Abstract
The standard values of mechanical properties are important performance indexes of original bamboo as a sustainable building material. Such values should be determined by combining the requirement of confidence level and the number of samples. In this paper, systematic tests of longitudinal compression, bending, longitudinal tensile, longitudinal shear, transverse compression, and transverse tensile of bamboo were performed. Based on parametric and non-parametric methods, the influencing factors of the standard values of mechanical properties of bamboo were analyzed. A calculation method and prediction formulas were proposed and the standard values of mechanical properties of bamboo were determined. The results show that the choice of parametric method to calculate the standard value of bamboo strength in the case of a small number of samples may lead to distortion of the results, and the use of non-parametric analysis can effectively reduce the error.
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Improved Method to Determine Standard Values of Mechanical Properties of Original Bamboo
Jianwei Li, Pengcheng Liu,* Haodi Chen, and Fangjie Cheng
The standard values of mechanical properties are important performance indexes of original bamboo as a sustainable building material. Such values should be determined by combining the requirement of confidence level and the number of samples. In this paper, systematic tests of longitudinal compression, bending, longitudinal tensile, longitudinal shear, transverse compression, and transverse tensile of bamboo were performed. Based on parametric and non-parametric methods, the influencing factors of the standard values of mechanical properties of bamboo were analyzed. A calculation method and prediction formulas were proposed and the standard values of mechanical properties of bamboo were determined. The results show that the choice of parametric method to calculate the standard value of bamboo strength in the case of a small number of samples may lead to distortion of the results, and the use of non-parametric analysis can effectively reduce the error.
DOI: 10.15376/biores.18.4.8374-8393
Keywords: Bamboo; Mechanical properties; Standard values; Calculation coefficient; Sampling sequence number
Contact information: School of Civil Engineering, Central South University, Changsha 410075, China; *Corresponding author: pengchengliuwork@163.com
INTRODUCTION
Bamboo is a natural, green, renewable material that can be an ideal building component. Bamboo has a wide distribution range, many varieties, and is rich in resources. China is the most developed country in the bamboo industry and its bamboo planting area and bamboo product production rank first in the world. Bamboo has a close connection with Chinese culture and people’s life. Bamboo is found everywhere, in clothing, food, housing, transportation, history, and culture. With its excellent mechanical properties, bamboo is known as “plant reinforcement” and “ultimate green material” and is an ideal green building material (Sun et al. 2019; Tian et al. 2019a; Dauletbek et al. 2023; Zhou et al. 2023). At present, industrial bamboo building products have been developed, including cladding materials (Von Seidlein et al. 2017), bamboo plywood (Li et al. 2019), bamboo laminate (Guan et al. 2022b), bamboo fiberboard (Shi et al. 2023), bamboo scrap board (Guan et al. 2022a), bamboo decorative materials (Chen et al. 2019), etc.
In 1984, a bamboo building (Fig. 1a) combining traditional Chinese construction techniques with modern science and technology was exhibited in Zurich, Switzerland. The building area was about 1200 m2, meeting the requirement load of 300 kN/m2 (Yang 2014). In 2008, the “Green School” (Fig. 1b) was built in Bali, Indonesia. The campus not only has the largest bamboo building complex in the world, but also adopts the green energy system for supporting facilities (Landwehr and Bambú 2016).
The German-Chinese Pavilion at the 2010 Shanghai World Expo (Fig. 1c) is a two-story building with original bamboo and bamboo laminated timber (Markus and Liu 2013), which has become a typical project symbolizing German-Chinese friendship. In 2011, the pure original bamboo bird wing structure (Fig. 1d) in Vinh Phuk Province, Vietnam was awarded the International Architecture Award by the Science Museum of Chicago as a typical example of eco-green architecture (Tian et al. 2019b).
In 2019, the bamboo and rattan pavilion of Beijing International Horticultural Exposition (Fig. 1e) adopted the original bamboo arch architecture system, with the span of bamboo arch reaching 32 m, which is the largest non-fulcrum arch of original bamboo architecture in northern China (Su et al. 2020). In 2021, the original bamboo building (Fig. 1f) of Baizhi Mountain Tourist Reception Center in Zunyi, Guizhou, developed by China Metallurgical Construction Engineering Group, was completed. The scale of the project is 1000 m2, the span is 28 m, and the height is 15 m. Under the background of the strategic goal of “carbon peak and carbon neutrality” stated by the Chinese government, ten departments of China have presented opinions on accelerating the innovation and development of the bamboo industry. Under the condition of satisfying the quality and safety, bamboo structure building and bamboo building materials should be gradually promoted.
For wood used in construction, the strength standard value is usually selected to determine its strength grade. Therefore, the reasonable determination of the standard value of structural wood strength is one of the keys to its reliable application in building structures.
The Chinese standard “Specification for Wood Structure Design” (GB 50005 2017) does not mention any method of obtaining values and formulas used to predict standard values of bamboo mechanical properties. It is assumed that the index values of mechanical properties obey a normal distribution, and that the calculation coefficient of standard values is uniformly stipulated as 1.645. This method has major disadvantages. Not only does it not consider the confidence level, but also ignores the influence of the number of samples on the results, which may lead to a large error in the results.
At present, other national specifications (ASTM D2915-17; EN 1058-2009) all take 5% quantile value under 75% confidence level as their standard strength value, and the methods to determine it include parametric and non-parametric methods. The key of parameter method analysis is to determine the calculation coefficient of standard value according to the number of samples. The key to non-parametric analysis is to determine the sampling sequence number of the standard value according to the number of samples. Based on three probability distribution models, this study derived the calculation formula of the standard value of bamboo, respectively, based on the parametric method and non-parametric method. Additionally, it provided the value requirements of the value coefficient of the standard value (parametric method) and the sampling sequence number of the standard value (non-parametric method) under different strength variation coefficient, sample number, and confidence level. The calculation method of strength standard value proposed in this paper can provide reference for material analysis and structural design.
Fig. 1. Application of original bamboo structures: (a) The Zulli Bamboo Tower in Switzerland; (b) Green School, Bali, Indonesia; (c) German-Chinese pavilions at the Shanghai World Expo; (d) Vietnamese bird-winged bamboo structure; (e) Bamboo and rattan Pavilion of Beijing World Horticultural Exhibition; (f) Baizhi Mountain Tourist Reception Center
EXPERIMENTAL
Materials and Test Methods
The bamboo species considered in this paper is P. edulis bamboo, which was collected from Hunan Province, China. The bamboo was 3 to 4 years old, and the average moisture content was approximately 11%. Multiple mechanical properties tests were performed on the bamboo with reference to JG/T199-2007 (2007) and ISO 22157-1-2019 (2019), and the following mechanical properties were obtained: longitudinal compressive strength (UCS), longitudinal compressive elastic modulus (UCE), bending strength (MOR), bending elastic modulus (MOE), longitudinal tensile strength (UTS), longitudinal tensile elastic modulus (UTE), longitudinal shear strength (USS), transverse compressive strength (CCS), and transverse tensile strength (CTS).
The design of the specimens is shown in Table 1 and Fig. 2. The size ratio H/D (height/diameter) of the longitudinal compression and longitudinal shear specimens was 1, and the loading rate was 0.01 mm/s.
The bending specimen size was 220 mm × 15 mm × t mm (t refers to the wall thickness), and the loading rate was 150 N/mm2 per minute. The size of the longitudinal tensile specimen was 330 mm × 15 mm × t mm, and the tensile rate was 0.01 mm/s. The size of the transverse compressive specimen was 15 mm × 15 mm × t mm, and the compressive rate was 20 N/mm2/min. The length of the transverse tensile specimen was 100 mm, and the tensile rate was 0.005 mm/s. And the mechanical properties were calculated using Eqs. 1 through 4,
where fW is the strength of the specimen under the moisture content W with UCS, USS, UTS, CCS, and CTS (MPa). EW is the elastic modulus along the grain direction under the moisture content W (MPa); MORW is the flexural strength under the moisture content W (MPa); MOEW is the flexural elastic modulus under the moisture content W (MPa); Pmax is failure load (N); A is the force area (mm2); t is the thickness of the specimen (mm); b is the height of the specimen (mm); ∆P is the difference between upper and lower loads (N); ∆l is the difference between the deformation value of the specimen under the upper and lower loads (mm); and δm is the pure deflection of the specimen under the action of ∆P (mm).
Table 1. Test Specimen Design
Note: In the table, t refers to the wall thickness.
Fig. 2. Specimen preparation
After the failure of the specimen, the small specimen was immediately cut off at the failure site for the determination of moisture content. Equation 5 is the calculation method of moisture content. The mechanical properties of bamboo were adjusted to the values under the standard moisture content (12%), and the calculation formula is Eq. 6,
where W is the air-dried moisture content (%); m1 and m0 are the mass of air dry and full dry, respectively (g); M12 is the strength or elastic modulus of the specimen under the standard moisture content (12%); MW is the strength or elastic modulus of the specimen when the moisture content is W; and KW is the moisture content correction factor.
The Calculation of Confidence of Standard Value under Parameter Method
Under the parameter method, the calculation coefficient K of the standard value of the mechanical properties of bamboo has nothing to do with the true mean value of the material (Zhong et al. 2018). Using MATLAB (MathWorks, R2022a, U.S.) programming, suppose the mean value of mechanical properties μ = 200 MPa, the range of coefficient of variation Cv is [0.05, 0.5], and the range of standard deviation δ is [10 MPa, 100 MPa]. The 5% quantile value P of the original bamboo strength sample data can be calculated according to the mean μ, standard deviation δ, and probability distribution model. First, it is assumed that the mechanical properties of bamboo obey the Normal distribution, Lognormal distribution, or 2-P-Weibull distribution, and a random sequence of columns I and rows J is generated according to the assumed μ and δ, where I = 10000. Assume that the mean value of each column of the resulting matrix is μi and the standard deviation is δi. If the calculation coefficient of the standard value is K, the standard value Xi of the mechanical properties of original bamboo can be calculated according to the following Eq. 7,
Compare the Xi of each column with the 5% percentile value P, and if the value of column Z is not greater than P, the confidence level r for the calculation coefficient K is calculated as follows:
The calculation flow chart of the confidence level r of the standard value of mechanical properties of the original bamboo based on the parameter method is shown in Fig. 3a.
Calculation of Confidence of Standard Value under Non-parameter Method
Under the non-parametric method, the calculation coefficient K of the standard value of the mechanical properties of bamboo has nothing to do with the true mean value of the material (Zhong et al. 2018). When analyzing the standard value of bamboo strength through the nonparametric method, using MATLAB (MathWorks, R2022a, U.S.) programming, each sample is sorted according to the value size from small to large, and then the data in the row of each sample is compared with the 5% quantile value P. If the value of W samples is less than or equal to P, the corresponding confidence level r can be calculated as follows for S = i:
The calculation flow chart of the confidence level r of the standard value of the mechanical properties of the original bamboo based on the non-parametric method is shown in Fig. 3b.
Fig. 3. Calculation flow chart: (a) Parameter method; (b) Non-parametric method
RESULTS AND DISCUSSION
Analysis of Test Results
The failure modes of mechanical properties of bamboo can be divided into ductile failure and brittle failure. The longitudinal compressive specimens have a long yield platform in the loading process, which provides obvious warning before failure. The bending deformation of the flexural specimen is visible to the naked eye in the loading process, and finally the specimen suddenly fails. The transverse tensile, transverse shear, and transverse tensile specimens all fail without warning during the test. The transverse compressive specimens are similar to the transverse compressive specimens in that the deformation varies greatly with loading. To summarize, the tests for ductile failure include longitudinal compression and transverse compression, while the tests for brittle failure include flexural, longitudinal tensile, longitudinal shear, and transverse tensile. Figure 4 shows the photos of the specimens when they are damaged.
The mechanical properties of bamboo were statistically analyzed, and the results as shown in Table 2 and Fig. 5 were obtained. The average UCS, UCE, MOR, MOE, UTS, UTE, USS, CCS, and CTS of bamboo were 57.48 MPa, 13.92 GPa, 132.36 MPa, 17.84 GPa, 145.08 MPa, 16.44 GPa, 15.92 MPa, 27.29 MPa, and 4.70 MPa, respectively. Bamboo has good longitudinal tensile, compressive, and flexural properties, but relatively poor longitudinal shear and transverse mechanical properties.
Fig. 4. Damage forms of bamboo
Table 2. Mechanical Properties Statistics
Note: μ is the average value, δ is the standard deviation, and Cv is the coefficient of variation.
Fig. 5. Statistics of mechanical properties of bamboo: (a) Strength; (b) Elastic modulus
Analysis of Influencing Factors of Standard Values under Parametric Method
The influencing factors of confidence
The calculation coefficient K of the characteristic values of the mechanical properties has nothing to do with the material mechanics performance of the real average. Therefore, the assumption is the average size of various mechanical properties of original bamboo (UCS, UCE, UTS, UTE, MOR, MOE, USS, CCS, and CTS) is 200 MPa. The range of variation coefficient Cv of various mechanical properties of bamboo is [0.05, 0.50]; that is, the range of standard deviation δ is [10 MPa, 100 MPa]. Normal model, Lognormal model, and 2-P-Weibull model are generally used as the probability distribution models of original bamboo. Different probability distribution models have certain influence on the value of mechanical properties characteristic values of original bamboo. The results under Normal model, Lognormal model, and 2-P-Weibull model are obtained through MATLAB programming and calculation. Figures 6 through 8 show the results of calculation and analysis under Normal model, Lognormal model, and 2-P-Weibull model, respectively, in which the coefficient of variation is 0.2 and 0.4, the number of samples n is 50, and the calculation coefficient K of parameter method is 1.5, 2.0, and 2.5, respectively. It can be seen from Fig. 6 that under Normal probability distribution model, when the coefficient of variation is constant, confidence r increases with the increase of calculation coefficient K. When Cv = 0.2, the confidence r corresponding to K 1.5, 2.0, and 2.5 are 0.2331, 0.9232, and 0.9985, respectively, that is, 2331, 9232, and 9985 mechanical properties characteristic values of original bamboo in 10,000 samples are less than 5% of their true values P. When Cv = 0.4, there are 2323, 9231, and 9989 mechanical properties of bamboo with K are 1.5, 2.0, and 2.5, respectively, which are less than 5% of their true values P. Through comparing the results of different coefficient of variation, it can be seen that Cv increases from 0.2 to 0.4, and the change of confidence r is extremely small and negligible.
Fig. 6. Influence of K and Cv on r under Normal distribution model
According to Fig. 7, under the Lognormal probability distribution model, confidence r gradually increases with the increase of K under the same Cv. For the same K, the confidence r increases with the increase of Cv. Through comparing Figs. 6 and 7, it can be seen that under the same conditions, the confidence r of Lognormal probability distribution model is higher than that of Normal probability distribution model.
Fig. 7. Influence of K and Cv on r under Lognormal distribution model