**Feasibility of predictive assessment of bending performance of CLT plates of Canadian hemlock**,"

*BioRes*. 14(3), 6047-6059.

#### Abstract

The correlation between the bending elastic modulus of lumbers along the primary direction and that of the resultant cross-laminated timber (CLT) plates in the full size suitable for slabs or wallboards was investigated to verify the feasibility of predicting the bending performance during the manufacturing of heavy building structures of this new type of material. A batch of Canada hemlocks lumber was graded based on a vibrational test that measures longitudinal elastic modulus. The elastic modulus and shear modulus in the transverse direction were also measured using the scheme of a torsional modal analysis of a cantilever plate. CLT were fabricated using the graded lumbers in sizes suitable for slabs or wallboards. The elastic moduli of these CLT products were measured using a conventional four-point static bending test. Finally, the static measurements of the elastic moduli of the CLT were compared with their predicted values that were calculated with the aforementioned data collected from the lumber pieces. The predicted elastic modulus along the primary direction of a CLT product agreed with the measured values. Therefore, the mathematical model of the CLT plate and the equation of its elastic modulus are feasible for the bending performance prediction in industrial production of CLT.

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#### Full Article

**Feasibility of Predictive Assessment of Bending Performance of CLT Plates of Canadian Hemlock**

Wenbo Xie, Yao Lu, Zheng Wang,* Xiwei Wang, Xiaoli Wu, and Zizhen Gao

The correlation between the bending elastic modulus of lumbers along the primary direction and that of the resultant cross-laminated timber (CLT) plates in the full size suitable for slabs or wallboards was investigated to verify the feasibility of predicting the bending performance during the manufacturing of heavy building structures of this new type of material. A batch of Canada hemlocks lumber was graded based on a vibrational test that measures longitudinal elastic modulus. The elastic modulus and shear modulus in the transverse direction were also measured using the scheme of a torsional modal analysis of a cantilever plate. CLT were fabricated using the graded lumbers in sizes suitable for slabs or wallboards. The elastic moduli of these CLT products were measured using a conventional four-point static bending test. Finally, the static measurements of the elastic moduli of the CLT were compared with their predicted values that were calculated with the aforementioned data collected from the lumber pieces. The predicted elastic modulus along the primary direction of a CLT product agreed with the measured values. Therefore, the mathematical model of the CLT plate and the equation of its elastic modulus are feasible for the bending performance prediction in industrial production of CLT.

*Keywords: Canadian hemlock; Lumber; Cross-laminated timber; Transverse vibration method; Bending performance; Prediction and evaluation; Application*

*Contact information: College of Materials Science and Engineering, Nanjing Forestry University, Nanjing, Jiangsu 210037, China; *Corresponding author: wangzheng63258@163.com*

**INTRODUCTION**

Cross-laminated timber (CLT) is a solid engineered wood product made of at least three layers of lumber or structural composite (SCL), bonded in a way that adjacent layers have orthogonal primary directions. Cross-laminated timber is a new-generation engineering material for wood products and heavy-duty wood structures for building systems that has the advantages of high strength-to-weight ratio, good load-bearing performance, anti-vibration, sound insulation, fire prevention, heat preservation, design flexibility, comfort and beauty, energy savings, and environmental friendliness, *etc*. Cross-laminated timber panels are modularized and prefabricated in a factory and then assembled onsite of construction, so that the building process is shortened. This is effective for shorter buildings, and it is suitable for buildings of intermediate height or even tall buildings over 20 stories. It is a competitive alternative to the traditional reinforced concrete and brick-concrete structures. Cross-laminated timber panels can be used in steel or reinforced concrete structures for partial replacement, making it very suitable for demonstration and promotion for China’s urbanization, holiday tourism, and rural construction (Fu 2012; Que *et al.* 2015; Yin 2015; Cao *et al. *2016; Wang *et al. *2019).

Western hemlock is widely grown in the coastal forests of British Columbia, Canada, and it is one of its main product species. Compared with spruce-pine-fir (SPF) and other species, western hemlock has the advantages of being inexpensive and having high flexural strength. It is better suited for a country like China, which lacks timber resources and relies on imports. However, hemlock is currently widely used in low value-added industries such as paper and plywood, not the construction industry. Although CLT is widely used in Europe and North America, CLT manufacturers are now limited to a few tree species in the production of CLT, such as Canadian SPF specifications, European red pine, and North American Douglas fir.

To provide a technical reference of CLT production in China, the feasibility and reliability of CLT sheet performance prediction and evaluation methods were verified.

**EXPERIMENTAL**

**Dynamic Test of the Elastic Modulus of the Serratus Sawn Timber and Its Quality Grading**

*Material and equipment*

The test materials were 550 samples of Western hemlock lumber, each 5500 mm × 140 mm × 40 mm in size and with an average dry density of 490 g/cm^{3} in and 16% to 19% in water content.

The instruments included a set of CRAS vibration and dynamic signal acquisition and analysis system (Nanjing Analyzer Software Engineering Co., Ltd., Nanjing, China), containing a signal acquisition box, signal conditioning box, and supporting analysis software, *etc*.; a CA-YD-125acceleration sensor (Sinocera Piezotronics Inc., Jiangsu, China), 1.5 g in mass, with sensitivity coefficient of 0.089 pc/ms^{-2}; a CA-YD-127 accelerometer (Sinocera Piezotronics Inc., Jiangsu, China), 38 g in mass, with a sensitivity coefficient of 3.2 pc/ms^{-2}; a rubber hammer; a free beam suspension; a scale (with a range to 100 kg and accuracy of 0.01 kg); and a steel tape measure (0 m to 10 m).

*Test principles and methods*

According to the lateral bending theory of the beam, the relationship between the first-order bending frequency of the free beam and the elastic modulus is,

(1)

where *E* is the dynamic elastic modulus of the free beam test material (Pa); *ρ* is the air-dry density (g/m^{3}); *f*_{1} is the first-order bending frequency value of the free beam (Hz); *l *is the free beam length (mm); and *h* is the free beam thickness (mm).

In this paper, the transient beam excitation method was used to test the grain elastic modulus value *E *(Wang *et al. *2015) of the hemlock sawn timber (CLT substrate) by using the free beam test piece. By testing the spectrum of the hemlock free beam test piece, it was identified from the spectrogram. The first-order bending frequency *f*_{1} of the free beam test piece was calculated using formula (1), and the test block diagram and the tested spectrum are shown in Figs. 1 and 2, respectively.

**Fig. 1.** Dynamic test block diagram of elastic modulus of lumber under free beam conditions

Figure 1 shows how first the free beam restraint was set up for the hemlock lumber specimen, which was wired with the dynamic signal acquisition and analysis system, and the accelerometer was firmly attached to the surface of the specimen. The parameters were set at 200 Hz analysis frequency, 4,096 FFT length, negative trigger acquisition mode, and ±5,000 mV voltage range. The hammer piece was struck with a rubber hammer to produce lateral free vibrations. After the accelerometer picked up the vibration, the mechanical vibration signal of the test piece was converted into an analog electric signal, and the lateral vibration spectrum of the sawn piece was obtained by signal amplification, filtering, A/D conversion, *etc*. Figure 2 is a spectrogram obtained by in the dynamic test of the specimen No. 101, and the first-order bending frequency value *f*_{1 }of the lateral vibration was obtained according to the spectrum identification method.

**Fig. 2. **Specimen 101 test spectrum of hemlock sawn timber

*Quality grading of elastic modulus of hemlock sawn timber*

The principle and method described above were used to test the dynamic elastic modulus of the same batch of 550 pieces of hemlock sawn timber specimens under free beam, and the probability distribution map was drawn (see Fig. 3 for details). The hemlock sawn timber specimens were divided into three grades according to their elastic modulus: less than 8,500 MPa for the CLT vertical layer laying materials; 8,500 MPa to 11,500 MPa for the wall panel CLT parallel layer laying materials, and more than 11,500 MPa for slab CLT parallel layers laying materials. The measured average elastic modulus of 550 hemlock sawn timber was 10,681 MPa, the standard deviation was 2,942 MPa, and the coefficient of variation was 27.5%. Among them, the amount of sawn timber with an elastic modulus of less than 8,500 MPa accounts for about 23% of the total.

**Fig. 3. **Probability distribution diagram of elastic modulus of hemlock lumber

**Dynamic Test of Transverse Elastic Modulus and Shear Modulus of Hemlock Sawn Timber**

*Material and equipment*

The test materials were 15 pieces of Western hemlock sawn timber used in previous test, 190 mm × (38.36 to 40.50) mm × (6.05 to 9.03) mm in size, 490 g/cm^{3} average air dry density *ρ* , and 16% to 19% in water content. The instruments for this test were the same as the ones used for the dynamic test of the elastic modulus of the serratus sawn timber described above.

*Test principle and method*

According to the cantilever beam bending vibration theory, the first-order bending frequency and elastic modulus of the cantilever beam conform to Eq. 2 (Gao *et al. *2016),

(2)

where *E* is the dynamic shear modulus of the cantilever plate test material (Pa); *f*_{b} is the first-order bending frequency value of the cantilever plate (Hz); *l *is the specimen length of cantilever (mm); and *h* is the test piece thickness (mm).

From the theory of torsional modal vibration of solid cantilevered rectangular members, the first-order torsional frequency and shear modulus are in accordance with Eqs. 3 through 6 (Wang *et al. *2016),

(3)

(4)

(5)

(6)

where *G* is the cantilever plate test material dynamic shear modulus (Pa) and *C _{1}*and

*C*are the vibration mode coefficient of the torsional vibration of the cantilever plate, respectively.

_{2}*β*is the rectangular section factor.

The spectrum block diagram of the cantilever plate test piece is shown in Fig. 4. According to the spectrum of the cantilever plate specimen (Fig. 5), the first-order bending frequency *f*_{b}and the first-order torsional frequency *f*_{1 }are obtained from the spectrum by cross-power spectrum identification.

**Fig. 4. **Dynamic test block diagram of shear modulus of fir lumber under cantilever plate

**Fig. 5.**Test spectrum of horizon of hemlock sawn timber specimens 12

Substituting the relevant parameters of the hemlock sawn timber into Eqs. 2 and 3, the elastic modulus value *E’* and the shear modulus *G* of the 15 pieces of the hemlock sawn timber transverse test piece were obtained, and the test results are shown in Table 1.

**Table 1. **Elastic Modulus and Shear Modulus of Horizontal Specimens of Hemlock Lumber under Cantilever Boar

**CLT Structural Design and Performance Prediction and Evaluation Normal Stress of Three-Layer CLT Beam**

*CLT blanking scheme and structural design*

The sawn timber pieces used to make six CLT plates were randomly selected from the classified sawn timbers, three of which were used as floor slabs and three as wall slabs. The CLT was a three-layer structure with a plate size of 5,500 mm × 1,200 mm ×105 mm.

**Table 2. **Performance Parameters of Sawn Timber Used in CLT