Bending performance of sugi cross-laminated timber (CLT) composed of different thickness laminae

This study aims to examine the influence of lamina thickness on the bending performance of sugi cross-laminated timber (CLT). The lamina specimens measuring 20 mm, 30 mm and 40 mm thick ×ばつ 115 mm wide, and the CLT specimens composed of 5-layer–5-ply of equally thick laminae with 20 mm-, 30 mm- and 40 mm-thick laminae, respectively, and 3-layer–3-ply with 40 mm-thick laminae for the outer layers and 20 mm-thick laminae for the inner layer were prepared. The Young’s modulus and shear modulus were measured by dynamic methods. The bending tests were conducted and the bending performances such as apparent bending Young’s modulus and bending strength were measured, and the failure behavior was observed. The results showed that the influence of lamina thickness on the bending strength and failure behavior of CLT was not clear. On the other hand, the shear modulus of the CLT specimens composed of 40 mm-thick laminae whose width-to-thickness ratio of the lamina in the transverse layer was less than 3.5 was small, indicating that the small width-to-thickness ratio of the lamina in the transverse layer influenced bending performance. Furthermore, it was considered that the bending Young’s modulus and bending strength of the CLT specimens could generally be estimated using the bending Young’s modulus and bending strength of the laminae specimens by composite theory under the conditions in this study.

Cross-laminated timber (CLT) is an engineered wood manufactured with layers stacked crosswise by gluing their surfaces together with an adhesive under pressure. One of the ways to control the strength properties of CLT is to change the lamina thickness in each layer. In Japan, there is a lot of data on CLT with 30 mm-thick laminae [1,2,3], because the main lamina thickness for glued laminated timber was 30 mm, and the use of 30 mm-thick laminae was efficient for manufacturing in domestic factories when studies on CLT began. In addition, the lamina thickness of CLT is regulated in the Japanese Agricultural Standards for CLT (JAS) [4], and the Notification 611 (2016) and 1024 (2001) of the Ministry of Land, Infrastructure, Transport and Tourism [5, 6]. The JAS defined that the lamina thickness is 12–50 mm, and each layer is basically equal in thickness. The Notification 611 (2016) and 1024 (2001) defined that the laminae thickness for the CLT structure is 24–36 mm and 12–36 mm, respectively. For these reasons, CLT with 30 mm-thick laminae, with each layer being of equal thickness, is the main one used at present in Japan. On the other hand, in Europe, CLT with different lamina thicknesses such as thicker laminae for the outer layer used to strengthen the bending strength and stiffness, is available in the market [7]. Increasing the use of CLT with different lamina thicknesses contributes toward improving the yield percentage of logs, and gives latitude to the design of CLT building. Therefore, in 2021, the Japanese Ministry of Agriculture, Forestry and Fisheries, and the Japanese Ministry of Land, Infrastructure, Transport and Tourism made plans to expand the standard for CLT with different lamina thicknesses [8]. Currently, data about strength performances are required for CLT with different lamina thicknesses.

As for the previous studies using CLT with different lamina thicknesses, Nakahara et al. [9] and Fujita et al. [10] reported the bending performance of sugi CLT with different lamina thicknesses of 20, 30, 38.57, and 42 mm. Their studies were focused on the difference of layups, and the edge glue condition of laminae in the transverse layers was different, so it is difficult to compare the influence of lamina thickness alone. Furthermore, it is reported that the width-to-thickness ratio of laminae in the transverse layer influences the shear strength [11,12,13], which needs to be considered when bending performance is investigated. JAS defined the ratio as larger than 3.5 [4]. Although the width-to-thickness ratios of the lamina prepared by Nakahara et al. [9] and Fujita et al. [10] were larger than 3.5, each value was different in the studies. To accurately investigate the effect of lamina thickness, the laminae with the same width or the same width-to-thickness ratio should be prepared. The effect of the layups of sugi CLT were investigated by Hiramatsu et al. [2]. Although they reported that the layup of CLT influenced the bending strength, the result was obtained by the bending test under in-plane loading only. The effects of lamina thickness and the layups of CLT were investigated by Conan et al. [14], Karol et al. [15], and He et al. [16] and Navaratnam et al. [17]. They reported that bending strength decreased with increasing CLT thickness. However, only 20 mm and 35 mm-thick laminae were used in the studies by He et al. [16] and Navaratnam et al. [17]. Since only two types of CLT composed of 3-layer–3-ply with the same thickness with 20 mm and 40 mm-thick laminae were used and the number of specimens was small, Karol et al. [15] suggested that further tests are required to confirm this trend.

The studies using different lamina dimensions and layups of CLT have been carried out as mentioned above. However, it is difficult to compare the effect of lamina thickness on the bending performance of CLT between these studies, because the parameters other than the lamina thickness are different. In addition, the bending Young’s modulus and bending strength were mainly investigated, and there are few studies that examined the influence of shear deflection and failure behavior on the bending test of CLT in detail. Furthermore, it is expected that the validity of the estimation method will be required to design the CLT building efficiently with the increasing use of CLT with different laminae thicknesses. Therefore, more knowledge is needed on the bending performance of CLT composed of different lamina thicknesses.

In this study, we conducted a bending test of CLT composed of 5-layer–5-ply of equal thickness with three kinds of lamina thickness, namely, 20, 30, and 40 mm. The 30 mm-thick laminae were prepared as the standard thickness, the 20 mm and 40 mm-thick laminae were prepared as thinner and thicker than the thickness defined in the Notification 611 (2016) [5] within the range of lamina thickness defined in the JAS [4], respectively. From the results obtained, the bending Young’s modulus, bending strength, shear modulus and failure behavior were compared and the effect of the lamina thickness on the bending performance of sugi CLT was investigated. In addition, we conducted the bending test of CLT composed of 3-layer–3-ply of unequal thickness with 40 mm-thick laminae for the outer layer and 20 mm-thick laminae for the inner layer, and the bending performance was compared with that of CLT composed of equal thickness layers. Furthermore, the mean Young’s modulus and bending strength of CLT were estimated using the mean bending Young’s modulus of lamina and the results were compared to the experimental results.

Materials

Laminae

The kiln-dried lumbers, whose sizes were 118 mm width, 4,100 mm length and three thickness: 24 mm, 33 mm and 43 mm, were prepared from sugi (Japanese cedar, Cryptomeria japonica) logs harvested in Kumamoto Prefecture, Japan. 24 mm-thick and 33 mm-thick lumber sections were cut from various positions of logs including pith, and 43 mm-thick lumber sections were cut without pith. Their Young’s modulus was measured by continuous mechanical grading machine, and the mean value (E_gm-lamina) was obtained. From the obtained value, lumbers were classified into two groups, namely, ranges from 7.0 to 11.0 kN/mm² for outer-layer laminae of CLT and from 2.5 to 7.0 kN/mm² for inner-layer laminae of CLT. Laminae in the same group were finger-jointed to a length of 15.0 mm along the horizontal direction, which the finger-jointed shape appears on the thickness surface, using aqueous polymer solution–isocyanate (API) adhesive. The finished dimensions of the laminae were 20 mm, 30 mm and 40 mm thick ×ばつ 115 mm wide. The length was 25 times the thickness of each lamina according to JAS [4] In this study, the 115 mm-wide laminae were used in consideration of efficiency of manufacturing and grading of laminae and the current situation in which the 105–120 mm-wide laminae were used mainly for glulam and CLT in Japan. Because the width was all the same, while the thickness varied, the width-to-thickness ratio in each lamina thickness was different; width-to-thickness ratio of 20 mm was 5.75, that of 30 mm was 3.83, and that of 40 mm was 2.88. In JAS [4], the standard value of the width-to-thickness ratio of laminae placed in the transverse layer is defined as 3.5 or more. The width-to-thickness ratio of 40 mm-thick laminae is smaller than the standard value.

CLT specimens

The CLT panels were manufactured using three different laminae thicknesses, as described in the section of Lamina. All CLT panels were Mx60 as defined in JAS [4]. The outer laminae layers run parallel to the major length direction of the CLT panel. The CLT panels was composed of 5-layer–5-ply of equally thick laminae and 3-layer–3-ply with 40 mm-thick laminae for the outer layers and 20 mm-thick laminae for the inner layer. The thickness of CLT panels of 5-layer–5-ply were 100 mm, 150 mm and 200 mm, and that of 3-layer–3-ply were 100 mm. Six CLT specimens were cut out from each original CLT panel. The length of CLT specimens was 23 times the thickness of each CLT specimen according to JAS [4]. The specimens of each condition are abbreviated as 20t, 30t, 40t, and 424t, respectively. The details of the CLT specimens are shown in Table 1. The layer in the longitudinal direction was composed of three laminae; the width of the middle lamina was 115 mm and that of both side laminae was approximately 92.5 mm, making a total width of 300 mm [4].

Non-destructive test and bending test

Laminae specimens

30 laminae were randomly selected as laminae specimens from the outer and inner layer laminae, respectively, in each laminae thickness manufactured in the section of Materials. The Young’s modulus of the lamina (E_fr-lamina) with different thicknesses was measured by a longitudinal vibration method. The apparent bending Young’s modulus including shear effect (E_app-lamina) and bending strength (σ_b-lamina) were measured using the static bending test, conducted in four-point bending test with a span length of 21 times of thickness, according to JAS [4], in a flatwise direction using a universal testing machine (Shimadzu Corporation, AG–X plus, 50kN capacity). The finger joint was placed in the middle between the loading points. A constant displacement loading rate of 5.0 mm/min was applied to the laminae specimens. E_app-lamina was calculated by measuring the displacement at the center of lamina specimen using a displacement gauge (Tokyo Measuring Instruments Laboratory Co, Ltd., CDP-50).

CLT specimens

The apparent bending Young’s modulus including shear effect (E_afb-CLT), the true bending Young’s modulus without shear effect (E_TGH-CLT) and the shear modulus (G_TGH-CLT) by the Timoshenko–Goens–Hearmon (TGH) flexural vibration method were measured as the dynamic method [18, 19]. The shear modulus was calculated assuming the shear distribution modulus of 1.0. They were measured under out-of-plane directions. The CLT specimen was supported at 0.224 times of its length from both ends. Flexural vibration was excited at the center using a hammer. The motion of the CLT was detected using an acceleration pickup at the edge.

The apparent bending Young’s modulus including shear effect (E_app-CLT) and the bending strength (σ_b-CLT) were measured using the static bending test, according to JAS [4]. The static bending test was conducted in four-point bending test with a span length of 21 times of thickness along the out-of-plane direction using a bending testing machine (Maekawa Testing Machine Mfg Co., Ltd., SAH-100-SS, 1000kN capacity). The finger joint in the bottom surface lamina was placed between the loading points. E_app-CLT was calculated by measuring the displacement at the center of one side of the CLT using a displacement gauge (Tokyo Measuring Instruments Laboratory Co, Ltd., SDP-200D). The true bending Young’s modulus without shear effect (E_true-CLT) was calculated by measuring the displacement using a displacement gauge (Tokyo Measuring Instruments Laboratory Co, Ltd., CDP-10) attached to the wedge-shaped fixture at the center of the top of the CLT specimen. The span length of the wedge-shaped fixture was 400 mm for 20t and 424t, and 800 mm for 30t and 40t. The proportional limit load was defined as the point, where the line connecting the load–deflection points at 10% and 40% of the maximum load and the point, where the load value on the load–deflection curve exceeded the value corresponding to 1% of the maximum load. After the static bending test, the failure of the CLT specimens was observed.

Distributions of E _gm-lamina and E _app-lamina of laminae

To confirm the distributions of Young’s modulus in the whole laminae which were prepared for manufacturing of the CLT specimens and in the selected lamiae from the whole laminae as laminae specimens, the cumulative rate of E_gm-lamina and E_app-lamina were compared. The results are shown in Fig. 1. In 20 mm-thick laminae (20 mm) and 30 mm-thick laminae (30 mm) for both inner and outer layer, E_app-lamina was higher than E_gm-lamina. The mean of E_app-lamina in 20 mm and 30 mm for the outer layer was 11.1% and 6.9% higher than that of E_gm-lamina, respectively. In 40 mm thick-laminae (40 mm) for the inner layer, the distribution of E_gm-lamina was smaller than E_app-lamina and both means were nearly identical. In 40 mm for the outer layer, E_app-lamina was higher than E_gm-lamina. The mean of E_app-lamina was 10% lower than the mean of E_gm-lamina. The results of 40 mm show a different tendency compared to 20 mm and 30 mm. Because the distribution of E_gm-lamina included 188 laminae of finished size that were not used for this study in the 40 mm due to the manufacturing process, it is possible that the distribution of E_gm-lamina changed in the 40 mm. Hence, it is difficult to compare the distribution of E_gm-lamina and E_app-lamina in the 40 mm specimens. Therefore, the results of the 40 mm are shown as reference data. The results obtained in this section were used to estimate the bending Young’s modulus and the bending strength of CLT.

Non-destructive test and bending test

Laminae specimens

The results of the non-destructive test and the bending test of laminae specimens are shown in Table 2. As for the outer-layer laminae which largely contribute to the bending performance of CLT specimens, the order of the mean in E_fr-lamina and E_app-lamina was 40 < 20 < 30 mm, and that in σ_b-lamina was 40 < 30 < 20 mm. Bending Young’s modulus among the three kinds of lamina thickness was not at the same level. This seemed to be, because the sawing pattern was different and there was variation in wood property. The σ_b-lamina of the 30 mm was low, although E_fr-lamina and E_app-lamina of the 30 mm were the greatest. The moisture content (MC) of the 30 mm was lower than that of the 20 mm and 40 mm. However, it was not in the range that influenced the shear strength of the joints [20] and the relationship between the bending strength and the moisture content was not clear [21]. Therefore, the main factor that made the bending strength of the 30 mm low did not seem to be MC. The order of the mean in the ratio of proportional limit load to maximum load was 40 < 20 < 30 mm, and that of the ratio of the deflection at maximum load to load span was 30 < 20 < 40 mm. It was considered that the deformation of the 30 mm was small, and the failure behavior was brittle fracture compared to the 20 mm and 40 mm. The variation in the manufacturing process and MC might have influenced the bending performances of the 30 mm. However, the detail factor is unclear. As for the 20 mm and 40 mm, the bending strength decreased with increasing laminae thickness, which was the same tendency as the previous study [22].

CLT specimens

The results of the non-destructive test and bending test of the CLT specimens are shown in Table 3. As for the 5-ply CLT specimens, the order of the mean in E_TGH-CLT, E_app-CLT, and E_true-CLT was 40t < 20t ≦ 30t. That in σ_b-CLT was 30t < 40t < 20t. Although the mean bending Young’s modulus of 30t was greater than that of 20t and 40t by 0–7.7% and 6.6–22.4%, respectively, the mean bending strength of 30t was lower than that of 20t and 40t by16.7% and 7.6%, respectively. The tendency for the bending strength to be low, while the bending Young’s modulus was great in 30t was similar to the results for the lamina specimen. The mean MC of 30t was lower than the others, which was also the same as in the laminae specimens. As mentioned in the section of Lamina specimens, it is considered that MC was not the main factor and that additional factors, such as the variation of finger joint property in CLT specimen, affected the results. As for the ratio of proportional limit load to maximum load, 20t was the highest, and 30t and 40t were lower than 20t by 18.4% and 12.3%, respectively. In the laminae specimen, 30 mm was the highest. Furthermore, as for ratio of deflection at maximum load to load span, 30t was the lowest. These results of the CLT specimen did not fully correspond to those of the lamina specimens. It is considered that the stress distribution in CLT specimens was different from that in the lamina specimen alone, because CLT is manufactured with layers stacked crosswise. Therefore, it was indicated that not only the laminae properties but also the other factors influenced the bending performance of CLT specimens. As for 424t, E_TGH-CLT, E_app-CLT, and E_true-CLT were high, because the ratio of laminae volume in the longitudinal direction to the total volume of CLT was high. As a result, its σ_b-CLT was also high.

Figure 2 shows the relationship between E_app-CLT andσ_b-CLT in this study and the previous studies [1, 9, 10]. Because the lamina width and the direction of FJ in the previous studies were different from those in this study, the values of the previous studies are shown as reference values. The distribution of E_app-CLT in 20t, 40t, and 424t was different; therefore, it was difficult to compare σ_b-CLT between them. Although the distribution of E_app-CLT in 30t was similar to that in 20t, the distribution ofσ_b-CLT in 30t tended to be lower than that in 20t. Shibusawa et al. [1] reported that the mean E_app-CLT and σ_b-CLT of CLT composed of 5-layer–5-ply with 30 mm thick lamina were 4.43 kN/mm² and 20.7 N/mm², respectively. Although the mean E_app-CLT was 43.2% lower than that of 30t, the mean σ_b-CLT was only 7.5% lower than that of 30t. Therefore, the mean σ_b-CLT of 30t in this study was low compared to that in the previous study [1]. The mean E_app-CLT and σ_b-CLT of CLT composed of 5-layer 5-ply with 20 mm-thick lamina (Nakahara et al. [9]) were 23.8% and 15.0% lower than those of 20t, respectively. The mean E_app-CLT and σ_b-CLT of CLT composed of 5-layer 5-ply with 42-mm thick lamina (Fujita et al. [10]) were 15.0% and 14.9% lower than those of 40t. As a result, it is not clear that the lamina thickness affects the bending strength in the range of 20–40 mm thickness. In Fig. 2, σ_b-CLT increased with increasing E_app-CLT, except for 30t. This indicates that the influence of lamina thickness on bending strength is small compared to the influence of bending Young’s modulus in CLT.

Bending failure behavior of CLT

Figure 3 shows the relationship between bending stress and the ratio of deflection to span length of the CLT specimens. Bending stress increased linearly, and then brittle failure occurred mainly at the end. In most of the 20t, after the failure occurred in the finger joints of the laminae in the longitudinal direction on the tension side between the loading points, the load was updated by redistribution of stress and the final failure occurred in the knot and wood in the laminae in the longitudinal direction. In two of the 40t, the same failure occurred as in the 20t. In the other 40t and in all of the 30t and 424t, the final failure occurred in the finger joints of the laminae in the longitudinal direction on the tension side without updating the load. This seemed to be one of the reasons why the deviation of σ_b-CLT in 20t was larger than the others. Regardless of the laminae thickness, finger joints of laminae in the longitudinal direction on the tension side between the loading points play a significant role in the bending failure behavior. The type of cracks in the side of the CLT specimens were classified into five groups: 1 cracks occurring in the wood along an adhesive layer; 2 cracks occurring along the growth rings; 3 cracks occurring in the radial direction of the growth rings; 4 splitting failures occurring in the layer in the longitudinal direction; and 5 cracks at the boundary between the laminae of the transverse direction (Fig. 4a–c). In addition, the failure behavior in which the boundary between the laminae was split and each lamina fell apart was observed in the layer in the transverse direction of 40t (Fig. 4d6).

In the 5-ply CLT specimens, the type of failure direction can be classified into two groups depending on the relationship between the positions of the finger joints of three laminae in the longitudinal direction on the tension side and the boundary of laminae in the transverse direction (Table 4), namely, (A) when more than two finger joints were located close to each other in the longitudinal direction on the tension side (the longitudinal distance between finger joints was 0–132 mm) and the boundary of the laminae in the transverse direction was close to them (the longitudinal distance between finger joints and the boundary was 0–131 mm), cracks occurred mainly in the depth direction of the CLT specimen, and (B) when the finger joints in the longitudinal direction on the tension side were separated (the longitudinal distance between finger joints was longer than 215 mm), cracks occurred mainly in the longitudinal direction along an adhesive layer on the tension side.

The results of crack type, failure direction type, and σ_b-CLT in each CLT specimen are shown in Table 5. The relationship between failure behavior and bending strength was not clear. Crack types 2, 3, and 5 were shown mainly in 20t, 30t and 40t. 424t specimens showed mainly crack types 1 and 4 in the outer layer. Failure behavior 6 was shown only in 40t. It is reported that the shear modulus decreased with the decrease in the ratio of width to thickness of the lamina [11]. In 40t, the width-to-thickness ratio of laminae in the transverse layers was small and G_TGH-CLT was lower than the others, as shown in Table 3. This could influence the failure behavior 6 caused by the specific deformation in transverse layers of 40t.

The relationship between shear modulus of CLT and the ratio of width to thickness of laminae

In the section of Bending failure behavior of CLT, it is considered that the failure behavior of 40t was influenced by the shear modulus which is related to the width-to-thickness of laminae. Therefore, from the data obtained in this study, the relationship between the width-to-thickness ratio and G_TGH-CLT/E_TGH-CLT are compared. The result is shown in Fig. 5. Because the lamina width was fixed and the lamina thickness was changed in this study, the difference of the width-to-thickness ratio means that the lamina thickness was different. As a result, G_TGH-CLT/E_TGH-CLT decreased as the width-to-thickness ratio of lamina decreased, that is, as the lamina thickness increased. G_TGH-CLT/E_TGH-CLT of 30t was 13.5% lower than that of 20t, and G_TGH-CLT/E_TGH-CLT of 40t was 30.3% lower than that of 30t. JAS defines the width-to-thickness ratio of lamina as 3.5 or more [4]. The value of 40t was 2.9 and G_TGH-CLT/E_TGH-CLT of 40t decreased significantly. Therefore, it is indicated that the width-to-thickness ratio of laminae in the transverse layer influences the shear modulus of CLT. To clarify the influence of the width-to-thickness ratio of laminae, further studies using laminae with the same thickness and different widths are needed.

Because Fig. 5 shows that the width-to-thickness ratio of the lamina, namely, the lamina thickness in this study, influenced G_TGH-CLT/E_TGH-CLT, it was expected that the portion of shear deflection would be different depending on the lamina thickness in the bending deflection. For this reason, bending Young’s modulus which takes into account the influence of shear deflection [E_{app-CLT-est.(τ)}] was calculated using Eq. (1) [4] and compared with the results of E_afb-CLT:

where l is load span, I is the moment of inertia of area, α is the shear distribution modulus and was set to 1.0, and A is the area in cross section.

The results of the ratio of E_afb-CLT to E_{app-CLT-est.(τ)} are shown in Table 6. The range of the results was 0.94–0.99, which means that E_{app-CLT-est.(τ)} was almost the same as E_afb-CLT. Hence, it was shown that all CLT specimens had the shear deflection in the bending test.

When the bending test is conducted, the total deflection (δ) is composed of deflections derived from bending stress and shear stress, which is represented as the following equation:

where δ_b is the deflection by bending stress and δ_s is the deflection by shear stress.

The shear–deflection-to-total-deflection ratio (δ_s/δ) was calculated using the following equation [23]:

As a result, 20t was 0.05, 30t was 0.06, 40t was 0.07, and 424t was 0.05. The shear–deflection-to-total-deflection ratio of 40t was the largest. This result can be explained by the small G_TGH–CLT/E_TGH–CLT of 40t. Therefore, it was suggested that a width-to-thickness ratio of the lamina in the transverse layer under 3.5 affects the shear modulus and increases the shear deflection.

MOE and MOR estimation of CLT

Using the results of the bending test of the laminae specimen, the bending Young’s modulus (E_app-CLT-est.) and the bending strength (σ_b-CLT-est.) of the CLT specimens were estimated by the following Eqs. (4) and (5) based on the composite theory [24]:

where σ₀ is the mean of bending strength of the outermost layer lamina specimen, n is the number of laminations, E_i is the mean of bending Young’s modulus of the lamina in the ith layer, I_i is the moment of inertia of area in the ith layer, A_i is the area of the cross section of lamina in the ith layer, z_i is the distance from the neutral axis of the CLT to the centroid of the lamina in the ith layer, E₀ is the mean of bending Young’s modulus of the outermost layer lamina specimen, I₀ is the moment of inertia of area in the CLT specimen.

The relationship between measured value and estimated value of the CLT specimens in the bending Young’s modulus and the bending strength is shown in Fig. 6. The ratio of the measured value to the estimated value in bending Young’s modulus and bending strength are shown in Table 7.

For the bending Young’s modulus, the measured value was 4–5% higher than the estimated value in 20t, 30t and 40t. The measured value of 424t was 16% higher than the estimated value. The E_app-CLT-est. was calculated using the mean of E_gm-laimna as the outer layer lamina instead of E_app-lamina. As a result, the ratio of the mean measured value to the estimated value of 20t, 30t, 40t, and 424t was 1.17, 1.11, 0.94, and 1.03, respectively.

For the bending strength, the measured value was 5% and 15% lower than the estimated value in 20t and 30t, and the measured value of 40t was the same as the estimated value. As for 30t, the experimental result which the bending strength was low, while the bending Young’s modulus was great might have influenced the difference between the measured and the estimated value. The measured value in 424t was 10% higher than the estimated value. In the previous study, it was reported that the bending Young’s modulus and bending strength could be estimated when the range of the ratio was 1.15 and 1.08 [2]. Therefore, it is considered that the bending Young’s modulus and bending strength can be estimated using the measured value of the laminae in this study, even considering the difference between the distribution of E_app-lamina and E_gm-lamina. However, as discussed in the section of the relationship between shear modulus of CLT and the ratio of width to thickness of laminae in the transverse layer, the amount of shear deflection was different in CLT specimens with different thicknesses. The estimation method using Eqs. (4) and (5) is based on composite theory [25]. Hence, the influence of shear deflection needs to be examined individually when estimating the bending Young’s modulus and bending strength of CLT composed of laminae with different cross section and layup.

The bending performance and failure behavior of 5-layer–5-ply and 3-layer–3-ply CLT composed of 20, 30, and 40 mm-thick laminae were investigated. The obtained results were as follows:

1. (1)

   It seemed that the influence of lamina thickness on bending strength of CLT is unclear, which is considered that the stress distribution in CLT specimens was different from that in the lamina specimen alone, because CLT is manufactured with layers stacked crosswise.

2. (2)

   The bending Young’s modulus and bending strength of 424t was greatest, because the ratio of parallel layer volume to the total volume was high.

3. (3)

   Regardless of the laminae thickness, finger joints of laminae in the longitudinal direction on the tension side between loading points play a significant role in the failure behavior of the CLT specimens. No clear relationship between bending strength or lamina thickness and failure behavior was observed.

4. (4)

   The shear modulus of 40t whose width-to-thickness ratio of the lamina in the transverse layer was less than 3.5 was 30.3% lower than that of 30t, and the failure behavior in which the boundary between the laminae was split and each lamina fell apart was observed in the transverse layer of 40t. It is possible that the specific deformation of the transverse layers caused by the small width-to-thickness ratio of the lamina in the transverse layers influenced the shear modulus. The effect of the width-to-thickness ratio of the laminae in the transverse needs to be studied in detail.

5. (5)

   The apparent bending Young’s modulus of CLT calculated by considering the influence of shear deflection agreed with the apparent bending Young’s modulus of CLT measured by TGH flexural vibration method. Therefore, it is considered that shear deflection occurred in the CLT specimens during the bending test and the thickness influenced to the amount of shear deflection.

6. (6)

   Under the conditions of this study, it was considered that the bending Young’s modulus and bending strength of the CLT specimens could generally be estimated using the bending Young’s modulus and bending strength of the laminae specimens by the composite theory. When estimating CLT specimens with different cross sections and layups from those in this study, it is necessary to examine the validity of the estimation method considering the influence of shear deflection.

The data sets generated and analyzed during the current study are available from the corresponding author on reasonable request.

E _gm-lamina :

Young’s modulus of lamina measured by continuous mechanical grading machine

E _fr-lamina :

Young’s modulus of lamina measured by the longitudinal vibration method

E _app-lamina :

Apparent bending modulus of lamina measured by the static bending test

σ _{b -lamina} :

Bending strength of lamina measured by the static bending test

E _afb-CLT :

Apparent bending Young’s modulus of CLT measured by TGH flexural vibration method

E _TGH–CLT :

True bending Young’s modulus of CLT measured by the Timoshenko–Goens–Hearmon (TGH) flexural vibration method

G _TGH-CLT :

Shear modulus of CLT measured by the TGH flexural vibration method

E _app-CLT :

Apparent bending Young’s modulus of CLT measured by the static bending test

E _true-CLT :

True bending Young’s modulus of CLT measured by the static bending test

σ _{b -CLT} :

Bending strength of CLT measured by the static bending test

E _{app-CLT-est .( τ)} :

Apparent bending Young’s modulus of CLT calculated by considering the influence of shear deflection

E _app-CLT-est. :

Apparent bending Young’s modulus of CLT estimated by the composite theory

σ _{b -CLT-est.} :

Bending strength of CLT estimated by the composite theory

CLT:

Cross-laminated timber

API:

Aqueous polymer solution-isocyanate

MC:

Moisture content

This study was conducted under a subsidiary project of the Forestry Agency in supplementary budget for fiscal 2022, the project for development and promotion of CLT and other wooden building materials. Part of this article was presented at the 42th Annual Meeting of Wood Technology Association of Japan in Kyoto, September 2024.

Not applicable.

Authors and Affiliations

1. Forestry and Forest Products Research Institute, 1 Matsunosato, Tsukuba, Ibaraki, 305-8687, Japan

   Miyuki Nakagawa, Yasushi Hiramatsu, Kenta Shindo, Fumiaki Ohki & Atsushi Miyatake

Contributions

All authors have read and approved the final manuscript.

Corresponding author

Correspondence to Miyuki Nakagawa.

Ethics approval and consent to participate

Not applicable.

Consent for publication

Not applicable.

Competing interests

The authors declare that they have no competing interests.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

Reprints and permissions