ponent is melted and enables a good handling of the adhesive. After cooling this adhesive shows a direct stiffness according to the melting component. The maximum stiffness is reached by the polyaddition.

* Acrylat (SikaFast-5211 VP) is a fast hardening 2-component adhesive.

<table><caption>TABLE 8: APPLICATED ADHESIVE THICKNESS</caption><thead><tr><th></th><th>PU-1</th><th>PU-2</th><th>PU-3</th><th>Acrylate</th></tr></thead><tbody><tr><th>Thickness [mm]</th><td>3.1 – 3.6</td><td>2.9 – 3.1</td><td>3.0 – 3.3</td><td>1.8 – 2.0</td></tr></tbody></table>

<figure><img src="image_226.png" /><figcaption>Fig. 16: Double splice test set up for short-term loads</figcaption></figure>

## B. Tests with short-term loads

### 1) Test specimen

Thick steel bars in double sided connections are used to exclude not desired stress peaks, which could occur in one sided overlapping specimen due to the bending moment generated by the eccentricity.

<figure><img src="image_227.png" /><figcaption>Fig. 15: Test specimen for short time loads</figcaption></figure>

### 2) Test set up

The test specimen are fixed in a steel frame and the force direction was controlled along the bond-line with a slide bearing and a pin joint.

### 3) Test results

#### a) Ultimate limit tests

The ultimate limit tests were conducted with a constant stress rate of $\Delta\tau = 0,05 \text{ N/mm}^2\text{s}$ and different temperatures of the adhesives. The shear strain $\tan \gamma$ and the shear modulus $G$ are calculated with:

$$ \tan \gamma = \frac{\nu}{d} \qquad (5) $$

$$ G = \frac{\tau}{\tan \gamma} \qquad (6) $$

v Displacement

d adhesive thickness

The tested polyurethanes and the Acrylate are much stiffer than the Silicone (DC 993) that is usually used in structural sealant glazing systems.

<figure><img src="image_228.png" /><figcaption>Fig. 17: stress-strain relation / $\Delta\tau=0,05 \text{ N/mm}^2\text{s} / T = 23^\circ\text{C}$</figcaption></figure>
<table><caption>TABLE 9: ELASTIC SHEAR MODULUS G<sub>ELASTIC</sub>
ULTIMATE SHEAR STRESS τ<sub>ULTIMATE</sub></caption><thead><tr><th></th><th>PU-1</th><th>PU-2</th><th>PU-3</th><th>Acrylate</th></tr></thead><tbody><tr><td>G<sub>elastic</sub> (measured, Δτ=0,05 N/mm²s)</td><td>0.83</td><td>2.1</td><td>3.3</td><td>33</td></tr><tr><td>G<sub>elastic</sub> (producer information)</td><td>0.84</td><td>2.5</td><td>3.3</td><td>-</td></tr><tr><td>τ<sub>ultimate</sub> (measured Δτ=0,05 N/mm²s)</td><td>4</td><td>4.7</td><td>4.7</td><td>6.7</td></tr><tr><td>τ<sub>ultimate</sub> (producer information)</td><td>(4.5)</td><td>(4.0)</td><td>(5.0)</td><td>(8.0)</td></tr></tbody></table>

The stiffness of *PU-1* is not affected by temperatures between 20°C and 80°C but with increasing temperature the ultimate shear stress decreases.

<figure><img src="image_229.png" /><figcaption>Fig.18: PU-1; stress-strain relation / Δτ=0,05 N/mm²s
T = 23°C; 40°C; 60°C; 80°C</figcaption></figure>

In fig. 19 the melting point of the melting component in *PU-3* can be detected. Between room temperature and 40°C is a shift in the stiffness.

<figure><img src="image_230.png" /><figcaption>Fig.19: PU-3; stress-strain relation / Δτ=0,05 N/mm²s
T = 23°C; 40°C; 60°C; 80°C</figcaption></figure>

The stiffness of *Acrylate* decreases extremely between room temperature and 40°C. This indicates its transitions temperature.

<figure><img src="image_231.png" /><figcaption>Fig.20: Acrylate; stress-strain relation / Δτ=0,05 N/mm²s
T = 23°C; 40°C; 60°C; 80°C</figcaption></figure>

b) *Dynamic tests*

A significant characteristic is the dynamic modulus G<sub>dyn</sub>:

$$G_{dyn} = \frac{\tau_{max} - \tau_{min}}{\tan \gamma_{max} - \tan \gamma_{min}} \quad (7)$$

Although the stiffness of *PU-1* and *PU-2* showed no relevance to temperatures in the ultimate limit tests the dynamic modulus decreases with rising temperature. The relevance of the frequency is of secondary importance.

<table><caption>TABLE 10: DYNAMIC SHEAR MODULUS G<sub>DYN</sub></caption><thead><tr><th rowspan="2"></th><th colspan="4">PU-1</th><th colspan="4">PU-2</th></tr><tr><th>0.1</th><th>0.25</th><th>0.5</th><th>1.0</th><th>0.1</th><th>0.25</th><th>0.5</th><th>1.0</th></tr></thead><tbody><tr><td>23°C</td><td>1.1</td><td>1.09</td><td>1.09</td><td>1.15</td><td>2.5</td><td>2.54</td><td>2.54</td><td>2.56</td></tr><tr><td>40°C</td><td>0.92</td><td>0.91</td><td>0.93</td><td>0.94</td><td>1.78</td><td>1.78</td><td>1.76</td><td>1.85</td></tr><tr><td>60°C</td><td>0.88</td><td>0.87</td><td>0.87</td><td>0.92</td><td>1.44</td><td>1.44</td><td>1.44</td><td>1.45</td></tr><tr><td>80°C</td><td>0.86</td><td>0.83</td><td>0.82</td><td>0.82</td><td>1.25</td><td>1.26</td><td>1.28</td><td>1.29</td></tr></tbody></table>

4) *Numerical Methods in FE Applications*

For the design of glued joints with finite elements different material models were developed to consider the viscoelastic behaviour of adhesives. Efficient energetic models were developed by MOONEY and RIVLIN or by OGDEN. In both models the same basic energy approach is used:

$$U = \sum_{m=1}^{N} \sum_{n=1}^{N} C_{m,n} (I_1 - 3)^m (I_2 - 3)^n \quad (8)$$

* I₁, I₂ invariants of the CAUCHY-GREEN deformation vector; they describe the deformation-energy relation.

* C<sub>m,n</sub> material parameter

* N order
With N=3 the approaches are:

• MOONEY-RIVLIN:

$$U = C_{10}(I_1 - 3) + C_{01}(I_2 - 3) + C_{11}(I_1 - 3)(I_2 - 3) \quad (9)$$

• OGDEN:

$$U = \sum_{n=1}^{3} \frac{\mu_n}{\alpha_n} (\lambda_1^{\alpha_n} + \lambda_2^{\alpha_n} + \lambda_3^{\alpha_n} - 3) \quad (10)$$

The viscous stress tensor can be calculated with:

$$\sigma_{m,n} = \frac{\partial U}{\partial \varepsilon_{m,n}} = \frac{\partial \Phi}{\partial \varepsilon_{m,n}} \quad (11)$$

U deformation energy

$\varepsilon_{m,n}$ deformation tensor

The identification of the material parameters in these models is the major task that is usually solved in two steps:

• Experimentally examination of the material behaviour in suitable tests that represent the real application load (stress and time) as good as possible (tensile tests, shear tests, compressive tests etc.)

• Determination of the unknown parameters by fitting the model response to the test data. The stability of the solutions to changes in the test data and the valid range of the identified parameters are important verification criteria's.

For the adhesive PU2 the following values are determined by fitting the measured shear-stress-strain relation.

• MOONEY-RIVLIN:

$$C_{10} = C_{01} = 0,5247977, C_{11} = 0$$

• OGDEN:

$$\mu_1 = 11,9431, \mu_2 = 19,1102, \mu_3 = 10,9421,$$

$$\alpha_1 = 0,10877, \alpha_2 = 0,12035, \alpha_3 = 0,0956804$$

An alternative linear-elastic description is:

$$E \approx 6 \cdot (C_{10} + C_{01}) = 6,5 \, \text{N/mm}^2$$

### C. Creeping Tests

#### 1) Test set up

Long-term loads are e.g. those due to self weights. Although the load could be multiplied by mechanical transformation the maximum load is limited. Therefore the length of the bond line was decreased to 50 mm. All other geometric parameters were the same as in the test series for short-

term loads. The dead weight of 50 kg steel blocks were transmitted with a see-saw. Before a test specimen was stretched in the steel frame the resulting force on the passive side of the see-saw was adjusted to the volitional value.

<figure><img src="image_232.png" /><figcaption>Fig.21: Creeping test steel frame</figcaption></figure>

#### 2) Test data and numerical approximations for design

A usual approximation for the time yieldingness is:

$$I = \frac{\tan \gamma}{\tau} = B \cdot t^{\alpha} \quad (12)$$

I time depending yieldingness

B, $\alpha$ material parameters

A linear curve in a double logarithmic scale is typical for the time depending shear strain of polymers under permanent load.

<figure><img src="image_233.png" /><figcaption>Fig. 22: characteristic values in creeping tests</figcaption></figure>

$\gamma_{I_0}, \gamma_{II_0}, \gamma_{III_0}$ shear strain at the beginning of the deformation regions I, II, III

$\Delta t_I, \Delta t_{II}, \Delta t_{III}$ time in the regions I, II, III

$\gamma_B, t_B$ ultimate limit values
For design purpose the level $\gamma_{III_0}$ should not be reached, because the failure of the connection is initialized at this level.

In the following graphs the parameters B and $\alpha$ are determined for the tested adhesives for different temperatures.

The test specimen S3 (PU-1; 20°C; $\tau=1.0$ N/mm²) failed after 40 h. in this case the parameters B and $\alpha$ are calculated with the deformation in the first 30 h.

<figure><img src="image_234.png" /><figcaption>Fig.23: PU-1 / creeping measurement and numerical approximation</figcaption></figure>

<figure><img src="image_235.png" /><figcaption>Fig.24: PU-2 / creeping measurement and numerical approximation</figcaption></figure>

The test specimen S2 (Arylate; 20°C; $\tau=1.0$ N/mm²) failed after 5 h and test specimen S5 (Arylate; 40°C; $\tau=0.0$ N/mm²) failed after 150 h. The parameters B and $\alpha$ are calculated with the deformation in the first 4 h and 100 h.

<figure><img src="image_236.png" /><figcaption>Fig.25: Acrylat / creeping measurement and numerical approximation</figcaption></figure>

## V. ACKNOWLEDGMENT

Special thanks to the companies SIKA, Switzerland and DELO, Germany. They sponsored the adhesives and provided us with their product information and their experiences.

## REFERENCES

[ETAG 002-P 1: 2001]

European Organisation for Technical Approvals; Guide-line for European Technical Approval for Structural Sealant Glazing Systems; Part 1, Supported and Un-supported Systems, Brussels 2001

[Ehrenstein 1999]

Ehrenstein, G.W.: *Polymer-Werkstoffe, Structur Einge-schaften Anwendungen*, 2. Auflage, Hanser Verlag 1999

[Lewen 1991]

Lewen B.: *Das nichtlinear viskoelastische Verhalten von Kunststoffen am Beispiel der Zeit- Temperatur-Verschiebung und der Querkontraktionszahl*, Disserta-tion, Institut für Kunststoffverarbeitung, RWTH Aa-chen, 1991

[Röder 1996]

Röder, T.: *Klebstoffkonstruktionen in Verbindung mit Kfz. Verglasungen*, 4. Fachkongress Innovatives Bauen mit Gas, Bauzentrum München 1996
# Glass facades of mid-rise steel buildings under seismic excitation

Charalambos C. Baniotopoulos, Institute of Steel Structures, Department of Civil Engineering, Aristotle University of Thessaloniki, GR-54124 Thessaloniki, Greece

Konstantinos T. Chatzinikos, Institute of Steel Structures, Department of Civil Engineering, Aristotle University of Thessaloniki, GR-54124 Thessaloniki, Greece

The present research work intends to propose a methodology that will provide engineers aiming to design glass facades of mid-rise steel buildings with the appropriate know-how regarding their performance under dynamic loadings. As a matter of fact, modern structural codes dictate that non-structural elements of buildings, which in case of failure may cause risks or - from a serviceability point of view - negatively affect the building, have to be verified to resist along with their supports the design actions with regard to dynamic loadings. Within such a framework, the glass facades were analysed applying well-known finite element method analysis software packages [Computers & Structures 1998] [Ansys Inc. 2002]. The analysis was performed for seismic loadings. In particular, the seismic analysis was carried out in two steps. The first step was to generate time history inter-storey drifts by imposing to the steel frame structures time history accelerations derived from accelerograms of a reference earthquake (c.f. the Athens 1999 earthquake). The second step was to develop and apply as input, drift or load histories for the seismic analysis of the glass facade under investigation [Truman et al. 1996], [Chatzinikos, Baniotopoulos 2003]. The proposed methodology is illustrated in the final part of the paper by means of a numerical application.

**Keywords:** aluminium, glass, curtain wall, seismic, building facade, dynamics

## I. INTRODUCTION

During the last decades, the use of glass facades being the envelope of mid-rise steel buildings is very common in modern construction. The development of modern and sophisticated curtain wall systems improved their reliability. However, the curtain wall systems are extremely vulnerable to natural (i.e. wind pressure, earthquakes, temperature variations) and human actions. Moreover, glass used in infill panels is exceptionally brittle. These facts render the detailed and well-documented structural analysis of glass facades a necessity.

The fact though, is that modern structural codes do not pay the proper attention to the assessment of the integrity and serviceability of non-structural elements and in particular, of curtain wall systems and their connections to the steel buildings [Baniotopoulos, Wald 2000] [Ivanyi, Baniotopoulos 2000]. Most modern building codes contain requirements to accommodate movements of non-structural elements due to lateral forces during an earthquake so as to minimize building envelope damage. In particular, modern seismic codes incorporate inter-storey drift limitations on the primary load-bearing structure for seismic forces. However, they do not provide engineers with a methodology for the modelling and the verification of glass facades and their supports to resist the de-
sign seismic actions [CEN 1998] [OASP 1999].

The intention of the present research work is to contribute to such a pilot methodology that will provide engineers aiming to design curtain walls with the appropriate technique regarding curtain wall modelling and performance during a seismic event. The modelling and analysis of the curtain wall systems has been performed using well-known finite element method software packages (e.g. ANSYS and SAP2000). The use of two different software packages for the same models using the same basic assumptions and the comparison of the obtained results makes the analysis more reliable.

The research effort has been developed in two steps. The first step was to model a typical mid-rise steel load-bearing structure with moment resisting and braced frames. At this step, the presence of the glass facade has not been taken into account apart from its dead load and mass, which have been properly distributed in the load-bearing structure model. The purpose of this analysis was to generate time history inter-storey drifts and load histories as input data for the seismic analysis of the glass facade. The aforementioned input data has been generated by imposing to the steel load-bearing structure time history accelerations derived from accelerograms of a reference earthquake (for the case at hand the Athens 1999 earthquake).

The second step was to use the generated input data for the seismic analysis of a standard curtain wall system together with its supports to the primary load-bearing structure. The curtain wall system has been modelled in detail so that the analysis to achieve a good level of reliability.

## II. GEOMETRY – MATERIAL PARAMETERS

The modelled steel structure is a six-storey office building. Each floor is 3m high and the total height of the building is 18m high. The resisting structure comprises six moment resisting frames and two braced frames parallel to the Y-Z plane and six moment resisting frames and two braced frames

parallel to the X-Z plane. The plan of the building was considered to be square with dimensions 42x42 m. The distance between two consecutive bays parallel to the Y-Z plane and parallel to the X-Z plane is 6m. The finite element method model of the steel load-bearing structure is presented in the following figure.

<figure><img src="image_237.png" /><figcaption>Figure 1: Steel load-bearing structure model</figcaption></figure>

The structure consists of IPE300 beams on the upper level and of IPE360 on the other levels. The columns are HEA320 for the lower two levels, HEA260 for the next two levels and HEA200 for the upper two levels. The braces are all QHS100x10 sections. In order to implement an integrated analysis of the steel frame structure it was necessary to take into account the dead load, the live load and the wind loading applied to this structure. The selection of the sections used to model the steel structure was based on a preliminary design regarding the aforementioned loadings according to Eurocodes 1 and 3 [CEN 1993] [CEN 1995].

The curtain wall consists of a grid of vertical and horizontal aluminium elements with dimensions 1.2x1.0 m. The vertical elements (mullions) are rigidly supported to the main load-bearing structure at every floor (at every 3.0 m) and they are 6.0 m high. The transoms are pin-connected at their edges to the mullions and their length is 1.2 m. All degrees of freedom were constrained at the connection of the curtain wall with the steel frame.

The glass panels are supported along their pe-
rimeter by the aluminium elements and they were meshed so as to obtain more accurate results. The curtain wall model is presented in Figure 2.

The materials that were simulated for the purposes of the analysis models are steel, aluminium and glass.

<figure><img src="image_238.png" /><figcaption>Figure 2: Curtain wall model</figcaption></figure>

The modulus of elasticity for steel is $2.0 \times 10^5$ MPa and the mass density is $7900 \text{ kg/m}^3$. Steel behaviour was considered to be linear-elastic, since the load-bearing steel structure was designed so as not to exhibit non-linear or plasticity effects.

The modulus of elasticity for aluminium is $7.0 \times 10^4$ MPa and the mass density is $2700 \text{ kg/m}^3$. The stress-strain curve used to simulate aluminium behaviour of the alloy used, is presented in Fig.3 and it is designed based on the following formula proposed by Ramberg-Osgood [Baniotopoulos et al. 1998]:

$$ \epsilon = \frac{\sigma}{E} + 0.002 * \left( \frac{\sigma}{\sigma_0} \right)^n \quad (1) $$

* $\epsilon$ is the strain that corresponds to stress $\sigma$

* $\sigma$ is the stress

* $E$ is the modulus of elasticity

* $\sigma_0$ is the actual 0.2% proof stress and

* $n$ is the index of curvature of the stress-strain relation

The two terms in this expression are the elastic and plastic strain respectively. The role of the in-

dex n is to control the curvature of the knee of the curve and depends on the aluminium alloy used. The actual 0.2% proof stress corresponds to a value of plastic strain equal to 0.002. For the analysis, 6082-T4 alloy was employed, the index n of which equals to 6.7, the $\sigma_0$ and the ultimate stress $\sigma_u$ equal to 110 and 205 MPa respectively [Mazzolani 1985] [Dwight 1998] [CEN 1999].

<figure><img src="image_239.png" /><figcaption>Figure 3: The aluminium stress-strain relation</figcaption></figure>

The glass behaviour is extremely brittle and exclusively elastic. The modulus of elasticity of glass is $7.0 \times 10^4$ MPa and the mass density is $2700 \text{ kg/m}^3$.

### III. EARTHQUAKE GROUND MOTION

A time history analysis of the steel load-bearing structure was performed based on the 9 September 1999 Athens earthquake accelerogram, which derived from the acceleration records of the aforementioned earthquake. The records used refer to longitudinal and transversal direction. Each record represents the value of ground acceleration in the corresponding direction and the recording time step was 0.005 seconds. The duration of the earthquake was about 39 seconds and the strong ground motion lasted 5.5 seconds. By the term strong ground motion we mean ground acceleration values over 0.05g. The peak ground acceleration was 0.264g (2.590 m/sec²) and 0.303g (2.970 m/sec²) for the longitudinal direction and the transversal direction respectively. The graphs of the longitudinal and transversal acceleration versus time are
shown in Figures 4 and 5. The vertical component of the reference earthquake has not been taken into consideration in the time history analysis because it was considered to be not significant.

The Athens 1999 earthquake was chosen because it was a disastrous seismic event and its characteristics are typical of earthquakes occurring in Greece.

<figure><img src="image_240.png" /><figcaption>Figure 4: Time history of longitudinal ground acceleration</figcaption></figure>

<figure><img src="image_241.png" /><figcaption>Figure 5: Time history of transversal ground acceleration</figcaption></figure>

## IV. MODELLING ASSUMPTIONS

All the floors are concrete (14 cm thick) over metal deck and therefore, were modelled as rigid diaphragms at the vertical axis. The rigid diaphragm assumption can be achieved in both software packages by using appropriate diaphragm constraints. By doing so, all the nodes of the plane of each floor belong to a diaphragm and therefore have the same displacements along the axes x and y. Furthermore, the floor masses were assumed to be concentrated at the centres of mass for each floor.

Both columns and beams were modelled using

two-node beam elements with 6 degrees of freedom at each node. The columns were fixed at the foundation and the beams rigidly attached to the columns at their joints. The bracings were assumed to be pin-connected to the frame structure.

The loads were distributed to the beam elements as uniformly distributed loads, such that each beam element carries one-quarter of the load of its respective bays. The curtain wall dead load was distributed to the outer beams such that one-half of the load of each panel is carried by the upper beam element and one-half by the below beam element. The elements of the load-bearing frames have been considered massless and their masses were calculated and added at the mass discretization points.

Dead load masses including the self-weight of the steel structure, the load of the concrete deck and the load of the glass panels of the facade, have been considered to produce inertia forces.

The mass discretization at joints was done so as to simulate the structure in such a way that the distribution and the magnitude of the developing inertia forces between the real structure and the model to be close enough. The discretization depends on the movement of the structure. For the given seismic movement the horizontal and transversal translational masses were distributed at the mass centres of each floor. The analysis did not take into account any vertical translational masses. The amplitudes of the masses are given in Table 1 (in $Ns^2/m^4$).

<table><caption>TABLE 1: MASS DISTRIBUTION AT EACH FLOOR</caption><thead><tr><th></th><th>Concrete deck</th><th>Dead load</th><th>Façade</th><th>Total mass</th></tr></thead><tbody><tr><td>Roof</td><td>629,36</td><td>33,1</td><td>7,71</td><td>670,17</td></tr><tr><td>Floor5</td><td>629,36</td><td>47,84</td><td>15,41</td><td>692,61</td></tr><tr><td>Floor4</td><td>629,36</td><td>50,32</td><td>15,41</td><td>695,09</td></tr><tr><td>Floor3</td><td>629,36</td><td>52,8</td><td>15,41</td><td>697,57</td></tr><tr><td>Floor2</td><td>629,36</td><td>55,59</td><td>15,41</td><td>700,36</td></tr><tr><td>Floor1</td><td>629,36</td><td>58,39</td><td>15,41</td><td>703,16</td></tr></tbody></table>

The damping coefficient of the structure was assumed to be 4% as the Greek Anti-Seismic Structural Code and Eurocode 8 dictate for steel structures with bolted connections for concentric braced steel frames [CEN 1998] [OASP 1999].
## V. MODAL ANALYSIS OF THE STEEL FRAME

The modal analysis of the steel frame structure has been performed so that its vibration characteristics (natural frequencies and mode shapes) to be determined. The modal analysis can also be the basis for a more detailed dynamic analysis of the structure such as the time-history analysis is. Within this framework, the generalized eigenvalue problem has been treated, which is described by Equation (2):

$$[K]\{\phi_i\} = \omega_i^2 [M]\{\phi_i\} \quad (2)$$

* [K] is the stiffness matrix of the structure

* $\phi_i$ is the mode shape i

* $\omega_i$ is the eigenvalue of mode i and

* [M] is the mass matrix of the structure

The first 10 periods for SAP2000 and ANSYS model are shown in Table 2. The modal participating mass factors for each mode are shown in Table 3. It is quite clear that the first 4 translational modes contribute for more than 90% to the total response of the structure.

<table><caption>TABLE 2: MODAL PERIODS</caption><thead><tr><th>Mode</th><th>SAP2000 (sec)</th><th>ANSYS (sec)</th><th>difference</th></tr></thead><tbody><tr><td>1</td><td>0.9222</td><td>0.9265</td><td>0.47%</td></tr><tr><td>2</td><td>0.8422</td><td>0.8292</td><td>1.57%</td></tr><tr><td>3</td><td>0.3056</td><td>0.3066</td><td>0.31%</td></tr><tr><td>4</td><td>0.2794</td><td>0.2742</td><td>1.91%</td></tr><tr><td>5</td><td>0.1694</td><td>0.1694</td><td>0.02%</td></tr><tr><td>6</td><td>0.1547</td><td>0.1511</td><td>2.36%</td></tr><tr><td>7</td><td>0.1231</td><td>0.1229</td><td>0.14%</td></tr><tr><td>8</td><td>0.1121</td><td>0.1098</td><td>2.12%</td></tr><tr><td>9</td><td>0.1018</td><td>0.1016</td><td>0.16%</td></tr><tr><td>10</td><td>0.0911</td><td>0.0894</td><td>1.89%</td></tr></tbody></table>

<table><caption>TABLE 3: MODAL PARTICIPATING MASS FACTORS</caption><thead><tr><th rowspan="2">Mode</th><th rowspan="2">Period</th><th colspan="2">Individual mode (%)</th><th colspan="2">Cumulative sum (%)</th></tr><tr><th>UX</th><th>UY</th><th>UX</th><th>UY</th></tr></thead><tbody><tr><td>1</td><td>0.9222</td><td>0.00</td><td>77.61</td><td>0.00</td><td>77.61</td></tr><tr><td>2</td><td>0.8422</td><td>77.08</td><td>0.00</td><td>77.08</td><td>77.61</td></tr><tr><td>3</td><td>0.3056</td><td>0.00</td><td>15.91</td><td>77.08</td><td>93.52</td></tr><tr><td>4</td><td>0.2794</td><td>15.21</td><td>0.00</td><td>92.29</td><td>93.52</td></tr><tr><td>5</td><td>0.1694</td><td>0.00</td><td>4.08</td><td>92.29</td><td>97.60</td></tr><tr><td>6</td><td>0.1547</td><td>4.35</td><td>0.00</td><td>96.64</td><td>97.60</td></tr><tr><td>7</td><td>0.1231</td><td>0.00</td><td>1.33</td><td>96.64</td><td>98.93</td></tr><tr><td>8</td><td>0.1121</td><td>1.49</td><td>0.00</td><td>98.13</td><td>98.93</td></tr><tr><td>9</td><td>0.1018</td><td>0.00</td><td>0.64</td><td>98.13</td><td>99.57</td></tr><tr><td>10</td><td>0.0911</td><td>0.90</td><td>0.00</td><td>99.03</td><td>99.57</td></tr></tbody></table>

## VI. TIME HISTORY ANALYSIS OF THE STEEL FRAME

The time-history analysis has been employed in order to determine the dynamic response of the steel frame structure subjected to earthquake loading, which is a time-varying loading. This way the time-varying deformations and forces of the steel frame structure have been calculated at the joints of the steel structure with the glass facade.

The aforementioned results of the time-history analysis have been derived from the time integration and solution of the following dynamic equilibrium equations of motion:

$$[M]\ddot{u} + [C]\dot{u} + [K]u = F(t) \quad (3)$$

* [M] is the mass matrix of the structure

* [C] is the damping matrix of the structure

* [K] is the stiffness matrix of the structure

* $u, u, u$ are the acceleration, velocity and displacement of the structure and

* $F(t)$ is the time-varying load vector

In SAP2000 a transient (time-history) analysis has been performed. The program solved the dynamic equilibrium equations of motion for the complete structure using the standard mode superposition method of response analysis. The mode superposition method summed factored mode shapes (eigenvectors) from the modal analysis to calculate the response of the structure. The time integration step used for the time-history analysis was 0.005 sec., which was the time step given by the Athens earthquake accelerographic data.

After retrieving and elaborating the time-history analysis results, the maximum displacements, maximum storey drifts and the time when they occurred were determined. The peak displacement was presented at the roof (3.18 cm along the x-direction and 4.54 cm along the y-direction). The maximum storey-drift along the x-direction was presented between the first and the second floor 3.91 seconds after the start of the earthquake excitation and had a value of 0.76 cm. The maximum storey-drift along the y-direction was presented be-
tween the third and the fourth floor 4.32 seconds after the start of the earthquake excitation and had a value of 1.07 cm. The maximum displacements and inter-storey drifts along x and y direction are presented in Table 4.

<table><caption>TABLE 4: MAXIMUM DISPLACEMENTS AND INTER-STOREY DRIFTS</caption><thead><tr><th rowspan="2"></th><th colspan="2">earthquake direction x</th><th colspan="2">earthquake direction y</th></tr><tr><th>displacements (cm)</th><th>maximum drift (cm)</th><th>displacements (cm)</th><th>maximum drift (cm)</th></tr></thead><tbody><tr><td>ROOF</td><td>3,18</td><td>0,49</td><td>4,54</td><td>0,63</td></tr><tr><td>FLOOR5</td><td>2,67</td><td>0,66</td><td>4,05</td><td>0,87</td></tr><tr><td>FLOOR4</td><td>2,20</td><td>0,69</td><td>3,39</td><td><b>1,07</b></td></tr><tr><td>FLOOR3</td><td>1,75</td><td>0,65</td><td>2,51</td><td>0,88</td></tr><tr><td>FLOOR2</td><td>1,13</td><td><b>0,76</b></td><td>1,46</td><td>0,86</td></tr><tr><td>FLOOR1</td><td>0,49</td><td>0,70</td><td>0,63</td><td>0,80</td></tr></tbody></table>

Eurocode 8 dictates that for building having non-structural elements composed of brittle materials (e.g. glass) attached to the main load-bearing structure, the following limit shall be observed:

$$d_r \nu \le 0.005h \quad (4)$$

$d_r$ is the design inter-storey drift

$h$ is the storey height and

$v$ is a reduction factor, depending on the importance class of the building

Assuming that the design inter-storey drifts are the drifts deriving from the time-history analysis and $v$ equal to 0.5 (recommended value for importance class III buildings), then the drift limit in meters is:

$$d_r \le 0.03 \quad (5)$$

The inter-storey drift values obtained from the time-history analysis of the main load-bearing structure are in good accordance with the aforementioned drift limit, since the maximum value obtained is 1.07 cm.

## VII. ANALYSIS AND DESIGN OF THE CURTAIN WALL

The horizontal and vertical aluminium elements were simulated by two-node beam elements with six degrees of freedom at each node. Common industrial sections have been considered for the mul-lion-transom aluminium structure. Such section is presented in Fig.6. The section properties (area, moments of inertia) have been calculated with the

aid of well-known design tools (such as Auto-CAD).

The glass panels were simulated by four-node shell elements with six degrees of freedom at each node and they were properly meshed in order to obtain more accurate and reliable results. The shell elements have both bending and membrane capabilities and their thickness is 12mm.

Mass density was issued for both aluminium and glass in order to calculate the inertia loads.

The curtain wall is symmetrical in two axes. We took advantage of the symmetry, hence only a part of the curtain wall has been analysed.

<figure><img src="image_242.png" /><figcaption>Figure 6: Typical load-bearing aluminium section</figcaption></figure>

The results generated by the time-history analysis of the steel frame structure can be used further as input either for computational analysis of curtain wall systems or for laboratory testing of the aforementioned systems. In the present research effort, the time-history displacements of the floors were used as input data at the joints of the curtain wall with the steel frame structure for a time-history analysis.

In ANSYS a transient (time-history) analysis has been performed, in order to take into account possible effects of geometry and material nonlinearities. The time integration step used was 0.02 sec. The input data considered the displacements at the first 20 sec, when the displacements are significant.

The results of this time-history analysis have been derived from the time integration and solution of the dynamic equilibrium equations of motion (3), which were also used for the time-history analysis.
lysis of the steel frame.

After retrieving and elaborating the time-history analysis results, the maximum displacements of the glass facade were determined and in particular the displacements of the glass facade in the transversal direction were examined. The conclusion of the processing of the aforementioned results showed no significant displacements of the glass facade in regard to the movement of the main load-bearing steel structure. The deformed shape of the glass facade is presented in Figure 7.

<figure><img src="image_243.png" /><figcaption>Figure 7: Deformed shape of the glass facade</figcaption></figure>

The time history of the longitudinal displacement at the roof height level is presented in Figure 8.

<figure><img src="image_244.png" /><figcaption>Figure 8: Time history of roof longitudinal displacement</figcaption></figure>

## VIII. CONCLUSIVE REMARKS

The curtain wall systems are in general analysed and designed empirically. The present research work intends to contribute to a pilot methodology that will provide engineers aiming to design curtain walls with the appropriate know-how regarding curtain wall performance during a seismic

event. In order to achieve the previously mentioned objective, the research effort has been developed in two steps. A time-history analysis of the steel load-bearing structure has been employed in order to generate input drift history to be applied at the curtain wall system. The computed values are the displacements of the joints of the mullion-transom system. After elaboration of the aforementioned values the relative displacements along the axes were extracted and compared to the restrictions dictated by Eurocode 8. More specifically, the maximum inter-storey drift rises to 1.07 cm, whereas Eurocode 8 defines that the limit in the case investigated is 3.0 cm [CEN 1998]. Furthermore, no significant displacements of the glass facade has been present in relation to the movement of the main load-bearing structure. It is noteworthy a similar methodology for the design of glass facades under wind loading has been recently proposed [Chatzinikos, Baniotopoulos 2005].

## IX. ACKNOWLEDGEMENT

The authors acknowledge with thanks the financial support of part of the present research activity by the Greek General Secretariat of Research and Technology (G.S.R.T.): Concerted Programme Renewable Energy Sources & Energy Saving E11: PhotoV-AluE – “Research, Development and Certification of Large Dimensions Aluminium Structural Members with Incorporated Modern Technology Photovoltaic Elements and Innovative Grid Connected Power Inverters, aiming to their Effective Application into Building Construction”.

## REFERENCES

[ANSYS Inc. 2002]

ANSYS Inc., *Theory Reference*, 2002.

[Baniotopoulos et al. 1998]

Baniotopoulos C. C., Koltsakis E., Preftitsi F., Panagiotopoulos P. D., *Aluminium Mullion-Transom Curtain Wall Systems: 3D F. E. Modelling of their Structural Behaviour*, Proc. ISCAS 4th Intern. Conf. on Steel and Aluminium Structures, pp. 433-440, Helsinki 1998.

[Baniotopoulos, Wald 2000]

Baniotopoulos C. C., Wald F. (eds.), *The Paramount Role of Joints into the Reliable Response of Structures*:
*From the Classic Pinned and Rigid Joints to the Notion of Semi-rigidity*, Kluwer, Dordrect, 2000

[Chatzinikos, Baniotopoulos 2003]

Chatzinikos K. T., Baniotopoulos C. C., *On the Performance of Glass-Aluminium Curtain Wall Systems of Mid-rise Buildings During Seismic Events*, Proc. Of the 10th Inter. Conf. On Metal Structures, Timisoara, 2003

[Chatzinikos, Baniotopoulos 2005]

Chatzinikos K. T., Baniotopoulos C. C., *Glass - Aluminium Facades in Steel Buildings: Analysis of their Performance under Dynamic Loadings*, Proc. of 4th European Conference, Maastricht, 2005 (in print)

[Computers & Structures 1998]

Computers & Structures, Inc., *SAP2000 Integrated Finite Element Analysis and Design of Structures: Analysis Reference*, 1998

[Dwight 1998]

Dwight J., *Aluminium Design and Construction*, E & FN Spon, 1998

[CEN 1995]

European Committee for Standardization, *Eurocode 1 – Actions on structure*, 1995.

[CEN 1993]

European Committee for Standardization, *Eurocode 3: Design of steel structures – Part 1-1: General rules – General rules and rules for buildings*, 1993.

[CEN 1998]

European Committee for Standardization, *Eurocode 8 – Part 1: Design of structures for earthquake resistance – General rules, seismic actions and rules for buildings*, 1998.

[CEN 1999]

European Committee for Standardization, *Eurocode 9 – Part 1-1: General rules and rules for buildings*, 1999.

[Ivanyi, Baniotopoulos 2000]

Ivanyi M., Baniotopoulos C. C. (eds.), *Semi-rigid Joints in Structural Steelwork*, Spinger, Wien, 2000

[Mazzolani 1985]

Mazzolani F. M., *Aluminium Alloy Structures*, Pitman Publishing Ltd., London, 1985

[OASP 1999]

Organization for Anti-Seismic Protection – Greece, *Greek Anti-Seismic Structural Code*, 1999.

[Truman et al. 1996]

Truman K. Z., Pantelides C. P., Behr R. A. and Belarbi A., *Comparison of linear and non-linear seismic drift histories for mid-rise steel frames*, Engineering Structures, Vol.18, No.8, pp. 577-588, 1996.
# Design, Engineering, Production & Realisation of Glass Structures for ‘Free-Form’ Architecture

Mick Eekhout, Professor Product Development at the Delft University of Technology & Director of Octatube Space Structures, Delft, The Netherlands

Structural designers are confronted in the last decade with architectural spatial schemes that greatly benefited from the aid of computer-operated design and modelling programs like Maya, Rhino and 3D-Studio Max. These architectural designs are referred to as ‘Fluid or Liquid Designs’ or ‘Blob Designs’. They contain sculptural building forms in arbitrary geometrical forms, which cannot be developed mathematically, or to be generated easily, even by computer. These building forms do not have a systematic and recognisable repetitive structure, either.

The gap between architects and structural engineers seems to open wide at first in each project and an even larger gap appears between architects, technical designers on the one hand and co-engineers, producers, co-makers, subcontractors and builders a little later in the same project. In the structural glass building parts, with its tight tolerances and high degree of prefabrication an enormous effort is necessary in the engineering phase to define accurately all individually shaped building components. This will definitely transform ‘production’ into ‘co-engineering & production’.

**Keywords:** blob, free-form architecture, glass, engineering, management

## I. INTRODUCTION

The second half of the 20th century has witnessed the development of a number of spatial and systemised lightweight structures: shell structures, space frames, tensile structures, cable net structures, pneumatic structures, folded plate structures and ‘tensegrity’ structures. Most of these structures were developed by dedicated pioneers in the 1950-ies who designed, analysed and built impressive amounts of ever new concepts: Felix Candela, Frei Otto, Max Mengeringhausen, Richard Buckminster Fuller, Zygmunt Makowski, Walter Bird, Peter Rice et all [Eekhout 1989]. The common basic idea was to minimize the amount of material consumed, and in order to attain this, extensive intellectual investments in man hours were necessary. Computer analysis programs assisted the accurate analysis of complex geometries of the components in these three-dimensional though – in our current view - highly regular 3D-structures. Thanks to the further development of accurate analysis programmes based on non-linear structural behaviour these 3D-structures can now be designed by structural engineers all over the world. They reached a status of accepted and mature technology. Peter Rice (or rather: R.F.R) introduced the intricate use of structural glass in buildings in the 1980-ies, based on regularity and systemization in the Serres of La Vilette, Paris in 1986 [Rice et al. 1995].

In the newest trend the forms of digital baroque buildings are non-rectilinear, non-repetitive and in their conceptual stage only derived as clay-modelled sculptures, as it were, either by making concepts really in clay or by modelling and gener-
ating them in a similar way on the computer. Computer rendering programs like 3D design ‘Maya’ nowadays are able to juggle and generate all kinds of geometric forms, including the ones without any regularity in its geometric patterns. In the conceptual design stage, architects usually do not look for geometrical repetitive forms and systemised structural schemes or behaviour at the same time, but design like artists a totally new building with a mega-surprise for the entire world.

Structural engineers are initially paralysed when they have to develop a load bearing structure in the contours of these geometrical forms in order to materialise the structural concept of the building's envelope. The same is valid for building technical engineers working these designs out more elaborately onto the level of shop drawings. The question is how to reconcile this ‘Computer Supported Sculpturalism’ with sound structural design and industrial prefabrication principles in a proper balance that revitalises the excellent and extensive experiences of 20<sup>th</sup> century 3D-lightweight structures. This should happen already in the conceptual stage, so that both existing know-how and experience are activated and the cost prices of these buildings are less of a surprise. The relation between pre-design principle and post-design application is at stake here. Principles were conquered and gained by pioneers and scientists later, while architects, acting as composers, but sometimes with the elitarism of prima ballerinas, do as they like in both surprising and pleasing society at the same time. It raises the question of relationship between principles and applications.

## II. ‘LIQUID DESIGN’ ARCHITECTURE AFTER GEHRY’S GUGGENHEIM

Out of the blue came the Guggenheim museum in Bilbao, opened in 1997. Perfectionist American design blended with a Spanish way of building. But after the opening of this Museum designed by Frank O. Gehry the world was amazed. It really boosted the ‘Liquid Design’ era. Gehry designs his buildings in clay as sculptures. The model that satisfies him most is measured electronically and fed into a geometrical computer program. Gehry’s office in Santa Monica uses the French Dassault-based program Catia for this purpose, developed

for engineering aeroplanes. By then the enlarged clay geometry is fixed and the building is tendered as a total package. Then the subscribing main-contractors have to find sub-contractors who are willing to engineer, produce and built the building parts exactly as designed by Gehry. Subcontractors have to buy the Catia program as well in order to detail the global geometry as given in the main design. From this 3D-Catia model the construction and composition of all elements and components of each different building part, taken care of by each sub-contractor, is derived and fixed, especially when these elements and components have to be prefabricated.

<figure><img src="image_245.png" /><figcaption>Figure 1: Guggenheim Museum Bilbao, Frank O. Gehry</figcaption></figure>

Gehry was also responsible for the design of the glass roof over the D.G.Bank in Berlin, built by Gartner. This type of experimental architecturally complex geometries can not at all be built by differently thinking building parties, as is usually the case. In case of unequal distribution of ‘say & duty’, the producing parties will pay these projects out of their own pockets, which means a short popularity of the architectural approach and many frustrations amongst participants in the building processes who get the blame and not the glory. Hence the nickname ‘Fluid Design Nightmares’ amongst producers.

## III. HIGHER DEGREE OF CO-OPERATION: COLLABORATION

A free-form geometry involving all building parts of the building design leads automatically to a very accurate co-operation, rather collaboration between the building team partners, much higher and more
intense than ever experienced before. It takes for
most of the concerned architects a number of pro-
jects to agree with this and to change their usual
distance to the production & building phase and
work towards an integrated approach of all build-
ing team parties concerned. The building team is to
be defined as the sum of all participating archi-
tects, designers, advisors, main contractor, building
managers, component designers, sub-contractors
and producers involved in the project.

One could define four major stages:

* *Design of the building and its components*

* Engineering of the building parts (elements, components and site parts)

* Productions of elements and assembly to components

* Building on site and installation of prefab components

Each of the 4 stages has its own characteristics of
taking design considerations and assuring quality
of the building as the end product being a composi-
tion of the different building parts, installed on the
building site by different building team partners.
The phase of design of the building and its compo-
nents will be the global domain of the architect and
his advisors. In ‘Liquid Designs’ the tendency is
for standard products to become systemized and
for building systems to become special project sys-
tems. The need for special components will in-
crease because of the special geometry of the
building, influencing the form and position of each
composing element/component. The tendency to-
wards individualisation can be described as: ‘In-
dustrialisation in lots of one’.

IV. CO-ENGINEERING, PRODUCTION AND INSTALLATION

Different building team parties are involved engi-
neering their own production. These engineering
activities all have to be based on the central 3D-
mother CAD model. This model is the basis for the
engineering of the total building. The keeper of
this model is indispensable in the office and will
become a crucial factor in each co-engineering
company. Despite computers, in-house logistics
will be depending on one master-engineer only!

For the co-ordination and integration of the differ-
ent co-engineering parties in the building team two
clearly distinct modus operandi can be followed:
**Separate Model**: Every party works on his own
program, taking the basic data from the mother
model. The problem will then how to check the
quality of these separate computer drawings and
outputs and how to relate them to the common de-
tails, where two or more building parts are joined,
each to be worked out by a separate building party.
In the Netherlands the steel construction engineers
work with Strucad or X-steel, while façade engi-
neers work with Autocad 2000 or 14. The two sys-
tems are not compatible. Installation engineers use
other programs. Checking of the different results is
extremely difficult and mistakes only appear on the
building site. The architect does not check any
drawing in its dimensions. This traditional pattern
is not satisfactory at all.

**Collaborative Model:** Each party works on the 3D-CAD mother model successively as it is allowed 'slot time' (like aeroplane traffic coordination). During the start the situation is fixed and detailing and modifications of elements and components can be fed in. The whole is to be worked through. The end situation will be fixed and communicated to all building parties. After the proper closing off of the slot time of one party, check and certification by the model keeper, the next is allowed his slot time. Simultaneous work on the 3D model by more than one engineering sub-contractor is not allowed, as it will lead to confusion and possible legal problems thereof. Gehry enforces the use of Catia in his projects. But now different teams in the engineering department of one producing company could be working with different programs. This will lead to mistakes and confusion. So a plea is made towards the development of an universal 3D-computer program to be used by all corresponding building team members, capable of handling the conceptual design, the presentations, the overall building design drawings, the static analysis, the engineering co-ordination drawings, the shop drawings up to the quantity lists. After each of the building-directed engineering contributions of all participants, regular geometrical checking has to be done. Neglect of this will lead to large problems in the integration and co-ordination of the engineering, in production and installation and hence, much effort has to be spent here. Liability is also at stake here. Four
building parties are able to execute this: the archi-
tect, the building technical engineer, the building
contractor and the geodetic surveyor. Each option
has its advantages and disadvantages. Each pro-
posed party has to realise assortment of forward or
backward integration.

V. CASE 1: GALLERIA, WILHELMINAHOF
METRO STATION ROTTERDAM, TENDER 1995

The first of the Dutch Blob buildings was a design
of Zwarts and Jansma for a railway station crossing
a tramway in Rotterdam-South: the Wilhelmina-
pier. The design of the main structure contained
steel trees with thicker and thinner branches in
varying heights. The tips of the top branches were
covered with a triangulated glass roof, in a hilly,
undulating form. The architects and the engineers
ABT had thought of a nodal system to suit the
many different corners in which the glass panels
had to be fixed.

ABT was smart enough to have a series with in-
formative talks with national and international spe-
cialist-companies to check the validity of the de-
sign and the price level. The international parties
declined. We made a material proposal for an al-
ternative node which would enable the steel riggers
to accurately position the tops of the steel top rods
supporting the glass nodes. The secret was the sur-
veying of the exact location of the centre lines of
the corners of the triangular glass panels. For all
components of the roof: both steel and glass are
produced simultaneously in different factories and
from theoretical drawings. The silicone seams be-
tween the glass panels are 10 to 15 mm at the most.
Disapproval already happens when there are larger
differences in seam widths than 2-3mm. That was
thought to be the wizardly domain of the glass sub-
contractor. We had thought out a logistic 'modus
operandi', which led to continuous 3D surveying
of all installed components, adjusting them to ex-
actly the required level and X,Y,Z position.

<figure><img src="image_246.png" /><figcaption>Figure 2: Rendering of the Galleria in Rotterdam
(image: courtesy of the architects Zwarts & Jansma)</figcaption></figure>

With these components we drafted our price and
were very astonished that we were the lowest bid-
der at 12 million guilders. Alas the architect and
engineers had grossly underestimated the complex-
ity of the design realisation, despite the warnings
that had sounded from the pre-talks. The budget
appeared to be only 4 million guilders. The archi-
tects and engineers were dismissed and architect
Cees Dam designed a flat glass lean-to roof which
met the budget but was not worth publishing here.

VI. CASE 2: DG BANK BERLIN,
OCTATUBE'S DESIGN ALTERNATIVE 1998

The design by Frank O. Gehry called for a triangu-
lar network in the form of the body of a whale, to
be constructed in stainless steel solid square rods,
in triangulated form, to be covered with double and
triple glazing panels. The nodes in finger form
with all fingers having different vertical and hori-
zontal directions. This was an extremely difficult
job as all nodes were different, all bars were differ-
ent and all panels were different.
<figure><img src="image_247.png" /><figcaption>Figure 3: Alternative geometry for the DG Bank by Octatube</figcaption></figure>

The Octatube alternative design consisted of hollow spherical cast nodes and tubular CHS members, all in stainless steel. The nodes were to be drilled in the exact direction. The length of the tubes would form the desired spatial envelope. The drawings show the illustrations. The tendering process resulted in a contract for Gartner in the original design at a dangerously low price, for which they suffered badly. The company is now taken over by Permasteelisa. The building has been completed in 2000. The accuracy, high degree of workmanship and finish of materials posed incredible high demands. The result has the quality of watchmakers accuracy, though!

<figure><img src="image_248.png" /><figcaption>Figure 4: Alternative detailing by Octatube</figcaption></figure>

## VII. CASE 3: MUNICIPAL FLORIADE PAVILION BY ASYMPTOTE ARCHITECTS, HOOFDDORP NL

The competition winning design of Asymptote Architects, New York, originally contained a building volume in an arbitrary form with two sloped all glass surfaces. In a later planning phase this glass roof was partly replaced by aluminium panels. Over both roof surfaces water is running continuously down, as a sign of the Dutch water-rich culture. The architects refer in their publications to 'the Hydra Pier'. There are three remarkable technical experiments.

The first experiment consists of the water filled frameless glass pond sized 5x12m², designed as a continuous curved glass volume filled with water, containing in its summit around 1.400mm of water. The target for development was to realise the laminated glass panels in 2D-, 2,5D- and 3-D glass frameless suspended glass. These panels were 1 x 1.4m in size. The still standing challenge of production was an experimental route of an initial thermal dual deformation into a 3D-form, subsequent (certified) chemical treatment, liquid lamination of the duo panels, testing these and comparing them with the theoretically calculated end results. Due to high costs and long replacement time the client choose for polygonal flat panels of 12.12.4 fully pre-stressed glass.

<figure><img src="image_249.png" /><figcaption>Figure 5: Glass pond of the Municipal Pavilion</figcaption></figure>

The second experiment contained cold deformed laminated glass panels, produced flat en bent by first fixing them on the four corners like the habit for spider glass and pressing two double points pushing outward on the upper and lower chord of the 2x2m² glass panels. The cold bent camber achieved was 80 mm over 2m side lengths. Bending stresses rose up to 35N/mm², while the allowable stresses including wind bending had a maximum of 55 N/mm². The cold bent panels had to be combined with hot bent monolithic panels for the smaller curvatures.

<figure><img src="image_250.png" /><figcaption>Figure 6: Cold deformed laminated glass panels</figcaption></figure>
The third experiment were 3D aluminium panels in the two outer corners of the roof. To this end an experimental route was followed of drafting a Maya file CAD/CAM, machining polystyrene blocks to the desired mould shape, smoothening tem with epoxy filled glass fibre weave, cast off with fibre reinforced concrete. After curing the concrete mould was covered with 5 mm aluminium sheet, in a 300mm water basin with an explosion loading of TNT, which subsequently was brought to explosion into the mould. After this global form-ing, the edged were checked on a timber model, the edges were fitted and welded on and the panels were smoothened and coated by air spray. The fit-ting on the site and sealing the 10 mm gasket in be-tween finalised the production and installation of these 14 panels. Industrialisation in lots of one. For the next project the Japanese adage of ‘half the time, half the effort and half the price’ will be the target.

<figure><img src="image_251.png" /><figcaption>Figure 7: Roof with the 3D aluminium panels</figcaption></figure>

## VIII. CASE 4: FRONT FAÇADE TOWN HALL
ALPHEN AAN DEN RIJN, NL

This design of architect Erick van Egeraat and ABT engineers is a pre-runner of Liquid Design Architecture. The main load bearing structure has not a single piece of repetition. Octatube was selected for the engineering, production & installation of the frameless glazing façades. This building has a façade of frameless glass panels, fully screened with graphical motives of trees, leaves and flowers in quite an ad hoc fashion. The panels are supported by elliptical façade mullions 75x150

and 110x220 up to 20m height, spaced at around 1.8m, with glass support nodes in between. The high yield, slender hot rolled elliptical mullions are excellent in freestanding use of frameless glazing. Their use in Quattro façades, either vertically or horizontally and suspended from the roof, is a standard system. The glass panels, around 850 pieces, are all unique in form and print design. The glass panels have been screened on surface 2 and have a low E coating on side 3. Most of the panels are 10.12.10 double glazed units in fully-tempered clear glass panels; the roof panels have laminated lower panels 6.6. All panels are fully tempered.

<figure><img src="image_252.png" /><figcaption>Figure 8: Exterior of the Town Hall with its triangulated and printed glass panels</figcaption></figure>

In the ‘semi-Blob’ geometry, parts of the façade are conical upward and downward, cylindrical, spherical, anti-clastical and only some parts are straight. Because of the geometrical differences between lining of the façade mullions and glass panels, the columns are positioned in varying angles to the glass panels. The glass connectors are irregular. Not one of the 90 mullions is equal to another. In the anti-clastical surface (roughly 10x10m²) the rectangular glass panels are twisted and the elliptical mullions have up to 9 bents in their longitudinal axis, which are cut and welded on jigs in the factory straight from the engineering drawings. They fitted perfectly.

At the double curved back of the building around 500 glass panels are installed, all of them in model form (i.e. non-rectangular) due to the at random form of the intersecting bays, called the ‘spaghetti strips’. The design called for a twisted glass panel. In the first development and engineering phase of 6 months a timber window firm tried to develop stepped glass windows and suitable details to that
purpose. After they gave up, Octatube brought forward a simple but fitting solution. The idea was to get rid of the window frames, and to use only double glass panels composed of two panes of fully tempered glass, laminated in panels under angles less than 80 degrees. The individual glass panels were to be warped slightly. The maximum size of 900 mm width and 1800 mm length was to be warped for 40 mm perpendicular on its surface. This was done by cold deformation. Tests in the Octatube laboratory showed that this was feasible. Static analysis of the tensions by bending showed that only 10 to 20% of the maximum tensions were used in bending. The stresses in the sealant were acceptably low and the sealant manufacturer gave his guarantee as usual. This was the first time in the history of Octatube that cold forming of insulated glass was performed in a solution much more simple than the original glazed timber window frame solution.

But this type of ‘Liquid Design’ architecture required the utmost of the engineering department: triple the time consumption of a regular project, including many problems with the matching of other building parts. An intensive collaboration was required in the final design stage, which took place after tender, involving all building parties. Opening of the town hall matured in June 2002.

<figure><img src="image_253.png" /><figcaption>Figure 9: The so-called ‘spaghetti-strips’ of cold formed glass panels</figcaption></figure>

## IX. CASE 5: RABIN CENTER IN TEL AVIV

Architect Moshe Safdie designed a memorial building for Yitzhak Rabin with two special halls on top: a Library and a Great Hall, overlooking the Ayalon valley in Tel Aviv. The form the roofs re-

sembles the wings of a (peace) dove. The tender, elaborated by Over Arup of New York, contained a random steel structure with open profiles and a concrete cladding to be constructed at the initiative of the sub-contractor. We tendered for a more systemized space frame and GRP covered foam cladding on top as a variation on the tender specification and a wild alternative idea of a load-bearing structure of a mega-sized GRP sandwich construction, able to span the 30x20m² size of the wings in one go. Initially the foam core was thought as 800 to 1000mm thick polystyrene and 10 mm glass fiber reinforced polyester. The wild alternative was 25% more expensive but a clean and structurally very straightforward construction, which was extremely convincing. The architect spoke about “an amazing solution”. We received a pre-engineering contract which contained a redesign in Maya of the design of the Great Hall in its overall design and its composing details, based on our propositions. We also made 4 real size material prototypes of the two alternatives. As a result of this pre-engineering contract, the prices dropped considerably. At the moment we have started with the engineering of the 30x20m² free spanning GRP sandwich construction with quite an intensive experimental route in front of us to test the bonding of the 200mm PIR foam core and the two GRP skins, specially in the 8m long cantilevering wing tips where fatigue due to changing wind loadings is suspected and the danger of punching-through of the steel columns supporting the front sides of the wings, is imminent. We agreed with the architect that Octatube as the specialist will solely do the redesign on a 3D-model in an appropriate computer program (Maya), the engineering in (AutoCAD with Pro-engineer) and the obligatory productions, assemblies and installations on site. As a result of all previous experiments, failures and new experiences with liquid design buildings as described above, the current process promises to be an adequate set-up. We are supported by an internationally recognized architect who unconditionally backs us, but remains critical as a designer on the quality of the outcome.
<figure><img src="image_254.png" /><figcaption>Figure 10: Model of the Library (left) and the Great Hall (right)</figcaption></figure>

## X. CASE 6: SUPER YACHT IN LONDON

For a hotel consortium in London naval architect Tim Saunders designed a floating 5-star hotel in the form of a super yacht of 144m length, in the best of the Mediterranean design fashions. The structure will be built on a steel pontoon as a skeleton with steel beams and columns, the hotel rooms will be completely furnished and prefabricated in Dubai and the cladding with 2D / 2,5D-aluminium and 3D-glass fiber reinforced polyester (GRP) panels plus flat glazing (2D), bent glazing (2,5D) and some 3D pieces of glazing are to be made to the latest state of the art by Octatube in Delft. The experiences in 3D cladding deformation, frameless glass structures and bent and twisted glass panels come together in this masterpiece. Inauguration of the hotel moored near Canary Wharf is foreseen in January 2007.

<figure><img src="image_255.png" /><figcaption>Figure 11: Super Yacht Luxury Hotel. Design by Tim Saunders (image: courtesy of Tim Saunders)</figcaption></figure>

## REFERENCES

[Eekhout 1989] Mick Eekhout, *Architecture in Space Structures*, 010 Publishers, Rotterdam, 1989, ISBN 9064500800

[Rice et al. 1995] Peter Rice, Hugh Dutton, *Structural Glass*, E&FN Spon, London, 1995, ISBN 0419199403

[Cook 1999] Peter Cook, *Archigram, Revised Edition*, Princeton Architectural Press, New York, 1999, ISBN 1-56898-194-5

[Gomez et al. 1996] Gomez, Coll, Melero, Burry, *La Sagrada Familia De Gaudí al Cad*, 1996

[Berkhout 2000] Guus Berkhout, *The Dynamic Role of Knowledge in Innovation*, Delft University Press, 2000, ISBN 90407207701

[Eekhout 1992] Mick Eekhout, *Between Tradition and Technology*, Publicatiebureau Bouwkunde, 1992, ISBN 9052691134

[Eekhout 1997] Mick Eekhout, *POPO, Procesorganisatie voor productontwikkeling*, Delft University Press, 1997, ISBN 904071631-5

[Zwarts & Jansma 2003] Zwarts & Jansma Architecten, 52°21′N 04°55′51″E, NAi uitgevers, Rotterdam, 2003, ISBN 9056623028 (English edition: ISBN 9056623036)

[Nijsse 2003] Rob Nijsse, *Glass in Structures*, Birkhäuser, Basel, 2003, ISBN 3764364394
Glass Canopy for the Office Center
of the DZ Bank in Berlin

Rudolf Hess,

GLASCONSULT, Structural Engineering of Glass Constructions,
8142 Uitikon, Switzerland

A building located on the "Pariser Platz" in Berlin, was designed by the famous architect Frank O. Gery and completed in 1999. Covering the main entrance is an interesting glass canopy measuring a total length of 14.30 meters and a cantilever of 1.50 meters without any support structures such as girders or hangers.

This paper, including an introduction about the building, describes the structural analysis of the glass canopy and the complicated attachment devices. A special analysis was performed to ensure that, in the case of failure of all the glass sheets, the remaining structure would be supported by the PVB layers.

The impact tests, carried out on an actual canopy in order to obtain the "declaration of consent" from the authorities of Berlin, are described in detail.

**Keywords:** glass canopy, cantilever, support structure, structural analysis, attachment devices, PVB-layer, impact test

# I. INTRODUCTION

At the Pariser Platz, a historical place in the center of Berlin, a multifunctional office center with conference area and independent apartment house was built on behalf of the DG Bank, today named DZ Bank. By building this finance- and service center, the DZ Bank wanted to demonstrate their unique solidarity with the city.

The original building, Pariser Platz 3, was constructed as nobility residence of the count of Rohdich. In the temporal circuit of the empire establishment of 1871, the traditional baroque building was demolished and a new building was erected

from 1878 to 1880. As part of the modernisation of Berlin as German capital after the fall of the Berlin wall in 1989, the reconstruction of the area of the Pariser Platz was a particular challenge. For the initiators of the building it was clear that for this exposed location particular demands would be required. Therefore an international competition was initiated by inviting eight internationally famous architects. The international jury unanimously chose the design of architect Frank O. Gehry. Frank O. Gehry founded the office Gehry & Associates, Inc in 1962. Over 90 awards in the field of architecture and furniture design were granted to him to date; the most prestigious in this impressive series is the Pritzkerprize in 1989. Gehry particularly became famous with the museum building in Bilbao and recently with the Disney Hall in Los Angeles.

In the near future, the building of the DZ Bankwill be flanked on the east side by the academy of arts and on the west side by the new building of the embassy of the United States of America. Gehry's success was, to "interpret" historic elements, without copying the history. The façade is not spectacular but it shows an exquisite well-proportioned elegance (Fig. 1). Typical of this façade are the large windows and the relatively broad glass balustrades. The windows are partially sliding windows with complicated closing mechanism.

The main entrance is discreetly covered by a glass canopy which is subject of this paper (Fig. 1 and 3).
<figure><img src="image_256.png" /><figcaption>Fig 1: Façade facing Pariser Platz</figcaption></figure>

Entering the building the visitor discovers a six
story Atrium. The light enters through a light glass
construction (glass sky). The "glass floor" of the
ground floor allows the view to the basement,
where the casino and a further conference room is
located. The back part of the atrium is a construc-
tion in the shape of a mussel, clad in stainless steel
(Fig. 2). The curved biomorphe form is partially
glazed and used as an auditorium for up to 100 par-
ticipants. The new location of the DZ Bank is a
place of encounter. In the atrium, a forum serves
for an extensive array of events. The separation be-
tween office and residential area is created through
an atmosphere in which the glass lifts connect the
floors. The building went into operation in the
course of the year 1999.

<figure><img src="image_257.png" /><figcaption>Fig. 2: glass sky, glass floor, conference room</figcaption></figure>

II. GLASS CANOPY FACING PARISER PLATZ

The glass canopy measures 14.30 m in length and a
free cantelever of 1.45 m (Fig. 3). The top lies ap-
proximately 4.15 m over the level of the entrance
floor.

<figure><img src="image_258.png" /><figcaption>Fig. 3: Glass canopy Pariser Platz</figcaption></figure>

A. Concept

Specific to this canopy is that neither suspens-
sions nor porters (swords) are available (Fig. 3).
The cantilevering glass roof is restrained in the
steel-girder construction behind the façade from
natural stone. The original concept anticipated an
entire glass depth of 2.25 m i.e. 1.50 m cantilever
and 0.75 m restrained in the façade construction.
This concept with additional modifications and
improvements is presented in Fig. 4.

<figure><img src="image_259.png" /></figure>

1 suspension M12 approximately every 500 mm

2 UNP with neoprene 5 mm shore 70-80

3 glass 3 x 12 mm heatstrengthened glass, PVB 3.04 mm

4 natural stone

<caption>Fig. 4: Original concept of the glass canopy (revised)</caption>
A first approximate analysis considering a restraint cantelevered beam of 1m width yielded a glass thickness of 3 x 12 mm tempered glass.

In the project stage, and in the phase of invitation to tender, the glass roof was intended to be constructed as one element of 14.30 m length and 2.25 m width. As a matter of fact, the glass roof was offered by the general contractor with these measurements, still in unaware of the static behaviour and the exact glass construction.

From the beginning, it was clear that for such an overhead construction only laminated glass could be used. The engineers responsible for the glass static proposed a construction with a laminated glass with three panes, considering that the use of three panes increases the safety at a possible break.

The original concept according to Fig. 4 shows a fastening of the glass to the existing steel girders of the façade construction. In the front area, the pane should be suspended with screws M12 mm every 500 mm. The screw heads would have been welded to the lower stainless steel plate, in order to hide the suspension from the underside view. For this purpose holes of 40 mm would be required in both lower panes and 20 mm in the upper pane. In the back part the pane would be fastened by a UNP-profile with a neoprene layer of at least 5 mm. The main disadvantage of this concept was that the façade construction was already erected at time of the installation of the glass canopy (Fig. 5).

<figure><img src="image_260.png" /><figcaption>Fig. 5: Steel-girder construction of the façade</figcaption></figure>

Six pairs of support consisting of HEB 140 (Fig. 4) therefore would have to penetrate the glass roof. For this concept glass slots would have been necessary, which would be unfavourable from the point of point of view of the concentrated stresses.

A float glass plant is basically able to produce

glass sheets of 3.21 m width and normally a length of 6.0 m. Theoretically the production of a pane of 14.3 x 2.25 m would have been possible. However a length of over 6 m would require a special production process. On the contrary, it was clear that no supplier could prestress a glass of 14.3 x 2.25 m nor produce a laminated glass of this size. This is due not only to fabrication but also to handling constraints.

The building owner and the architect however still insisted in the construction proposed of one piece of 14.30 m length. There was no other solution, than to subdivide the canopy in longitudinal direction into several parts.

According to the concept in Fig. 4, given a glass depth of 2250 mm it would have been possible to manufacture glass up to a length of 3800 mm. This would have yielded a division in longitudinal direction in at least four elements. Such a subdivision was basically refused by the architect. However after lengthy negotiations, the architect agreed to a subdivision into three parts, such that the gaps between the individual elements would be situated in the middle of the large pillars (Fig. 1 and 3).

Gaps of a maximum width of 15 mm between the elements was accepted, resulting in a center piece of 5.48 m length and two edge elements of 4.395 m each leading to a total length of 14.3 m. As a consequence the largest piece to be delivered measured 5.48 x 2.25 m. At the time of the construction, laminated glasses of this size with heat strengthened or tempered glass was not available, at least not in Europe.

Therefore another solution of the restraint had to be found, so that the depth of the glasses could be reduced. A supplier was found who could deliver laminated glass with a total thickness of 70 mm with heatstrengthened glass (HSG) or tempered glass (TG) up to the measurements of 1670 x 7000 mm. With a modification at the production plant, the same supplier was able to increase the width to 1700 mm.

With a depth of 1.7 m and a cantilever of 1.5 m only 200 mm were available for the restraint of the glass sections. After negotiations with the client and the architect a reduction of the cantilever length could be achieved from 1.50 m to 1.45 m.
With this reduction a depth of 250 mm to restraint the glass could be realized.

The engineers responsible for the glass construction developed a concept whereby the glass was clamped between two steel plates and covered with elastomer stripes of approximately 5 mm thickness, bolted together with chrome steel screws (Fig. 6).

<figure><img src="image_261.png" /></figure>

<table><caption>Fig. 6: Final solution of the construction of the glass canopy</caption><tr><td>1</td><td>3 x 12 mm glass PVB 4 x 0.76</td><td>7 stainless steel 2 mm</td></tr><tr><td>2</td><td>Neoprene 50 x 5 mm Shore 75</td><td>8 installation Light</td></tr><tr><td>3</td><td>Flat steel plate 700 x 40 mm</td><td>9 Girder HEM 120</td></tr><tr><td>4</td><td>Flat steel plate 200 x 8 mm</td><td>10 Girder UNP 240</td></tr><tr><td>5</td><td>Plate 250 x 15 mm St 52</td><td>11 natural stone</td></tr><tr><td>6</td><td>bolts CNS M16 every 330 mm</td><td></td></tr></table>

The lower steel plate (5) could be used over the whole depth of 250 mm. The canopy has a slope of 2% against the façade. The upper plate (4) had to be shortened by 200 mm, in order to allow a drainage system in longitudinal direction. In Fig. 7 the system of the restraints of the glass structure is presented enlarged.

First it was considered to weld a RHS tube of about 1000 mm length on to the upper steel plate (4) every 300 mm and to fasten these tubes to the girders UNP 240, which are a part of the façade construction. As a consequence of the lever mechanism heavy loads would have been transferred to the girders UNP 240; the front girder would have experienced a bending force downwards and the back girder one upwards. The large forces mentioned above were not considered in the static calculation of the steel-girder construction of the façade, which was already erected at that stage. The two girders UNP 240 (10) s. Fig. 6 and 7 could not support the large forces from the glass canopy. Therefore a separate construction had to be found for fixing it.

<figure><img src="image_262.png" /></figure>

<table><caption>Fig. 7: Detail of the restraint construction</caption><tr><td>1</td><td>3 x 12 mm glass<br>PVB 4 x 0.76 each</td><td>7 stainless steel 2 mm</td></tr><tr><td>2</td><td>Neoprene 50 x 5 mm Shore 75</td><td>8 installation Light</td></tr><tr><td>3</td><td>Flat steel plate 700 x 40 mm</td><td>9 Girder HEM 120</td></tr><tr><td>4</td><td>Flat steel plate 200 x 8 mm</td><td>10 Girder UNP 240</td></tr><tr><td>5</td><td>Plate 250 x 15 mm St 52</td><td>11 natural stone</td></tr><tr><td>6</td><td>bolts CNS M16 every 330 mm</td><td></td></tr></table>

Two additional steel girders HEM 120 (9) were introduced as continuous beam over five spans similar to the UNP 240 (10) positioned above. The upper steel plate of the construction (4) was welded on to a plate of 40 mm thickness and 700 mm depth (3), which was welded to the steel girders HEM 120, thus no additional loads were transferred to the girders UNP 240.

## B. Structural Analysis

The glass thickness of 3 x 12 mm found in the preliminary analysis was adopted. Whether TG or HSG was still undecided.

<table><tr><td colspan="2">1) Normal loads :</td></tr><tr><td>Proper weight</td><td>0.90 kN/m²</td></tr><tr><td>Snow load for Berlin according to code [DIN 1055 Teil 5 1990]</td><td>0.75 kN/m²</td></tr></table>

The final analysis was performed by means of the method of finite elements using the computer program [CEDRUS3+]. Thereby the construction of the restraint was modelled in an exact way. Due to the cantelever forces the glass is held within the
restraint by the elastomer supports (2) and (4) in Fig. 7 the forces acting in opposite directions. From the Shore hardness of the neoprene the compression modulus could be determined and as a result the spring constants for both plate supports. At an assumed Shore hardness of 70, a width of the neoprene stripe of 50 mm and a thickness of 5 mm a compression modulus of 159.5 MPa could be determined according to [Angst & Pfister 1996]. The stiffness of the bolts was considered in the spring constant.

Both for the load case proper weight as well as proper weight + snow no composite between the individual glass panes was considered (layered construction). Own experiences and tests years ago have shown, that the compound effect is lost fast due to long term loads [Hess 1988].

a) *Maximum edge stresses:*

* proper weight: $\sigma_{max} = 13.6$ MPa

* proper weight + snow: $\sigma_{max} = 25.0$ MPa

The allowable stress for TG is 50 MPa and for HSG 29 MPa. Thus the stresses are below the allowable limits. In addition, the case was investigated where a pane of the construction is broken due to mechanical damage for instance.

The load capacity is guaranteed for this case only through two panes (no composite effect).

* proper weight: $\sigma_{max} = 20.7$ MPa

* proper weight + snow: $\sigma_{max} = 38.0$ MPa

The stresses are below the allowable stress of 50 MPa for tempered glass. For the load case proper weight + snow the allowable stress of 29 MPa for HSG is exceeded. With a strength of 70 MPa for HSG the safety margin amounts to 1.8, which can be considered as sufficient.

Finally the extreme case is investigated, where both the upper as well as the lowest pane is broken due to mechanical damage. The remainder load capacity must be guaranteed through the medium pane alone. For this case only the influence of the proper weight is considered.

The maximum stress amounts to 41 MPa. This is smaller than the allowable stress of 50 MPa for tempered glass. With a strength of 70 MPa for

HSG the safety margin amounts to 1.7, which can be considered as sufficient for this extreme case.

b) *Maximum Deflections*

For the load case proper weight the deflection at the outer edge, without considering composite effect can be determined to 21.3 mm, this corresponds to a value of 1/115 of the span width (double of cantelever span). The canopy was installed with a slope of 2 %, so that the drainage can flow against the building. The deflection for the load case snow under neglect of the composite effect yields a value of 17.8 mm, together with the proper weight a total of 39.1 mm corresponding to 1/74 of the span width, which lies within the allowable limit. The effective deflection at the outer edge for the load case proper weight + snow under consideration of the slope amounts to 11.2 mm, the canopy is still sloped towards the façade.

The above analyses for the normal load cases have shown that the canopy can be realized with TG as well as with HSG.

2) *Extreme load cases :*

By order of the Berlin authorities, the impact of a steel ball of 4.0 kg with a minimal drop height of 3.0 m had to be investigated, whereby the following both cases were considered:

* Impact at the free edge in the middle of the plate

* Impact at the free edge in the plate corner

By means of equivalent static load method according to [Pilkey 1994] static calculations were accomplished. Since these load cases are short term loads, full composite (monolithic construction) is considered. The load case proper weight was superimposed. Separate calculations were performed for the panes of 4.395 m and 5.48 m.

a) *Maximum stresses:*

The resulting stresses for the governing case totals: $\sigma_{max} = 28.3$ MPa.

On demand of the Berlin senate authority the impact should occur under consideration of an existing snow load. Therefore the above-mentioned stress is superimposed with the stresses from proper weight + snow, without composite effect. This yields an entire stress of 54 MPa. This stress
lies above the allowable stress of TG of 50 MPa as well as the one for HSG of 29 MPa. If the stress is compared with the strength of 120 MPa for TG and 70 MPa for HSG, safety factors against failure of 2.2 and 1.3 respectively are found. These values are sufficient for these unusual load cases.

b) *Maximum deflections:*

For the impact at the free edge in the middle of the plate the deflection totals at the outer edge 16.1 mm and for the impact in plate corner 24.3 mm. This corresponds to a value of 1/180 and 1/119 respectively of the span width. Superimposing the this deflection with the deflection of proper weight + snow, neglecting the composite effect, total values of 26.2 mm and 34.4 mm respectively are found. These values have indeed only academic character.

These calculations have shown that also for the extreme load cases, the canopy can be realized with TG as well as with HSG. For the determination of the stresses in the upper and the lower steel plates of the restraint system as well as for chrome steel screws the load case impact is governing, likewise for the remaining fastening constructions.

The determination of the forces in the screws were performed with a modified FE-Model. It turned out that a screw CNS M 16 was necessary every 330 mm. The screws were prestressed up to about 70%.

Furthermore a calculation was accomplished for the case that all three panes of the laminated glass would be broken. A model was assumed, whereupon the complete failure occurs near the restraint, the pane revolving as a hinge around the point O (Fig. 8). Through the complete failure of the glass, the remainder load capacity is guaranteed only through the PVB-folios.

<figure><img src="image_263.png" /><figcaption>Fig. 8: Failure of all glasses (hinge effect)</figcaption></figure>

In the case of the failure of all panes using the model in Fig. 8 the safety against rupture of the PVB can be determined as follows:

Assumed strength of PVB 20 MPa

Cantilever span a= 1.45 m

PVB thickness t₁ 4 x 0.76 mm= 3.04 mm each

Tensile forces in the folios due to the proper weight g for the worst case where the glass stays in horizontal position φ = 0° (Fig.

$$8): M_{\text{rupture}} = \frac{g \cdot a^2}{2} = \frac{0.9 \cdot 1.45^2}{2} = 0.95 \text{ kN/m}$$

From the strain plane through point O it can be determined:

$$M_O = Z_1 \cdot h_1 + Z_2 \cdot h_2$$

Assuming $Z_2 = 2 \cdot Z_1$:

$$M_O = Z_1 \cdot (h_1 + 2 \cdot h_2)$$

and from $M_O = M_{\text{rupture}}$

$$Z_1 = \frac{M_{\text{rupture}}}{h_1 + 2 \cdot h_2} = \frac{0.95}{0.0135 + 2 \cdot 0.0285} = 14.48 \text{ kN/m}$$

$$Z_2 = 2 \cdot Z_1 = 26.95 \text{ kN/m}$$

The stresses in the PVB can now be determined to:

$$\text{Folio 1: } \sigma_1 = \frac{Z_1}{t_1 \cdot 1000} = \frac{14480}{3040} = 4.8 \text{ MPa}$$

$$\text{Folio 2: } \sigma_2 = 2 \cdot \sigma_1 = 9.6 \text{ MPa}$$

With an average strength of 20 MPa of the PVB a safety factor of 2.1 can be determined in interlayer 2. The safety in interlayer 1 is accordingly double. A global safety factor of 2.1 can be considered as sufficient for the extreme case of the failure of all panes.
### C. Declaration of consent

In Germany a declaration of consent has to be applied for constructions which are not regulated. The canopy under consideration was such a structure, therefore an application had to be turned in at the Berlin senate-authority. Besides the presentation of a detailed structural analysis, impact tests using a 1:1 mockup were required. To reduce the costs of the tests, the authority allowed, that the tests be carried out with a body of 2 m length instead of the largest effective length of 5.48 m. The panes of 2.0 x 1.70 m were erected on a special steel structure, where the restraint was modelled exactly. The requirement was, that if all the glass panes failed, that the glass or glass pieces should not fall on to the busy entrance area. For the tests a steel ball of 4.0 kg was used. Two panes were available, one laminated glass with 3 x 12 mm TG and second with 3 x 12 mm HSG, with 4 x 0.76 mm PVB interlayer. The glass was loaded first with sandbags to simulate the snow load of 0.75 kN/m² (Fig. 9).

<figure><img src="image_264.png" /><figcaption>Fig. 9: Mockup for the impact tests at the construction site</figcaption></figure>

At the first test with tempered glass with a drop height of 3.0 m the lowest pane broke (Fig. 10).

<figure><img src="image_265.png" /><figcaption>Fig. 10: failure of the lowest pane TG at a drop height 3.0 m</figcaption></figure>

The other two panes remained intact. Only after an impact with a drop height of 10 m all three glasses failed (Fig. 11).

<figure><img src="image_266.png" /><figcaption>Fig. 11 Failure of all panes TG after an impact from 10 m</figcaption></figure>

Fig. 11 clearly shows, that the destroyed pane remained in a position under a certain angle, thereby the sandbags slipped away. The considerations previously presented, that the pane is held only by the PVB-interlayers, were confirmed. The pane remained in this position.

The panel was pressed subsequently by force into the vertical position (Fig. 12).

<figure><img src="image_267.png" /><figcaption>Fig. 12: Broken TG forced into vertical position</figcaption></figure>

After the first tests with the glass assembly of 3 x 12 mm TG the analogous test series with 3 x 12 mm HSG were carried out. At the first test with a drop height of 3 m no failure occurred. After several throws with different drop heights only the upper pane was destroyed (Fig. 13).
<figure><img src="image_268.png" /><figcaption>Fig. 13: Test HSG (failure uppermost pane)</figcaption></figure>

Only at an impact with a drop level of 10 m all panes failed. The PVB-interlayer was to be held again in the position under an angle of approximately 30 degrees (φ in Fig. 8). Thereby the sand-bags slid slowly down (Fig. 14). The formerly made considerations, that the pane is still held only by the PVB-interlayers, was confirmed here again.

<figure><img src="image_269.png" /><figcaption>Fig. 14: Test HSG (failure of all panes)</figcaption></figure>

Subsequently the glass assembly was pressed into the vertical position and left for some days. The weight had to be supported by the PVB-interlayer only (Fig. 15). The folios withstood these loads, no failure of the PVB occurred. The stresses could be the determined as 0.21 MPa which is far below the strength of the material.

<figure><img src="image_270.png" /><figcaption>Fig. 15: Test HSG pressed into vertical position</figcaption></figure>

After these successful tests, the declaration of consent was given orally by the participants of the Berlin authority on site. The variant HSG was preferred because the pane did not brake at an impact level of 3 m. The written declaration of consent was presented later including a series of additional requirements. Most of them could be fulfilled relatively easy. The only requirement that could not be fulfilled was that the front girder HEM 120 (Fig. 6 and 7) should only have a maximum deflection of 0.5 mm. The purpose of this requirement was that the glass should not be stressed additionally through the deflection of the steel girder. It could be shown that this concern was excessive. A mathematical proof yielded, that under the load proper weight + snow with consideration of the stiffness of the steel plate of 40 mm thickness (Fig. 7) the deflection was 2.45 mm. These deflections of the girders were considered as external loads in a finite element analysis of the glass plate. Both cases, monolithic as well as layered were investigated. With the layered system a maximum stress of 26.4 MPa resulted, below the allowable stress of 29 MPa. The monolithic approach leads to larger bending moments, but smaller stresses, namely 12 MPa. As an extreme case, the stress is determined for the bending moment obtained from monolithic system with the resistance of the layered systems. A value of 34 MPa was obtained. This value for the extreme conservative approach lies only slightly above the allowable stress of 29 MPa, it might hardly appear. With the presentation of these calculations, the requirement mentioned above was withdrawn by the authorities.
### III. GLASS CANOPY ON THE BUILDING SIDE
BEHRENSTRASSE

Two additional canopies illustrating the same principle with smaller cantelevers and reduced lengths were realized on the building side of Behrenstrasse (Fig. 16).

<figure><img src="image_271.png" /><figcaption>Fig. 16: Glass canopies at the building side facing Behrenstrasse</figcaption></figure>

The larger canopy has a cantelever span of 1.20 m and the smaller one of 0.90 m.

Despite the smaller cantilever size the same glass thickness and the same concept as on the Pariser Platz building side were applied.

The reason was architectural considerations and to avoid having to go through additional declaration of consent.

The process of fastening the glass panes was essentially simpler than for the canopy on the Pariser Platz building side.

### IV. ACKNOWLEDGMENT

The following partners took part in the building construction concerning the glass canopy:

**Building owner:**

Pariser Platz 3 property Ltd. & Co building KG
10117 Berlin, Germany

**Project management:**

DG real estate management company GmbH
Frankfurt, Germany
and

HINES, property management Ltd., Berlin, Hines

real estate Ltd.

10117 Berlin, Germany

**Architect:**

Frank O, Gehry & Associates Inc.

Santa Monica, California, USA

**General contractor and site supervision:**

Müller-Altvatter, building enterprise Ltd. & Co.

10117 Berlin, Germany

**Structural Steel for the fixing of the canopy**

Ingenieurbüro Dr. Janßen

33739 Bielefeld / Germany

**Glass static and construction:**

GLASCONSULT, Structural engineering of glass constructions,

8142 Uitikon/ Zurich Switzerland

**Glass delivery:**

Bischoff glass technology

75015 Bretten Germany

**Erections of canopies:**

Aepli & Co metal contractor

9201 Gossau / Switzerland

### REFERENCES

* [DIN 1055 Teil 5 1990]

Lastannahmen für Bauten; Schneelast und Eislast 1990

* [CEDRUS3+]

Finite Element Program Scheiben / Platten Cubus Inc, Zurich

* [Angst & Pfister 1996]

Katalog Schwingungs- und Schallschutztechnik 1996
Technische Informationen.

* [Hess 1988]

Zürcher S-Bahn/ Bahnhof Stadelhofen Teilprojekt 5,
Glasüberdeckung Perrondach, Technischer Bericht, 15.
Dec 1988.

* [Pilkey 1994]

Formulas for stress, Strain and Structural Matrices. 1994
John Wley & Sons Inc. New York. ISBN 0-471-52746-7.
<figure><img src="image_272.png" /></figure>
# All-Glass Staircase, Notting Hill, London

Wilfried Laufs, Werner Sobek Ingenieure, Stuttgart, Germany

To bring direct day-light into a domestic housing staircase area in London, an all-glass staircase has been built, where all treads are purely made of glass. The following article describes the design, detailing, calculation and construction of the staircase, which was also tested for sufficient strength and post-failure security aspects.

**Keywords:** all-glass staircase, glass testing

## I. INTRODUCTION

Staircases next to walls without windows might be dark and non-spectacular. If the staircase is yet to be constructed, why not use glass as the leading construction material, acting as the primary structural element. The following article describes such an all-glass staircase, which was designed and constructed in Notting Hill, London, in 2003 according to Figure 1. It is meant to give a practical example of the capacity of modern glazing, combined with structural as well as detailing knowledge within the field of structural glass engineering.

## II. STRUCTURAL CONCEPT AND DETAILING

### 2.1 Global Structural System

To keep opaque structural material to a minimum, each tread was designed as an individual C-section, cantilevering out from the adjacent wall, where a hidden pair of steel beams spans across from concrete floor to concrete floor level with sufficient bending and torsional capacity, see Figure 2.

<figure><img src="image_273.png" /><figcaption>Fig. 1: All-glass staircase Notting Hill, London</figcaption></figure>

### 2.2 Glass Tread Profile

Each C-profile is composed of three flat laminated glazing panels, rigidly glued to each other by means of acrylic bond, see Figure 3. For aesthetic clarity, the 90° corners of the C-section were chamfered to 45° at adjacent glass mitred joint edges before toughening and lamination. As internal temperature load cases are small (ΔT ~ 10 K only) and very little UV-light is hitting the intermediate bonding layers, acrylic bond was chosen as a suitable material instead of a PVB-interlayer. To achieve a good grip on each tread, non-slippery lines of ~ 0.5 mm depth were manufactured into the top surface (water jet).
<figure><img src="image_274.png" /><figcaption>Fig. 2: Global structural system of glass stair (during construction)</figcaption></figure>

<figure><img src="image_275.png" /><figcaption>Fig. 3: All-glass tread C-section</figcaption></figure>

## 2.3 Construction

In order to avoid a direct steel-glass contact, but still transfer all support forces from the glass treads into the main steel support structure within the wall, a “shoe-connection” detail was developed according to Figure 4. A two-component resin was squeezed as the compatible intermediate mortar material between the glazing and mild steel flat profiles of the support (Figure 4), in addition to some distant- holding plastic support pads locally. Each glass tread was bonded together and fixed into its steel shoe. Each shoe was then bolted to the main steel beam in the wall, with options to adjust tolerances both vertically and horizontally. Neoprene pads ($t = 3$mm) were placed underneath each bolt to guarantee some spring behaviour against impact (abrupt steps); also shims can be added to align each tread in its exact final position.

<figure><img src="image_276.png" /><figcaption>Fig. 4: Glass “shoe support” construction detail; all edges polished</figcaption></figure>

## 2.4 Structural Calculations
A load case according to Figure 5 was considered relevant, which two persons (100 kg each) crossing each other's way on the stair and stepping onto one tread at the same time, where a dynamic amplification factor of 1.5 was assumed.

<figure><img src="image_277.png" /><figcaption>Fig. 5: Structural system and relevant loading per tread</figcaption></figure>

Assuming linear- elastic theory, the above loading would lead to a maximum un- factored upper tensile stress of max $\sigma_1 = M/ W_{1 yy \ upper} = 2.13 \ kNm / 390585 \ cm^3 \sim 5.5 \ N/mm^2$ (with full shear interaction of the bonding layers) and $\sigma_2 = M/ W_{2 yy \ lower} = 2.13 \ kNm / 57772 \ cm^3 \sim 37 \ N/mm^2$ (with no shear interaction) respectively, with $\sigma_{allowable} = 50 \ N/mm^2 > 37 > 5$. One might expect the primary crack to start from the area of highest tensile stresses at the top, but as will be explained further down, this was not the case under high loads during every test.

### III. TESTING

#### 3.1 General

As for most of modern glass constructions with primary load- carrying function, both strength and durability tests for regular usage as well as post-failure security tests for accidental cases need to be performed to satisfy all safety aspects and learn about the glass stair treads behaviour by means of 1:1 testing.

#### 3.2 Ultimate limit state (static)

Breakage of toughened glass usually is in the order of 120 to 200 N/mm² for short- term loading

and would be expected at the area of highest tensile stresses. However, due to the unknown exact support condition (shoe with resin), where local pressure peaks or friction may occur, a 1:1 testing series was performed. A first glass tread with support shoe was tested, where the load $P_1$ (see Figure 5) was increased in steps of 25 kg sand bags each (one bag per minute) up to failure (see Figure 6). The tip deflection at the free cantilever end was measured with results according to Figure 7. Due to a lack of budget, the shoe support itself was bolted to a non- rigid steel frame, simulating the wall behind, which also deflected under loading. Nevertheless, a rather linear load- deflection curve was obtained, with the first crack coming from the centre of the left flange at 835 kg loading. The loading could be further increased, until the second glazing panel on the left flange side failed. The partially broken tread kept in place until at a 925 kg loading the system collapsed as a whole.

<figure><img src="image_278.png" /><figcaption>Fig. 6: Testing set- up with sand- bag loading for $P_1$ (top); primary crack at centre of inner laminate of flange (bottom)</figcaption></figure>
<figure><img src="image_279.png" /><figcaption>Fig. 7: Indicative force – deformation behaviour of test rig with glass tread</figcaption></figure>

<table><caption>Table 1: Theoretical breakage stresses</caption><thead><tr><th rowspan="2">Test<br>[no]</th><th>Breakage force</th><th colspan="2">Breakage stress</th><th rowspan="2">comment</th></tr><tr><th>P<sub>1</sub><br>[kN]</th><th>Full shear interaction<br>[N/mm<sup>2</sup>]</th><th>no shear interaction<br>[N/mm<sup>2</sup>]</th></tr></thead><tbody><tr><td>1</td><td>825</td><td>19</td><td>129</td><td>first crack</td></tr><tr><td>2</td><td>1250</td><td>29</td><td>196</td><td>at collapse</td></tr><tr><td>3</td><td>1125</td><td>26</td><td>176</td><td>at collapse</td></tr></tbody></table>

However, as a system strength rather than a glass strength was tested within the steel shoe system test set-up, Table 2 cannot be taken directly for design, which is much rather achieved by 1:1 testing here, with 825 kg >> 2* P₁ = 300 kg for short-term ultimate loading conditions.

### 3.3 Ultimate limit state (dynamic impact)

To examine the glass tread under possible abrupt high impact loads, a drop test was carried out using a 25 kg weight landing on the end of the tread and dropped from a height of 4 m. No glass or joints failed (Figure 8).
<figure><img src="image_280.png" /><figcaption>Fig. 8: Drop test with a 25kg weight landing on the End of the tread, ΔH ~ 4m, no failure</figcaption></figure>

### 3.4 Serviceability limit state (long-term durability)

As the glass strength might decrease with time and the steel shoe system needs to be durable, a cycle test was performed with the same test rig by loading the tread with 300 kg and measuring a tip deflection $f_0$, and mounting an electric motor with an eccentric cam which applied $f_0$, simulating the 300 kg load (approximately two people on one tread). The motor was left running 830 rounds per minute for approximately 10 hours (498000 cycles). This simulated an average family of 4, each using the stairs 4 times a day for 40 years (up and down). There was no breakdown of any of the joints, laminate or resin observed.

### 3.5 Post-Failure security

To learn about remaining capacities of partially broken steps, both panels of one flange were broken on purpose by hammer. As shown in Figure 10 and Figure 11, the tread was still able to fully carry one person for at least 10 minutes.

<figure><img src="image_281.png" /><figcaption>Fig. 9: Testing set up for cycling test</figcaption></figure>

Here, the acrylic bonding appears to be advantageous compared to the usual PVB-interlayer or resin products for laminate safety glazing: the fine broken glazing pieces stick to each other and still transfer compressive forces at the bottom of each flange for a long time and keep the C-section working under loading. Therefore, if one glass panel breaks, each laminate would stay in position long enough for a person to step on adjacent unbroken steps to be safe. In this context, it has to be added that the glass stair did not have to perform in case of fire, as there are other escape routes in the house. Therefore, fire resistance was not tested.

<figure><img src="image_282.png" /><figcaption>Fig. 10: Both panels of one flange broken, tread still carries one person</figcaption></figure>
<figure><img src="image_283.png" /><figcaption>Fig. 11: Sufficient post-failure security observed</figcaption></figure>

Construction and testing: Peter Collins, Hourglass Havant Hampshire

<figure><img src="image_284.png" /><figcaption>Fig. 12: Finished glass tread and balustrade
(not touching the treads)</figcaption></figure>

## IV. SUMMARY

As shown above, a modern all-glass-stair construction is capable to carry high ultimate short-term loads as well as give a long-term durability for many years. Testing the system as a whole is recommended to find the true failure modes and learn from the broken system in terms of its post-failure capacity and breakage behaviour. In this case, even a partially broken tread can still carry a person long enough to walk down the staircase. The presented glass tread (Figure 12) represents a new generation of structural glazing applications and appears to be the first of its kind.

## V. ACKNOWLEDGEMENTS

Client: Chris Shirley, Notting Hill London

Structural concept and Engineering: Whitbybird London, Wilfried Laufs / Will Stevens
# Glass House Badenweiler

Hans Schober, Partner, Hannes Gerber, Jens Schneider, Senior Engineers
Schlaich Bergermann und Partner, Stuttgart, Germany

For a connecting structure between two bath houses at *Therme Badenweiler*, Germany, an all glass structure was designed and built. The glass house consists of vertical glass columns (l=7,60 m) and horizontal glass girders (l = 6,20 m) to support the vertical and horizontal loads of the facade. The roof structure is supported by glass beams (l = 6,20 m) that are formed according to the bending moment and are suspended by a steel cable within a channel in the laminated glass. The glass structure and all details were worked out diffident to include the new structure within the ambiance.

**Keywords:** glass structure, glass beams, glass columns, glass design

## I. INTRODUCTION

The last part of the modernisation of *Therme Badenweiler* was the renovation of the *Lindebad*, a famous building designed 1957 by Prof. Linde. To connect the old *Marmorbad* with the *Lindebad*, we designed a small all-glass structure with maximum transparency. All structural elements, girders, columns and beams are made of tempered laminated safety glass.

## II. SITUATION

A light, decent structure with a maximum of transparency was selected to guarantee a structure that preserves the independence of the old *Mamorbad* and the “new” *Lindebad* in the centre of Badenweiler. The all-glass structure consists of a 6,20 m wide and 7,60 m long glass façade and 6,20 m wide and 7,80 m long glass roof.

<figure><img src="image_285.png" /><figcaption>Fig. 1 The small glass house between *Marmorbad* and *Lindebad*</figcaption></figure>

The slope of the roof (2%) is to the back side of the roof to prevent a gutter at the front side. The width of 6,20 m between the old and new part made it possible to use glass beams and girders without joint as the typical size of float panes is 3,20 m x 6,00 m. The shape of the roof beams is formed according to the moment diagram of a simple beam. They are pre-stressed by means of steel cables from stainless steel. These are used to decrease the tension stresses in the glass and to improve the post-breakage behaviour of the beams [Bucak 2003]. The beams are stiffened horizontally by the roof glazing (insulating glass, 10 mm tempered glass/ 2 x 10 mm laminated heat strengthened glass) that spans between the beams. Small steel T-Profiles were introduced in the other direction between the roof glazing to improve its post-breakage behaviour as the roof may be stepped on for cleaning reasons. In Germany, building authorities insist on breaking all glasses of
an insulating glass unit for testing the post-breakage behaviour.

The horizontal façade girders are supported and stiffened by vertical glass columns. The façade grid size includes the glass door to ensure a structure without a door frame. The top of the façade is connected to a stainless steel frame with fin windows to ensure natural air vent.

### III. FACADE STRUCTURE

The façade structure consists of three horizontal glass girders and five vertical glass columns. The horizontal girders are made of three panes of 10 mm tempered laminated safety glass. They run horizontally with a width of 280 mm whereas the vertical columns with a width of 260 mm and a length of 2300 mm for each section span between them. The columns are connected to the girders by a small stainless steel box so that vertical and horizontal loads can be transferred. This small box is glued to the girders by a structural silicone sealant. An additional steel bolt was included and glued in with a 2-component epoxy mortar to prevent additional tests for the glued connection by the building authorities. The complete horizontal force could be transferred by the bolted connection without using the sealant.

The façade columns consist of laminated safety glass, two panes of 15 mm tempered glass. Our original design used three panes where the edge of interior pane should be set back to prevent a destruction of all three panes at a time from the edge. The authorities nevertheless insisted on having a scenario of a complete destruction of all three panes a column. Therefore, the steel frame on top of the façade was strengthened and the columns were reduced to two panes. Now the frame is strong enough to carry the loads although a complete column is destroyed.

<figure><img src="image_286.png" /><figcaption>Fig. 2 Interior view of the glass house and the façade</figcaption></figure>

<figure><img src="image_287.png" /><figcaption>Fig. 3 Detail connection façade column – façade girder with small stainless steel box</figcaption></figure>

The façade panes have a four side support for wind pressure from the columns and the girders, wind suction is transferred through glass fittings at the corners. The glass fittings are connected to the glass girders through the small steel box.

The horizontal glass girder is connected to the existing structures of *Mamorbad* and *Lindebad* by mounting parts that are fixed to the walls with anchors.

The top end of the façade is a stainless steel frame of flats 20 mm x 80 mm with included fin
windows. This frame is also used to support the roof glazing. The vertical loads from the frame are supported by the glass columns by simple contact. In case of a complete destruction of a façade column, the deformation of the façade girder above the destroyed column is greater than the deformation of the steel frame. So vertical loads are transferred by the steel frame to the next columns. The horizontal girder only has to transfer self-weight and the load of two column parts as a maximum but no additional loads from the roof structure. A safety calculation with reduced safety factors showed the reliability of the system.

## IV. ROOF STRUCTURE

The glass roof structure consists of four glass beams of laminated glass (each three panes of tempered glass, 10 mm outer panes, 15 mm inner pane) in a distance of 1,70 m and with a span of 6,20 m between the existing buildings (Fig. 4, 5). To decrease the tension stresses in the glass beam and to improve the post-breakage behaviour of the beams, a stainless steel cable runs in a small channel in the bottom of the laminated glass (open spiral strand 1x37, diameter 10 mm). This channel simply results from letting the inner pane of the laminated glass stand back. The cable is anchored in a stainless steel box at the edges of the glass beams. The gap between the box and the glass is filled by a two-component epoxy mortar (Fig. 6).

<figure><img src="image_288.png" /><figcaption>Fig. 4 Interior view of the roof structure</figcaption></figure>

<figure><img src="image_289.png" /><figcaption>Fig. 5 Roof girder</figcaption></figure>

<figure><img src="image_290.png" /></figure>

<figure><img src="image_291.png" /><figcaption>Fig. 6 Glass beam support and cable bracing</figcaption></figure>

The steel boxes are supported by steel consoles that are fixed in the walls with anchors. The insulating glass units of the roof (top layer 10 mm tempered glass, bottom layer laminated heat strengthened glass, 2 x 10 mm) spans between the beams. To ensure a post-breakage behaviour of the
glass after a complete breakage of all three glasses that was demanded by the building authorities, small steel T-Profiles were placed in the joints between the insulating glasses perpendicular to the glass beams. This results in a four-sided supported of the panes. The crack pattern of four-side supported glasses with the cracks perpendicular to the principal stress isochores ensures a much better post-breakage behaviour than the crack pattern of a two-side supported glass. Two-side supported glasses usually have a crack pattern where all cracks are in the centre of the panes which leads to a “hinge” and the pane slips off the supports.

# V. DESIGN

## A. Global Structural Analysis

The internal forces of the system were studied with a global structural model to ensure that the interaction between roof and façade structure is acquired realistically. Especially the fail-safe scenarios with a complete failure of single glass columns can only be simulated in such a global model (figure 7).

<figure><img src="image_292.png" /><figcaption>Fig. 7 Global structural system</figcaption></figure>

The load transfer between the steel frame of the façade and the glass columns was simulated by non-linear springs that only transfer compression. The stiffness of the springs was adapted to the material parameters of the EPDM-interlayer. So the load distribution between the frame and the still

intact glass columns - which depends on the stiffness and the deformation of the different partners - could be simulated realistically. The loads on the structure were taken from the German load design code DIN 1055. Different load cases with and without safety factors had to be calculated to account for the different safety concepts for glass (global safety concept), steel (partial safety factors) and the failure scenarios.

## B. Local Stress Concentrations

The local design for stress concentrations in the glass elements was done by using detailed Finite-Element-Models [Schneider 2001]. The finite-element-model of the bolted connection in the façade girders and the notch of the girder at the supports is showed in figure 8.

<figure><img src="image_293.png" /><figcaption>Fig. 8 FE-Model of a façade girder detail</figcaption></figure>

For roof-panes, the controlling load case is usually the concentrated load of a person on the pane. In Germany, the load to be applied for a glass pane is 150 kg on an area of 10 cm x 10 cm at the moment. Moreover, it has to be assumed for the design that the top glass layer failed and the load is only transferred by the bottom laminated layer. The shear connection between the glass panes by the PVB-interlayer must not be considered for that
load [TRLV 1998, Wörner 2001]. Figure 9 shows
the stress distribution in the bottom glass layer for
this load case. Finally, the impact load and post-
breakage behaviour of a falling person on the roof
has to be proved. This was done by using results of
similar tests on glass panes with four-side support
[Bucak 2003].

<figure><img src="image_294.png" /><figcaption>Fig. 9 Stress Distribution in the bottom glass layer of the roof pane</figcaption></figure>

C. Stability Analysis

The stability analysis of the glass columns and the
glass beams (lateral buckling) were also done by
using finite-element models, neglecting the shear
stiffness of the PVB-interlayer. For the columns, a
simple column (EULER type II) was calculated.
The imperfection of the column was assumed to be
1/300, which means 7,7 mm for the given length of
2300 mm. Research at the EPFL in Lausanne
[Luible 2002] showed that this value is realistic for
tempered glasses. Calculations showed a sufficient
safety even for the failure of one of the two panes.
As explained in section A, the whole structure is
nevertheless capable of a total failure of a column.
The stability analysis of the roof beams were done
using a finite-element-model of the beam with
realistic boundary conditions and the steel cable
suspension. The resulting deformations from the
first eigenvalue of stability failure were calculated
with a dynamic analysis (Fig. 10). These
deformations were scaled to a maximum of 1/300
and applied to the model as an imperfection by
means of node deformations. The deformed system
was now calculated with the unfavourable load
cases. Again, the shear stiffness of the PVB-
interlayer was neglected and the failure of two of
the three panes was also considered. Calculations

showed that the glass beams are not suspected to
stability failure.

<figure><img src="image_295.png" /><figcaption>Fig. 10 Lateral buckling eigenform of the roof girder and resulting stress distribution</figcaption></figure>

VI. SAFETY AND REDUNDANCY CONCEPT

First of all, the whole structure is designed to use
laminated safety glass for all structural glass
elements to make a total collapse of an element
unlikely. The design values for the bending
strength of glass were taken from the German
design code for linear supported glass [TRLV
1998]. The values base upon a global safety
concept:

- tempered glass: 50 MPa

- heat strengthened glass: 29 MPa,

- laminated safety float glass in the overhead area: 15 MPa,

- laminated safety float glass in the overhead in insulating glass panes after collapse of the top layer: 25 MPa.

Moreover, as explained in the respective chapters,
different failure scenarios of the glass columns and
the glass beams were analysed. The structure is
capable of a total collapse of a column; the post-
breakage behaviour of the glass beams with a steel
cable suspension was tested for similar structures
[Bucak 2003] and showed good results even after the collapse of all panes.

The post-breakage behaviour of the roof panes after impact of a falling person was improved by using a four-side support which showed acceptable results in comparable tests [Bucak 2003].

To prove the behaviour of the glass beams under impact load of a falling person on the roof, a simplified mass-spring-mass-spring model was used to calculate static equivalent load (≈ 38 kN) from the dynamic soft body impact [Schneider 2001]. This load results in a maximum principal tension stress of 66 MPa for the tempered glass which is acceptable for the extreme load situation.

## VII. FINAL REMARK

This small project shows that all-glass structures require very detailed engineering design. This does not only affect the local stress analysis but also a stability analysis and a safety concept. Due to a lack of consistent design codes for structural glass, the engineer is challenged to get most of the knowledge from research results.

## VIII. PROJECT PARTNERS

**Client:**
Staatliches Vermögens- und Hochbauamt Freiburg
Germany

**Architect:**
Architektengruppe F70, Freiburg, Dipl.-Ing. (FH)
Spathelf

**Construction:**
Hunsrücker Glasveredelung Wagener, Kirchberg,
Germany

**Checking engineer:**
Prof. Dr.-Ing. J.-D. Wörner, Darmstadt, Germany

**Expert's report on roof structure:**
Prof. Dr.-Ing. Ö. Bucak, Munich, Germany

## REFERENCES

**[Bucak 2003]**
Bucak, Ö., Gutachterliche Stellungnahme zur Glasdachkonstruktion beim Bauvorhaben Therme Badenweiler, June 2003, unpublished

**[BÜV 2001]**
BÜV-Empfehlung für die Bemessung und Konstruktion von Glas im Bauwesen, Der Prüfingenieur (2001) Vol. 4

**[Luible 2002]**
Luible, A., „Auf Biegen und Brechen“ tec21 (2002), Vol. 12

**[Schneider 2001]**
SCHNEIDER, J.: Festigkeit und Bemessung von Glas: Punktgelagerte Verglasungen, Dynamisch beanspruchte Verglasungen bei weichem Stoß. Dissertation (PhD-thesis), Institut für Statik TU Darmstadt, 2001.

**[TRLV 1998]**
Technische Regeln für die Verwendung von linienförmig gelagerten Verglasungen (TRLV), Fassung September 1998, Mitteilungen Deutsches Institut für Bautechnik 6/1998.

**[Wörner 2001]**
Wörner, J.D., Schneider, J., Fink, A. Glasbau. Springer-Verlag, Berlin, 2001
# Designing Double Glazed Façade Constructions

Olavi Tenhunen, Helsinki University of Technology, Espoo, Finland
Sini Uuttu, Lumon Oy/ Parvekenikkarit Oy, Vantaa, Finland
Aki Vuolio, Helsinki University of Technology, Espoo, Finland

**ABSTRACT.** Useful data of materials, loads, design methods, breakage causes and maintenance for designing double glazed façade constructions have been introduced.

**Keywords:** double skin, facade, glass

## I. CHARACTERISTICS AND METHODS

The characteristics of the facade have to correspond to the demands. The demands must be presented so that by designing and implementing according to those demands the wanted result is gained. The properties may be defined at different levels. The profile of the demands may be different in each building. The minimum demands are given in laws and regulations. The methods for rating and classifying have to be such that it is possible to prove the fulfilment of all the important property requirements. A comparison with the demands is sensible only when the demands are given in advance.

## II. STRUCTURES

### A. General

Movements of the structure have to be born in mind during the design and the implementation. Drying of wood, hardening of concrete, strain, creep, increasing and varying stresses in the course of the erection and movements because of the temperature variations keep the structure in movement all the time. The order of the assembly also affects

the result especially in the facade.

<figure><img src="image_296.png" /><figcaption>Fig 1: Cantilever beams as a supporting structure</figcaption></figure>

<figure><img src="image_297.png" /><figcaption>Fig 2: Suspended structure</figcaption></figure>
<figure><img src="image_298.png" /><figcaption>Fig 3: Vertical frames as a supporting structure</figcaption></figure>

## B. Metal structures

The frame of the outer glass skin is usually made of aluminium, hot dip galvanized steel, stainless steel or weathering steel. Gratings are made of hot dip galvanized steel, stainless steel or aluminium.

Hot dip galvanizing is usually more economic against corrosion of steel than painting of equal protecting ability. Directions for design are presented in the standard EN ISO 14713. Also zinc coated cold rolled products are used.

The insulated wall is usually constructed of light non-bearing wall elements. The frame of the elements is often made of steel sheet profiles. Webs of the steel sheet studs are often perforated for diminishing thermal conductivity. Surface of the element is usually metal or glass, but may be also more sensitive material, because it is sheltered by the outer glass skin.

Paint coated, enamelled or COR-TEN steel sheet products can be used in visible surfaces of the intermediate space (cavity) of the double façade. If painted in the factory the PVDF coating is preferred. Polyester paint is recommended for powder painted products.

Stainless steel may be used in bearing structures, door and window structures, lists, gratings and fixings (screws, bolts, nuts, washers, expansion bolts

and fixing plates on the concrete). Chromium nickel steel of low carbon percentage 1.4307 (AISI304L) is usually good enough. If the building is situated quite on the shore of the sea, it is maybe reasonable to use stainless steel with molybdenum content 1.4404 (AISI316L), because it tolerates better chlorides of the sea water. Bigger content of nitrogen increases a resistance to the climate corrosion.

Aluminium bars used in constructions are strengthened by alloying. Extruded profiles are commonly made of alloys EN AW-6060 [EN AW – Al MgSi] and EN AW-6063 [EN AW - Al Mg0,7Si], which have good physical properties and which are very suitable for anodizing. EN AW-6005A [EN AW – Al SiMg(A)] is an alloy suitable for anodizing with a little more strength. EN AW-6082 [EN AW – Al Si1MgMn] is intended specially for constructions, but is not so suitable for anodizing. The most common of the weldable structural alloys is EN AW-7020 [EN AW – Al Zn4.5Mg1]. The physical properties of alloys and the tolerances of products are given in the standard EN 755-1...9. Because the tolerances in facades are minor, the standard EN 12020-1...2 can be followed. Aluminium structures in double glazed facades are usually ready-made products belonging to a facade system.

Weathering steels with high phosphorus content (e.g. COR-TEN A, phosphorus 0.07...0.15% and COR-TEN B, phosphorus 0...0.35%) have the best corrosion resistance. Granted impact resistance, however, requires low content of phosphorus (<0.025%) and sulphur (<0.020%) (e.g. COR-TEN B-D).

When different materials are combined, different behaviour in temperature variations and under varying loads have to be kept in mind.

## C. Glass structures

Four different types of glass are classified according to the strength: annealed float glass, heat-strengthened glass according to the standard
EN 1863-1, thermally tempered (also called fully tempered or toughened) glass according to the standard EN 12150-1 and laminated glass according to the standard EN ISO 12543. The single plies of laminated glass are glued to each other with membranes of polyvinyl butyral (PVB) and may be of any kind of float glass. All these types of glass may be used as a single glass pane or joined to an insulating glass unit. Quality classes and minimum requirements are presented in the standard EN 572-2.

Emissivity of float glass is 0.84 (property to radiate long wave heat radiation, proportion to the emission of the black body, which has the emissivity of 1). Lower values are possible to get by coating. If the emissivity is not more than 0.20, the glass is called Low E glass.

The most advanced glasses for regulation of solar radiation are chromogenic glasses, which change their properties depending on the sunlight (photochromic) or surroundings temperature (thermochromic or thermotropic) or which are activated by electric current.

Coatings of metal or metal oxide usually conduct electric current. The resistance gets them to warm up. If the coating is on the innermost glass pane of the insulation glass unit and electric current is switched on the coating, 90% of the heat radiates into the room.

Fire-resistant glasses may be used in facades to stop the spreading of smoke or fire. Fire-resistant glasses form a unity with all the surrounding structures. These glasses are classified by entity (E- classes), heat radiation (EW-classes) and heat insulation (EI-classes).

There is not any kind of glass that would be the best for all purposes. Even in the same building several kinds of glasses may be used depending on the cardinal points, local climate and needs of heating, cooling, light, shading and appearance.

The cut edge of the glass pane has to be as smooth as possible. Untreated edges can be used only in inaccessible places. The strength of the

glass pane can be increased by grinding edges. At Helsinki University of Technology, the edge strengths of glasses with different edge treatments were examined with 80 glass bars of the size 8 mm x 30 mm x 320 mm. Following are microscope photos from the edges of the glass bars.

<figure><img src="image_299.png" /><figcaption>Fig 4: Cut edge of the annealed float glass</figcaption></figure>

<figure><img src="image_300.png" /><figcaption>Fig 5: Arrissed edge of the annealed float glass</figcaption></figure>

<figure><img src="image_301.png" /></figure>
<figure><img src="image_302.png" /><figcaption>Fig 7: Polished edge</figcaption></figure>

Results of the tests are in the table below.

<table><caption>TABLE 1:
EDGE STRENGTH ACCORDING TO THE TESTS</caption><thead><tr><td>Edge treatment</td><td>Tensile strength at the edge N/mm²</td><td>Corresponding temperature difference ΔT °C</td></tr></thead><tbody><tr><td>Annealed float glass, arrissed edge</td><td>35</td><td>16</td></tr><tr><td>Annealed float glass, smooth ground edge</td><td>46</td><td>22</td></tr><tr><td>Annealed float glass, polished edge</td><td>55</td><td>26</td></tr><tr><td>Heat-strengthened glass, smooth ground edge</td><td>125</td><td>94</td></tr><tr><td>Heat-strengthened glass, polished edge</td><td>141</td><td>101</td></tr><tr><td>Tempered glass, smooth ground edge</td><td>160</td><td>145</td></tr><tr><td>Tempered glass, polished edge</td><td>187</td><td>159</td></tr></tbody></table>

If these values are used, the small amount of samples and the required safety level (safety factors) must be considered.

According to the measurements done by Helsinki University of Technology, the biggest temperature variations during 24 hours on the inner surface of the outermost glass pane in a double glazed facade were over 40°C. Temperature at the edge of the pane was at any time not more than about 10°C lower than in the middle of the pane and not more than 16°C higher.

### III. LOADS

#### A. Wind load

The determination of wind load is a fundamental task in structural design of façade structures. It is done in compliance with part 2-4 of Eurocode 1, when the structures are designed in accordance with the European CEN design standards.

In the particular case of double glazed facades, an important design aspect is the consideration of the wind actions during execution. The reference wind load during execution may be taken as about 75 % of the characteristic value, which corresponds to a wind speed with a return period of 10 years. It is important to note, however, that even though the reference load may be reduced in the design for the temporary situation, the combination of the aerodynamic factors may be more unfavourable temporarily during execution than in the final situation.

#### B. Other loads

Other loads to consider include

* Permanent loads from the self-weight of the glasses and the frame structures as well as service equipment, lighting fixtures, shades etc.

* Snow load, if the facade contains horizontal surfaces where snow may accumulate.

* Vertical imposed loads, if the facade frame carries the loads from a service platform.

* Horizontal imposed loads from human impact for structures working as safety barriers. Façade structures within a certain height from the floor level need to be designed for these loads if otherwise there is a risk of a person falling down.

* Thermal loads resulting from temperature differentials between structures and temperature differentials within a structure.

* Internal loads in the design of insulating glass units.

* Actions in accidental situations, such as fire, explosion or earthquake, may sometimes need to be considered.
# IV. STRUCTURAL DESIGN OF GLASS PANES IN FACADES

## A. General

Recently, parts 1 (1999) and 2 (2000) of the European standard proposal prEN 13474 dealing with the structural design of glass panes, have been published. Part 1 of the standard proposal presents general basis of design and part 2 covers the design for uniformly distributed loads. The exact contents of the design code may be changed considerably before the final approval of the EN standard. However, the draft versions already provide useful information about the design of glass structure, as accurate design methods have been lacking so far in many countries. The principles of fracture mechanics are combined with the Weibull statistics to determine the strength of glass. The geometrical non-linearity induced by the so-called membrane effect is taken into account in the formulas for four-edge supported rectangular panes. The membrane effect arises when the deflection of a glass pane exceeds about half of the pane thickness. As the deflections become large, the use of linear theory, that has been generally used before the introduction of the new code proposals, leads to overestimation of stresses and deflections so that the design may become significantly conservative.

The strength of glass is dictated by the geometry and distribution of surface flaws. In addition, glass has a lower strength against long-term than short-term loading because of the slow sub-critical crack propagation known as static fatigue. Therefore, the design strength is influenced by the duration of the load, size of the pane and the distribution of tensile stresses. For heat-strengthened and tempered glass, the strength is the sum of the compressive prestress at the surface and the tensile strength of float glass.

The design is carried out by using limit state method in accordance with EN 1990 and other Eurocode standards. The strength verifications are made in the ultimate limit state. The required level

of structural safety of glass structures is now determined in the same manner as for other structural materials, and it depends on the consequences of possible failure. The introduction of the national partial factor in the design code provides a possibility for national adjustment of the safety level, since historically the levels of structural safety for glass design have differed notably from country to country. The serviceability limit state design comprises checking that specified service limits, concerning usually the displacements and vibration of the structure, are not exceeded. The exact serviceability requirements are not outlined in the design code proposals, so they should be adopted by the designer based on national or other regulations and guidelines.

## B. Insulating glass units

Insulating glass units (IGU's) usually consist of two or three parallel glass panes that are connected to each other by the spacer and sealants at the edges, so that there is an insulating, hermetically closed cavity between the panes. The width of the cavity is typically 12 mm or 15 mm, but also widths of 6 mm and 9 mm are sometimes used. The cavity contains air or, to improve insulating capacity, some other gas like argon or krypton.

As the gas in the cavity may be assumed to satisfy the Boyle's law of ideal gases

$$ \frac{p \cdot V}{T} = (\text{constant}) $$

a change in its temperature T causes a change in the pressure p, and vice versa, when the volume V is fixed. On the other hand, the pressure acting on the panes makes the panes to deform and thus induces a change in the volume V, which makes the problem non-linear. The membrane effect further complicates the problem when the deflections of the panes become large. The pressure inside the cavity depends also on the ambient atmospheric pressure: when the ambient pressure drops, an overpressure develops inside the cavity, and vice versa. The climatic effects arising from variations of atmospheric pressure and temperature may re-
result in considerable internal loads for IGU's, especially for small-sized units.

The panes of an IGU may be single or laminated, and the individual plies may be normal float, tempered or heat-strengthened glass. Each pane is designed in accordance with the rules given for the specific type of glass. Relatively complicated calculations are required in the design of IGU's according to the code proposals. The difficulty is determining the load applied to the panes, considering the internal loads, load sharing between the panes and several load combinations with varying duration. In the design code proposals, a hand calculation method is presented for the design of continuously supported IGU's consisting of two glass panes. For the design of IGU's consisting of three or more panes, finite element (FE) analysis with fluid elements modelling the cavity may be used to determine the stresses and deflections. The FE modelling is advisable also for the design of curved IGU's or when the support conditions are exceptional.

# V. FACTORS CAUSING BREAKAGE OF GLASS PANES IN FACADES

## A. General

The probability of failure seems still to be much higher for glass structures than for structures of other materials. Often the breakage is spontaneous in nature and the exact reason for it cannot be specified easily. It should be noted, that despite exact formulas for strength verification are given in the design codes, it is not possible to determine the level of structural safety for glass structures as accurately as for other load-bearing structures. This is due to the fact that the strength of glass depends almost entirely on the flaws on its surface, so the variation of strength between panes is large. Therefore, the strength may deteriorate significantly during the life cycle of a glass structure, if flaws more critical than expected in design occur e.g. as a consequence of contacts with sharp objects.

The potential actions that may induce failure are presented below divided into three groups.

## B. Actions allowed for in the design code

The main load, that the glass panes in facades are designed for, is wind. It can be shown that when a glass pane is designed in accordance with the design code drafts prEN 13474-1 and -2, the failure probability due to wind load is lower than required from normal load-bearing structures belonging to reliability class CC2 of EN 1990. This means, practically, that glass panes, that are properly designed, manufactured, installed, used and maintained, do not break due to wind load.

For internal loads of IGU's a slightly higher probability of failure is allowed, as the strength verification is made only in the serviceability limit state instead of the ultimate limit state. Still, a breakage of an IGU due to internal loads alone is extremely rare occasion.

## C. Actions not allowed for in the code

In the design code, the strength of glass signifies the tensile strength at the central area of the pane, corresponding to the so-called ring-on-ring test method where the strength is determined. The tensile strength at the edge of the pane, however, is usually significantly lower than the one specified in the design code and it depends strongly on the quality of the edge finish. Although the influence of reduced strength has not been at all allowed for in the design code proposals, notable tensile stresses may occur at the edges of the pane as a consequence of e.g. temperature differentials within the glass pane, membrane effect of thin plates subjected to wind loads and displacements of the supporting structure when the joint between the glass and the support is rigid enough to transfer stresses as in structural glazing.

Critical thermal stresses occur when the temperature at the middle areas of the pane is higher than at the edges. That may be the case, if the central areas of the pane become hot due to solar radiation while the edges behind the glazing beads
remain cool, or if the pane is otherwise partially shaded. Thermal effects are most significant in coated glasses as they absorb more heat than clear glasses. In the northern climate, the inner panes of IGU's may become subjected to high edge stresses in cold weather, if the edge profile conducts heat and consequently makes the temperature at the edges of the pane lower than in the central areas.

It is evident that in many cases the failure probability due to thermal stresses is higher than due to loads considered in the design code. The edge strength of a glass pane can be improved by using either heat-strengthened or tempered glass instead of normal float glass or by improving the quality of edge finish of the pane.

### D. Defects in material, design, execution or use

Most of the failures of glass structures in facades are consequences of some kind of defect or negligence either in material technique, design, execution or use. Because of the slow sub-critical crack propagation of glass, the failure may take place long after the initial flaw has been induced.

Tempered glass is sometimes sensitive to two specific problems related with the material, namely excessive pre-stresses and nickel sulphide (NiS) inclusions. There are no upper limits for the pre-stress in the standards for tempered glass, but it is recommended that the pre-stress should not be much higher than 110 MPa to minimize spontaneous breakages and to guarantee the intended safe failure pattern. The higher risk of failure caused by nickel sulphide inclusions may be eliminated almost totally by using heat soaked tempered glass.

As glass does not possess any plastic deformation capacity, even a small error in the design or installation may lead to a total failure of a structure. The designer should be especially careful with the details. The joints between glass and its metal frame must be designed in a way that the glass-to-metal contact is not possible. Therefore, adequate clearances need to be arranged so that the displacements of the frame, thermal movements

and the tolerances in the manufacture and mounting are all allowed for. The materials for sealings and bushings must be correctly selected, so that adequate resistance to environmental conditions, such as UV radiation and variations in temperature, is ensured.

The installation of the panes and the supporting frame requires great accuracy as tolerances are much smaller than in construction usually. During the construction stage there is a high risk of degradation of the glass surface, and hence a notable decrease in strength, caused by e.g. accidental impacts of sharp objects or spatters from welding. Therefore, the pane should be properly protected at the construction site.

During the use of the glass structure, particularly the maintenance and service work near the glass panes may induce initial flaws that could later cause a spontaneous breakage. For example, impacts by service trolleys may be detrimental to the glass pane.

## VI. ISSUES ON EXECUTION

No specific one of the various types of supporting structures has turned out to be overwhelmingly good. It depends more on a personal choice of an architect which type is chosen. However, both designers and contractors emphasize that the supporting structure of the double-skin façade should be erected as an independent structure from the floor slabs because of the totally different tolerances. The supporting structure can be connected to a column instead of the intermediate floor's edge. In this way the possible movements of the intermediate floors will not have an effect on the supporting structures of the double-skin façade. This kind of structure is shown in fig 8. The cantilever bracket is hidden under the service platform.
<figure><img src="image_303.png" /><figcaption>Fig 8: Double-skin structure connected to an I-section column</figcaption></figure>

<figure><img src="image_304.png" /><figcaption>Fig 9: The completed structure of fig 8 seen from outside.</figcaption></figure>

The supporting structure should be designed with adjustable joints in every direction. The sus-

pended structure gives these adjustment possibilities in all directions. However, the rigidity of this type of supporting structure under the erection phase is still causing some problems.

Rough weather (rain, snow, wind, cold) is often hindering the construction work of double-skin façades. The benefit of pre-glazed elements is that the glazing can be performed in standard conditions and standard temperature. The typical glue (sealant) used in the joints requires a minimum temperature of + 5°C. The construction site is also less jammed. On the other hand there is a risk that pre-glazed elements will be damaged during transport.

The double-skin façade projects in Finland involve a lot of different parties (owner, client, architect, structural designer, façade designer, main contractor, façade contractor, workshops, glass manufacturer, HVAC-designer etc). The responsibilities of each party are sometimes unclear. This leads easily to delays and misunderstandings. It is important that all these parties work together from the beginning and divide responsibilities clearly. A very common problem is that plastering and levelling works are not completed when the aluminium profiles are erected. Fresh plaster and concrete in contact with aluminium profiles will induce corrosion. Early determination of requirements, criteria and delivery lots specified in cooperation with experts is the key for a successful progress of a double-skin façade project. Especially experts of building physics and glass structures and manufacture are needed.

## VII. ISSUES ON FIRE AND MAINTENANCE

After the flashover in the fire situation, the room temperature becomes so high that even tempered glasses break. Spreading of the fire in the intermediate space of the double skin facade depends on the openings and on the depth of the space. The fire of 2 MW through the 1 m² opening to the intermediate space needs about 2 m² openings at the top and bottom of the intermediate space to keep
20 m high, 10 m wide and 0.4 – 1.0 m deep intermediate space smokeless. [Hietaniemi et al. 2002]

The most common maintenance work in the double glazed facade is washing. It can be minimized by avoiding outside details that corrode, catch dirt or form water streams, and by using self-cleaning glasses. Maintenance has to be taken into consideration as early as possible. For outside washing the mobile cranes or the service cages may be used. Crane locations, use of the cage and necessary structures have to be designed. For inside washing the service platforms or service cages have to be used. It is necessary to fit the service platforms with handrails or other barriers or lifelines. Maintenance may be easier if there are sockets for electricity and also wall taps and hose connections for water in the intermediate space. The space has to be so deep that it is possible to do maintenance works taking into account also Venetian blinds. Fittings on the gratings make the walking difficult. Fittings on the insulated external wall may hinder opening of the doors and windows. Diagonal bars in the space may be harmful for using the service cage.

<figure><img src="image_305.png" /><figcaption>Fig 10: The service cage for the maintenance of the intermediate space.</figcaption></figure>

## REFERENCES

### [Hietaniemi et al. 2002]

HIETANIEMI, J., HAKKARAINEN, T., HUHTA, J., KORHONEN, T., SIISKONEN, J., VAARI, J., *Ontelotilojen paloturvallisuus, Ontelopalojen tutkimus kokeellisesti ja mallintamalla*. Espoo 2002: VTT, Vuorimiehentie 5, PL2000, 02044 VTT, VTT Tiedotteita 2128. 125 s. + liitt. 63 s. ISBN 951-38-5953-3. ISSN 1235-0605. (in Finnish).

### [Mäkeläinen et al. 2002]

MÄKELÄINEN, P., TENHUNEN, O., VUOLIO, A., LINTULA, K., VILJANEN, M., BERGMAN, J., HÄNNINEN, J., ALINIKULA, T., PALMI, P., *Kaksoisjulkisivun suunnitteluohjeet*. Espoo 2003: Helsinki University of Technology, Laboratory of Steel Structures, P.O. Box 2100, FIN-02015 HUT. Publications 26. 166 p. ISBN 951-22-6649-0. ISSN 1456-4327. http://www.hut.fi/Yksikot/Rakennus/Teras/Julkaisut/jsarj.htm l. (in Finnish).

### [Tenhunen, O. 2003]

TENHUNEN, O., *Metalli-lasirakenteisen kaksoisjulkiisivun materiaalien soveltamiskriteerit*. Espoo 2003: Helsinki University of Technology, Laboratory of Steel Structures, P.O. Box 2100, FIN-02015 HUT. Publications 28. 104 p. + appendices 43 p. ISBN 951-22-6780-2. ISSN 1456-4327. http://www.hut.fi/Yksikot/Rakennus/Teras/Julkaisut/jsarj.html. (in Finnish).

### [Uuttu, S. 2001]

UUTTU, S., *Study of Current Structures in Double-Skin Façades*. Espoo, 21.8.2001: Helsinki University of Technology, Department of Civil and Environmental Engineering, Laboratory of Steel Structures, Master's Thesis. http://www.hut.fi/Yksikot/Rakennus/Teras/Tutkimus/tproj_mela.htm

### [Vuolio, A. 2003]

VUOLIO, A., *Structural Behaviour of Glass Structures in Facades*. Espoo 2003: Helsinki University of Technology, Laboratory of Steel Structures, P.O. Box 2100, FIN-02015 HUT. Publications 27. 127 p. + appendices 34 p. ISBN 951-22-6843-4. ISSN 1456-4327. http://www.hut.fi/Yksikot/Rakennus/Teras/Julkaisut/jsarj.htm l

### [Keski-Rahkonen, O. 1998]

KESKI-RAHKONEN, O., *Breaking of Window Glass Close to Fire, Fire and Materials*, Vol 12, pp. 61-69, 1998.

### [SFS-ENV 1991-2-4, 1995]

*Eurocode 1: Basis of design and actions on structures. Part 2-4: Actions on structures. Wind actions.*

### [prEN 1990, 2001]

*Eurocode: Basis of structural design*. Draft, January 2001.

### [prEN 13474-1, 1999]

*Glass in building – Design of glass panes – Part 1: General basis of design*. Draft, January 1999.

### [prEN 13474-2, 2000]
Glass in building – Design of glass panes – Part 2: Design for uniformly distributed loads. Draft, February 2000.
# Shaping Glass Plate Structures

Ture Wester

Royal Danish Academy of Fine Arts, School of Architecture, Copenhagen, Denmark

Buildings using glass sheets in the load carrying structure is not a new idea. The large and elegant Victorian palm houses from the time of the industrial revolution often used glass sheets as a bracing element for a steel lattice structure. This very appropriate way of using glass in the primary structure has unfortunately disappeared. Glass is recently very slowly being reintroduced as a structural element for beams, walls, columns, as member in steel trusses etc, but very few projects seem to use glass according to its unique properties. Because of the special structural behaviour of glass it seems that optimal shaping of the structures is essential in order to reduce stresses in general and concentrated stresses in particular. The paper will discuss these properties and express the morphological consequences for the shaping, faceting and detailing of structures that are made from glass and other similar types of tiles. A number of Nature's solutions and of projects and ideas will be discussed.

**Keywords:** cost, glass, morphology, plate structures, shaping, duality.

## I. GLASS IN NATURE

Glass ($SiO_2$ being the main component) is widely used in nature as a material for skeletal force-resistant structures. Organisms like e.g. Radiolaria [Haeckel 1887] and Glass Sponges (fig.2) are examples of morphologically highly sophisticated structural configurations. However, these structures do not use glass sheets. They are built from clusters of specules in such a way that they are comparable to fibre-glass. Nature discovered a long time before we did, that fibre-glass in every way (strength, elasticity, reliability, fragility etc.) is a far better building material than plane glass. The best option for the structural use of glass seems therefore to be as fibres, and it would be of great interest to try to use glass fibre in structures far more extensively than today where it normally appears as reinforcement for plastics and cements, only. But when we talk about the use of glass in

<figure><img src="image_306.png" /><figcaption>Fig.1 Kibbles Palace in Glasgow (1873). Note the slight out-of-plane curvature of the vertical iron arches on the right photo. This indicates the bracing action of the glass panels.</figcaption></figure>

<figure><img src="image_307.png" /></figure>
building structures we usually mean transparent plane or curved glass sheets. However, in nature we find structures built from calcite plates which have almost similar general mechanical properties as glass e.g. coccolithophores [Winter et al.] and sea-urchins [Wester 1983] see fig.3. Among these we might find inspiration for efficient use of plane glass for structural purposes. Material Properties of Plane Glass

## II. MATERIAL PROPERTIES OF PLANE GLASS

For structural use it is evident to consider tempered or hardened glass as this has much better properties than plain untreated glass. In order to discuss the morphological possibilities for glass structures, it is not necessary to go into details in the field of Material Science. In order to get a rough idea of the properties of plane hardened glass, we can compare it to some well known

<figure><img src="image_308.png" /><figcaption>Fig.2 The siliceous marine plankton Radiolaria (left) and a deep sea Glass Sponges (right) show examples of Nature's way of using fibre-glass for its skeletal structure</figcaption></figure>
structural materials:

- It has double the strength of mild steel for compression, but half the strength for tension.

- Its rigidity (E-value) is one third of that of steel, or approximately as aluminium, or 5 times higher than that of wood.

- Thermal expansion, which is important in case of transfer of forces between glass and e.g. the metal frame, is typically 75% of steel or 30% of aluminium, i.e. closest to steel.

- The specific gravity is one third of steel, or approximately the same as aluminium, or 4 times the value for timber.

- The maximum working temperature, i.e. without losing much strength is as for aluminium or half of that of steel.

- The "Achilles' heel" of glass is its brittleness. One of the most appropriate ways to reduce this problem is to laminate two or more glass sheets together. As failure will normally only affect one layer, the other layer(s) must hold enough carrying capacity to prevent failure - or the forces must be able to rearrange in the structure until the glass element is replaced.

### III. PURE PLATE ACTION

In a similar way of stabilizing a pure lattice (bar-and-node) structure by tension and compression, a

pure plate structure (plane plates hinged together along shear lines) can be stabilized by the transfer of shear forces across the shear lines. The well known characteristic pattern for lattice action is the triangle while it is a 3-valent vertex for plate action (fig.4). These two configurations are geometrical duals in our 3-dimensional space, i.e. if inter-connected vertices are substituted with equally intersecting planes, a triangle becomes a 3-valent vertex and vice-versa [Wester 1983]. This duality can be extended to the level of statical properties as rigidity, forces and elasticity [Wester 1987].

As it is not the purpose of this paper to go into detail about this, but some of the relevant general results are as follows (see also "further reading"):

A single-layer triangulated structural configuration can only be rigid as a pure lattice structure, and it is rigid if closed (like a ball), even that there are some special non-convex exceptions. The facets are not structurally active and may be removed. Only nodes and bars are needed.

A single-layer structural configuration with only 3-branched vertices can only be rigid as a pure plate structure, and it is rigid if closed (here are also some special non-convex exceptions).

A single-layer configuration which is neither fully triangulated nor fully 3-branched cannot be rigid as a pure plate or as a pure lattice structure, but is rigid (with similar exceptions as above) as a

<figure><img src="image_309.png" /><figcaption>Fig.3 Left column: microscopic coccolithophores (Nishida). Center: macroscopic sea-urchins in a natural and computer version, showing 3-branched vertex pattern which is significant for pure plate action. Right: SEM of the teeth-like shear-resistant suture between plates in a sea-urchin</figcaption></figure>
combined lattice and plate structure, even it may be a sensitive structure.

Pure lattice structures are characterized by having concentrated internal forces in bars and nodes, hence well suitable for the use of strong materials as e.g. steel. Pure plate structures distribute the internal forces along the whole length of the shear lines and the total surface of the plates. Distributed forces are of course much better

sional structural elements.

This knowledge, embedded in the structural duality, enables plate structures to be generated just as complex as lattice structures are today - in a very simple way. The geometrical transformation, which has the quality to preserve all structural data, is called Polar Reciprocation, and is thoroughly explained in [Cundy et al. 1961] while the structural transformation is explained in [Wester 1987]. In order to handle the geometrical and structural duality, a computer program has been developed, see [Wester].

This method of dual transformations has been used in a number of projects made by the author in collaboration with architects, artists and students, as discussed below.

<figure><img src="image_310.png" /><figcaption>Fig.4 Structural duality follows the well-known geometrical duality. The triangulated polyhedra (tetra-, octa- and icosahedra) are stable by pure lattice action (axial forces in the bars), while the 3-branched (tetra-, hexa- and dodecahedron) are stable by pure plate action i.e. transfer of shear forces across the intersecting lines</figcaption></figure>

<figure><img src="image_311.png" /><figcaption>Fig.5 The Bella Dome is a polyhedral pure plate structure with plates as open rigid frames. The openings might be adequately closed by plane glass, which then will overtake the plate action. In fact the wooden frames could then be eliminated, leaving a pure glass plate dome as indicated at the right. This seems to be the ultimate solution for glass structures.</figcaption></figure>

for the use of glass and other similar two-dimen- as the casement for the glass, and the glass would,

## IV. BELLA DOME

Originally the dome in fig.5 was suspended from a roof in Bella Centre in Copenhagen for a building exhibition, and later placed on the ground as shown. This 12m diameter and 6m high dome is a class II, frequency 4 of the Cube (or Octahedron) family and is designed by the author in collaboration with architect T. Ebert, Copenhagen. The plate units are rigid closed frames and made from 68*68 mm timber, bevelled on one side to fit the adjacent frame. The triangular frame-knees are made from 19 mm plywood, depressed and glued.

The intention was to open up the plates as much as possible. The open rigid frame structure is strong enough for the original indoor use, but not strong enough as an outdoor structure. The idea was therefore to strengthen the open wooden frames by adding glass plates. In this situation the wooden bars would act
as it is much stiffer than the frame, overtake the plate action almost completely.

## V. MUSEUM LOUNGE

The very regular polyhedral shapes as the above are often considered 'too mathematical and too regular' and not fit for good architecture. However, these polyhedral shapes may easily be altered to something more appropriate and interesting from an architectural as well as a structural point of view.

<figure><img src="image_312.png" /><figcaption>Fig.6 Upper row: class I, frequency 4 cube breakdown has for uniform load in the direction of the arrow an efficiency of 38% (100% is perfect shape for the load). b: The same polyhedron rotated 45 degrees shows an increase of the efficiency to 50%. It is interesting to notice that a spherical polyhedron has a different efficiency when it is rotated. c: Now, the polyhedron is manipulated into a much more interesting configuration and, at the same time, the efficiency has increased to 75%. Lower row: Further manipulation led to the final shape, and finally the physical model.</figcaption></figure>

By geometrical manipulations, CADual can produce a number of different shapes and facets. At the same time it can evaluate the actual configuration from a statical point of view. For given loadings, it can determine the efficiency of the structure, i.e. how close the shape is to the equally loaded kinetic net. This enables an interactive design process, dealing with shapes, faceting and structural behaviour. Fig.6 shows a procedure for generating structurally and architecturally improved configurations.

The final project was designed in collaboration with the Danish sculptors M. Jørgensen and G. Steenberg for an architectural competition. It was considered whether the glass covering should be structurally active or not, but even if it was absolutely possible, it was chosen to brace the plates by steel rods. Still it gives an appropriate configuration for plane glass used as structural elements.

## VI. PENTAGONIA CERAMIC DOME

<figure><img src="image_313.png" /><figcaption>Fig.7 The ceramic dome Pentagonia, the computer model and the cutting pattern for the clay.</figcaption></figure>

This project is based on plane ceramic tiles, which have qualitatively similar properties as glass.

Pentagonia (fig.7) is a single layer plate dome-shaped sculpture, 2.8m high and made from 10 to 15mm thick ceramic tiles, its name is derived from the regular pentagonal top tile and ground plan. The thickness of the tiles is greater than needed from a structural point of view but is necessary to prevent warping of the tiles during firing of the clay. To produce the sculpture, clay slabs of the required thickness were cut directly to the cutting pattern generated by CADual. An ordinary sand/cement mortar was used to connect the ceramic tile plates together. Ceramic artists Esben
Madsen and Gunhild Rudjord created the form - a paraboloid of revolution - in collaboration with the author. CADual indicated that this form is ideal to resist uniform vertical load - as is close to the distribution of the self-weight of the structure.

As ceramic tiles is in every way are much weaker than glass, it shows at the same time an almost ideal shape and faceting for a pure plate pure glass structure. The investigations by CADual

of Pentagonia makes this configuration quite unique and very appropriate for glass structures. It seems to be the first time that this configuration has been suggested and statically documented. The closest seems to be Gaudi's visionary work with kinetic nets and ceramic tiles [Zerbst 1987], even Gaudi used reversed chain curves and did not use the tiles as structural elements.

<figure><img src="image_314.png" /><figcaption>Fig.8 Palm House project. Note the perfect regular pattern for the horizontal projection of the structure</figcaption></figure>

show that shape, faceting and structural properties
## VII. PALM HOUSE PROJECT

The Pentagonia concept for an ideally shaped glass structure was used as a basis for the final examination project by two B.Sc.(eng.) students [Ohannessian et al. 1991]. The project shows a 30 m high botanical glass house (fig.8). In order to secure the glass plate structure from progressive collapse in case of breakage of a single glass sheet, the 3-branched fine-meshed glass structure was complemented by a triangulated coarse-meshed steel lattice structure. Both the steel nodes and the glass planes follow the same theoretical paraboloid of revolution with the steel nodes on the surface and the bars inside, whilst the glass plates are all external intersecting tangential planes to the same surface. The apparently quite complicated geometry is generated extremely easily by the Dual Method on CADual.

A well-known problem when building together doubly curved facetted shells are matching along intersections, but the combination of equivalent paraboloids fit perfectly together without awkwardly shaped facets along the intersecting lines. As the glass is a part of the structure and as it is relatively heavy, it is important that the shape is

optimised for its self-weight, hence the parabolic form. In the case of wind load on the smooth and aero-dynamic shape combined with the relatively large self-weight, the total efficiency of the shape will only slightly decrease.

As the lattice structure is only introduced for emergency reasons, it can be constructed quite slender.

The structural design showed that all the glass plates might be cut from long glass strips of 2 m width, which is very relevant for glass production. The static analysis resulted in 12mm hardened glass which was laminated on 3 mm soft glass.

The connection between the glass plates was suggested as cogged which is directly inspired by the toothed join between the plates of the sea-urchin.

## VIII. MARKET HALL PROJECT

The same two students continued their studies and finished their M.Sc. with a project [Ohannessian et al. 1993] which was a continuation of the palm house. This time they chose a 16 m tall and 45 m long market hall roof as a different type of combined glass plate and steel

<figure><img src="image_315.png" /><figcaption>Fig.9 Market Hall project. Note that the horizontal projection creates perfect squares. This project has structural similarities to Kibbles Palace as shown in fig.1.</figcaption></figure>
lattice structure (fig.9). The main parabolic shape
is the same as before, but in this structure, the steel
and glass structure works intimately together as
one structural envelope. The geometry shows
quadrilateral plane plates, four-branched nodes
which give a projection of perfect squares. The
hardened glass plates, cut from a 2 m wide glass
strip, was calculated to be of 8 mm thickness,
laminated with 3 mm ordinary glass. Because of
the necessary transfer of forces between glass and
steel bars, and because of the different thermal
expansion of these two materials, a friction
connection as a steel plate fitting with an elastomer
as lining and fastened by a prestressed bolt was
suggested as a realistic possibility.

IX. CONCLUSION

The projects described in this paper are
connected to the author's research on the concept
of structural duality and plate action. It has been
fascinating to see that these overlooked concepts
have led to a deeper insight into Nature's structures
as well as suggestions for new and appropriate
morphological design and computation of
structures made by plane glass sheets.

FURTHER READING

- *A Geodesic Dome-Type Based on Pure Plate Action*, paper in the International Journal of Space Structures, Vol.5 Nos 3 & 4. Special Issue on Geodesic Forms, edited by T.Tarnai, 1990

- *Structural Morphology and Natural Structures* Paper in Evolution of Natural Structures, Part 9. Edited by M.Hilliges. SFB 230, University of Stuttgart and Tübingen, Germany, 1994

- *The Fabulous Paraboloid:* Dual Transformation as a Design Method, paper in *Katachi U Symmetry*, pp. 323-330, Springer Verlag Tokyo 1996

- *The Structural Morphology of Basic Polyhedera*, article in J.F. Gabriel (ed) *Beyond the Cube*, pp. 301-342, John Wiley & Sons, Inc. NY, 1997

REFERENCES

[Cundy et al. 1961]

CUNDY, H.M. AND ROLLET, A.P., *Mathematical Models*, Tarquin Publications, Oxford University Press, 1961

[Haeckel 1887]

HAECKEL, E., *Report on the Radiolaria* collected by H.M.S. Challenger expedition during the years 1873-1876, by Vol. XVIII, 1887

[Ohannessian et al. 1991]

OHANNESSIAN, P., GRUNNET, N., Projektering af en Glasskivekuppel (The Design of a Glass Plate Dome). Final examination project (B.Sc.eng.) at the Danish Engineering Academy, Lyngby, Denmark. In Danish. 1991

[Ohannessian et al. 1993]

OHANNESSIAN, P., GRUNNET, N., Samvirkning mellem Gitter- og Skivekonstruktioner (Co-operation between Plate and Lattice Structures). Final examination project (M.Sc.eng.) at the Danish Technical University, Lyngby, Denmark (in Danish) 1993

[Wester]

WESTER, T., *CADual: Computer Aided Duality*. Royal Academy of Fine Arts, Copenhagen. Please contact the author for further information

[Wester 1983]

WESTER, T., *Structural Order in Space*. Royal Danish Academy of Fine Arts. Copenhagen, Denmark, 1983

[Wester 1987]

WESTER, T., *The Plate-Lattice Dualism*, paper in the Proceedings of the IASS Colloquium on Space Structures for Sports Buildings, edited By Lan & Zhilian. Elsevier Applied Science, London, 1987

[Winter et al. 1994]

WINTER, A., SIESSER, W. G. (eds), *Coccolithophores*, Cambridge University Press 1994

[Zerbst 1987]

ZERBST. R., *Antoni Gaudi*. pp.80-81. Taschen Verlag Köln 1987
# Construction Practice in Glass Structures

Philip Wilson, Malishev Wilson Engineers, London, UK

The paper gives a summary of various key principles that should be applied to the design of glass elements. Consistency in design can be achieved more easily where there are well-established codes of practice, but the situation with glass is that currently no design standards exist and engineering judgement needs to be applied from first principles. The information in this paper gives an insight into the design of glass structures and might be useful to the practicing engineer as a guide to initial design and detailing. Where there is uncertainty it would always be wise to base the final design on test results.

The application to design problems is referenced to built projects where glass acts as a structural material, starting with early work at Dewhurst Macfarlane and Partners on annealed glass beams, then entire structural frames.

## I. INTRODUCTION

Glass, being a brittle material, fails abruptly without first yielding or permanent deformation. Failure always results from a tensile component of stress. A key principle is that of redundancy in the event of sudden failure of an element or leaf of glass, due to impact loading or spontaneous fracture by impurities inherent in glass, and to design to avoid the possibility of collapse disproportionate to the cause of breakage. The consequences of such a breakage should be considered and it is often necessary to laminate to provide redundancy.

## II. GENERAL PRINCIPLES

### A. Soda-lime glass

There are many different glasses produced using chemical compositions appropriate to their application. The majority of sheet glass used in the construction industry is soda-lime glass. This glass has generally a green tint due to the presence of iron in the mix used to lower the melt temperature and to reduce float glass production costs. Some of the properties of soda-lime glass are given in Table 1.

<table><caption>TABLE 1: PROPERTIES OF SODA-LIME GLASS</caption><tr><td>Density</td><td>2500 kg/m³</td></tr><tr><td>Refractive Index</td><td>1.52</td></tr><tr><td>Hardness (MoH scale)</td><td>6</td></tr><tr><td>Youngs Modulus</td><td>70 kN/mm²</td></tr><tr><td>Poisson's ratio</td><td>0.23</td></tr><tr><td>Coefficient of thermal expansion</td><td>7.75 x 10<sup>-6</sup>/°C</td></tr></table>

The viscosity of glass increases very rapidly with decreasing temperature. The term glass transition temperature ($T_g$) has been given to the approximation when glass changes instantly from an infinitely mobile fluid to an elastic solid and is also noted as the 'annealing point' as defined in Table 2.

<table><caption>TABLE 2: TEMPERATURE DATA</caption><tr><td>Strain point</td><td>510°C</td></tr><tr><td>Annealing point</td><td>555°C</td></tr><tr><td>Softening point</td><td>740°C</td></tr></table>

### B. Design stresses

The design thickness of glass should be the minimum tolerance allowed for monolithic glass.
Standards of production in the UK set the design thickness of 12 mm thick glass as 11.7 mm and for 15 mm and 19 mm thicknesses the design thickness would be 14.5 mm and 18 mm respectively.

The properties of glass have been known for some time, notably the publication by E B Shand [Shand 1958]. The forthcoming Eurocodes (prEN 13474-1, Glass in Building [prEN 13474-1], currently in draft form, obtained data from 740 samples of 6 mm thick annealed glass from 30 batches from 9 different float plants over Europe tested for bending strength. The range of failure stresses, between 30 N/mm² and 120 N/mm², was very wide, with a mean of 70 N/mm², and no significant variation between different suppliers. Based on these data, the draft Eurocode gives the following characteristic strengths (strength exceeded by 95% of samples tested):

<table><caption>TABLE 3:
CHARACTERISTIC STRENGTHS</caption><tr><td>Annealed</td><td>45 N/mm²</td></tr><tr><td>Heat strengthened</td><td>70 N/mm²</td></tr><tr><td>Toughened</td><td>120 N/mm²</td></tr></table>

For the TIF Yurakucho canopy tests were carried out at City University, London, where the load and reactions for a three-point bending tests were applied to the glass sample through holes in bearing rather than edge loading. Failure in each test was at the extreme fibre and not at the point of loading which may often be the case. Results showed a mean strength of toughened glass as 160 N/mm².

A guide to allowable stresses for initial design of glass for short duration loads, based on unfactored loads and using simple elastic formulae, can be taken as the mean failure strength with a factor of safety of 3. The allowable stress for annealed glass can be assumed as 23 N/mm² and toughened glass as 53 N/mm².

### C. Annealed glass

Standard thicknesses, in mm, are 3, 4, 6, 8, 10, 12, 15, 19, and 25. Typically the maximum sheet size is 3.0 m x 6.0 m, but 3.2 m x 8.0 m is possible, and larger by special order.

Annealed glass is subject to stress corrosion cracking under long duration loads. This phenomenon is due to chemical corrosion at the tips of surface micro-cracks caused by the action of water, which elongate the crack. There is a threshold stress below which stress corrosion cracking is no longer a significant factor and this is taken as 7 N/mm².

Another phenomenon to which annealed glass is vulnerable is thermal shock. This causes cracking due to internal stresses resulting from temperature differences between different parts of the same sheet of glass. The critical temperature difference has been found to be 33°C. The possibility of thermal shock is greatest where parts of the glass are in shadow, within the frame rebate for example, while other parts are exposed to direct sun. If thermal shock is found to be a problem then the glass needs to be specified as heat-strengthened or toughened.

### D. Heat strengthened and toughened glass

Annealed glass can be tempered by re-heating the glass, to a temperature around 650°C, and then rapidly cooling the outside surface in a carefully controlled manner. The cooling prestresses the outside skin and greatly enhances the capacity of the extreme fibres to resist tensile stress. The magnitude of stress, referred to as 'residual' are determined largely by the rate of cooling. Toughened glass is often specified to have a minimum residual surface stress of 100 N/mm², and heat strengthened glass to have a minimum residual surface stress of between 40-50 N/mm².

Glass thickness for heat strengthening follows annealed glass up to a maximum thickness of 12 mm. For toughened glass all thicknesses are possible although 25 mm thick glass is difficult to toughened adequately. Maximum sheet size depends on the furnace used, and is normally 2.14 m wide and 4.5 m long. Larger tempering furnaces are available up to a maximum of 3.0 m x 6.0 m.

To minimise the risk of spontaneous shattering due to nickel sulphide inclusions, toughened glass may be specified to be heat soaked following toughening. Heat soaking would take place at a
temperature of around 280°C. It is important to note that, while heat soaking will minimise the risk of spontaneous shattering, there is still some small residual risk. This spontaneous shattering due to nickel sulphide inclusions is caused by the rapid cooling during toughening inhibiting the phase change of nickel sulphide crystals. It is therefore a phenomenon that is a problem for toughened glass, but not for heat-strengthened glass, where the cooling rate is slower.

### E. Laminated glass and interlayers

Interlayers are either in sheet materials, such as PVB (PolyVinylButrly) or polyurethane, or liquid cast resins. The design thickness of a laminated glass depends on the duration of load and the temperature. Following the guidance of the Canadian Code (CAN/CGSB 12.20-M89, Structural design of glass for buildings) [CAN/CGSB 12.20-M89], leaves in glass should be treated as composite only under wind loads and at temperature less than 70 °C. For all other situations, the glass should be treated as two separate leaves, with the load divided between the leaves in proportion to their stiffness. The performance of an interlayer, whether tacting as a composite or layered, is related to the T<sub>g</sub>. Generally, when designing in laminated glass, it should be assumed that, under serviceability conditions, when deflection is usually the design criterion, both sheets are acting. When checking for robustness with one sheet failed, the stress in the remaining sheet is important, but not its deflection.

## III. CONNECTIONS

In order to go beyond the production limits of a single sheet of flat glass, to support a span of over 5.0m, a connection which links a series of elements becomes necessary and this joint becomes the critical area in the design of the glass structure.

The designer's choice of connection type is based on various criteria, notably strength requirements, adequate tolerance for construction, cost, method of fabrication and aesthetics. The transfer of load through a bearing connection makes use of the high strength capacity of glass

and minimises the depth and complexity of the connection. Alternative connections such as friction grip connections result in deeper sections to achieve sufficient moment capacity with a greater number of parts to install on site. However, the bearing detail requires a high level of machining precision in the fabrication of both metal and glass elements.

### A. Edge bearing connections

The load transfer between the horizontal glass beam and glass fin is by bearing through an acetal, acrylic or nylon block. The overlapping beam and fin allow for redundancy in the event of failure of a single element. The 'mortise and tenon' joint detail is borrowed from timber construction. An example of this type of construction is the glass conservatory for Tregardock Cottage, Cornwall (1996).

The glass beams are each 4.0 m long, and made of 10 mm annealed sheets of triple compound glass. The joint with the 2.2 m vertical fin is similar to a timber 'mortise and tenon' joint, with the two side wings of the beam resting on the two side wings of the fin. This is an adequate method because the joint is not required to resist moment, and the lateral stability is provided through the attachment to the building.

<figure><img src="image_316.png" /><figcaption>Fig 1: Tregardock Cottage, Cornwall</figcaption></figure>
## B. Hole bearing connections

This solution were first developed for the glass canopy of the Yurakucho subway station at the Tokyo International Forum (1996) and followed with the façade of the Samsung Jong-Ro Building (1997) in Seoul, Korea.

The glass canopy is 4.2 m wide with a cantilever span of 11 m. As the maximum length of toughened sheets of glass available at that time in England was 5 m, a series of laminated toughened beams with leaves 19 mm thick are joined together by a bearing connection through holes in each of the beams. The number of beams that overlap increases towards the support, in line with the bending moment and force in each pin connection.

<figure><img src="image_317.png" /><figcaption>Fig 2: TIF Yurakucho canopy</figcaption></figure>

The key to the design was the method of transferring force at the connections, to ensure that the bearing areas were sufficient and accurately fabricated to prevent high stress concentrations, which would cause failure. The process of toughening the glass puts the whole surface of the glass into compression, including the internal surface of the holes provided. Detailed analysis of the stresses, by using conventional formulae with stress concentration factors, or by finite element analysis, or by physical testing with strain gauges, allows the stress around holes to be accurately determined

Initial tests at a University laboratory on a 48 mm diameter hole in a 19 mm thick toughened glass sample with the load applied in pure tension gave a mean failure capacity of 77 kN. These results compared well with prediction by elastic analysis of stress concentrations around holes and led to full scale testing of single and laminated

glass beams.

<figure><img src="image_318.png" /><figcaption>Fig 3: Full scale testing of glass beam</figcaption></figure>

<figure><img src="image_319.png" /><figcaption>Fig 4: Stress concentrations around hole</figcaption></figure>

The interlayer material used was a UV cured acrylic resin. Before the glass beams were shipped out to site each individual toughened glass element was fully tested to three times working load.

A similar technology was used for the 50 m x 50 m façade of the Samsung Jong-Ro Building in Soeul, to create 12m long beams. The upper part of the façade is supported by horizontal laminated, toughened glass beams made of two 19 mm thick leaves, which span 12 m between columns. The lower part to the foyer is supported by similar vertical beams made of two 15 mm thick leaves. The weight of the glass is supported by steel hangers.
<figure><img src="image_320.png" /><figcaption>Fig 5: Horizontal glass beams span 12m</figcaption></figure>

Load was transferred through square edges holes in contrast to chamfered holes for the Yurakucho canopy.

<figure><img src="image_321.png" /><figcaption>Fig 5: Vertical glass panels brace facade</figcaption></figure>

In order to determine the distribution of load through bushes in laminated glass, tensile tests were carried out an representative samples. With the highest tolerance drills holes in glass and machined fittings the load sharing between the leaves was 60% to 40% and at worst 85% to 15%. The importance of tight fitting bushes in true circular holes in glass is a major factor in determining the load capacity.

<figure><img src="image_322.png" /><figcaption>Fig 6: Tensile tests in laminated glass and square edged holes</figcaption></figure>

Other projects where the principle of carrying load through holes in glass include the Transport Stack, Discovery Centre, Birmingham (2000) and the staircase to the Fleming Gallery, London (2001).

<figure><img src="image_323.png" /><figcaption>Fig 7: Transport Stack, Discovery Centre, Birmingham</figcaption></figure>

<figure><img src="image_324.png" /><figcaption>Fig 8: Glass sided staircase, Fleming Gallery, London</figcaption></figure>
### C. Friction grip connections

These were first pioneered by Pilkington Glass and have been used for many years with single-ply toughened glass. For the Glass Reading Room of the Arab Urban Development Institute in Riyadh, Saudi Arabia (1998) a solution was found to friction-grip laminated glass and overcome the problem of interlayer creep relaxing the bolt tension and hence losing the friction in the long term.

The cube is 8 m x 8 m x 8 m and has no internal structure. Toughened glass beams 2.67 m in length formed of two 15 mm thick leaves were joined using friction grip connectors to create portal frames which carry the glazing loads and provide stability. Because of the high forces that arise when the bolts are tightened, an aluminium spacer of low temper yet creep-resistant was inserted between the glass leaves at the connection.

<figure><img src="image_325.png" /><figcaption>Fig 9: Glass cube, AUDI, Riyadh</figcaption></figure>

We have found that for these connections attention to detail at manufacturing stage is vital. Key things to watch for are: the steel surfaces at the friction connection must be milled perfectly flat; the fibre gaskets must be used only once and should be made of semi-flex vulcanised fibre; the thickness of aluminium must be carefully matched to the edge tape thickness to provide 5-10% compression to the tape; the joint must be clamped during UV curing of the resin.

<figure><img src="image_326.png" /><figcaption>Fig 10: Detail of roof construction</figcaption></figure>

### D. Compression plates

The use of glass plates in compression presents the possibility of withstanding high loads. The concept of stacked glass plates for a structure over 30 m high was first concieved for the Construction Tower competition (2000). The tower reached 100 ft and comprised 2000 sheets of 15 mm thick annealed glass. Tests on the flatness of glass plates was carried out to determine whether high points could cause the glass to fracture. The structure was both robust and durable as it could withstand breakage of multiple sheets. Chosen as the winning entry the project was never built.

<figure><img src="image_327.png" /><figcaption>Fig 10: Construction Tower, Birmingham</figcaption></figure>

The same concept was, however, applied to the construction of three stacked glass structures for The Bullring, Birmingham. Internal glass fins and beams restrain the structure from overturning, with all vertical load taken through the annealed glass plates.
<figure><img src="image_328.png" /><figcaption>Fig 9: Glass and Water feature, St Martins Square, The Bullring, Birmingham</figcaption></figure>

## IV. FUTURE DEVELOPMENT

Early tests on double-overlap joints using a cast resin interlayer gave positive results in the short-term. The average failure shear stress of 3.0 N/mm² was found to be greater than the figure of 1.1 N/mm² reported by the manufacturer. However, creep tests of the resin interlayer, at an elevated temperature of 60°C, gave a poor performance with a delay period of 100 hrs and failure of the sample after 120 hrs, with an applied constant stress of less than 0.1 N/mm². The reason for failure can be understood when realised that the T<sub>g</sub> for resin interlayers is only 17°C and approximately 20°C for PVB interlayers. The test results were conclusive, under the conditions set, in indicating that the resin laminate overlap joint would not be suitable for the proposed structural design. However, the composite performance of laminates are of special interest to the manufacturers, with DuPont now marketing a higher grade material, Sentry Glas-Plus, of higher stiffness and a T<sub>g</sub> of 55°C.

## V. SUMMARY

The selection of the connection method depends largely on the tolerance of production processes available. The transfer of load through a bearing connection requires a high level of precision in fabrication.

The work carried out over the last decade has shown that, with suitable attention to detail in both

design and construction and by the provision of redundancy by using laminated glass where appropriate, glass can be used as a structural material with adequate safety.

## VI. ACKNOWLEDGMENT

Each of the projects mentioned draws upon personal experience while working at Dewhurst Macfarlane and Partners. For that experience I would like to thank Tim Macfarlane for his direction and guidance. Thanks are also due to John Hodgson and Mark Leddra, both at F A Firman (Harold Wood) Ltd, who acted as fabricators for many of the projects, for showing willingness to experiment when it was never sure there would be a definite job.

## REFERENCES

**[Shand 1958]**
SHAND, E.B., Glass Engineering Handbook, 2nd Edition, McGraw-Hill Book Company, New York, USA, 1958.

**[CAN/CGSB 12.20-M89]**
Structural Design of Glass for Buildings, CAN/CGSB 12.20-M89, Canadian General Standards Board, Canada, 1989.

**[prEN 13474-1]**
Glass in Building – Design of Glass Panes – Part 1: General basis of design, DRAFT, 1999.
<figure><img src="image_329.png" /></figure>