Experimental investigations of statically indeterminate reinforced glass beams

Construction and Building Materials 119 (2016) 296–307

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Experimental investigations of statically indeterminate reinforced glass beams K. Martens ⇑, R. Caspeele, J. Belis Ghent University, Department of Structural Engineering, Ghent, Belgium

h i g h l i g h t s  A custom-made statically indeterminate five-point bending setup was successfully built.  The effectiveness of applying statically indeterminacy for reinforced glass beams was proven.  Structural element safety as well as system safety were achieved.  Temperature and reinforcement have a significant effect on the load-carrying behaviour.  A good design of the glass-to-reinforcement bond is critical to achieve satisfying load-carrying behaviour.

a r t i c l e

i n f o

Article history: Received 22 December 2015 Received in revised form 18 April 2016 Accepted 29 April 2016

Keywords: Reinforced glass beams Statically indeterminate systems Experiments Load redistribution Load-carrying behaviour System safety

a b s t r a c t A lot of ‘hybrid’ structural glass beam concepts were developed in the past years to overcome the brittle failure behaviour of glass. These beams possess a safe failure behaviour through post-fracture strength and ductility. Promising is the concept of reinforced laminated glass beams in which stainless steel reinforcement sections are included in the glass laminate and provide a post-fracture load-carrying mechanism. This type of beams was extensively tested in three- and four-point bending for a variety of environmental conditions (e.g. temperature and humidity), geometrical scale, reinforcement percentage and element robustness. The concept proved to be satisfying. In addition to element safety, today’s buildings also require significant system safety. This paper presents an experimental test programme in which the load-carrying behaviour of statically indeterminate reinforced laminated glass beams is investigated. The beam specimens were tested in five-point bending (three supports and two load points) at 23 °C and 60 °C, at a humidity level of 55%. In addition, two different reinforcement percentages were investigated. The beams illustrated satisfying failure behaviour in all cases, proving the effectiveness of applying reinforced laminated glass beams in statically indeterminate systems. The effect of temperature is primarily observed in the fractured and plastic phases. There, the specimens at 60 °C illustrated lower bending stiffness and slip of reinforcement, which resulted in a lower post-fracture strength. The temperature effect was larger for the beams with high reinforcement percentage. The load-carrying behaviour and load redistribution were highly dependent on the reinforcement percentage. A higher reinforcement percentage resulted in higher bending stiffness in all phases of the model. In addition, a higher initial failure load, yield point and post-fracture strength was achieved. Finally, also a different collapse mechanism was observed for both tested reinforcement percentages. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction Aiming for increased transparency, researchers and engineers have been investigating ways to apply structural glass elements in buildings. Today, structural elements are required to possess a safe failure behaviour (element safety). As glass is a brittle ⇑ Corresponding author at: Technologiepark Zwijnaarde 904, 9052 Zwijnaarde, Ghent, Belgium. E-mail address: [email protected] (K. Martens). http://dx.doi.org/10.1016/j.conbuildmat.2016.04.151 0950-0618/Ó 2016 Elsevier Ltd. All rights reserved.

material, safe failure behaviour is translated into sufficient postfracture strength and ductility. Especially in the field of structural glass beams, previously basic research has been performed to develop beams that meet those requirements. In a final stage, this has led to the ’hybrid glass beam’ in which glass is combined with another material that provides post-fracture strength and ductility to the beam. A broad overview of investigated concepts can be found in [1,2]. A promising concept for practical applications is the stainless steel reinforced laminated glass beam which is developed considering the concept of reinforced concrete. Stainless steel

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sections are added at the tensile sides of the glass laminate and serve as crack bridges for the fractured glass zone. As a result, the reinforcement and intact compressive glass zone form an internal resisting moment that provides the beam with its post-fracture load-carrying capacity. As stainless steel is a ductile material, the reinforced glass beam’s post-fracture behaviour usually also is ductile (if the interlayer possesses a sufficiently high shear modulus and strength) the reinforced glass beam also fails in a ductile way. 1.1. Verifying effectiveness in a statically determinate system The concept was intensively investigated, through experimental four-point bending tests, to assess the effects of temperature (cycles), humidity, reinforcement percentage, glass type and beam size [3,4]. As the beam specimens in the current paper are based on those in [3,4] (using SentryGlasÒ as interlayer material), the main results of the latter tests are briefly discussed here. To investigate the effect of temperature, four-point bending tests were performed at 20 °C, 23 °C and 60 °C. It was concluded that low as well as high temperatures had a negative effect on the post-fracture response of the beams, as more excessive local debonding of reinforcement occurred. However, the overall load-carrying behaviour had significant post-fracture bearing capacity. Thermal cycling had an insignificant effect on the structural behaviour but could become more important for larger beam configurations due to larger differences in thermal expansion between glass and reinforcement. Applying the beams in a humid environment remains questionable, as two out of three tested beams illustrated the same performance as a non-exposed beam. However, the other one suffered extensive delamination in the post-fracture stage. It was concluded that additional research is required. The beams also performed well during the long-duration loading tests. Despite some creep deformation due to creep in the interlayer and glass fracture, a fractured beam was able to carry 80% of the predicted ultimate failure load for more than 22 months. Testing beams composed of stronger glass types (heat-strengthened and fully tempered glass) yielded higher initial failure loads. However, a reduction of post-fracture strength and deformation capacity due to the finer fracture pattern has to be taken into account. Larger glass shards (typical for ANG) are easier for the interlayer to hold together and make stress transfer more feasible. Reinforcement percentage significantly influences the beam’s structural response, as it increases the initial failure load, post-fracture strength and bending stiffness. Finally, it was concluded that beam size has only a limited effect on the load-carrying behaviour, as a slightly lower post-fracture strength was encountered than expected. However, additional research is required to explain this phenomenon. In addition, the inherent element robustness of these reinforced glass beams was confirmed by testing beams in which one and/or two glass panes were artificially damaged prior to testing [5]. The reinforcement forms a secondary load-transfer path wich easily bridges the damaged glass zones. 1.2. Benefits of the statically indeterminate system In addition to their individual element safety, the structural members making up (a part of) the entire structure should collectively provide a sufficient level of safety (i.e. system safety). This requirement is for example realised by introducing redundancy into the structure so that there are several ways to transfer the loads to the foundation (i.e. enabling alternative load paths). A way to incorporate this kind of safety for the case of structural beams is the application of statically indeterminate support conditions. Stress redistribution between supports and spans can enable such a system to withstand extensive damage and even accidental support failure due to e.g. a terrorist attack, car accident, etc.

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Moreover, statical indeterminacy enables the engineer to come up with a more economic design than would be possible with statically determinate systems. Despite the general acknowledgement of its benefits in steel and concrete construction, the statically indeterminate beam system is hardly applied in glass construction. The main reason for this is the lack of sufficient research to prove its effectiveness. To the authors’ best knowledge, only a single hybrid glass beam concept was tested for statically indeterminate support conditions. In the latter research, glass-GFRP composite beams were subjected to five-point bending with two spans of 1.40 m, at room temperature [6]. In addition to an assessment of the overall load-carrying behaviour and its features, the effect of adhesive stiffness (to realise the glass-GFRP bond) on the latter was investigated. The investigation concluded that it is feasible to apply the glass-GFRP composite beams in statically indeterminate systems, as safe pseudo-ductile failure behaviour was encountered. Furthermore, the post-fracture performance is dependent on adhesive stiffness. The beams composed with the least stiff adhesive yielded the highest relative post-fracture strength (relative to the load at first glass fracture). Moreover, all beams illustrated stress redistribution capacity in the fractured phase, in particular the ones composed with the least stiff adhesive. However, it is stated that stress redistribution was only triggered due to glass fracture and therefore the former was only momentarily observed. As GFRP is not a ductile material, no classic stress redistribution (i.e. through the formation of plastic hinges as for steel and reinforced concrete beams) was possible. For the case of steel reinforced glass beams, stress redistribution is expected to be possible through glass fracture and plastic hinge formation. Preliminary numerical simulations were performed by the authors to assess the load-carrying behaviour of statically indeterminate reinforced glass beams, assuming rigid supports [7]. The effect of reinforcement percentage and load redistribution capacity were investigated. It was concluded that the beam specimens illustrated safe failure behaviour with significant post-fracture strength and ductility. A lower reinforcement percentage led to lower bending stiffness, initial failure load and ultimate collapse load. Furthermore, the simulations illustrated load redistribution in two phases: (1) minor redistribution in the fractured phase and (2) major redistribution in the plastic phase. From this research, it was concluded that reinforced laminated glass beams could be applied in statically indeterminate systems, illustrating safe failure behaviour and load redistribution capacity. This paper presents an experimental test programme in which the effectiveness of applying reinforced laminated glass beams in statically indeterminate systems is investigated. Two criteria are important, namely structural element safety and system safety. To satisfy both, the beam has to exhibit a post-fracture phase characterised by significant load-carrying capacity and ductility on one hand (element safety) and should form all plastic hinges, thus illustrating stress redistribution, prior to ultimate collapse (system safety). In addition, an assessment of the effects of temperature and reinforcement percentage on the load-carrying behaviour is performed. Finally, the effect of reinforcement slip is explained and related to experimental observations. 2. Experimental test specimens and setup In this section, the different beam specimens and their composing materials are explained followed by a detailed presentation of the experimental setup. 2.1. Geometry and materials The only difference between both laminated beam sections, depicted in Fig. 1, is the reinforcement section, which is either a solid (a) or a hollow square profile (b). A typical specimen is composed of a 6 mm  125 mm–10 mm  105 mm– 6 mm  125 mm triple-layered laminate of annealed float glass (ANG) panes, in

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Fig. 1. Schematic representation of the beam sections: (a) solid reinforced and (b) hollow profile reinforced section (I = second moment of area, calculated accounting for the relative stiffness difference between the materials, taking glass as reference).

which the central panel is recessed by 10 mm at top and bottom to house the 10 mm  10 mm (1 mm) stainless steel EN1.4301 reinforcement sections. All glass edges were polished. The ensemble is bonded using 1.52 mm sheets of SentryGlasÒ (SG). The geometry of the beam sections is the same as in [3,4], however with the addition of a second reinforcement section at the beam’s top edge. Both second moments of area are added in Fig. 1. These were calculated considering the relative stiffness difference of the materials with respect to glass by means of including the Young’s modulus in the calculation. The bending stiffness of both beam sections can then be calculated by multiplying the Young’s modulus of glass with the second moment of area, resulting in respectively 337 kN m2 and 252 kN m2 for the solid and hollow profile reinforced beam specimens. Hence, the latter’s bending stiffness is about 75% of the former. Practically, the beams were produced by means of the ‘vacuum bag’ process. After the beams were built up layer by layer, they were put in a vacuum bag and cured in an autoclave. As denoted in Fig. 1, all beam specimens are composed of three materials namely ANG, SG and stainless steel. Table 1 gives an overview of their most important material properties. It is noted that the tensile strength of glass is not a constant value but varies due to surface flaws. The value of 45 MPa is set as a characteristic value according to (product standard) NBN EN 572-1 [8]. Also the glass transition temperatures of glass and SG (which have characteristic values of respectively 575 °C [9] and 55 °C [10]) can be considered as variables with a significant standard deviation. When the temperature is exceeding this limit, the SG interlayer transforms into a soft state and significantly looses stiffness. As a result, the interlayer is expected to be less able to ensure the integrity of the glass laminate and to redistribute tensile stresses to intact glass zones and reinforcement, which is why tests at 60 °C are required. This was also observed during the tests in [3].

and a temperature of either 23 °C or 60 °C. Therefore, the test setup was placed in a 3.0 m by 3.9 m climatic chamber with a height of 2.4 m, in which temperature and humidity were continuously controlled. The test setup, depicted in Fig. 2, is composed out of a main steel frame on which the vertical supports, lateral supports and actuator are mounted. The steel frame (painted in blue) consists of a welded horizontal base frame composed of HEA 120 grade S235 profiles on which two vertical HEA 120 profiles of the same steel grade are welded. The columns are interrupted to limit the height of the frame for transportation purposes. The columns can be reconnected with a heavy bolted connection consisting of M16 bolts grade 8.8. To increase the overall stiffness of the frame, four 70 mm  25 mm diagonal S235 steel bars connect the top of the columns (using M10 8.8 bolts) to the outer corners of the base frame (using M8 8.8 bolts), creating four large triangles.

2.2. Experimental setup A statically indeterminate five-point bending test setup was constructed at the Laboratory for Research on Structural Models, Ghent University. In the design phase, the aim was to make it as compact and adjustable as possible, as this test setup is required to be moveable and allow for a variety of beam heights and support conditions. Furthermore, the setup had to fit in the climatic chamber of the lab, so that a variety of temperature and humidity conditions could be applied during the tests. The tests presented here were carried out at a relative humidity of 55%

Fig. 2. Picture of the overall test setup.

Table 1 List of material properties for Annealed float glass [9,8], SentryGlasÒ [10] and stainless steel [11,12]. Material 3

Density (kg/m ) Young’s modulus (MPa) Shear modulus (MPa) Poisson ratio (–) Yield strength (MPa) Tensile strength(MPa) Elongation at fracture (%) Glass transition temperature (°C) Coefficient of thermal expansion (10 a b c

6

/K)

Annealed float glass

SentryGlasÒ

Stainless steel EN1.4301

2500 70,000 28455.3 0.20 n/a 45a n/a 575a 9

950 110.53b; 12.17c 37.3b; 4.1c 0.49b; 0.50c n/a 34.5b 400b 55a n/a

7900 200,000 77519.4 0.29 203–210 520–750 45 n/a 16

Variables with a significant standard deviation; all other values are considered deterministic. For a temperature of 23 °C and a load duration of 30 min. For a temperature of 60 °C and a load duration of 30 min.

K. Martens et al. / Construction and Building Materials 119 (2016) 296–307 Two outer vertical supports composed of 50 mm  50 mm  2 mm hollow S235 steel sections are mounted on the base frame using 6 M8 8.8 bolts (see Fig. 3(a)). Small positional adjustments of these supports are enabled by applying slotted holes for the bolted connections. The beam specimens are directly supported by half-cylindrical S235 steel heads with a diameter of 60 mm, that are welded on 30 mm  50 mm  80 mm S235 steel blocks. The steel blocks transfer the reaction force to the hollow steel sections through two M10 grade 8.8 bolts. The central support is composed of a screw jack on which a 40 mm  40 mm  250 mm S235 steel section is welded (see Fig. 3(b)). The motion of the screw jack is limited to the vertical direction by two vertical U-shaped guiding S235 steel profiles that hold the 250 mm steel section in position. A steel pin is welded on the latter to house a load cell (which has a tube-like shape). The screw jack, wich is used to level the beam specimens before the start of the test, is fixed (during the test) by placing 20 mm  40 mm  300 mm S235 steel bars in the guiding profiles. All supports are equipped with half-cylindrical S235 steel heads with a diameter of 60 mm to realise simple supports.

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A 100 kN single-acting actuator with a stroke of 250 mm is fixed to a HEM 100 grade S235 steel profile which is placed in between and bolted to the columns of the main steel frame with M12 8.8 bolts. The latter are endowed with a vertical array of holes so that the actuator can be shifted vertically. A loading beam (IPE 240 grade S235 steel profile) with two bolted (using M6 8.8 bolts) load punches and welded lateral supports is hinged attached to the actuator’s press pod. The position of the load punches can be shifted so that a variety of load spans is possible. As the actuator is single-acting (it pushes out hydraulically and slides back to its original position by means of springs), a pulley system with S235 steel blocks was required to compensate for the loading beam’s weight (see Fig. 2) and and hence to enable the actuator to slide back upon unloading. The lateral supports consist of a double system. First, S235 steel U-sections are butt-welded to the bottom flange of the loading beam to laterally hold the glass beams in place by means of 10 mm  50 mm  300 mm aluminium (EN AW-5083 [Al Mg4,5Mn0,7] H111) pads. The latter can be positioned by screws to allow for varying beam thickness (see Fig. 4(a)). Second, as the loading beam itself

Fig. 3. Picture of the supports: (a) outer support and (b) central support.

Fig. 4. Picture of test setup details: lateral supports for the (a) glass beam and (b) loading beam; steel U-pieces for (c) load introduction and (d) central support.

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can rotate freely about the vertical axis, four welded triangles composed of 50 mm  50 mm  2 mm hollow steel sections of grade S235 are placed close to the loading beam and fixed to a HEA 100 S235 steel profile by means of screw clamps. The steel profile is fixed to the steel base frame using M8 8.8 bolts (see Fig. 4(b)). In this way, the horizontal rotation of the beam is restrained. The position of the latter lateral supports can be varied as a horizontal array of holes is present in the base frame. To avoid direct contact between glass and steel at the outer supports, 25 mm aluminium (EN AW-5083 [Al Mg4,5Mn0,7] H111) plates with a thickness of 2 mm were placed between the glass beam and the cylindrical steel heads. At the load introduction points and the central support, wire-cut medium-carbon steel U-shaped pieces with a width of 30 mm, equipped with a 5 mm  25 mm  30 mm rubber strip (Shore 70A hardness), are slided on the glass beam. The outer side of the U-shaped pieces has a cylindrical shape (with a diameter of 60 mm) and perfectly fits the support heads (see Fig. 4(c) and (d)). To avoid influence on possible local buckling effects, the cilindrical contact surface was greased so that sliding between the load introduction point and the U-shaped element was possible. Furthermore, the overlap with the vertical glass panes was limited to 25 mm, which is only one fifth of the nominal beam height. The measurement system consists of 5 linear variable differential transformers (LVDTs) and two load cells (see Fig. 5). Three LVDTs measure the vertical displacement of the supports (a and b). The other two measure both midspan displacements of the glass beam specimen (c). One load cell (integrated in the pump station of the actuator) measures the total load, while the other one is placed at the central support to measure the reaction force (b). In Fig. 6, the positions of the LVDTs and load cells, together with the vertical supports, lateral supports and load introduction points are schematically illustrated. To capture as much information as possible during the tests, a film and photo camera are placed to capture the entire test specimen. In addition, three highdefinition webcams were located at the central support and both spans to record the growing crack pattern and reinforcement yielding in the glass beam specimens.

2.3. Test procedure From the moment of delivery, the beam specimens were stored for four months in a climatic chamber at 20 °C and 60% relative humidity. All preparations were performed in this chamber. First, the beams were thoroughly measured after which meshes were drawn on the beams to monitor the crack growth during the tests. In addition, also reference lines were drawn at the top and bottom sides of the beams. By visual inspection and taking high-resolution pictures of these possibly shifted lines after testing, it can be decided whether or not slip occurred and to what extent (by comparing the slip distance to the measured beam thickness). Four different test series, each containing three test specimens out of a total of 12, were established. An overview is given in Table 2. The varying parameters are the reinforcement percentage (‘H’ = 10 mm  10 mm  1 mm hollow profile reinforcmement and ‘S’ = 10 mm  10 mm solid reinforcement) and temperature level (23 °C and 60 °C). In a first step, the beams are preconditioned in the climatic chamber. Conditioning durations are at least equal to conditioning durations used in earlier work, i.e. at least one week for the tests at 23 °C and 48 h for those at 60 °C [3]. Temperature measurements on several beams confirmed that the beams were adequately conditioned after this period.

Once conditioned, the beam specimen is mounted into the test setup. The test itself starts with the lowering of the loading beam (by manually pushing out the actuator) so that the position of the U-pieces can be fine-tuned and sufficient oil pressure is present in the actuator. At this stage, the loading beam makes contact with the U-pieces on the beam. Subsequently, the test is started by activating the actuator in a displacement-controlled way, implementing a rate of 0.1 mm/s. This rate is continuously controlled by the pump station. Once the beam specimen has collapsed or its remaining load-carrying capacity has become insignificant, the test is stopped by manually deactivating the actuator with the pump station after which it returns to its original position by means of the pulley system. After capturing the final shape of the tested beam specimen, it is removed from the test setup and a new beam specimen is placed after which the test procedure can be repeated. A typical procedure lasted about 60 min, of which the test itself took about 30 min. 2.4. Stiffness of the central support As the central support had a different design compared to the outer vertical support, differences in support stiffness could be expected, which have an influence on the bending moment line. During the tests, both LVDT readings of the outer vertical supports were very small (maxima in the order of 0.05 mm) which is close to the accuracy of the used LVDTs. However, the measurements of the central support were not that small (maxima in the order of 4 mm). As a result, it is concluded that the influence of the outer vertical support deformation on the bending moment line can be neglected, but that of the central support certainly not. Two features contribute to the overall stiffness of the central support: (1) the load-deformation behaviour of the support itself (i.e. screw jack and vertical steel bars) and (2) the load-deformation behaviour of the rubber. The support can theoretically be translated into a system of two springs in series. As a result, the local vertical displacement of the beam is the sum of the vertical displacements of the rubber and support. The vertical deformation of the support was measured by an LVDT (see Fig. 5(b)). For the rubber, additional compression tests were performed in which the testing conditions were resembling the loading of the rubber during a test on a beam. In Fig. 7, the averaged displacement-load behaviour of both features and the total effect is presented. This diagram can be fitted by a polynomial function and directly implemented in the theoretical calculation of the bending moment line. In Figs. 8 and 9, the variation of the midspan and central support bending moment values are presented in function of the applied total load and compared to the values of the theoretical bending moment line for rigid supports, up to the point of initial glass fracture (which was calculated considering a linear elastic model, using a tensile stress of glass equal to 45 MPa and the equivalent second moments of area given in Fig. 1). As the displacement of the central support is also dependent on the beam’s second moment of area, the behaviour is different for glass beams reinforced with a hollow or a solid profile. The bending moment in the spans is larger than in the reference case and the difference also increases. For the central support, the bending moment is lower and the difference with the reference case also grows. The most important difference is the position of initial glass fracture. For the experimental case, glass fracture is expected to begin at the beam spans (at a load of respectively 24.6 kN and 19.1 kN for the solid and hollow profile reinforced beams) while the theoretical case predicts it at the central support (at a load of respectively 23.6 kN and 17.9 kN). For the tests at 60 °C, lower initial failure loads are expected as the tensile strength of glass is affected [9] and differences in thermal expansion between reinforcement and glass could induce tensile stress in the latter [3].

Fig. 5. Measuring devices: (a) LVDT at the outer support, (b) LVDT and load cell at the central support, (c) LVDT at midspan.

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Fig. 6. Schematic representation of the test setup.

Table 2 Overview of test series.

3. Results and discussion

Series

Reinforcement type

Test temperature (°C)

Number of specimens

S-23 S-60 H-23 H-60 Total

Solid Solid Hollow Hollow

23 60 23 60

3 3 3 3 12

In this section, an overview of the experimental test results for each beam composition by means of load–displacement diagrams is provided, followed by a discussion of the load-carrying behaviour. For the displacement, the mean value of the recorded values in both spans was taken. In addition, an assessment of the effects of temperature and reinforcement percentage is made, followed by a

Fig. 7. Stiffness of the central support: load–deflection diagrams for the support, rubber and combined effect.

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Fig. 8. Analytical comparison of the bending moment for the solid reinforced beam series: ‘Real’ = experimental support stiffness; ‘Theoretical’ = rigid supports.

Fig. 9. Analytical comparison of the bending moment for the hollow profile reinforced beam series: ‘Real’ = experimental support stiffness; ‘Theoretical’ = rigid supports.

Table 3 Test results for the 4 test series (StDev = standard deviation; COV = coefficient of variation). Series

S-23

S-60

H-23

H-60

Initial failure load

Average (kN) StDev (kN)

23.43 0.69

21.37 1.01

17.78 1.81

16.72 3.66

Ultimate capacity

Average (kN) StDev (kN)

82.78 0.76

60.99 2.97

37.62 0.34

34.34 1.28

Post-fracture performance

Average (–) StDev (–)

3.54 0.14

2.86 0.17

2.12 0.12

1.88 0.36

Residual load*

Value (kN)

Residual performance

Value (–)

20.0 0.85

14.0 0.66

12.0 0.67

14.0 or 23.0** 0.75 or 1.23**

(The post-fracture performance is calculated as the ‘ultimate capacity’ divided by the ‘initial failure load’; the residual performance is calculated as the ‘residual load’ divided by the ‘initial failure load’; *not all tests were continued to final collapse, hence it is not relevant to report standard deviations and COV values; **values corresponding to the case where first reinforcement failure respectively occurred at the beam’s span and central support).

comparison with the results of similar statically determinate tests reported in [3,4]. Values for the initial failure load (corresponding to first glass fracture), ultimate capacity, post-fracture performance (i.e. ultimate capacity/initial failure load), residual load and residual performance (i.e. residual load/initial failure load) are provided in Table 3. Fig. 10 gives an overview of all load–displacement diagrams. The main failure mechanisms are depicted next to each series of curves. For all beam specimens generally four phases were observed during the tests: (1) the beams behaved linear elastically up to first glass fracture (corresponding to the initial failure load)

at one of the zones suffering maximum bending moment; (2) fractures in the other midspan and/or central support zones directly followed and the glass beams further fractured near these zones up to the point where the reinforcement started to yield; (3) in most cases (S-23, H-23 and H-60 test series), the reinforcement sections yielded further, forming plastic hinges at the central support and midspan zones, resulting in ductile behaviour. Subsequently, one of the plastic hinge zones of the beam collapsed leading to a strong load drop; (4) the beams were still able to carry some load due to load redistribution (an inherent benefit of the statically indeterminate system over the statically determinate

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Fig. 10. Load–displacement diagrams for the investigated beam specimens (the residual phase is indicated by dashed lines); for the H-60 beam series, two residual load levels were found of which one is the same as for the S-60 beam series.

system), albeit smaller than the maximum reached load. In Fig. 10, this final phase is indicated by dashed lines to maintain clarity in the diagram. The four mentioned phases are here defined as respectively ‘the linear elastic phase’, ‘the fractured phase’, ‘the plastic phase’ and ‘the residual phase’. 3.1. Test results The solid reinforced beams tested at 23 °C (S-23) demonstrated linear elastic behaviour up to an average load of 23.43 kN. At this load, first glass fracture was observed in one of the spans (which is consistent with the analytically determined bending moment line, which estimated a value of 24.6 kN), resulting in a load drop. However, glass fracture at the other critical zones followed almost immediately (within seconds). In the fractured phase, the displacement could further be increased together with a significant load increase as the tensile stresses could bridge the fractured glass zone through the reinforcement. At the same time, existing glass fractures expanded and new ones developed at the critical moment zones, resulting in a gradual lowering of the overall bending stiffness with increasing displacement. Typically, the span zones illustrated more extensive fracture than the central support zone, meaning that in the span zone fractures are more distributed over the beam’s length compared to the central support zone. At a load of about 60 kN, the beams entered the plastic phase and at about 80 kN, the tensile and compressive reinforcement yielded both at the central support and in the spans, forming plastic hinges. The

load hardly increased up to an average maximum of 82.78 kN due to limited strain hardening of the reinforcement. During this phase, glass fracture further expanded and significantly damaged the glass compressive zones, especially in the spans. Further increasing the displacement resulted in a gradual lowering of the load as the glass compressive zone started to collapse in one of the spans. Compressive glass failure, directly followed by instant local buckling of the crushed section, led to ultimate collapse at one of the spans (see Fig. 11(a)–(c)). The displacement was further increased and led to a residual load-carrying capacity of about 20 kN. During this phase, the damaged interlayer and plastically deformed reinforcement at the collapsed glass section further buckled out of plane until the test was stopped. No reinforcement slip was encountered during the tests (see Fig. 11(d)). Similar beams tested at 60 °C (S-60) reached an average initial failure load of 21.37 kN. This value is lower than observed at 23 °C, as expected. Also here, first fracture was directly followed (within seconds) by fractures in the other critical sections. In the subsequent phase, the glass fractures further expanded, however to a much lesser extent than in the tests at 23 °C. Nevertheless, the bending stiffness of the beams significantly decreased during this phase. Again, glass fracture damaged the beam spans more extensively than the central support zone. This continued until an average load of 58 kN was reached at which initial reinforcement yielding started at one of the spans. However, at a maximum load of 60.99 kN the compressive glass zone failed in the same span, resulting in instant buckling of this zone (see Fig. 12(a)–(c)).

Fig. 11. Pictures of tested S-23 beam specimens: (a) overview of tested beam, (b) failed span zone, (c) close-up of the failed span zone and (d) reinforcement slip reference markings on the beam’s bottom edge near the vertical outer supports to assess reinforcement slip.

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Fig. 12. Pictures of tested S-60 beam specimens: (a) overview of tested beam, (b) failed span zone, (c) close-up of the failed span zone and (d) reinforcement slip reference markings on the beam’s bottom edge near the vertical outer supports.

The load significantly dropped to about 14 kN after which it stabilised. Further increasing the displacement led to a load plateau of 14 kN in which the local collapsed section further buckled out of plane and the reinforcement further yielded until the end of the test. Significant reinforcement slip was observed during these tests (see Fig. 12(d)), creating the horizontal load plateau prior to collapse, as can be seen on the load–displacement diagrams. The hollow profile reinforced beams, tested at 23 °C (H-23), could be loaded up to 17.78 kN at which first glass fracture appeared in one of the spans. Analytically, a value of 19.1 kN was predicted. Also for these beams, fracture in the other critical zones followed immediately after (within seconds). The fracture pattern further expanded in both the span and central support zones during the subsequent phase, giving rise to a gradual decrease of the overall bending stiffness. Also for these beams, the spans suffered more weakening than the central support zone. The beams entered the plastic phase at a load of about 27 kN. In this phase, all three plastic hinges were formed at a load of about 33 kN and due to strain hardening, the load could further be increased to an average of 37.62 kN. Upon increasing the displacement to about 60 mm, the tensile reinforcement failed at one of the spans, giving rise to a significant load drop (see Fig. 13(a)–(c)). However, the beams were still able to carry a reduced load of about 12 kN and the displacement could further be increased until the tensile reinforcement at the central support failed and the test was stopped (see Fig. 13(a)). No reinforcement slip was encountered during these tests (see Fig. 13(d)).

Finally, also the latter beams were tested at 60 °C (H-60). First fracture was encountered at an average load of 16.72 kN (which is again lower compared to the case at 23 °C, as expected) at one of the spans. In the fractured phase, the other intact critical zones followed within seconds, exhibiting first glass fractures. The fracture pattern evolved similar to the other beam series, but again illustrated less extensive fracture compared to the tests at 23 °C. At a load of about 24 kN, the beams entered the plastic phase and formed all three plastic hinges at a load of 31 kN. After a maximum load of 34.34 kN, the load decreased gradually up to the point where the tensile reinforcement failed at one of the span zones or the central support zone (see Fig. 14(a)–(c)). As was the case for the tests at 23 °C, the beam had not failed completely and the test was continued until the reinforcement failed in a second zone. For two beam specimens, the tensile reinforcement at the support zone first failed followed by failure at one of the spans (see Fig. 14(a)). For these cases, a residual load of about 23 kN was reached. The other beam specimen suffered first reinforcement failure at one of the beam spans followed by failure at the central support. Only a residual load of about 14 kN was observed for this case. This difference in residual load level is explained by the mechanism of load redistribution. In the first case, where reinforcement failure first occurs at the central support, the load can be redistributed to both span zones. For the other case, all load redistribution has to pass the central support, resulting in only one zone to receive all redistributed load. Hence, the residual load level corresponding to the latter case is much lower. Contrarily to

Fig. 13. Pictures of tested H-23 beam specimens: (a) overview of tested beam, (b) failed span zone, (c) close-up of the failed span zone and (d) reinforcement slip reference markings on the beam’s bottom edge near the vertical outer supports.

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Fig. 14. Pictures of tested H-60 beam specimens: (a) overview of tested beam, (b) failed span zone, (c) close-up of the failed span zone and (d) reinforcement slip reference markings on the beam’s bottom edge near the vertical outer supports.

the S-60 series, no reinforcement slip was observed for these beam specimens (see Fig. 14(d)). 3.2. Effect of temperature As can be observed from the above, temperature is a significant parameter for the load-carrying behaviour of the beams. Compared to the tests at ambient temperature (23 °C), the solid reinforced beam specimens tested at 60 °C demonstrated a lower initial failure load. In the fractured phase, a stronger decrease in bending stiffness was observed and the fracture pattern was less extensive. Furthermore, no plastic phase was observed prior to collapse and a significantly lower maximum load was achieved. In addition, significant slip of the reinforcement was observed. The hollow profile reinforced beam specimens had a more similar load-carrying behaviour as their counterparts tested at 23 °C. They reached a similar initial failure load. However, as was the case for the solid reinforced beams, a stronger decrease in bending stiffness and less dense fracture pattern was found in the fractured phase. The H-60 beams did reach a plastic phase with similar ductility as those tested at 23 °C. However, a slightly lower maximum load was achieved. The above observations are explained by the preconditioning and testing of the beam specimens at 60 °C. The most important effect of the high temperature is concentrated on the properties of the interlayer. Above the glass transition temperature (55 °C [10]) SG transforms from a stiff, solid state to a soft or even fluid state (at temperatures above the current test temperature) with a very low stiffness and low shear modulus (see Table 1). Moreover, SG is responsible for the glass-to-glass and glass-toreinforcement bonds that constitute the beam section’s integrity. The lower the shear modulus of SG, the less composite action between the glass panes and reinforcement sections can be expected. In the linear elastic phase, this results in lower initial failure loads compared to those at 23 °C. Less shear transfer is possible between glass and reinforcement, resulting in higher tensile stress in the glass for a certain load value. As the stiffness of stainless steel is much higher than that of glass (see Table 1), it makes a significant contribution to the second moment of area of the beam section, resulting in a significant difference in initial failure load between both temperature cases (almost 10%). For the hollow profile reinforced beam series, the difference in initial failure load between both temperature cases is lower (almost 6%) as the smaller section results in a smaller contribution to the second moment of area of the beam. Other possible contributions to a lower initial failure load at 60 °C are: (1) the dependence of glass tensile strength on temperature [9] and (2) the difference in thermal

expansion between glass and reinforcement, resulting in tensile stresses in the glass. However, little is known about the first phenomenon and the second one can only be significant if sufficient shear transfer is possible between reinforcement and glass, which is not the case at 60 °C. As a result, the first explanation seems most reasonable. The observations in the fractured phase can also be explained by the reduced shear stiffness and strength of the interlayer. Once the glass has fractured, the tensile stresses are redistributed to the other intact glass zones and reinforcement sections through shear in the interlayer. However, as this interlayer has a low shear modulus, only little stress can be redistributed and the stresses remain in the same zone. As a result, the bending stiffness of the beams is as low as the weakest section, which weakens further upon further loading. In addition, as the stresses remain localised, the fracture pattern is less extensive. The lack of a significant plastic phase for the S-60 beams is explained by the lack of sufficient stress transfer to the reinforcement sections, which are very stiff and can principally attract a lot of stress. The shear modulus and shear strength of the interlayer is too low to transfer this amount of stress from glass to reinforcement, resulting in compressive glass failure at lower displacement and load values and the absence of plastic hinge formation. However, in the hollow reinforced case on the contrary, the stresses transferred by the weak interlayer were still sufficient to induce yielding (and even failure) of the reinforcement, establishing a plastic phase. The lower maximum load in this case is explained by the less extensive redistribution of stresses in the glass panes, which results in a severe local weakening of the beam section and hence a slightly lower ultimate capacity. 3.3. Effect of reinforcement percentage The reinforcement percentage directly influenced the loadcarrying behaviour of the beams. Compared to their solid reinforced counterparts, the hollow profile reinforced beams provided lower initial bending stiffness and lower initial failure load. In the fractured phase, the bending stiffness was also lower. For the tests at 23 °C, yielding initiated at a significantly lower load. In addition, the maximum achieved load is lower than half of that achieved with solid reinforcement. Also a different collapse mechanism, reinforcement failure, as opposed to glass compressive failure in the solid series, was encountered (at a smaller displacement value). At 60 °C, besides another collapse mechanism, the hollow reinforced beam specimens also demonstrated a plastic phase, which also resulted in higher ductility, compared to their solid reinforced counterparts.

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Most of these observations are directly due to the reduced amount of reinforcement. In the linear elastic phase, the bending stiffness and initial failure load are directly dependent on the second moment of area, which is 25% lower for the hollow reinforced beam section (3.602 * 106 mm4 compared to 4.813 * 106 mm4 for a solid reinforced section). As a result, the bending stiffness is also 25% lower for the hollow profile reinforced specimens. This is also the case for the stiffness in the fractured phase. Moreover, as the share of the reinforcement in the beam’s second moment of area is increasing due to glass fracture, the relative difference in bending stiffness is also increasing in this phase. At 23 °C, the lower yield point (in terms of load) and maximum load are also directly related to the smaller reinforcement section, as a smaller bending moment is needed to make the hollow reinforcement yield and eventually fail compared to the case of solid reinforcement. Another consequence is a lower deformation capacity, which resulted in reinforcement failure before the glass could fail in compression. As a result, a lower ductility was encountered compared to the solid reinforced case. At 60 °C, the lower reinforcement percentage enabled these beams to have a plastic phase followed by reinforcement failure instead of instant compressive glass failure (as explained in Section 3.2). Due to this additional load-carrying mechanism, a higher ductility was observed for the beams reinforced with hollow profile sections compared to their counterparts with solid reinforcement, tested at 60 °C. 3.4. Reinforcement slip Reinforcement slip was only encountered for the solid reinforced beam specimens tested at 60 °C (S-60). For the hollow reinforced counterparts (H-60), no slip occurred and the beams entered the plastic phase and failed by reinforcement failure. For the tests at 23 °C (S-23 and H-23), slip was negligible and both beam types had a plastic phase prior to collapse. Observing the load–displacement diagrams for the S-60 series, it is concluded that the slip phenomenon started in the plastic phase, close to the point at which the maximum load was achieved. In this phase, the reinforcement gets increasingly loaded, and therefore also the glass-to-reinforcement bond. At a certain load, reinforcement slip occurs, which results in an increased vertical displacement rate of the beam spans. As no full plastic phase was encountered, the horizontal plateau just before beam failure can be regarded as an indication of the mentioned phenomenon and hence the location at which slip starts. The observations can be explained by considering the loadcarrying mechanism in the fractured phase. When the glass fractures, the SG-interlayer redistributes the tensile stresses to the other (intact) glass panes and the reinforcement through shear transfer. When severely cracked, almost all stresses are transferred to the reinforcement by means of shear stresses in the interlayer. The maximum amount of stress that can be transferred is directly related to the reinforcement section, the bond area, the interlayer shear stiffness and shear strength and the interlayer-steel and interlayer-glass adhesive strength [13,2]. The higher the values of all parameters, the higher the transferable stress. However, two types of limit states can be considered in this regard. In limit state 1, the amount of stress transferred by the interlayer is too big for the reinforcement section, resulting in yielding and possibly failure of the reinforcement. In limit state 2, the reinforcement section is so big that it attracts more stress than the interlayer can handle, resulting in bond failure (cohesive or adhesive failure) and reinforcement slip. A higher temperature affects the interlayer shear properties and therefore lowers the failure stresses corresponding to limit state 2. A smaller reinforcement section lowers the failure stresses corresponding to limit state 1. For the S-23 and H-23 beam specimens, limit state 1 was more critical than limit state 2. The

reverse is true for the S-60 beam specimens, in which the interlayer was too weak to transfer the stresses attracted by the solid reinforcement section. For the H-60 beam specimens, both types of maximum values were lowered compared to the S-23 series. However, the reduction in limit state 1 stresses was relatively higher than that of limit state 2, explaining the absence of reinforcement slip. 3.5. Comparison with statically determinate tests A lot of similarities exist with the observed load-carrying behaviour of statically determinate bending tests [3,4]. In general, the first three phases (i.e. linear elastic, fractured and plastic phases) are observed for both cases. However, the statically indeterminate system possesses some differences. In the first and second phases, the bending stiffness is larger than in the statically determinate case due to the smaller maximum moment values, which are also distributed over three sections (at the midspans and central support) instead of one. Contributing to a lesser extent, the second moment of area is slightly larger due to the addition of a second reinforcement bar to the beam’s section. However, this decrease in ductility is counteracted by the vertical deformation of the central support, which enhanced the vertical displacement of the beam midspans. In the statically determinate tests, initial glass fracture corresponds with a significant drop in bending stiffness. For the statically indeterminate case, this drop is postponed to the point where all critical glass sections (both midspans and the central support zone) illustrated initial fracture. During this short phase, the system redistributed the load from the fractured section to the other intact ones, resulting in a load–displacement behaviour in which the bending stiffness is only slightly reduced. Similar observations were made in [6]. In the plastic phase, the yield plateau is reached directly after the formation of one plastic hinge in the statically determinate case, whereas this only occurs after the formation of three plastic hinges in the current case. After the formation of the first plastic hinge, moment redistribution will transfer the load from this section to the other ones, maintaining significant bending stiffness up to the point where all three hinges are formed. The load increase corresponding to this phase is a direct strength reserve which is absent in statically determinate systems. During the plastic phase, similar ductility levels were reached for both support systems. The S-23 beam series in this research and the solid reinforced beam specimens tested at 23 °C in [4] illustrated the same collapse mechanism: compressive glass failure. For the other beam specimens, the tests were stopped prior to collapse due to limits of the test setup [3]. The post-fracture performance of the S-23, H-23 and H-60 beam series is significantly higher than those obtained in statically determinate testing (respectively 3.5 vs. 2.4, 2.12 vs. 1.5 and 1.88 vs. 1.6), which can be attributed to the inherent strength reserve of the statically indeterminate system. Furthermore, it is also stated that all statically indeterminate tests illustrated a residual phase after beam collapse, which was not detected during statically determinate testing. This latter phase is caused by load redistribution in the system. In general, it is concluded that the overall load-carrying behaviour of the beams is the same for both support systems. However, the statically indeterminate beams performed even better due to their abilities concerning load redistribution. 4. Conclusions Statically indeterminate five-point bending tests have been performed on two-sided reinforced laminated glass beams to evaluate the effectiveness of applying reinforced glass beams in statically indeterminate systems. In addition, the effect of reinforcement

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percentage and temperature was assessed by performing tests with solid and hollow profile reinforcement, at 23 °C and 60 °C (i.e. below and above the glass transition temperature of SG, respectively). Finally, reinforcement slip was qualitatively investigated. It was concluded that all tested beam specimens demonstrated safe failure behaviour characterised by significant postfracture performance. The S-23, H-23 and H-60 beam series exhibited an initial linear elastic phase, fractured phase, plastic phase and residual phase, resulting in high ductility. For the S-60 series, a significant plastic phase was absent, resulting in less ductility. The solid reinforced beam specimens ultimately collapsed by compressive glass failure, whereas their hollow profile reinforced counterparts failed by reinforcement failure. Increasing the temperature primarily affects the shear stiffness and strength of the SG-interlayer, resulting in a slightly lower initial failure load due to lower shear transfer capacity between glass and reinforcement. In the fractured phase, the bending stiffness decreases at a higher rate and the fracture pattern of the glass is less elaborated compared to tests at 23 °C, as the interlayer is less able to redistribute significant stresses. Furthermore, also the yield point was reached at lower loads. In the plastic phase (only achieved by the H-60 series), the ultimate load was slightly lower. The S-60 series was not able to achieve a significant plastic phase as the interlayer was not able to transfer sufficient stress to the reinforcement, resulting in bond failure followed by compressive glass failure. The effects of temperature are amplified when a higher reinforcement percentage is used. Lowering the reinforcement percentage has a significant effect on the load-carrying behaviour of the beams. In the linear elastic phase, the bending stiffness and initial failure load is lower compared to their solid reinforced counterparts. Also in the fractured phase, the bending stiffness was significantly lower and the same was observed for the yield load. In the plastic phase, the maximum load and displacement at reinforcement failure is significantly reduced. Finally, the post-fracture performance is also reduced (but still considerable). Significant reinforcement slip was only encountered for the S60 beam tests. For the mentioned beams, the reinforcement section was so big that it attracted more stress than the interlayer (weakened by the higher temperature) could handle, resulting in bond failure and hence reinforcement slip. The inability of the interlayer to transfer sufficient shear stress resulted in the absence of a significant plastic phase prior to compressive glass failure and beam collapse. For the tests at 23 °C, the interlayer was stiff and strong enough in shear to transfer sufficient stress to make the reinforcement yield and form all three plastic hinges in the system. At 60 °C, the interlayer was only stiff and strong enough to transfer sufficient stress to achieve plastic hinges in the H-60 beam series. In general, it seems feasible to achieve a beneficial failure behaviour (i.e. with a significant ductile phase and post-fracture capacity) by a combined fine-tuning of the glass-to-reinforcement bond and reinforcement percentage. In practice, an appropriate reinforcement section concerning the required post-fracture strength level should be chosen, after which the glass-to-reinforcement bond can be designed so that it is able to transfer sufficient stress for this reinforcement to reach its plastic phase, accounting for the loading time and temperature exposure in the specific situation. However, in all cases a compromise between post-fracture strength level and bond design will be inevitable, as it is better to have ductile collapse with a lower post-fracture strength level than brittle collapse of the beam due to delamination.

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From the above, it is also concluded that temperature and reinforcement have a combined effect on the load-carrying behaviour of the beams considering the specific phenomenon of reinforcement slip, and therefore cannot be considered as fully independent parameters. Comparing the statically indeterminate beam tests to statically determinate tests, it is concluded that the overall load-carrying behaviour is similar. However, due to their ability for load redistribution, the statically indeterminate beam system performs better. In general, it can be concluded that where the reinforced glass beam proved satisfactory in statically determinate applications, it also proves its effectiveness for applications in statically indeterminate systems. When the glass-to-reinforcement bond is well designed (as in the H-23, S-23 and H-60 test cases), these beams not only exhibit significant structural element safety through post-fracture strength and ductility, but also significant system safety through the formation of multiple plastic hinges prior to collapse. Moreover, even after collapse, a residual load-carrying phase based on load redistribution was detected.

Acknowledgements The ‘‘Agency for Innovation by Science and Technology in Flanders (IWT)” is gratefully acknowledged for supporting this work (grant nr. 141526). In addition, Kuraray Co. Ltd. (SentryGlasÒ) and Lerobel N.V. (glass processing) are acknowledged for supporting the production of the test specimens.

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