Figure 1.
Schematic representation of timber-glass composite beam concept: cross-section of hybrid beam (left), side-view of hybrid beam with cracked glass web (middle), force-displacement diagram showing ductility and post-breakage strength (right)
Figure 2.
Cross-section of timber-glass composite beams: type TGCB1
Table 1.
Overview of TGCB1, manufactured beam type TGCB1, n is the number of specimens produced
| Beam type | Adhesive | Glass type | Length [mm] | Total height [mm] | Glass pane size [mm2] | Glass thickness [mm] | Timber block size [mm2] | Groove size [mm] |
|---|---|---|---|---|---|---|---|---|
| TGCB1 | Epoxy (n=6) | Annealed float | 4800 | 240 | 4800×190 | 8 | 45×60 | 12×20 |
| Epoxy (n=2) Acrylate (n=2) Silicone (n=2) | Heat-strengthened |
Figure 3.
Four-point bending set-up
Table 2.
| Beam type | Adhesive | Glass type | Length [mm] | Total height [mm] | Glass pane size [mm2] | Glass thickness [mm] | Timber block size [mm2] | Groove size [mm] |
|---|---|---|---|---|---|---|---|---|
| TGCB1 | (n=1) | Annealed float | 3500 | 240 | 3500×200 | 10 | 45×60 | 13(15)×25 |
Figure 4.
Experimental load-displacement plots for beams type TGCB1 obtained from the four-point bending tests [26,27,28]. Notation: E = Epoxy, A = Acrylate, S = Silicone, AF = annealed float, HS = heat-strengthened
Figure 5.
Experimental load-displacement plots for beams type TGCB2 obtained from the four-point bending tests [13,14]. Notation: A = Acrylate, S = Silicone, LN = large groove (no edge treatment), SP = small groove (polished edges)
Figure 6
Cross-section, loading and boundary conditions for numerical model of beam type TGCB1
Figure 7.
Cross-section, loading and boundary conditions for numerical model of beam type TGCB2
Figure 8.
Crack criterion in Mode I and post-failure stress-fracture energy curve
Figure 9.
Traction-separation Law as damage definition
Table 3.
| Material | Et,l | Et,r | Et,t | νt, lr | νlt | νrt | Glr | Glt | Grt | ρt | ft |
|---|---|---|---|---|---|---|---|---|---|---|---|
| [MPa] | [MPa] | [MPa] | - | - | - | [MPa] | [MPa] | [MPa] | [kg/m3] | [MPa] | |
| Pine wood | 12 410 | 880 | 880 | 0.44 | 0.40 | 0.52 | 1 090 | 1 090 | 140 | 510 | 34.9 |
| LVL | 11 600 | 750 | 750 | 0.44 | 0.40 | 0.52 | 930 | 930 | 120 | 510 | 50 |
Table 4.
Material properties used in numerical models for adhesives [27]
| Adhesive | ρ [kN/m3] | E [MPa] | ν [-] |
| Silicone | 5 | 3 | 0.49 |
| Acrylate | 5 | 100 | 0.40 |
| Epoxy | 5 | 1 595 | 0.46 |
Figure 10.
Notation system for the cross-section (left), timber flange (center) and bond connection (right).
Figure 11.
Plot of the change in load-displacement of the TGCB1 beam (silicone adhesive) as a function of the glass web material model used, together with locations of probable damage from Implicit analysis
Figure 12.
Plot of the change in load-displacement of the TGCB1 beam (acrylate adhesive) as a function of the glass web material model used, together with locations of probable damage from Implicit analysis
Figure 13.
Plot of the change in load-displacement of the TGCB1 beam (epoxy adhesive) as a function of the glass web material model used, together with locations of probable damage from Implicit analysis
Figure 14
Plot of change in stiffness of TGCB1 beam to percentage of displacement using Silicone as adhesive
Figure 15.
Plot of change in stiffness of TGCB1 beam to percentage of displacement when using Acrylate as adhesive
Figure 16.
Plot of change in stiffness of TGCB1 beam to percentage of displacement when using Epoxy as adhesive
Table 5.
Mechanical and geometrical properties of parametric models. Notation: R = Rectangular, P = Prism
| Variation | FE/model | ft [MPa] | FE size [mm] | FE geometry [-] | Eint [MPa] |
|---|---|---|---|---|---|
| Reference | M-REF | 45.0 | 8 | P | 100 |
| Variation of tensile strength of glass | M-FT-40.5 | 40.5 | 8 | P | 100 |
| M-FT-49.5 | 49.5 | 8 | P | 100 | |
| Variation of FE size | M-FE-R | 45 | 8 | R | 100 |
| Variation of FE geometry | M-FE-16 | 45 | 16 | P | 100 |
| M-FE-4 | 45 | 4 | P | 100 | |
| M-FE-2 | 45 | 2 | P | 100 | |
| Variation of adhesive stiffness | M-AE-10 | 45 | 8 | P | 10 |
| M-AE-1000 | 45 | 8 | P | 1000 |
Figure 17
Progressive failure of reference model. Load-displacement plot (a), comparison of crack patterns in glass web at different failure stages and displacements (b-d). Note symmetry of model at right vertical edge
Figure 18.
Effects of tensile strength of glass. Comparison of load-displacement plots (a), comparison of crack patterns in glass web at displacement of ≈ 23.8 mm (b-d). Note symmetry of numerical model at right vertical edge
Figure 19.
Effects of FE geometry. Comparison of load-displacement plots (a), comparison of crack patterns in glass web at displacement of ≈ 23.8 mm (b, c). Note symmetry of numerical model at right vertical edge
Figure 20.
Effects of FE size. Comparison of load-displacement plots (a), comparison of crack patterns in glass web at displacement of ≈ 23.8 mm (b-e). Note symmetry of numerical model at right vertical edge
Figure 21.
Effects of adhesive stiffness. Comparison of load-displacement plots (a), comparison of crack patterns in glass web at displacement of ≈ 23.8 mm (b-d). Note symmetry of numerical model at right vertical edge
Figure 22.
Comparison between numerical and experimental [27] loaddisplacement plots for the beam TBCB1_E_AF. Effects of different tensile strength of glass
Figure 23.
Comparison between numerical and experimental [13,14] load-displacement plots for the beam type TBCB2
Table 6
Experimental results (mean values and standard deviations) for beam specimens [13,14,26,27,28] and corresponding FE and analytical predictions. Notation: PBSI – Post-breakage strength index PBSI = 100 × (Finit - Fult) / Fult., PCDI - Post-cracking ductility index, PCDI = 100 × (uinit - uult) / uult, FE = 100 × (resultFE – resultEXP) / resultEXP, AN = 100 × (resultAN – resultEXP) / resultEXP
| Experiments | Finite Element | Analytical | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Beam model | Fint [kN] | Fult [kN] | PBSI [%] | PCDI [%] | Kinit [MNm2] | Model | Fint [kN] | Fult [kN] | PBSI [%] | PCDI [%] | Kinit [MNm2] | Fint [kN] | Kinit [MNm2] |
| TGCB1_E_AF | 11.6 (2.8) | 16.4 (2.2) | 51.5 (50) | 91.2 (86.7) | 0.898 (0.042) | E_AF_FE_FT45 | 7.2 | 12.2 | 70.6 | 176.9 | 0.920 | 7.5 | 0.817 |
| ΔFE/ΔAN= | -38.4% | -25.7% | 41.3% | 94.3% | 4.9% | ||||||||
| E_AF_FE_FT66 | 10.5 | 15.6 | 48.2 | 109.7 | 2.5% | 10.9 | -9.0% | ||||||
| ΔFE/ΔAN= | -9.3% | -4.94% | -3.6% | 20.5% | 3.6% | ||||||||
| TGCB1_E_HS | 25.5 (-) | 25.5 (-) | - | - | 0.898 (-) | E_HS_FE_FT45 | 25.5 | 25.5 | - | - | 24.5 | ||
| ΔFE/ΔAN= | 0.1% | 0.1% | -3.9% | ||||||||||
| TGCB1_A_HS | 25.5 (-) | 25.5 (-) | - | - | 0.907 | A_HS_FE_FT45 | 24.6 | 24.6 | - | - | 0.904 | 24.4 | 0.808 |
| ΔFE/ΔAN= | -2.4% | -2.4% | -0.3% | -3.9% | -10.6% | ||||||||
| TGCB1_S_HS | 19.8 (-) | 19.8 (-) | - | - | 0.720 | S_HS_FE_FT45 | 18.3 | 18.3 | - | - | 0.692 | 19.1 | 0.630 |
| ΔFE/ΔAN= | -7.7% | -7.7% | -3.9% | -3.5% | -12.5% | ||||||||
| TGCB2_A_AF_L | 11.1 (1.3) | 28.3 (2.4) | 158 (24.0) | 298 (51.2) | 1.253 () | A_AF_FE_L_ FT45 | 10.3 | 27.0 | 162 | 325.5 | 1.349 | 9.4 | 1.069 |
| ΔFE/ΔAN= | -7.4% | -4.7% | 4.9% | 8.9% | 7.66% | -15.3% | 3.8% | ||||||
| TGCB2_A_AF_S | 13.0 (1.1) | 28.7 (2.3) | 122 (24.0) | 210 (39.0) | 1.237 () | A_AF_FE_SG_FT45 | 10.5 | 21.8 | 108 | 302 | 1.367 | 9.6 | 1.081 |
| ΔFE/ΔAN= | -19.2% | -23.8% | -11.4 | -43.6% | 10.5% | -26.2% | 6.3% | ||||||
| TGCB2_S_AF_L | 8.8 (-) | 20.3 (-) | 131 (-) | 536 (-) | 0.918 (-) | S_AF_FE_SG_ FT45 | 8.2 | 22.8 | 179 | 465 | 1.075 | 7.4 | 0.826 |
| ΔFE/ΔAN= | -6.9% | 12.4% | 36.7% | -13.3% | 17.1% | -15.9% | -10.0% | ||||||