Cross-species bamboo grading based on flexural properties

This experiment studied five species of bamboo culms [e.g. B. vulgaris (ampel), D. asper (betung), G. apus (tali), G. atroviolacea (hitam), and G. pseudoarundinaceae (andong)], then analyzed the possibility to develop cross-species bamboo structural grading (both strength and capacity grading) models by mean of dummy variable regression. Since the regression analysis resulted the significantly different coefficient values of the dummy variables, any coincided trendline did not found, but some parallel ones were obtained. The non-coincided but parallel trendlines indicated that a linear equation can estimate the average value of the grade determining property (GDP) of cross-species bamboo structural grading, while the constants must be added to consider the species influence. Meanwhile the non-parallel trendlines indicated that the different linear equation must be applied for every bamboo species. The crossspecies bamboo structural grading could not reliably justify in this study. Species have a strong influence on bamboo grading. Therefore, the authors suggest considering the species identification in the bamboo structural grading.


Introduction
Bamboo has been recognized as an environmentally friendly construction material since ancient time and was traditionally used in culm form. The process for structural properties determination of natural materials such as wood or bamboo differs significantly from that of factory-made materials because their genetics and environment condition during their growth periods are varied and less controlled. Reliable knowledge of the mechanical properties of each structural material forms the basis of any design code or standard [1]. Structural grading is necessary to justify bamboo as construction materials and to guide the designers choosing the adequate bamboo culms for the member resisting the planned design load [2][3][4][5][6][7]. The initial research on bamboo engineering properties as construction materials was carried out by Janssen in 1981 [8]. The stiffness and maximum moment can be used as indicators in the machine assisted grading of bamboo [1,6,7,9]. Aside from machine assisted grading, visual grading can also be performed on a bamboo culm including observation on its geometry, size, shape, weight, and imperfections to estimate the strength and load-bearing capacity as designated by ISO 19624:2018 [10].
Previous studies [1][2][3][4][5][6][7] reported that structural grading is more reliable by applying the capacity grading than the strength grading. Pradhan and Dimitrakopoulos [11] have attempted to implements capacity grading to achieve the capacity-based design for multi culms bamboo axial members. Capacity grading is the process of sorting every piece of material in a sample into grades according its modulus of elasticity and flexural rigidity (EI), while strength grading measure its modulus of elasticity and flexural strength. [6]. Strength grading determines the allowable stress of a material, while capacity grading determines the reference load-carrying capacity of a member.

External diameter (D) and wall thickness (δ) measurement.
The external diameter was measure on two perpendicular axes, namely x-axis and z-axis and were measured on each node and mid-internode as seen in Figure 1.a. The average measurements represented the external diameter (D) of a culm. Wall thickness (δ) is the average thickness measured at four positions at each bottom and top section. (Figure 1.b).

External taper measurement (αe).
External taper is the ratio between the difference in the top and bottom diameter (Db -Dt) to the length (L) (Equation 1). The taper value in this study was obtained from the average taper in the vertical and horizontal direction when it was placed on a special pedestal (Figure 1

Bow (bo) measurement. Bow measurement steps were:
• Bamboo is placed on a pedestal, then two parallel strings were placed with a constant distance of 30 cm. • The distances of the furthest culm (z 1 and z 2 ) to the two strings were measured using a caliper in each node twice on the most curved side then in a 90° rotated position (x-axis and z-axis). Furthermore, he bows measurement results in x-axis and z-axis are recorded and plotted in a graph as seen in Figure 2. (2) The value of the eccentricity of the culms is obtained from the average value of the eccentricity for each node and internode in the form of the ratio between the distances at each point on the conic side of a focus to the distance in the corresponding direction [21]. In this study, the major axis is the maximum diameter, while the minor axis is the minimum diameter. The eccentricity value of 0 (zero) shows a perfectly round cross section of the bamboo. Eccentricity (e c ) was calculated per Equation 6.

Moisture content (w)
Moisture content (w) measurement was carried out using the needle type moisture meter MC7828T soon after the bending test. For calibration purpose, the moisture content measurement by an oven dry method referring to ISO 22157-1 [22] was also conducted. A small piece (1D for each species) was cut from each specimen and weighed to determine the initial weight (W1), then those small pieces were oven-dried at 103 ± 2 ºC for 48 hours to obtain the oven-dry weight (W0). The moisture content (w) was calculated per Equation 6.

Linear mass (q) and density (ρ)
Linear mass (q) is ratio of the mass (W) to the length (L) (Equation 8). Meanwhile, density is determined by assuming the bamboo is a hollow cylinder which results in the density of the bamboo walls (ρ). Density (ρ) is calculated by dividing the mass (W) against the volume (V) of bamboo walls (Equation 9). Linear mass and density values were calculated under two conditions, namely at the air-dry (qa, ρa) and at the 12% moisture content (q12, ρ12).

Bending test
The bending test were carried out in two points loading configuration using 30 tons capacity SATEC/Baldwin Universal Testing Machine ( Figure 3). The test configuration referred to ISO 22157-1 [22] with some modifications [1,6,7], which are similar with the current ISO 22157:2019 [20]. The modulus of elasticity (E), represented the material stiffness, were calculated within the proportional limit. Two modulus of elasticities were obtained, namely true modulus of elasticity (Etrue) and apparent modulus of elasticity (Eapp). In addition, the beam stiffness (EI) values were also obtained, both true beam stiffness EI true and apparent beam stiffness (EI app  The bending tests were carried out until the bamboo specimen failure. The failure type was identified, and the maximum moment (Mmax) calculation was carried out if the damage position is in the area between two load points (Equation 14). The flexural strength of bamboo (modulus of rupture/SR) was calculated according to Equation 15.
with: a = distance between the support to the nearest load point (mm) Δ = deformation measured at the center of the span along the span length (L) (mm) ΔLb = deformation measured at the center of the span along two load points (Lb) (mm) L = distance between two supports (mm) Lb = distance between two load points (mm) P = load under the proportion limit (N) Pmax = maximum load (N)

Ungraded bamboo.
The distribution of Etrue, Eapp, and SR data of ungraded bamboo in this study were fitted by the Weibull distribution to obtain the shape (α) and scale (µ) parameters. The estimation of the fifth percent exclusion limit (R0.05) following parametric tolerance limit (PTL) method referred to ASTM D5457 [23] (Equation 16) while the characteristics value (Rk) measurement referred to ISO 22157-19 [22] (Equation 17) with the k-factors referring to confident level factor presented in Table 3 ASTM D2915-17 [24]. This Rk value is equivalent to the reference resistance.  . Structural bamboo grading. The data were analyzed using multiple regression with dummy variables. The independent variable in this study is the indicating predictor (IP) which has been recommended [1,6,7] to estimate the grade determining property (GDP) in bamboo structural grading. Density (ρ) was chosen as the independent variable (xi) to estimate the modulus of rupture (SR) and the modulus of elasticity (E), the combination of linear mass and diameter (qD) to estimate the maximum moment (Mmax), and the combination of linear mass and squared diameter (qD 2 ) to estimate the beam stiffness (EI). The multiple regression model is Equation18.

yi = a + bizi + cizixi + dxi + εi
Regression lines for each species are tested for non-parallel and non-coincided following Drapper and Smith [25] with the 95% confident level, so that it can determine whether one regression equation can be applied for all species, some species, or only one species of bamboo. After a regression equation is selected and proven to be reliable for all species, some species, or one species, structural quality classification is carried out using the confident band method [4][5][6][7]. Each quality class has a 5% lower limit value (R0.05), standard deviation (s), and characteristic value (Rk). The R0.05 is the 5 th percentile value determined in Equation 19. The 5 th percentile value indicates the near minimum strength or the weakest 5% resistance which is chosen as the representative value of all culms with a confidence of 75%. The characteristic value (Rk) of bamboo grading refers to the modified ISO 22156 [13], by substituting the standard deviation (s) with the standard error of regression (SE) for the estimated value (Eq. 20) to obtain Equation 21 [25].

Geometrical properties
The geometrical properties of bamboo culms include dimensions and imperfections of the culm. The dimension measurements were the internode length (L in ), external diameter (D) and thickness (δ). The average diameter of betung is the biggest compared to the other species in this study. Overall, diameter of the bottom is greater than the top. The variation in thickness of five species of bamboo shows similarity with variation in diameter ( Figure 5). The largest thickness at the bottom of the culm and decreases with the height of the culm. Thickness is influenced by genetic factors so that the wall's culms are different in each genus and species [26].  Bamboo with 5-20 cm of diameter can be used for structural purposes [27]. Since its big diameter, betung can be applied for a heavy construction material, while the other four species (i.e., ampel, tali, andong, and hitam) are suitable for medium construction material in accordance with SNI 8020:2014 [28]. Outer diameter (D) indicated the flexural moment-carrying capacity (Mmax), beam stiffness (EI) [5,6,9], and ultimate-load (Fu) on compression [3,4], while thickness (δ) is an important criterion considered for tension perpendicular and shear capacities. Harries et al. [29] also made a classification of structural bamboos based on the ratio of diameter to thickness (D/δ), which is divided into two classes. Bamboo with D/δ > 8 is classified into thin-walled bamboo, while bamboo with D/δ < 8 is classified into thick-walled bamboo. Based on this classification, ampel and tali bamboo are classified into thick-walled bamboo with D/δ 7.93 and 7.66, respectively, while andong, hitam and betung bamboo are classified as thin-walled bamboo with D/δ respectively 8.71, 8.35 and 11.73. The D/δ classification is found less precise for the species in this study because the ratio of diameter and wall thickness can vary within a species. A species can be classified as both thin-walled and thick-walled ( Figure 4).
The correlation between diameter and wall thickness is weak within a species (Figure 4a) but strong for cross-species ( Figure 4b) and generally positive. In this study, the diameter is measured at the node and the mid-internode, while the thicknesses were measured at both ends only. The weak positive correlation between diameter and thickness of andong, hitam, and tali were also found [4], while the moderate positive correlation was reported for guadua [3]. Since its positive correlation, the diameter-to-thickness relationship in a specific species may roughly estimate the wall thickness.
The geometric shape of bamboo is always assumed to be a tapered hollow pipe [30]. Geometry of bamboo is influenced by genetic characteristics and the environment in which it grows. Therefore, each bamboo species has different geometric characteristics [31]. The variations of imperfections that affect the geometry of bamboo culm are taper (e, %), eccentricity (ec) and bow (bo). The imperfections of the culm did not affect the results of two points loading bending test in this study because the resulting e, ec, and bo values can still be tolerated for structural purpose. The range of e, ec, and bo were 0.09%-0.67%, 0.0321-0.2181, and 0.009-0.015, respectively. Taper does not significantly affect to bamboo flexural properties if the measurement is conducted in third point loading [32] but it reduces modulus of rupture (SR) value in center point loading if its value is greater than 2.3% [30].

Moisture content
Natural drying process this study was carried out in indoor environment assisted by fan for three to five months. The moisture content of bamboo changes following its ambient temperature and relative humidity, considering that bamboo is a hygroscopic material. Moisture content of the specimens ranged from 14.4% to 16.9%, similar with previous reports [3,[5][6][7]. Mechanical properties of bamboo are better in dry conditions [33,34]. The variation in moisture content between species is not significant because the bamboo culms have uniformly reached equilibrium moisture content [35]. Evaluation of standard procedures for adjusting the properties of wood to changes in moisture content shows that small samples can increase flexural strength along with decreasing moisture content [7,36].

Linear mass and density
Based on ISO 22157:2019 [21], bamboo moisture content should be standardized to 12% so that the determination of the linear mass and density values is also adjusted. Density value in this study is in accordance with the research of Liese and Tang [26], which is 400 to 900 kg/m 3 . Sa et al. [37] reported that density can be used to determine flexural strength and stiffness of the raw bamboo culm with reasonable confidence, while several researchers [5,6,38,39] reported that their correlation was weak. Bamboo density is influenced by the volume of the vascular bundles fraction [40][41][42]. The outer layers of bamboo culms have better stiffness and strength properties [43], because the vascular bundle distribution is denser on the outer than on the inner layers [44,45].
Linear mass is the ratio of the weight to the length of the culms. Tali has the smallest linear mass value (qa = 0.86 kg/m, q12 = 0.82 kg/m) because its culm is the lightest among others. In contrast, betung has the heaviest culm, so its linear mass value is the highest (qa = 2.89 kg/m, q12 = 2.72 kg/m). Linear mass is a good predictor for estimating maximum flexural moment (Mmax), flexural stiffness (EI) [5,6,9], and ultimate load (Fu) [1][2][3][4] because of their strong correlation. Furthermore, estimating the mechanical properties using linear mass provides an advantage, given the tools required and the simple process of measuring it [9].

Flexural resistance
Strength of material is characterized by an ultimate stress (σu) at which failure occurs. Flexural strength, defined by maximum fiber stress in bending just before its failure, is indicated by its modulus of rupture (SR) value. The SR is calculated as maximum bending moment at failure, divided by the section modulus. The modulus of rupture is an accepted criterion of strength, although it is not an actual stress because the calculation formula is only applying to within the elastic range, whereas failure occurs beyond the elastic range. Two points loading bending test produces modulus of rupture (SR) and maximum moment carrying-capacity (Mmax). According to Table 2, the average SR of five species bamboo tested for bending at two points loading was 40.05 to 99.74 MPa, with SR of andong is the lowest and SR of betung is the highest. The mean SR of the bamboo culms in this experiment is greater than that of fast-growing softwood and Pinus merkusii plantation wood [46], Persian silk wood [47], but lower than SR of G. scortechinii [48], LVL and PSL made from softwood [49,50]. The SR and Mmax of a bamboo culm in this study was calculated if the specimen failure was in the area of maximum moment, which was between the two test load points, and the results is summarized in Table 2.

Characteristic value of ungraded bamboo.
The SR values of bamboo in this study are varied. The variation in strength is generally caused by the density and defects in the bamboo. The distribution of bamboo strength and capacity was evaluated using the Weibull distribution following ASTM D5457:2004 [22]. The Weibull distribution is the smallest extreme value distribution, and is generally used for materials that have brittle failure properties, and have only positive values [51]. R0.05 and Rk indicate the safety limits that can be reliably used for bamboo structural design analysis. Table 3 shows that the structural material quality of betung, hitam, and tali are better than ampel and andong because their modulus of rupture's (SR) fifth percentile value (R0.05) and characteristics value (Rk) are much greater than those of the later. Their R0.05 and Rk values are higher than softwood in the Douglas-Fir-Larch group [52] and structural timber from hardwood and softwood from natural forest and plantation forest [46]. As natural material, round bamboo culm has higher variability than the engineered bamboo, thus the round bamboo's R0. 05 and Rk values in this study are lower than laminated bamboo esterilla sheets (LBES) from ater bamboo [53].  Table 4. Density (ρa and ρ12) was moderately correlated with SR for overall specimens. Within species, the coefficient of correlation between density at 12% moisture content (ρ12) and SR of hitam bamboo are moderate (r=0.564), the ρ12 of betung and tali are strongly correlated to SR (r = 0.79 and 0.75), but those of ampel and andong are weakly correlated (r = 0.15 and 0.11). Similarly, Uribe and Durán [54] reported a moderate correlation between the density and SR relationship of guadua bamboo. Meanwhile, Trujillo et al. [9] found a weak correlation between guadua's density and bending strength, whereas Bahtiar et al. [3] also reported that the relationship between density and compressive strength of three sympodial was weak. Correlation between density and SR of moso (Phyllostachys pubescens), guadua (Guadua angustifolia), Tre gai (Bambusa stenostachya) [41,42], Ampel, Andong, Betung, Hitam and Tali are positive. Density proportionally affects the strength properties with different correlation values for each bamboo species. Density generally mediocrity correlates to biomaterial's strength e.g. timber [46] and round bamboo [5,6,9,39].

Indicating predictors determination for structural grading. The coefficient of correlation (r) between indicating-predictor (IP) and flexural-resistance grade-determining-property (GDP) are summarized in
Furthermore, for all species, Mmax correlates strongly with q, qD and qD 2 and has a weak correlation with density. Similar phenomenons were also found within species of bamboo. Mmax strongly correlates with q, qD and qD 2 within species of Betung, Hitam, and Tali and those within species of Ampel and Andong were moderately correlated. Overall, the correlation coefficient between qD and Mmax was the strongest (0.972) among others, much stronger than the correlation value between ρ and SR. This result supports the previous studies findings [4][5][6]8,9], which state that the capacity grading is better for round bamboo structural member than the strength grading.

Structural grading.
Allowable stress (σ') or reference load-carrying capacity (F') is used to determine the minimum dimension of materials used for reliable construction. In bamboo construction, the round culms' geometry is given in non-unison, thus the structural analysis is better approached by capacity-based design rather than strength-based design. The capacity-based design was firstly studied for reinforced-concrete structures [55], and currently applied for wooden structures [56] to increase the robustness and reliability of a building structure. In capacity-based design, the member's allowable load and moment-resisting capacity (F' and M') play more significant role than the material's allowable stress (σ'). Strength grading determines the allowable stress of a material, while capacity grading determines the reference load-carrying capacity of a member. The dummy variables regression analysis attempt to fit the flexural resistance's IP and GDP relationship ( Table 5). The IP for flexural strength is density (ρ), and the IP for flexural capacity grading is combination of linear mass and diameter (qD). Although the coefficient of determinations (R 2 ) were high (0.60-0.91), the parallel or coinciding regression lines were not found. All linear curves between the corresponding IP and GDP of a species are statistically nonparallel and non-coincided. Each species has different density-flexural strength (ρ-SR) relationship. The linier mass and diameter combination to the maximum moment-resisting capacity (qD-Mmax) relationships are also different between species. Therefore, the concept of grading bamboo regardless to species cannot be reliably applied in this study. Each species requires different specific linear equations. The structural grades should be developed for each bamboo species, with each species having its respective mean value (μ), R0.05, and Rk values. Similar with our previous reports [3], IP at 12% moisture content (ρ12 and q12D) resulted linear regressions with slightly higher values of coefficient of determination (R 2 ) and adjusted coefficient of determination (Adj-R 2 ), and the lower standard error (SE) than those of IP at airdry condition (ρa and qaD). Therefore, it is worthy to convert the linear mass and density measurement from air-dry condition to the standardized 12% moisture content condition. ISO 19624:2018 [10] also suggested to standardize the density and linear mass into 12% moisture content. Structural grading produces a different number of classes for each species if the range of each class is fix. Narrow class intervals result in efficient classification because the characteristic values of each bamboo culm justiably close to their approximate values and provide safe and reliable values [5]. Structural grading based of the flexural resistance of five species of bamboo were developed in this study for strength grading (Figure 5a) and capacity grading (Figure 5b).
In strength-based design, structural designers need reference strength value for conducting structural analysis. The strength grading is developed to estimate the characteristic strength value of round bamboo culm by measuring its indicating predictor (IP). The strength grading in Fig. 5a estimates the mean value (μ), the five percent exclusion limit (R0.05), and the characteristics value of modulus of rupture (SR) of five bamboo species using the density (ρ) as the indicating predictor. Capacity grading provides the reference load-carrying capacity or moment-resisting capacity. Using linear mass and diameter combination (qD) as indicating predictor, capacity grading in Fig.  5b estimates the μ, R0.05, and Rk of maximum moment resisting capacity (Mmax) in bending of a round bamboo culm. As seen on Figure 5a and 5b, each species' regression lines are non-parallel and non-coincided.

Flexural stiffness
The safety of building construction is usually characterized by the maximum load the structure can safely resist without failure. However, in broader perspective, building's failure implies that collapse has occurred, or the deformation has reached an excessively large value. Reference resistances (allowable stress and load-carrying capacity) are useful to consider the maximum load failure, while stiffnesses (modulus of elasticity and bending stiffness) are useful to predict the deformation. The average value (μ)of modulus elasticity (E) and stiffness (EI) are usually used in serviceability limit state design, while the near minimum value (R0.05) and characteristics value (Rk) of E and EI are suitable in safety limit state design. This experiment measured the flexural stiffness including apparent stiffness (EIapp) and true stiffness (EItrue). In addition, the apparent and true modulus of elasticity (Eapp and Etrue) were also calculated. The flexural stiffness was available for three bamboo species. The highest modulus of elasticity (E) was observed in Betung, while the lowest in Andong. Likewise, for culm stiffness (EI), because it is a function of E and I (moment of inertia). If compared with several studies, the modulus of elasticity of Andong, Betung and Tali was higher than B. vulgaris var striata [57], Dendrocalamus strictus [58] and Guadua angustifolia [59], and lower than of M. baccifera [60] and Accacia mangium [46]. According to Javadian et al. [61], modulus of elasticity is not affected by the culm height. EI is fundamental to the design of any element subject to flexure. Its value shows the amount of deflection that occurs. The lower the EI value, the higher the deflection.  Table 7. Moreover, the fifth percentile limit (R0.05) and characteristic value (Rk) were calculated. R0.05 of Eapp for andong is higher than betung and tali, while R0.05 of Etrue of tali is the highest compare with two other species.  (Table 8), similar with the reports of Trujillo et al. [9], Nurmadina et al. [5], and Nugroho et al. [6]. Since their positive correlation value, the E value proportionally increase with the increasing ρ. Dixon et al. and Sá et al. [37,42] reported that the correlation between density and flexural properties varied between bamboo species. Similar with wood [46,47,62], the correlation between ρ and SR is stronger than the correlation between ρ and E. Correlation coefficient between beam stiffness (EI) and combination of linear mass and square diameter (qD 2 ) are generally stronger than that of between modulus of elasticity (E) and density (ρ). The strongest correlation coefficient was found between EIapp and q12D 2 . Similar with this finding, Nurmadina et al. [5] reported that EI and q12D 2 of Tali resulted the strongest correlation (r = 0.915-0.980).

Structural grading regardless of species.
The dummy regression analysis for structural grading based on the flexural stiffness are summarized in Table 9. The linear lines generated on structural classification based on flexural stiffness are non-parallel and non-coincided for ρ vs Eapp (Figure 6a), and q vs EIapp, while the other linear lines were parallel but non-coincided (i.e. Figure 6a, 7a, and 7b). The non-parallel and non-coincided regression lines indicate that the structural grading of flexural stiffness should be conducted for each specific species, while the parallel but non-coincided linear curves show that the structural grading can be developed for average of all species and a constant can be added to consider the effect of each bamboo species. =-9139+23317q12 0.740 0.733 44340 np, nc qaD 2 EIapp =19249+2018947qaD 2 =71611+2018947qaD 2 =2343+2018947qaD 2 0.739 0.735 44172 p, nc q12D 2 EIapp =17953+2179584q12D 2 =70316+2179584q12D 2 =2087+2179584q12D 2 0.743 0.739 43858 p, nc qa EItrue =-30818+33814qa =7673+33814qa =-21919+33814qa 0.577 0.570 41828 p, nc q12 EItrue =-31597+35679q12 =8338+35679q12 =-22214+35679q12 0.576 0.568 41912 p, nc qaD 2 EItrue =5929+1441051qaD 2 =40360+1441051qaD 2 =1637+1441051qaD 2 0.596 0.589 40878 p, nc q12D 2 EItrue =5199+1544288q12D 2 =39919+1544288q12D 2 =1496+1544288q12D 2 0.597 0.590 40834 p, nc Note: p=parallel; np=non-parallel; c=coincided; nc=non-coincided Similar those of flexural resistance, the structural grading of flexural stiffness round bamboo culm member capacity resulted more reliable value than the structural grading of the material's modulus of elasticity because of their high values of coefficient of determination (R 2 ) and adjusted coefficient of determination (Adj-R 2 ). Therefore, authors recommend applying the capacity-  15 based design rather than strength-based design to conduct structural analysis for a building construction using round bamboo culm. The structural grading based on its modulus of elasticity are sketched in Figure 6.  This study resulted the non-coincided linear regression line, therefore cross-species structural grading is not reliable. Structural grading of round bamboo culms should consider the species identification. Bamboo identification based on its morphological characteristics [45,63] are considered more conventional and time consuming, and several alternative methods including