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Investigation into the effects of humidity on the mechanical and physical properties of bamboo
Construction and Building Materials 194 (2019) 386–396
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Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Investigation into the effects of humidity on the mechanical and physical properties of bamboo Suzana Jakovljevic´ ⇑, Dragutin Lisjak Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, Ivana Lucˇic´a 5, 10002 Zagreb, Croatia
h i g h l i g h t s Mechanical properties of bamboos in aggressive wet condition. Statistical analysis of measures of central tendency. Models for predicting mechanical properties in dependence on the number of days of exposure to wet conditions.
a r t i c l e
i n f o
Article history: Received 7 July 2018 Received in revised form 25 October 2018 Accepted 2 November 2018
Keywords: Bamboo Humidity Mechanical properties Statistical analyses Predictive models
a b s t r a c t This paper presents an investigation into the influence of humidity on the mass changes and the mechanical (buckling, toughness) properties of Pseudosasa amabilis bamboo. The tests were carried out in different conditions, the dry laboratory conditions and the wet chamber conditions. A detailed statistical analysis of measures of central tendency was carried out and models for predicting the behaviour of properties in dependence on the number of days spent in wet conditions were obtained. The COV results for mass and mechanical properties are below 30%. The values of R2 obtained from the model are: mass = 0.9652, buckling = 0.1630, and toughness = 0.0000. Ó 2018 Elsevier Ltd. All rights reserved.
1. Introduction Bamboo is a biological composite and an eco-friendly material. It is often used in engineering and in civil construction, car industry, furniture industry, and in many other applications [1–3]. Extensive research on good mechanical properties of bamboo is presented in [4–13]. The mechanical properties of bamboo are determined by the properties of fibres and matrices and by the fibre density [6,9,13]; extensive research has been performed on fracture and toughening mechanisms in bamboo structures [14– 16]. Bamboo is hygroscopic and it adsorbs and desorbs moisture to equilibrate with the ambient moisture content [17,18]. The mechanical properties of bamboo as a bio-composite material depend on the water content [19–26]. The influence of humidity on the mechanical properties of bamboo has been investigated at a cellular level [19–23] and at a macroscopic level [24–26]. Askarinejad et al. [23] investigated the effects of different humidity
⇑ Corresponding author. E-mail address: [email protected] (S. Jakovljevic´). https://doi.org/10.1016/j.conbuildmat.2018.11.030 0950-0618/Ó 2018 Elsevier Ltd. All rights reserved.
levels on the shear behaviour of bamboo and found out that bamboo exhibits a higher degree of ductility under torsion as the humidity level of the samples increases. In their study, Xu et al. [24] presented an investigation into the mechanical properties of bamboo samples that had been immersed in water for one and for seven days. They found out that the compressive strength and longitudinal shear were significantly reduced with the prolonged immersion in water. Chung and Yu [25] studied the mechanical properties (compressive strength and bending strength) of Bambusa pervariabilis (or Kao Jue) and Phyllostachy pubescens (or Mao Jue) used in bamboo scaffoldings in the dry and the wet conditions. Both types of bamboo have great mechanical properties in the dry conditions but wet tests showed that the exposure of bamboo to high humidity negatively affects its mechanical properties. In [26], the authors investigated the influence of humidity on the mechanical properties of Pseudosasa amabilis (or Tonkin Cane) and Pleioblastus amarus (or Ku Zhu) bamboo, which are commonly used for bicycles. They found out that the tensile strength of bamboo samples significantly decreased after their 21-day exposure to a relative humidity of 60 ± 2% at a temperature of 20 ± 2 °C in the wet chamber.
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Investigations into the influence of water/humidity on mechanical properties (compression, tension, bending, and buckling) and the influence of the duration of exposure to humidity at the cellular level and at the macroscopic level are still lacking. In this study, the influence of humidity on the mechanical properties of Pseudosasa amabilis (or Tonkin Cane) that is used for bicycle frames is investigated. The paper deals with the changes in the mass of samples and the changes in the mechanical properties (buckling and toughness) of the bamboo samples after they had been exposed to aggressive conditions in the wet chamber with a relative humidity of 100 ± 2% and a temperature of (40 ± 3) °C for 1, 5, and 10 days.
2. Materials and methods The Tonkin Cane bamboo poles were obtained from China and every pole was cut from a bamboo culm older than 5 years. After the harvest, they were dried for six months in a warehouse with 40% humidity without any chemical treatment (they were preserved by traditional preservation methods, such as curing, smoking, soaking, and lime-washing) and then were stored in a ventilated warehouse at room temperature (22 °C) for at least a year. 2.1. Sample preparation The condition of bamboo culms was verified visually and the culms with no observable defects were marked. Samples were ordered from a sales company in the diameter and the length that fit the bicycle frame. The Tonkin Cane stalks have a length of 460 mm that fits a bicycle frame and their outer diameter is 30 mm. Samples for each testing were cut randomly from bamboo culms according to the results presented in the authors’ previous study [26]. In order to determine the influence of humidity on buckling and toughness of each bamboo species, tests were carried out in different laboratory conditions, dry and wet: (a) Dry tests. The tests were intended for measuring the buckling and the toughness of the samples tested in dry laboratory conditions at a temperature of 22 °C and a relative humidity of 31%. Tests were carried out on a quarter of Tonkin Cane bamboo samples. (b) Wet tests. The tests were aimed at measuring the buckling and the toughness of the samples tested after they had been exposed to aggressive conditions, such as a relative humidity of 100 ± 2% and a temperature of 40 ± 2 °C, in the wet chamber for different periods of time. The second quarter of Tonkin Cane bamboo samples were exposed to these conditions in the wet chamber for 1 day, the third quarter of samples for 5 days, and the last quarter for 10 days. Since bamboo has hollow culms, ends of culms were covered by Parafilm M(R) to simulate realistic environmental conditions, i.e. to allow moisture to penetrate only through the outer wall. After the defined periods of time (one, five, and ten days), the stalks were removed, cut to the sample dimensions and immediately tested. Buckling and toughness tests were carried out on 20 samples of Tonkin Cane bamboo.
ferent periods of time; after that the samples were weighed on KERN ABS and METTLER TOLEDO devices.
2.3. Buckling Samples to be tested for buckling were cut from culms. The selected length of the samples of 460 mm was adjusted to the dimensions of the wet chamber allowing up to 500 mm long samples; the length of 460 mm fits to seat tube of a bicycle size M. All samples had one node in the length. Tests were carried out on a Heckert test machine, type WPM, EU 40 MOD, accuracy class 0.5 at a temperature of 22 °C and a loading rate of 10 mm/min. The bamboo sample placed between two steel plates was tested under load. Pieces of sponge were put between the plates and at the ends of the bamboo sample to avoid the sliding of the sample from the steel surface, as shown in Fig. 1. The tested samples were loaded continuously to the point of failure, at a displacement rate of 10 mm/min (see Fig. 1). The average external diameter D of the bamboo sample was 29.79 mm and the internal diameter d was 20.66 mm.
2.4. Toughness Samples used for the Charpy impact test were cut from bamboo slices, as shown in Fig. 2, where l is the length of the sample in millimetres, b is its width, mm, h is its thickness, mm. They were without nodes. Tests were performed according to the HRN EN ISO 179 standard at a temperature of 22 °C. Load was perpendicular to the fibres in the matrix. The toughness test was carried out on a K. Frank GMBH test machine having maximum impact energy of 4 J.
Fig. 1. Buckling test.
2.2. The mass of samples after different periods of time of exposure – gravimetric analysis Culm samples placed in the wet chamber were exposed to a relative humidity of 100 ± 2% and a temperature of 40 ± 3 °C for dif-
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Fig. 2. The Charpy impact test; dimensions of the sample.
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2.5. Statistical tests
3. Results and discussion
For each property (mass, buckling, and toughness) and for each mode of testing (1-Day, 5-Day, and 10-Day), the following measures of central tendency were determined: Average, Standard deviation, Coefficient of variation, Min./Max., Skewness, and Kurtosis. In addition, using the Shapiro-Wilk and Kolmogorov-Smirnov Tests, the distribution of measured data was compared to a normal distribution. The measures of central tendency are presented by Boxand-Whisker Diagrams while the distribution of data is presented by the Normal Probability Plot. The testing of all statistical hypotheses was performed at the significance level a = 0.05. Analysis of Variance (ANOVA) test and the Multiple Range test with the Least Significant Difference (LSD) procedure were done to determine the differences in the values of particular properties in dependence on the number of days of exposure to wet conditions. The values of determined differences are shown in Box-and-Whisker Diagrams. After the integration of measured values of each property from the three modes into one set, the previously mentioned measures of central tendency were recalculated and graphically presented by the Box-and-Whisker Diagrams and the Normal Probability Plots in order to determine the data distribution normality. This is a condition for obtaining a predictive model. For the unique set of data from all three modes of testing, a model for predicting the change in the value of a particular property with respect to the mode, i.e. the number of days of exposure to wet conditions, was generated with a purpose of obtaining an exact mathematical expression. In order to prove the significance of the change in the value of a particular property, ANOVA test was performed with p-values shown. The Correlation (R) and RSquared (R2) coefficients were calculated to determine the predictive power of the model. The predictive models used are shown graphically using the upper/lower confidence intervals and error intervals.
Table 1 summarizes the test results of measured mechanical properties (bending and toughness) of the Tonkin Cane bamboo samples in dry conditions. The ranges of the physical properties are presented in Table 1. The results for Young’s modulus for Tonkin Cane bamboo obtained in this study correspond well with the values reported in literature [27], which range from 7 to 20 MPa. The buckling and the toughness results for Tonkin Cane bamboo are almost within the, 40.1–73.6 N/mm2 range reported in the literature for the buckling of structural bamboos [28,29] and the 53.0–57.7 kJ/ m2 range for toughness [30]. The buckling and the toughness results for the samples of bamboo tested in literature were for the structural bamboo such as Kao Jue or Mao Jue. Since no other results for Tonkin Cane are reported in literature, a direct comparison cannot be made.
3.1. The mass of samples after different periods of exposure The calculated average data on mass related to the number of days of exposure in the wet chamber are given in Tables 2–4, where Mass-1 denotes the mass after one day of testing, Mass-5 after five days, and Mass-10 after ten days (Figs. 3 and 4). Prediction limits (Fig. 5) are the outer bounds in the above plot and describe how precisely one could predict where a single new observation would lie. Regardless of the size of the sample, new observations will vary around the true line with a standard deviation. Confidence limits (Fig. 5) are the inner bounds and describe how well the location of the line has been estimated given the available data sample. The width of the bounds varies as a function of X, with the line estimated most precisely near the average value.
Table 1 Physical and mechanical properties of Tonkin Cane bamboo in dry conditions.
External diameter, D (mm) Internal diameter, d (mm) Cross – sectional area, A (mm2) Second moment of area, I (mm4) Buckling, rk (N/mm2) Young’s modulus E (kN/mm2) Toughness, (kJ/m2)
Maximum
Minimum
Average
Standard deviation
31.68 23.24 366.79 30820.6 82.52 25.12 77.31
27.58 16.55 351.49 28304.7 61.23 16.26 44.56
29.79 20.66 359.69 29708.60 74.62 19.98 59.77
1.1770 1.7131 36.1842 909.7500 6.9707 2.9025 11.1123
Table 2 Statistics for mass.
Number of samples Average Standard deviation Coeff. of variation Min. Max. Skewness Kurtosis Shapiro-Wilk (W) p-value (p) K-S test Median (Md) Lower quartile (Q1) Upper quartile (Q3) Interquartile range (IRQ)
Mass – 1, g
Mass – 5, g
Mass – 10, g
20 7.8265 0.6221 7.9497% 6.36 9.2 0.5184 1.2135 0.961 0.568 DN = 0.1429; p-value = 0.808 7.92 7.505 8.145 0.64
20 21.6765 3.7052 17.093% 14.17 30.47 16.3 0.0645 0.946 0.314 DN = 0.170; p-value = 0.607 21.04 19.815 23.62 3.805
20 36.8245 2.9971 8.1390% 31.3 43.12 0.726 0.006 0.963 0.623 DN = 0.132; p-value = 0.876 36.52 34.775 38.1 3.325
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Table 3 Multiple sample comparison for mass-1-5-10, g. Number of samples
20-20-20
ANOVA Between groups Within groups Total (Corr.)
Sum of Squares
Df
Mean Square
F-ratio
p-value
8414.46 438.884 8853.34
2 57 59
4207.23 7.6997
546.41
0.0000
Multiple Range Tests (LSD) Mean
Homogeneous Groups
Mass-1 Mass-5 Mass-10 Contrast
7.826 21.676 36.824 Sig.
x
Mass-1 – Mass-5 Mass-1 – Mass-10 Mass-5 – Mass-10
* * *
x X Difference 13.85 28.998 15.148
+/
Limits
1.7571 1.7571 1.7571
Table 4 Statistics for mass-1-5-10, g. Number of samples Average Standard deviation Coeff. of variation Min. Max. Skewness Kurtosis Shapiro-Wilk (W) p-value (p) K-S test
60 22.0608 12.3066 55.7848% 6.36 43.12 0.3593 2.3244 0.882 0.000 DN = 0.195; p-value = 0.020 Fig. 5. Predictive model – mass vs. days.
3.2. Discussion on the effect of humidity on mass The values of measures of the asymmetry (Standard skewness = 0.5184, Standard kurtosis = 1.2135) for the 1-Day mode are within the 2 to +2 range, which indicates that the data for the 1-Day mode are normally distributed. The data distribution is negatively skewed since the mean data value is smaller than the median value (x < Me). P-values of the Shapiro-Wilk test (p = 0.568) and Kolmogorov-Smirnov test (p = 0.808) show that the data of the 1-Day mode testing are distributed according to a normal distribution at the level of statistical significance (a = 0.05). Fig. 3. Box-and-Whisker for mass-1-5-10, g.
Fig. 4. (a) Box-and-Whisker; (b) Normal probability for mass-1-5-10.
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The values of measures of the asymmetry (Standard skewness = 0.0645, Standard kurtosis = 1.1882) for the 5-Day mode of testing are both within the 2 to +2 range, which indicates that the data for the 5-Day mode are normally distributed. The data distribution is positively skewed since the mean data value is greater than the median value (x > Me). P-values of the Shapiro-Wilk test (p = 0.946) and Kolmogorov-Smirnov test (p = 0.314) show that the data of the 5-Day mode testing are distributed according to a normal distribution at the level of statistical significance (a = 0.05). The values of measures of the asymmetry (Standard skewness = (0.7263, Standard kurtosis = 0.0065) for the 10-Day mode of testing are both within the 2 to +2 range, which indicates that the data for the 10-Day mode are normally distributed. The data distribution is positively skewed since the mean data value is greater than the median value (x > Me). P-values of the Shapiro-Wilk test (p = 0.963) and Kolmogorov-Smirnov test (p = 0.623) show that the data of the 5-Day mode testing are distributed according to a normal distribution at the level of statistical significance (a = 0.05). As shown in Table 2, the coefficients of variation in the data on mass for all three modes of testing (1-Day, 5-Day, and 10-Day) according to the methods proposed by Gomes & Costa [31,32] are within acceptable limits (7.9497%, 17.0936%, and 8.1390%). The minimum mass values are 6.36 g, 14.17 g, and 31.3 g, while the maximum ones are 9.2 g, 30.47 g, and 43.12 g; the values of their respective ranges are 2.84 g, 16.30 g, and 11.82 g. The highest value of the range (16.30 g) occurred in the 5-Day mode of testing. The ANOVA results (Table 3) show that there are significant differences at the level of statistical significance (a = 0.05) in the mass values both among all three modes of testing (1-Day, 5-Day, and 10-Day) and among individual values in each mode (F-ratio = 546.41; p-value = 0.000). Multiple Range Test (Fisher’s Least Significant Difference procedure – LSD) denotes a statistically significant difference (95% confidence level) in the mass values of samples among all modes of testing (Mass_1-Mass_5 = 13.85, +/ Limits = 1.7571; Mass_1-Mass_10 = 28.998, +/ Limits = 1.7571; Mass_5Mass_10 = 15.148, +/ Limits = 1.7571). This is shown by the Box-and-Whisker Diagram in Fig. 3. After the integration of measured values of mass from the three modes (1-Day, 5-Day, and 10-Day) into one set, the analysis of measures of central tendency shows that there are significant changes in the value of statistical features important for assessing the normal distribution of data (Table 4): the coefficient of variation which amounts to 55.7848% is not within acceptable limits (<50%) and the standard kurtosis of 2.32441 is not in the 2 to
+2 range. The fact that the data from the common set are not distributed according to a normal distribution is proved by the values of the Shapiro-Wilk (W = 0.882, p = 0.000) and Kolmogorov-Smirnov (DN = 0.195, p = 0.020) tests. P-values in both tests are less than 0.005. A statistical analysis of models for an approximate estimation of the trend in the variability in mass in dependence on the number of days of sample treatment (Table 5) shows a strong positive trend with a correlation coefficient of R = 0.982484, while the R-Squared statistics (R2 = 96.5275%) indicates that the model as fitted explains the variability in mass. The equation of the fitted model is: Mass 1-5-10 = e(2.02261 + 0.672988*ln(Days)). 3.3. Discussion on mechanical properties 3.3.1. Buckling results The calculated average data on buckling related to the number of days of exposure in the wet chamber are given in Tables 6–8, where Buckling-1 denotes the buckling after one day of testing, Buckling-5 after five days, and Buckling-10 after ten days (Figs. 6 and 7). 3.3.2. Discussion on the effect of humidity on buckling The values of measures of the asymmetry (Standard skewness = 1.16086, Standard kurtosis = 0.949588) for the 1-Day mode are within the 2 to +2 range, which indicates that the data for the 1-Day mode are normally distributed. The data distribution is positively skewed since the mean data value is greater than the median value (x > Me). P-values of the Shapiro-Wilk test (p = 0.534) and Kolmogorov-Smirnov test (p = 0.549) show that the data of the 1-Day mode testing are distributed according to a normal distribution at the level of statistical significance (a = 0.05). The values of measures of the asymmetry (Standard skewness = ( 0.942036, Standard kurtosis = 0.636021) for the 5-Day mode of testing are within the 2 to +2 range, which indicates that the data for the 5-Day mode are normally distributed. The data distribution is negatively skewed since the mean data value is smaller than the median value (x < Me). P-values of the Shapiro-Wilk test (p = 0.117) and Kolmogorov-Smirnov test (p = 0.658) show that the data of the 5-Day mode testing are distributed according to a normal distribution at the level of statistical significance (a = 0.05). The values of measures of the asymmetry (Standard skewness = 1.6779, Standard kurtosis = 1.44872) for the 10-Day mode of testing are within the 2 to +2 range, which indicates that the
Table 5 Predictive model – mass vs. days. Number of samples Dependent variable Independent variable
60 Mass Days
Coefficients Parameter
Least Squares Estimate
Standard Error
T Statistic
p-value
Intercept Slope
2.0226 0.6729
0.0271 0.0167
74.402 40.1529
0.0000 0.0000
ANOVA Source
Sum of Squares
Df
Mean Square
F-Ratio
p-value
Model Residual Total (Corr.)
25.2805 0.9094 26.19
1 58 59
25.2805 0.0156
1612.26
0.0000
Predictive model Equation R R2
Mass 1-5-10 = e(2.02261 + 0.672988*ln(Days)) 0.9824 0.9652 (96.52%)
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Table 6 Statistics for buckling.
Number of samples Average Standard deviation Coeff. of variation Min. Max. Skewness Kurtosis Shapiro-Wilk (W) p-value (p) K-S test Median (Md) Lower quartile (Q1) Upper quartile (Q3) Interquartile range (IRQ)
Buckling-1
Buckling-5
Buckling-10
20 59.7585 6.5634 10.9833% 47.32 75.92 1.1608 0.9495 0.959 0.534 DN = 0.180; p-value = 0.549 58.96 56.465 63.225 6.76
20 57.3195 6.1859 10.7921% 43.62 64.96 0.9420 0.6360 0.923 0.117 DN = 0.163; p-value = 0.658 58.84 52.085 62.47 10.385
20 52.967 4.6672 8.8116% 46.55 65.77 1.6779 1.4487 0.938 0.224 DN = 0.096; p-value = 0.992 53.145 49.525 55.375 5.85
Table 7 Multiple sample comparison for buckling-1-5-10, N/mm2. Number of samples
20-20-20
ANOVA Between groups Within groups Total (Corr.)
Sum of Squares
Df
Mean Square
F-ratio
p-value
473.45 1959.44 2432.89
2 57 59
236.725 34.3761
6.89
0.0021
Mean
Homogeneous Groups
52.967 57.3195 59.7585 Sig.
x
Multiple Range Tests (LSD) Mass-10 Mass-5 Mass-1 Contrast Mass-1 – Mass-5 Mass-1 – Mass-10 Mass-5 – Mass-10
* *
Difference
x x +/
2.439 6.7915 4.3525
3.71274 3.71274 3.71274
Limits
Table 8 Statistics for buckling-1-5-10, N/mm2. Number of samples Average Standard deviation Coeff. of variation Min. Max. Skewness Kurtosis Shapiro-Wilk (W) p-value (p) K-S test
60 56.6817 6.4214 11.329% 43.62 75.92 1.3569 0.3418 0.984 0.630 DN = 0.059; p-value = 0.982
data for the 10-Day mode are normally distributed. The data distribution is negatively skewed since the mean data value is smaller than the median value (x < Me). P-values of the Shapiro-Wilk test (p = 0.224) and Kolmogorov-Smirnov test (p = 0.922) show that the data of the 10-Day mode testing are distributed according to a normal distribution at the level of statistical significance (a = 0.05). As shown in Table 6, the coefficients of variation in the data on buckling for all three modes of testing (1-Day, 5-Day, and 10-Day) according to the methods proposed by Gomes & Costa [31,32] are within acceptable limits (10.9833%, 10.7921%, and 8.8116%). The minimum values for buckling are 47.32 N/mm2, 43.62 N/ mm2, and 46.55 N/mm2, while the maximum ones are 75.92 N/ mm2, 64.96 N/mm2, and 65.77 N/mm2; the values of their respective ranges are 28.6 N/mm2, 21.34 N/mm2, and 19.22 N/mm2. The
Fig. 6. Box-and-Whisker diagram for buckling-1-5-10, N/mm2.
highest value of the range (28.6 N/mm2) occurred in the 1-Day mode of testing. The ANOVA results (Table 7) show that there are significant differences in the values for buckling at the level of statistical significance (a = 0.05) among all three modes of testing, i.e. 1-Day, 5Day, and 10-Day (F-ratio = 6.89; p-value = 0.0021). Multiple Range Test (Fisher’s Least Significant Difference procedure – LSD) denotes a statistically significant difference (95% confidence level) in the values of sample buckling between the following modes of testing: Mass_1-Mass_10 = 6.7915, +/ Limits = 3.7127; and Mass_5-Mass_10 = 4.3525, +/ Limits = 3.7127.
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Fig. 7. (a) Box-and-Whisker diagram; (b) normal probability plot for buckling-1-5-10, N/mm2.
There is no significant difference between the modes Mass_1Mass_5 = 2.439, +/ Limits = 3.7127. This is shown by the Boxand-Whisker Diagram in Fig. 7 (* denotes a statistically significant difference) (Fig. 8). After the integration of measured values of buckling from the three modes (1-Day, 5-Day, and 10-Day) into one set, the analysis of measures of central tendency shows that there are no significant changes in the value of statistical features important for assessing the normal distribution of data (Table 8): the coefficient of varia-
tion = 11.329% (<50%), the standard skewness = 1.3569, and the standard kurtosis = 0.341846 ( 2 to +2 range). The fact that the data from the common set are distributed according to a normal distribution is proved by the values of the Shapiro-Wilk (W = 0.984, p = 0.630) and Kolmogorov-Smirnov (DN = 0.059, p = 0.982) tests. P-values in both tests are greater than 0.005. A statistical analysis of models for an approximate estimation of the trend in buckling in dependence on the number of days of sample treatment (Table 9) shows a weak positive trend with a correlation coefficient of R = 0.194604, while the R-Squared statistics (R2 = 16.6344%) indicates that the model as fitted explains the variability in buckling. The equation of the fitted model is: Buckling 1-510 = 10108.2 + 34.3307*Days 0.0289*Days2. 3.3.3. Toughness results The calculated average data on toughness on related to the number of days exposure in the wet camber are given in Tables 10– 12, where Toughness-1 denotes the toughness after one day of testing, Toughness-5 after five days, and Toughness-10 after ten days (Figs. 9 and 10). 3.3.4. Discussion on the effect of humidity on toughness The values of measures of the asymmetry (Standard skewness = 1.1078, Standard kurtosis = 0.4424) for the 1-Day mode
Fig. 8. Predictive model – buckling vs. days.
Table 9 Predictive model – buckling vs. days. Number of samples Dependent variable Independent variable
60 Buckling Days
Coefficients Parameter
Estimate
Standard Error
T Statistic
p-value
Constant Days Days2
10108.2 34.3307 0.0289722
29502.2 97.4372 0.080449
0.3426 0.3523 0.360131
0.7331 0.7259 0.7201
ANOVA Source
Sum of Squares
Df
Mean Square
F-Ratio
p-value
Model Residual Total (Corr.)
473.45 1959.44 2432.89
2 57 59
236.725 34.3761
6.89
0.0021
Predictive model Equation R R2
Buckling 1-5-10 = 0.1940 0.1630 (16.30%)
10108.2 + 34.3307*Days
0.0289722*Days2
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Table 10 Statistics for toughness.
Number of samples Average Standard deviation Coeff. of variation Min. Max. Skewness Kurtosis Shapiro-Wilk (W) p-value (p) K-S test Median (Md) Lower quartile (Q1) Upper quartile (Q3) Interquartile range (IRQ)
Toughness-1
Toughness-5
Toughness-10
20 45.7335 3.0981 6.7742% 39.6 50.54 1.1078 0.4424 0.943 0.273 DN = 0.169; p-value = 0.615 46.455 44.035 47.88 3.845
20 47.0315 13.0149 27.6726% 22.87 71.18 0.5228 0.1441 0.955 0.449 DN = 0.172; p-value = 0.592 48.09 38.75 52.63 13.88
20 46.303 6.5258 14.0939% 30.54 58.53 0.5533 0.7965 0.973 0.817 DN = 0.129; p-value = 0.893 45.885 42.605 49.595 6.99
Table 11 Multiple sample comparison for Toughness-1-5-10, N/mm2. Number of samples
20–20–20
ANOVA Between groups Within groups Total (Corr.)
Sum of Squares
Df
Mean Square
F-ratio
p-value
16.9323 4209.87 4226.8
2 57 59
8.4661 73.8574
0.11
0.8919
Mean
Homogeneous Groups
Mass-10 Mass-5 Mass-1
46.303 47.0315 45.7335
x x x
Contrast
Sig.
Difference
+/
1.298 0.5695 0.7285
5.4420 5.4420 5.4420
Mass-1 – Mass-5 Mass-1 – Mass-10 Mass-5 – Mass-10
Table 12 Statistics for toughness-1-5-10, KJ/m2. Number of samples Average Standard deviation Coeff. of variation Min. Max. Skewness Kurtosis Shapiro-Wilk (W) p-value (p) K-S test
60 46.7815 7.6605 16.3751% 30.59 71.18 3.0203 4.4802 0.895 0.000 DN = 0.190; p-value = 0.025
Limits
are within the 2 to +2 range, which indicates that the data for the 1-Day mode are normally distributed. The data distribution is negatively skewed since the mean data value is smaller than the median value (x < Me). P-values of the Shapiro-Wilk test (p = 0.273) and Kolmogorov-Smirnov test (p = 0.615) show that the data of the 1Day mode testing are distributed according to a normal distribution at the level of statistical significance (a = 0.05). The values of measures of the asymmetry (Standard skewness = 0.522809, Standard kurtosis = 0.144121) for the 5-Day mode of testing are within the 2 to +2 range, which indicates that the data for the 5-Day mode are normally distributed. The data distribution is negatively skewed since the mean data value is smaller than the median value (x < Me). P-values of the Shapiro-Wilk test (p = 0.449) and Kolmogorov-Smirnov test (p = 0.592) show that the data of the 5-Day mode testing are distributed according to a normal distribution at the level of statistical significance (a = 0.05). The values of measures of the asymmetry (Standard skewness = 0.553396, Standard kurtosis = 0.796536) for the 10-Day mode of testing are within the 2 to +2 range, which indicates that the data for the 10-Day mode are normally distributed. The data distribution is positively skewed since the mean data value is
Fig. 9. Box-and-Whisker toughness-1-5-10, N/mm2.
greater than the median value (x > Me). P-values of the ShapiroWilk test (p = 0.817) and Kolmogorov-Smirnov test (p = 0.893) show that the data of the 10-Day mode testing are distributed according to a normal distribution at the level of statistical significance (a = 0.05). As shown in Table 10, the coefficients of variation in the data on toughness for all three modes of testing (1-Day, 5-Day, and 10-
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Fig. 10. (a) Box-and-Whisker; (b) normal probability for toughness-1-5-10, KJ/m2.
Fig. 11. Predictive model – toughness vs. days.
Day) according to the methods proposed by Gomes & Costa [31,32] are within acceptable limits (6.7742%, 27.6726%, and 14.0939%). The minimum values for toughness are 39.6 KJ/m2, 22.87 KJ/m2, and 30.54 KJ/m2, while the maximum ones are 50.54 KJ/m2, 71.18 KJ/m2, and 58.53 KJ/m2; the values of their respective ranges are10.94 KJ/m2, 71.18 KJ/m2, and 58.53 KJ/m2. The largest value of the range (71.18 N/mm2) occurred in the 5-Day mode of testing.
The ANOVA results (Table 11) show that there are no significant differences at the level of statistical significance (a = 0.05) in the values for toughness among all three modes of testing, i.e. 1-Day, 5-Day, and 10-Day (F-ratio = 0.11; p-value = 0.8919). Multiple Range Test (Fisher’s Least Significant Difference procedure – LSD) shows that there are no statistically significant differences (95% confidence level) in the values of toughness between the following modes of testing: Mass_1-Mass_5 = 1.298, +/ Limits = 5.44205; Mass_1-Mass_10 = 0.5695, +/ Limits = 5.44205; Mass_5-Mass_10 = 0.7285, +/ Limits = 5.44205. This is shown by the Box-and-Whisker Diagram in Fig. 9 (* denotes a statistically significant difference) (Fig. 11). After the integration of measured values of toughness from the three modes (1-Day, 5-Day, and 10-Day) into one set, the analysis of measures of central tendency shows that there are significant changes in the value of statistical features important for assessing the normal distribution of data (Table 12): the coefficient of variation = 16.3751% (<50%), the standard skewness = 3.02037, and the standard kurtosis = 4.48026 ( 2 to +2 range). The fact that the data from the common set are not distributed according to a normal distribution is proved by the values of the Shapiro-Wilk (W = 0.895, p = 0.000) and Kolmogorov-Smirnov (DN = 0.190, p = 0.025) tests. P-values in both tests are less than 0.05. A statistical analysis of models for an approximate estimation of the trend in toughness in dependence on the number of days of sample treatment (Table 13) shows a very weak positive trend
Table 13 Predictive model – toughness vs. days. Number of samples Dependent variable Independent variable
60 Toughness Days
Coefficients Parameter
Estimate
Standard Error
T Statistic
p-value
Constant Days Days2
44.7115 1.1142 0.0922
2.5607 1.2156 0.1061
17.4604 0.9165 0.8685
0.0000 0.3633 0.3887
ANOVA Source
Sum of Squares
Df
Mean Square
F-Ratio
p-value
Model Residual Total (Corr.)
51.0125 3411.31 3462.32
2 57 59
25.5062 59.8475
0.43
0.6551
Predictive model Equation R R2
Toughness 1-5-10 = 44.7115 + 1.1142*Days 0.0140 0.0000 (0.00%)
0.0922*Days2
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with a correlation coefficient of R = 0.014, while the R-Squared statistics R2 = 0.000% indicates that the proposed predictive model for an approximate estimation of the trend in toughness as fitted explains 0.000% of the variability in toughness. The equation of the fitted model is: Toughness 1-5-10 = 44.7115 + 1.1142*Days 0.0922*Days2.
4. Conclusion The purpose of this research was to investigate the effects of humidity on the mechanical and physical properties of bamboo. As a result of this study, the key novel findings about the mechanical and physical properties of bamboo under aggressive wet conditions are as follows:
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ity trend can be considered very reliable due to the high value of RSquared statistics (R2). Predictive models of other features show a relatively low level of reliability due to a relatively small value of R2 and it is concluded that the tested features do not show significant changes in their values (either rise or fall) within 1, 5 or 10 days of the test. For further research, we plan to test the dynamic durability of bamboo in dry and wet conditions; it is also planned to obtain a predictive model for the behaviour of mechanical properties in dependence on the number of days of exposure to defined conditions.
Conflicts of interest The authors declare no conflict of interest.
- Mass. Results for all three modes of testing (1-Day, 5-Day, and 10-Day) are dispersed according to a normal distribution, which is proved by the Shapiro-Wilk and Kolmogorov-Smirnov tests, and they are mostly positively skewed. The Multiple Sample Comparison and Multiple Range tests prove that there are significant differences among the values of mass in dependence on the mode of testing, i.e. the number of days of sample exposure to wet conditions. The R-Squared statistics (R2) of the proposed predictive model for an approximate estimation of the trend in mass variability as fitted explains 96.52% of the variability in mass, which is a very high percentage. - Buckling. Results for all three modes of testing (1-Day, 5-Day, and 10-Day) are dispersed according to a normal distribution, which is proved by the Shapiro-Wilk and KolmogorovSmirnov tests, and they are mostly negatively skewed. The Multiple Sample Comparison test proves that there are significant differences among the values of buckling in dependence on the mode of testing, i.e. the number of days of sample exposure to wet conditions. The Multiple Range test proves that there are no differences in the values of buckling in the 1–5 day period. The R-Squared statistics (R2) of the proposed predictive model for an approximate estimation of the trend in buckling as fitted explains only 16.30% of the variability in buckling, which is a very low percentage. - Toughness. Results for all three modes of testing (1-Day, 5-Day, and 10-Day) are dispersed according to a normal distribution, which is proved by the Shapiro-Wilk and KolmogorovSmirnov tests; the results are mostly negatively skewed. The Multiple Sample Comparison test proves that there are significant differences among the values of toughness in dependence on the mode of testing, i.e. the number of days of sample exposure to wet conditions. In addition, the Multiple Range test proves that there are no differences among the modes of testing. The R-Squared statistics (R2) of the proposed predictive model for an approximate estimation of the trend in toughness as fitted explains 0% of the variability in toughness; therefore, it can be rejected. Given the above, it can be concluded that all the properties (Mass, Buckling, Toughness) tested in all the three modes of testing (1-Day, 5-Day, 10-Day) exhibit changes in their values (upward or downward trends) with respect to the number of days of testing at the level of statistical significance (a = 0.05). The measured values of all the properties within a mode of testing are distributed according to a normal distribution, and the coefficients of variation are mostly within acceptable limits. The previously stated facts were the reason for studying models for the prediction of the trend in the variability of values of properties in dependence on the number of days of testing, i.e. the mode of testing. The research results have shown that the model for predicting the mass variabil-
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Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Investigation into the effects of humidity on the mechanical and physical properties of bamboo Suzana Jakovljevic´ ⇑, Dragutin Lisjak Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, Ivana Lucˇic´a 5, 10002 Zagreb, Croatia
h i g h l i g h t s Mechanical properties of bamboos in aggressive wet condition. Statistical analysis of measures of central tendency. Models for predicting mechanical properties in dependence on the number of days of exposure to wet conditions.
a r t i c l e
i n f o
Article history: Received 7 July 2018 Received in revised form 25 October 2018 Accepted 2 November 2018
Keywords: Bamboo Humidity Mechanical properties Statistical analyses Predictive models
a b s t r a c t This paper presents an investigation into the influence of humidity on the mass changes and the mechanical (buckling, toughness) properties of Pseudosasa amabilis bamboo. The tests were carried out in different conditions, the dry laboratory conditions and the wet chamber conditions. A detailed statistical analysis of measures of central tendency was carried out and models for predicting the behaviour of properties in dependence on the number of days spent in wet conditions were obtained. The COV results for mass and mechanical properties are below 30%. The values of R2 obtained from the model are: mass = 0.9652, buckling = 0.1630, and toughness = 0.0000. Ó 2018 Elsevier Ltd. All rights reserved.
1. Introduction Bamboo is a biological composite and an eco-friendly material. It is often used in engineering and in civil construction, car industry, furniture industry, and in many other applications [1–3]. Extensive research on good mechanical properties of bamboo is presented in [4–13]. The mechanical properties of bamboo are determined by the properties of fibres and matrices and by the fibre density [6,9,13]; extensive research has been performed on fracture and toughening mechanisms in bamboo structures [14– 16]. Bamboo is hygroscopic and it adsorbs and desorbs moisture to equilibrate with the ambient moisture content [17,18]. The mechanical properties of bamboo as a bio-composite material depend on the water content [19–26]. The influence of humidity on the mechanical properties of bamboo has been investigated at a cellular level [19–23] and at a macroscopic level [24–26]. Askarinejad et al. [23] investigated the effects of different humidity
⇑ Corresponding author. E-mail address: [email protected] (S. Jakovljevic´). https://doi.org/10.1016/j.conbuildmat.2018.11.030 0950-0618/Ó 2018 Elsevier Ltd. All rights reserved.
levels on the shear behaviour of bamboo and found out that bamboo exhibits a higher degree of ductility under torsion as the humidity level of the samples increases. In their study, Xu et al. [24] presented an investigation into the mechanical properties of bamboo samples that had been immersed in water for one and for seven days. They found out that the compressive strength and longitudinal shear were significantly reduced with the prolonged immersion in water. Chung and Yu [25] studied the mechanical properties (compressive strength and bending strength) of Bambusa pervariabilis (or Kao Jue) and Phyllostachy pubescens (or Mao Jue) used in bamboo scaffoldings in the dry and the wet conditions. Both types of bamboo have great mechanical properties in the dry conditions but wet tests showed that the exposure of bamboo to high humidity negatively affects its mechanical properties. In [26], the authors investigated the influence of humidity on the mechanical properties of Pseudosasa amabilis (or Tonkin Cane) and Pleioblastus amarus (or Ku Zhu) bamboo, which are commonly used for bicycles. They found out that the tensile strength of bamboo samples significantly decreased after their 21-day exposure to a relative humidity of 60 ± 2% at a temperature of 20 ± 2 °C in the wet chamber.
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Investigations into the influence of water/humidity on mechanical properties (compression, tension, bending, and buckling) and the influence of the duration of exposure to humidity at the cellular level and at the macroscopic level are still lacking. In this study, the influence of humidity on the mechanical properties of Pseudosasa amabilis (or Tonkin Cane) that is used for bicycle frames is investigated. The paper deals with the changes in the mass of samples and the changes in the mechanical properties (buckling and toughness) of the bamboo samples after they had been exposed to aggressive conditions in the wet chamber with a relative humidity of 100 ± 2% and a temperature of (40 ± 3) °C for 1, 5, and 10 days.
2. Materials and methods The Tonkin Cane bamboo poles were obtained from China and every pole was cut from a bamboo culm older than 5 years. After the harvest, they were dried for six months in a warehouse with 40% humidity without any chemical treatment (they were preserved by traditional preservation methods, such as curing, smoking, soaking, and lime-washing) and then were stored in a ventilated warehouse at room temperature (22 °C) for at least a year. 2.1. Sample preparation The condition of bamboo culms was verified visually and the culms with no observable defects were marked. Samples were ordered from a sales company in the diameter and the length that fit the bicycle frame. The Tonkin Cane stalks have a length of 460 mm that fits a bicycle frame and their outer diameter is 30 mm. Samples for each testing were cut randomly from bamboo culms according to the results presented in the authors’ previous study [26]. In order to determine the influence of humidity on buckling and toughness of each bamboo species, tests were carried out in different laboratory conditions, dry and wet: (a) Dry tests. The tests were intended for measuring the buckling and the toughness of the samples tested in dry laboratory conditions at a temperature of 22 °C and a relative humidity of 31%. Tests were carried out on a quarter of Tonkin Cane bamboo samples. (b) Wet tests. The tests were aimed at measuring the buckling and the toughness of the samples tested after they had been exposed to aggressive conditions, such as a relative humidity of 100 ± 2% and a temperature of 40 ± 2 °C, in the wet chamber for different periods of time. The second quarter of Tonkin Cane bamboo samples were exposed to these conditions in the wet chamber for 1 day, the third quarter of samples for 5 days, and the last quarter for 10 days. Since bamboo has hollow culms, ends of culms were covered by Parafilm M(R) to simulate realistic environmental conditions, i.e. to allow moisture to penetrate only through the outer wall. After the defined periods of time (one, five, and ten days), the stalks were removed, cut to the sample dimensions and immediately tested. Buckling and toughness tests were carried out on 20 samples of Tonkin Cane bamboo.
ferent periods of time; after that the samples were weighed on KERN ABS and METTLER TOLEDO devices.
2.3. Buckling Samples to be tested for buckling were cut from culms. The selected length of the samples of 460 mm was adjusted to the dimensions of the wet chamber allowing up to 500 mm long samples; the length of 460 mm fits to seat tube of a bicycle size M. All samples had one node in the length. Tests were carried out on a Heckert test machine, type WPM, EU 40 MOD, accuracy class 0.5 at a temperature of 22 °C and a loading rate of 10 mm/min. The bamboo sample placed between two steel plates was tested under load. Pieces of sponge were put between the plates and at the ends of the bamboo sample to avoid the sliding of the sample from the steel surface, as shown in Fig. 1. The tested samples were loaded continuously to the point of failure, at a displacement rate of 10 mm/min (see Fig. 1). The average external diameter D of the bamboo sample was 29.79 mm and the internal diameter d was 20.66 mm.
2.4. Toughness Samples used for the Charpy impact test were cut from bamboo slices, as shown in Fig. 2, where l is the length of the sample in millimetres, b is its width, mm, h is its thickness, mm. They were without nodes. Tests were performed according to the HRN EN ISO 179 standard at a temperature of 22 °C. Load was perpendicular to the fibres in the matrix. The toughness test was carried out on a K. Frank GMBH test machine having maximum impact energy of 4 J.
Fig. 1. Buckling test.
2.2. The mass of samples after different periods of time of exposure – gravimetric analysis Culm samples placed in the wet chamber were exposed to a relative humidity of 100 ± 2% and a temperature of 40 ± 3 °C for dif-
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Fig. 2. The Charpy impact test; dimensions of the sample.
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2.5. Statistical tests
3. Results and discussion
For each property (mass, buckling, and toughness) and for each mode of testing (1-Day, 5-Day, and 10-Day), the following measures of central tendency were determined: Average, Standard deviation, Coefficient of variation, Min./Max., Skewness, and Kurtosis. In addition, using the Shapiro-Wilk and Kolmogorov-Smirnov Tests, the distribution of measured data was compared to a normal distribution. The measures of central tendency are presented by Boxand-Whisker Diagrams while the distribution of data is presented by the Normal Probability Plot. The testing of all statistical hypotheses was performed at the significance level a = 0.05. Analysis of Variance (ANOVA) test and the Multiple Range test with the Least Significant Difference (LSD) procedure were done to determine the differences in the values of particular properties in dependence on the number of days of exposure to wet conditions. The values of determined differences are shown in Box-and-Whisker Diagrams. After the integration of measured values of each property from the three modes into one set, the previously mentioned measures of central tendency were recalculated and graphically presented by the Box-and-Whisker Diagrams and the Normal Probability Plots in order to determine the data distribution normality. This is a condition for obtaining a predictive model. For the unique set of data from all three modes of testing, a model for predicting the change in the value of a particular property with respect to the mode, i.e. the number of days of exposure to wet conditions, was generated with a purpose of obtaining an exact mathematical expression. In order to prove the significance of the change in the value of a particular property, ANOVA test was performed with p-values shown. The Correlation (R) and RSquared (R2) coefficients were calculated to determine the predictive power of the model. The predictive models used are shown graphically using the upper/lower confidence intervals and error intervals.
Table 1 summarizes the test results of measured mechanical properties (bending and toughness) of the Tonkin Cane bamboo samples in dry conditions. The ranges of the physical properties are presented in Table 1. The results for Young’s modulus for Tonkin Cane bamboo obtained in this study correspond well with the values reported in literature [27], which range from 7 to 20 MPa. The buckling and the toughness results for Tonkin Cane bamboo are almost within the, 40.1–73.6 N/mm2 range reported in the literature for the buckling of structural bamboos [28,29] and the 53.0–57.7 kJ/ m2 range for toughness [30]. The buckling and the toughness results for the samples of bamboo tested in literature were for the structural bamboo such as Kao Jue or Mao Jue. Since no other results for Tonkin Cane are reported in literature, a direct comparison cannot be made.
3.1. The mass of samples after different periods of exposure The calculated average data on mass related to the number of days of exposure in the wet chamber are given in Tables 2–4, where Mass-1 denotes the mass after one day of testing, Mass-5 after five days, and Mass-10 after ten days (Figs. 3 and 4). Prediction limits (Fig. 5) are the outer bounds in the above plot and describe how precisely one could predict where a single new observation would lie. Regardless of the size of the sample, new observations will vary around the true line with a standard deviation. Confidence limits (Fig. 5) are the inner bounds and describe how well the location of the line has been estimated given the available data sample. The width of the bounds varies as a function of X, with the line estimated most precisely near the average value.
Table 1 Physical and mechanical properties of Tonkin Cane bamboo in dry conditions.
External diameter, D (mm) Internal diameter, d (mm) Cross – sectional area, A (mm2) Second moment of area, I (mm4) Buckling, rk (N/mm2) Young’s modulus E (kN/mm2) Toughness, (kJ/m2)
Maximum
Minimum
Average
Standard deviation
31.68 23.24 366.79 30820.6 82.52 25.12 77.31
27.58 16.55 351.49 28304.7 61.23 16.26 44.56
29.79 20.66 359.69 29708.60 74.62 19.98 59.77
1.1770 1.7131 36.1842 909.7500 6.9707 2.9025 11.1123
Table 2 Statistics for mass.
Number of samples Average Standard deviation Coeff. of variation Min. Max. Skewness Kurtosis Shapiro-Wilk (W) p-value (p) K-S test Median (Md) Lower quartile (Q1) Upper quartile (Q3) Interquartile range (IRQ)
Mass – 1, g
Mass – 5, g
Mass – 10, g
20 7.8265 0.6221 7.9497% 6.36 9.2 0.5184 1.2135 0.961 0.568 DN = 0.1429; p-value = 0.808 7.92 7.505 8.145 0.64
20 21.6765 3.7052 17.093% 14.17 30.47 16.3 0.0645 0.946 0.314 DN = 0.170; p-value = 0.607 21.04 19.815 23.62 3.805
20 36.8245 2.9971 8.1390% 31.3 43.12 0.726 0.006 0.963 0.623 DN = 0.132; p-value = 0.876 36.52 34.775 38.1 3.325
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Table 3 Multiple sample comparison for mass-1-5-10, g. Number of samples
20-20-20
ANOVA Between groups Within groups Total (Corr.)
Sum of Squares
Df
Mean Square
F-ratio
p-value
8414.46 438.884 8853.34
2 57 59
4207.23 7.6997
546.41
0.0000
Multiple Range Tests (LSD) Mean
Homogeneous Groups
Mass-1 Mass-5 Mass-10 Contrast
7.826 21.676 36.824 Sig.
x
Mass-1 – Mass-5 Mass-1 – Mass-10 Mass-5 – Mass-10
* * *
x X Difference 13.85 28.998 15.148
+/
Limits
1.7571 1.7571 1.7571
Table 4 Statistics for mass-1-5-10, g. Number of samples Average Standard deviation Coeff. of variation Min. Max. Skewness Kurtosis Shapiro-Wilk (W) p-value (p) K-S test
60 22.0608 12.3066 55.7848% 6.36 43.12 0.3593 2.3244 0.882 0.000 DN = 0.195; p-value = 0.020 Fig. 5. Predictive model – mass vs. days.
3.2. Discussion on the effect of humidity on mass The values of measures of the asymmetry (Standard skewness = 0.5184, Standard kurtosis = 1.2135) for the 1-Day mode are within the 2 to +2 range, which indicates that the data for the 1-Day mode are normally distributed. The data distribution is negatively skewed since the mean data value is smaller than the median value (x < Me). P-values of the Shapiro-Wilk test (p = 0.568) and Kolmogorov-Smirnov test (p = 0.808) show that the data of the 1-Day mode testing are distributed according to a normal distribution at the level of statistical significance (a = 0.05). Fig. 3. Box-and-Whisker for mass-1-5-10, g.
Fig. 4. (a) Box-and-Whisker; (b) Normal probability for mass-1-5-10.
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The values of measures of the asymmetry (Standard skewness = 0.0645, Standard kurtosis = 1.1882) for the 5-Day mode of testing are both within the 2 to +2 range, which indicates that the data for the 5-Day mode are normally distributed. The data distribution is positively skewed since the mean data value is greater than the median value (x > Me). P-values of the Shapiro-Wilk test (p = 0.946) and Kolmogorov-Smirnov test (p = 0.314) show that the data of the 5-Day mode testing are distributed according to a normal distribution at the level of statistical significance (a = 0.05). The values of measures of the asymmetry (Standard skewness = (0.7263, Standard kurtosis = 0.0065) for the 10-Day mode of testing are both within the 2 to +2 range, which indicates that the data for the 10-Day mode are normally distributed. The data distribution is positively skewed since the mean data value is greater than the median value (x > Me). P-values of the Shapiro-Wilk test (p = 0.963) and Kolmogorov-Smirnov test (p = 0.623) show that the data of the 5-Day mode testing are distributed according to a normal distribution at the level of statistical significance (a = 0.05). As shown in Table 2, the coefficients of variation in the data on mass for all three modes of testing (1-Day, 5-Day, and 10-Day) according to the methods proposed by Gomes & Costa [31,32] are within acceptable limits (7.9497%, 17.0936%, and 8.1390%). The minimum mass values are 6.36 g, 14.17 g, and 31.3 g, while the maximum ones are 9.2 g, 30.47 g, and 43.12 g; the values of their respective ranges are 2.84 g, 16.30 g, and 11.82 g. The highest value of the range (16.30 g) occurred in the 5-Day mode of testing. The ANOVA results (Table 3) show that there are significant differences at the level of statistical significance (a = 0.05) in the mass values both among all three modes of testing (1-Day, 5-Day, and 10-Day) and among individual values in each mode (F-ratio = 546.41; p-value = 0.000). Multiple Range Test (Fisher’s Least Significant Difference procedure – LSD) denotes a statistically significant difference (95% confidence level) in the mass values of samples among all modes of testing (Mass_1-Mass_5 = 13.85, +/ Limits = 1.7571; Mass_1-Mass_10 = 28.998, +/ Limits = 1.7571; Mass_5Mass_10 = 15.148, +/ Limits = 1.7571). This is shown by the Box-and-Whisker Diagram in Fig. 3. After the integration of measured values of mass from the three modes (1-Day, 5-Day, and 10-Day) into one set, the analysis of measures of central tendency shows that there are significant changes in the value of statistical features important for assessing the normal distribution of data (Table 4): the coefficient of variation which amounts to 55.7848% is not within acceptable limits (<50%) and the standard kurtosis of 2.32441 is not in the 2 to
+2 range. The fact that the data from the common set are not distributed according to a normal distribution is proved by the values of the Shapiro-Wilk (W = 0.882, p = 0.000) and Kolmogorov-Smirnov (DN = 0.195, p = 0.020) tests. P-values in both tests are less than 0.005. A statistical analysis of models for an approximate estimation of the trend in the variability in mass in dependence on the number of days of sample treatment (Table 5) shows a strong positive trend with a correlation coefficient of R = 0.982484, while the R-Squared statistics (R2 = 96.5275%) indicates that the model as fitted explains the variability in mass. The equation of the fitted model is: Mass 1-5-10 = e(2.02261 + 0.672988*ln(Days)). 3.3. Discussion on mechanical properties 3.3.1. Buckling results The calculated average data on buckling related to the number of days of exposure in the wet chamber are given in Tables 6–8, where Buckling-1 denotes the buckling after one day of testing, Buckling-5 after five days, and Buckling-10 after ten days (Figs. 6 and 7). 3.3.2. Discussion on the effect of humidity on buckling The values of measures of the asymmetry (Standard skewness = 1.16086, Standard kurtosis = 0.949588) for the 1-Day mode are within the 2 to +2 range, which indicates that the data for the 1-Day mode are normally distributed. The data distribution is positively skewed since the mean data value is greater than the median value (x > Me). P-values of the Shapiro-Wilk test (p = 0.534) and Kolmogorov-Smirnov test (p = 0.549) show that the data of the 1-Day mode testing are distributed according to a normal distribution at the level of statistical significance (a = 0.05). The values of measures of the asymmetry (Standard skewness = ( 0.942036, Standard kurtosis = 0.636021) for the 5-Day mode of testing are within the 2 to +2 range, which indicates that the data for the 5-Day mode are normally distributed. The data distribution is negatively skewed since the mean data value is smaller than the median value (x < Me). P-values of the Shapiro-Wilk test (p = 0.117) and Kolmogorov-Smirnov test (p = 0.658) show that the data of the 5-Day mode testing are distributed according to a normal distribution at the level of statistical significance (a = 0.05). The values of measures of the asymmetry (Standard skewness = 1.6779, Standard kurtosis = 1.44872) for the 10-Day mode of testing are within the 2 to +2 range, which indicates that the
Table 5 Predictive model – mass vs. days. Number of samples Dependent variable Independent variable
60 Mass Days
Coefficients Parameter
Least Squares Estimate
Standard Error
T Statistic
p-value
Intercept Slope
2.0226 0.6729
0.0271 0.0167
74.402 40.1529
0.0000 0.0000
ANOVA Source
Sum of Squares
Df
Mean Square
F-Ratio
p-value
Model Residual Total (Corr.)
25.2805 0.9094 26.19
1 58 59
25.2805 0.0156
1612.26
0.0000
Predictive model Equation R R2
Mass 1-5-10 = e(2.02261 + 0.672988*ln(Days)) 0.9824 0.9652 (96.52%)
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Table 6 Statistics for buckling.
Number of samples Average Standard deviation Coeff. of variation Min. Max. Skewness Kurtosis Shapiro-Wilk (W) p-value (p) K-S test Median (Md) Lower quartile (Q1) Upper quartile (Q3) Interquartile range (IRQ)
Buckling-1
Buckling-5
Buckling-10
20 59.7585 6.5634 10.9833% 47.32 75.92 1.1608 0.9495 0.959 0.534 DN = 0.180; p-value = 0.549 58.96 56.465 63.225 6.76
20 57.3195 6.1859 10.7921% 43.62 64.96 0.9420 0.6360 0.923 0.117 DN = 0.163; p-value = 0.658 58.84 52.085 62.47 10.385
20 52.967 4.6672 8.8116% 46.55 65.77 1.6779 1.4487 0.938 0.224 DN = 0.096; p-value = 0.992 53.145 49.525 55.375 5.85
Table 7 Multiple sample comparison for buckling-1-5-10, N/mm2. Number of samples
20-20-20
ANOVA Between groups Within groups Total (Corr.)
Sum of Squares
Df
Mean Square
F-ratio
p-value
473.45 1959.44 2432.89
2 57 59
236.725 34.3761
6.89
0.0021
Mean
Homogeneous Groups
52.967 57.3195 59.7585 Sig.
x
Multiple Range Tests (LSD) Mass-10 Mass-5 Mass-1 Contrast Mass-1 – Mass-5 Mass-1 – Mass-10 Mass-5 – Mass-10
* *
Difference
x x +/
2.439 6.7915 4.3525
3.71274 3.71274 3.71274
Limits
Table 8 Statistics for buckling-1-5-10, N/mm2. Number of samples Average Standard deviation Coeff. of variation Min. Max. Skewness Kurtosis Shapiro-Wilk (W) p-value (p) K-S test
60 56.6817 6.4214 11.329% 43.62 75.92 1.3569 0.3418 0.984 0.630 DN = 0.059; p-value = 0.982
data for the 10-Day mode are normally distributed. The data distribution is negatively skewed since the mean data value is smaller than the median value (x < Me). P-values of the Shapiro-Wilk test (p = 0.224) and Kolmogorov-Smirnov test (p = 0.922) show that the data of the 10-Day mode testing are distributed according to a normal distribution at the level of statistical significance (a = 0.05). As shown in Table 6, the coefficients of variation in the data on buckling for all three modes of testing (1-Day, 5-Day, and 10-Day) according to the methods proposed by Gomes & Costa [31,32] are within acceptable limits (10.9833%, 10.7921%, and 8.8116%). The minimum values for buckling are 47.32 N/mm2, 43.62 N/ mm2, and 46.55 N/mm2, while the maximum ones are 75.92 N/ mm2, 64.96 N/mm2, and 65.77 N/mm2; the values of their respective ranges are 28.6 N/mm2, 21.34 N/mm2, and 19.22 N/mm2. The
Fig. 6. Box-and-Whisker diagram for buckling-1-5-10, N/mm2.
highest value of the range (28.6 N/mm2) occurred in the 1-Day mode of testing. The ANOVA results (Table 7) show that there are significant differences in the values for buckling at the level of statistical significance (a = 0.05) among all three modes of testing, i.e. 1-Day, 5Day, and 10-Day (F-ratio = 6.89; p-value = 0.0021). Multiple Range Test (Fisher’s Least Significant Difference procedure – LSD) denotes a statistically significant difference (95% confidence level) in the values of sample buckling between the following modes of testing: Mass_1-Mass_10 = 6.7915, +/ Limits = 3.7127; and Mass_5-Mass_10 = 4.3525, +/ Limits = 3.7127.
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Fig. 7. (a) Box-and-Whisker diagram; (b) normal probability plot for buckling-1-5-10, N/mm2.
There is no significant difference between the modes Mass_1Mass_5 = 2.439, +/ Limits = 3.7127. This is shown by the Boxand-Whisker Diagram in Fig. 7 (* denotes a statistically significant difference) (Fig. 8). After the integration of measured values of buckling from the three modes (1-Day, 5-Day, and 10-Day) into one set, the analysis of measures of central tendency shows that there are no significant changes in the value of statistical features important for assessing the normal distribution of data (Table 8): the coefficient of varia-
tion = 11.329% (<50%), the standard skewness = 1.3569, and the standard kurtosis = 0.341846 ( 2 to +2 range). The fact that the data from the common set are distributed according to a normal distribution is proved by the values of the Shapiro-Wilk (W = 0.984, p = 0.630) and Kolmogorov-Smirnov (DN = 0.059, p = 0.982) tests. P-values in both tests are greater than 0.005. A statistical analysis of models for an approximate estimation of the trend in buckling in dependence on the number of days of sample treatment (Table 9) shows a weak positive trend with a correlation coefficient of R = 0.194604, while the R-Squared statistics (R2 = 16.6344%) indicates that the model as fitted explains the variability in buckling. The equation of the fitted model is: Buckling 1-510 = 10108.2 + 34.3307*Days 0.0289*Days2. 3.3.3. Toughness results The calculated average data on toughness on related to the number of days exposure in the wet camber are given in Tables 10– 12, where Toughness-1 denotes the toughness after one day of testing, Toughness-5 after five days, and Toughness-10 after ten days (Figs. 9 and 10). 3.3.4. Discussion on the effect of humidity on toughness The values of measures of the asymmetry (Standard skewness = 1.1078, Standard kurtosis = 0.4424) for the 1-Day mode
Fig. 8. Predictive model – buckling vs. days.
Table 9 Predictive model – buckling vs. days. Number of samples Dependent variable Independent variable
60 Buckling Days
Coefficients Parameter
Estimate
Standard Error
T Statistic
p-value
Constant Days Days2
10108.2 34.3307 0.0289722
29502.2 97.4372 0.080449
0.3426 0.3523 0.360131
0.7331 0.7259 0.7201
ANOVA Source
Sum of Squares
Df
Mean Square
F-Ratio
p-value
Model Residual Total (Corr.)
473.45 1959.44 2432.89
2 57 59
236.725 34.3761
6.89
0.0021
Predictive model Equation R R2
Buckling 1-5-10 = 0.1940 0.1630 (16.30%)
10108.2 + 34.3307*Days
0.0289722*Days2
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Table 10 Statistics for toughness.
Number of samples Average Standard deviation Coeff. of variation Min. Max. Skewness Kurtosis Shapiro-Wilk (W) p-value (p) K-S test Median (Md) Lower quartile (Q1) Upper quartile (Q3) Interquartile range (IRQ)
Toughness-1
Toughness-5
Toughness-10
20 45.7335 3.0981 6.7742% 39.6 50.54 1.1078 0.4424 0.943 0.273 DN = 0.169; p-value = 0.615 46.455 44.035 47.88 3.845
20 47.0315 13.0149 27.6726% 22.87 71.18 0.5228 0.1441 0.955 0.449 DN = 0.172; p-value = 0.592 48.09 38.75 52.63 13.88
20 46.303 6.5258 14.0939% 30.54 58.53 0.5533 0.7965 0.973 0.817 DN = 0.129; p-value = 0.893 45.885 42.605 49.595 6.99
Table 11 Multiple sample comparison for Toughness-1-5-10, N/mm2. Number of samples
20–20–20
ANOVA Between groups Within groups Total (Corr.)
Sum of Squares
Df
Mean Square
F-ratio
p-value
16.9323 4209.87 4226.8
2 57 59
8.4661 73.8574
0.11
0.8919
Mean
Homogeneous Groups
Mass-10 Mass-5 Mass-1
46.303 47.0315 45.7335
x x x
Contrast
Sig.
Difference
+/
1.298 0.5695 0.7285
5.4420 5.4420 5.4420
Mass-1 – Mass-5 Mass-1 – Mass-10 Mass-5 – Mass-10
Table 12 Statistics for toughness-1-5-10, KJ/m2. Number of samples Average Standard deviation Coeff. of variation Min. Max. Skewness Kurtosis Shapiro-Wilk (W) p-value (p) K-S test
60 46.7815 7.6605 16.3751% 30.59 71.18 3.0203 4.4802 0.895 0.000 DN = 0.190; p-value = 0.025
Limits
are within the 2 to +2 range, which indicates that the data for the 1-Day mode are normally distributed. The data distribution is negatively skewed since the mean data value is smaller than the median value (x < Me). P-values of the Shapiro-Wilk test (p = 0.273) and Kolmogorov-Smirnov test (p = 0.615) show that the data of the 1Day mode testing are distributed according to a normal distribution at the level of statistical significance (a = 0.05). The values of measures of the asymmetry (Standard skewness = 0.522809, Standard kurtosis = 0.144121) for the 5-Day mode of testing are within the 2 to +2 range, which indicates that the data for the 5-Day mode are normally distributed. The data distribution is negatively skewed since the mean data value is smaller than the median value (x < Me). P-values of the Shapiro-Wilk test (p = 0.449) and Kolmogorov-Smirnov test (p = 0.592) show that the data of the 5-Day mode testing are distributed according to a normal distribution at the level of statistical significance (a = 0.05). The values of measures of the asymmetry (Standard skewness = 0.553396, Standard kurtosis = 0.796536) for the 10-Day mode of testing are within the 2 to +2 range, which indicates that the data for the 10-Day mode are normally distributed. The data distribution is positively skewed since the mean data value is
Fig. 9. Box-and-Whisker toughness-1-5-10, N/mm2.
greater than the median value (x > Me). P-values of the ShapiroWilk test (p = 0.817) and Kolmogorov-Smirnov test (p = 0.893) show that the data of the 10-Day mode testing are distributed according to a normal distribution at the level of statistical significance (a = 0.05). As shown in Table 10, the coefficients of variation in the data on toughness for all three modes of testing (1-Day, 5-Day, and 10-
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Fig. 10. (a) Box-and-Whisker; (b) normal probability for toughness-1-5-10, KJ/m2.
Fig. 11. Predictive model – toughness vs. days.
Day) according to the methods proposed by Gomes & Costa [31,32] are within acceptable limits (6.7742%, 27.6726%, and 14.0939%). The minimum values for toughness are 39.6 KJ/m2, 22.87 KJ/m2, and 30.54 KJ/m2, while the maximum ones are 50.54 KJ/m2, 71.18 KJ/m2, and 58.53 KJ/m2; the values of their respective ranges are10.94 KJ/m2, 71.18 KJ/m2, and 58.53 KJ/m2. The largest value of the range (71.18 N/mm2) occurred in the 5-Day mode of testing.
The ANOVA results (Table 11) show that there are no significant differences at the level of statistical significance (a = 0.05) in the values for toughness among all three modes of testing, i.e. 1-Day, 5-Day, and 10-Day (F-ratio = 0.11; p-value = 0.8919). Multiple Range Test (Fisher’s Least Significant Difference procedure – LSD) shows that there are no statistically significant differences (95% confidence level) in the values of toughness between the following modes of testing: Mass_1-Mass_5 = 1.298, +/ Limits = 5.44205; Mass_1-Mass_10 = 0.5695, +/ Limits = 5.44205; Mass_5-Mass_10 = 0.7285, +/ Limits = 5.44205. This is shown by the Box-and-Whisker Diagram in Fig. 9 (* denotes a statistically significant difference) (Fig. 11). After the integration of measured values of toughness from the three modes (1-Day, 5-Day, and 10-Day) into one set, the analysis of measures of central tendency shows that there are significant changes in the value of statistical features important for assessing the normal distribution of data (Table 12): the coefficient of variation = 16.3751% (<50%), the standard skewness = 3.02037, and the standard kurtosis = 4.48026 ( 2 to +2 range). The fact that the data from the common set are not distributed according to a normal distribution is proved by the values of the Shapiro-Wilk (W = 0.895, p = 0.000) and Kolmogorov-Smirnov (DN = 0.190, p = 0.025) tests. P-values in both tests are less than 0.05. A statistical analysis of models for an approximate estimation of the trend in toughness in dependence on the number of days of sample treatment (Table 13) shows a very weak positive trend
Table 13 Predictive model – toughness vs. days. Number of samples Dependent variable Independent variable
60 Toughness Days
Coefficients Parameter
Estimate
Standard Error
T Statistic
p-value
Constant Days Days2
44.7115 1.1142 0.0922
2.5607 1.2156 0.1061
17.4604 0.9165 0.8685
0.0000 0.3633 0.3887
ANOVA Source
Sum of Squares
Df
Mean Square
F-Ratio
p-value
Model Residual Total (Corr.)
51.0125 3411.31 3462.32
2 57 59
25.5062 59.8475
0.43
0.6551
Predictive model Equation R R2
Toughness 1-5-10 = 44.7115 + 1.1142*Days 0.0140 0.0000 (0.00%)
0.0922*Days2
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with a correlation coefficient of R = 0.014, while the R-Squared statistics R2 = 0.000% indicates that the proposed predictive model for an approximate estimation of the trend in toughness as fitted explains 0.000% of the variability in toughness. The equation of the fitted model is: Toughness 1-5-10 = 44.7115 + 1.1142*Days 0.0922*Days2.
4. Conclusion The purpose of this research was to investigate the effects of humidity on the mechanical and physical properties of bamboo. As a result of this study, the key novel findings about the mechanical and physical properties of bamboo under aggressive wet conditions are as follows:
395
ity trend can be considered very reliable due to the high value of RSquared statistics (R2). Predictive models of other features show a relatively low level of reliability due to a relatively small value of R2 and it is concluded that the tested features do not show significant changes in their values (either rise or fall) within 1, 5 or 10 days of the test. For further research, we plan to test the dynamic durability of bamboo in dry and wet conditions; it is also planned to obtain a predictive model for the behaviour of mechanical properties in dependence on the number of days of exposure to defined conditions.
Conflicts of interest The authors declare no conflict of interest.
- Mass. Results for all three modes of testing (1-Day, 5-Day, and 10-Day) are dispersed according to a normal distribution, which is proved by the Shapiro-Wilk and Kolmogorov-Smirnov tests, and they are mostly positively skewed. The Multiple Sample Comparison and Multiple Range tests prove that there are significant differences among the values of mass in dependence on the mode of testing, i.e. the number of days of sample exposure to wet conditions. The R-Squared statistics (R2) of the proposed predictive model for an approximate estimation of the trend in mass variability as fitted explains 96.52% of the variability in mass, which is a very high percentage. - Buckling. Results for all three modes of testing (1-Day, 5-Day, and 10-Day) are dispersed according to a normal distribution, which is proved by the Shapiro-Wilk and KolmogorovSmirnov tests, and they are mostly negatively skewed. The Multiple Sample Comparison test proves that there are significant differences among the values of buckling in dependence on the mode of testing, i.e. the number of days of sample exposure to wet conditions. The Multiple Range test proves that there are no differences in the values of buckling in the 1–5 day period. The R-Squared statistics (R2) of the proposed predictive model for an approximate estimation of the trend in buckling as fitted explains only 16.30% of the variability in buckling, which is a very low percentage. - Toughness. Results for all three modes of testing (1-Day, 5-Day, and 10-Day) are dispersed according to a normal distribution, which is proved by the Shapiro-Wilk and KolmogorovSmirnov tests; the results are mostly negatively skewed. The Multiple Sample Comparison test proves that there are significant differences among the values of toughness in dependence on the mode of testing, i.e. the number of days of sample exposure to wet conditions. In addition, the Multiple Range test proves that there are no differences among the modes of testing. The R-Squared statistics (R2) of the proposed predictive model for an approximate estimation of the trend in toughness as fitted explains 0% of the variability in toughness; therefore, it can be rejected. Given the above, it can be concluded that all the properties (Mass, Buckling, Toughness) tested in all the three modes of testing (1-Day, 5-Day, 10-Day) exhibit changes in their values (upward or downward trends) with respect to the number of days of testing at the level of statistical significance (a = 0.05). The measured values of all the properties within a mode of testing are distributed according to a normal distribution, and the coefficients of variation are mostly within acceptable limits. The previously stated facts were the reason for studying models for the prediction of the trend in the variability of values of properties in dependence on the number of days of testing, i.e. the mode of testing. The research results have shown that the model for predicting the mass variabil-
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