## 2 Materials and Methods
### Reduced Outer Diameter and Ovality of the Samples  
One of the objectives of this study is to reduce irregular bamboo ends to give them a uniform and round diameter without any damage to the bamboo culms. Table 1 summarizes the basic statistics of the outer diameters of Gui and Moso bamboo specimens before and after the reduction. A paired \(t\)-test was performed to compare the mean diameters of the samples accordingly. The reduced outer diameters are significantly smaller than the original outer diameters of both Gui and Moso bamboo samples.  
Figure 6: (**a**) Reducing process. (**b**) Typical load–displacement curves.  
Figure 7: The reducing forces for various reduction ratios for the samples.  
It appears that the outer diameter of the bamboo samples could be reduced by the thermo-hydro-mechanical process under the specified maximum reduction of 0.15. The standard deviations of the original and the reduced outer diameters were compared by a two-variance F-test. The standard deviations of the reduced diameters of the specimens were significantly smaller than those of the original outer diameters, indicating that the reduced bamboo ends had a more uniform diameter.  
Bamboo culms are usually not perfectly round in shape. To simplify their out-of-roundness, it was assumed that the cross-section of bamboo was oval. The ovality or the out-of-roundness can be defined as the difference between the long axis and the short axis. When ovality equals to zero, the cross-section is assumed to be circular. The histograms of ovality for Gui and Moso bamboos are shown in Figure 8. The average ovality and the standard deviation values of Moso bamboo samples, before and after the reduction, were 2.18 and 0.89 mm, respectively. Corresponding values of Gui bamboo samples were found as 1.71 and 0.38 mm. The statistical analysis proved that the average ovality and the standard deviation values of the samples after reduction were significantly smaller than those of the original specimens, indicating that the cross-sections of reduced bamboos were a uniform circular shape. According to Eurocode 3 (CEN 2007), the out-of-roundness of pipes is defined by the difference between the long and short axes divided by the nominal diameter. The ovality limits are 0.014, 0.02, and 0.03 for Class Av(Excellent), Class Bv(High), and Class Cv(Normal), respectively. If the ovality values in Figure 8 are divided by the associated nominal diameters, the values of out-of-roundness for Gui and Moso bamboos would be 0.011 and 0.016, which can be considered in Class A and Class B, respectively. This reveals that the ovalities of the reduced bamboo ends have met the industrial standard.  
\begin{table}
\begin{tabular}{l c c c c} \hline \hline  & \multicolumn{2}{c}{**Moso Bamboo**} & \multicolumn{2}{c}{**Gui Bamboo**} \\ \hline  & **Original** & **Reduced** & **Original** & **Reduced** \\ \hline Minimum (mm) & 55.70 & 54.95 & 34.65 & 32.64 \\ Maximum (mm) & 65.25 & 58.62 & 38.90 & 33.88 \\ Mean (mm) & 60.66 & 57.02 & 36.71 & 33.2 \\ Paired \(t\)-test for equal means & \multicolumn{2}{c}{t = 12.59} & \multicolumn{2}{c}{t = 20.71} \\ \(p\) (single tail) & \multicolumn{2}{c}{\(p<0.001\)} & \multicolumn{2}{c}{\(p<0.001\)} \\ Standard Deviation (mm) & 2.542 & 0.848 & 1.319 & 0.262 \\ \(t\)-test for equal variances & \multicolumn{2}{c}{f = 9.00} & \multicolumn{2}{c}{f = 25.21} \\ \(p\) (single tail) & \multicolumn{2}{c}{\(p<0.001\)} & \multicolumn{2}{c}{\(p<0.001\)} \\ \hline \hline \end{tabular}
\end{table}
Table 1: Comparison of means and variances of outer diameters before and after reducing.  
Figure 8: The histograms of ovality before and after the reduction of the samples.