Bamboo is a renewable natural building material with good mechanical properties. However, due to the heterogeneity and anisotropy of bamboo stalk, a large amount of material performance testing costs are required in engineering applications. In this work, longitudinal compression, bending, longitudinal shear, longitudinal tensile, transverse compression and transverse tensile tests of bamboo materials are conducted, considering the influence of the bamboo nodes. The mechanical properties of the whole bamboo stalk with the wall thickness and outer circumference are explored. Through univariate and multiple regression analysis, the relationship between mechanical properties and wall thickness and perimeter is fitted, and the conversion parameters between different mechanical properties are derived. The research results show that the transverse compressive strength of nodal specimen, and transverse tensile strength of nodal and inter-node specimens increase with the increase of wall thickness and outer circumference, but other mechanical properties decrease with the increase of wall thickness and outer circumference. The prediction formula and conversion parameters of bamboo mechanical properties proposed in this research have high applicability and accuracy. Moreover, this research can provide references for the evaluation of bamboo performance and saving test costs.
Bamboo is a natural, renewable, fast-growing green building material with wide distribution and excellent mechanical properties [1–6]. China is the center of the distribution of bamboo resources in the world, and bamboo is the most commonly used species in structure and has been applied in engineering [7–9]. A clear understanding of the mechanical properties is crucial to the engineering application of structural bamboo. It is also important for steam softening and bamboo flattening technology [10]. Due to the inhomogeneous and anisotropic characteristics of bamboo, the mechanical properties of bamboo with different sizes, directions and heights are not the same, which leads to a large amount of time and cost of bamboo performance test in engineering application.
In order to explore the correlation between bamboo properties and predict the mechanical properties, experiments were carried out to study the correlation between the physical and mechanical properties of bamboo and relevant results were obtained. Sá Ribeiro et al. [11] carried out a bending test of bamboo stalks and obtained a model for predicting bending strength through bending elastic modulus and predicting the elastic modulus and bending strength through the density. Ren et al. [12] and Kumar et al. [13] studied the relationship between the compressive strength, bending strength, tensile strength, and density of bamboo along the grain, and the results showed that the mechanical properties of bamboo have a correlational relationship with density. Dixon et al. [14] studied the relationship between the axial compressive properties of moso bamboo and the density, and the results showed that a linear correlation existed between them. At present, there are few literatures on the prediction of the mechanical properties of bamboo, and some of them are mainly based on a small number of samples to study the tensile, compressive and bending performance indicators along the grain. There is still a lack of research on the relationship between the mechanical properties of moso bamboo materials and growth parameters, conversion model between different mechanical properties of bamboo has not been put forward.
In order to systematically study the mechanical properties of bamboo, predict the mechanical properties through growth parameters, and facilitate the conversion between mechanical properties, this paper mainly carried out the following works on the bamboo materials produced in China: (1) considering the influence of bamboo nodes, a system was developed on moso bamboo longitudinal compression, bending resistance, longitudinal shear, longitudinal tensile, transverse compression, and transverse tensile performance test; (2) the relationship between the mechanical properties of moso bamboo and wall thickness and perimeter was fitted by univariate and multiple regression methods, and the prediction formula was given; (3) the conversion parameters between the various mechanical properties of moso bamboo materials are derived, proposed and verified. In addition, through the prediction formula and conversion method proposed in this paper, the mechanical properties of bamboo can be predicted by using simple size measuring tools.
Materials and MethodsBamboo Selection and Mechanical Performance Test
The moso bamboo materials used in this research is obtained from Chenzhou, Hunan, China. In a bamboo forest, 160 straight bamboos with the age of 3–4 years, diameters of around 100 mm, and the height of 6 m were randomly collected in December (Fig. 1a), from which 25 samples were selected for mechanical properties tests. The cut bamboos were transported to the test site and stacked in the shading shed. The location of the stacked bamboos was ventilated and irritable to avoid mildew.
Schematic diagram of material selection and loading
As shown in the Fig. 1b of bamboo structure, t and C are the wall thickness and outer circumference of the bamboo, respectively. The preparation of each specimen is under full consideration of factors such as bamboo nodes and height, and the sampling is based on the principle of uniform distribution of the whole bamboo stalk along the height.
Refer to the standard JG/T199-2007 [15] and ISO 22157-1-2019 [16], six types of specimens of longitudinal compression (UC), bending (B), longitudinal shear (US), longitudinal tensile (UT), transverse compression (CC) and transverse tensile (CT) were made for the investigation of mechanical properties. The ratio of length to diameter of the UC and US specimens is 1, the size of the B specimen is 220 mm × 15 mm × t mm, the size of the UT specimen is 330 mm × 15 mm × t mm, the size of the CC specimen is 15 mm × 15 mm × t mm, and the length of CT specimen is 100 mm.
The mechanical performance tests was carried out according to the standards [15,16]. Universal testing machines were used to load various specimens for mechanical properties as shown in Fig. 1c. During the loading, the UC, US, and UT test loading rate is 0.01 mm/s, the B test loading rate is 150 N/mm2 per minute, the CC test loading rate is 20 N/mm2 per minute, and the CT test loading rate is 0.005 mm/s. The formula of the strength and elastic modulus of the specimen is as follows:
fW=PmaxA
EW=20ΔPAΔl
MORW=150Pmaxtb2
MOEW=1920000ΔP8δmtb3
where, fW is the strength of UC, US, UT, CC and CT specimens with the moisture content W (MPa); EW is the elastic modulus along the grain with the moisture content W (MPa); MORW is the bending strength with the moisture content W (MPa); MOEW is the flexural modulus of elasticity with the moisture content W (MPa); Pmax is the failure load (N); A is the surface area (mm2); t is the thickness of the specimen (mm); b is the specimen height (mm); ∆P is the difference between the upper and lower limit loads (N); ∆l is the difference between the deformation values of the specimen under the upper and lower limit loads (mm); δm is the pure bending deflection value of the specimen under the action of ∆P (mm).
The Adjustment of Moisture Content
After the failure of specimens, a test specimen with a mass of not less than 1.5 g near the damage zone was collected immediately for the moisture content test. The moisture content is calculated according to formula (5). As the moisture content has a significant impact on the mechanical properties of bamboo [17], in this study, the value of the mechanical properties was uniformly adjusted to the value under the standard moisture content (12%). The adjustment formula (6) is shown in equation [15].
W=m1−m0m0×100
M12=KWMW
KW=1a+becw
where, W is the air-dry moisture content (%); m1 and m0 are the air-dry and full-dry mass (g), respectively; M12 is the strength or elastic modulus of the specimen under the standard moisture content (12%); MW is the strength or elastic modulus of the specimen when the moisture content is W; KW is the moisture content correction coefficient, which is related to the specific mechanical properties and moisture content. Parameter a, b and c refer to Standard [15].
Results and DiscussionStatistical Analysis of Characteristic Values
Statistics of various mechanical properties of bamboo under standard moisture content (12%) are shown in the box diagram Fig. 2. Excluding the outliers in the box chart, the results are obtained and shown in Tab. 1. It can be seen from the results that the mechanical properties of bamboo show significant anisotropy, and the longitudinal tensile, longitudinal compressive and bending properties are particularly excellent. The longitudinal tensile and longitudinal compressive strengths are significantly greater than the transverse tensile and transverse compressive strengths. The longitudinal tensile strength is slightly greater than the bending strength. The longitudinal tensile and bending strengths are obviously greater than the longitudinal compressive strength. The transverse compressive strength is obviously greater than the transverse tensile strength. Meanwhile, the bamboo nodes have a certain influence on the value of various mechanical properties, especially the mechanical properties in the transverse direction.
Statistical results of characteristic values of mechanical properties
Mechanical performance index
Quantity
Mean
Standard deviation
Coefficient of variation
UCSN
74
59.790 MPa
4.129 MPa
0.069
UCSI
231
57.196 MPa
4.682 MPa
0.082
UCEN
74
14.498 GPa
1.165 GPa
0.080
UCEI
231
13.577 GPa
1.179 GPa
0.087
MORN
75
130.658 MPa
6.649 MPa
0.046
MORI
80
133.129 MPa
7.191 MPa
0.054
MOEN
75
17.380 GPa
0.804 GPa
0.046
MOEI
80
17.727 GPa
1.365 GPa
0.077
USSN
61
15.908 MPa
1.621 MPa
0.109
USSI
144
15.921 MPa
1.095 MPa
0.069
UTSN
167
140.064 MPa
12.280 MPa
0.088
UTSI
147
149.174 MPa 9.40926
9.409 MPa
0.063
UTEN
167
16.548 GPa
1.154 GPa
0.070
UTEI
158
16.321 GPa
1.182 GPa
0.072
CCSN
77
37.317 MPa
4.646 MPa
0.125
CCSI
100
27.928 MPa
1.370 MPa
0.049
CTSN
47
6.333 MPa
0.489 MPa
0.077
CTSI
73
3.767 MPa
0.517 MPa
0.137
Note: UCS, UCE, MOR, MOE, USS, UTS, UTE, CCS, and CTS respectively represent the longitudinal compressive strength, the longitudinal compressive elastic modulus, the bending strength, the bending elastic modulus, the longitudinal shear strength, longitudinal tensile strength, longitudinal tensile elastic modulus, transverse compressive strength, and transverse tensile strength. The nodes and inter-nodes are indicated by the subscripts “N” and “I” respectively, and the rests are the same.
The Relationship between Growth Parameters
Based on the least-squares method, considering the differences between the nodes and the inter-nodes, the linear function, exponential function, and power function are used to fit t and C to obtain the fitting curve as shown in Fig. 3. The curve and relationship in the figure are the best fitting curves with its relational expression. The fitting relational expressions are shown in Tab. 2. The coefficient of determination R2 is used to evaluate the fitting effect, and the results show that t and C have a strong correlation, and from the relationship in Tab. 2, t and C can be converted.
Fitting curve between <italic>t</italic> and <italic>C</italic>: (a) <italic>C-t</italic>; (b) <italic>t-C</italic>
The fitting relationship between <italic>t</italic> and <italic>C</italic>
Linear
Exponential
Power
Relational formula
R2
Relational formula
R2
Relational formula
R2
CN-tN
CN=17.95tN+112.2
0.524
CN=147.44e0.0677tN
0.510
CN=75.027tN0.589
0.422
CI-tI
CI=23.324tI+73.228
0.650
CI=119.37e0.0941tI
0.472
CI=50.17tI0.7889
0.505
tN-CN
tN=0.0292CN+0.791
0.524
tN=3.404e0.0034CN
0.530
tN=0.0616CN0.883
0.520
tI-CI
tI=0.0279CI+0.798
0.650
tI=3.199e0.0035CI
0.654
tI=0.227CI0.641
0.505
The Relationship between Mechanical Properties and Wall Thickness
By equating the UCS, UCE, MOR, MOE, USS, UTS, UTE, CCS and CTS of bamboo materials to t, respectively, the fitting curve shown in Fig. 4 and the fitting relationship are obtained and shown in Tab. 3. The results show that the R2 values fitted by the three functions are relatively close, and the best fitting functions under different fitting materials are different. The longitudinal mechanical properties, the bending resistance, and the CCS of the inter-node specimens decrease with the increase of t. The CCS of node specimen and CTS of the node & inter-node specimens increase with the increase of t. The result clearly shows that bamboo joints have a significant effect on CCS and CTS.
The fitting curve of mechanical properties and <italic>t</italic>: (a) <italic>UCS</italic>; (b) <italic>UCE</italic>; (c) <italic>MOR</italic>; (d) <italic>MOE</italic>; (e) <italic>USS</italic>; (f) <italic>UTS</italic>; (g) <italic>UTE</italic>; (h) <italic>CCS</italic>; (i) <italic>CTS</italic>
The fitting relationship between mechanical properties and <italic>t</italic>
Linear
Exponential
Power
Relational formula
R2
Relational formula
R2
Relational formula
R2
UCSN-t
UCSN=−1.587t+72.583
0.421
UCSN=73.968e−0.027t
0.428
UCSN=99.023t−0.235
0.422
UCSI-t
UCSI=−1.544t+70.339
0.462
UCSI=71.807e−0.027t
0.464
UCSI=92.356t−0.227
0.466
UCEN-t
UCEN=−0.722t+21.092
0.560
UCEN=22.545e−0.049t
0.572
UCEN=36.813t−0.426
0.588
UCEI-t
UCEI=−0.663t+19.006
0.650
UCEI=20.285e−0.05t
0.663
UCEI=32.112t−0.415
0.665
MORN-t
MORN=−2.898t+155.59
0.394
MORN=158.16e−0.022t
0.401
MORN=205.03t−0.211
0.422
MORI-t
MORI=−3.146t+159.99
0.437
MORI=162.77e−0.024t
0.439
MORI=209.74t−0.214
0.462
MOEN-t
MOEN=−0.262t+19.633
0.220
MOEN=19.78e−0.015t
0.224
MOEN=23.613t−0.144
0.237
MOEI-t
MORI=−0.439t+21.476
0.227
MOEI=21.829e−0.025t
0.224
MOEI=28.651t−0.227
0.244
USSN-t
USSN=−0.568t+20.311
0.432
USSN=21.041e−0.036t
0.434
USSN=28.869t−0.294
0.432
USSI-t
USSI=−0.404t+18.934
0.397
USSI=19.296e−0.026t
0.405
USSI=24.505t−0.217
0.408
UTSN-t
UTSN=−3.329t+168.26
0.269
UTSN=171.03e−0.024t
0.268
UTSN=215.16t−0.204
0.270
UTSI-t
UTSI=−3.762t+179.28
0.220
UTSI=182.99e−0.026t
0.223
UTSI=230.65t−0.212
0.217
UTEN-t
UTEN=−0.452t+20.312
0.215
UTEN=20.762e−0.028t
0.214
UTEN=27.056t−0.235
0.220
UTEI-t
UTEI=−0.371t+19.332
0.219
UTEI=19.634e−0.023t
0.222
UTEI=24.147t−0.189
0.217
CCSN-t
CCSN=2.015t+17.806
0.311
CCSN=21.683e0.0552t
0.304
CCSN=11.556t0.515
0.312
CCSI-t
CCSI=−0.347t+30.675
0.152
CCSI=30.462e−0.013t
0.190
CCSI=34.305t−0.106
0.198
CTSN-t
CTSN=0.435t+2.5
0.182
CTSN=3.218e0.0729t
0.190
CTSN=1.502t0.651
0172
CTSI-t
CTSI=0.161t+2.46
0.230
CTSI=2.572e0.0443t
0.217
CTSI=1.821t0.349
0.177
The relationship between the mechanical properties of bamboo and t shows the above rules and is related to the structure of bamboo. Bamboo is mainly composed of vascular bundles that play a bearing role and basic tissues that connect and transfer loads [18]. With the increase of t, that is, with the decrease of bamboo height h, the density of bamboo vascular bundles gradually decreases. Because the vascular bundles play a decisive role in the stress along the grain direction, the vascular bundles against the growth direction of bamboo stalk are not orderly arranged and the photosynthesis is weaker, which makes the mechanical properties of bamboo along the grain direction decrease with the increase of t. The vascular bundle also plays a major role in bending and transverse compression, so the MOR and CCS of the inter-node specimens gradually decrease with the increase of t. However, due to the polishing treatment of node during the production of CC specimens, the proportion of polished vascular bundles decreases with the increase of t. Thus, the CCS of the node specimens gradually increase as t increases. As the basic tissue plays a major role in the transverse tension, the proportion of basic tissue increases with the increase of t, so CTS and t are positively correlated.
The Relationship between Mechanical Properties and the Outer Circumference
The relationship between the mechanical properties of bamboo and C, and the relationship between the mechanical properties of bamboo and t are similar. The fitting results are shown in Fig. 5 and Tab. 4. The mechanical properties along the grain and the CCS of the inter-node specimens decrease with the increase of C, while the CCS of node specimen and CTS of the node & inter-node specimens increase with the increase of C. Obviously, the bamboo joints have a significant effect on the CCS and CTS specimens; and the R2 value and the best fitting function of the same mechanical properties obtained by fitting t and C are not the same.
The fitting curve of mechanical properties and <italic>C</italic>: (a) <italic>UCS</italic>; (b) <italic>UCE</italic>; (c) <italic>MOR</italic>; (d) <italic>MOE</italic>; (e) <italic>USS</italic>; (f) <italic>UTS</italic>; (g) <italic>UTE</italic>; (h) <italic>CCS</italic>; (i) <italic>CTS</italic>
The fitting relationship between mechanical properties and <italic>C</italic>
Linear
Exponential
Power
Relational formula
R2
Relational formula
R2
Relational formula
R2
UCSN-C
UCSN=−0.0649C+77.191
0.279
UCSN=80.031e−0.001C
0.282
UCSN=309.31t−0.295
0.281
UCSI-C
UCSI=−0.053C+71.94
0.308
UCSI=73.744e−0.001C
0.305
UCSI=226.24C−0.245
0.307
UCEN-C
UCEN=−0.0257C+22.546
0.524
UCEN=24.789e−0.002C
0.519
UCEN=251.19C−0.504
0.522
UCEI-C
UCEI=−0.0249C+20.293
0.616
UCEI=22.264e−0.002C
0.609
UCEI=207.35C−0.489
0.604
MORN-C
MORN=−0.144C+173.23
0.490
MORN=180.73e−0.001C
0.492
MORN=792.23C−0.317
0.486
MORI-C
MORI=−0.171C+183.22
0.557
MORI=193.46e−0.001C
0.554
MORI=1050C−0.364
0.550
MOEN-C
MOEN=−0.0119C+20.889
0.228
MOEN=21.233e−0.001C
0.228
MOEN=53.449C−0.198
0.229
MOEI-C
MOEI=−0.0252C+25.116
0.323
MOEI=26.744e−0.001C
0.317
MOEI=174.76C−0.404
0.318
USSN-C
USSN=−0.0236C+22.087
0.566
USSN=23.506e−0.001C
0.569
USSN=137.91C−0.389
0.556
USSI-C
USSI=−0.0183C+20.665
0.481
USSI=21.544e−0.01C
0.484
USSI=92.081C−0.317
0.481
UTSN-C
UTSN=−0.156C+179.84
0.313
UTSN=186.08e−0.001C
0.310
UTSN=686.41C−0.288
0.315
UTSI-C
UTSI=−0.184C+196.95
0.300
UTSI=204.99e−0.001C
0.298
UTSI=857.39C−0.316
0.301
UTEN-C
UTEN=−0.0175C+20.807
0.273
UTEN=21.493e−0.001C
0.273
UTEN=73.683C−0.273
0.268
UTEI-C
UTEI=−0.0177C+20.861
0.283
UTEI=21.514e−0.001C
0.279
UTEI=76.173C−0.279
0.282
CCSN-C
CCSN=0.0803C+15.37
0.339
CCSN=20.025e0.0022C
0.339
CCSN=1.365C0.589
0.342
CCSI-C
CCSI=−0.0129C+31.131
0.120
CCSI=31.307e−5×10−4C
0.119
CCSI=55.433C−0.125
0.124
CTSN-C
CTSN=0.0056C+4.866
0.218
CTSN=4.716e0.001C
0.221
CTSN=1.321C0.277
0.220
CTSI-C
CTSI=0.0048C+2.598
0.195
CTSI=2.684e0.0013C
0.204
CTSI=1.107C0.225
0.211
Multiple Regression Analysis of Mechanical Properties, Wall Thickness, and the Outer Circumference
To compare the effects of multiple regression fitting and univariate fitting, a binary linear function was used to fit the mechanical properties of bamboo with t and C, and the results were obtained and presented in Fig. 6 and Tab. 5. The comparison of R2 of the best-fitting relations in Tabs. 3 and 4 and the results in Tab. 5 shows that using t to predict UCS (including UCSN and UCSI), UCEI, MOEN, and CCSI is better, and C is used to predict MOR, MOEI, USSN, UTS, UTEI, CCSN, and CTSN, which also has better prediction effects. The use of t and C bivariate has a better fitting effect for the prediction of UCEN, USSI, UTEN, and CTSI. In general, the relationship between bamboo material and growth parameter plays a significant role in fitting and analysis [11,14]. Through the univariate and bivariate fitting relations of mechanical properties and growth parameters, simple size measurement tools can be used. In the absence of test conditions, the mechanical properties of bamboo can be tested efficiently and quickly. The best prediction effect can be obtained by using the relationship formula with the highest R2 value in the univariate and bivariate fitting.
The fitting relationship between mechanical properties and <italic>t</italic>, <italic>C</italic>
Mechanical performance index
Relational formula
R2
UCSN
UCSN = 77.81 − 0.658t − 0.0482C
0.373
UCSI
UCSI = 72.57 − 1.031t − 0.0239C
0.394
UCEN
UCEN = 22.58 − 0.467t − 0.0134C
0.671
UCEI
UCEI = 19.32 − 0.379t − 0.00969C
0.636
MORN
MORN = 172 − 0.141t − 0.132C
0.371
MORI
MORI = 190.3 + 0.735t − 0.215C
0.550
MOEN
MOEN = 22.75 + 0.133t − 0.0214C
0.203
MOEI
MOEI = 25 + 0.372t − 0.0354C
0.247
USSN
USSN = 21.23 − 0.102t − 0.0174C
0.465
USSI
USSI = 20.5 − 0.252t − 0.00101C
0.530
UTSN
UTSN = 185.7 − 0.445t − 0.161C
0.311
UTSI
UTSI = 181.7 − 0.944t − 0.0971C
0.198
UTEN
UTEN = 21.94 − 0.183t − 0.0151C
0.375
UTEI
UTEI = 20.69 − 0.0351t − 0.0181C
0.267
CCSN
CCSN = 19.93 − 0.409t − 0.081C
0.305
CCSI
CCSI = 31.47 − 0.00534t − 0.0133C
0.117
CTSN
CTSN = 1.929 − 0.335t − 0.00525C
0.210
CTSI
CTSI = 2.44 − 0.0842t − 0.00262C
0.454
The Relationship between the Mechanical Properties of Nodes and Inter-Nodes
Based on the fitting results between the mechanical properties and t & C in this research, a method is proposed to derive the relationship between the mechanical properties of bamboo through the linear fitting relationship between the mechanical properties and the growth parameters. The average value of the determination coefficient R2 of the linear fitting of various mechanical properties of bamboo with t (Tab. 3) is 0.333, and the average value of the determination coefficient R2 for linear fitting with C (Tab. 4) is 0.356. Among the 18 linear fitting relationships between mechanical properties and growth parameters, the larger values of R2 of t and C are 6 and 12, respectively. Generally, the linear relationship between mechanical properties and C is used to derive the relationship between the mechanical properties of bamboo, and the operability of measuring C is also stronger in practical engineering. Based on the linear relationship between the mechanical properties of the node and inter-node specimens and C, the relationship between the mechanical properties of the node and inter-node specimens at the same position of the bamboo is deduced and shown in Tab. 6.
The relationship between the mechanical properties of bamboo nodes and internodes
Mechanical performance index
Node-internode
Internode-node
UCS
UCSN = 1.225UCSI − 10.902
UCSI = 0.817UCSN + 8.903
UCE
UCEN = 1.032UCEI + 1.601
UCEI = 0.969UCEN − 1.551
MOR
MORN = 0.842UCEI + 18.939
MORI = 1.188UCEN − 22.491
MOE
MOEN = 0.472UCEI + 9.008
MOEI = 2.118UCEN − 19.12
USS
USSN = 1.29USSI − 4.563
USSI = 0.775USSN + 3.538
UTS
UTSN = 0.848UTSI + 12.861
UTSI = 1.179UTSN − 15.169
UTE
UTEN = 0.898UTEI + 0.182
UTEI = 1.011UTEN − 0.184
CCS
CCSN = − 6.225CCSI + 209.154
CCSI = − 0.161CCSN + 33.6
CTS
CTSN = 1.167CTSI + 1.835
CTSI = 0.857CTSN − 1.573
Conversion Parameters of Mechanical Properties
It is impossible to measure multiple mechanical properties of test specimens at the same time, and the relationship between the mechanical properties plays a vital role in the establishment of the mechanical property evaluation system of bamboo. The establishment of the relationship between the mechanical properties can greatly reduce the consumption and testing of materials cost. To solve this problem, a linear relationship between mechanical properties and C is used to derive the relationship between multiply mechanical properties. Eq. (7) is the conversion formula between mechanical properties.
M2=ηM1+θ
where, M1 and M2 are mechanical performance indicators.
η and θ are defined as the conversion parameters of bamboo mechanical properties, as shown in Tabs. 7 and 8 for details. Since a large number of bamboo stalk materials are used in the application of the original bamboo structure, predicting the mechanical properties of a batch of bamboo stalks through a certain mechanical property can save a lot of materials, time and test costs. Also, the conversion parameters can provide a reference for the prediction of the mechanical properties of bamboo.
Conversion parameters of mechanical properties of bamboo node specimens
Parameter
M2/M1
UCSN2
UCEN2
MORN2
MOEN2
USSN2
UTSN2
UTEN2
CCSN2
CTSN2
η
UCSN1
1
0.396
2.219
0.183
0.364
2.404
0.27
–1.237
–0.086
UCEN1
2.525
1
5.603
0.463
0.918
6.07
0.681
–3.125
–0.218
MORN1
0.451
0.178
1
0.083
0.164
1.083
0.122
–0.558
–0.039
MOEN1
5.454
2.160
12.101
1
1.983
13.109
1.471
–6.748
–0.471
USSN1
2.75
1.089
6.102
0.504
1
6.61
0.742
–3.403
–0.237
UTSN1
0.416
0.165
0.923
0.076
0.151
1
0.112
–0.515
–0.036
UTEN1
3.709
1.469
8.229
0.68
1.349
8.914
1
–4.589
–0.32
CCSN1
–0.808
–0.32
–1.793
–0.148
–0.294
–1.943
–0.218
1
0.07
CTSN1
–11.589
–4.589
–25.714
–2.125
–4.214
–27.857
–3.125
14.339
1
θ
UCSN1
0
–8.021
1.959
6.735
–5.982
–5.704
–0.007
110.878
11.527
UCEN1
20.256
0
46.902
10.449
1.383
42.985
5.455
85.815
9.779
MORN1
–0.883
–8.371
0
6.573
–6.303
–7.826
–0.245
111.97
11.603
MOEN1
–36.733
–22.567
–79.544
0
–19.34
–93.999
–9.912
156.327
14.696
USSN1
16.452
–1.506
38.462
9.752
0
33.841
4.429
90.522
10.107
UTSN1
2.373
–7.081
7.224
7.17
–5.12
0
0.633
107.941
11.322
UTEN1
0.027
–8.011
2.018
6.74
–5.973
–5.64
0
110.844
11.524
CCSN1
89.613
27.465
200.793
23.167
26.604
209.7
24.157
0
3.794
CTSN1
133.584
44.877
298.356
31.229
42.594
315.393
36.013
–54.405
0
Conversion parameters of mechanical properties of bamboo internode specimens
Parameter
M2/M1
UCSI2
UCEI2
MORI2
MOEI2
USSI2
UTSI2
UTEI2
CCSI2
CTSI2
η
UCSI1
1
0.47
3.226
0.475
0.345
3.472
0.334
0.243
–0.091
UCEI1
2.129
1
6.867
1.012
0.735
7.39
0.711
0.518
–0.193
MORI1
0.31
0.146
1
0.147
0.107
1.076
0.104
0.075
–0.028
MOEI1
2.103
0.988
6.786
1
0.726
7.302
0.702
0.512
–0.19
USSI1
2.896
1.361
9.344
1.377
1
10.055
0.967
0.705
–0.262
UTSI1
0.288
0.135
0.929
0.137
0.099
1
0.096
0.07
–0.026
UTEI1
2.994
1.407
9.661
1.424
1.034
10.395
1
0.729
–0.271
CCSI1
4.109
1.93
13.256
1.953
1.419
14.264
1.372
1
–0.372
CTSI1
–11.042
–5.188
–35.625
–5.250
–3.813
–38.333
–3.688
–2.688
1
θ
UCSI1
0
–13.505
–48.888
–9.089
–4.175
–52.804
–3.164
13.621
9.113
UCEI1
28.746
0
43.858
4.579
5.751
46.994
6.436
20.618
6.51
MORI1
15.153
–6.386
0
–1.885
1.057
–0.199
1.896
17.309
7.741
MOEI1
19.117
–4.524
12.79
0
2.426
13.563
3.22
18.274
7.382
USSI1
12.091
–7.825
–9.879
–3.341
0
–10.829
0.874
16.564
8.018
UTSI1
15.21
–6.359
0.185
–1.858
1.077
0
1.915
17.323
7.736
UTEI1
9.475
–9.054
–18.318
–4.584
–0.903
–19.91
0
15.927
8.255
CCSI1
–55.963
–39.797
–229.447
–35.698
–23.498
–247.089
–21.854
0
14.182
CTSI1
100.626
33.77
275.774
38.756
30.57
296.54
30.441
38.113
0
Verification of Prediction Formula
In order to verify the accuracy of the proposed prediction formula, UCSI is used as an independent variable, and the measured values of the mechanical properties of bamboo in the literature [12,19–21] are compared with the predicted values obtained in Tab. 8. The comparison results are summarized in Tab. 9. It can be seen that the predicted results by the proposed method are relatively close to the measured values of experiment, indicating that the prediction formula and conversion parameters of mechanical properties of moso bamboo obtained in this research have certain applicability and accuracy, and are useful for the application of bamboo structure.
Comparison of prediction results between literature and this paper
Literature
Mechanical performance index
Measured value in literature/MPa
The predicted value of this article/MPa
Absolute error
[13]
Bottom partUCSI
69.1
–
–
Bottom part MORI
158.2
174.029
10.01%
Bottom part UTSI
185.1
187.111
1.09%
Centralpart UCSI
70.9
–
–
Centralpart MORI
170.3
179.835
5.60%
Centralpart UTSI
194.9
190.361
2.33%
Upper part UCSI
76.3
–
–
Upper part MORI
184.6
197.256
6.86%
Upper part UTSI
212.6
212.110
0.23%
[19]
UCSI
54
–
–
UCEI
11930
11875
0.46%
[20]
UCSI
59.46
–
–
MORI
132.46
142.930
7.90%
[21]
UCSI
56.4
–
–
MORI
150.96
133.058
11.86%
UTSI
154.24
143.017
7.28%
Conclusions
In this research, the mechanical performance tests of bamboo were carried out for longitudinal compression, bending, longitudinal shear, transverse compression and transverse tension. In addition, the mechanical characteristic values of bamboo nodes and inter-nodes specimens were statistically analyzed. The results show that the mechanical properties of bamboo show significant anisotropy. The longitudinal tensile and compressive strengths are obviously greater than the transverse tensile and compressive strengths, and the longitudinal tensile strength is slightly greater than the bending strength. The longitudinal tensile and bending strengths are obviously greater than the longitudinal compressive strengths, and the transverse compressive strength is obviously greater than the transverse tensile strength. However, the bamboo nodes have a certain influence on the value of various mechanical properties, especially the mechanical properties in the transverse direction.
The Linear function, Exponential function and Power function were used to fit the performance indicators and growth parameters (wall thickness and outer circumference) of bamboo. It is concluded from the results that longitudinal mechanical properties, bending, and the transverse compressive strength of inter-node specimens decrease with the increase of wall thickness and outer circumference, while transverse compressive strength of nodal specimen and transverse tensile strength of nodal and inter-node specimen increase with the increase of wall thickness and outer circumference.
There is a good correlation between the growth parameters, mechanical properties and the univariate and bivariate fitting of growth parameters. It is better to use wall thickness to predict the longitudinal compressive strength, the compressive elastic modulus of the inter-nodes, the bending elastic modulus of the nodes and the transverse compressive strength of the inter-nodes. On the other hand, it is better to use the outer circumference for the prediction of bending strength, the inter-node bending elastic modulus, node longitudinal shear strength, the inter-node longitudinal tensile strength, the node transverse compressive strength and node transverse tensile strength. The bivariate linear function of wall thickness and outer circumference is effective in predicting the longitudinal compressive elastic modulus of the node specimen, the longitudinal inter-node shear strength, the node longitudinal tensile elastic modulus and the inter-node transverse tensile strength.
Comparing the fitting effects of mechanical properties by using wall thickness and outer perimeter, the linear fitting relationship between mechanical properties and outer perimeter is used to derive the bamboo mechanical property conversion parameter, which provides a reference for the prediction of the mechanical properties of bamboo. By comparing with the relevant results in literatures, the applicability and accuracy of the prediction formula and conversion parameters proposed in this work are verified.
The work described in this paper is supported by grants from the National Key R&D Program of China “Green Ecological Wooden bamboo structure and Demonstration Application”.
Funding Statement: This research was funded by the National Key Research & Development Program (Grant No. 2017YFC0703500).
Conflicts of Interest: The authors declare that they have no conflicts of interest to report regarding the present study.
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