**"2D model of strength parameters for bamboo scrimber,"**

*BioRes*. 9(4), 7073-7085.

#### Abstract

Experiments were performed to test the compressive strength of bamboo scrimber board at different grain angle directions. Investigation of test samples allows for the identification of the correlation between compression failure stress and various failure mechanisms at different grain angles. The results of the experiments showed that the density of bamboo scrimber influenced compression failure stress linearly. A new approach to describe the failure stresses of bamboo scrimber was proposed. The density was introduced as a model parameter to describe compressive properties at varying angles of grain. In comparison to a one-dimensional model, there was much less relative error between predicted values and measured values by this 2D model. This report aims to improve the precision of existing strength models for various grain angles and to provide a competing method for the practical use of bamboo scrimber.

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#### Full Article

**2D Model of Strength Parameters for Bamboo Scrimber**

Weiwei Shangguan, Yong Zhong, Xinting Xing, Rongjun Zhao, and Haiqing Ren*

Experiments were performed to test the compressive strength of bamboo scrimber board at different grain angle directions. Investigation of test samples allows for the identification of the correlation between compression failure stress and various failure mechanisms at different grain angles. The results of the experiments showed that the density of bamboo scrimber influenced compression failure stress linearly. A new approach to describe the failure stresses of bamboo scrimber was proposed. The density was introduced as a model parameter to describe compressive properties at varying angles of grain. In comparison to a one-dimensional model, there was much less relative error between predicted values and measured values by this 2D model. This report aims to improve the precision of existing strength models for various grain angles and to provide a competing method for the practical use of bamboo scrimber.

*Keywords: Bamboo scrimber; Compressive properties; Density; Grain angle; 2D model*

*Contact information: Research Institute of Wood Industry, Chinese Academy of Forestry, 1 Dong Xiao Fu, Xiang Shan Road, Hai Dian, Beijing, China, 100091; *Corresponding author: renhq@caf.ac.cn*

**INTRODUCTION**

A bamboo scrimber includes a plurality of pressure-pressed bamboo strips impregnated with an adhesive and modified through heat-treatment. Each of the bamboo strips is formed with a plurality of slots penetrating through the bamboo strip substantially in a direction of thickness defined by the bamboo strip (Zhang* et al*. 2011). Reconsolidated wood, which is proposed by Coleman (Coleman and Hills 1980), provides references for bamboo scrimber. Research related to bamboo scrimber started about 20 years ago in Asian countries (Zhang and Yu 2008). Due to its excellent processing performance, bamboo scrimber has been widely used in indoor decoration and in the civil engineering field (Zhang *et al*. 2008; Zhang *et al*. 2012; Yu *et al*. 2014). In the development of manufacturing technique for bamboo scrimber, press technology and glue immersion have been studied, and ideal process parameters for bamboo scrimber have been determined (Cheng* et al*. 2009; Wang *et al*. 2013; Yu and Yu 2013). However, mechanical models of bamboo scrimber have not been widely reported. In the aspect of being as a building material for wooden structures, the development of strength models for bamboo scrimber is important for future applications of the material and in the dissemination of the material in the wood structure field.

Grain angle, which affects the mechanical properties, is a significant factor in the application of bamboo scrimber. Researchers have proposed many strength models regarding to the relationship between grain angle and mechanical properties. Among those models, the Hankinson formula (Hankinson 1921), Norris formula (Norris 1962), Maximum stress theory, and Tsai-Hill theory (Tsai 1965) are the most widely used criteria for predicting mechanical properties of structural materials (Liu 1984; Mascia and Simoni 2013). The compressive behavior of spruce wood under uniaxial loading has been studied by Reiterer and Stanzl-Tschegg (2001) at different orientations with regard to the longitudinal and radial direction. Tsai-Hill strength criterion was used to describe the tendency of crushing strength at various grain angles. The predicted values from the model were in accordance with the observed values because the density of the wood sample was fairly uniform. The Hankinson formula, Maximum stress theory, and Tsai-Hill theory are applied to estimate the strength of laminated veneer lumber by uniaxial tension test at various angles to the grain (Oh 2011). These criteria predict the approximate tension strength at different grain angles. However, there are errors between prediction data and measured values. This may be due to density variation caused by uneven sizing. However, the presumption of these models is the uniform density of samples used in them. Materials with uneven density in real processes are normal. This reality should not be neglected.

Density is another strength parameter affecting the mechanical properties of biomass materials. In most studies, material density and grain angle are studied separately (Galicki and Czech 2005; Machado* et al*. 2014). A linear regression analysis indicated that 84% of the variability of compression strength could be explained by density (Gindl and Teischinger 2002). Failure mechanisms of pine wood under off-axis compression had been studied by Oh (2011), but the correlation between density and off-axis strength was not considered as in the study of Galicki and Czech (2013), causing errors in the practical application for biomass materials with various densities. Density and grain angle have been considered in a 2D model by Galicki (2009) and resulted in a high degree of agreement between experimental and model data. Therefore, establishing a 2D strength model relating to density and grain angle as two parameters of strength could be a potential method for predicting bamboo scrimber mechanical properties.

Due to uneven sizing during the production process and the density discrepancy between bamboo fiber and adhesive, density differences exist on the same bamboo scrimber board. The predicted values from existing strength models are not accurate when including both the parameters of density and grain angle. In this paper, a 2D model for strength parameters of bamboo scrimber was established. The new model improves prediction accuracy, refines the compressive model for various grain angles, and provides technical support to the field of wood structure for the application of bamboo scrimber.

**EXPERIMENTAL**

**Materials**

*Neosino calamus affinis*, age 3-4 years, was used as a raw material to produce bamboo scrimber. The nominal dimension of each board was 250 cm (length) × 64 cm (width) × 3.4 cm (thickness). Untreated bamboo fiber bundles were laid in parallel, and a PF162510 phenol-formaldehyde resin (Dynea Co., Beijing City, China) (45.59% of solids content, 36CP·s of viscosity, 10-11 pH) was used. The amount of glue was controlled to about 15% of the dry weight of the bamboo scrimber during dipping glue process. After that, bamboo scrimber fiber bundles were kept at a temperature of 140 °C and a pressing pressure of 5.0 MPa for a holding time of 34 min (1 min/mm ×34 mm). The average air-dry density and moisture content of the bamboo scrimber boards were 1.12±0.9 g/cm^{3} and 7.42±0.96%, respectively.

The nominal dimension of the sample used for compression studies was 20 mm (length) × 20 mm (width) × 30 mm (height). Specimens with grain angles of 0°, 10°, 20°, 30°, 40°, 50°, 60°, 70°, 80°, and 90° were prepared for the compression test, as shown in Fig. 1.

**Fig. 1.** Specimens for compressive test at *θ* (ranged from 0 º to 90 º). P is compressive load; a, b and c are 20 mm, 20 mm and 30 mm, respectively

**Methods**

*Compression testing*

Bamboo scrimber is an orthotropic material, so there are three principal axes for which the mechanical properties differ. The angles (*θ*) between loading direction and fiber direction ranged from 0° to 90°. A total of 400 samples were tested, 40 samples at each grain angle.

The densities of the samples (total of 400 samples) ranged from 0.85 g/cm^{3} to 1.35 g/cm^{3}. To ensure the random distribution of the samples, specimens of one grain angle were cut from different parts of the five boards, as shown in Fig. 2.

**Fig. 2.** Sawing pattern of grain angles

Eight samples for each grain angle were prepared from one board. The sampling distribution for ten grain angles on each board is shown in Fig. 2. Sawing patterns in Fig. 2 could guarantee the samples of each grain angle to be obtained from both the middle and the edge of the board.

Forty samples, with known densities, were prepared and tested at each grain angle on an Instron 5582 Universal Testing Machine with an accuracy of 0.001MPa (Instron Co., Grove City, PA, USA) (Fig. 3). The samples were loaded to failure at 1 mm/min, and the maximum load was taken as the failure load.

**Fig. 3.** Compression test set-up

*Model formulas*

The mechanical models used to predict compressive properties at various grain angles in this experiment were the Hankinson formula (Hankinson 1921) and the Chinese National Standard GB 50005 (2003) formula,

Hankinson formula:

GB 50005 formula:

where *f* denotes the compressive properties when the angle is *θ* between loading direction and grain direction (Fig. 1), and *f*_{1} and *f*_{2} are the compressive properties parallel and perpendicular to the grain, respectively.

*Kolmogorov-Smirnov test*

The Kolmogorov-Smirnov test (K-S test) can serve as a goodness of fit test (Kolmogorov 1933). In the case of testing for normality of distribution, samples are standardized and compared with a standard normal distribution. The formula is,

where *S(x)* and *F(x) *are the cumulative probability value from the sample and theoretical distribution, respectively. Normal distribution is chosen to be *F(x),* and maximum absolute difference between* S(x)* and *F(x)* was taken as *D*.

If *D*<, then the difference between *F(x)* and *S(x) *is significant. If *D*>, the difference between *F(x)* and *S(x)* is not significant. The is chosen to be 0.05.

*Shapiro-Wilk test*

The Shapiro-Wilk test can check whether a sample came from a normal distributed population (Shapiro and Wilk 1965). The test formula is,

where *x _{i}* is the

*i*th order statistic, is the sample mean, and the

*a*

_{i}_{ }series represents the constants, which are calculated by,

where *m=(**m _{1}, . . ., m_{n} )^{T}*,

*m*

_{1}, . . ., m_{n}_{ }are the expected values of the order statistics of independent and identically distributed random variables sampled from the standard normal distribution, and

*V*is the covariance matrix of the order statistic.

If *W*<, then the difference between the normal distribution and the tested distribution is significant. If *W*>, then the difference between the normal distribution and the tested distribution is not significant. The value is chosen to be 0.05.

**RESULTS AND DISCUSSION**

**Failure Types**

The failure types of the tested bamboo scrimber samples according to grain direction are shown in Fig. 4. The shear failure parallel to grain was predominant at all grain angles except for 0° and 90°. The failure type of 10° samples was similar to the 0° sample due to the slight grain angle of 10° samples.

Dislocation occurred from 20° to 50° grain angles samples. This was because shear force parallel to grain was large among these grain angles. Samples from 60° to 90° displayed cracking along the sample grain and approached compression perpendicular to the grain gradually.

**Test of Normality for Density**

A histogram and the normal distribution curve of density for the 400 samples are shown in Fig. 5. Kolmogorov-Smirnov test was used in the normality test of density.

**Fig. 4.** Failure types of tested bamboo scrimber specimens according to grain direction (from left to right: 0°, 10°, 20°, 30°, 40°, 50°, 60°, 70°, 80°, 90°)

**Fig. 5.** Histogram and the normal distribution curve for sample density data

**Table 1. **Normality Test of Density using Kolmogorov-Smirnov (K-S) Method

The maximum frequency of the sample density was around 1.1 g/cm^{3}, which was close to the average density of the sample. This result shows that density deviation, which can affect mechanical properties, exists in bamboo scrimber board despite much efforts directed to alleviating it during manufacturing. In Table 1, the K-S test, which requires a relatively large number of data points (Zhang 2004), shows that the level of significance is over 5%. It indicates that density data are consistent with a normal distribution. Since normal distribution of the sample density illustrates the independence and randomness of sampling, the data are considered reliable and can be used for modeling.

**Test of Normality for Ultimate Strength**

Samples of various grain angles were selected from five boards. The ultimate strengths were tested, and the data followed normal distributions. Histograms and normal distribution curves for the angles *θ*=0° and *θ*=90°, which are the required angles in Hankinson formula and the GB 50005 formula, are shown in Fig. 6. Shapiro-Wilk test was used in the normality test of ultimate strength.

**Fig. 6.** Histograms and normal distribution curves for ultimate strength with θ = 0° and θ = 90°

**Table 2. **Normality Tests of Ultimate Strengths using Shapiro-Wilk Method

The ultimate strengths for specimens of *θ *= 0° and *θ *= 90° show normal distributions. The maximum frequency of ultimate strength parallel to grain was around 133 MPa, which equals the average strength for *θ *= 0° angle samples. The maximum frequency of ultimate strength perpendicular to grain was around the average strength (21 MPa). The Shapiro-Wilk test (Table 2), which is limited to samples between 3 and 50 elements (Zhang 2004), shows that significance levels for both 0° and 90° samples are over 5%. This result verifies that samples of *θ *= 0° and *θ *= 90° obey normal distribution and that the ultimate strength data are reliable for use in modeling.

**Compressive strengths of grain angles**

Compressive strength of bamboo scrimber declined while the grain angles increased from 0° to 90°. In Fig. 7, compressive strength decreased dramatically from 0° to 50° grain angles, and changed slightly from 60° to 90°. Thus, more attention should be paid to grain angles from 0° to 50° than from 60° to 90° in the application of bamboo scrimber. The trend of the curves predicted by GB 50005 formula and Hankinson formula agreed with the test values. Calculated values by GB 50005 formula were higher than that predicted by Hankinson formula, and values predicted by GB 50005 deviated from test values greater than that of Hankinson formula from 0° to 50° grain angles. However, predicted values of GB 50005 formula were closer to test values from 60° to 90° grain angles. From Fig. 7, it can be seen that the accuracy of Hankinson formula was higher than GB 50005 formula.