\) compression)

4 Experimental evaluation

The two glass geometries are further assessed in a life-size experiment at room temperature. The specimens—one for the square and one for the rectangular shape—comprise tempered glass panes with a thickness of \(t=8\) mm. The glass is glued along its edges to an adapter frame made of birch plywood. The joint is 12 mm wide and 3 mm thick. This geometry corresponds to the computational model and the facade system described in chapter 1.2. The two specimens were produced by the facade manufacturer and delivered to the test facilities after full curing of the adhesive.

The bending tests are performed on a specific wooden test frame (Fig. 11) that forms the substructure of the timber-glass composite element. The position of one corner of the frame (point B) can be adjusted vertically to different offsets by threaded rods. The whole test frame is mounted to rigid bedplate to avoid uplift of the frame when the glass pane is warped. The deformation is applied in three stages: dZ = 70 mm, 90 mm and 110 mm. Between each stage the warped element remains in the set state for 30 minutes before the next step is initiated. At the beginning, the specimens are fixed along the timber mullions, which remain in plane (edge 1 and 2). The free corner is then adjusted to the offset values of the respective stage. Sandbags bring the glass edge down until there is contact between the plywood adapter and the frame members. Finally the two remaining adapters (edge 3 and 4) are screwed to the members of the test frame so that the element is fixed along all four edges. Deformation and strain are recorded on relevant positions throughout the test procedure. The specimens are released after the last stage.
Fig. 11

Support frame for the cold-bending tests on timber-glass elements (1000 \(\times \) 2000 mm: a without specimen, one corner is adjustable in vertical direction to apply the predefined offset b with specimen, sandbags are used to warp the glass until limit stop at the free corner

Strain gauges enable the evaluation of strain and stresses in the glass. Figure 12 shows their positions which are defined on the basis of the computed stress distribution in the glass pane. Most strain gauges are attached to the upper glass surface while one strain gauge per specimen (DMS 14/24) is located on the lower surface in the center of the glass edge. This aims on the measurement of maximum tensile stresses. The three strain gauges at the edges (DMS 11/21, DMS 12/22 and DMS 14/24) have a linear pattern and thus measure the strain parallel to the glass edge. The central position DMS 13/23 is a biaxial strain gauge which is rotated by \(45{^{\circ }}\) to capture the principal stresses in the direction of the main axes. The angle was determined from the numerical calculation (Fig. 10). Three displacement transducers along the diagonal, one on point A (W 11/W 21), one on point B (W 13/23) and one in the center (W 12/22), measure the displacement of the glass pane. For close-ups of the main measuring devices and sensors see Fig. 13.
Fig. 12

Sensor positions on the glass surface of the timber-glass composite specimens (DMS = strain gauge, W = displacement transducer)

Fig. 13

Measuring equipment used for the component testing: a displacement transducer (W11/21), b displacement transducer (W12/22) and c biaxial strain gauge in the center of the glass pane (DMS13/23)

Fig. 14

Specimens warped by an offset of \({ dZ} =110\) mm at point B: a Specimen 1—1500 \(\times \) 1500 mm, b Specimen 2—1000 \(\times \) 2000 mm

Fig. 15

Deformations measured in the component test compared to the computed shapes (simplified model 1 and model 3, detailed model) along the diagonal from point A to B

Within the limits of the predefined offset values the component testing of two timber-glass composite element geometries delivers successful results. The expected anticlastic, double curved surface is achieved by displacing on node out of plane. The edges of the glass sheet remain almost straight since they are fixed via the circumferential adhesive bond. As estimated only a small load was necessary to warp the glass in all three stages. None of the specimens failed. Figure 14 shows both specimens in their ultimate deflected state (dZ = 110 mm). It was predicted that the glass would resist the forced deformation since the computed tensile stresses were always below the resistance of tempered glass. But, also the adhesive bond remains intact, although the joint was severely distorted in the zone close to the node where the offset is applied. Furthermore, no creep deformation or relaxation was observed during the 30 minutes holding phases. However, this time period is regarded as very short in relation to the service life of a facade element. No damage was observed on the plywood adapter and the screws throughout the tests.

The deformation along the diagonal between the warped node (point B) and the node that remains in the plane (point A) enable a sound interpretation of the curved shape (Fig. 15). The measured data is marked with an orange plus sign for an offset of 70 mm at point B. The colored graphs display the computed results along the diagonal. It becomes apparent that the curved shape of the detailed model corresponds very well to the measured deformation. The simplified models lead both to stronger curvature which at the same time lead to higher stresses in the glass. Buckling of one diagonal as described by Eekhout and Staaks (2004) was not observed on neither deformation stage of both specimens. This is in line with the assumption that the critical value for instability is \({ dZ} =16.8 \times 8\hbox { mm}=134\) mm. The critical value is not exceed in the experiments.
Table 3

Stresses derived from strain gauge measurements compared to calculated stresses from the FEA in \(\hbox {N/mm}^{2}\) (detailed model)

Specimen- size (mm)

dZ (mm)

DMS 11/21

FEA Edge 1

DMS 12/22

FEA Edge 2

DMS 14/24

FEA Edge4

DMS 13/23-1

FEA mid \(\sigma _{1}\)

DMS 13/23-2

FEA mid \(\sigma _{3}\)

1500 \(\times \) 1500










\(-\) 10.5

\(-\) 9.1










\(-\) 13.3

\(-\) 11.6

1000 \(\times \) 2000










\(-\) 11.0

\(-\) 10.2










\(-\) 14.4

\(-\) 13.7

The measured strain values on the glass surface are converted to stresses. All given stress values are recorded directly after the deformation. The results are listed in Table 3 and compared to the computed values at the same positions and in the same direction than in the experiments using the detailed model. The stresses from the component testing exhibit a sufficient agreement to the FEA-calculation. However, the deviation is slightly higher than for the deformations. The gauges along the edges 1 and 2 indicate a slightly lower stress level compared to the calculation for the square specimen. The opposite applies to the rectangular geometry. In the middle of edge 4, the gauges recorded marginally lower values than calculated in the FEA for both aspect ratios. The strain recorded in the center of the glass sheet also shows a good correlation with the numerical analysis. The computed values are slightly smaller. This could lead to an unsafe design. Overall, we see a rather good correlation of the results from the detailed model with the experiments.

5 Conclusion

Wood as a renewable material offers a good opportunity to provide sustainable alternatives to conventional facade materials. Thus, timber-glass composite facade elements may be of high interest for architects and the building industry because they help to reduce the grey energy consumption of the building envelope. This paper aimed at a further enhancement of timber-glass composite elements by adding new geometric options for the architectural design. Cold-bending of the elements may be a cost-effective way to build curved facades and roofs on the basis of this sustainable system. The idea was assessed by means of numerical modelling and component testing.

Warping the timber-glass composite elements by means of shifting one of the corners out of the initial plane deforms the pane to a double curved shape which may be described as a hyperbolic paraboloid. While the edges remain straight, the diagonals bend in opposite directions. Based on the numerical model developed in this work, which takes into account the adhesive joint as an elastic support of the pane, the deformation behavior exhibits a good agreement with the component test. The detailed model is capable of computing the geometry of a warped timber-glass element. Further effort has to be put into the modelling of the adapter which may lead to more precise stress prediction. Maximum stresses occur along the edges. The study revealed that the curved shaped as well as the stresses in the glass are strongly sensitive to the support conditions along the glass edges. The testing of two prototypes proved that all major components of a timber-glass composite element—the glass pane, the adapter and the adhesive joint—could be bent in the same manner than conventional facade systems. The plywood adapter and the silicone joint offer even a higher flexibility than clamped solutions.

Future research should also take into account long-term tests where emphasis is put on the creep behavior of the adhesives joint. The load duration in the component test was too short to detect any time-dependent deformation of the joint. Additional challenges arise from glass configurations that are closer to standard application practice. This study was done only on monolithic glass sheets in order to reduce complexity. However, the interlayer in laminated glass and the edge seal of insulating glass units have a significant impact on the behavior and serviceability limits of cold-bent glass facade systems.

In the end, only built constructions can bring certainty about the performance and advantages of the adhesive connection. An important step in this direction would be the realization of a pilot facade. This would help to study various production stages of the whole process chain such as work preparation, cleaning of the joining materials, gluing, logistics, on site-bending and assembly. The completed facade would further allow for monitoring of the permanently loaded adhesive joint under real environmental and service load conditions.



The authors would like to thank the Petschenig Glastec GmbH, Austria for its support through the production of timber-glass-composite specimen components.

Compliance with ethical standards

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute of Building ConstructionTechnische Universität DresdenDresdenGermany

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