 Original Article
 Open access
 Published:
Bending, shear, and compressive properties of three and fivelayer crosslaminated timber fabricated with black spruce
Journal of Wood Science volume 66, Article number: 38 (2020)
Abstract
Crosslaminated timber (CLT) is an innovative engineering wood product made by gluing layers of solidsawn lumber at perpendicular angles. The commonly used wood species for CLT manufacturing include sprucepinefir (SPF), douglas firlarch, and southern pine lumber. With the hope of broadening the wood species for CLT manufacturing, the purposes of this study include evaluating the mechanical properties of black spruce CLT and analyzing the influence of CLT thickness on its bending or shear properties. In this paper, bending, shear, and compressive tests were conducted respectively on 3layer CLT panels with a thickness of 105 mm and on 5layer CLT panels with a thickness of 155 mm, both of which were fabricated with No. 2grade Canadian black spruce. Their bending or shear resisting properties as well as the failure modes were analyzed. Furthermore, comparison of mechanical properties was conducted between the black spruce CLT panels and the CLT panels fabricated with some other common wood species. Finally, for both the CLT bending panels and the CLT shear panels, their numerical models were developed and calibrated with the experimental results. For the CLT bending panels, results show that increasing the CLT thickness whilst maintaining identical spantothickness ratios can even slightly reduce the characteristic bending strength of the black spruce CLT. For the CLT shear panels, results show that increasing the CLT thickness whilst maintaining identical spantothickness ratios has little enhancement on their characteristic shear strength. For the CLT bending panels, their effective bending stiffness based on the Shear Analogy theory can be used as a more accurate prediction on their experimentbased global bending stiffness. The model of the CLT bending specimens is capable of predicting their bending properties; whereas, the model of the CLT shear specimens would underestimate their ultimate shear resisting capacity due to the absence of the rolling shear mechanism in the model, although the elastic stiffness can be predicted accurately. Overall, it is attested that the black spruce CLT can provide ideal bending or shear properties, which can be comparable to those of the CLT fabricated with other commonly used wood species. Besides, further efforts should focus on developing a numerical model that can consider the influence of the rolling shear mechanism.
Introduction
Crosslaminated timber (CLT) is one kind of prefabricated engineered wood products, made of at least three orthogonal crosswise layers of graded sawn lumber that are laminated by gluing with structural adhesives [1, 2]. Compared to other commonly used engineered wood products, CLT panels can perform with the advantages of higher inplane compressive strength and stiffness, better acoustic and thermal performance, better integrity, etc. These advantages make the CLT panels pretty suitable and competitive for constructing mid and highrise timber buildings.
Since CLT has illustrated its potentials and competitiveness of using as dominant building materials for the mid and highrise timber buildings, a series of studies have focused on comprehending the mechanical properties (e.g., bending, rolling shear, compression, tension, etc.) of CLT panels based on tests. He et al. [3] tested the bending and compressive properties of CLT panels made from Canadian hemlock, and calibrated the theoretical bending stiffness using the experimental values. Sikora et al. [4] tested the bending and shear properties of three and fivelayer CLT panels fabricated with Irish Sitka spruce. It was attested that the bending or rolling shear strength decreased with an increase of the CLT thickness. Navaratnam et al. [5] tested both the bending and shear properties of CLT fabricated with Australian Radiate pine; furthermore, one numerical model for predicting its mechanical properties was developed. It highlighted that the shear strength could not be enhanced with an increase of the CLT thickness. Li [6] tested the rolling shear properties of CLT fabricated with New Zealand Radiata pine, and found that the lamination thickness affected its rolling shear strength significantly. Ukyo et al. [7] tested the rolling shear properties of CLT fabricated with Japanese cedar, and found that its rolling shear strength was highly correlated with the shear modulus. Oh et al. [8] proposed a laminapropertybased model for predicting the compressive strength of CLT panels, and revealed that the CLT compressive strength increased with an increase of the lamina number. Ido et al. [9] analyzed the effects of width and layups on the CLT tensile strength, and found that the tensile strength calculated using the Young’s modulus of the lamina of each layer was in agreement with the measured tensile strength.
As for the numerical analysis on CLT panels, different methods can be applied for simulating the mechanical behaviors of CLT panels. Chen et al. [10] developed an orthotropically elastic model with different strengths in compression and tension for modeling work of timber structures; furthermore, Chen et al. [11] developed a constitutive model named Woodst combining a number of mechanicsbased submodels for numerical simulation of woodbased materials under forces and fire. It is proven capable of simulating the thermomechanical response of timber beams or glulam connections under force and fire. Ceccotti [12] and Franco et al. [13] studied the inplane properties of CLT panels. In their CLT models, a set of elastic truss elements combined with nonlinear spring elements were used for simulating the CLT panels. D’Arenzo et al. [14] and Wilson et al. [15] studied the inplane elastic properties of CLT floor diaphragms and the compressive plastic properties of CLT wall panels, respectively. In their CLT models, twodimensional shell elements were used for simulating the CLT panels; furthermore, more complicated shell elements (e.g., ShellMIC4 element within OpenSees [16]) can be used to simulate the mechanical behavior of CLT, when the layup of the CLT panels should be considered. For achieving higher calculation accuracy, threedimensional solid elements can be used to simulate the inplane and outofplane behaviors of CLT panels. For instance, Hashemi et al. [17] investigated the compressive stress distribution within the CLT laminations using linear hexstructured shape elements. He et al. [3] developed one predictive model for 5layer CLT bending panels using 8node solid elements (i.e., SOLID45 element within ANSYS [18]).
A series of experimental research and theoretical analysis have been conducted for comprehending the mechanical properties of CLT panels [19]; whereas, systematical experimental research for comprehending the effect of CLT thickness on its outofplane bending or outofplane shear properties is still limited. Furthermore, few studies provide one modeling method for developing a reliable numerical model that can predict the CLT bending or shear behaviors. In this work, comprehensive bending tests as well as shear tests on both 3 and 5layer CLT panels fabricated with Canadian black spruce (Picea mariana) were conducted. For the black spruce CLT panels, the effects of the thickness on their bending properties and on their shear properties were analyzed, respectively. Comparison of mechanical properties was conducted comprehensively between the black spruce CLT panels and the CLT panels fabricated with some other common wood species; besides, for the CLT bending specimens, comparison between their experimental bending stiffness and their analytical bending stiffness (i.e., the effective bending stiffness) was also conducted. Finally, for both the CLT bending specimens and the CLT shear specimens, their numerical models were developed and then calibrated with the experimental results. The research can provide fundamental basis for comprehending the effect of CLT thickness on its bending or shear properties; furthermore, the summary on the mechanical properties of different types of CLT panels fabricated with various wood species can provide meaningful reference values for engineering design.
Materials and test methods
Materials and specimens
Both the 5layer and the 3layer CLT panels were manufactured with a width of 310 mm, using the No.2grade Canadian black spruce lumber [20]. The fabrication of the CLT panels met the requirements of PRG 320 [1]. The 5layer CLT panels were fabricated with 35/25/35/25/35 mm layups with a 155mm total thickness (CL5/155); the lumber with a nominal crosssection dimension of 140 mm × 35 mm and that with a nominal crosssection dimension of 140 mm × 25 mm were respectively used for the longitudinal laminations and transverse laminations. The 3layer CLT panels were fabricated with 35/35/35 mm layups with a 105mm total thickness (CL3/105); the 140 mm × 35 mm crosssection lumber was used for both the longitudinal and the transverse laminations. All the CLT panels were assembled in cold press using a polyurethane adhesive; furthermore, edge gluing was performed. The average moisture content of the lumber was 12.5% with a coefficient of variation (COV) of 9.0%. For releasing the stress and then reducing the chances of developing cracks when the moisture content declined, lumber shrinkage relief was introduced to these CLT panels by sawing, forming the relief kerfs in the longitudinal laminations (Fig. 1). A detailed introduction of the relief kerfs is provided in CLT Handbook [21]. The relief kerfs cannot be too wide or too deep because they may reduce the bonding area, and affect the panel capacity and fire performance. Based on the requirements from CLT Handbook [21], the height of the relief kerfs should be less than half of the lamination thickness; whilst, it should ensures that less than 10% of the lamination crosssection or 5% of the lamination width is removed. The details of both the 3layer and the 5layer black spruce CLT panels are listed in Table 1.
Material properties
Threepoint bending tests on the dimensional lumber for gluing the CLT panels were conducted for obtaining their bending stiffness. The crosssection of the bending lumber was 35 mm × 35 mm (width × depth). The total length of the bending lumber was 900 mm, which should be larger than 25 times of the lumber thickness (i.e., 875 mm); the net span of the lumber for the threepoint bending tests should be 750 mm. A constant displacement loading rate of 5.0 mm/min was applied on these bending specimens. Both the dimensions of the specimens and the loading configurations were determined based on the code GB/T 26899 [22]. Based on the test results, the average MOE of the No. 2grade Canadian black spruce lumber in the paralleltograin direction (E_{l,0}) and that in the perpendiculartograin direction (E_{l,90}) were 10925.0 MPa with a COV of 9.2% and 993.2 MPa with a COV of 11.0%, respectively. Therefore, based on the equivalent stiffness method suggested by CLT Handbook [21] for multilayer orthotropic materials (e.g., CLT), the inplane MOE of the 3layer CLT panels in major compressive direction (E_{c3,0}) and that in minor compressive direction (E_{c3,90}) were 7614.4 MPa and 4303.8 MPa, respectively; the inplane MOE of the 5layer CLT panels in major compressive direction (E_{c5,0}) and that in minor compressive direction (E_{c5,90}) were 6838.8 MPa and 3717.4 MPa, respectively. Based on the experimental results from the CLT manufacturer, the average compressive strength of the black spruce lumber in the paralleltograin direction (f_{lc,0}) and that in the perpendiculartograin direction (f_{lc,90}) were 28.7 MPa with a COV of 9.2% and 5.8 MPa with a COV of 10.4%, respectively. The material properties of the black spruce lumber are listed in Table 2. Furthermore, for comprehending the inplane compressive properties of the 3 and 5layer CLT panels in both the major strength and the minor strength directions, 72 rectangular specimens with a sampling area of 100 mm × 100 mm were respectively extracted from the 3layer CLT panels and from the 5layer CLT panels; the thickness of these extracted rectangular specimens was equal to that of the 3layer or 5layer CLT panels, as shown in Fig. 2. These 72 extracted rectangular specimens were divided into two groups, with one group of 36 specimens tested for the major inplane compressive properties, and the other group of 36 specimens tested for the minor inplane compressive properties. Considering the discreteness of wood properties, the number of 36 per group was determined based on GB/T 50329 [23], which specified that at least 30 specimens were required for one group of compressive tests on timber.
Bending test method
Totally ten 3300mmlength 3layer black spruce CLT panels with 35/35/35 mm layups (CL3/105/3300) were tested for comprehending the bending performance in the major strength direction; whereas ten 4800mmlength 5layer black spruce CLT panels with 35/25/35/25/35 mm layups (CL5/155/4800) were tested for comprehending the bending performance in the major strength direction. Both the 3layer and the 5layer CLT panels with a width of 310 mm were fabricated with the lumber in the outermost laminations running parallel to the span direction. Since the distance between the support and the nearest end of the panel accounted for half of the CLT thickness, for the 3layer CLT bending panels and for the 5layer CLT bending panels, their spantothickness ratios were 30.4 and 30.0, respectively. Both the width and the spantothickness ratio were determined based on ANSI/APA PRG 320 [1], which specified a spantothickness ratio of 30 and a width larger than 305 mm for CLT bending specimens. For the CLT bending tests (taking the 5layer CLT bending specimens as an example), the loading configurations (i.e., momentcritical configurations) of a fourpoint bending test determined based on prEN 16351 [24] are shown in Fig. 3a. Two loading points with a distance equal to six times of the CLT thickness h were applied to the central span of the bending specimens. A constant displacement loading rate of 6.4 mm/min was applied on the CLT bending specimens. Furthermore, for measuring both the local displacement and the global displacement of the CLT bending specimens, as recommended by EN 408 [25], four linear voltage displacement transducers (LVDTs 14) were used in each CLT bending specimen. The LVDTs 1–2 positioned in the midspan on both sides of the bending specimens were used to measure the global displacements that could reflect both the bending and the shear mechanisms. The average displacement measured from the LVDTs 1–2 was namely the global displacement of the CLT bending specimens. The LVDTs 3–4 positioned in the neutral axis on both sides of the bending specimens with a central gauge length of 5h were used to measure the displacements corresponding to the shearfree zone (Fig. 3a). Actually, the relative vertical displacement between the ends of the shearfree zone and the midspan of the entire CLT bending specimen is the local displacement reflecting the pure bending mechanism. In this study, the local displacement was calculated by deducting the average displacement measured from the LVDTs 3–4 from the global displacement. The bending test setup is shown in Fig. 3b. The details of the CLT bending specimens are listed in Table 3.
Shear test method
Totally ten 680mmlength 3layer black spruce CLT panels with 35/35/35 mm layups (CL3/105/680) were tested for comprehending the shear performance in the major strength direction; whereas ten 1000mmlength 5layer black spruce CLT panels with 35/25/35/25/35 mm layups (CL5/155/1000) were tested for comprehending the shear performance in the major strength direction. Both the 3layer and the 5layer CLT panels with a width of 310 mm were fabricated with the lumber in the outermost laminations running parallel to the span direction. For the 3layer or the 5layer CLT shear panels, their spantothickness ratios were 5.5, which was determined based on ANSI/APA PRG 320 [1] specifying a spantothickness ratio between 5 and 6. One loading point with a constant displacement loading rate of 6.4 mm/min was applied in the midspan of the CLT shear specimens (taking the 5layer CLT shear specimen as an example), as shown in Fig. 4a. The LVDTs 1–2 were positioned in the midspan on both sides of the CLT shear specimens, and the average displacement measured from the LVDTs 1–2 was namely the shear deformation. The shear test setup is shown in Fig. 4b. The details of the CLT shear specimens are listed in Table 4.
Results and discussion
Compressive test
Based on the compressive tests on the aforementioned rectangular specimens extracted from the 3layer or the 5layer CLT panels, the major or minor compressive stress–strain relationships for both the 3layer and the 5layer CLT panels are obtained (Fig. 5). For the 3layer CLT panels, the average inplane major compressive strength (f_{c3,0}) and the average inplane minor compressive strength (f_{c3,90}) were 21.1 MPa with a COV of 6.7% and 13.4 MPa with a COV of 9.8%, respectively. For the 5layer CLT panels, the average inplane major compressive strength (f_{c5,0}) and the average inplane minor compressive strength (f_{c5,90}) were 23.5 MPa with a COV of 6.0% and 14.7 MPa with a COV of 6.5%, respectively. In the major or minor compressive direction, the inplane compressive strength of the CLT panels increases slightly with an increase of the CLT thickness. It is found that the ratio of the f_{c3,0} to the f_{c5,0} (i.e., 0.90) or that of the f_{c3,90} to the f_{c5,90} (i.e., 0.92) is similar to the ratio between (t_{1} + t_{3})/(t_{1} + t_{2} + t_{3}) of the 3layer CLT and (t_{1} + t_{3} + t_{5})/(t_{1} + t_{2} + t_{3} + t_{4} + t_{5}) of the 5layer CLT (t_{i} is the thickness of lamination i). Such a relation was stated by Chen et al. [26]. Furthermore, the f_{c3,90} or the f_{c5,90} is more than twice of the perpendiculartograin compressive strength of the lumber (f_{lc,90}). It is partly due to the reason that the crosslaminated structure restrains the horizontal expansion in the laminations under vertical compression, thus enhancing the minor compressive strength of CLT. The enhancing effect increases with the number of the CLT layers [26]. Furthermore, the inplane MOEs of the CLT panels calculated following the equivalent stiffness method are slightly larger than those estimated from the stress–strain relationships shown in Fig. 5. It is because of the gap existing along the interface between the loading plates and the rectangular specimens, which can cause larger measurements of the compressive deformation for these rectangular specimens, and therefore less inplane MOEs based on the stress–strain relationships. The inplane MOEs calculated following the equivalent stiffness method are more accurate. The material properties of both the 3layer and the 5layer CLT panels are listed in Table 5.
Bending test
For the CLT bending specimens, both the local bending stiffness (EI_{m,l}) and the global bending stiffness (EI_{m,g}) can be calculated respectively based on Eqs. (1) and (2) originally from EN 408 [25] and further modified by Christovasilis et al. [27] for CLT; in Eq. (1), a is the distance between the loading head and the nearest support, l_{1} is equal to the gauge length for the local displacement measurement (i.e., 5h), F_{1} and F_{2} are respectively 10% and 40% of the ultimate loadresisting capacity (F_{max}), and w_{1} and w_{2} are the local displacements corresponding to the F_{1} and the F_{2}, respectively; whereas, in Eq. (2), w_{1} and w_{2} are the global displacements corresponding to the F_{1} and the F_{2}, l is the span between the supports. The effective shear stiffness GA_{eff} can be calculated using Eq. (3), in which b_{i} and h_{i} are the width and the thickness of lamination i, respectively; G_{i} represents the shear modulus parallel to grain (G_{0}) for longitudinal laminations and represents the rolling shear modulus (G_{90}) for transverse laminations, respectively. Κ is the shear correlation factor, which was adopted as 0.23 in this study for common layups [28]. For the tested black spruce CLT panels, G_{0} and G_{90} were adopted as 682.8 MPa and 68.3 MPa, respectively, based on the definitions from EN 338 [29] (i.e., G_{0} = E_{l,0}/16, G_{90} = G_{0}/10).
For the 3layer black spruce CLT bending specimens, the relations between the load versus the average displacement from LVDTs 1–2 (i.e., global displacement) as well as the relations between the load versus the average displacement from LVDTs 3–4 are shown in Fig. 6a, b, respectively. For each CLT bending specimen, the global displacement corresponding to F_{max} is approximately 5.6 mm larger than the corresponding average displacement from the LVDTs 3–4. The gap between the average displacement from the LVDTs 1–2 and the average displacement from the LVDTs 3–4 is namely the local displacement for the 3layer CLT bending specimens. For the 5layer black spruce CLT bending specimens, the relations between the load versus the average displacement from LVDTs 1–2 (i.e., global displacement) as well as the relations between the load versus the average displacement from LVDTs 3–4 are shown in Fig. 7a, b, respectively. When the load reaches F_{max}, the gap between the average displacement from the LVDTs 1–2 (i.e., global displacement) and the average displacement from the LVDTs 3–4 is around 3.0 mm, which is namely the local displacement for the 5layer CLT bending specimens.
For both the 3layer and the 5layer black spruce CLT bending specimens, the dominant failure mode is the brittle tension failure occurring in the CLT bottom longitudinal laminations, as shown in Fig. 8. Furthermore, for one 3layer CLT bending specimen with a finger joint located in the bottom longitudinal lamination close to the midspan, the finger joint zone is prone to the brittle tension failure, as shown in Fig. 9. Therefore, for CLT manufacturers, special attentions should be paid to the location of the finger joints, which should be remained an enough distance from the midspan of CLT bending components. Furthermore, it should be noted that the finger joint effect maybe pronounced when the original CLT panel is divided into several ones with smaller width (e.g., 310 mm). For the fabricated CLT panels satisfying the requirements from PRG 320 [1], this failure mode can be avoided.
For the 3layer or the 5layer black spruce CLT bending specimens, their characteristic bending strength (f_{b}) can be calculated using Eq. (4) based on the Timoshenko Beam theory [27, 30], in which M_{max} is the maximum bending moment. S_{eff} is the effective section modulus calculated using Eq. (5), in which EI_{m,l} is the local bending stiffness representing the pure bending mechanism; h is the CLT thickness; E_{1} is the MOE of the CLT outermost laminations (i.e., E_{1} = E_{l,0} = 10925 MPa).
Based on these aforementioned Eqs. (1)–(5), the bending properties of both the 3layer CLT panels and the 5layer CLT panels can be calculated, as listed in Tables 6 and 7. For the 3layer CLT bending panels fabricated with No.2grade black spruce, the average ultimate loadresisting capacity (F_{max}) is 33.722 kN (the range is 25.480–41.500 kN) with a COV of 12.4%. The average global initial elastic stiffness (K_{e}), which is the average slope ratio of those load–displacement curves shown in Fig. 6a, is 508.294 N/mm (the range is 448.592–578.424 N/mm) with a COV of 9.5%. The average local bending stiffness (EI_{m,l}) and the average global bending stiffness (EI_{m,g}) are 4.024 × 10^{11} N mm^{2} (COV is 11.1%) and 3.596 × 10^{11} N mm^{2} (COV is 10.5%), respectively. The average characteristic bending strength (f_{b}) is 30.909 MPa with a COV of 9.8%. In contrast, for the 5layer CLT bending panels fabricated with No.2grade black spruce, the average F_{max} is 36.914 kN (the range is 30.310–45.090 kN) with a COV of 12.6%. The average global K_{e} is 426.533 N/mm (the range is 390.907–463.979 N/mm) with a COV of 6.0%. The average EI_{m,l} and the average EI_{m,g} are 9.816 × 10^{11} N mm^{2} (COV is 10.9%) and 9.080 × 10^{11} N mm^{2} (COV is 6.5%), respectively. The average f_{b} is 29.633 MPa with a COV of 9.5%.
Shear test
In this study, the compressive deformation of the CLT shear specimens at the supports was ignored, which was extremely small (less than 1 mm). The dominant failure mode for both the 3layer and the 5layer CLT shear specimens is the rolling shear failure occurring in the transverse laminations, as shown in Fig. 10. Since delamination failure resulting from CLT manufacturing defects was observed in one 3layer CLT shear specimen, which cannot reflect the typical shear mechanism of CLT panels, its experimental result was excluded from the shear properties analyses. Then, for the 9 3layer CLT shear specimens and for the 10 5layer CLT shear specimens, their load–displacement curves are shown in Fig. 11a ,b, respectively. The midspan displacement is the average vertical displacement measured from the LVDTs 1–2, as shown in Fig. 4a. For the 3layer CLT shear specimens, their average ultimate shear resisting capacity (FV_{max}) is 51.639 kN with a COV of 7.5%; for the 5layer CLT shear specimens, their average FV_{max} is 69.806 kN with a COV of 5.6%. For both the 3layer and the 5layer CLT shear specimens, their characteristic shear strength (f_{v}) can be calculated using Eqs. (6) and (7) from CLT Handbook [21], in which EI_{eff,shear} is the effective bending stiffness calculated based on the Shear Analogy theory; E_{i} represents E_{l,0} for the longitudinal lamination and represents E_{l,90} for the transverse lamination, respectively; h_{i} is the thickness of lamination i, except for the middle lamination, which is half of its thickness; z_{i} is the distance from the centroid of the lamination to the CLT neutral axis, except for the middle lamination, where it is to the centroid of the top half of that lamination. EI_{eff,shear} can be calculated using Eq. (8), in which A_{i} is the crosssection area of lamination i. Whereas, compared to the EI_{eff,shear}, the EI_{m,l} reflecting the pure bending mechanism of the specimens is more related to the CLT bending properties; furthermore, the experimentbased EI_{m,l} can consider almost all affecting factors of bending stiffness. Therefore, in this paper, the EI_{m,l} instead of the EI_{eff,shear} was used in Eq. (6) for calculating the f_{v} of the CLT shear specimens. The experimental properties of both the 3layer and the 5layer CLT shear specimens are listed in Table 8. The average characteristic shear strength (f_{v}) of the 3layer CLT panels is 1.737 MPa with a COV of 7.5%; in contrast, the average f_{v} of the 5layer CLT panels is 1.803 MPa with a COV of 6.5%. Based on the definitions from ANSI/APA PRG 320 [1], the characteristic rolling shear strength (f_{r}) can be estimated as onethird of the characteristic shear strength (f_{v}). Therefore, for the 3layer CLT panels and for the 5layer CLT panels, their f_{r} is approximately 0.579 MPa and 0.601 MPa, respectively.
Effect of thickness
For the 5layer CLT panels with a thickness of 155 mm and for the 3layer CLT panels with a thickness of 105 mm, their bending and shear properties are compared, as listed in Table 9. For those CLT bending specimens, the F_{max} of the 5layer CLT panels is only 9.46% higher than that of the 3layer CLT panels; furthermore, the f_{b} of the 5layer CLT panels is even less than that of the 3layer CLT panels. It indicates that increasing the CLT thickness whilst maintaining identical spantothickness ratios cannot enhance their ultimate loadresisting capacity F_{max}. Besides, increasing the CLT thickness cannot enhance the characteristic bending strength f_{b} of the CLT panels with identical spantothickness ratios. It is because that the f_{b} of one CLT panel is mainly determined by the bending strength of the outermost lamination of the CLT. Similar findings were also reported by Sikora et al. [4] and Navaratnam et al. [5]. Furthermore, when the thickness of the outermost lamination of one CLT enhances, the f_{b} of the CLT panel would decrease, due to the size effect of the outermost lamination on its bending strength. The Global K_{e} (i.e., average slope ratio of those load–displacement curves) of the 5layer CLT panels is 16.08% less than that of the 3layer CLT panels, which means that increasing the CLT thickness whilst maintaining identical spantothickness ratios can weaken the global K_{e} of the CLT bending specimens. Although increasing the thickness from 3layer CLT to 5layer CLT has enhanced the moment of inertia for the CLT crosssection; whereas, maintaining identical spantothickness ratios can simultaneously increase the span of the bending CLT, which is more dominant in weakening the slope ratio of CLT load–displacement curve (i.e., Global K_{e}). When the CLT configurations enhance from three laminations with a thickness of 105 mm to five laminations with a thickness of 155 mm, the local bending stiffness EI_{m,l} and the global bending stiffness EI_{m,g} increase by 145.0% and 152.0%, respectively; therefore, for those CLT bending specimens, increasing their thickness can enhance their EI_{m,l} or EI_{m,g} significantly.
For those CLT shear specimens, the FV_{max} of the 5layer CLT panels with a thickness of 155 mm is 35.18% higher than that of the 3layer CLT panels with a thickness of 105 mm. Therefore, increasing the CLT thickness whilst maintaining identical spantothickness ratios can have a significant enhancement on its ultimate shearresisting capacity FV_{max}; whereas, that arrangement has little enhancement on its characteristic shear strength f_{v}, because the f_{v} of the 5layer CLT shear panels is only 3.8% higher than that of the 3layer CLT shear panels. It is because the f_{v} of one CLT panel is mainly determined by the shear strength of the transverse laminations of the CLT. The f_{v} of the 3layer CLT with 35mmthickness transverse laminations is slightly less than that of the 5layer CLT with 25mmthickness transverse laminations, which is caused by the size effect of the transverse laminations on their shear strength.
Experimental and analytical bending stiffness
For the CLT bending specimens, their experimentbased bending stiffness (i.e., EI_{m,l} and EI_{m,g}) can be estimated using the theoretical bending stiffness (i.e., effective bending stiffness EI_{eff}). The theorybased EI_{eff} can be calculated without the time and energyconsuming bending tests; besides, EI_{eff} can be calculated directly using the geometric characteristics of CLT sections and the MOEs of CLT laminations, based on the Shear Analogy theory (i.e., EI_{eff,shear}) or the Modified Gamma theory (i.e., EI_{eff,Gamma}). The aforementioned Eq. (8) is used for calculating the EI_{eff,shear}. As for the EI_{eff,Gamma}, it can be calculated using Eq. (9) following the Modified Gamma theory, which stems from the Mechanically Jointed Beams theory or the Gamma theory [31] that takes no shear deformation into consideration, in which z_{i} is the distance from the centroid of the lamination to the CLT neutral axis; E_{i} is the MOE of lamination i; h_{i} and b_{i} are the thickness and width of lamination i, respectively; γ_{i} is the connection efficiency factor (nonzero only for the longitudinal laminations and equal to unity for the middle lamination). γ_{i} can be calculated using Eq. (10), in which L_{eff} is the effective length of the beam, which is 3195 mm for the 3layer CLT bending specimens and 4645 mm for the 5layer CLT bending specimens, respectively; j is the transverse lamination connecting the ith longitudinal lamination with the central lamination. As mentioned above, the rolling shear modulus G_{90} (i.e., the shear modulus of the transverse laminations) was adopted as 68.3 MPa. Therefore, for the 3layer CLT bending specimens and for the 5layer CLT bending specimens, their EI_{eff,shear} was calculated as 3.157 × 10^{11} N mm^{2} and 9.044 × 10^{11} N mm^{2}, respectively; their EI_{eff,Gamma} was calculated as 2.654 × 10^{11} N mm^{2} and 8.532 × 10^{11} N mm^{2}, respectively.
For the 3layer or the 5layer CLT bending specimens, their experimental bending stiffness (i.e., EI_{m,l} and EI_{m,g}) are compared with their theoretical bending stiffness (i.e., EI_{eff,shear} and EI_{eff,Gamma}), as shown in Fig. 12. For the 3layer CLT bending specimens, their EI_{eff,shear} is 21.55% less than the average EI_{m,l} and 12.21% less than the average EI_{m,g}, respectively; in contrast, their EI_{eff,Gamma} is 34.05% less than the average EI_{m,l} and 26.20% less than the average EI_{m,g}, respectively. For the 5layer CLT bending specimens, their EI_{eff,shear} is 7.86% less than the average EI_{m,l} and 0.40% less than the average EI_{m,g}, respectively; in contrast, their EI_{eff,Gamma} is 13.08% less than the average EI_{m,l} and 6.04% less than the average EI_{m,g}, respectively. Therefore, for either the 3layer CLT bending panels or the 5layer CLT bending panels, their EI_{eff,shear} is much closer to the EI_{m,g}, because the EI_{eff,shear} based on the Shear Analogy theory takes both shear and flexural deformations into consideration. It indicates that the EI_{eff,shear} can be used as a more accurate prediction on the EI_{m,g} of the CLT bending panels.
Properties’ comparison
The mechanical properties of CLT panels fabricated with different wood species are listed in Table 10, in which the flexural MOE (E_{b}) of the CLT bending specimens is calculated by dividing the local bending stiffness (EI_{m,l}) by the second moment of the crosssectional inertia (I). Some findings can be concluded as: (1) the 3layer CLT fabricated with No.2grade black spruce lumber can provide the largest E_{b} among all the CLT types listed in Table 10; furthermore, their mechanical properties are even better than those of E1grade CLT defined in ANSI/APA PRG 320 [1]; (2) the mechanical properties of the 5layer CLT fabricated with No.2grade black spruce lumber are similar to those of E2grade CLT defined in ANSI/APA PRG 320 [1], except for the f_{b}, which is higher than that of most CLT types (e.g., E2grade CLT); (3) compared to the CLT panels fabricated with No.2grade Canadian hemlock [3], the CLT panels fabricated with No.2grade Canadian black spruce lumber can provide better bending or shear properties; (4) except for the E_{b} of the 3layer black spruce CLT, the mechanical properties of those CLT fabricated with No. 2grade black spruce lumber are less than those of the hybrid CLT manufactured by both Sprucepinefir (SPF) and laminated strand lumber (LSL) [32]; (5) overall, the CLT fabricated with No. 2grade black spruce lumber can provide ideal bending or shear properties, which can be comparable to those of the CLT fabricated with other commonly used wood species. Furthermore, in this study, edgegluing was performed for the 3 or 5layer CLT specimens. Compared to the edgeglued CLT panels, the inplane shear stiffness of the nonedgeglued CLT is lower significantly [34]. More studies are required for comprehending the influence of edgegluing on the structural performance of CLT.
Numerical model
Both the fullscale numerical model of the CLT bending specimens and that of the CLT shear specimens were developed based on ANSYS [18]. The 8node SOLID45 element was used for simulating the black spruce lumber. The dimensions of the SOLID45 elements were defined as half of the lamination thickness (i.e., 17.5 mm or 12.5 mm). Since little delamination failure occurred during the aforementioned bending or shear tests, it was assumed that no slide movement occurred within the interface of the CLT neighboring laminations. Therefore, in the model of the CLT bending or shear specimens, the neighboring laminations were bonded. The orthotropic elastoplastic performance of the spruce lumber was simulated based on the material model of HILL Plasticity combined with the model of KINH Multilinear Kinematic Hardening. For the CLT numerical model, the material properties were assigned to each lamination of the CLT panels, based on the lumber grain orientation within this lamination. In the paralleltograin direction of the lumber, the tensile strength and the compressive strength were equal to f_{b} (i.e., 30.91 MPa for CL3/105 and 29.63 MPa for CL5/155) and equal to f_{lc,0} (i.e., 28.7 MPa), respectively. In the perpendiculartograin direction of the lumber, the compressive strength was equal to f_{lc,90} (i.e., 5.8 MPa); the tensile strength (f_{lt,90}) was estimated as 2.7 MPa. Since the HILL Plasticity model cannot consider the difference between tensile and compressive strengths in the same direction [35]; therefore, in the paralleltograin direction of the lumber, the lower of the f_{b} and f_{lc,0} (i.e., 28.7 MPa) was adopted; meanwhile, in the perpendiculartograin direction of the lumber, the lower of the f_{lc,90} and f_{lt,90} was adopted (i.e., 2.7 MPa). Similar arrangement was also adopted by Nowak et al. [36] for the material law of glulam. The shear modulus of the longitudinal lamination (i.e., G_{0}) and that of the transverse lamination (i.e., G_{90}) were defined as 682.8 MPa and 68.3 MPa (G_{0} = E_{l,0}/16, G_{90} = G_{0}/10), respectively. It should be noted that size effects of these strengths input in the numerical model were not considered in the study, which should be investigated in the future. For the models of both the CLT bending specimens and the CLT shear specimens, contour plots of their vertical deformation are shown in Fig. 13.
Both the model of the CLT bending specimens and that of the CLT shear specimens can provide accurate predictions on their initial elastic stiffness K_{e}, as shown in Fig. 14. For the 3layer CLT bending specimens and for the 5layer CLT bending specimens, their predictive F_{max} from the numerical model are respectively 30.37 kN and 36.21 kN, which are 9.94% less and 1.91% less than their average experimental F_{max}, respectively. In contrast, for the 3layer CLT shear specimens and for the 5layer CLT shear specimens, their predictive FV_{max} from the numerical model are respectively 45.05 kN and 58.55 kN, which are 12.76% less and 16.12% less than their average experimental FV_{max}, respectively. Therefore, compared to the predictive FV_{max} from the CLT shear model, the predictive F_{max} from the CLT bending model is more close to the average experimental F_{max}. For these CLT shear specimens, their FV_{max} can be underestimated significantly, when using the developed model of the CLT shear specimens. It is because the experimental FV_{max} can still remain increasing after slight rolling shear failure occurring in the CLT shear specimens; whereas the mechanism of the rolling shear failure cannot be reflected in the developed model. Future efforts should focus on developing a numerical model of CLT shear panels that can consider the influence of the rolling shear mechanism.
Conclusions
Based on the experimental investigation and theoretical analysis on both the bending and the shear properties of black spruce CLT panels, the conclusions can be drawn as follows:
 (1)
For the CLT bending panels, increasing the CLT thickness whilst maintaining identical spantothickness ratios can even slightly reduce their characteristic bending strength f_{b}. Besides, for the CLT shear panels, increasing the CLT thickness whilst maintaining identical spantothickness ratios has little enhancement on their characteristic shear strength f_{v}.
 (2)
For both the 3layer and the 5layer CLT bending panels, their effective bending stiffness based on the Shear Analogy theory can be used as a more accurate prediction on their experimentbased global bending stiffness.
 (3)
The dominant failure mode of the CLT bending specimens is the brittle tension failure occurring in the CLT bottom longitudinal lamination; whereas, that of the CLT shear specimens is the rolling shear failure occurring in the transverse laminations.
 (4)
Both the 3layer and the 5layer CLT panels fabricated with the No.2grade black spruce can provide ideal bending or shear properties, which can be comparable to those of the CLT fabricated with other commonly used wood species.
 (5)
The numerical model of the CLT bending specimens is capable of predicting both their initial elastic stiffness K_{e} and their ultimate loadresisting capacity F_{max}. Whereas, based on the numerical model of the CLT shear specimens that cannot reflect the rolling shear mechanism, the initial elastic stiffness K_{e} can be predicted accurately but the ultimate shearresisting capacity FV_{max} is underestimated.
Availability of data and materials
The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.
Abbreviations
 E _{l,0} :

Modulus of elasticity of the lumber in paralleltograin direction
 E _{l,90} :

Modulus of elasticity of the lumber in perpendiculartograin direction
 E _{c3,0} :

Modulus of elasticity of the 3layer CLT panels in major inplane compressive direction
 E _{c3,90} :

Modulus of elasticity of the 3layer CLT panels in minor inplane compressive direction
 E _{c5,0} :

Modulus of elasticity of the 5layer CLT panels in major inplane compressive direction
 E _{c5,90} :

Modulus of elasticity of the 5layer CLT panels in minor inplane compressive direction
 f _{lc,0} :

Compressive strength of the lumber in the paralleltograin direction
 f _{lc,90} :

Compressive strength of the lumber in the perpendiculartograin direction
 f _{c3,0} :

Inplane major compressive strength of the 3layer CLT panels
 f _{c3,90} :

Inplane minor compressive strength of the 3layer CLT panels
 f _{c5,0} :

Inplane major compressive strength of the 5layer CLT panels
 f _{c5,90} :

Inplane minor compressive strength of the 5layer CLT panels
 EI _{ m,l } :

Local bending stiffness of CLT bending panels
 EI _{ m,g } :

Global bending stiffness of CLT bending panels
 F _{max} :

Ultimate loadresisting capacity of CLT bending panels
 GA _{eff} :

Effective shear stiffness of CLT panels
 G _{0} :

Shear modulus parallel to grain for CLT longitudinal laminations
 G _{90} :

Rolling shear modulus for CLT transverse laminations
 h :

Total thickness of CLT panels
 h _{ i } :

The thickness of CLT lamination i
 E _{ i } :

Modulus of elasticity of CLT lamination i
 E _{1} :

Modulus of elasticity of the CLT outer most lamination
 f _{b} :

The characteristic bending strength of CLT bending panels (i.e., characteristic bending strength of the CLT outermost lamination)
 S _{eff} :

The effective section modulus of CLT panels
 K _{ e } :

Initial elastic stiffness obtained from the load–displacement curves
 FV _{max} :

Ultimate shear resisting capacity of CLT shear panels
 f _{ v } :

The characteristic shear strength of CLT shear panels
 EI _{eff} :

The effective bending stiffness of CLT bending panels
 EI _{eff,shear} :

The effective bending stiffness calculated based on the Shear Analogy theory
 EI _{eff,Gamma} :

The effective bending stiffness calculated based on the Modified Gamma theory
 f _{ r } :

The characteristic rolling shear strength
 γ _{ i } :

The connection efficiency factor for CLT longitudinal laminations
 E _{b} :

Flexural modulus of elasticity of the CLT bending specimens
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The authors also gratefully acknowledge the support from National Natural Science Foundation of China (Grant NO. 51778460) and China Scholarship Council (Grant NO. 201706260124).
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MH: conceptualization, methodology, and investigation. XS: data curation, methodology, investigation, software, and writing–review and editing. ZLi: conceptualization, methodology, and investigation. WF: software and validation. All authors read and approved the final manuscript.
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He, M., Sun, X., Li, Z. et al. Bending, shear, and compressive properties of three and fivelayer crosslaminated timber fabricated with black spruce. J Wood Sci 66, 38 (2020). https://doi.org/10.1186/s1008602001886z
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DOI: https://doi.org/10.1186/s1008602001886z