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Prestressed glulam timbers reinforced with steel bars
Construction and Building Materials 30 (2012) 206–217
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Prestressed glulam timbers reinforced with steel bars Vincenzo De Luca ⇑, Cosimo Marano Department DITEC, University of Basilicata, 85100 Potenza, Italy
a r t i c l e
i n f o
Article history: Received 2 February 2011 Received in revised form 22 October 2011 Accepted 24 November 2011 Available online 29 December 2011 Keywords: Glulam timber beams Timber structures Timber constructions Prestressed glulam timber Steel reinforcements Bending tests
a b s t r a c t This paper discusses a series of four-point bending tests that were conducted to failure on unreinforced, reinforced and reinforced-prestressed glue laminated (glulam) timber beams with steel-bars in a simplysupported scheme to determine their flexural behavior. The cross sectional ratio between the steel and the wood was 0.82%. To increase the level of reinforcement, some reinforced beams were prestressed by applying a moderate force to the lower bar. The experimental and numerical data provided the load–deflection, load–strain relationships and strain profiles of the tested beams. The results of the reinforced beams showed that the mechanical strength, the load-carrying capacity and the stiffness for both the simple and prestressed beams were enhanced compared to the unreinforced beams. For the simply reinforced beams, the stiffness increased by 25.9%, the ultimate load increased by 48.1% and the ductility increased by 43.8%. For the reinforced and prestressed beams, the stiffness increased by 37.9%, the ultimate load increased by 40.2%, and the ductility increased by 79.1%. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction To improve the seismic safety of a complex structure, it is crucial to design the structure based on the concept of ductile response because the concept is defined by ‘‘post-elastic resources’’. To limit our interest to ‘‘post-elastic resources’’, such as the structural glued laminated (glulam) timber, it is worthwhile to note the relevant scientific research. The field of ‘‘lamped ductility’’ is concerned with connections between structural elements; however, few studies and advances are notable in the field of ‘‘widespread ductility’’, especially when traditional structural materials such as steel and reinforced concrete are considered. Current research on timber construction often neglects the post-elastic behavior of a single structural element. This may be insufficient for structural safety when static loads of variable magnitudes are present on a house floor or in a bridge deck. Within this research field, one possible strategy to improve the mechanical properties of a beam of glulam timber is to insert steel bars and apply a moderate level of prestress to the bars placed in the face of the beam under tension. This strategy could provide adequate levels of widespread ductility.
2. Literature review Even though there are no specific and systematic studies on glulam timbers reinforced with steel bars within the scientific
⇑ Corresponding author. Tel.: +39 0971 20 5438; fax: +39 0971 20 5429. E-mail address: [email protected] (V. De Luca). 0950-0618/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.conbuildmat.2011.11.016
literature, the effects of prestressed glulam timber are evident in scientific research and technological applications [1]; the combination of traditional glulam timber with steel reinforcement bars has been used in fields such as house floors and roofs. Research on the application of metal reinforcements are rarely published; more recent research projects are focused on the application of fiber reinforced polymer (FRP) reinforcements [2] and on the sometimes transversal prestressing of laminated wood by reinforcing fibers, particularly in the field of bridge beam recovery [3–7]. Early studies used metal reinforcements to strengthen timber beams; unfortunately, none of these systems of reinforcement was successfully used in the construction market. The long-term reliability and efficiency of these reinforcement systems are still unknown due to the lack of experimental data. Early research adopted both strengthening and prestressed techniques using steel or fiber reinforced polymer (FRP), reinforced bars or reinforced plates. Studies by Mark [8], Sliker [9], Bohannan [10], Peterson [11], Lantos [12] and Bulleit et al. [13] tested the effect of prestressing using steel plates or cables bonded in the tension zone of glulam beams. Other studies on CFRP reinforcements were performed by Hemandez et al. [14] and Haiman and Zagar [15]. Drawbacks such as buckling, relaxation of the pretension force due to creep, separation and delamination of bonded layers, the transmission of the prestressing force toward the laminate and the occurrence of adhesive high shear stresses localized at both the edges of a beam were observed in certain works [16–18]. However, all these studies reported a lower statistical variance in the strength of strengthened beams compared with the unstrengthened ones. More recently, some researchers studied the use of steel bars in reinforcing wood. Kim and Harries [19] and Issa and Kmeid [20]
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compared experiments on glulam beams reinforced by plates. Their results confirmed the importance of the reinforcements in enhancing the overall mechanical behavior of a timber beam. Jasien´ko [21,22] studied the interaction of a glued-in steel bar over the cross section of a reinforced wood element. The experimental data showed an irregular distribution along the bonding joint of normal and shear stresses. Nowak et al. [23] experimented with an innovative technique using a photoelastic coating to measure the strain distribution between the timber beams and their reinforcing elements. The above experimental evidence showed that reinforcing timber beams with steel reinforcements could greatly improve the strength, stiffness and load-carrying capacity of the beams; less deformation, less tensile stresses at the tension face, and more compressive stresses at the compression face would be observed. Additional benefits could be achieved when additional reinforcements are added in the compressive face of a structure while a moderate level of pretension is applied to the bars in the tensile face of a timber element. The authors of this paper have already begun the study of reinforcement steel bars with a general-purpose research project [24–26]. This is a timely research subject for the following reasons: – there is a lack of scientific literature on beams reinforced with steel bars, and even less literature on those strengthened with prestressed reinforcements; – the few existing works on this subject are outdated and use obsolete adhesives; – stronger and more novel adhesives are available. In this paper, we investigated the strengthening solutions for glulam timbers by comparing the results from laboratory tests and numerical analysis. Experimental bending tests on a four-point scheme were conducted on glulam beams made of white spruce and reinforced with longitudinal steel bars. The steel bars were inserted and glued in the tensile and compressive faces of the beam, and the bars within the tensile face of certain specimens were prestressed to determine the level of strengthening provided by the bars. A theoretical model for the composite wood–steel with nonlinear stress–strain paths was then applied to calculate the moment of rupture. Subsequently, the experimental results were compared with the theoretical predictions. The main objective of this work is to enhance the overall strength and stiffness of timber beams and to redistribute the stress field in the cross section of the beams; we also aim to create a pronounced region of ductility. 3. Materials and methods A total of 12 white spruce glulam beams were machined with a cross section of 80 mm 117 mm and a length of 2000 mm. The reinforced beams were further machined with two longitudinal slots at the top and bottom faces. The slots were 20 mm deep and 20 mm wide. The beams were then divided into three series (Table 1):
(1) The T series, which included three unreinforced simple beams. (2) The R series, which included three beams reinforced with steel bars bonded to wood by an adhesive. (3) The P series, which included six reinforced and prestressed beams. The reinforcing steel bars were bonded to the wood by an adhesive, and the bottom bars were pre-tensioned by a force of 18 kN. 3.1. Material specifications The glulam beams, steel bars and adhesive used in the present work were furnished by the manufactures and fabricated as described below. 3.1.1. Glulams The white spruce glulam was characterized by its manufacturer as grade GL28 according to the standard prEN1194; its mechanical characteristics are listed in Table 2. 3.1.2. Steel bars The steel bars were characterized as grade C45 by its manufacturer according to the standard UNI EN 10083/1998. The steel bars were also directly characterized using experimental tests. Specifically, steel bar number 9 was tested in tension and compression to determine the stress–strain path of the material. The steel bars that underwent tension tests were 10 mm in diameter and cut to a length of 500 mm. The steel bars for compression tests were 10 mm in diameter and 18 mm long. The tests were performed with a Universal Press Tecnotest F60 with a 600 kN load capacity. The rate of loading was 5 N/min for tension tests and 5 N/min for compression tests. The experimental values of the mechanical characteristics of the steel bars are listed in Table 3. 3.1.3. Adhesive The adhesive used in this experiment was a two-component polyurethane resin (PurbondÒ CR 421) manufactured without solvents or formaldehyde. This adhesive was suitable for anchoring the glued-in steel rebar in the wooden components of structural beams. The mechanical characteristics of the adhesive were furnished by its manufacturer (as shown in Table 4). Smooth steel bars without corrugated surfaces were used in the reinforcement technique adopted in this experiment. Before inserting and bonding the steel bars along the slots on the beams, the bars were carefully cleaned by a nonionic surfactant and detergent to eliminate dust or grease. The cross sections of all the specimens are shown in Fig. 1. Two 15-mm thick perforated steel plates were bonded to each end of the beams by the adhesive (Fig. 2). The reinforcing steel bars with a diameter of 10 mm were cut to 2100 mm long and bonded to the beams through the longitudinal slots by the adhesive (Fig. 2). Both ends of each bar were then blocked by the above-mentioned plates and fixed by bolts. For the prestressed beams, a tensioning stage, involving an 18 kN pretension force that was applied by a mechanical tensioning device to the bottom bar, occurred before the bars were fixed to the beams (Figs. 3 and 4). The adhesive was allowed to set for more than 30 days before testing. The experimental stages of the work were executed at room temperature in the Material Laboratory of the DITEC Department, University of Basilicata, Italy. A simply-supported four-point bending scheme was adopted (Fig. 5) to apply uniform bending without any shear in the middle of the beam span; the beam had a load span of 1800 mm and a support span of 600 mm. The roller supports were covered by a rubber sheet to reduce the bearing failure effect. Bending tests were executed with an electro-mechanical press (model PMA10 Galdabini, as shown in Fig. 6), which was able to digitally control the applied load and the frame displacement pattern. The test equipment consisted of a force transducer (with a load cell that had a carrying capacity of 100 kN) and a linear variable displacement transducer (LVDT) that were used to measure the total force and the mid-span deflection, respectively. Electric resistance strain gauges (SG) made by HBMÒ were distributed at six locations along the height of the beam at mid-span to measure the strains of the horizontal fibers. The SGs had measuring grid lengths of 10 mm for the ‘‘T’’ and ‘‘R’’ series and a grid length of 20 mm for the ‘‘P’’ series. For reinforced beams, two more SGs were installed at the mid-span: one was installed on the bottom bar to measure the tensile strain, and one was installed on the top bar to measure the
Table 1 Reinforcement type, diameter and cross sectional ratio between the steel and the wood. Specimen code
Number of specimens
Reinforcements Type
T1, T2, T3 R1, R2, R3 P1, P2, P3, P4, P5, P6
3 3 6
Total
12
Diameter (mm)
Cross-section ratio steel/wood (%)
Prestressing (kN)
Bottom
Top
Bottom
Top
Bottom
Top
Bottom
None Steel bar Steel bar prestressed
None Steel bar Steel bar
– 10 10
– 10 10
0.00 0.82 0.82
0.00 0.82 0.82
– 0 18.00
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Table 2 Glulam manufacturer specifications (N/mm2). Material specification
Value
Bending strength, characteristic value Tensile strength parallel to the fiber, characteristic value Tensile strength perpendicular to the fiber, characteristic value Compression parallel to the fiber, characteristic value Compression perpendicular to the fiber, characteristic value Shear strength, characteristic value Modulus of elasticity parallel to the fiber, average value Modulus of elasticity parallel to the fiber, 5% fractile value Modulus of elasticity perpendicular to the fiber, average value Tangential modulus of elasticity, average value
28 19.5 0.45 26.5 3.0 3.2 12,600 10,200 420 780
Table 3 Steel bar characteristics – summary of results (number of specimens tested: 9). Characteristic Ultimate Ultimate Ultimate Ultimate Modulus Modulus
tensile stress (N/mm2) compressive stress (N/mm2) tensile strain (dimensionless) compressive strain (dimensionless) of elasticity in tension (N/mm2) of elasticity in compression (N/mm2)
Mean
5% Fractile
675.8 1510.0 0.2256 0.4944 342,375 342,588
425.2 1091.2 0.1970 0.4100 213,190 205,238 Fig. 2. Procedure for bonding bar reinforcements in the glulam beams.
Table 4 Adhesive manufacturer specifications. Specification
Value
Tensile strength at approx. 2% elongation/at break (N/mm2) Elongation at break (%) Compressive strength (at 20 °C) (N/mm2) Modulus of elasticity (at 20 °C) (N/mm2)
25/30 2.0 79.9 1560
compressive strain. The placement of the SGs is schematically illustrated in Fig. 7. The SGs were bonded by the adhesive HBM X60 and connected by a Wheatstone bridge circuit with an amplifier in a full-bridge configuration. Another SG was mounted in the Wheatstone bridge circuit for temperature compensation [27]. The computer controlling the testing machine recorded the measured middle displacement (mm) and load (kN) at a sampling rate of 0.01 Hz using software. In addition, the SGs readings were recorded every two seconds by a computerized data acquisition system (CR10 CampbellÒ, as shown in Fig. 8). Loading was continued beyond peak load in the post-failure zone. All bending tests were performed with controlled displacement with a test speed of 4 mm/min. The results between the different types of beam tests were presented in graphs and tables for comparison. Graphs illustrated load–deflection and load–strain curves along with the strain profiles at selected loads. The strength improvement is shown through the changes in stiffness, load carrying capacity, the elastic modulus, ductility, and the mid-span deflection at the proportional limit, the ultimate limit and post-failure. The elastic modulus is calculated using the linear-elastic behavior for each beam during the initial deformation path by the following relationship:
E¼
Fp a ð3L2 4a2 Þ 48I dp
ð1Þ
where E (kN/mm2): elastic modulus; Fp (kN): total applied load at the proportional limit; a (mm): edge support distance; L (mm): beam span; I (mm4): inertia moment of gross section; and dp (mm): mid-span deflection at the proportional limit. The ductility is defined by:
lf ¼ df =du
ð2Þ
where lf (dimensionless): ductility; du (mm): deflection at ultimate load; and df (mm): post-failure deflection.
3.2. Theoretical model A theoretical model of the beam in bending was used to predict the resistant moment until the proportional limit, Mp, and the ultimate moment, Mu, were reached under loading. The analytical values were then compared with experimental ones. In scientific literature, similar models have been used by many researchers to analyze the stress distribution in the cross section of a reinforced glulam timber [28–32]. The model adopted here assumed the following: – the cross sections remained planar after they were deformed by bending; – there was no slipping between the adhesive and the adjacent wood lamellas or between the steel rebar, the adhesive and the glulam; – the stress–strain relationship for the glulam was elastic-brittle in tension, and elastic-perfectly plastic in compression (Fig. 9); – the stress–strain relationship for the steel bar in tension and in compression was elastic-perfectly plastic (Fig. 10).
Fig. 1. Details of the cross section types: unreinforced beams, simply strengthened beams with upper and lower steel bar, 10 mm in diameter, and strengthened beams with an upper steel bar, 10 mm in diameter, and a lower prestressed bar, 10 mm in diameter.
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R1 ¼ As1 f1 ; d1 ¼ ds1 R2 ¼ ðp bÞ f2 ; d2 ¼ p 1=2
ð3:1Þ ð3:2Þ
R3 ¼ ½ðyn pÞ b 1=2 f3 ; R4 ¼ ½ðh yn Þ b 1=2 f4 ; R5 ¼ As2 f5 ; d5 ¼ ds2
ð3:3Þ ð3:4Þ ð3:5Þ
d3 ¼ ðyn pÞ 1=3 d3 ¼ yn þ ðh yn Þ 2=3
where fi is the stress value; h, the cross section depth; b, the cross section width; p, the depth of the plastic stress diagram of the glulam, and i is a subscript indicating: i = 1: indicates the steel bar under compression; i = 2: indicates the compressive face of the plastic part of the glulam; i = 3: indicates the compressive face of the elastic part of the glulam; i = 4: indicates the tensile face of the glulam; i = 5: indicates the steel bar under tension. The curvature v is defined as:
v ¼ je2 j=yn
ð4Þ
The strains (ei) in the cross section could be calculated by assuming the position of the neutral axis according to the assumption that the sections remain planar (as shown in Fig. 11):
e ¼ v yi
ð5Þ
where yi is the distance of the centroid of the areas away from the neutral axis:
Fig. 3. The mechanical tensioning device for applying the pretension to bar.
y1 ¼ ðyn ds1 Þ
ð6:1Þ
y2 ¼ yn y3 ¼ ðyn pÞ y4 ¼ ðh yn Þ
ð6:2Þ ð6:3Þ ð6:4Þ
y5 ¼ ds2 yn
ð6:5Þ
From the values of strain (ei), the corresponding stress values (fi) of wood and steel could be calculated according to the previously assumed stress–strain relationships (Figs. 9 and 10, respectively). Then, the equilibrium of the internal force requires that: 5 X
Ri þ N p ¼ 0
ð7Þ
i
where Np is the prestressing force acting on the steel bar on the bottom of the beam. The resultant resistant moment could be computed as:
M¼
5 X
Ri di þ N p d5
ð8Þ
i
Note that in the unreinforced beam, the cross sections of the steel bars and the prestressing force were clearly assumed to equal zero; the prestressing force was assumed to equal zero in the simply reinforced beam. 3.3. Material properties for theoretical model The values used in the theoretical model to calculate the mechanical characteristics of the glulam and steel were carefully derived from the experimental data recorded. Therefore, the results from the bending tests of the unreinforced timber beams (the T series of specimens) were used as the mechanical constants for glulam (shown in Fig. 9); the 5% fractile values of the experimental results of the steel bars in tension and compression were used as the mechanical constants for steel (shown in Fig. 10).
Fig. 4. Detail of the attachment to steel bar end in the mechanical tensioning device for applying the pretension to bar.
The geometric characteristics of the composite beams used in the numeric calculations within the theoretical model were the same as those used in the calculations based on experimental data. Based on the stress–strain patterns of the materials, the resistant bending moment could be evaluated using the equilibrium condition of the compressive and tensile forces on the cross section with respect to, for instance, the neutral axis; this could be done by considering the tension to be positive and the compression to be negative. The non-linear pattern of the moment – curvature relationship of the cross sections of the beam was therefore analyzed incrementally within an iterative numerical scheme starting from an initial assumption of the curvature. This procedure allowed the neutral axis depth, yn, to be computed until the ultimate condition was reached in either the wood or the steel. The internal forces (Ri) and the corresponding lever arms (di) (for i = 1, 2, . . . , 5) with respect to the top face of the cross sections were defined by the following (as shown in Fig. 11):
4. Results and discussion The test results (Fig. 12 shows a typical stage of a bending test) for the strengthened beams and strengthened-prestressed beams were compared with those for the unreinforced beams to determine their behavior in terms of strength, deflection, stiffness and ductility. These results are shown in Figs. 13–21 and summarized in Table 5. The numerical calculations were executed using the theoretical model and the relative material parameters were derived as described in the previous chapter. 4.1. Experimental results The load–deflection curves of the unstrengthened beams (in the T series), the strengthened beams (the R series), and the strengthened-prestressed beams (the P series) are shown in Figs. 13–15, respectively:
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Fig. 5. Testing set-up for bending test of the glulam beams.
Fig. 6. Testing machine and digital equipment used in the research. Fig. 8. Datalogger system for data recording of the strain gauges.
– Fig. 13 plots the load–deflection curves of the three unreinforced beams (T1, T2 and T3). The stiffness of a beam without any reinforcement remained almost constant, and there was no residual deflection after the first loading range. The initial part of the curve remained linear until the timber cracked at or shortly beyond the maximum load in the tension zone.
– Fig. 14 plots the load–deflection curves of the three strengthened beams (R1, R2 and R3). For all three curves, the initial path was linear until the timber cracked at approximately the maximum load in the tension zone. Then, the stiffness gradually decreased until a subsequent relative maximum load was
Fig. 7. Strain gauges placement along the beam depth at the mid-span.
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reached, and crushing began in the compression zone. Finally, failure occurred in the compression zone and caused a drop in load. – Fig. 15 illustrates the load–deflection curves of the six strengthened-prestressed beams (P1–P6). For all six curves, the initial path was linear until the timber cracked under the maximum load in the tension zone. Then the beams deflected consistently under a residual stress, indicating high ductility. The ultimate rupture occurred in the compression zone, corresponding to a final drop in the plot.
load-carrying capacity than the unreinforced beams. In those figures, the load corresponding to the ultimate load-carrying capacity was well defined. The modulus of elasticity of a beam was calculated according to Eq. (1), where the load at the proportional limit was estimated at a minimal correlation coefficient of 0.9975 by linear regression applied to the points in the linear portion of the load–deflection curve. The results for all the beams are reported in Table 5 with the means and standard deviations. Table 5 also reports the comparison between the deflection and load at the proportional limit, the ultimate limit and at post-failure for the un-strengthened, strengthened and strengthened-prestressed beams. The ductility of the beam was calculated according to Eq. (2) and reported in Table 5 for all beam types. In addition, the strength increase calculated over the strength of the unreinforced beams is reported in Table 5 for all beams. The results showed that strengthening was effective in the reinforced beams compared to the unreinforced beams: the maximum load capacity increased by 48.1%, the elastic modulus increased by 25.9% and the ductility increased by 43.8%. Furthermore, the deflection at post-failure of all the reinforced beams was greater than that of the unreinforced beams. The strength improvements in the reinforced-prestressed beams were more pronounced: the maximum load capacity increased by 40.2%, the elastic modulus increased by 37.9%, and the ductility increased by 79.1%. However, the deflection at post-failure of all the reinforced beams was greater than that of the unreinforced beams. The steel bar reinforcement in the timber beams increased the bending stiffness of the glulam timber element and reduced the deflection compared to an unstrengthened beam at the same load levels. We should note that the longitudinal slots used to insert the bars weakened the beam by disturbing the grain while reducing the moment of inertia and the ultimate load-carrying capacity of the beam. Furthermore, the steel bar in one reinforced beam was seen to break, indicating that the glulam-steel composite structure needed steel bars with adequate strength. The bar strength could be estimated by a suitable analytical model of the overall system. Typical load–strain curves, which are discussed as follows, for the unreinforced, simply reinforced and reinforced-prestressed timbers are illustrated in Figs. 16–18, respectively.
Certain drops in load observed in the above curves corresponded to internal cracks of the beam. The cracks were caused by delamination, which occurred due to slipping between two bonded laminates. We should note that this observation only concerned the glulam adhesive and not the overall composite system of glulam and the steel bars. As clearly indicated in Figs. 13–15, all of the simply reinforced beams and the reinforced-prestressed beams had higher ultimate
– The load–strain relationship for the unreinforced beams (shown in Fig. 16) remained nearly linear in both the compression and tension zone. Cracking occurred at 22 kN and corresponded to drops in the load–deflection plot (Fig. 13). – For the simply reinforced beams, the load–strain distribution (shown in Fig. 17) remained linear until cracks initiated at a load of 18 kN for both the compression and tension zones. Cracking could be seen as discontinuities in the load–deflection
Fig. 9. Stress–strain relationship for glulam adopted in the theoretical model.
Fig. 10. Stress–strain relationship for steel bar adopted in the theoretical model.
Fig. 11. Cross section of the timber beam with the notations of the theoretical model.
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Fig. 12. Typical stage of a bending test. Fig. 15. Load–deflection curve for the strengthened-prestressed beams (P series), with steel bars, 10 mm in diameter.
Fig. 13. Load–deflection curve for the unstrengthened beams (T series) (from [26]).
Fig. 16. Typical load–strain curve for an unstrengthened beam (T2).
Fig. 14. Load–deflection curve for the simply strengthened beams (R series), with steel bars, 10 mm in diameter (from [26]).
curve (Fig. 14), and it occurred at a load of 38 kN in the load– strain curve. After cracking, the load–strain curve became non-linear as the stiffness progressively decayed due to the cracks opening through the tension region.
Fig. 17. Typical load–strain curve for a simply strengthened beam (R2), with steel bars, 10 mm in diameter.
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Fig. 18. Typical load–strain curve for a strengthened–prestressed beam (P6), with steel bars, 10 mm in diameter.
213
Fig. 21. Typical strain profile for a strengthened–prestressed beam (P6), with steel bars, 10 mm in diameter, at selected loads.
compression and tension zones (Fig. 18). Cracking at a load of 39 kN was observed as discontinuities in the load–deflection curve (Fig. 15). After cracking, the stiffness progressively decayed because cracks opened through the tension region, and the load–strain curve became non-linear. Graphs of the strain profiles (that is, the strain versus beam depth) are plotted in Figs. 19–21 for typical specimen types at four selected load levels. The position of the neutral axis along the depth of the beam could be determined from those graphs because it varied as the load increased until failure. The strain profiles, which plot the strain gauge measures along the beam height, are useful in the analysis of changing relative neutral axis position due to beam strengthening:
Fig. 19. Typical strain profile for an unstrengthened beam (T2), at selected loads.
Fig. 20. Typical strain profile for a simply strengthened beam (R2), with steel bars, 10 mm in diameter, at selected loads.
– For the reinforced-prestressed beams, the strain distribution along the depth of the beam remained linear until the cracks initiated in the tensile region at a load of 24 kN for both the
– in the unreinforced beam, the neutral axis was localized (Fig. 19) at approximately +2 to +5 mm of the beam depth in the compressive region of strain; – in the simply reinforced beam, the neutral axis position (Fig. 20) was at approximately 5 to 9 mm of the beam depth in the tensile region of strain, a region opposite of that in an unreinforced beam. The steel rebars caused the neutral axis depth to shift from the compression to the tension region of strain; – in the reinforced-prestressed beam type (Fig. 21), the neutral axis position was shifted to the tension region of strain; however, it was only slightly shifted to approximately 4 mm. As clearly shown in Figs. 19–21, the strains in the typical reinforced and reinforced-prestressed beams were approximately 50% lower than the strains in typical unreinforced beams. These results showed that simple bar reinforcements shifted the neutral axis position downward, implying a more favorable redistribution of the stress field in the section. Less tensile stresses were observed at the tension face, and more compressive stresses were observed at the compression face as the stresses were transferred to the steel bars inserted in the tension and compression regions of the section. A similarly positive effect occurred in the reinforced-prestressed beam; however, it was partially reduced by prestressing because the neutral axis was slightly redirected toward the compression region. All of the beams first cracked in the tension edge, they then failed in a different mode depending on their beam type:
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Table 5 Comparison between the deflection and load at the proportional, ultimate limit, at post-failure and ductility for the tested beams – experimental results [26]. Specimen type
Beam code
Elastic Modulus
At proportional limit
At ultimate limit
Load Fp (kN)
Mid-span deflection du (mm)
Load
E (kN/mm )
Mid-span deflection dp (mm)
T1 T2 T3
8.597 6.604 7.703
16.3 34.0 25.0
14.064 22.569 19.419
45.9 34.0 45.7
27.237 22.569 26.923
46.3 34.2 59.1
1.011 1.008 1.293
Mean
7.635
25.1
18.684
41.8
25.576
46.5
1.104
St. dev.
0.998
8.8
4.300
6.8
2.609
12.4
0.164
R1 R2 R3
10.030 10.392 8.414
22.1 18.3 29.2
22.087 18.997 25.362
41.0 57.3 50.3
36.117 38.983 38.560
63.7 80.5 90.7
1.554 1.403 1.805
Mean
9.612
23.2
22.148
49.5
37.886
78.3
1.587
St.dev.
1.053
5.5
3.183
8.2
1.547
13.6
0.203
P1 P2 P3 P4 P5 P6
10.401 11.787 10.706 10.004 9.831 10.439
30.0 27.5 29.9 23.6 28.6 22.8
30.717 31.750 31.621 24.472 27.995 24.540
33.8 51.7 58.0 28.2 29.8 43.7
33.711 46.220 37.719 28.735 29.040 39.731
62.6 68.5 70.5 85.6 62.9 101.5
1.850 1.325 1.215 3.035 2.112 2.322
Mean
10.528
27.1
28.516
40.9
35.859
75.2
1.977
St. dev.
0.693
3.1
3.388
12.3
6.748
15.3
0.675
2
Un-reinforced glulam beam, T series (from [26])
Steel reinforced glulam beam, R series (from [26])
Steel reinforced plus pre-stressed glulam beam, P series
Fu (kN)
At post-failure
Ductility
Mid-span deflection df (mm)
lf (dimensionless)
Increment reinforced versus un-reinforced beam
Mean
25.9%
7.6%
18.5%
18.4%
48.1%
68.2%
43.8%
Increment reinforced-prestressed versus unreinforced beam
Mean
37.9%
7.8%
52.6%
2.3%
40.2%
61.6%
79.1%
Increment reinforced-prestressed versus simple reinforced beam
Mean
9.5%
16.6%
28.7%
17.5%
5.4%
3.9%
24.5%
– All of the unreinforced beams (the T series) failed due to tension failure from brittle tension in which crushing occurred in the tension region at the maximum measured load; no crush was observed in the compression region, and most of the wood fibers below the neutral axis were stretched. Fig. 22 shows a typical beam subjected to this failure mode. – The failure of the simply reinforced beams (the R series) was tension-initiated, followed by compression failure. The beams exhibited crushing initially in the tension zone and then in the compression zone at maximum load. This type of failure is shown in Fig. 23.
Fig. 23. Failure in mixed tension–compression of a typical reinforced beam (R2).
– The prestressed beams (the P series) underwent compression failure in which the beams exhibited crushing in the compression zone at maximum load. This type of failure (shown in Fig. 24) occurred when the prestressed bar was used to bear the traction in the tension zone, where the amount of the stretched wooden fiber was very low and limited to the bottom face.
Fig. 22. Failure in tension of a typical unreinforced beam (T3).
In a few cases of the reinforced and reinforced-prestressed specimens, failure was preceded by singular types of crushing such as the following:
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forcement, were not available because the strain measurements of this work were limited to only the mid-span section. All these issues could be addressed in a future study. Generally, the strain profile that plotted the strain gauge measures along the beam height remained approximately linear along the section depth within the elastic path. The strain profiles revealed no significant strain peaks at least in the elastic path and just below the ultimate phase. Shear stress failure on the edge beam between two lamellas was observed; yet no shear stress failure of glue and wood–steel was observed on the edge sections below the ultimate phase. On the contrary, significant debonding and strain peaks were often observed between two adjacent wood lamellas, particularly when they were close to the failure phase. In addition, the two thick plates glued to each end of the beams in all the simply reinforced and reinforced-prestressed beams often helped to avoid the delamination between two wooden lamellas; this fact highlighted the importance of the two stiff end plates. 4.2. Theoretical results
Fig. 24. Failure in compression of a typical reinforced–prestressed beam (P5).
– the delamination along the bonded layer between two wooden lamellas; – the failure of the tension steel bar; – the debonding of the bar from the slot in the timber and the buckling of compressed steel bars (see Fig. 25 for a simply reinforced beam). Remarkably, the addition of steel bars shifted the failure mode from the brittle tension mode to the compressive mode despite the ductile nature of the bars. These observations demonstrated the effectiveness of the reinforcing techniques by using simple steel rebars and by prestressing. However, the latter reinforcement technique could further improve the effectiveness as shown in Table 5. As already highlighted in the analysis of strain profiles and relative neutral axis position, the steel bars were clearly bearing stress in the simple and the reinforced-prestressed beams. However, additional quantitative details such as the optimization of the ‘‘wood–steel’’ system, which would require a comparison with many other specimens prepared at various percentages of rein-
All constants on which the theoretical model was based can be defined for numeric calculations as follows (they were also reported in Table 6 for glulam and Table 7 for the steel bar): Using the mean load Fp at the proportional limit (supplied from the T series bending tests), the bending moment Mp at the proportional limit can be computed. Then, the stresses at the cross section at the proportional limit could be calculated. The strains of the bottom and top fibers (ewtu and ewcy, respectively) at the proportional
Table 6 Mechanical constants in bending, strength, strain and modulus of elasticity of glulam, adopted in the theoretical model. Constants
Computed/adopted value
Ultimate tensile stress fwtu (N/mm2)
11210:4 Nm ¼ Wpp ¼ 182;520 ¼ þ61:42 mm3
Compressive stress at yielding fwcu (N/ mm2) Ultimate tensile strain ewtu (dimensionless) Compressive strain at yielding ewcy (dimensionless) Ultimate compressive strain ewcu (dimensionless) Modulus of elasticity in tension Ewt (N/mm2) Modulus of elasticity in compression Ewc (N/mm2)
Nm ¼ Wpp ¼ 11210:4 ¼ 61:42 182;520 mm3
M M
=+0.002574 =0.003244 =0.012000 2
þ61:42 N=mm ¼ efwtu ¼ 0:002574 ¼ þ23; 862 dimensionless wtu 2
61:42 N=mm ¼ efwcu ¼ 0:003244 ¼ 18; 933 dimensionless wcy
Where F p ¼ þ18; 684 N: is the load at the proportional limit; Mp ¼ F p a ¼ þ18; 684 N 600 mm ¼ þ11; 210:4 Nm: is the bending moment at the proportional limit; a ¼ 600 mm: is the edge support distance; 2 W p ¼ bh6 ¼ 182; 520 mm3 : is the moment of resistance of the cross section; b ¼ 80 mm: is the width of the beam; and h ¼ 117 mm: is the depth of the beam.
Table 7 Mechanical constants in bending, strength, strain and modulus of elasticity of steel bar, adopted in the theoretical model.
Fig. 25. Buckling of a compressed steel-bar in a reinforced beam (R5).
Constants
Adopted value
Ultimate tensile stress fstu (N/mm2) Ultimate compressive stress fscu (N/mm2) Yield tensile strain (offset = 0.2%) esty (dimensionless) Yield compressive strain (offset = 0.2%) escy (dimensionless) Ultimate tensile strain estu (dimensionless) Ultimate compressive strain escu (dimensionless) Modulus of elasticity in tension Est (N/mm2) Modulus of elasticity in compression Esc (N/mm2)
+425.2 1091.2 +0.00200 0.00200 +0.1970 0.4100 +213,190 205,238
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Table 8 Comparison between experimental and theoretical values of: loads and resistant moments, at proportional and ultimate limits, for the T, R and P series of beams. Beam series
T R P
Experimental results (mean values)
Analytical results
Proportional limit
Ultimate limit
Proportional limit
Ultimate limit
Fp (kN)
Mp (kNm)
Fu (kN)
Mu (kNm)
Fp (kN)
Mp (kNm)
Fu (kN)
Mu (kNm)
18.684 22.148 28.516
11.210 13.289 17.110
25.576 37.886 35.859
15.346 22.732 21.515
16.624 21.504 23.817
9.975 12.903 14.290
24.739 33.303 34.870
14.843 19.982 20.922
F: Indicates the load. M: Indicates the resistant moment. p and u: Are subscripts which denote proportional and ultimate limit, respectively.
limit were obtained from the mean of the experimental data recorded by the SGs for the T series bending tests. From these values, the modulus of elasticity in the paths of tension (Ewt) and compression (Ewc) could be obtained. These values represented the local constants of the theoretical model. The ultimate compressive strain (ewcu) was assumed from Brunner [28]. Similarly, the constants for the steel bars were derived from the experimental data previously listed in Table 3. The theoretical model of the unreinforced, reinforced and reinforced-prestressed beams was tested with the above-mentioned material constants to predict the resistant moment at the proportional and ultimate limits during loading. 4.3. Comparison between experimental and theoretical results Using the procedures described previously, the resistant moments were calculated and compared with the corresponding experimental mean values for the T, R and P series of beams (Table 8). The analytical values agreed well with the experimental ones, which proved the validity of the theoretical model. The predicted values of the resistant moment were lower than the experimental values, indicating that the model was much more conservative. The results obtained in these tests showed that these reinforcement techniques were valid; nevertheless, they had technical issues, these techniques would be provided of detailed technological measures as discussed below. One technological problem was regarding the longitudinal slots along the beam span. The slots were open along the beam faces and facilitated the insertion and gluing operations; however, the steel bars were unconfined. Furthermore, the slots reduced the bonding surface and could cause buckling (Fig. 25). A solution could be to reduce the dimensions of the slot and close the open side by preparing a circular hole instead of an open slot during the lamination process of glulam. Another issue was regarding the two end plates. We observed that the thickness of these plates was important in supporting and reducing the strain peaks on the border of the beam due to shear stress, the strain peaks between two adjacent wood lamellas and the strain peaks between the glued steel-wood interfaces. The plates also helped the bond between the plate and the glulam to remain intact until failure occurred. In this study, the 15-mm thick steel plates ensured a relatively high stiffness by drastically reducing shear stress failure at the beam edge. However, the plates could be substituted by a rectangular tubular steel element with adequate stiffness to further prevent the shear failure at the beam border. Another issue was the inadequacy of the resorcinol glue used in the manufacturing process of the glulam beam. When reinforcements such as the steel rebars were used for the beams, the increasing load-carrying capacity required a more resistant glue to bond the lamellas.
Finally, the glulam-steel adherence could be enhanced by gluing corrugated steel bars. However, these questions could be explored in a specific study on the manufacturing process. 5. Conclusions The following conclusions can be drawn by analyzing the results of this study on glulam timbers (white spruce), which had simple reinforcements and a combination of reinforcements and prestressing: – Simple strengthening using steel bars located at the bottom and the top of the beams increased the maximum load-carrying capacity by 48.1% and the stiffness by 25.9%. – Strengthening with steel bars combined with prestressing increased the maximum load-carrying capacity by 40.2% and the stiffness by 37.9%. – The strains in both the simply reinforced and the reinforced-prestressed beams were approximately 50% lower in comparison with the strains in the unreinforced beams, which is favorable for the serviceability of a timber element. – The unreinforced timber beams failed in bending with a failure mode characterized by brittle traction due to broken fibers. The beams were not flexible, as already reported. – The reinforced beams presented a compression-initiated flexural failure mode characterized by increased ductility. – The reinforced-prestressed beams failed in bending with a compression failure mode, characterized by increased ductility. – The failure tensile strain in the reinforced and reinforcedprestressed beams significantly increased. The steel bars reduced the cracks opening and bordered the rupture into a narrow zone. – With the exception of one specimen, no debonding or delamination occurred between two bonded materials. This meant that the strength of glulam-steel was well utilized. – In a few specimens debonding between the adhesive and wooden lamellas occurred, this showed that the strength of the glulam-steel composite was not completely utilized (leading to premature failure), and the adhesives commonly employed in the manufacture of glulam element were used inadequately. – In one specimen, the steel bar ruptured. This suggested that the bar strength needed to be adequately designed. This study showed that steel bars could be used effectively to strengthen the flexural capacity of timber beams. These preliminary results confirmed the experimental evidence presented by other authors, which showed that the bending strength could be improved by strengthening and prestressing glulam beams with steel bars. Remarkably, a pronounced ductile zone in a reinforced beam was observed in this work, whereas unreinforced beams are completely brittle. However, further experimental work with
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a large number of specimens with additional numerical analysis is needed to investigate the problem. Acknowledgements The present work was funded by the University of Basilicata under Local Interest Scientific Research, E.F. 2006, Grant No 030886008. The authors would like to thank Davide Forlanelli of HenkelItaly for providing us the technical specifications of the adhesive. References [1] Maule A. Vantaggi della coazione del legno. Thesis. Venezia (Italy): University IUAV; 1999. [2] Plevris N, Triantafillou TC. FRP reinforced wood as structural material. J Mater Civ Eng, ASCE 1992;4(3):300–17. [3] Gentile C, Svecova D. Timber beams strengthened with GFRP bars: development and applications. J Comput Const 2002;6(1):11–20. [4] Borri A, Corradi M, Speranzini E. Travi in legno rinforzate con barre o con tessuti in fibre di carbonio. L’Edilizia 2001(4):48–56. [5] Habid JD, Tod EK, Stephen M. Effect of FRP reinforcement on low grade eastern hemlock glulams. University of Maine; 1996. [6] Galloway TL, Fogstad C, Dolan CW, Puckett JA. Initial tests of kevlar prestressed timber beams. University of Wyoming; 1996. [7] Guan ZW, Rodd PD. Study of glulam beams pre-stressed with pultruded GRP. Comput Struct 1995;83(28–30):2476–87. [8] Mark R. Wood–aluminum beams within and beyond the elastic range. Forest Prod J 1961;11(10):477–84. [9] Sliker A. Reinforced wood laminated beams. Forest Prod J 1962;12(1):91–6. [10] Bohannan B. Prestressed wood members. Forest Prod J 1962;12(12):596–602. [11] Peterson J. Wood beams prestressed with bonded tension elements. J Struct Eng, ASCE 1965;91(l):103–19. [12] Lantos G. The flexural behaviour of steel reinforced laminated timber beams. Wood Sci 1970;2(3):136–43. [13] Bulleit WM, Sandberg LB, Woods GJ. Steel-reinforced glued laminated timber. J Struct Eng, ASCE 1989;115(2):433–44. [14] Hemandez R, Davalos JF, Sonti SS, Kim Y, Moody RC. Strength and stiffness of reinforced yellow-poplar glued laminated beams. Res. Pap. FPL-RP-554, Madison (Wisconsin, USA): Department of Agriculture, Forest Service, Forest Products Laboratory; 1997. [15] Haiman M, Zagar M. Strengthening the timber glulam beams with FRP plates. In: Proceedings of 7th world conference on timber engineering, WCTE 2002, August 12–15, 2002, Malaysia: Perpustakaan Negara; 2002. p. 270–6.
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[16] Triantafillou TC, Deskovic N. Innovative prestressing with FRP sheets: mechanics of short-term behavior. J Eng Mech, ASCE 1991;117(7): 1652–72. [17] Triantafillou TC, Deskovic N. Prestressed FRP sheets as external reinforcement of wood members. J Struct Eng, ASCE 1992;118(5):1270–84. [18] Brunner M, Schnuriger M. Towards a future with ductile timber beams. In: Proceedings of 7th world conference on timber engineering, WCTE 2002, August 12–15, 2002, Malaysia: Perpustakaan Negara; 2002. p. 270–6. [19] Kim YJ, Harries KA. Modeling of timber beams strengthened with various CFRP composites. Eng Struct 2010;32:3225–34. [20] Issa CA, Kmeid Z. Advanced wood engineering: glulam beams. Constr Build Mater 2005;19:99–106. [21] Jasienko J. Experimental investigation into the force distribution in glued steel bars and wooden joints. Arch Civ Eng 2002(1) [Poland]. [22] Jasienko J. On modeling of behaviour of glued steel bar and wood joints. Arch Civ Eng 2002(2) [Poland]. [23] Nowak TP, Jankowski LJ, Jasienko J. Application of photoelastic coating technique in tests of solid wooden beams reinforced with CFRP strips. Arch Civ Mech Eng 2010(2) [Poland]. [24] De Luca V, Sabia D. Travi in legno lamellare precompresso con barre in acciaio – Prove Preliminari. L’Edilizia, Milano 2007;150:68–71. [25] De Luca V, Sabia D. Legno lamellare precompresso con barre in acciaio – Prima sperimentazione. Res rep 1-07, Potenza (Italy): Dipartimento DITEC, Università degli Studi della Basilicata; 2007b. p. 5. [26] De Luca V, Marano C. A comparison of unreinforced and reinforced glulam timber with steel bars. Eur J Technol Adv Eng Res 2011;2:45–54. [27] HBM. Analysis of the properties of strain gage measuring points on wood. Reports in applied measurement. Martin Stockmann, editor, Chemnitz (Germany): Institute of Mechanics, University of Chemnitz, ISSN:1614-9912, 2008. [28] Brunner M. On the plastic design of timber beams with a complex crosssection. In: World conference on timber engineering, British Columbia, Canada, July 31–August 3, 2000; 2000. [29] Fiorelli J, Alves DA. Analysis of the strength and stiffness of timber beams reinforced with carbon fiber and glass fiber. Mater Res 2003;6(2): 193–202. [30] Del Senno M, Piazza M, Tomasi R. A pseudo-ductile approach design of glued laminated timber beams. In: Proceedings of 8th world conference on timber engineering, WCTE 2004, Lahti, Finland; vol. II, 2004. p. 517–22. [31] Duarte A, Negrao J, Cruz E. Rehabilitation of timber beams with reinforced epoxy plates. In: Proceedings of 8th world conference on timber engineering, WCTE 2004, Lahti, Finland; vol. I, 2004. p. 351–6. [32] Kliger R, Johansson M, Crocetti R. Strengthening timber with CFRP or steel plates – short and long-term performance. In: Proceedings of 9th world conference on timber engineering, WCTE 2008, Miyazaki, Japan; vol. II, 2008. p. 517–22.
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Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Prestressed glulam timbers reinforced with steel bars Vincenzo De Luca ⇑, Cosimo Marano Department DITEC, University of Basilicata, 85100 Potenza, Italy
a r t i c l e
i n f o
Article history: Received 2 February 2011 Received in revised form 22 October 2011 Accepted 24 November 2011 Available online 29 December 2011 Keywords: Glulam timber beams Timber structures Timber constructions Prestressed glulam timber Steel reinforcements Bending tests
a b s t r a c t This paper discusses a series of four-point bending tests that were conducted to failure on unreinforced, reinforced and reinforced-prestressed glue laminated (glulam) timber beams with steel-bars in a simplysupported scheme to determine their flexural behavior. The cross sectional ratio between the steel and the wood was 0.82%. To increase the level of reinforcement, some reinforced beams were prestressed by applying a moderate force to the lower bar. The experimental and numerical data provided the load–deflection, load–strain relationships and strain profiles of the tested beams. The results of the reinforced beams showed that the mechanical strength, the load-carrying capacity and the stiffness for both the simple and prestressed beams were enhanced compared to the unreinforced beams. For the simply reinforced beams, the stiffness increased by 25.9%, the ultimate load increased by 48.1% and the ductility increased by 43.8%. For the reinforced and prestressed beams, the stiffness increased by 37.9%, the ultimate load increased by 40.2%, and the ductility increased by 79.1%. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction To improve the seismic safety of a complex structure, it is crucial to design the structure based on the concept of ductile response because the concept is defined by ‘‘post-elastic resources’’. To limit our interest to ‘‘post-elastic resources’’, such as the structural glued laminated (glulam) timber, it is worthwhile to note the relevant scientific research. The field of ‘‘lamped ductility’’ is concerned with connections between structural elements; however, few studies and advances are notable in the field of ‘‘widespread ductility’’, especially when traditional structural materials such as steel and reinforced concrete are considered. Current research on timber construction often neglects the post-elastic behavior of a single structural element. This may be insufficient for structural safety when static loads of variable magnitudes are present on a house floor or in a bridge deck. Within this research field, one possible strategy to improve the mechanical properties of a beam of glulam timber is to insert steel bars and apply a moderate level of prestress to the bars placed in the face of the beam under tension. This strategy could provide adequate levels of widespread ductility.
2. Literature review Even though there are no specific and systematic studies on glulam timbers reinforced with steel bars within the scientific
⇑ Corresponding author. Tel.: +39 0971 20 5438; fax: +39 0971 20 5429. E-mail address: [email protected] (V. De Luca). 0950-0618/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.conbuildmat.2011.11.016
literature, the effects of prestressed glulam timber are evident in scientific research and technological applications [1]; the combination of traditional glulam timber with steel reinforcement bars has been used in fields such as house floors and roofs. Research on the application of metal reinforcements are rarely published; more recent research projects are focused on the application of fiber reinforced polymer (FRP) reinforcements [2] and on the sometimes transversal prestressing of laminated wood by reinforcing fibers, particularly in the field of bridge beam recovery [3–7]. Early studies used metal reinforcements to strengthen timber beams; unfortunately, none of these systems of reinforcement was successfully used in the construction market. The long-term reliability and efficiency of these reinforcement systems are still unknown due to the lack of experimental data. Early research adopted both strengthening and prestressed techniques using steel or fiber reinforced polymer (FRP), reinforced bars or reinforced plates. Studies by Mark [8], Sliker [9], Bohannan [10], Peterson [11], Lantos [12] and Bulleit et al. [13] tested the effect of prestressing using steel plates or cables bonded in the tension zone of glulam beams. Other studies on CFRP reinforcements were performed by Hemandez et al. [14] and Haiman and Zagar [15]. Drawbacks such as buckling, relaxation of the pretension force due to creep, separation and delamination of bonded layers, the transmission of the prestressing force toward the laminate and the occurrence of adhesive high shear stresses localized at both the edges of a beam were observed in certain works [16–18]. However, all these studies reported a lower statistical variance in the strength of strengthened beams compared with the unstrengthened ones. More recently, some researchers studied the use of steel bars in reinforcing wood. Kim and Harries [19] and Issa and Kmeid [20]
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compared experiments on glulam beams reinforced by plates. Their results confirmed the importance of the reinforcements in enhancing the overall mechanical behavior of a timber beam. Jasien´ko [21,22] studied the interaction of a glued-in steel bar over the cross section of a reinforced wood element. The experimental data showed an irregular distribution along the bonding joint of normal and shear stresses. Nowak et al. [23] experimented with an innovative technique using a photoelastic coating to measure the strain distribution between the timber beams and their reinforcing elements. The above experimental evidence showed that reinforcing timber beams with steel reinforcements could greatly improve the strength, stiffness and load-carrying capacity of the beams; less deformation, less tensile stresses at the tension face, and more compressive stresses at the compression face would be observed. Additional benefits could be achieved when additional reinforcements are added in the compressive face of a structure while a moderate level of pretension is applied to the bars in the tensile face of a timber element. The authors of this paper have already begun the study of reinforcement steel bars with a general-purpose research project [24–26]. This is a timely research subject for the following reasons: – there is a lack of scientific literature on beams reinforced with steel bars, and even less literature on those strengthened with prestressed reinforcements; – the few existing works on this subject are outdated and use obsolete adhesives; – stronger and more novel adhesives are available. In this paper, we investigated the strengthening solutions for glulam timbers by comparing the results from laboratory tests and numerical analysis. Experimental bending tests on a four-point scheme were conducted on glulam beams made of white spruce and reinforced with longitudinal steel bars. The steel bars were inserted and glued in the tensile and compressive faces of the beam, and the bars within the tensile face of certain specimens were prestressed to determine the level of strengthening provided by the bars. A theoretical model for the composite wood–steel with nonlinear stress–strain paths was then applied to calculate the moment of rupture. Subsequently, the experimental results were compared with the theoretical predictions. The main objective of this work is to enhance the overall strength and stiffness of timber beams and to redistribute the stress field in the cross section of the beams; we also aim to create a pronounced region of ductility. 3. Materials and methods A total of 12 white spruce glulam beams were machined with a cross section of 80 mm 117 mm and a length of 2000 mm. The reinforced beams were further machined with two longitudinal slots at the top and bottom faces. The slots were 20 mm deep and 20 mm wide. The beams were then divided into three series (Table 1):
(1) The T series, which included three unreinforced simple beams. (2) The R series, which included three beams reinforced with steel bars bonded to wood by an adhesive. (3) The P series, which included six reinforced and prestressed beams. The reinforcing steel bars were bonded to the wood by an adhesive, and the bottom bars were pre-tensioned by a force of 18 kN. 3.1. Material specifications The glulam beams, steel bars and adhesive used in the present work were furnished by the manufactures and fabricated as described below. 3.1.1. Glulams The white spruce glulam was characterized by its manufacturer as grade GL28 according to the standard prEN1194; its mechanical characteristics are listed in Table 2. 3.1.2. Steel bars The steel bars were characterized as grade C45 by its manufacturer according to the standard UNI EN 10083/1998. The steel bars were also directly characterized using experimental tests. Specifically, steel bar number 9 was tested in tension and compression to determine the stress–strain path of the material. The steel bars that underwent tension tests were 10 mm in diameter and cut to a length of 500 mm. The steel bars for compression tests were 10 mm in diameter and 18 mm long. The tests were performed with a Universal Press Tecnotest F60 with a 600 kN load capacity. The rate of loading was 5 N/min for tension tests and 5 N/min for compression tests. The experimental values of the mechanical characteristics of the steel bars are listed in Table 3. 3.1.3. Adhesive The adhesive used in this experiment was a two-component polyurethane resin (PurbondÒ CR 421) manufactured without solvents or formaldehyde. This adhesive was suitable for anchoring the glued-in steel rebar in the wooden components of structural beams. The mechanical characteristics of the adhesive were furnished by its manufacturer (as shown in Table 4). Smooth steel bars without corrugated surfaces were used in the reinforcement technique adopted in this experiment. Before inserting and bonding the steel bars along the slots on the beams, the bars were carefully cleaned by a nonionic surfactant and detergent to eliminate dust or grease. The cross sections of all the specimens are shown in Fig. 1. Two 15-mm thick perforated steel plates were bonded to each end of the beams by the adhesive (Fig. 2). The reinforcing steel bars with a diameter of 10 mm were cut to 2100 mm long and bonded to the beams through the longitudinal slots by the adhesive (Fig. 2). Both ends of each bar were then blocked by the above-mentioned plates and fixed by bolts. For the prestressed beams, a tensioning stage, involving an 18 kN pretension force that was applied by a mechanical tensioning device to the bottom bar, occurred before the bars were fixed to the beams (Figs. 3 and 4). The adhesive was allowed to set for more than 30 days before testing. The experimental stages of the work were executed at room temperature in the Material Laboratory of the DITEC Department, University of Basilicata, Italy. A simply-supported four-point bending scheme was adopted (Fig. 5) to apply uniform bending without any shear in the middle of the beam span; the beam had a load span of 1800 mm and a support span of 600 mm. The roller supports were covered by a rubber sheet to reduce the bearing failure effect. Bending tests were executed with an electro-mechanical press (model PMA10 Galdabini, as shown in Fig. 6), which was able to digitally control the applied load and the frame displacement pattern. The test equipment consisted of a force transducer (with a load cell that had a carrying capacity of 100 kN) and a linear variable displacement transducer (LVDT) that were used to measure the total force and the mid-span deflection, respectively. Electric resistance strain gauges (SG) made by HBMÒ were distributed at six locations along the height of the beam at mid-span to measure the strains of the horizontal fibers. The SGs had measuring grid lengths of 10 mm for the ‘‘T’’ and ‘‘R’’ series and a grid length of 20 mm for the ‘‘P’’ series. For reinforced beams, two more SGs were installed at the mid-span: one was installed on the bottom bar to measure the tensile strain, and one was installed on the top bar to measure the
Table 1 Reinforcement type, diameter and cross sectional ratio between the steel and the wood. Specimen code
Number of specimens
Reinforcements Type
T1, T2, T3 R1, R2, R3 P1, P2, P3, P4, P5, P6
3 3 6
Total
12
Diameter (mm)
Cross-section ratio steel/wood (%)
Prestressing (kN)
Bottom
Top
Bottom
Top
Bottom
Top
Bottom
None Steel bar Steel bar prestressed
None Steel bar Steel bar
– 10 10
– 10 10
0.00 0.82 0.82
0.00 0.82 0.82
– 0 18.00
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Table 2 Glulam manufacturer specifications (N/mm2). Material specification
Value
Bending strength, characteristic value Tensile strength parallel to the fiber, characteristic value Tensile strength perpendicular to the fiber, characteristic value Compression parallel to the fiber, characteristic value Compression perpendicular to the fiber, characteristic value Shear strength, characteristic value Modulus of elasticity parallel to the fiber, average value Modulus of elasticity parallel to the fiber, 5% fractile value Modulus of elasticity perpendicular to the fiber, average value Tangential modulus of elasticity, average value
28 19.5 0.45 26.5 3.0 3.2 12,600 10,200 420 780
Table 3 Steel bar characteristics – summary of results (number of specimens tested: 9). Characteristic Ultimate Ultimate Ultimate Ultimate Modulus Modulus
tensile stress (N/mm2) compressive stress (N/mm2) tensile strain (dimensionless) compressive strain (dimensionless) of elasticity in tension (N/mm2) of elasticity in compression (N/mm2)
Mean
5% Fractile
675.8 1510.0 0.2256 0.4944 342,375 342,588
425.2 1091.2 0.1970 0.4100 213,190 205,238 Fig. 2. Procedure for bonding bar reinforcements in the glulam beams.
Table 4 Adhesive manufacturer specifications. Specification
Value
Tensile strength at approx. 2% elongation/at break (N/mm2) Elongation at break (%) Compressive strength (at 20 °C) (N/mm2) Modulus of elasticity (at 20 °C) (N/mm2)
25/30 2.0 79.9 1560
compressive strain. The placement of the SGs is schematically illustrated in Fig. 7. The SGs were bonded by the adhesive HBM X60 and connected by a Wheatstone bridge circuit with an amplifier in a full-bridge configuration. Another SG was mounted in the Wheatstone bridge circuit for temperature compensation [27]. The computer controlling the testing machine recorded the measured middle displacement (mm) and load (kN) at a sampling rate of 0.01 Hz using software. In addition, the SGs readings were recorded every two seconds by a computerized data acquisition system (CR10 CampbellÒ, as shown in Fig. 8). Loading was continued beyond peak load in the post-failure zone. All bending tests were performed with controlled displacement with a test speed of 4 mm/min. The results between the different types of beam tests were presented in graphs and tables for comparison. Graphs illustrated load–deflection and load–strain curves along with the strain profiles at selected loads. The strength improvement is shown through the changes in stiffness, load carrying capacity, the elastic modulus, ductility, and the mid-span deflection at the proportional limit, the ultimate limit and post-failure. The elastic modulus is calculated using the linear-elastic behavior for each beam during the initial deformation path by the following relationship:
E¼
Fp a ð3L2 4a2 Þ 48I dp
ð1Þ
where E (kN/mm2): elastic modulus; Fp (kN): total applied load at the proportional limit; a (mm): edge support distance; L (mm): beam span; I (mm4): inertia moment of gross section; and dp (mm): mid-span deflection at the proportional limit. The ductility is defined by:
lf ¼ df =du
ð2Þ
where lf (dimensionless): ductility; du (mm): deflection at ultimate load; and df (mm): post-failure deflection.
3.2. Theoretical model A theoretical model of the beam in bending was used to predict the resistant moment until the proportional limit, Mp, and the ultimate moment, Mu, were reached under loading. The analytical values were then compared with experimental ones. In scientific literature, similar models have been used by many researchers to analyze the stress distribution in the cross section of a reinforced glulam timber [28–32]. The model adopted here assumed the following: – the cross sections remained planar after they were deformed by bending; – there was no slipping between the adhesive and the adjacent wood lamellas or between the steel rebar, the adhesive and the glulam; – the stress–strain relationship for the glulam was elastic-brittle in tension, and elastic-perfectly plastic in compression (Fig. 9); – the stress–strain relationship for the steel bar in tension and in compression was elastic-perfectly plastic (Fig. 10).
Fig. 1. Details of the cross section types: unreinforced beams, simply strengthened beams with upper and lower steel bar, 10 mm in diameter, and strengthened beams with an upper steel bar, 10 mm in diameter, and a lower prestressed bar, 10 mm in diameter.
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R1 ¼ As1 f1 ; d1 ¼ ds1 R2 ¼ ðp bÞ f2 ; d2 ¼ p 1=2
ð3:1Þ ð3:2Þ
R3 ¼ ½ðyn pÞ b 1=2 f3 ; R4 ¼ ½ðh yn Þ b 1=2 f4 ; R5 ¼ As2 f5 ; d5 ¼ ds2
ð3:3Þ ð3:4Þ ð3:5Þ
d3 ¼ ðyn pÞ 1=3 d3 ¼ yn þ ðh yn Þ 2=3
where fi is the stress value; h, the cross section depth; b, the cross section width; p, the depth of the plastic stress diagram of the glulam, and i is a subscript indicating: i = 1: indicates the steel bar under compression; i = 2: indicates the compressive face of the plastic part of the glulam; i = 3: indicates the compressive face of the elastic part of the glulam; i = 4: indicates the tensile face of the glulam; i = 5: indicates the steel bar under tension. The curvature v is defined as:
v ¼ je2 j=yn
ð4Þ
The strains (ei) in the cross section could be calculated by assuming the position of the neutral axis according to the assumption that the sections remain planar (as shown in Fig. 11):
e ¼ v yi
ð5Þ
where yi is the distance of the centroid of the areas away from the neutral axis:
Fig. 3. The mechanical tensioning device for applying the pretension to bar.
y1 ¼ ðyn ds1 Þ
ð6:1Þ
y2 ¼ yn y3 ¼ ðyn pÞ y4 ¼ ðh yn Þ
ð6:2Þ ð6:3Þ ð6:4Þ
y5 ¼ ds2 yn
ð6:5Þ
From the values of strain (ei), the corresponding stress values (fi) of wood and steel could be calculated according to the previously assumed stress–strain relationships (Figs. 9 and 10, respectively). Then, the equilibrium of the internal force requires that: 5 X
Ri þ N p ¼ 0
ð7Þ
i
where Np is the prestressing force acting on the steel bar on the bottom of the beam. The resultant resistant moment could be computed as:
M¼
5 X
Ri di þ N p d5
ð8Þ
i
Note that in the unreinforced beam, the cross sections of the steel bars and the prestressing force were clearly assumed to equal zero; the prestressing force was assumed to equal zero in the simply reinforced beam. 3.3. Material properties for theoretical model The values used in the theoretical model to calculate the mechanical characteristics of the glulam and steel were carefully derived from the experimental data recorded. Therefore, the results from the bending tests of the unreinforced timber beams (the T series of specimens) were used as the mechanical constants for glulam (shown in Fig. 9); the 5% fractile values of the experimental results of the steel bars in tension and compression were used as the mechanical constants for steel (shown in Fig. 10).
Fig. 4. Detail of the attachment to steel bar end in the mechanical tensioning device for applying the pretension to bar.
The geometric characteristics of the composite beams used in the numeric calculations within the theoretical model were the same as those used in the calculations based on experimental data. Based on the stress–strain patterns of the materials, the resistant bending moment could be evaluated using the equilibrium condition of the compressive and tensile forces on the cross section with respect to, for instance, the neutral axis; this could be done by considering the tension to be positive and the compression to be negative. The non-linear pattern of the moment – curvature relationship of the cross sections of the beam was therefore analyzed incrementally within an iterative numerical scheme starting from an initial assumption of the curvature. This procedure allowed the neutral axis depth, yn, to be computed until the ultimate condition was reached in either the wood or the steel. The internal forces (Ri) and the corresponding lever arms (di) (for i = 1, 2, . . . , 5) with respect to the top face of the cross sections were defined by the following (as shown in Fig. 11):
4. Results and discussion The test results (Fig. 12 shows a typical stage of a bending test) for the strengthened beams and strengthened-prestressed beams were compared with those for the unreinforced beams to determine their behavior in terms of strength, deflection, stiffness and ductility. These results are shown in Figs. 13–21 and summarized in Table 5. The numerical calculations were executed using the theoretical model and the relative material parameters were derived as described in the previous chapter. 4.1. Experimental results The load–deflection curves of the unstrengthened beams (in the T series), the strengthened beams (the R series), and the strengthened-prestressed beams (the P series) are shown in Figs. 13–15, respectively:
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Fig. 5. Testing set-up for bending test of the glulam beams.
Fig. 6. Testing machine and digital equipment used in the research. Fig. 8. Datalogger system for data recording of the strain gauges.
– Fig. 13 plots the load–deflection curves of the three unreinforced beams (T1, T2 and T3). The stiffness of a beam without any reinforcement remained almost constant, and there was no residual deflection after the first loading range. The initial part of the curve remained linear until the timber cracked at or shortly beyond the maximum load in the tension zone.
– Fig. 14 plots the load–deflection curves of the three strengthened beams (R1, R2 and R3). For all three curves, the initial path was linear until the timber cracked at approximately the maximum load in the tension zone. Then, the stiffness gradually decreased until a subsequent relative maximum load was
Fig. 7. Strain gauges placement along the beam depth at the mid-span.
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reached, and crushing began in the compression zone. Finally, failure occurred in the compression zone and caused a drop in load. – Fig. 15 illustrates the load–deflection curves of the six strengthened-prestressed beams (P1–P6). For all six curves, the initial path was linear until the timber cracked under the maximum load in the tension zone. Then the beams deflected consistently under a residual stress, indicating high ductility. The ultimate rupture occurred in the compression zone, corresponding to a final drop in the plot.
load-carrying capacity than the unreinforced beams. In those figures, the load corresponding to the ultimate load-carrying capacity was well defined. The modulus of elasticity of a beam was calculated according to Eq. (1), where the load at the proportional limit was estimated at a minimal correlation coefficient of 0.9975 by linear regression applied to the points in the linear portion of the load–deflection curve. The results for all the beams are reported in Table 5 with the means and standard deviations. Table 5 also reports the comparison between the deflection and load at the proportional limit, the ultimate limit and at post-failure for the un-strengthened, strengthened and strengthened-prestressed beams. The ductility of the beam was calculated according to Eq. (2) and reported in Table 5 for all beam types. In addition, the strength increase calculated over the strength of the unreinforced beams is reported in Table 5 for all beams. The results showed that strengthening was effective in the reinforced beams compared to the unreinforced beams: the maximum load capacity increased by 48.1%, the elastic modulus increased by 25.9% and the ductility increased by 43.8%. Furthermore, the deflection at post-failure of all the reinforced beams was greater than that of the unreinforced beams. The strength improvements in the reinforced-prestressed beams were more pronounced: the maximum load capacity increased by 40.2%, the elastic modulus increased by 37.9%, and the ductility increased by 79.1%. However, the deflection at post-failure of all the reinforced beams was greater than that of the unreinforced beams. The steel bar reinforcement in the timber beams increased the bending stiffness of the glulam timber element and reduced the deflection compared to an unstrengthened beam at the same load levels. We should note that the longitudinal slots used to insert the bars weakened the beam by disturbing the grain while reducing the moment of inertia and the ultimate load-carrying capacity of the beam. Furthermore, the steel bar in one reinforced beam was seen to break, indicating that the glulam-steel composite structure needed steel bars with adequate strength. The bar strength could be estimated by a suitable analytical model of the overall system. Typical load–strain curves, which are discussed as follows, for the unreinforced, simply reinforced and reinforced-prestressed timbers are illustrated in Figs. 16–18, respectively.
Certain drops in load observed in the above curves corresponded to internal cracks of the beam. The cracks were caused by delamination, which occurred due to slipping between two bonded laminates. We should note that this observation only concerned the glulam adhesive and not the overall composite system of glulam and the steel bars. As clearly indicated in Figs. 13–15, all of the simply reinforced beams and the reinforced-prestressed beams had higher ultimate
– The load–strain relationship for the unreinforced beams (shown in Fig. 16) remained nearly linear in both the compression and tension zone. Cracking occurred at 22 kN and corresponded to drops in the load–deflection plot (Fig. 13). – For the simply reinforced beams, the load–strain distribution (shown in Fig. 17) remained linear until cracks initiated at a load of 18 kN for both the compression and tension zones. Cracking could be seen as discontinuities in the load–deflection
Fig. 9. Stress–strain relationship for glulam adopted in the theoretical model.
Fig. 10. Stress–strain relationship for steel bar adopted in the theoretical model.
Fig. 11. Cross section of the timber beam with the notations of the theoretical model.
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Fig. 12. Typical stage of a bending test. Fig. 15. Load–deflection curve for the strengthened-prestressed beams (P series), with steel bars, 10 mm in diameter.
Fig. 13. Load–deflection curve for the unstrengthened beams (T series) (from [26]).
Fig. 16. Typical load–strain curve for an unstrengthened beam (T2).
Fig. 14. Load–deflection curve for the simply strengthened beams (R series), with steel bars, 10 mm in diameter (from [26]).
curve (Fig. 14), and it occurred at a load of 38 kN in the load– strain curve. After cracking, the load–strain curve became non-linear as the stiffness progressively decayed due to the cracks opening through the tension region.
Fig. 17. Typical load–strain curve for a simply strengthened beam (R2), with steel bars, 10 mm in diameter.
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Fig. 18. Typical load–strain curve for a strengthened–prestressed beam (P6), with steel bars, 10 mm in diameter.
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Fig. 21. Typical strain profile for a strengthened–prestressed beam (P6), with steel bars, 10 mm in diameter, at selected loads.
compression and tension zones (Fig. 18). Cracking at a load of 39 kN was observed as discontinuities in the load–deflection curve (Fig. 15). After cracking, the stiffness progressively decayed because cracks opened through the tension region, and the load–strain curve became non-linear. Graphs of the strain profiles (that is, the strain versus beam depth) are plotted in Figs. 19–21 for typical specimen types at four selected load levels. The position of the neutral axis along the depth of the beam could be determined from those graphs because it varied as the load increased until failure. The strain profiles, which plot the strain gauge measures along the beam height, are useful in the analysis of changing relative neutral axis position due to beam strengthening:
Fig. 19. Typical strain profile for an unstrengthened beam (T2), at selected loads.
Fig. 20. Typical strain profile for a simply strengthened beam (R2), with steel bars, 10 mm in diameter, at selected loads.
– For the reinforced-prestressed beams, the strain distribution along the depth of the beam remained linear until the cracks initiated in the tensile region at a load of 24 kN for both the
– in the unreinforced beam, the neutral axis was localized (Fig. 19) at approximately +2 to +5 mm of the beam depth in the compressive region of strain; – in the simply reinforced beam, the neutral axis position (Fig. 20) was at approximately 5 to 9 mm of the beam depth in the tensile region of strain, a region opposite of that in an unreinforced beam. The steel rebars caused the neutral axis depth to shift from the compression to the tension region of strain; – in the reinforced-prestressed beam type (Fig. 21), the neutral axis position was shifted to the tension region of strain; however, it was only slightly shifted to approximately 4 mm. As clearly shown in Figs. 19–21, the strains in the typical reinforced and reinforced-prestressed beams were approximately 50% lower than the strains in typical unreinforced beams. These results showed that simple bar reinforcements shifted the neutral axis position downward, implying a more favorable redistribution of the stress field in the section. Less tensile stresses were observed at the tension face, and more compressive stresses were observed at the compression face as the stresses were transferred to the steel bars inserted in the tension and compression regions of the section. A similarly positive effect occurred in the reinforced-prestressed beam; however, it was partially reduced by prestressing because the neutral axis was slightly redirected toward the compression region. All of the beams first cracked in the tension edge, they then failed in a different mode depending on their beam type:
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Table 5 Comparison between the deflection and load at the proportional, ultimate limit, at post-failure and ductility for the tested beams – experimental results [26]. Specimen type
Beam code
Elastic Modulus
At proportional limit
At ultimate limit
Load Fp (kN)
Mid-span deflection du (mm)
Load
E (kN/mm )
Mid-span deflection dp (mm)
T1 T2 T3
8.597 6.604 7.703
16.3 34.0 25.0
14.064 22.569 19.419
45.9 34.0 45.7
27.237 22.569 26.923
46.3 34.2 59.1
1.011 1.008 1.293
Mean
7.635
25.1
18.684
41.8
25.576
46.5
1.104
St. dev.
0.998
8.8
4.300
6.8
2.609
12.4
0.164
R1 R2 R3
10.030 10.392 8.414
22.1 18.3 29.2
22.087 18.997 25.362
41.0 57.3 50.3
36.117 38.983 38.560
63.7 80.5 90.7
1.554 1.403 1.805
Mean
9.612
23.2
22.148
49.5
37.886
78.3
1.587
St.dev.
1.053
5.5
3.183
8.2
1.547
13.6
0.203
P1 P2 P3 P4 P5 P6
10.401 11.787 10.706 10.004 9.831 10.439
30.0 27.5 29.9 23.6 28.6 22.8
30.717 31.750 31.621 24.472 27.995 24.540
33.8 51.7 58.0 28.2 29.8 43.7
33.711 46.220 37.719 28.735 29.040 39.731
62.6 68.5 70.5 85.6 62.9 101.5
1.850 1.325 1.215 3.035 2.112 2.322
Mean
10.528
27.1
28.516
40.9
35.859
75.2
1.977
St. dev.
0.693
3.1
3.388
12.3
6.748
15.3
0.675
2
Un-reinforced glulam beam, T series (from [26])
Steel reinforced glulam beam, R series (from [26])
Steel reinforced plus pre-stressed glulam beam, P series
Fu (kN)
At post-failure
Ductility
Mid-span deflection df (mm)
lf (dimensionless)
Increment reinforced versus un-reinforced beam
Mean
25.9%
7.6%
18.5%
18.4%
48.1%
68.2%
43.8%
Increment reinforced-prestressed versus unreinforced beam
Mean
37.9%
7.8%
52.6%
2.3%
40.2%
61.6%
79.1%
Increment reinforced-prestressed versus simple reinforced beam
Mean
9.5%
16.6%
28.7%
17.5%
5.4%
3.9%
24.5%
– All of the unreinforced beams (the T series) failed due to tension failure from brittle tension in which crushing occurred in the tension region at the maximum measured load; no crush was observed in the compression region, and most of the wood fibers below the neutral axis were stretched. Fig. 22 shows a typical beam subjected to this failure mode. – The failure of the simply reinforced beams (the R series) was tension-initiated, followed by compression failure. The beams exhibited crushing initially in the tension zone and then in the compression zone at maximum load. This type of failure is shown in Fig. 23.
Fig. 23. Failure in mixed tension–compression of a typical reinforced beam (R2).
– The prestressed beams (the P series) underwent compression failure in which the beams exhibited crushing in the compression zone at maximum load. This type of failure (shown in Fig. 24) occurred when the prestressed bar was used to bear the traction in the tension zone, where the amount of the stretched wooden fiber was very low and limited to the bottom face.
Fig. 22. Failure in tension of a typical unreinforced beam (T3).
In a few cases of the reinforced and reinforced-prestressed specimens, failure was preceded by singular types of crushing such as the following:
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forcement, were not available because the strain measurements of this work were limited to only the mid-span section. All these issues could be addressed in a future study. Generally, the strain profile that plotted the strain gauge measures along the beam height remained approximately linear along the section depth within the elastic path. The strain profiles revealed no significant strain peaks at least in the elastic path and just below the ultimate phase. Shear stress failure on the edge beam between two lamellas was observed; yet no shear stress failure of glue and wood–steel was observed on the edge sections below the ultimate phase. On the contrary, significant debonding and strain peaks were often observed between two adjacent wood lamellas, particularly when they were close to the failure phase. In addition, the two thick plates glued to each end of the beams in all the simply reinforced and reinforced-prestressed beams often helped to avoid the delamination between two wooden lamellas; this fact highlighted the importance of the two stiff end plates. 4.2. Theoretical results
Fig. 24. Failure in compression of a typical reinforced–prestressed beam (P5).
– the delamination along the bonded layer between two wooden lamellas; – the failure of the tension steel bar; – the debonding of the bar from the slot in the timber and the buckling of compressed steel bars (see Fig. 25 for a simply reinforced beam). Remarkably, the addition of steel bars shifted the failure mode from the brittle tension mode to the compressive mode despite the ductile nature of the bars. These observations demonstrated the effectiveness of the reinforcing techniques by using simple steel rebars and by prestressing. However, the latter reinforcement technique could further improve the effectiveness as shown in Table 5. As already highlighted in the analysis of strain profiles and relative neutral axis position, the steel bars were clearly bearing stress in the simple and the reinforced-prestressed beams. However, additional quantitative details such as the optimization of the ‘‘wood–steel’’ system, which would require a comparison with many other specimens prepared at various percentages of rein-
All constants on which the theoretical model was based can be defined for numeric calculations as follows (they were also reported in Table 6 for glulam and Table 7 for the steel bar): Using the mean load Fp at the proportional limit (supplied from the T series bending tests), the bending moment Mp at the proportional limit can be computed. Then, the stresses at the cross section at the proportional limit could be calculated. The strains of the bottom and top fibers (ewtu and ewcy, respectively) at the proportional
Table 6 Mechanical constants in bending, strength, strain and modulus of elasticity of glulam, adopted in the theoretical model. Constants
Computed/adopted value
Ultimate tensile stress fwtu (N/mm2)
11210:4 Nm ¼ Wpp ¼ 182;520 ¼ þ61:42 mm3
Compressive stress at yielding fwcu (N/ mm2) Ultimate tensile strain ewtu (dimensionless) Compressive strain at yielding ewcy (dimensionless) Ultimate compressive strain ewcu (dimensionless) Modulus of elasticity in tension Ewt (N/mm2) Modulus of elasticity in compression Ewc (N/mm2)
Nm ¼ Wpp ¼ 11210:4 ¼ 61:42 182;520 mm3
M M
=+0.002574 =0.003244 =0.012000 2
þ61:42 N=mm ¼ efwtu ¼ 0:002574 ¼ þ23; 862 dimensionless wtu 2
61:42 N=mm ¼ efwcu ¼ 0:003244 ¼ 18; 933 dimensionless wcy
Where F p ¼ þ18; 684 N: is the load at the proportional limit; Mp ¼ F p a ¼ þ18; 684 N 600 mm ¼ þ11; 210:4 Nm: is the bending moment at the proportional limit; a ¼ 600 mm: is the edge support distance; 2 W p ¼ bh6 ¼ 182; 520 mm3 : is the moment of resistance of the cross section; b ¼ 80 mm: is the width of the beam; and h ¼ 117 mm: is the depth of the beam.
Table 7 Mechanical constants in bending, strength, strain and modulus of elasticity of steel bar, adopted in the theoretical model.
Fig. 25. Buckling of a compressed steel-bar in a reinforced beam (R5).
Constants
Adopted value
Ultimate tensile stress fstu (N/mm2) Ultimate compressive stress fscu (N/mm2) Yield tensile strain (offset = 0.2%) esty (dimensionless) Yield compressive strain (offset = 0.2%) escy (dimensionless) Ultimate tensile strain estu (dimensionless) Ultimate compressive strain escu (dimensionless) Modulus of elasticity in tension Est (N/mm2) Modulus of elasticity in compression Esc (N/mm2)
+425.2 1091.2 +0.00200 0.00200 +0.1970 0.4100 +213,190 205,238
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Table 8 Comparison between experimental and theoretical values of: loads and resistant moments, at proportional and ultimate limits, for the T, R and P series of beams. Beam series
T R P
Experimental results (mean values)
Analytical results
Proportional limit
Ultimate limit
Proportional limit
Ultimate limit
Fp (kN)
Mp (kNm)
Fu (kN)
Mu (kNm)
Fp (kN)
Mp (kNm)
Fu (kN)
Mu (kNm)
18.684 22.148 28.516
11.210 13.289 17.110
25.576 37.886 35.859
15.346 22.732 21.515
16.624 21.504 23.817
9.975 12.903 14.290
24.739 33.303 34.870
14.843 19.982 20.922
F: Indicates the load. M: Indicates the resistant moment. p and u: Are subscripts which denote proportional and ultimate limit, respectively.
limit were obtained from the mean of the experimental data recorded by the SGs for the T series bending tests. From these values, the modulus of elasticity in the paths of tension (Ewt) and compression (Ewc) could be obtained. These values represented the local constants of the theoretical model. The ultimate compressive strain (ewcu) was assumed from Brunner [28]. Similarly, the constants for the steel bars were derived from the experimental data previously listed in Table 3. The theoretical model of the unreinforced, reinforced and reinforced-prestressed beams was tested with the above-mentioned material constants to predict the resistant moment at the proportional and ultimate limits during loading. 4.3. Comparison between experimental and theoretical results Using the procedures described previously, the resistant moments were calculated and compared with the corresponding experimental mean values for the T, R and P series of beams (Table 8). The analytical values agreed well with the experimental ones, which proved the validity of the theoretical model. The predicted values of the resistant moment were lower than the experimental values, indicating that the model was much more conservative. The results obtained in these tests showed that these reinforcement techniques were valid; nevertheless, they had technical issues, these techniques would be provided of detailed technological measures as discussed below. One technological problem was regarding the longitudinal slots along the beam span. The slots were open along the beam faces and facilitated the insertion and gluing operations; however, the steel bars were unconfined. Furthermore, the slots reduced the bonding surface and could cause buckling (Fig. 25). A solution could be to reduce the dimensions of the slot and close the open side by preparing a circular hole instead of an open slot during the lamination process of glulam. Another issue was regarding the two end plates. We observed that the thickness of these plates was important in supporting and reducing the strain peaks on the border of the beam due to shear stress, the strain peaks between two adjacent wood lamellas and the strain peaks between the glued steel-wood interfaces. The plates also helped the bond between the plate and the glulam to remain intact until failure occurred. In this study, the 15-mm thick steel plates ensured a relatively high stiffness by drastically reducing shear stress failure at the beam edge. However, the plates could be substituted by a rectangular tubular steel element with adequate stiffness to further prevent the shear failure at the beam border. Another issue was the inadequacy of the resorcinol glue used in the manufacturing process of the glulam beam. When reinforcements such as the steel rebars were used for the beams, the increasing load-carrying capacity required a more resistant glue to bond the lamellas.
Finally, the glulam-steel adherence could be enhanced by gluing corrugated steel bars. However, these questions could be explored in a specific study on the manufacturing process. 5. Conclusions The following conclusions can be drawn by analyzing the results of this study on glulam timbers (white spruce), which had simple reinforcements and a combination of reinforcements and prestressing: – Simple strengthening using steel bars located at the bottom and the top of the beams increased the maximum load-carrying capacity by 48.1% and the stiffness by 25.9%. – Strengthening with steel bars combined with prestressing increased the maximum load-carrying capacity by 40.2% and the stiffness by 37.9%. – The strains in both the simply reinforced and the reinforced-prestressed beams were approximately 50% lower in comparison with the strains in the unreinforced beams, which is favorable for the serviceability of a timber element. – The unreinforced timber beams failed in bending with a failure mode characterized by brittle traction due to broken fibers. The beams were not flexible, as already reported. – The reinforced beams presented a compression-initiated flexural failure mode characterized by increased ductility. – The reinforced-prestressed beams failed in bending with a compression failure mode, characterized by increased ductility. – The failure tensile strain in the reinforced and reinforcedprestressed beams significantly increased. The steel bars reduced the cracks opening and bordered the rupture into a narrow zone. – With the exception of one specimen, no debonding or delamination occurred between two bonded materials. This meant that the strength of glulam-steel was well utilized. – In a few specimens debonding between the adhesive and wooden lamellas occurred, this showed that the strength of the glulam-steel composite was not completely utilized (leading to premature failure), and the adhesives commonly employed in the manufacture of glulam element were used inadequately. – In one specimen, the steel bar ruptured. This suggested that the bar strength needed to be adequately designed. This study showed that steel bars could be used effectively to strengthen the flexural capacity of timber beams. These preliminary results confirmed the experimental evidence presented by other authors, which showed that the bending strength could be improved by strengthening and prestressing glulam beams with steel bars. Remarkably, a pronounced ductile zone in a reinforced beam was observed in this work, whereas unreinforced beams are completely brittle. However, further experimental work with
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