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Glass Structures & Engineering

, Volume 4, Issue 1, pp 83–97 | Cite as

Residual load-bearing capacity of spannglass-beams: effect of post-tensioned reinforcement

  • Michael EngelmannEmail author
  • Bernhard Weller
SI: Challenging Glass
  • 138 Downloads

Abstract

Reinforcement and pre-compression of concrete beams results in a ductile response and allows for the design of structures that are more reliable and efficient. Therefore, this approach has been adapted to structural glass producing reinforced and post-tensioned glass beams. Unbonded tendons in Spannglass Beams are one structural example for realising this idea and are the subject of the presented study. Two individual laminated safety glass packages connected locally by metal dividers characterise these beams. A gap between the packages was used to guide tendons in a either three- or a four-point bending configuration. This eccentric layout allowed for an initial uplift of the cross section and a mechanical pre-compression of the vulnerable glass edge. This was the primary objective during the initial design stage of the concept of Spannglass Beams. However, proving sufficient residual load-bearing capacity is a further requirement to ensure the safety of glass structures and requires additional study. During this stage, a common approach is to evaluate the effect of broken layers in the glass section, which may result in eccentric loading by the tendon and introduce additional bending about the minor axis. Thus, the novel structural design may cause an early (lateral) failure of the structure even during a service load condition. We examined a set of 16 Spannglass Beams with 5.0, 8.1 and 10.1 mm post-tensioned cables in an experimental study during four-point bending. Additionally, four un-reinforced specimens and four beams with untensioned tendons were tested. The paper includes a testing method to evaluate the residual load-bearing behaviour. First, the specimens were loaded in bending, after which a single glass layer was damaged manually by a hammer and a chisel. Finally, the assembly was left for 24 h before taking a next step to damage a consecutive layer. In this manner, it was possible to evaluate the residual load-bearing behaviour in terms of residual service-life as a function of damage scenario and load. Additionally, the crack pattern after each step, the evolvement of the deflection and the change in cable load were analysed before the final failure modes were characterised. This report aims to describe the effects of post-tensioning on the residual load-bearing capacity of glass beams. It was possible to influence the structural response considerably by reinforcing and post-tensioning glass beams. Due to excessive lateral deflection, an additional cable load reduced the residual service-life. However, the number of connectors in Spannglass Beams determined the shape during bending with a special focus on the buckling length and thus contributed to increasing the service-life as a major parameter during design. Finally, we derived structural recommendations for a future design of effective glass beams in facades, roofs or even “floating” glass bridges.

Keywords

Glass beam Reinforcement Experimental investigation Bending tests Post-tensioning Robustness Post-fracture limit Fracture safe 

1 Introduction

1.1 Glass beams: plain, reinforced, post-tensioned

Glass fascinates because of its outstanding optical properties. The transparent material allows for a design of “floating” structures with reduced opaque parts. This especially refers to glass beams—longitudinal bending members—in facades and roofs. However, glass is known to be a brittle material. Additionally, its compressive strength exceeds its tensile capacities drastically. This leads to a premature tensile failure in bending without ductile pre-failure behaviour. Therefore, glass beams were reinforced according to principles of reinforced concrete design. This led to quasi-ductile structures in several research projects. Weller et al. (2010), Louter (2011) and Martens et al. (2015) explain representative examples. An advanced approach included the adoption of prestressed concrete structures in glass design such as Jordão et al. (2014), Louter et al. (2014) and Weller and Engelmann (2014a, b). Herein, glass beams were post-tensioned with centric or eccentric tendons that were either unbonded or adhesively bonded along the vulnerable glass edge. Martens et al. (2015) give additional details and a broader summary. This approach even led to projects involving multi-span beams (Cupac et al. 2017; Martens et al. 2017) and the use of post-tensioned fibres (Bedon and Louter 2017). Additionally, unbonded tendons are in the focus of a wide experimental study presented in Engelmann (2017). In summary, the idea to reinforce and even pre-compress glass beams is applicable and shows promising results.

1.2 Problem: what is residual load-bearing capacity?

Load-bearing building structures need to show sufficient robustness. This means that they will behave in a non-problematic manner in situations that were not anticipated beforehand or cannot be quantified. Therefore, glass standards such as [DIN 18008] give structural guideline details and demand for a proof of residual load-bearing capacity. A widely applicable and accepted definition, however, is still missing. Consequently, the following section summarises the available information from the literature and provides some details regarding the implementation of the upcoming “Eurocode Glass”.

Available sources such as DIN 18008 (2010–2013) and Kott (2006) agree on the fact that a glass structure needs to withstand a (partial) failure scenario with the inclusion of a defined load (post-fracture resistance) during a defined period of time (post-fracture service-life). This may be shown through an experimental investigation or by a calculation while unbroken glass plies carry the load.

Currently, an appropriate Eurocode design philosophy is under creation. It includes the definition of Glass Component Fracture Consequence Classes (CCC). Herein, primarily load-bearing glass beams need to meet the “fracture-safe” (FLS) property and the “post fracture limit state” (condition). “Fracture Limit State: Limit State that concerns the protection of people and/or the structure during fracture. The fractured glass component does not necessarily provide residual (post-fracture) load bearing capacity”. Post fracture limit state (PFLS) defines “[t]he condition where one or more glass plies have fractured and the glass component (or a suitable alternative load path) provides load-bearing capacity for a defined [pre-determined] accidental design situation for a defined [pre-determined] period of time” (CEN TC250/SC11 2018). Thus, it makes use of available information and links the two requirements in the face of the semi-probabilistic design philosophy.

In general, a proof of sufficient residual load-bearing capacity includes the need to offer an alternate loading path in case of (local) fracture to prevent a progressive collapse. In case of reinforced and post-tensioned glass beams, the reinforcement needs to show those capabilities even during fracture or failure. As no vast experience is available today, this paper presents a first study on the effects of reinforcing and pre-compressing glass members on the residual load-bearing capacity. This is done though the analysis of the results from an experimental study on Spannglass Beams.

1.3 State of the art: review of residual load-bearing capacity in research and projects

Technical requirements demand an individual experimental investigation in the field of structural glass beams, due to a lack of available information and standardisation. Hess (2000) conducted experiments involving un-reinforced glass beams. The specimens were loaded up to 42% of the fracture stress. At this loading stage, a hard body impacted the flange of the beams. Hereby, steel balls of different sizes and masses, suspended from a chord, were dropped from a variety of heights to show a sufficient fracture robustness (FLS). Afterwards, an additional bending test confirmed the load-bearing capacity of the fractured cross-section. Thus, a post fracture stiffness was determined without a wide study on the residual service-life. Additionally, the investigation was limited to a number of three specimens made from fully tempered glass.

The residual load-bearing capacity of un-reinforced glass beams in the building project “Alte Mensa” at the Technische Universität Dresden (Zschippang et al. 2006) was assessed during an experimental investigation as well. Two outside panes in the quadruple laminate composed of fully tempered glass were fractured intentionally using a steel hammer during a bending load of 50% of the design snow load and dead weight. The change in deflection was recorded for executing three tests for 12 h each. However, no substantial change in deflection was documented, which led to the conclusion that the demand by the building authorities was met. The behaviour during the fracture event and a post fracture service-life were evaluated, both requirements of FLS and PFLS were basically covered.

In contrast to the given examples, the project “Therme Badenweiler” did not demand for any testing according to Schober et al. (2004). In fact, a numerical calculation assuming failure of two outside layers was conducted. The reinforced and post-tensioned samples from fully tempered glass were able to demonstrate their structural safety.

In a laboratory sized study, Louter et al. (2012) conduced small-scale pull-out tests and full-scale bending tests to show the durability of reinforced glass beams during long-term loading in a post fracture situation. The authors concluded that the reinforcement allowed for an exceptional post fracture robustness for up to 22 months of time. Thus both, FLS and PFLS were covered in this investigation. Nevertheless, the external load tensioned the specimen without any initial post-tensioning. Additionally, the concept included shear between the reinforcement bars and the glass. Thus, the results from this contribution may be considered un-comparable to the results from the study presented.

Härth (2013) tested hybrid glass beams made from a glass-polycarbonate-glass sandwich in a long-term bending test to show the residual load-bearing capacity. Annealed float glass layers were fractured using a sharp metal tool during a bending stress of 14 N/mm\(^{2}\) that equalled three times the identified (long-term) design strength of 4.7 N/mm\(^{2}\). After each cracking event, the samples rested for 24 h. During this period, a load redistribution from the glass to the polycarbonate interlayer was observed, which resulted in a time- dependent creep of the material.

Jordão et al. (2014) developed hybrid I-shaped beams with a vertical laminated glass web and adhesively bonded steel flanges. Additionally, pre-stressed steel cables suspended the structure and gave a pre-bending load to the beam. Destructive bending tests revealed robustness after initial fracture. However, the specimen failed in an explosive manner after exceeding their ultimate limit. Thus, no considerable post fracture service-life was recorded due to the concept of testing.

Louter et al. (2014) published another experimental study on post-tensioned structural glass beams to show the mechanical response of numerous types of structures. The concept allowed for a significant post fracture robustness until final failure. Thus, the experimental concept approach did not include a study on the residual service-life.
Fig. 1

Specimens: cross section and deviator. (1) Bearing blocking (POM-C); (2) EPDM blocking; (3) compression blocking (POM-C); (4) stainless steel deviator (1.4571); (5) laminated glass from heat-strengthened glass and PVB interlayer 2 \(\times \) 2 \(\times \) 6 mm; (6) cable; (7) adhesive joint

In total, three principle methods were used to evaluate the residual load-bearing capacity:
  • An experimental bending test was executed at a load level below the glass strength and at a specified state of damage. Glass layers were fractured either before or after exposing the beams to bending. Additionally, a waiting period was demanded.

  • After initialising a state of damage intentionally, an external bending load was increased, which finally revealed the ultimate (post-fracture) bending strength.

  • A state of damage was assumed theoretically and implemented in a numerical model for a numerical proof without experimental tests.

1.4 Aim and course of action

This study is based on Engelmann (2017) and aims at describing the effects caused by post-tensioning of glass beams on the residual load-bearing capacity. An experimental approach on a set of specimens with varied cable diameters and initial cable loads as well as a set of reinforced and un-reinforced specimens allowed for a discussion of possible causes and quantification of the recorded effects. More specifically, the post-fracture loading time was observed during a varied artificial glass damage state. This happened during a constant (residual) bending load to meet the post-fracture limit-state as a first step. A second step may include considerations regarding a specific application and a human risk assessment to meet the property “fracture-safe” in the future.

2 Method

2.1 Specimens

Figure 1 depicts the structural details of the specimens. Two different cable layouts with either one (I) or two (II) deviators (4) were used. Two packages of laminated safety glass (5) of 2 \(\times \) 6 mm each, made from heat-strengthened glass, spanned two meters between stainless steel bearing shoes that contained a set of plastic blockings (1–3). A gap in between the glass packages was used to guide cables (6 and Table 2) from a fixation (fixed anchor), around the deviators to the tension side (tensioned anchor).
Table 1

Specimens. All series made use of a set of bonded deviators at the glass edges

Series

Specimen name

Reinforcement (Table 2)

Initial cable load

Bending load

Number

(–)

d\(_\mathrm{p}\) (mm)

Type

P\(_{0}\) (kN)

F (kN)

(–)

PX-II

RT01 PX-II

RT04 PX-II

None

Open image in new window

Un-reinforced reference

10

4

P0-8.1-II

RT05 P0-II

RT08 P0-II

8.1

Open image in new window

Reinforced reference

10

4

P9-5.0-I

RT9 P9-I

RT12 P9-I

5.0

Open image in new window

9.0

10

4

P9-5.0-II

RT13 P9-II

RT16 P9-II

5.0

Open image in new window

9.0

10

4

P15-8.1-I

RT17 P15-I

RT18 P15-I

8.1

Open image in new window

15.0

10

2

P15-8.1-II

RT19 P15-II

RT20 P15-II

8.1

Open image in new window

15.0

10

2

P15-10.1-I

RT21 P15-I

RT22 P15-I

10.1

Open image in new window

15.0

10

2

P15-10.1-II

RT23 P15-II

RT24 P15-II

10.1

Open image in new window

15.0

10

2

Table 2

Reinforcement according to manufacturer’s specifications, see Ahrens (2016) and ETA-11/0160 (2011)

Cable diameter

Metal area

Cable type

Material

Characteristic strength

Thermal expansion

Modulus of elasticity

d\(_\mathrm{p}\) (mm)

A\(_\mathrm{p}\) (mm\(^{2}\))

(–)

(–)

f\(_\mathrm{y,k}\) (N/mm\(^{2}\))

Z\(_\mathrm{B,k}\) (kN)

\(\alpha _\mathrm{T}\) (K\(^{-1}\))

E\(_\mathrm{Q}\) (N/mm\(^{2}\))

5.0

21

1 \(\times \) 19

1.4401

1570

21

Not specified

130,000

8.1

59

1 \(\times \) 19

1.4401

1770

59

12 \(\times \) 10\(^{-6}\)

160,000

10.1

93

1 \(\times \) 19

1.4401

1770

93

12 \(\times \) 10\(^{-6}\)

160,000

Altogether, a set of 24 specimens were tested to final failure (Table 1). This included four un-reinforced and four reinforced each with an untensioned option as well as 16 post-tensioned beams. Apart from the diameter of the cables d\(_\mathrm{p}\), the initial cable load P\(_{0}\) and the number of deviators were altered while the bending load F was kept at 10 kN to set the post-fracture load as a constant. This equalled about one third of the expected failure load (see Engelmann 2017) and represented a possible serviceability level.

2.2 Test set-up and test procedure

Figure 2 illustrates the four-point bending test-rig. Each single span beam was fixed and restrained in torsion at the ends. A loading beam (4) was set at the third points of the span and connected to a cantilever arm (5) to introduce the aspired level of loading. A set of concrete blocks (6) was placed and fixed at the end of the cantilever to ensure a constant bending load during all stages of the test. The actual bending load was measured before the test started. Therefore, the approach may be labelled as force-controlled.
Fig. 2

Test set-up. (1) Load cell at cable, (2) displacement transducer (vertical deflection), (3) displacement transducer (lateral deflection), (4) loading beam, (5) cantilever arm, (6) concrete loading blocks, (7) fixed anchor, (8) strain gauges

The deformation and acting cable forces were recorded during the test. This included the documentation of the cable force using a load cell in line with the cable at the beam’s end (1 in Fig. 2). Displacement transducers recorded the vertical deflection at centre span and at the bearings (2), as well as the horizontal deflection of the top glass edge at centre span (3). Finally, three strain gauges at the bottom glass edge at centre span (8) were used to estimate the stress in the intact glass layer.

As multiple parameters of the residual post-breakage capacity remain unknown a priori, an economic approach was realised according to Fig. 3. After loading the specimens, the first layer was hit with a chisel and a hammer at the bottom edge about 800 mm away from the bearing. The glass was left for 24 h in the test assembly. Afterwards, layer number 4 was damaged in the same way and left for another 24 h. The method was repeated for the remaining two panes of glass until the specimen lost integrity. This allowed for a description of the post-fracture service-life as a function of the damage scenario, at a constant level of bending load (post-fracture resistance). As an assumption, this course resulted in the most unfavourable lateral instability and supported the expected failure mode.
Fig. 3

Test procedure

2.3 Evaluation of results

Each test resulted in a value of the vertical and lateral deflection of the top chord, the strain of the intact layers, as well as the change in cable force over time. Recording times are 10 seconds before and after breaking of a layer to determine the fraction of load carried by a broken pane.

Additionally, a set of photos during the test was used to evaluate the crack patterns, as the load-bearing behaviour depended on their course and numbers. The images were straightened using a commercial software package \((\hbox {Adobe}^{\circledR } \hbox {Illustrator}^{\copyright } \hbox {Version}~15)\), which resulted in a frontal depiction of the crack pattern across the full height of the glass (H). This illustration allowed for a contactless post-measurement of the height of the crack fan (h\(_\mathrm{Z})\) and the height of the remaining compressive zone (H–h\(_\mathrm{Z})\). However, it should be mentioned that the straightening of the image was performed manually and had a subjective character included. This means that the result need additional discussion before implementation during augmented research.

Finally, the ultimate loss of integrity marked the end of the test and defined the post-fracture service-life. A verbal description of the failure mode allowed for a classification of the results for future derivation of design rules.

2.4 Analytic approach

The internal forces within the single-span beam may be estimated using linear beam theory. Firstly, the cable force during post-tensioning caused a deformation Weller and Engelmann (2014a). Anchoring the cable to the beam resulted in a shift of the structural system: the internal forces turn into functions of the deflection, which required a statically undetermined calculation. Those are covered by commonly known principles of mechanics. Thus, any fracturing of single glass panes cause a reduction of stiffness and changed the cable force and deflection. As an assumption, we assigned no stiffness to a fractured pane. Table 3 summarises the relevant results.

As an example, a beam reinforced with a 10.1 mm cable, post-tensioned to 15 kN, and loaded with 10.6 kN in bending will show a final cable load of 17.74 kN and a total vertical deflection of \(-\,1.99\) mm in the intact state. Breaking the first layer reduces the stiffness to 75% and results in an increase of the cable force to 18.21 kN. At the same time, the deflection increases to \(-\,2.62\) mm with a positive sign convention according to Fig. 2.

A comparison of un-reinforced with reinforced options (8.1 mm cable) revealed a decrease of deflection to 96% (3.06/3.18) in the intact state, but up to 85% (10.85/12.74) during a post-breakage situation. At the same time, any fracture of a single glass pane results in a redistribution of load to the cable, which increases its stress considerably. Compared with cable forces during bending tests, the relevant design situation for the tendon occurs in a post-breakage state. However, those numbers refer to the stiffness of the depicted specimens in this investigation and may not be generalised.
Table 3

Analytic results: cable force and deflection with adapted stiffness and cross-sectional area of the glass during bending at F = 10.6 kN

Cable diameter

Initial cable force

Cable force at a fraction of stiffness (kN)

Vertical deflection at a fraction of stiffness (mm)

d\(_\mathrm{p}\) (mm)

P\(_{0}\) (kN)

100%

75%

50%

25%

100%

75%

50%

25%

Un-reinforced reference

\(-\,3.18\)

\(-\,4.25\)

\(-\,6.37\)

\(-\,12.74\)

8.1

0

1.88

2.49

3.68

7.03

\(-\,3.06\)

\(-\,4.02\)

\(-\,5.88\)

\(-\,10.85\)

5.0

9.0

9.60

9.73

10.01

10.83

\(-\,2.54\)

\(-\,3.38\)

\(-\,5.02\)

\(-\,9.83\)

8.1

15.0

16.83

17.14

17.76

19.65

\(-\,2.05\)

\(-\,2.71\)

\(-\,3.98\)

\(-\,7.46\)

10.1

15.0

17.74

18.21

19.16

21.99

\(-\,1.99\)

\(-\,2.62\)

\(-\,3.80\)

\(-\,6.83\)

Fig. 4

Typical crack pattern. a Single broken layer (t = 0 h), b two broken layers (t = 24 h), c three broken layers (t = 48 h). (1) fracture origin; (2) crack fan; (3) compression zone; (4) horizontally deviated cracks; (5) crack delta; (6) single, horizontal crack in compression zone

3 Experimental results

3.1 Cracking: change in deformation and cable force

The first fracture resulted in a characteristic fracture pattern (Fig. 4a). Numerous single cracks in the form of a typical fan (2) branched from the fracture origin (1) upwards to spread horizontally (4) near the compressive zone (3) towards the bearings. It was observed that several single lines merged to form a conjunct crack. Subsequently, they branched out close to the third points of the span below the points of load introduction at the bottom edge of the beams. At this point, the typical crack delta (5) of heat-strengthened glass was clearly visible. As the load span was not considerably exceeded, the cracks were not associated with shear forces. This pattern was repeated in the moment of fracture of the remaining panes as illustrated in Fig. 4b, c. The figures also show the distance between fracture origins in the adjacent layers. Practical implementation caused this deviation. However, the depicted form was considered acceptable.
Fig. 5

a Change of vertical and horizontal (lateral) deflection, b change in strain, c change in cable force during testing of RT19 P15-II

Fig. 6

Change in cable force. Series P15-10.1 and P9-5.1 on the left-hand side, series P15-8.1 and P0-8.1 on the right-hand side

Figure 5 shows an exemplary course of the test through the example of specimen RT19 P15-II. The left image (Fig. 5a) displays a rapid increase in vertical differential deflection (w\(_\mathrm{z})\) of 0.22 mm, from \(-\,3.59\) to \(-\,3.81\) mm, as a result of the first fracture, a subsequent alteration of 0.66 mm due to the second fracture and finally 1.55 mm because of the third hit to the glass after 48 h. The specimen deflected continuously as expected until the displacement transducer lost contact to the glass at a total deflection of \(-\,5.22\) mm after 72 h. Therefore, successive data was removed from the chart. This principle behaviour was recorded for all specimens and confirmed the assumptions made in an analytic calculation.

At the same time, the specimen deflected horizontally, which is not covered in the analytic approach. However, previous investigations in Weller and Engelmann (2014a, b) and Engelmann and Weller (2016) predicted this effect. Breaking the first layer of the laminated glass caused an unsymmetrical cross-section, which resulted in additional bending about the minor axis and a lateral deflection. This loaded the interlayer as well, which was known to exhibit a considerable time-dependent creep deformation. Thus, the horizontal deflection v\(_\mathrm{y}\) increased during the first 24-h period. However, fracturing the second layer (layer 4) resulted in a horizontal deflection in the opposing direction. Also, after breaking the third layer (layer 2), no considerable additional horizontal deflection was observed. The breaking of the last layer showed a substantial increase in lateral deflection, which finally initiates the loss of integrity after 88.6 h of post-fracture service-life. Compared with the vertical deflection, a noticeable correlation with a structural parameter, such as the initial cable force or the diameter of the tendon, was not observed.

The subsequent graphs in Fig. 5b, c illustrate the redistribution of bending load. Primarily, Fig. 5b reveals a stepwise increase in strain of the intact glass layers every 24 h in accordance with the increase in vertical deflection. As a second result, the cable load in Fig. 5c also changed every 24 h without any considerable change during the waiting period. After 72 h, the graph stops running as smoothly and repeats the unsteady behaviour of the lateral deflection during the same period. In this stage, the specimen seemed to destabilise as a result of an increase in the number of single glass cracks, which will be evaluated in a following section. Nevertheless, the change in strain and cable load was typical for all tests.
Fig. 7

a Change of cable force, b deflection during testing of RT21

All recorded changes in cable force are depicted in Fig. 6 for assessment with the analytical results from Table 3. The comparison reveals a ratio between 95 and 102% during the first period (0–24 h). Thus, any load share of the first layer is almost entirely lost and the analytic assumptions prove to be realistic. In the subsequent periods (24–48 h and 48–72 h) the ratio drops to ranges between 79–96% and 71–95%. The results fall significantly short. Therefore, it is reasonable to assume that the analytic assumption of a full removal of shattered layers is unrealistic, nevertheless, a standard PVB-interlayer was used. Broken panes also carry parts of the total load, but this effect presents itself at a considerably sever stage of fracturing. Additionally, the realistic load capacity of the cable will be used to a smaller degree, increasing the number of fractured panes. Thus, the use of the analytic result remains on the safe side and represents the load-bearing behaviour of the cable in this limited study to a realistic degree.

In comparison with the previously analysed results, two specimens (RT21 and RT22 of series P15-10.1-I) reacted differently and thus deviated considerable from the analytical results. After fracture of layer 1, as depicted in Fig. 7a for one exemplary specimen, the cable force showed a decreasing trend during the first 30 min of the test. In the same timeframe, the strain of the intact glass layers increased gradually. Additionally, both components of deflection (Fig. 7b) showed the same tendency. The specimen escaped from the load by increasing deflection and a growth in bending until the glass reached a critical amount of stress, which led to premature failure.

3.2 Post-fracture service-life

One initial question that motivated this research included a possible increase in post-fracture service-life caused by reinforcing and post-tensioning of glass beams in the given configuration. Therefore, Fig. 8 depicts the relation between the reinforcement layout and the measured time until loss of integrity including the obvious correlation with the degree of intentional fracturing of the glass as shown in Fig. 3. The un-reinforced reference specimens lost their load-bearing capacity after fracturing the second layer. Solely a single specimen was able to withstand the bending load for an additional 5 h. After failure, all beams deflected considerably and sunk down because of crack expansion until they settled on the test-rig.
Fig. 8

Post-fracture service-life

Fig. 9

Crack pattern and lateral deflection of specimen RT21 P15-I. (1) Crack origin; (2) coarse lines of cracking; (3) crack pattern over full area

Two reinforced reference specimens also collapsed after 48 h and the fracturing of the second layer. However, two additional samples of this test group remained active with a single intact glass pane for an additional 24 h. After breakage, the cable remained intact and was able to carry the fragmented glass above the test-rig. This behaviour was analogously observed during short-term bending tests in Engelmann (2017) and was considered beneficial in comparison with un-reinforced samples.

A comparable result was achieved for post-tensioned specimens with a 5.0 mm tendon. One-half of the samples failed after fracturing the third layer or shortly afterwards. The other half remained active for another 24 h. After 72 h however, this group of specimens lacked the ability to carry the bending load for an additional amount of time. It was suspected that the reinforcement content and the prestress was too small to result in a substantial effect on the residual service-life.

The group of specimens with 15 kN of initial cable force showed a considerably broader set of results. As seen before, the specimens with a single deviator and a tendon size of 8.1 mm failed after 48 h. In contrast to that, the same samples with doubled deviators were able to find an equilibrium between the compression zone of the fractured glass and the tendon. Additionally, it was suspected that overlapping shards in the laminated glass carried part of the tensile load. Those specimens failed after 88.6 and 112.5 h of service-life. In contrast to the post-tensioned specimen with 5.0 mm of tendon diameter, the prestress resulted in a considerably favourable effect on the residual load-bearing capacity.
Fig. 10

a Crack pattern of specimen RT20 (exemplary), b change of height of tensile zone

The influence of the number of deviators was noticeably displayed while analysing the beams with the largest tendon size of 10.1 mm and an initial cable force of 15 kN. The samples with two deviators showed an increased residual service-life of 72 h, while two samples with a single deviator failed early within the first hour of testing. Hereby, a large-area crack pattern formed with a considerably high density of single cracks as depicted in Fig. 9. This layout overlapped the regular crack pattern (see Fig. 4). The possible causes for this behaviour are diverse and will be discussed in the following sections.

As the crack pattern of glass is closely connected with the thermal treatment of the material, an irregular state of thermal prestress was suspected. This reason, however, was rejected as all specimens belonged to the same production batch and were chosen randomly to form the individual specimens. Coarse lines of cracking with small branches were found near the top edge (2 in Fig. 9). Additionally, the observed crack pattern did not correspond with the expected pattern of fully tempered glass as examined previously (Weller and Engelmann 2014b). On the one hand, the crack pattern was strongly visible and announced a possible loss of integrity early on. On the other hand, this behaviour occurred after the fracture of the first pane. Thus, the redundancy aspect was not sufficiently met and the residual load-bearing capacity was considered insufficient in those cases.

Moreover, the affected samples showed a tremendous tendency to lean in the direction of the fractured layer 1. Therefore, an above-average natural imperfection and the structural choice of only a single deviator may be suspected as the mayor reason behind the observed behaviour. It is recommended to record the initial shape of each sample prior to the tests. This result revealed an unfavourable effect of the post-tensioning procedure. In comparison with the options with doubled deviators, the samples were able to deflect laterally to a higher degree, which caused a divergent crack pattern. In summary, the result showed a considerable effect of the crack pattern on the load-bearing behaviour and illustrated the relevance of a closer analysis of this parameter.

3.3 Crack pattern

As a novel approach, the crack pattern was analysed in depth using graphics software in this section. With an increase in service-life, the typical crack fan augmented its height and width as depicted in Fig. 10a. The release of strain energy increased as well, which resulted in an increase in the density of single cracks. Even more, the number of single cracks propagating to the short edge of the glass and into the bearing shoe, grew as well. During each waiting period, several cracks propagated but without an obvious classification or correlation to structural circumstances. This referred to both; the last fractured panes as well as the adjacent layers, which were broken earlier. The reasons for this behaviour remained unknown. However, it may be argued that the observed additional deformation caused a redistribution of stress as a result of time-dependent strain of the interlayer. This effect may cause a local exceedance of strength to produce additional cracks.

From those illustrations, the height of the tensile zone h\(_\mathrm{Z}\) was estimated. Figure 10b shows the related summary grouped by reinforcement layout. The number of deviators did not reveal to be important (RT21 and RT22 were excluded). Comparing the reference groups did not expose any major difference during fracturing of layer 1 and layer 4—all results turned out to be close. Increasing the initial cable force, however, reduced the height of the crack fan. Herein, the results of samples with 5.0 mm in tendon size showed the largest variance. It should be noted that in the further progression of the blue and green line in Fig. 10b an increasing tendency is visible. Thus, an increase in tendon size up to 10.1 mm did not result in an apparent benefit. Even more, this option may even indicate a possible drop in efficiency, which raises a need for further investigation. The analysis for layer 2 (orange line in Fig. 10) showed a decreasing tendency more tremendously: the height of the crack fan reduced on average from 118 to 107 mm, then 105 mm and finally to 100 mm. Thus, the remaining compression zone increased with an increase in initial cable load. Hence, a beneficial effect of the post-tensioning technique on the residual load-bearing behaviour was concluded.
Fig. 11

Loss of integrity. Un-reinforced samples sacked down to the test-rig, as the interlayer (1) was not able to transfer the tensile loads (left). Reinforced specimens folded to the side as the tendon prevented any progression downwards (right)

Fig. 12

Loss of integrity. Samples RT10, RT14 and RT17 failed in a double-waved manner (left). Deviators teared off in particular cases (right)

It appears as through post-tensioned glass beams provide a beneficial residual load-bearing behaviour. This may lead to the conclusion that the concept of Spannglass Beams proved its potential leading to safer glass structures in principle. The results, however, are strongly restricted: quantitative values were relatively close and affected by a subjective evaluation. Additionally, taking into consideration the small number of samples, the results were assessed qualitatively only. The given results are therefore a first tendency. Follow-up investigations in the field of post-tensioned glass beams, especially the discovery of a beneficial combination of initial cable load, stiffness of the glass section and the reinforcement, need to confirm this outcome.

3.4 Loss of integrity

The loss of integrity after breaking the last layer occurred case-by-case only in this investigation. Usually, the final collapse happened earlier. Therefore, the following section attempts to standardise the final failure for characterisation and systematisation. This intends to lead to a deeper understanding of the effects in the future.

After final collapse, the un-reinfoced samples sagged down to the test-rig (Fig. 11, left). The accumulation of fracture origins in a narrow range allowed for the opening of a large crack across all layers, which was solemnly bridged directly by the interlayer. This type of overloading provoked a considerable strain (1). On the contrary, reinforced and post-tensioned options leaned to the side as the tendon prevented any further deflection. This finally resulted in a folding of the glass layers (Fig. 11, right). The cable was able to carry the failed samples above the test-rig. A comparative behaviour was observed during short-term bending tests as well (see Engelmann 2017). Therefore, the test scenario resulted in comparative collapse situations and was therefore considered reasonable and appropriate.

Nevertheless, other types of integrity loss emerged as well. Their analysis is necessary to create safer structures in the future. Specimens RT10 P9-1, RT14 P9-II and RT17 P15-I showed two folding lines and failed in a double-curved manner (Fig. 12, left). Obviously, a larger energy was released during fracture, which was indicated by a considerably large lateral deflection during the course of the experiment and a planar crack pattern across the whole span of the beams. In contrast to that, only single cracks appeared in other samples (see Fig. 10a). This indicated a remarkable failure scenario in comparison with the striking results of RT21 and RT22 (Fig. 9). Additionally, adhesively bonded deviators tore off (Fig. 12, right). Remnants of the glass edge persisted at the stainless steel element. Thus, the failure originated within the laminated glass rather than within the adhesive joint. Naturally, this state has to be prevented as parts of the beams are not carried by the tendon anymore and the crack pattern results in a considerable loss of stiffness. Those cases showed similarities with the commonly known “wet-towel-effect” in fully tempered laminated glass sheets. Therefore, it was concluded, that the structural details, including material research on the adhesives, have to be investigated.

Apart from folding of the glass layers, sample RT15 showed shearing of the deviator, as the glass edges on both sides of the element were misaligned after failure. In this area, a large concentration of cracks was observed, which resulted in a situation comparable to a plastic hinge in the glass cross-section. An analogous behaviour was observed in samples RT11 and RT16 at centre span between two deviators where the glass edge showed a full offset.

3.5 Discussion

This research comprised a summary of the results of bending tests to evaluate the residual load-bearing capacity of Spannglass Beams and the effect of reinforcement and post-tensioning. A method was proposed and executed to find a relation between the structural parameters, the post-fracture resistance and the post-fracture service-life.

During the chosen loading situation, the condition after 48 h and the breaking of the third pane proved to be critical. Herein, one glass package was fully fractured. An effective structure is possible, while all layers are broken during a serviceability load, including a considerable post-fracture service-life. This case will allow for an elimination of “sacrificial layers”. This goal was achieved in part and needs further evaluation in the future.

Nevertheless, this type of analysis was—to the knowledge of the author—executed for the first time. Comparative results are not available. Therefore, the observed effects, crack patterns and states of destruction were described comprehensively. It was possible to influence the service-life after fracture by reinforcing and post-tensioning the glass beams. It should be emphasised that beneficial as well as unfavourable effects were observed:

Due to a considerable lateral deflection, the service-life decreased. This direction of deflection is promoted by the additional load introduced by tensioning the cables (see Weller and Engelmann 2014a). This structural option with an eccentric load revealed to be unprofitable. A relevant situation occurred during bending loads below the actual strength of the beams. This situation is not covered by an exceptional ductile post-fracture behaviour. An individual proof for both situations, as recommended by the “Eurocode Glass” committee, is necessary. Thus, further investigation on this effect is proposed.

Reinforcing and post-tensioning of glass beams is supposed to reveal beneficial effects. Those options showed similar, as well as an increased, post-fracture service-life in conjunction with a support of fragmented glass sections by the tendons. This allowed for a redundant path of load transfer. Particular samples with two deviators revealed those properties. Thus, the choice of structural details, especially those influencing the lateral stiffness and buckling shape, have a critical influence on the load-bearing properties.

Additionally, the mechanical prestress of the glass decreased the number of cracks and showed a decrease in the height of the crack fan as a tendency. Further detailing of the structure is required to make use of this effect. A full definition of beneficial and unfavourable effects, however, remains within the scope of extended investigations as a relatively small number of samples and the considerably large amount of observed failure states raises the need for additional follow-up studies.

In summary, the occurred effects were described and grouped for the first time. This led to a first dataset for further analysis. The concept of “Spannglass Beams” revealed a residual load bearing capacity upon the proper choice and combination of structural options.

4 Summary, conclusions and outlook

The paper introduced a concept for a prove of the residual load-bearing capacity of Spannglass Beams. A design philosophy is available but its precise implementation into an experimental or numerical practice is missing. Especially as the underlying assumptions for an experimental investigation in projects and previous research lack full documentation. Therefore, it is suggested to extend the presented results with existing knowledge in a database. Tests for individual approvals or summaries of cases of damage may contribute as well.

In total, 24 specimens were tested using the proposed method, which included an increasing state of damage. This marks a first comprehensive evaluation of this safety aspect. An increase in post-fracture service-life in comparison with reference samples was possible. However, it should be emphasised that post-tensioning of glass beams may result in unfavourable effects as well—a remarkable scatter was included in the results. An asymmetrical fracture state leads to additional bending about the minor axis and promotes lateral instability. Furthermore, this may lead to premature failure at a comparatively low level of load. This aspect is not necessarily covered by the proof of ductility (FLS) and justifies additional research.

In principle, reinforced options may be labelled robust during the proposed method of experimental testing. However, residual load-bearing capacity depends on several, even contradictory trends and may not be summarised in a single value right away. Apart from that, the load-bearing capacity of novel glass structures need a numerical background. Existing approaches need further development to suit a practical implementation. Therefore, it is suggested to evaluate the crack behaviour of glass constructions in a computer model for an economic analysis and a broader parameter study to limit experimental studies. This needs to include the fracture of thermally tempered glass to study the load-bearing behaviour of the fractured glass part. The collected fracture patterns and boundary conditions will contribute to validate numerical models.

Main findings of the research are an assessment of existing knowledge from the perspective of the upcoming Eurocode philosophy. The presented methodology included both aspects of failure safety and post fracture service-life. This promotes a summary of operating experience for the development of load bearing glass beams in general and post-tensioned Spannglass beams as a particular case. This may lead to efficient, economical and safer glass beams in general and more impressive and spectacular glass architecture in the future.

Notes

Acknowledgements

The research project was sponsored by the German Federal Ministry of Economics and Technology (BMWi) and was executed corporately with Thiele Glas Werk GmbH (Wermsdorf, Germany) and KL-megla GmbH (Eitorf, Germany). Additionally, PFEIFER Seil- und Hebetechnik GmbH (Memmingen, Germany) gave valuable support.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Josef Gartner GmbHGundelfingenGermany
  2. 2.Institute of Building ConstructionTechnische Universität DresdenDresdenGermany

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