MechanicalPropertiesandStrengthGradingofEngineered ...ASTM D143-14 [19] Tension Parallel to grain 80 1 60 95 63 95 60 25 375 5 R444 9.5 Perpendicular to grain 80 1 63 50 13 6 25 50

Research ArticleMechanical Properties and Strength Grading of EngineeredBamboo Composites in China

Siyuan Tang 12 Aiping Zhou 1 and Jiannan Li3

1National Engineering Research Center of Biomaterials Nanjing Forestry University Nanjing China2School of Architecture and Transportation Engineering Guilin University of Electronic Technology Guilin China3School of Civil Engineering Changzhou Institute of Technology Changzhou China

Correspondence should be addressed to Siyuan Tang 404533342163com

Received 24 December 2020 Revised 1 March 2021 Accepted 29 March 2021 Published 22 April 2021

Academic Editor Giosue Boscato

Copyright copy 2021 Siyuan Tang et al is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Engineered bamboo composite (EBC) is a new high-strength anisotropic structural material which has standardized sections andless inherent variability than the natural material For safety reasons in structural applications the characteristic values ofmechanical behaviors are needed to build the design values utilized in practical application Recent research studies on EBCfocused on the mechanical properties from a single source with little research on the sampling of the manufacturers e presentwork investigates mechanical properties of two types of commercially available EBCmdashparallel strand bamboo (PSB) andlaminated veneer bamboo (LVB) e main aim of this work is to evaluate the best probability distribution model (normallognormal andWeibull) and mechanical properties for EBC in China and determine the characteristic values indicated by ASTMD2915 e mechanical properties in tensile compression and shear were evaluated using about 4300 small clear specimens fromseven manufacturers in five raw bamboo origins of China Based on the confidence band method the strength grading of EBCsubjected to compressive strength was developed with two predictors (density and MOE) By using intervals of each predictorseveral strength grades were built Each grade has the mean compressive strength 5th percentile lower value (R005) andcharacteristic value (Rk) which could be used in structural designis research contributes to the establishment of EBC standardsand is essential for further accepting these materials in structural engineering

1 Introduction

Bamboo is a sustainable and natural material It is a crucialforest resource other than timber erefore bamboo hasbeen used as a building material for thousands of years Dueto bamboorsquos circular hollow section and range of availablesizes the scope of possible structural applications for naturalround culms is limited Instead EBCs have become morepopular in academic and engineering application fields Inrecent years several forms of engineered bamboo compositehave been rapidly developed and applied [1] Figure 1 showssome examples of EBC structure

China presents an enormous potential for EBC appli-cations since Moso bamboo (the primary raw material ofEBC) resources are widespread in natural forests and arecultivated over large areas in Mainland China including

Hunan Jiangxi Hubei Zhejiang Fujian and AnhuiProvinces (see Figure 2) e EBCs are bamboo-basedcomposites designed for structural applications with spe-cific mechanical properties including parallel strandbamboo (PSB) and laminated veneer bamboo (LVB) ePSB is a composite of bamboo strand elements withbamboo fibers primarily orientated along the memberrsquoslongitudinal axis (see Figure 3) LVB is also a composite ofbamboo strand elements edge-bonded to form veneer sheetsof uniform sectional dimensions which are then face-bondedto develop finished products with bamboo fibers primarilyoriented along the longitudinal axis of the member (seeFigure 3)

e EBC shows the anisotropic behavior typical ofnatural bamboo comparable to that of fiber reinforcedcomposites [3 4] A significant number of experiments

HindawiAdvances in Civil EngineeringVolume 2021 Article ID 6666059 13 pageshttpsdoiorg10115520216666059

have been conducted to investigate the mechanical prop-erties of bamboo composites Huang [5 6] studied themechanical properties of PSB by experiments and inves-tigated stress-strain relationships and failure mechanismsin each stress state Wei [7] provided a comprehensiveresearch on the mechanical behavior and failure modes ofbamboo scrimber (PSB) and laminated bamboo (LVB) and

proposed the stress-strain models for EBC Xiao [1 8]studied the mechanical properties of glubam boards andfound that the Weibull distribution and normal distribu-tion are best fit for shear strength and the in-plane shearstrength respectively and suggested the characteristicvalues and the design values Sharma et al [9] provided acomprehensive study that compares bamboo scrimber

(a) (b) (c)

Figure 1 Examples of EBC structure

75degE 90degE 105degE 120degE 135degE

20degN

30degN

40degN

50degN

20degN

30degN

40degN

50degN

90degE 105degE 120degE

0 310 620 1240 km

Climate stationMoso bamboo absentMoso bamboo present

Figure 2 e information on the distribution of Moso bamboo in Mainland China by Shi [2]

2 Advances in Civil Engineering

laminated bamboo timber and engineered timber prod-ucts for mechanical properties Kumar et al [10] studiedthe influence of bamboo scrimber densities on the me-chanical properties and concluded that the density hassignificant influence on the mechanical properties ofbamboo scrimber ere is no sampling and statisticalresearch on the physical and mechanical properties of EBCproducts from different manufacturers which makes theformulation of standards lack data reference

e characteristic value is the representative value of amaterial property used for design e standards [11 12]define the 5th percentile value at the 75 confidence level forstructural materials as characteristic value of strength andthe determination method includes nonparametric andparametric e parametric approach calculates the char-acteristic value of strengths according to the estimatedstatistical average and standard deviation of the sample enonparametric approach is to sort the sample data fromsmall to large to determine the strength corresponding to thedata point as the characteristic value of strength ereforeit is vital to determine the characteristic values of mechanicalproperty of EBC for engineering applications and it is alsothe basis for determining its strength design value in thefuture

EBC for structural applications has to be strength gradedbefore its use For economic reasons the most importantphysical and mechanical properties (eg density modulusand strength) are the basic grading principles For bambooculm Trujillo et al [13] indicated that grading could beutilized based on physical properties and flexural stiffnessNurmadina et al [14] and Bahtiar [15 16] studied severalpotentials including Mc density and linear mass forbamboo culm both in flexural and compressive strengthgrading e grading of timber and bamboo are constantlystudied but the strength grading of EBC subject to com-pressive properties is still missed

In order to build the EBC standards and contribute to theuse of EBC for structural purposes this research aimed todetermine the probability distribution and the characteristicvalue of the mechanical properties for EBC by tests Af-terward the Indicating Properties (IPs) which were the bestfor predicting compressive strength of EBC were deter-mined e strength grading was developed by the

confidence band method for EBC based on compressiveproperties It will provide more design-relevant data forengineering applications

2 Materials and Methods

21 Materials In order to objectively reflect the mechanicalproperties of EBC in China this study randomly took EBCproducts from seven manufacturers with raw materials fromfive primary bamboo origins Different types of EBC frommanufacturers were divided into nine groups All of the EBCproducts were manufactured of Moso bamboo (Phyllos-tachys pubescens) and the material information is shown inTable 1 Each group of materials required the same batch ofproducts from the same manufacturer Test specimens wereprocessed to the specified dimensions (Table 2) and trans-ported to the laboratory

22 Sample Size e population is characterized by thesample therefore enough sample size must be adopted Inthis study the sample size is obtained based on ASTMD2915[13] On the 95 confidence level the required minimumsample size n of specimens is

n ts

αX1113874 1113875

t

αCV1113874 1113875

2 (1)

where s is the standard deviation of specimen values X is thespecimen mean value CV is the coefficient of variation (itwas assumed first as 01 for physical properties and 02 formechanical properties) α is the estimate of precision takenas 005 and t is the value of the t statistic taken as 2093(physical properties) and 2 (mechanical properties) for 095confidence level e minimum number of specimens is 18(physical properties) and 64 (mechanical properties) foreach test based on the testing standard To ensure an ade-quate test sample size the number of specimens for physicalproperties and mechanical properties is 80

23 Testing Methods e mechanical properties of testingincluded tensile compressive and shear tests in both di-rections to the grain e same method of testing was usedfor both PSB and LVB e dimensions were measured

2

3

1

(a)

1

3

2

(b)

Figure 3 Engineered bamboo composites parallel strand bamboo (a) laminated veneer bamboo (b)

Advances in Civil Engineering 3

thrice for each specimen All parameters of dimension weremeasured using a vernier caliper with an accuracy of0001mm e EBC specimens were conditioned in achamber at 65 (plusmn5) relative humidity and 20degC (plusmn2degC)temperature prior to testing for one month

Since the EBC is a new composite and no test standardhas been established the standards for timber structure andcomposite materials are referenced in studying the me-chanical properties of EBC For each group density andmoisture content were determined based on the specimensof compression in parallel to grain according to GBT 1933[17] Method for determination of the density of wood andGBT 1931 (air-dry method) [18] respectively e tests oftensile and compressive were conducted following ASTMD143 [19] Standard test methods for small clear specimensof timber e tests of shear were in accordance withprinciples of ASTM D7078 [20] Standard test method forshear properties of composite materials by V-notched railshear method e mechanical properties were measuredwith a universal testing machine using load cell of 100 kNcapacity Two strain gauges were affixed to the surface in themiddle of the specimen to measure the strains along withtwo directions namely parallel and perpendicular to graindirections respectively e data logger (TML TDS-640)automatically recorded the load and the strains during thetests e standards test methods number of specimensand test parameters used are summarized in Table 2

24 Data Analysis Statistical distributions were fitted to theexperimental data obtained by the maximum likelihoodestimates method e KolmogorovndashSmirnov [21] test wasused to verify the goodness of fit analysis Both methodswere using the software MATLABreg version R2018b In thisstudy the probability distributions were fitted with normallognormal and Weibull models e general equations forprobability density functions and cumulative distributionfunctions are calculated using equations (2)ndash(7)

x minus N(μ σ) f(x) 12π

radicσ

eminus (xminus μ)22σ2

(2)

F(x) Φx minus μσ

1113874 1113875 (3)

x minus L μln σ2ln1113872 1113873 f(x) 1

2π

radicσ lnx

eminus lnxminus μln( )

22σ2ln (4)

F(x) Φlnx minus μln

σln1113888 1113889 (5)

x minus W(k λ)f(x) k

λx

λ1113874 1113875

kminus 1e

minus (xλ)k

(6)

F(x) 1 minus eminus (xλ)k

(7)

where x is the strength μ is the mean value of the distri-bution σ is the standard deviation μln is the mean value oflogarithmic σ ln is the standard deviation value of loga-rithmic k is the shape parameter and λ is the scaleparameter

In this study the mean value of the best-fit distribution isused for the characteristic value of moduli e 5th per-centile value with 75 confidence level from test results shallbe the characteristic value for strengths According to theASTM D2915 the characteristic value of strength corre-sponding to the 5th percentile value with 75 confidencelevel for the normal lognormal and Weibull distribution ofthe strengths can be calculated as follows

fk005 μ minus KNσ

fk005 μIn minus KInσIn

fk005 X minus KWS

(8)

where μ is the mean of the normal distribution σ is thestandard deviation of the normal distribution KN is theconfidence level factor of the normal distribution μIn is the

Table 1 e raw material information of engineered bamboo composites

Group Material Origin of rawbamboo

Age of rawbamboo Resin types Manufacturer

EBC1 PSB Jiangxi Province 4 years Urea formaldehyde resin Jiangxi Feiyu Bamboo Co LTD

EBC2 PSB Hunan Province 5 years Phenol formaldehyderesin

Hunan Taohuajiang Bamboo Technology CoLTD

EBC3 PSB Fujian Province 5 years Phenol formaldehyderesin Fujiang Jinzhu Bamboo Co LTD

EBC4 PSB Zhejiang Province 3ndash5 years Phenol formaldehyderesin Guangyu Bamboo Industry Co LTD

EBC5 PSB Anhui Province 3ndash6 years Phenol formaldehyderesin Anhui Hongyu Bamboo Technology Co LTD

EBC6 LVB Jiangxi Province 5 years Urea formaldehyde resin Jiangxi Feiyu Bamboo Co LTD

EBC7 LVB Hunan Province 5 years Phenol formaldehyderesin


EBC8 LVB Fujian Province 3ndash5 years Phenol formaldehyderesin Shaowu Xingda Bamboo Co LTD

EBC9 LVB Zhejiang Province 5 years Phenol formaldehyderesin Zhejiang Shanglin Bamboo Co LTD


Table 2 Experimental methods for EBC

Standard Test method Directionn (foreachgroup)

Loading rate(mmmin) Dimensions (mm)

GBT 1933[17] Density mdash 80 mdash 25times 25times100

GBT 1931[18]

Moisturecontent mdash 80 mdash

ASTM D143-14 [19] Compression

Parallel to grain 80 15

25

25 100

Perpendicular tograin 80 15

25

25 100

ASTM D143-14 [19] Tension

Parallel to grain 80 1 60 95 63 95 60

25

375

5

95R444


63

50

13 625

R132450

ASTMD7078 -12[20]

Shear


25 1376

3013

13

5

R13

90iexclatilde

45iexclatilde

56


25 1376

3013

13

5

R13

90iexclatilde

45iexclatilde

56


mean of the lognormal distribution σIn is the standarddeviation of the lognormal distribution KIn is the confi-dence level factor of the lognormal distributionX is themean of the Weibull distribution S is the standard deviationof the Weibull distribution and KW is the confidence levelfactor of the Weibull distribution

e EBC strength grading was conducted using a con-fidence band approach as described by Bahtiar et al [16]Statistical analysis was developed using correlation andlinear regression e parameters that had a strong corre-lation with strength will be considered potential predictorsfor EBC strength grading Based on the confidence band inregression analysis class intervals are created in similarranges According to the confidence band method the 5thpercentile lower value (R005) was calculated using equation(9) en the adaptation is applied by substituting thestandard deviation (SD) value with standard error for esti-mation in regression (SE) (equation (10)) Finally thecharacteristic value for each class (Rk) was obtained withequation (11)

R005 1113954y minus t(v095) 1 +1n

+(x minus x)2

Σ(x minus x)21113888 1113889

05

Sr (9)

SE 1 +1n

+(x minus x)2

Σ(x minus x)21113888 1113889

05

Sr (10)

Rk R005 1 minusk005075SE

mn

radic1113888 1113889

05

(11)

wherem is the average of strength from the test data n is thesample size x is the mean of predictor value 1113954y is the es-timated strength when the predictor has x value Sr is thestandard error of regression SE is the standard error ofprediction at a given value of x t(v095) is the one-tailedStudentrsquos t-distribution value with v degree of freedom for95 probability and k005075 is the confidence level factorfor 75 confidence and 5 probability which is interpolatedfrom confidence level factor table in ASTM 2915 [12]

3 Results and Discussion

31 Mechanical Properties A summary of the mechanicalproperty test results according to the procedure defined instandards is presented in Table 3 e test results are as-sembled in Figure 4 which shows column plots for me-chanical properties e average value is indicated with avertical column and a vertical black whisker denotes thewidth of the standard deviation

It is shown that the moisture content of EBC ranges from53 to 918 ere is a slight difference between PSB andLVB However the air-dry density of PSB is 098ndash131 gcm3and LVB is 065ndash070 gcm3 respectively Because of dif-ferences in manufacturing processes adhesive content andelements PSB density is greater than LVB which is closer tothe density of raw bamboo

In general the mechanical behaviors of PSB and LVB arecorresponding both parallel and perpendicular to the grain

However the PSB groups are superior to that of LVB inmechanical properties except for EBC4 which has the lowestdensity (98 gcm3) of PSB is is a rare and unexpectedresult It is considered that this tendency is given by thefibers within the phenol formaldehyde resin which are notdense enough leading to more imperfections Because thetensile strength of EBC is mainly determined by the bamboofiber the tensile strength in parallel to the grain of PSB andLVB is extremely close to the tensile strength of bambooWith the exception of EBC4 the compressive strength ofPSB is in the range of 9929ndash11904MPa which is signifi-cantly higher than that of LVB in the range of5593ndash6922MPa

To compare the variability in mechanical properties thecoefficient of variations (CV) are examined to the test re-sults Lower CV values suggest a smaller expected scatteringin the corresponding variable e compressive behavior inperpendicular to the grain shows the highest variability forall mechanical properties It can be attributed to the inho-mogeneity of the formaldehyde resin layer geometry whichleads to a nonhomogeneous fiber volume fraction over thesample volumee group of EBC4 shows great variability inmost tests for mechanical properties It can be inferred thatthe density of PSB has a certain correlation with the strengthparallel to the grain Once the PSB density is less than thecritical value the mechanical properties will be significantlyreduced even lower than that of the LVB whose density issmaller than that of PSB erefore in the PSBmanufacturing process it is necessary to find and exceed thecritical density which makes the material manufacturingmore homogeneous to reduce the nonhomogeneous fibervolume fraction

32 Probability Distribution In order to characterize thestatistical distributions of mechanical properties for EBCthe test data are fitted to normal lognormal and Weibullmodels and the goodness of fit analysis is conductedFigure 5 shows the details of the best-fit distribution forthe tension strength parallel to the grain of EBC5 as anexample of the choice of distribution model H indicatesnull hypothesis and P is the probability of observing a teststatistic as extreme as or more extreme than the observedvalue under the null hypothesis D is computed from thelargest difference (in absolute value) between the observedand theoretical cumulative distribution functions in thefigure e details of the best-fit probability distributionfunctions of mechanical properties are shown in Table 4and Table 5 For most groups of EBC the normal dis-tribution best-fitted the tensile strength parallel to thegrain and shear strength perpendicular to the grain andcompressive properties the Weibull model presented thebest fit for both shear strength parallel to the grain andtensile strength perpendicular to the grain and the log-normal distribution best-fitted the tensile and shearmodulus which is inconsistent with research studies onother composite materials [22] Table 6 shows the rec-ommended best-fit distribution functions of the me-chanical properties for EBC


Table 3 Summary of experimental results and characteristic values for EBC

EBC1 EBC2 EBC3 EBC4 EBC5 EBC6 EBC7 EBC8 EBC9ρ (gcm3) 131 (004) 131 (006) 123 (006) 098 (006) 114 (005) 068 (004) 065 (004) 067 (002) 070 (005)Mcmean () 530 (004) 575 (007) 756 (006) 726 (005) 918 (006) 838 (004) 752 (003) 759 (004) 707 (006)Compression

fc0mean (MPa) 11289(008)

11904(008) 9929 (004) 6672

(011)10195(006) 5944 (007) 5593 (009) 5936 (008) 6922 (006)

fc90mean(MPa) 4615 (011) 5119 (018) 4764 (012) 2709

(019) 3554 (020) 151 (021) 1608 (012) 1524 (013) 1637 (008)

fc0k (MPa) 9766 10273 9149 5344 9024 5179 4694 5094 6150fc90k (MPa) 4615 5119 4764 1813 3554 1510 1608 1524 1637

Ec0mean (GPa) 1948 (008) 1743 (010) 1537 (005) 1252(010) 1682 (010) 1303 (007) 1045 (009) 1161 (008) 1287 (006)

Ec90mean(GPa) 404 (016) 453 (020) 388 (010) 277 (016) 344 (012) 187 (023) 187 (013) 219 (022) 201 (010)

Tension

ft0mean (MPa) 14173(024)

13060(020)

13319(013)

9991(033)

12586(020)

12771(010)

12425(024)

10371(018)

11705(019)

ft90mean(MPa) 52 (022) 729 (015) 938 (021) 252 (031) 314 (034) 430 (018) 503 (011) 545 (031) 679 (018)

ft0k (MPa) 8115 8386 10355 3989 8106 8989 7138 7005 8038ft90k (MPa) 315 559 585 117 111 284 392 237 446

Et0mean (GPa) 1911 (010) 1658 (012) 1448 (009) 1402(022) 1696 (015) 1319 (013) 1282 (022) 982 (017) 1156 (016)

Et90mean(GPa) 322 (026) 898 (026) 709 (025) 106 (022) 144 (025) 37 (024) 843 (026) 374 (025) 651 (026)

Shearfs0mean (MPa) 199 (019) 161 5 (024) 1879 (016) 901 (029) 1069 (026) 1544 (017) 1036 (028) 146 (017) 1189 (020)fs90mean(MPa) 2611 (023) 4035 (015) 3445 (012) 2077

(016) 3263 (015) 1849 (012) 2168 (017) 1787 (013) 1283 (020)

fs0k (MPa) 1277 888 1254 405 519 1075 489 969 816fs90k (MPa) 1544 2948 2728 1444 2392 1463 1517 1368 824Gs0mean (GPa) 513 (013) 422 (012) 445 (010) 217 (015) 380 (010) 262 (014) 235 (015) 295 (011) 258 (010)Gs90mean(GPa) 58 (012) 503 (015) 462 (016) 277 (017) 445 (012) 299 (013) 286 (017) 306 (015) 254 (009)

Note e coefficient of variation is shown in parentheses

EBC1 EBC2 EBC3 EBC4 EBC5 EBC6 EBC7 EBC8 EBC9

CompressionTensionShear

Strengths of EBC parallel to the grain

0

20

40

60

80

100

120

140

160

180

Stre

ngth

(MPa

)

(a)



Strengths of EBC perpendicular to the grain

0

10

20

30

40

50

60

70

Stre

ngth

(MPa

)

(b)

Figure 4 Continued


33 Strength Grading of EBC e objective of this sectionwas to develop the strength grading of EBC which is ex-pected that the results can be applied in structural designe first step is to determine the potential predictors with astronger correlation with compressive strength throughcorrelation analysis which was chosen as IPs Density andMOE frequently show a strong correlation with strengthproperties of European hardwoods [23ndash25] For this workdensity and compressive modulus were chosen as potentialpredictors for compressive strength To verify potential

predictors a simple linear regression was conducted be-tween predictors (ρ and Ec 0) and response (fc 0) Accordingto the linear regression the correlation coefficient between ρand fc 0 was in the range of 058ndash079 and between Ec 0 andfc 0 it was 058ndash079 (Table 7) Hence the density andcompressive MOE were selected as IPs for strength grading

In this research EBC grading based on compressivestrength was established by the confidence band e outlierand extreme values were justified and removed from furtheranalysis by utilizing a 99 ellipse band and 95 predicted



MOE of EBC parallel to the grain

0

5

10

15

20

25M

OE

(GPa

)

(c)



MOE of EBC perpendicular to the grain

0

2

4

6

8

10

12

14

MO

E (G

Pa)

(d)

Figure 4 Strengths and moduli distributions of experimental data strengths in parallel to the grain (a) strengths in perpendicular to thegrain (b) moduli in parallel to the grain (c) moduli in perpendicular to the grain (d)

60 80 100 120 140 160 180 200

Tension strength parallel to the grain (MPa)

0

02

04

06

08

1

01

03

05

07

09

Cum

ulat

ive p

roba

bilit

y

Empirical CDF

TestNormal H = 0 P = 098 D = 005Lognormal H = 0 P = 039 D = 010Weibull H = 0 P = 096 D = 005

Figure 5 Example of the KolmogorovndashSmirnov tests for the goodness of fit analysis


band e examples of ellipse confidence band analysis areshown in Figure 6

Density and MOE were IPs for strength grading for EBCsince they were strong correlation with compressivestrength Using the confidence band approach to perform

regression analysis on the EBC for strength grading R2 issufficiently high in the range of 044 to 087 Figure 7 showsthe confidence bands used to develop the EBC strengthgrading e confidence band method generates a contin-uous function and the stair function can be used to

Table 4 e details of the best-fit distribution functions of modulus for EBC

GroupCompression Tension Shear

Ec0 Ec90 Et0 Et90 Gs0 Gs90

EBC1 x minus L (297 0082) x minus N (404 0642) x minus L (294 0102) x minus N (322 0842) x minus L (163 0132) x minus L 149 0122)EBC2 x minus N (1739 1802) x minus L (149 0192) x minus L (280 0122) x minus L (216 0262) x minus L (143 0122) x minus L (160 0152)EBC3 x minus L (273 0052) x minus L (135 0102) x minus L (267 0092) x minus L (193 0252) x minus W (464 986) x minus W (492 753)EBC4 x minus N (943 0102) x minus N (277 0432) x minus L (262 0222) x minus W (125 336) x minus L (077 0172) x minus L (101 0162)EBC5 x minus N (1682 1692) x minus N (344 0402) x minus N (1696 2532) x minus W (158 456) x minus L (143 0122) x minus L 149 0122)EBC6 x minus N (1303 0942) x minus W (205 482) x minus N (1319 1772) x minus L (128 0252) x minus N (262 0352) x minus N (254 0232)EBC7 x minus N (1045 0892) x minus N (188 0242) x minus L (253 0222) x minus W (926 439) x minus L (085 0142) x minus N (299 0382)EBC8 x minus L (245 0082) x minus W (238 510) x minus L (227 0172) x minus L (184 0262) x minus N (295 0322) x minus W (307 595)EBC9 x minus L (255 0062) x minus N (201 0202) x minus N (1156 1822) x minus L (129 0252) x minus L (094 0102) x minus L (111 0152)

Table 5 e details of the best-fit distribution functions of strengths for EBC


fc 0 fc 90 ft 0 ft 90 fs 0 fs 90EBC1 x minus N (11289 8572) x minus N (4615 5022) x minus N (14173 34092) x minus W (563 562) x minus W (2441 623) x minus N (2611 6022)EBC2 x minus N (11904 9202) x minus N (5119 9132) x minus N (13060 26352) x minus L (198 0152) x minus W (1764 485) x minus N (4035 6132)EBC3 x minus N (9929 4402) x minus N (4764 5682) x minus N (13319 16722) x minus W (1013 588) x minus W (2009 677) x minus N (3445 4042)EBC4 x minus N (6672 7492) x minus N (2709 5052) x minus N (9990 33852) x minus N (266 0842) x minus L (216 0302) x minus N (302 0172)EBC5 x minus N (10195 6592) x minus N (3554 7042) x minus N (12586 25272) x minus W (351 323) x minus W (1175 420) x minus W (3465 810)EBC6 x minus N (5944 4302) x minus N (1510 3182) x minus N (12771 21332) x minus W (461 660) x minus W (1651 738) x minus N (1849 2182)EBC7 x minus N (5593 5072) x minus N (1608 1982) x minus N (12425 29802) x minus N (503 0542) x minus W (1145 406) x minus W (2319 720)EBC8 x minus N (5936 4752) x minus N (1524 1972) x minus N (10371 18972) x minus W (604 377) x minus W (1560 671) x minus N (1787 2362)EBC9 x minus N (6922 4362) x minus N (1637 1332) x minus L (475 0192) x minus W (730 653) x minus L (246 0202) x minus N (1283 2572)Note x minus N (μ σ2) f(x) (1

2π

radicσ)exp(minus (x minus μ)22σ2) x minus L (μln σ2ln) f(x) (1

2π

radicσlnx)eminus (ln xminus μln)22σ2ln x minus W (k λ) f(x) (kλ)(xλ)kminus 1eminus (xλ)k

Table 6 e recommended best-fit distribution functions of the mechanical properties for EBC

Property Best-fit distributionfc 0 Normalfc 90 NormalEc 0 NormalEc 90 Normalft 0 Normalft 90 2-P WeibullEt 0 LognormalEt 90 Lognormalfs 0 2-P Weibullfs 90 NormalGs 0 LognormalGs 90 Lognormal

Table 7 Correlation coefficients (R2) between predictors and response for EBC

Compressive strength parallel to the grain (fc0)EBC1 EBC2 EBC3 EBC4 EBC5 EBC6 EBC7 EBC8 EBC9

Density (ρ) 060 073 072 062 075 058 064 063 079Compressive modulus (Ec0) 062 068 058 062 070 073 072 073 079Note e correlations significant at plt 005 are displayed in bold


PSB

40

60

80

100

120

140

160f c

0 (M

Pa)

7500 10000 12500 15000 17500 20000 22500 250005000Ec0 (MPa)

(a)

LVB

30

40

50

60

70

80

90

f c0 (

MPa

)

10000 12000 14000 160008000Ec0 (MPa)

(b)

PSB

40

60

80

100

120

140

160

f c0 (

MPa

)

09 10 11 12 13 1408ρ (gcm3)

(c)

LVB

30

40

50

60

70

80

f c0 (

MPa

)

060 065 070 075 080055ρ (gcm3)

(d)

Figure 6 Ellipse band and predicted band analysis of linear regression fc0 against Ec 0 for PSB (a) fc 0 against Ec 0 for LVB (b) fc0 against ρfor PSB (c) fc0 against ρ for LVB (d)

R2 = 070

PSB

40

60

80

100

120

140

f c0 (

MPa

)

10000 12000 14000 16000 18000 20000 22000 240008000Ec0 (MPa)

GradeRkMeasured data

MeanR005

fc0 = 2823 + 0006Ec0

(a)

LVB

30

40

50

60

70

80

90

f c0 (

MPa

)

9000 10000 11000 12000 13000 14000 15000 16000 170008000Ec0 (MPa)


MeanR005

R2 = 044fc0 = 21932 + 0003Ec0

(b)

Figure 7 Continued


PSB

40

60

80

100

120

140

160f c

0 (M

Pa)

09 10 11 12 13 14 1508ρ (gcm3)


MeanR005

R2 = 087fc0 = ndash55799 + 130327ρ

(c)

LVB

30

40

50

60

70

80

90

f c0 (

MPa

)

060 063 066 069 072 075 078057ρ (gcm3)


MeanR005

R2 = 075fc0 = ndash62598 + 182512ρ

(d)

Figure 7 Compressive strength grading of EBC based on compressive modulus for PSB (a) based on compressive modulus for LVB (b)based on density for PSB (c) based on density for LVB (d)

Table 8 Compressive strength grade classification of EBC based on compressive modulus

Grade (Ec 0) Compressive strength (fc 0 MPa)Interval (MPa) Mean R005 Rk

PSB10000ndash11999 6310 5112 507012000ndash13999 7258 6316 626414000ndash15999 9813 7520 745816000ndash17999 10871 8724 865218000ndash19999 11516 9928 9846ge20000 11607 11132 11040LVB9000ndash9999 5400 4521 448010000ndash10999 5541 4855 481111000ndash11999 5874 5189 514212000ndash12999 6308 5523 547313000ndash13999 6645 5857 5804ge14000 6722 6191 6135

Table 9 Compressive strength grade classification of EBC based on density

Grade (ρ) Compressive strength (fc 0 MPa)Interval (gcm3) Mean R005 Rk



subdivide the function into several grades at the specifiedinterval of IP Each grade had R005 and Rk of fc 0 whichcould be utilized in EBC structural design following astrength-based approach Table 8 and Table 9 show thegrading of PSB and LVB into strength grades based ondensity and MOE e higher quality grades have higherstrength e designer can estimate the characteristic valueof compressive strength based on the IPs according to Ta-ble 8 and Table 9 for modern engineered bamboo structuraldesign

4 Conclusions

is study statistically investigates the mechanical propertiesof two types of EBC for seven manufacturers with rawmaterials from five regions in China To study the me-chanical behaviors of groups for EBC tensile compressiveand shear tests were carried out on small clear specimense study utilized wood standards for characterizationdetermining the probability distributions and characteristicvalues for mechanical properties Except for the PSB withlower density the mechanical properties of PSB are generallyhigher than those of LVB

In addition the statistical parameters of the best-fitprobability distribution models for mechanical propertiescan be utilized to determine the characteristic values andbuild the probabilistic design approach e results areconducive to developing design standards and reliabilityevaluation practices for EBC structures and extending theparticular applications in engineering

Due to their more significant correlation coefficientsdensity and compressive modulus were considered the mostsuitable IPs for strength grading of EBC subject to com-pressive strength According to the confidence bandmethodgrade intervals are built in similar ranges and the charac-teristic value in each grade can be calculated

After comparing the results from different sources it isfound that although the results obtained from the test aresimilar there is significant variation in the differences be-tween different sources of the same material e researchshows that future work needs to determine the source ofvariation in testing and establish a complete reliabilityanalysis and strength grading

Nomenclature

Ec0 Compressive modulus parallel to the grainEc 0mean Mean compressive parallel to the grainfs 0 Shear strength parallel to the grainfs 0 k Characteristic shear strength parallel to the

grainEc 90 Compressive modulus parallel perpendicular

to the grainEc 90 mean Mean compressive modulus parallel

perpendicular to the grainfs 90 Shear strength perpendicular to the grainfs 90 k Characteristic shear strength perpendicular to

the grainEt 0 Tensile modulus parallel to the grain

Et 0 mean Mean tensile modulus parallel to the grainGs 0 Shear modulus parallel to the grainGs 0 mean Mean shear modulus parallel to the grainEt 90 Tensile modulus perpendicular to the grainEt 90 mean Mean tensile modulus perpendicular to the

grainGs 90 Shear modulus perpendicular to the grainGs 90 mean Mean shear modulus perpendicular to the

grainfc 0 Compressive strength parallel to the grainfc 0 k Characteristic compressive strength parallel to

the grainMc Moisture contentMcmean Mean moisture contentfc 90 Compressive strength perpendicular to the

grainfc 90 k Characteristic compressive strength

perpendicular to the grainρ Mean air-dry densityMOE Modulus of elasticft 0 Tensile strength parallel to the grainft 0 k Characteristic tensile strength parallel to the

grainft 90 Tensile strength perpendicular to the grainft 90 k Characteristic tensile strength perpendicular

to the grain

Data Availability

e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is research was supported by the National Natural ScienceFoundation ofChina (no 51978338) BasicAbility ImprovementProgram of Young and Middle-Aged Scholar for the EducationOffice of Guangxi Province (no 2019KY0236) and PriorityAcademic Program Development of Jiangsu Higher EducationInstitutions (PAPD)

References

[1] Y Xiao R Z Yang and B Shan ldquoCorrigendum to ldquoPro-duction environmental impact and mechanical properties ofglubamrdquordquo Construction and Building Materials vol 44 p 8052013

[2] P J Shi ldquoPrecipitation is the most crucial factor determiningthe distribution of moso bamboo in Mainland Chinardquo GlobalEcology and Conservation vol 22 2020

[3] S Amada and S Untao ldquoFracture properties of bamboordquoComposites Part B-Engineering vol 32 no 5 pp 449ndash4572001

[4] F Wang Z Shao and Y Wu ldquoMode II interlaminar fractureproperties of Moso bamboordquo Composites Part B Engineeringvol 44 no 1 pp 242ndash247 2013


[5] D S Huang A P Zhou and Y L Bian ldquoExperimental andanalytical study on the nonlinear bending of parallel strandbamboo beamsrdquo Construction and Building Materials vol 44pp 585ndash592 2013

[6] D Huang Y Bian A Zhou and B Sheng ldquoExperimentalstudy on stress-strain relationships and failure mechanisms ofparallel strand bamboo made from phyllostachysrdquo Con-struction and Building Materials vol 77 pp 130ndash138 2015

[7] Y Wei ldquoStress-strain relationship model of glulam bamboounder axial loadingrdquo Advanced Composites Letters vol 292020

[8] Y Xiao Y Wu J Li and R Z Yang ldquoAn experimental studyon shear strength of glubamrdquo Construction and BuildingMaterials vol 150 pp 490ndash500 2017

[9] B Sharma A Gatoo M Bock and M Ramage ldquoEngineeredbamboo for structural applicationsrdquo Construction andBuilding Materials vol 81 pp 66ndash73 2015

[10] A Kumar T Vlach L Laiblova et al ldquoEngineered bambooscrimber influence of density on the mechanical and waterabsorption propertiesrdquo Construction and Building Materialsvol 127 pp 815ndash827 2016

[11] B S Institution Bs En 384 - Structural Timber - Determi-nation of Characteristic Values of Mechanical Properties andDensity 2018

[12] ASTM Practice for Sampling and Data-Analysis for StructuralWood and Wood-Based Products ASTM International WestConshohocken PA USA 2017

[13] D Trujillo S Jangra and J M Gibson ldquoFlexural properties asa basis for bamboo strength gradingrdquo Proceedings of theInstitution of Civil Engineers - Structures and Buildingsvol 170 no 4 pp 284ndash294 2017

[14] N N Nurmadina N Nugroho and E T Bahtiar ldquoStructuralgrading of Gigantochloa apus bamboo based on its flexuralpropertiesrdquo Construction and Building Materials vol 157pp 1173ndash1189 2017

[15] E T Bahtiar A P Imanullah D Hermawan N Nugrohoand fnm Abdurachman ldquoStructural grading of three sym-podial bamboo culms (Hitam Andong and Tali) subjected toaxial compressive loadrdquo Engineering Structures vol 181pp 233ndash245 2019

[16] E T Bahtiar D Trujillo and N Nugroho ldquoCompressionresistance of short members as the basis for structural gradingof Guadua angustifoliardquo Construction and Building Materialsvol 249 2020

[17] China SAOMethod for Determination of the Density of WoodGBT 1933-2009 Macau China 2009

[18] China SAOMethod for Determination of Moisture Content ofWood GBT 1931-2009 Macau China 2009

[19] ASTM Standard Test Methods for Small Clear Specimens ofTimber ASTM International West Conshohocken Con-shohocken PA USA 2014

[20] ASTM Standard Test Method for Shear Properties of Com-posite Materials by V-Notched Rail Shear Method ASTMInternational West Conshohocken Conshohocken PA USA2012

[21] B P Murphy I M Chakravarti R G Laha and J RoyldquoHandbook of methods of applied statistics Vol I techniquesof computation descriptive methods and statistical infer-encerdquo Applied Statistics vol 17 no 3 p 293 1968

[22] J P Torres L-J Vandi M Veidt and M T Heitzmann ldquoemechanical properties of natural fibre composite laminates astatistical studyrdquo Composites Part A Applied Science andManufacturing vol 98 pp 99ndash104 2017

[23] CEN Structural Timber ndash Strength Classes EN 338 2016European Committee for Standardisation Brussels Belgium

[24] G Riesco Muntildeoz A Remacha Gete and F Pedras SaavedraldquoImplications in the design of a method for visual grading andmechanical testing of hardwood structural timber for des-ignation within the European strength classesrdquo Forest Sys-tems vol 20 no 2 pp 235ndash244 2011

[25] A Kovryga P Stapel and JW G van de Kuilen ldquoMechanicalproperties and their interrelationships for medium-densityEuropean hardwoods focusing on ash and beechrdquo WoodMaterial Science amp Engineering vol 15 no 5 pp 289ndash3022020


have been conducted to investigate the mechanical prop-erties of bamboo composites Huang [5 6] studied themechanical properties of PSB by experiments and inves-tigated stress-strain relationships and failure mechanismsin each stress state Wei [7] provided a comprehensiveresearch on the mechanical behavior and failure modes ofbamboo scrimber (PSB) and laminated bamboo (LVB) and

proposed the stress-strain models for EBC Xiao [1 8]studied the mechanical properties of glubam boards andfound that the Weibull distribution and normal distribu-tion are best fit for shear strength and the in-plane shearstrength respectively and suggested the characteristicvalues and the design values Sharma et al [9] provided acomprehensive study that compares bamboo scrimber

(a) (b) (c)

Figure 1 Examples of EBC structure

75degE 90degE 105degE 120degE 135degE

20degN

30degN

40degN

50degN

20degN

30degN

40degN

50degN

90degE 105degE 120degE

0 310 620 1240 km

Climate stationMoso bamboo absentMoso bamboo present

Figure 2 e information on the distribution of Moso bamboo in Mainland China by Shi [2]










n ts

αX1113874 1113875

t

αCV1113874 1113875

2 (1)



2

3

1

(a)

1

3

2

(b)







radicσ


(2)

F(x) Φx minus μσ

1113874 1113875 (3)


2π

radicσ lnx


22σ2ln (4)


σln1113888 1113889 (5)


λx

λ1113874 1113875

kminus 1e

minus (xλ)k

(6)


(7)



fk005 μ minus KNσ


fk005 X minus KWS

(8)





















GBT 1931[18]




25

25 100


25

25 100



25

375

5

95R444


63

50

13 625

R132450

ASTMD7078 -12[20]

Shear


25 1376

3013

13

5

R13

90iexclatilde

45iexclatilde

56


25 1376

3013

13

5

R13

90iexclatilde

45iexclatilde

56




R005 1113954y minus t(v095) 1 +1n

+(x minus x)2

Σ(x minus x)21113888 1113889

05

Sr (9)

SE 1 +1n

+(x minus x)2

Σ(x minus x)21113888 1113889

05

Sr (10)


mn

radic1113888 1113889

05

(11)












fc0mean (MPa) 11289(008)

11904(008) 9929 (004) 6672

(011)10195(006) 5944 (007) 5593 (009) 5936 (008) 6922 (006)

fc90mean(MPa) 4615 (011) 5119 (018) 4764 (012) 2709

(019) 3554 (020) 151 (021) 1608 (012) 1524 (013) 1637 (008)

fc0k (MPa) 9766 10273 9149 5344 9024 5179 4694 5094 6150fc90k (MPa) 4615 5119 4764 1813 3554 1510 1608 1524 1637

Ec0mean (GPa) 1948 (008) 1743 (010) 1537 (005) 1252(010) 1682 (010) 1303 (007) 1045 (009) 1161 (008) 1287 (006)

Ec90mean(GPa) 404 (016) 453 (020) 388 (010) 277 (016) 344 (012) 187 (023) 187 (013) 219 (022) 201 (010)

Tension

ft0mean (MPa) 14173(024)

13060(020)

13319(013)

9991(033)

12586(020)

12771(010)

12425(024)

10371(018)

11705(019)

ft90mean(MPa) 52 (022) 729 (015) 938 (021) 252 (031) 314 (034) 430 (018) 503 (011) 545 (031) 679 (018)

ft0k (MPa) 8115 8386 10355 3989 8106 8989 7138 7005 8038ft90k (MPa) 315 559 585 117 111 284 392 237 446

Et0mean (GPa) 1911 (010) 1658 (012) 1448 (009) 1402(022) 1696 (015) 1319 (013) 1282 (022) 982 (017) 1156 (016)

Et90mean(GPa) 322 (026) 898 (026) 709 (025) 106 (022) 144 (025) 37 (024) 843 (026) 374 (025) 651 (026)


(016) 3263 (015) 1849 (012) 2168 (017) 1787 (013) 1283 (020)






0

20

40

60

80

100

120

140

160

180

Stre

ngth

(MPa

)

(a)




0

10

20

30

40

50

60

70

Stre

ngth

(MPa

)

(b)

Figure 4 Continued








0

5

10

15

20

25M

OE

(GPa

)

(c)




0

2

4

6

8

10

12

14

MO

E (G

Pa)

(d)


60 80 100 120 140 160 180 200


0

02

04

06

08

1

01

03

05

07

09

Cum

ulat

ive p

roba

bilit

y

Empirical CDF














2π


2π








PSB

40

60

80

100

120

140

160f c

0 (M

Pa)

7500 10000 12500 15000 17500 20000 22500 250005000Ec0 (MPa)

(a)

LVB

30

40

50

60

70

80

90

f c0 (

MPa

)

10000 12000 14000 160008000Ec0 (MPa)

(b)

PSB

40

60

80

100

120

140

160

f c0 (

MPa

)

09 10 11 12 13 1408ρ (gcm3)

(c)

LVB

30

40

50

60

70

80

f c0 (

MPa

)

060 065 070 075 080055ρ (gcm3)

(d)


R2 = 070

PSB

40

60

80

100

120

140

f c0 (

MPa

)

10000 12000 14000 16000 18000 20000 22000 240008000Ec0 (MPa)


MeanR005

fc0 = 2823 + 0006Ec0

(a)

LVB

30

40

50

60

70

80

90

f c0 (

MPa

)

9000 10000 11000 12000 13000 14000 15000 16000 170008000Ec0 (MPa)


MeanR005

R2 = 044fc0 = 21932 + 0003Ec0

(b)

Figure 7 Continued


PSB

40

60

80

100

120

140

160f c

0 (M

Pa)

09 10 11 12 13 14 1508ρ (gcm3)


MeanR005

R2 = 087fc0 = ndash55799 + 130327ρ

(c)

LVB

30

40

50

60

70

80

90

f c0 (

MPa

)

060 063 066 069 072 075 078057ρ (gcm3)


MeanR005

R2 = 075fc0 = ndash62598 + 182512ρ

(d)










4 Conclusions





Nomenclature













to the grain

Data Availability




Acknowledgments


References




































n ts

αX1113874 1113875

t

αCV1113874 1113875

2 (1)



2

3

1

(a)

1

3

2

(b)







radicσ


(2)

F(x) Φx minus μσ

1113874 1113875 (3)


2π

radicσ lnx


22σ2ln (4)


σln1113888 1113889 (5)


λx

λ1113874 1113875

kminus 1e

minus (xλ)k

(6)


(7)



fk005 μ minus KNσ


fk005 X minus KWS

(8)





















GBT 1931[18]




25

25 100


25

25 100



25

375

5

95R444


63

50

13 625

R132450

ASTMD7078 -12[20]

Shear


25 1376

3013

13

5

R13

90iexclatilde

45iexclatilde

56


25 1376

3013

13

5

R13

90iexclatilde

45iexclatilde

56




R005 1113954y minus t(v095) 1 +1n

+(x minus x)2

Σ(x minus x)21113888 1113889

05

Sr (9)

SE 1 +1n

+(x minus x)2

Σ(x minus x)21113888 1113889

05

Sr (10)


mn

radic1113888 1113889

05

(11)












fc0mean (MPa) 11289(008)

11904(008) 9929 (004) 6672

(011)10195(006) 5944 (007) 5593 (009) 5936 (008) 6922 (006)

fc90mean(MPa) 4615 (011) 5119 (018) 4764 (012) 2709

(019) 3554 (020) 151 (021) 1608 (012) 1524 (013) 1637 (008)

fc0k (MPa) 9766 10273 9149 5344 9024 5179 4694 5094 6150fc90k (MPa) 4615 5119 4764 1813 3554 1510 1608 1524 1637

Ec0mean (GPa) 1948 (008) 1743 (010) 1537 (005) 1252(010) 1682 (010) 1303 (007) 1045 (009) 1161 (008) 1287 (006)

Ec90mean(GPa) 404 (016) 453 (020) 388 (010) 277 (016) 344 (012) 187 (023) 187 (013) 219 (022) 201 (010)

Tension

ft0mean (MPa) 14173(024)

13060(020)

13319(013)

9991(033)

12586(020)

12771(010)

12425(024)

10371(018)

11705(019)

ft90mean(MPa) 52 (022) 729 (015) 938 (021) 252 (031) 314 (034) 430 (018) 503 (011) 545 (031) 679 (018)

ft0k (MPa) 8115 8386 10355 3989 8106 8989 7138 7005 8038ft90k (MPa) 315 559 585 117 111 284 392 237 446

Et0mean (GPa) 1911 (010) 1658 (012) 1448 (009) 1402(022) 1696 (015) 1319 (013) 1282 (022) 982 (017) 1156 (016)

Et90mean(GPa) 322 (026) 898 (026) 709 (025) 106 (022) 144 (025) 37 (024) 843 (026) 374 (025) 651 (026)


(016) 3263 (015) 1849 (012) 2168 (017) 1787 (013) 1283 (020)






0

20

40

60

80

100

120

140

160

180

Stre

ngth

(MPa

)

(a)




0

10

20

30

40

50

60

70

Stre

ngth

(MPa

)

(b)

Figure 4 Continued








0

5

10

15

20

25M

OE

(GPa

)

(c)




0

2

4

6

8

10

12

14

MO

E (G

Pa)

(d)


60 80 100 120 140 160 180 200


0

02

04

06

08

1

01

03

05

07

09

Cum

ulat

ive p

roba

bilit

y

Empirical CDF














2π


2π








PSB

40

60

80

100

120

140

160f c

0 (M

Pa)

7500 10000 12500 15000 17500 20000 22500 250005000Ec0 (MPa)

(a)

LVB

30

40

50

60

70

80

90

f c0 (

MPa

)

10000 12000 14000 160008000Ec0 (MPa)

(b)

PSB

40

60

80

100

120

140

160

f c0 (

MPa

)

09 10 11 12 13 1408ρ (gcm3)

(c)

LVB

30

40

50

60

70

80

f c0 (

MPa

)

060 065 070 075 080055ρ (gcm3)

(d)


R2 = 070

PSB

40

60

80

100

120

140

f c0 (

MPa

)

10000 12000 14000 16000 18000 20000 22000 240008000Ec0 (MPa)


MeanR005

fc0 = 2823 + 0006Ec0

(a)

LVB

30

40

50

60

70

80

90

f c0 (

MPa

)

9000 10000 11000 12000 13000 14000 15000 16000 170008000Ec0 (MPa)


MeanR005

R2 = 044fc0 = 21932 + 0003Ec0

(b)

Figure 7 Continued


PSB

40

60

80

100

120

140

160f c

0 (M

Pa)

09 10 11 12 13 14 1508ρ (gcm3)


MeanR005

R2 = 087fc0 = ndash55799 + 130327ρ

(c)

LVB

30

40

50

60

70

80

90

f c0 (

MPa

)

060 063 066 069 072 075 078057ρ (gcm3)


MeanR005

R2 = 075fc0 = ndash62598 + 182512ρ

(d)










4 Conclusions





Nomenclature













to the grain

Data Availability




Acknowledgments


References
































radicσ


(2)

F(x) Φx minus μσ

1113874 1113875 (3)


2π

radicσ lnx


22σ2ln (4)


σln1113888 1113889 (5)


λx

λ1113874 1113875

kminus 1e

minus (xλ)k

(6)


(7)



fk005 μ minus KNσ


fk005 X minus KWS

(8)





















GBT 1931[18]




25

25 100


25

25 100



25

375

5

95R444


63

50

13 625

R132450

ASTMD7078 -12[20]

Shear


25 1376

3013

13

5

R13

90iexclatilde

45iexclatilde

56


25 1376

3013

13

5

R13

90iexclatilde

45iexclatilde

56




R005 1113954y minus t(v095) 1 +1n

+(x minus x)2

Σ(x minus x)21113888 1113889

05

Sr (9)

SE 1 +1n

+(x minus x)2

Σ(x minus x)21113888 1113889

05

Sr (10)


mn

radic1113888 1113889

05

(11)












fc0mean (MPa) 11289(008)

11904(008) 9929 (004) 6672

(011)10195(006) 5944 (007) 5593 (009) 5936 (008) 6922 (006)

fc90mean(MPa) 4615 (011) 5119 (018) 4764 (012) 2709

(019) 3554 (020) 151 (021) 1608 (012) 1524 (013) 1637 (008)

fc0k (MPa) 9766 10273 9149 5344 9024 5179 4694 5094 6150fc90k (MPa) 4615 5119 4764 1813 3554 1510 1608 1524 1637

Ec0mean (GPa) 1948 (008) 1743 (010) 1537 (005) 1252(010) 1682 (010) 1303 (007) 1045 (009) 1161 (008) 1287 (006)

Ec90mean(GPa) 404 (016) 453 (020) 388 (010) 277 (016) 344 (012) 187 (023) 187 (013) 219 (022) 201 (010)

Tension

ft0mean (MPa) 14173(024)

13060(020)

13319(013)

9991(033)

12586(020)

12771(010)

12425(024)

10371(018)

11705(019)

ft90mean(MPa) 52 (022) 729 (015) 938 (021) 252 (031) 314 (034) 430 (018) 503 (011) 545 (031) 679 (018)

ft0k (MPa) 8115 8386 10355 3989 8106 8989 7138 7005 8038ft90k (MPa) 315 559 585 117 111 284 392 237 446

Et0mean (GPa) 1911 (010) 1658 (012) 1448 (009) 1402(022) 1696 (015) 1319 (013) 1282 (022) 982 (017) 1156 (016)

Et90mean(GPa) 322 (026) 898 (026) 709 (025) 106 (022) 144 (025) 37 (024) 843 (026) 374 (025) 651 (026)


(016) 3263 (015) 1849 (012) 2168 (017) 1787 (013) 1283 (020)






0

20

40

60

80

100

120

140

160

180

Stre

ngth

(MPa

)

(a)




0

10

20

30

40

50

60

70

Stre

ngth

(MPa

)

(b)

Figure 4 Continued








0

5

10

15

20

25M

OE

(GPa

)

(c)




0

2

4

6

8

10

12

14

MO

E (G

Pa)

(d)


60 80 100 120 140 160 180 200


0

02

04

06

08

1

01

03

05

07

09

Cum

ulat

ive p

roba

bilit

y

Empirical CDF














2π


2π








PSB

40

60

80

100

120

140

160f c

0 (M

Pa)

7500 10000 12500 15000 17500 20000 22500 250005000Ec0 (MPa)

(a)

LVB

30

40

50

60

70

80

90

f c0 (

MPa

)

10000 12000 14000 160008000Ec0 (MPa)

(b)

PSB

40

60

80

100

120

140

160

f c0 (

MPa

)

09 10 11 12 13 1408ρ (gcm3)

(c)

LVB

30

40

50

60

70

80

f c0 (

MPa

)

060 065 070 075 080055ρ (gcm3)

(d)


R2 = 070

PSB

40

60

80

100

120

140

f c0 (

MPa

)

10000 12000 14000 16000 18000 20000 22000 240008000Ec0 (MPa)


MeanR005

fc0 = 2823 + 0006Ec0

(a)

LVB

30

40

50

60

70

80

90

f c0 (

MPa

)

9000 10000 11000 12000 13000 14000 15000 16000 170008000Ec0 (MPa)


MeanR005

R2 = 044fc0 = 21932 + 0003Ec0

(b)

Figure 7 Continued


PSB

40

60

80

100

120

140

160f c

0 (M

Pa)

09 10 11 12 13 14 1508ρ (gcm3)


MeanR005

R2 = 087fc0 = ndash55799 + 130327ρ

(c)

LVB

30

40

50

60

70

80

90

f c0 (

MPa

)

060 063 066 069 072 075 078057ρ (gcm3)


MeanR005

R2 = 075fc0 = ndash62598 + 182512ρ

(d)










4 Conclusions





Nomenclature













to the grain

Data Availability




Acknowledgments


References
































GBT 1931[18]




25

25 100


25

25 100



25

375

5

95R444


63

50

13 625

R132450

ASTMD7078 -12[20]

Shear


25 1376

3013

13

5

R13

90iexclatilde

45iexclatilde

56


25 1376

3013

13

5

R13

90iexclatilde

45iexclatilde

56




R005 1113954y minus t(v095) 1 +1n

+(x minus x)2

Σ(x minus x)21113888 1113889

05

Sr (9)

SE 1 +1n

+(x minus x)2

Σ(x minus x)21113888 1113889

05

Sr (10)


mn

radic1113888 1113889

05

(11)












fc0mean (MPa) 11289(008)

11904(008) 9929 (004) 6672

(011)10195(006) 5944 (007) 5593 (009) 5936 (008) 6922 (006)

fc90mean(MPa) 4615 (011) 5119 (018) 4764 (012) 2709

(019) 3554 (020) 151 (021) 1608 (012) 1524 (013) 1637 (008)

fc0k (MPa) 9766 10273 9149 5344 9024 5179 4694 5094 6150fc90k (MPa) 4615 5119 4764 1813 3554 1510 1608 1524 1637

Ec0mean (GPa) 1948 (008) 1743 (010) 1537 (005) 1252(010) 1682 (010) 1303 (007) 1045 (009) 1161 (008) 1287 (006)

Ec90mean(GPa) 404 (016) 453 (020) 388 (010) 277 (016) 344 (012) 187 (023) 187 (013) 219 (022) 201 (010)

Tension

ft0mean (MPa) 14173(024)

13060(020)

13319(013)

9991(033)

12586(020)

12771(010)

12425(024)

10371(018)

11705(019)

ft90mean(MPa) 52 (022) 729 (015) 938 (021) 252 (031) 314 (034) 430 (018) 503 (011) 545 (031) 679 (018)

ft0k (MPa) 8115 8386 10355 3989 8106 8989 7138 7005 8038ft90k (MPa) 315 559 585 117 111 284 392 237 446

Et0mean (GPa) 1911 (010) 1658 (012) 1448 (009) 1402(022) 1696 (015) 1319 (013) 1282 (022) 982 (017) 1156 (016)

Et90mean(GPa) 322 (026) 898 (026) 709 (025) 106 (022) 144 (025) 37 (024) 843 (026) 374 (025) 651 (026)


(016) 3263 (015) 1849 (012) 2168 (017) 1787 (013) 1283 (020)






0

20

40

60

80

100

120

140

160

180

Stre

ngth

(MPa

)

(a)




0

10

20

30

40

50

60

70

Stre

ngth

(MPa

)

(b)

Figure 4 Continued








0

5

10

15

20

25M

OE

(GPa

)

(c)




0

2

4

6

8

10

12

14

MO

E (G

Pa)

(d)


60 80 100 120 140 160 180 200


0

02

04

06

08

1

01

03

05

07

09

Cum

ulat

ive p

roba

bilit

y

Empirical CDF














2π


2π








PSB

40

60

80

100

120

140

160f c

0 (M

Pa)

7500 10000 12500 15000 17500 20000 22500 250005000Ec0 (MPa)

(a)

LVB

30

40

50

60

70

80

90

f c0 (

MPa

)

10000 12000 14000 160008000Ec0 (MPa)

(b)

PSB

40

60

80

100

120

140

160

f c0 (

MPa

)

09 10 11 12 13 1408ρ (gcm3)

(c)

LVB

30

40

50

60

70

80

f c0 (

MPa

)

060 065 070 075 080055ρ (gcm3)

(d)


R2 = 070

PSB

40

60

80

100

120

140

f c0 (

MPa

)

10000 12000 14000 16000 18000 20000 22000 240008000Ec0 (MPa)


MeanR005

fc0 = 2823 + 0006Ec0

(a)

LVB

30

40

50

60

70

80

90

f c0 (

MPa

)

9000 10000 11000 12000 13000 14000 15000 16000 170008000Ec0 (MPa)


MeanR005

R2 = 044fc0 = 21932 + 0003Ec0

(b)

Figure 7 Continued


PSB

40

60

80

100

120

140

160f c

0 (M

Pa)

09 10 11 12 13 14 1508ρ (gcm3)


MeanR005

R2 = 087fc0 = ndash55799 + 130327ρ

(c)

LVB

30

40

50

60

70

80

90

f c0 (

MPa

)

060 063 066 069 072 075 078057ρ (gcm3)


MeanR005

R2 = 075fc0 = ndash62598 + 182512ρ

(d)










4 Conclusions





Nomenclature













to the grain

Data Availability




Acknowledgments


References






























R005 1113954y minus t(v095) 1 +1n

+(x minus x)2

Σ(x minus x)21113888 1113889

05

Sr (9)

SE 1 +1n

+(x minus x)2

Σ(x minus x)21113888 1113889

05

Sr (10)


mn

radic1113888 1113889

05

(11)












fc0mean (MPa) 11289(008)

11904(008) 9929 (004) 6672

(011)10195(006) 5944 (007) 5593 (009) 5936 (008) 6922 (006)

fc90mean(MPa) 4615 (011) 5119 (018) 4764 (012) 2709

(019) 3554 (020) 151 (021) 1608 (012) 1524 (013) 1637 (008)

fc0k (MPa) 9766 10273 9149 5344 9024 5179 4694 5094 6150fc90k (MPa) 4615 5119 4764 1813 3554 1510 1608 1524 1637

Ec0mean (GPa) 1948 (008) 1743 (010) 1537 (005) 1252(010) 1682 (010) 1303 (007) 1045 (009) 1161 (008) 1287 (006)

Ec90mean(GPa) 404 (016) 453 (020) 388 (010) 277 (016) 344 (012) 187 (023) 187 (013) 219 (022) 201 (010)

Tension

ft0mean (MPa) 14173(024)

13060(020)

13319(013)

9991(033)

12586(020)

12771(010)

12425(024)

10371(018)

11705(019)

ft90mean(MPa) 52 (022) 729 (015) 938 (021) 252 (031) 314 (034) 430 (018) 503 (011) 545 (031) 679 (018)

ft0k (MPa) 8115 8386 10355 3989 8106 8989 7138 7005 8038ft90k (MPa) 315 559 585 117 111 284 392 237 446

Et0mean (GPa) 1911 (010) 1658 (012) 1448 (009) 1402(022) 1696 (015) 1319 (013) 1282 (022) 982 (017) 1156 (016)

Et90mean(GPa) 322 (026) 898 (026) 709 (025) 106 (022) 144 (025) 37 (024) 843 (026) 374 (025) 651 (026)


(016) 3263 (015) 1849 (012) 2168 (017) 1787 (013) 1283 (020)






0

20

40

60

80

100

120

140

160

180

Stre

ngth

(MPa

)

(a)




0

10

20

30

40

50

60

70

Stre

ngth

(MPa

)

(b)

Figure 4 Continued








0

5

10

15

20

25M

OE

(GPa

)

(c)




0

2

4

6

8

10

12

14

MO

E (G

Pa)

(d)


60 80 100 120 140 160 180 200


0

02

04

06

08

1

01

03

05

07

09

Cum

ulat

ive p

roba

bilit

y

Empirical CDF














2π


2π








PSB

40

60

80

100

120

140

160f c

0 (M

Pa)

7500 10000 12500 15000 17500 20000 22500 250005000Ec0 (MPa)

(a)

LVB

30

40

50

60

70

80

90

f c0 (

MPa

)

10000 12000 14000 160008000Ec0 (MPa)

(b)

PSB

40

60

80

100

120

140

160

f c0 (

MPa

)

09 10 11 12 13 1408ρ (gcm3)

(c)

LVB

30

40

50

60

70

80

f c0 (

MPa

)

060 065 070 075 080055ρ (gcm3)

(d)


R2 = 070

PSB

40

60

80

100

120

140

f c0 (

MPa

)

10000 12000 14000 16000 18000 20000 22000 240008000Ec0 (MPa)


MeanR005

fc0 = 2823 + 0006Ec0

(a)

LVB

30

40

50

60

70

80

90

f c0 (

MPa

)

9000 10000 11000 12000 13000 14000 15000 16000 170008000Ec0 (MPa)


MeanR005

R2 = 044fc0 = 21932 + 0003Ec0

(b)

Figure 7 Continued


PSB

40

60

80

100

120

140

160f c

0 (M

Pa)

09 10 11 12 13 14 1508ρ (gcm3)


MeanR005

R2 = 087fc0 = ndash55799 + 130327ρ

(c)

LVB

30

40

50

60

70

80

90

f c0 (

MPa

)

060 063 066 069 072 075 078057ρ (gcm3)


MeanR005

R2 = 075fc0 = ndash62598 + 182512ρ

(d)










4 Conclusions





Nomenclature













to the grain

Data Availability




Acknowledgments


References






























fc0mean (MPa) 11289(008)

11904(008) 9929 (004) 6672

(011)10195(006) 5944 (007) 5593 (009) 5936 (008) 6922 (006)

fc90mean(MPa) 4615 (011) 5119 (018) 4764 (012) 2709

(019) 3554 (020) 151 (021) 1608 (012) 1524 (013) 1637 (008)

fc0k (MPa) 9766 10273 9149 5344 9024 5179 4694 5094 6150fc90k (MPa) 4615 5119 4764 1813 3554 1510 1608 1524 1637

Ec0mean (GPa) 1948 (008) 1743 (010) 1537 (005) 1252(010) 1682 (010) 1303 (007) 1045 (009) 1161 (008) 1287 (006)

Ec90mean(GPa) 404 (016) 453 (020) 388 (010) 277 (016) 344 (012) 187 (023) 187 (013) 219 (022) 201 (010)

Tension

ft0mean (MPa) 14173(024)

13060(020)

13319(013)

9991(033)

12586(020)

12771(010)

12425(024)

10371(018)

11705(019)

ft90mean(MPa) 52 (022) 729 (015) 938 (021) 252 (031) 314 (034) 430 (018) 503 (011) 545 (031) 679 (018)

ft0k (MPa) 8115 8386 10355 3989 8106 8989 7138 7005 8038ft90k (MPa) 315 559 585 117 111 284 392 237 446

Et0mean (GPa) 1911 (010) 1658 (012) 1448 (009) 1402(022) 1696 (015) 1319 (013) 1282 (022) 982 (017) 1156 (016)

Et90mean(GPa) 322 (026) 898 (026) 709 (025) 106 (022) 144 (025) 37 (024) 843 (026) 374 (025) 651 (026)


(016) 3263 (015) 1849 (012) 2168 (017) 1787 (013) 1283 (020)






0

20

40

60

80

100

120

140

160

180

Stre

ngth

(MPa

)

(a)




0

10

20

30

40

50

60

70

Stre

ngth

(MPa

)

(b)

Figure 4 Continued








0

5

10

15

20

25M

OE

(GPa

)

(c)




0

2

4

6

8

10

12

14

MO

E (G

Pa)

(d)


60 80 100 120 140 160 180 200


0

02

04

06

08

1

01

03

05

07

09

Cum

ulat

ive p

roba

bilit

y

Empirical CDF














2π


2π








PSB

40

60

80

100

120

140

160f c

0 (M

Pa)

7500 10000 12500 15000 17500 20000 22500 250005000Ec0 (MPa)

(a)

LVB

30

40

50

60

70

80

90

f c0 (

MPa

)

10000 12000 14000 160008000Ec0 (MPa)

(b)

PSB

40

60

80

100

120

140

160

f c0 (

MPa

)

09 10 11 12 13 1408ρ (gcm3)

(c)

LVB

30

40

50

60

70

80

f c0 (

MPa

)

060 065 070 075 080055ρ (gcm3)

(d)


R2 = 070

PSB

40

60

80

100

120

140

f c0 (

MPa

)

10000 12000 14000 16000 18000 20000 22000 240008000Ec0 (MPa)


MeanR005

fc0 = 2823 + 0006Ec0

(a)

LVB

30

40

50

60

70

80

90

f c0 (

MPa

)

9000 10000 11000 12000 13000 14000 15000 16000 170008000Ec0 (MPa)


MeanR005

R2 = 044fc0 = 21932 + 0003Ec0

(b)

Figure 7 Continued


PSB

40

60

80

100

120

140

160f c

0 (M

Pa)

09 10 11 12 13 14 1508ρ (gcm3)


MeanR005

R2 = 087fc0 = ndash55799 + 130327ρ

(c)

LVB

30

40

50

60

70

80

90

f c0 (

MPa

)

060 063 066 069 072 075 078057ρ (gcm3)


MeanR005

R2 = 075fc0 = ndash62598 + 182512ρ

(d)










4 Conclusions





Nomenclature













to the grain

Data Availability




Acknowledgments


References


































0

5

10

15

20

25M

OE

(GPa

)

(c)




0

2

4

6

8

10

12

14

MO

E (G

Pa)

(d)


60 80 100 120 140 160 180 200


0

02

04

06

08

1

01

03

05

07

09

Cum

ulat

ive p

roba

bilit

y

Empirical CDF














2π


2π








PSB

40

60

80

100

120

140

160f c

0 (M

Pa)

7500 10000 12500 15000 17500 20000 22500 250005000Ec0 (MPa)

(a)

LVB

30

40

50

60

70

80

90

f c0 (

MPa

)

10000 12000 14000 160008000Ec0 (MPa)

(b)

PSB

40

60

80

100

120

140

160

f c0 (

MPa

)

09 10 11 12 13 1408ρ (gcm3)

(c)

LVB

30

40

50

60

70

80

f c0 (

MPa

)

060 065 070 075 080055ρ (gcm3)

(d)


R2 = 070

PSB

40

60

80

100

120

140

f c0 (

MPa

)

10000 12000 14000 16000 18000 20000 22000 240008000Ec0 (MPa)


MeanR005

fc0 = 2823 + 0006Ec0

(a)

LVB

30

40

50

60

70

80

90

f c0 (

MPa

)

9000 10000 11000 12000 13000 14000 15000 16000 170008000Ec0 (MPa)


MeanR005

R2 = 044fc0 = 21932 + 0003Ec0

(b)

Figure 7 Continued


PSB

40

60

80

100

120

140

160f c

0 (M

Pa)

09 10 11 12 13 14 1508ρ (gcm3)


MeanR005

R2 = 087fc0 = ndash55799 + 130327ρ

(c)

LVB

30

40

50

60

70

80

90

f c0 (

MPa

)

060 063 066 069 072 075 078057ρ (gcm3)


MeanR005

R2 = 075fc0 = ndash62598 + 182512ρ

(d)










4 Conclusions





Nomenclature













to the grain

Data Availability




Acknowledgments


References






































2π


2π








PSB

40

60

80

100

120

140

160f c

0 (M

Pa)

7500 10000 12500 15000 17500 20000 22500 250005000Ec0 (MPa)

(a)

LVB

30

40

50

60

70

80

90

f c0 (

MPa

)

10000 12000 14000 160008000Ec0 (MPa)

(b)

PSB

40

60

80

100

120

140

160

f c0 (

MPa

)

09 10 11 12 13 1408ρ (gcm3)

(c)

LVB

30

40

50

60

70

80

f c0 (

MPa

)

060 065 070 075 080055ρ (gcm3)

(d)


R2 = 070

PSB

40

60

80

100

120

140

f c0 (

MPa

)

10000 12000 14000 16000 18000 20000 22000 240008000Ec0 (MPa)


MeanR005

fc0 = 2823 + 0006Ec0

(a)

LVB

30

40

50

60

70

80

90

f c0 (

MPa

)

9000 10000 11000 12000 13000 14000 15000 16000 170008000Ec0 (MPa)


MeanR005

R2 = 044fc0 = 21932 + 0003Ec0

(b)

Figure 7 Continued


PSB

40

60

80

100

120

140

160f c

0 (M

Pa)

09 10 11 12 13 14 1508ρ (gcm3)


MeanR005

R2 = 087fc0 = ndash55799 + 130327ρ

(c)

LVB

30

40

50

60

70

80

90

f c0 (

MPa

)

060 063 066 069 072 075 078057ρ (gcm3)


MeanR005

R2 = 075fc0 = ndash62598 + 182512ρ

(d)










4 Conclusions





Nomenclature













to the grain

Data Availability




Acknowledgments


References




























PSB

40

60

80

100

120

140

160f c

0 (M

Pa)

7500 10000 12500 15000 17500 20000 22500 250005000Ec0 (MPa)

(a)

LVB

30

40

50

60

70

80

90

f c0 (

MPa

)

10000 12000 14000 160008000Ec0 (MPa)

(b)

PSB

40

60

80

100

120

140

160

f c0 (

MPa

)

09 10 11 12 13 1408ρ (gcm3)

(c)

LVB

30

40

50

60

70

80

f c0 (

MPa

)

060 065 070 075 080055ρ (gcm3)

(d)


R2 = 070

PSB

40

60

80

100

120

140

f c0 (

MPa

)

10000 12000 14000 16000 18000 20000 22000 240008000Ec0 (MPa)


MeanR005

fc0 = 2823 + 0006Ec0

(a)

LVB

30

40

50

60

70

80

90

f c0 (

MPa

)

9000 10000 11000 12000 13000 14000 15000 16000 170008000Ec0 (MPa)


MeanR005

R2 = 044fc0 = 21932 + 0003Ec0

(b)

Figure 7 Continued


PSB

40

60

80

100

120

140

160f c

0 (M

Pa)

09 10 11 12 13 14 1508ρ (gcm3)


MeanR005

R2 = 087fc0 = ndash55799 + 130327ρ

(c)

LVB

30

40

50

60

70

80

90

f c0 (

MPa

)

060 063 066 069 072 075 078057ρ (gcm3)


MeanR005

R2 = 075fc0 = ndash62598 + 182512ρ

(d)










4 Conclusions





Nomenclature













to the grain

Data Availability




Acknowledgments


References




























PSB

40

60

80

100

120

140

160f c

0 (M

Pa)

09 10 11 12 13 14 1508ρ (gcm3)


MeanR005

R2 = 087fc0 = ndash55799 + 130327ρ

(c)

LVB

30

40

50

60

70

80

90

f c0 (

MPa

)

060 063 066 069 072 075 078057ρ (gcm3)


MeanR005

R2 = 075fc0 = ndash62598 + 182512ρ

(d)










4 Conclusions





Nomenclature













to the grain

Data Availability




Acknowledgments


References





























4 Conclusions





Nomenclature













to the grain

Data Availability




Acknowledgments


References


















































Documents

MechanicalPropertiesandStrengthGradingofEngineered ...ASTM D143-14 [19] Tension Parallel to grain 80 1 60 95 63 95 60 25 375 5 R444 9.5 Perpendicular to grain 80 1 63 50 13 6 25 50