- Original article
- Open Access
Research on design value of compressive strength for Chinese fir dimension lumber based on full-size testing
- Yingchun Gong^{1},
- Guofang Wu^{1},
- Xiuqin Luo^{1},
- Zhaohui Wang^{1},
- Jinghui Jiang^{1} and
- Haiqing Ren^{2}Email author
https://doi.org/10.1007/s10086-016-1592-1
© The Japan Wood Research Society 2016
- Received: 29 July 2016
- Accepted: 15 October 2016
- Published: 25 November 2016
Abstract
The objective of this study was to obtain design value, which was calculated according to the limit states design method, for the utilization of Chinese fir in the building structure field as a green building material. A total of 342 specimens were tested by static compression method. The normal and lognormal distributions were selected to fit the experimental data. The results indicated that reliability index increased nonlinearly with the live-to-dead ratio and resistance partial coefficient increased. To meet the target index (β _{0} = 3.2), it was suggested that design values of compressive strength of Chinese fir were set to 13.751, 13.186, and 13.123 MPa for SS, No. 1, and No. 2 grade, respectively.
Keywords
- Design value
- Chinese fir
- Compressive strength
- Limit states design method
Introduction
With the rapid development of the wooden structure in China, the demand for wood resources has been increasing in recent years. However, due to enforcing logging-ban at the natural forest effective in 2015 in China, wood nature resources is in serious shortage. Therefore, plantation resources need to be developed and utilized in China. Chinese fir (Cunninghamia lanceolata) is one of the three main plantation tree species in China. It distributes from latitude 22–34°N and longitude 100–122°E. Chinese eighth national forest resources survey shows that the area of plantation of Chinese fir is 9.21 million ha [1, 2]. In the meantime, Chinese fir has many advantages, such as fast-growing, good mechanical performance, and decay resistance. It has been widely used to fabricate dimension lumber, glued lumber, and wood-based composites [3, 4]. However, due to the lack of design values of mechanical properties for engineered wood products, thus it is unsafe to use these in the building structure filed.
Dimension lumber has standardized design dimensions. It has been used in a variety of applications including in building frame, floor, and wall components [5, 6]. The visual grading and machine stress rated methods were applied to evaluate the strength grading of dimension lumber. According to National Lumber Grades Authority (NLGA)–Standard Grading Rules for Canadian Lumber [7], the visual grading divided lumber into four grade including SS, No. 1, No. 2, and No. 3, based on wood growth characteristics. It lines up with the classification in Chinese National Code [8] including Ic, IIc, IIIc, and IVc grade.
There are significant differences on the design value of mechanical properties for the same grade dimension lumber, because different countries have different evaluation methods, load statistics, and load combinations. For example, the statistics of snow load (q), which equals the ratio average value and standard value, is 1.04 in China, but q value ranges from 0.61 to 0.82 in the United States [9]. Furthermore,design value of wood strength is generally determined by full-size testing and small clear specimens testing [10]. Comparing these two methods, the full-size testing takes natural defect, size effect, and other factors into consideration. Therefore, the test results are much closer to the actual situation. The previous research [11] reported that the length had significant effect on tensile strength of visually graded Chinese fir dimension lumber. Currently,the full-size testing method has been applied in the United States, Canada, and Japan to determine the flexural, compressive, and tensile strength of dimension lumber [12, 13]. However, according to Code for design of timber structures [8], the design value is still based on small clear specimens testing for dimension lumber fabricated with native tree species.
In this study, a total of 342 specimens were tested by static compressive method. The object was to determine design values of full-size compression strength parallel to grain (UCS) for Chinese fir dimension lumber based on the first-order second-moment reliability analysis. The research on design value will provide basic data for the application of Chinese fir in the building structures filed.
Materials and methods
Materials
Sample size of each grade
Grade | Sample size |
---|---|
SS | 136 |
No. 1 | 98 |
No. 2 | 108 |
Static test methods
Probability distribution
The normal and lognormal distributions are generally adopted as parametric statistical model in the analysis of mechanical properties. The probability density function
f (x) and cumulative distribution function of standard normal distribution ϕ (x) can be expressed as follows:
1. Normal distribution
2. Lognormal distribution
Kolmogorov–Smirnov test
At the 0.05 level of significance,the D _{0.05} is equal to \( {{1.36} \mathord{\left/ {\vphantom {{1.36} {\sqrt n }}} \right. \kern-0pt} {\sqrt n }} \) and n is the number of samples. If D is smaller than D _{0.05}, the theoretical distribution s(x) can provide a good fit to the cumulative probability value ϕ(x) obtained by the static testing. If D is larger than D _{0.05}, the theoretical fitting distribution s(x) failed.
Results and discussion
Results of compressive test
The compression strength adjusted to 15% moisture content for Chinese Fir dimension lumber
Statistical parameters | UCS_{15} | In(UCS_{15}) | ||||
---|---|---|---|---|---|---|
SS | No. 1 | No. 2 | SS | No. 1 | No. 2 | |
Mean value (MPa) | 30.71 | 28.38 | 29.37 | 3.41 | 3.28 | 3.30 |
Standard deviation (MPa) | 4.88 | 3.84 | 4.61 | 0.16 | 0.11 | 0.14 |
COV (%) | 15.90 | 13.55 | 15.70 | 4.70 | 3.35 | 4.24 |
Difference between measurement data of each grade was conducted through analysis of variance (ANOVA). The results showed that the UCS_{15} values showed the highly significant differences between each grade of dimension lumber (P < 0.05, at the significance level of 0.05). Therefore, the NLGA visual grading method is an adequate method to divide the UCS_{15} for Chinese fir dimension lumber.
Probability distribution
Results of compressive strength using K–S method
Distribution | K–S test (D value) | ||
---|---|---|---|
SS | No. 1 | No. 2 | |
Normal | 0.081 | 0.070 | 0.063 |
Lognormal | 0.052 | 0.086 | 0.071 |
Critical value | 0.117 | 0.137 | 0.131 |
Characteristic values
The characteristic values of UCS_{15} according to different standards and distributions
Distribution | Characteristic values | UCS_{15} (MPa) | ||
---|---|---|---|---|
SS | No. 1 | No. 2 | ||
Lognormal | f _{1} | 23.25 | 22.18 | 21.54 |
f _{2} | 22.90 | 21.90 | 21.20 | |
Normal | f _{3} | 22.67 | 22.05 | 21.78 |
f _{4} | 22.12 | 21.62 | 21.26 |
Table 4 indicated that the calculated characteristic value for SS grade was the highest. There were no significant differences for the characteristic values of UCS_{15} calculated according to the GB 50068-2001 [19] and ASTM D2915-2010 [20]. It is because confidence level factor k value is not significantly different between GB 50068-2001 [19] and ASTM D2915-2010 [20]. Meanwhile, according to the Chinese National Standards, the calculated characteristic values of UCS_{15} (f _{3}) were 22.67, 22.05, and 21.78 MPa for SS, No. 1, and No. 2 grade, respectively, corresponding with the normal distribution, which were less than those of lognormal distribution (f _{1}). From the structure security concerns, the calculated characteristic values of UCS_{15} using Chinese National Code (f _{3}) were selected to calculate the design values.
Design values
Statistical parameters of the adjusting factors (GB 50005-2003 [8])
Parameters | k _{1} | k _{2} | k _{3} |
---|---|---|---|
Mean value | 1.00 | 0.96 | 0.72 |
COV (%) | 5.00 | 6.00 | 12.00 |
Statistical parameters of resistance stress (R) for each grade dimension lumber
Statistical parameters | Resistance stress (R) | ||
---|---|---|---|
SS | No. 1 | No. 2 | |
Mean value (MPa) | 21.23 | 19.62 | 20.30 |
Standard deviation (MPa) | 4.54 | 3.87 | 4.40 |
COV (%) | 21.40 | 19.71 | 21.25 |
Statistical parameters of the loads (GB 50009-2012 [21])
Statistical parameters | Load types | ||||
---|---|---|---|---|---|
G | L _{ O } | L _{ R } | L _{ W } | L _{ S } | |
Mean/nominal | 1.060 | 0.524 | 0.644 | 1.000 | 1.040 |
COV (%) | 7.0 | 28.8 | 23.3 | 19.0 | 22.0 |
Distribution types | Normal | Extreme-I | Extreme-I | Extreme-I | Extreme-I |
In addition, live-to-dead load ration is an important factor to determine the target reliability assessment. The reliability index (β), which needs to meet the target index (β _{0} = 3.2), is used to determine the design value of UCS_{15}. This is acquired by taking an average of the reliability index under the live-to-dead load ratio (ρ), which is specified as 0.25, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, and 4.0. Four load combinations, including G + L _{ O }, G + L _{ R }, G + L _{ W }, and G + L _{ S }, were used in the target reliability assessment.
Fitting results by various model
Grade | Model | Calculation formula | r ^{2} | Std. error |
---|---|---|---|---|
SS | Cubic | \( y = 0.215x^{3} - 1.828x^{2} + 6.450x - 2.275 \) | 0.999 | 0.150 |
Logarithm | \( y = 2.957 + 3.261\ln (x - 0.116) \) | 1000 | 0.015 | |
Allometric | \( y = 2.881x^{0.754} \) | 0.981 | 0.101 | |
No. 1 | Cubic | \( y = 0.228x^{3} - 1.933x^{2} + 6.779x - 2.572 \) | 0.999 | 0.163 |
Logarithm | \( y = 2.937 + 3.383\ln (x - 0.123) \) | 1.000 | 0.021 | |
Allometric | \( y = 2.848x^{0.781} \) | 0.979 | 0.108 | |
No. 2 | Cubic | \( y = 0.216x^{3} - 1.837x^{2} + 6.479x - 2.301 \) | 0.999 | 0.151 |
Logarithm | \( y = 2.955 + 3.271\ln (x - 0.117) \) | 1.000 | 0.016 | |
Allometric | \( y = 2.878x^{0.757} \) | 0.981 | 0.101 |
To meet the reliability index (β) of 3.2, the resistance partial coefficients (γ _{ R }) were 1.187, 1.204, and 1.195 for SS, No. 1, and No. 2 grade, respectively. And the design values of compressive strength calculated by Eq. 10 were set to 13.751, 13.186, and 13.123 MPa for SS, No. 1, and No. 2 grade, respectively.
Conclusions
- 1.
The mean values of UCS_{15} for SS, No. 1, and No. 2 grade were 30.71, 28.38, and 29.37 MPa, respectively.
- 2.
The results of reliability analysis indicated that reliability index increased nonlinearly with the live-to-dead ratio and resistance partial coefficient increased. The logarithm model fitted the data better than other models.
- 3.
To meet the reliability index (β = 3.2), it was suggested that the design values of compressive strength were set to 13.751, 13.18, and 13.123 MPa for SS, No. 1, and No. 2 grade, respectively.
Declarations
Acknowledgements
This work was supported by the Central Public-Interest Scientific Institution Basal Research Fund: (CAFYBB2016ZX002).
Authors’ Affiliations
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