Bending, shear, and compressive properties of three- and five-layer cross-laminated timber fabricated with black spruce

Cross-laminated timber (CLT) is an innovative engineering wood product made by gluing layers of solid-sawn lumber at perpendicular angles. The commonly used wood species for CLT manufacturing include spruce-pine-fir (SPF), douglas fir-larch, 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 3-layer CLT panels with a thickness of 105 mm and on 5-layer CLT panels with a thickness of 155 mm, both of which were fabricated with No. 2-grade 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 span-to-thickness 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 span-to-thickness 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 experiment-based 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.

Since CLT has illustrated its potentials and competitiveness of using as dominant building materials for the mid-and high-rise 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 five-layer 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 lamina-property-based 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 mechanics-based sub-models for numerical simulation of wood-based materials under forces and fire. It is proven capable of simulating the thermo-mechanical response of timber beams or glulam connections under force and fire. Ceccotti [12] and Franco et al. [13] studied the in-plane 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 in-plane elastic properties of CLT floor diaphragms and the compressive plastic properties of CLT wall panels, respectively. In their CLT models, two-dimensional 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, three-dimensional solid elements can be used to simulate the in-plane and out-ofplane behaviors of CLT panels. For instance, Hashemi et al. [17] investigated the compressive stress distribution within the CLT laminations using linear hex-structured shape elements. He et al. [3] developed one predictive model for 5-layer CLT bending panels using 8-node 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 out-of-plane bending or out-ofplane 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 5-layer 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 specimens
Both the 5-layer and the 3-layer CLT panels were manufactured with a width of 310 mm, using the No.2-grade Canadian black spruce lumber [20]. The fabrication of the CLT panels met the requirements of PRG 320 [1]. The 5-layer CLT panels were fabricated with 35/25/35/25/35 mm layups with a 155-mm total thickness (CL5/155); the lumber with a nominal cross-section dimension of 140 mm × 35 mm and that with a nominal cross-section dimension of 140 mm × 25 mm were respectively used for the longitudinal laminations and transverse laminations. The 3-layer CLT panels were fabricated with 35/35/35 mm layups with a 105-mm total thickness (CL3/105); the 140 mm × 35 mm cross-section 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 cross-section or 5% of the lamination width is removed. The details of both the 3-layer and the 5-layer black spruce CLT panels are listed in Table 1.

Material properties
Three-point bending tests on the dimensional lumber for gluing the CLT panels were conducted for obtaining their bending stiffness. The cross-section 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 three-point 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. 2-grade Canadian black spruce lumber in the parallel-to-grain direction (E l,0 ) and that in the perpendicular-to-grain 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 multi-layer orthotropic materials (e.g., CLT), the in-plane MOE of the 3-layer 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 in-plane MOE of the 5-layer 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 parallel-to-grain direction (f lc,0 ) and that in the perpendicular-to-grain 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 in-plane compressive properties of the 3and 5-layer 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 3-layer CLT panels and from the 5-layer CLT panels; the thickness of these extracted rectangular specimens was equal to that of the 3-layer or    5-layer 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 in-plane 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 3300-mm-length 3-layer 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 4800-mm-length 5-layer 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 3-layer and the 5-layer 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 3-layer CLT bending panels and for the 5-layer CLT bending panels, their span-tothickness ratios were 30.4 and 30.0, respectively. Both the width and the span-to-thickness ratio were determined based on ANSI/APA PRG 320 [1], which specified a spanto-thickness ratio of 30   on both sides of the bending specimens with a central gauge length of 5h were used to measure the displacements corresponding to the shear-free zone (Fig. 3a). Actually, the relative vertical displacement between the ends of the shear-free zone and the mid-span 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 680-mm-length 3-layer 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 1000-mm-length 5-layer 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 3-layer and the 5-layer 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 3-layer or the 5-layer CLT shear panels, their span-to-thickness ratios were 5.5, which was determined based on ANSI/ APA PRG 320 [1] specifying a span-to-thickness ratio between 5 and 6. One loading point with a constant displacement loading rate of 6.4 mm/min was applied in the mid-span of the CLT shear specimens (taking the 5-layer 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.

Compressive test
Based on the compressive tests on the aforementioned rectangular specimens extracted from the 3-layer or the 5-layer CLT panels, the major or minor compressive stress-strain relationships for both the 3-layer and the 5-layer CLT panels are obtained (Fig. 5). For the 3-layer CLT panels, the average in-plane major compressive strength (f c3,0 ) and the average in-plane 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 5-layer CLT panels, the average in-plane major compressive strength (f c5,0 ) and the average in-plane 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 (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 perpendicular-to-grain compressive strength of the lumber (f lc,90 ). It is partly due to the reason that the cross-laminated 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 in-plane MOEs of the CLT panels calculated following the equivalent stiffness method are slightly larger than those estimated from the stressstrain 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 in-plane MOEs calculated following the equivalent stiffness method are more accurate. The material properties of both the 3-layer and the 5-layer 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 load-resisting 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 3-layer 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 Average displacement from LVDTs 3-4 Fig. 6 The 3-layer CLT bending specimens displacement from the LVDTs 3-4 is namely the local displacement for the 3-layer CLT bending specimens. For the 5-layer 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 5-layer CLT bending specimens. For both the 3-layer and the 5-layer 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 3-layer CLT bending specimen with a finger joint located in the bottom longitudinal lamination close to the mid-span, 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 mid-span 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).  fabricated CLT panels satisfying the requirements from PRG 320 [1], this failure mode can be avoided.
For the 3-layer or the 5-layer 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 3-layer CLT panels and the 5-layer CLT panels can be calculated, as listed in Tables 6 and 7. For the 3-layer CLT bending panels fabricated with No.2-grade black spruce, the average

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 3-layer and the 5-layer CLT shear specimens is the rolling shear failure occurring in the transverse laminations, as shown in Fig. 10. Since de-lamination failure resulting from CLT manufacturing defects was observed in one 3-layer 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 3-layer CLT shear specimens and for the 10 5-layer CLT shear specimens, their load-displacement curves are shown in Fig. 11a ,b, respectively. The mid-span displacement is the average vertical displacement measured from the LVDTs 1-2, as shown in Fig. 4a. For the 3-layer CLT shear specimens, their average ultimate shear resisting capacity (FV max ) is 51.639 kN with a COV of 7.5%; for the 5-layer CLT shear specimens, their average FV max is 69.806 kN with a COV of 5.6%. For both the 3-layer and the 5-layer 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 Average displacement from LVDTs 1-2

Fig. 11 CLT shear tests
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 experiment-based 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 3-layer and the 5-layer CLT shear specimens are listed in Table 8. The average characteristic shear strength (f v ) of the 3-layer CLT panels is 1.737 MPa with a COV of 7.5%; in contrast, the average f v of the 5-layer 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 one-third of the characteristic shear strength (f v ). Therefore, for the 3-layer CLT panels and for the 5-layer CLT panels, their f r is approximately 0.579 MPa and 0.601 MPa, respectively.

Effect of thickness
For the 5-layer CLT panels with a thickness of 155 mm and for the 3-layer 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 5-layer CLT panels is only 9.46% higher than that of the 3-layer CLT panels; furthermore, the f b of the 5-layer CLT panels is even less than that of the 3-layer CLT panels. It indicates that increasing the CLT thickness whilst maintaining identical span-to-thickness ratios cannot enhance their ultimate load-resisting capacity F max . Besides, increasing the CLT thickness cannot enhance the characteristic bending strength f b of the CLT panels with identical span-tothickness 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 5-layer CLT panels is 16.08% less than that of the 3-layer CLT panels, which means that increasing the CLT thickness whilst maintaining identical span-to-thickness ratios can weaken the global K e of the CLT bending specimens. Although increasing the thickness from 3-layer CLT to 5-layer CLT has enhanced the moment of inertia  for the CLT cross-section; whereas, maintaining identical span-to-thickness 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 5-layer CLT panels with a thickness of 155 mm is 35.18% higher than that of the 3-layer CLT panels with a thickness of 105 mm. Therefore, increasing the CLT thickness whilst maintaining identical span-to-thickness 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 5-layer CLT shear panels is only 3.8% higher than that of the 3-layer 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 3-layer CLT with 35-mm-thickness transverse laminations is slightly less than that of the 5-layer CLT with 25-mm-thickness 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 experiment-based 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 theory-based EI eff can be calculated without the time-and energy-consuming 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 (non-zero 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 3-layer CLT bending specimens and 4645 mm for the 5-layer 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 3-layer CLT bending specimens and for the 5-layer 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 3-layer or the 5-layer 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 3-layer 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 5-layer 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 3-layer CLT bending panels or the 5-layer 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 cross-sectional inertia (I). Some findings can be concluded as: (1) the 3-layer CLT fabricated with No.2-grade 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 E1-grade CLT defined in ANSI/APA PRG 320 [1]; (2) the mechanical properties of the 5-layer  Furthermore, in this study, edge-gluing was performed for the 3-or 5-layer CLT specimens. Compared to the edge-glued CLT panels, the in-plane shear stiffness of the non-edge-glued CLT is lower significantly [34]. More studies are required for comprehending the influence of edge-gluing on the structural performance of CLT.

Numerical model
Both the full-scale numerical model of the CLT bending specimens and that of the CLT shear specimens were developed based on ANSYS [18]. The 8-node 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 de-lamination 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 elasto-plastic performance of the spruce lumber was simulated based on the material model of HILL Plasticity combined with the model of KINH Multi-linear 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 parallel-to-grain 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 perpendicular-to-grain 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 parallel-to-grain direction of the lumber, the lower of the f b and f lc,0 (i.e., 28.7 MPa) was adopted; meanwhile, in the perpendicular-to-grain 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 3-layer CLT bending specimens and for the 5-layer 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 3-layer CLT shear specimens and for the 5-layer 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 span-tothickness ratios can even slightly reduce their characteristic bending strength f b . Besides, for the CLT shear panels, increasing the CLT thickness whilst maintaining identical span-to-thickness ratios has little enhancement on their characteristic shear strength f v .
(2) For both the 3-layer and the 5-layer CLT bending panels, their effective bending stiffness based on the Shear Analogy theory can be used as a more accurate prediction on their experiment-based 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 3-layer and the 5-layer CLT panels fabricated with the No.2-grade 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 load-resisting 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 shear-resisting capacity FV max is underestimated.