Construction and Building Materials 160 (2018) 365–375

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Construction and Building Materials

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Ultimate bending capacity evaluation of laminated bamboo lumberbeams

https://doi.org/10.1016/j.conbuildmat.2017.11.0580950-0618/Crown Copyright � 2017 Published by Elsevier Ltd. All rights reserved.

⇑ Corresponding authors at: College of Civil Engineering, Nanjing ForestryUniversity, Nanjing 210037, China (H. Li).

E-mail addresses: haitao1116@njfu.edu.cn (H. Li), andrew.deeks@ucd.ie(A.J. Deeks).

Haitao Li a,b,⇑, Gang Wub, Qisheng Zhang a, Andrew John Deeks c,⇑, Jingwen Su d

aCollege of Civil Engineering, Nanjing Forestry University, Nanjing 210037, ChinabCollege of Civil Engineering, Southeast University, Nanjing 210096, ChinacCollege of Engineering and Architecture, University College Dublin, Dublin, IrelanddNanjing Technical Vocational College, Nanjing 210019, China

h i g h l i g h t s

� How the internal joints influence the bending direction was discussed.� The simplified strain-stress relationship was proposed.� The calculation approaches for the ultimate bending moment are proposed for three bending failure modes.

a r t i c l e i n f o

Article history:Received 10 February 2017Received in revised form 15 October 2017Accepted 14 November 2017

Keywords:Laminated bambooTangential bending directionRadial bending directionBending momentDeflection

a b s t r a c t

In order to evaluate the bending capacity of laminated bamboo lumber (LBL) beams, material perfor-mance tests and beam tests have been carried out. A strain-stress relationship is proposed based on com-pression and tensile tests conducted parallel to the grain. Two failure modes are identified based on thelocations of cracks in the beam specimens. Direction of bending and the location of internal joints areshown to influence the mechanical properties of LBL beams. Internal joints have more influence on spec-imens under tangential bending (where the culms are bent across their width) than that under radialbending (where the culms are bent across their thickness). Irrespective of the bending direction, thestrain across the cross-section of the laminated bamboo beam is shown to be linear throughout the testprocess, following standard beam theory. Based on this theory and the proposed simplified strain–stressrelationship for the beam, calculation approaches for the ultimate bending moment and ultimate bendingdeflection are proposed for three bending failure modes which give a good agreement with the testresults.

Crown Copyright � 2017 Published by Elsevier Ltd. All rights reserved.

1. Introduction

A relatively new type of engineered bamboo [1–8] buildingmaterial formed by laminating the thin flat bamboo culms togetherwith adhesive, known as laminated bamboo lumber (LBL), has beenattracting more and more attention from researchers [9–34]. Themechanical properties of laminated bamboo compare favorablywith those of common wood, and so laminated bamboo rectangu-lar structural members are competitive with commonly usedbuilding materials, whilst also having renewable characteristics[10–15]. Laminated bamboo lumber columns [16–22] and the

effects that the layered structure, bamboo species, oil treatment,and glue type on the mechanical properties of laminated bambooboarding have been investigated in literature [23–28].

Some researchers also have studied the bending performance oflaminated bamboo lumber. Lee et al. [29] examined the effect ofglue spread rate and moisture content on the bending propertiesof 24 laboratory-manufactured LBL beams. Wei et al. [30] foundthat the cross-sectional stiffness was the control condition fordesign load after examining the failure of laminated bamboobeams in detail. In order to look at the effect of orientation of thelaminate layers on the strength, Verma and Charier [14] performeda number of bending tests on specimens of layered laminate bam-boo composite (LLBC) with a cross-section of 16 mm � 10 mm. Yehand Lin [31] examined the effect of growth height on bendingstrength of LBL, and tested both un-jointed and jointed specimenswith the cross-section of 30 mm � 30 mm and the length of

366 H. Li et al. / Construction and Building Materials 160 (2018) 365–375

1000 mm. Considering the influencing factors of shear span ratioand height to width ratio, Li et al. [32,33] have studied the bendingperformance of laminated bamboo lumber beam considering thesize effect and shear span ratio. Bhavna et al. [15] have performedtests on beams under two bending directions, and found that whileachieving similar maximum loads, the flatwise orientation had anincreased modulus of elasticity with a gain of approximately 18%over the edgewise orientation. Sinha et al. [34] evaluated the lam-inated bamboo lumber (LBL) and bamboo glulam beams (BGBs)’spotential application as a structural material. They found that thereis potential to use LBL in framing applications. However, certainissues need to be addressed and investigated before there will bewidespread acceptance of LBL and BGB in the construction market-place. As a contribution to this process, this paper will investigatehow the bending direction and internal joints influence the bend-ing properties of LBL beams. In addition, an approach to calculatingthe ultimate bending capacity of laminated bamboo lumber beamswill be evaluated.

2. Materials performance

2.1. Manufacturing process

The source Moso bamboo (Phyllostachys pubescens, fromFujian province) was harvested at the age of 3–6 years. Bamboostrips from the lower growth portions of 2005 mm tall culms wereselected. The culms were then split into 22–24 mm wide strips,and the outer skin (epidermal) and inner cavity layer (pith periph-eral) were removed using a planer. All the culm strips were thendried and charred. Final thicknesses of 7 mm were obtained forthe flat strips from the lower growth portions, and the final stripwidths were of 21 mm. Phenol glue was chosen with the densityof 300 g/m2. Finally the strips were transformed into laminatedbamboo lumbers. The manufacturing process can be seen fromFig. 1.

2.2. Tensile and compressive tests parallel to grain

In order to investigate the tensile performance and compressiveperformance parallel to grain of bamboo, 30 specimens weredesigned [35] and tested correspondingly. Detailed size informa-tion for the specimens can be seen from Fig. 2.

Table 1 shows the tensile and compressive test results. Here At

and Ac are the real measured cross-section areas for tensile speci-mens and compressive specimens respectively; Ftu and Fcu are theultimate tensile load and compressive load respectively; f tu and f cuare the ultimate tensile strength and compressive strength respec-tively; the elastic modulus values Et and Ec are obtained from ten-sile tests and compressive tests respectively, as are the Poisson’sratio values tt and tc. Besides the values mentioned above, themean values, the values for standard deviation (SDV), the values

(a) Bamboo tube (b) Bamboo strip (

Fig. 1. Manufactu

for coefficient of variation (SOV) and the characteristic values(CHV) were calculated.

According to these 30 tensile specimens, the mean ultimatestrength is 84.53 MPa with a standard deviation of 9.59 MPa, giv-ing a CHV (expected to be exceeded by 95% of specimens) of68.77 MPa. Similarly, the mean Et is 7007 MPa with a standarddeviation of 549 MPa and the mean tt is 0.27 with a standard devi-ation of 0.03. The characteristic values for Et and tt are 6104 MPaand 0.23 respectively. The average ultimate compressive strengthof 30 specimens is 68.8 MPa, with a low standard deviation of2.49 MPa, giving a CHV of 64.8 MPa. The mean Ec is 9393 MPa witha standard deviation of 435.3 MPa and a CHV of 8677 MPa whilethe mean tc is 0.29 with a standard deviation of 0.01 and a CHVof 0.27. The moisture content of the specimens is 8.76%.

2.3. Strain stress relationship

Fig. 3 plots the strain stress relationship for the laminated bam-boo lumbers under tensile and compressive condition parallel tograin. Based on the test results (Fig. 3(a)), the strain stress relation-ship model shown in Fig. 3(b) was proposed. The mean values forecy and ec0 are about 4150 me and 22749 me respectively.

The proposed model can be expressed as the followingequations,

r ¼

Ete ð0 6 e 6 etuÞEce ð�ecy 6 �e 6 0Þrcy þ kcepEcðe� ecyÞ ð�ec0 6 �e 6 �ecyÞrc0 ð�ecu 6 �e 6 �ec0Þ

8>>><>>>:

ð1Þ

kcep ¼ rc0 � rcy

ðec0 � ecyÞEc¼ rep � rcy

ðeep � ecyÞEcð2Þ

Here r is the stress value of the laminated bamboo lumber; Et andEc are the modulus of elasticity under tensile condition and com-pressive condition respectively; e is the strain value of the lami-nated bamboo lumber; ecy is the strain for the yield point; etu isthe ultimate tensile strain value; eep is the elastic-to-plastic strainvalue;rcy is the compression yield stress value; rep is the elastic-to-plastic stress value; kcep is the ratio of the elastic-plastic slope;ec0 is the compression peak strain value; rc0 is the compressionpeak stress value; and ecu is the ultimate compression strain value.

3. Experimental study on beams

3.1. Design beam specimens

As can be seen from Table 2, 4 groups of LBL beams (20 speci-mens in total) were designed with the cross-section of 56 mm �110 mm. Fig. 4(a) and (b) plot the radial bending direction (RBD)and tangential bending direction (TBD) respectively. In order tomake longer structural members, internal joints as shown inFig. 5 were always chosen for connecting the bamboo strips. The

c) Laminated bamboo layer (d) LBL

ring process.

100mm 95mm 95mm63mm 100mm

15mm

21mm

R905 R905

5mm

50mm50mm

200mm

(a) Tensile specimen (b) Compressive specimen

Fig. 2. Tensile specimen and compressive specimen.

Table 1Tensile and compressive test results.

Specimen At /mm2 Ftu /kN ftu /MPa Et /MPa tt Specimen Ac /mm2 Fcu /kN fcu /MPa Ec /MPa tc

TS-1 117.7 11.1 94.03 7450 0.25 CS-1 2518.5 170.6 67.7 10022 0.33TS-2 112.6 9.18 81.54 6337 0.27 CS-2 2513.5 173.2 68.9 9589 0.30TS-3 115.8 12.3 106.1 6745 0.28 CS-3 2521.5 167.3 66.3 9281 0.29TS-4 114.7 9.26 80.78 7657 0.32 CS-4 2516.5 169.2 67.2 9011 0.28TS-5 119.0 10.4 87.48 6733 0.27 CS-5 2517.5 169.4 67.3 9683 0.29TS-6 121.6 11.1 91.45 6449 0.25 CS-6 2531.6 183.6 72.5 10006 0.28TS-7 117.2 9.0 76.77 7260 0.27 CS-7 2516.0 169.2 67.2 9110 0.28TS-8 112.3 7.48 66.61 6919 0.35 CS-8 2519.0 184.2 73.1 10075 0.30TS-9 116.5 11.2 95.77 7455 0.30 CS-9 2515.5 168.5 67.0 8805 0.31TS-10 113.5 9.67 85.19 7074 0.19 CS-10 2514.5 178.0 70.8 9326 0.28TS-11 107.0 9.47 88.54 6856 0.26 CS-11 2512 174.5 69.5 9880 0.29TS-12 118.0 9.72 82.34 6949 0.22 CS-12 2527.6 167.6 66.3 8879 0.28TS-13 113.4 10.9 96.55 8062 0.26 CS-13 2500.0 186.7 74.7 9023 0.30TS-14 111.6 8.23 73.75 5751 0.27 CS-14 2505.5 176.2 70.3 9099 0.28TS-15 114.7 8.8 76.71 7272 0.27 CS-15 2517.5 180.1 71.5 10112 0.30TS-16 117.1 10.8 92.21 6772 0.28 CS-16 2509.0 173.5 69.1 8996 0.28TS-17 105.4 8.23 78.06 6063 0.30 CS-17 2503.5 161.8 64.6 9856 0.28TS-18 112.1 10.1 90.11 6580 0.27 CS-18 2526.6 171.7 68.0 9159 0.30TS-19 111.4 9.95 89.35 6877 0.26 CS-19 2517.0 176.7 70.2 9230 0.29TS-20 118.0 8.66 73.32 7693 0.24 CS-20 2488.0 166.5 66.9 9284 0.31TS-21 118.0 10.7 90.6 7490 0.28 CS-21 2513.5 183.1 72.8 9376 0.29TS-22 106.0 9.44 88.99 6329 0.28 CS-22 2516.0 168.0 66.8 9506 0.29TS-23 105.0 8.21 78.21 6714 0.27 CS-23 2512.5 172.6 68.7 9081 0.28TS-24 110.9 9.57 86.27 8014 0.29 CS-24 2517.5 167.4 66.5 9246 0.29TS-25 114.5 7.05 61.52 6834 0.26 CS-25 2533.6 170.1 67.1 8537 0.26TS-26 113.0 10.1 89.52 7571 0.28 CS-26 2539.1 173.4 68.3 10053 0.32TS-27 115.9 10.4 89.51 7232 0.30 CS-27 2509.5 164.0 65.3 8917 0.29TS-28 117.7 10.4 87.97 7428 0.28 CS-28 2507.0 176.1 70.2 9169 0.28TS-29 110.2 7.75 70.31 6592 0.28 CS-29 2517.0 180.1 71.6 9676 0.30TS-30 117.2 10.1 86.31 7057 0.30 CS-30 2530.6 173.4 68.5 9820 0.30

Mean 9.64 84.53 7007 0.27 Mean 173.2 68.8 9393 0.29SDV 1.23 9.59 549.2 0.03 SDV 6.25 2.49 435.3 0.01COV 0.13 0.113 0.078 0.11 COV 0.036 0.04 0.046 0.05CHV 7.62 68.77 6104 0.23 CHV 162.9 64.8 8677 0.27

H. Li et al. / Construction and Building Materials 160 (2018) 365–375 367

distance between the two internal joints along the length of thespecimens is 250 mm for the beams tested in this paper. GroupNNCH without internal joints (Fig. 5) and Group NH with internaljoints (Fig. 5) contain 4 identical specimens under radial bendingdirection (RBD) for each. Group NNCV without internal joints(Fig. 5) and Group NV with internal joints (Fig. 5) contain 6 identi-cal specimens under tangential bending direction (TBD)respectively.

3.2. Beam test methods

The four point bending test setup was chosen for the beamspecimens, as shown in Fig. 6. The mid-span deflection and dis-placement of the loading points were measured by three Laser Dis-

placement Sensors (LDS), while the displacements of the twosupports were measured by two strain beam displacement sensors(SBDS). The beams were strain gauged longitudinally at the middlecross section, with five strain gauges pasted on one side face ateven spacing through the depth, and one strain gauge pasted oneach of the bottom and the top faces, as shown in Fig. 6a. The beamtest was performed using a microcomputer-controlled electro-hydraulic servo universal testing machine (Fig. 6b) with a capacityof 300 kN. A TDS Data Acquisition System was used for the tests.

3.3. Failure modes and mechanism analysis

Based on the final failure photos for 20 beam specimens, twotypical failure modes can be classified, as shown in Figs. 7and 8.

tu

tu

cy

cy

c0

c0

cu ---

--

tE

cEep-

ep-

(a) Test results (b) Proposed model

Fig. 3. Strain stress relationship.

Table 2Designed specimens.

Group Width/mm Height/mm Length/mm Span/mm Number Bending direction

NNCH 56 110 1950 1800 4 RBDNH 56 110 1950 1800 4 RBDNNCV 56 110 1950 1800 6 TBDNV 56 110 1950 1800 6 TBD

(a) Radial bending direction (b) Tangential bending direction

Fig. 4. Bending direction.

368 H. Li et al. / Construction and Building Materials 160 (2018) 365–375

The characteristic for failure mode 1 (Fig. 7) is that one maincrack appeared along the neutral axis and the beam split intotwo main parts. Failure mode 1 occurred in three specimens:NV-3, NV-4 and NNCV-5. This failure is a shear failure of the glue

60°200 250 2

(a) Internal joints (b) Internal joints di

Fig. 5. Internal joint distribution in the

along the neutral axis, which could not support the shear stresscaused by the ‘shear flow’ phenomenon. This is a quality controlproblem in the construction of the specimens, perhaps due toinsufficient compression being applied while the glue dried. Allthree specimens that failed in this way were loaded in the tangen-tial bending direction (TBD), with two having internal joints andone having no internal joints.

The remaining 17 specimens failed in failure mode 2 (Fig. 8).These specimens fractured in tension at the bottom surface nearthe mid-span, and split up through the depth of the beam, withno evident failure occurring on the compressed face at the top ofthe specimen. Natural bamboo joints and internal joints near thebottom surface, as the weak points under tension, are the main ini-tiators of failure mode 2. All these specimens behaved elastically atthe start of loading and then elasto-plastically (Fig. 9), with a finalsudden brittle tensile failure.

As can be seen from Fig. 8, more fractures appeared for the spec-imens under the radial bending direction (RBD), as these speci-mens have more bamboo strips layers. Considering the internal

50 250 250 250 250 250

1950

7

stribution in laminated bamboo layer (unit: mm)

laminated bamboo layers (Fig. 1c).

Load sensorActuator Distributing girder

LDSStrain gauge

SBDS

a a aL

SBDS

(a) Test scheme (b) test photos

Fig. 6. Beam test.

(a) Failure photo for NV-4 (b) Failure photo for NNCV-5

Fig. 7. Failure mode 1.

H. Li et al. / Construction and Building Materials 160 (2018) 365–375 369

joints, the specimen from group NH has more fractured layers thanthat from group NNCH, and similarly the specimen from group NVhas more fractured layers than that from group NNCV. This demon-strates that internal joints are one of the main initiators of cracksunder ultimate loading conditions.

3.4. Load-displacement response

Fig. 9 plots the load-displacement curves for the four groups ofbeam specimens. The three specimens for failure mode 1 are indi-cated in the figures. As can be seen from these figures, the loadvalue for the initial yield point is about 16 kN. The ultimate loadvalues for NNCV-5 and NV-3 are 12.13 kN and 15.12 kN respec-tively, which are smaller than 16 kN, indicating that these twospecimens behaved elastically from the beginning of loading untilthe final brittle split. However, the maximum load for NV-4 is25.28 kN, which is bigger than 16 kN (Fig. 9(d)). Even though thefinal failure mode for NV-4 is different from other 17 specimens,its load-displacement response is similar to the specimens for fail-ure mode 2, which behaved elastically before the yield point, fol-lowed by non-linear softening, and a brittle failure. This indicatesthat the shear strength of the glue in this specimen was almoststrong enough to sustain the shear flow through to failure of thebamboo.

These figures demonstrate consistency in the initial elasticstage of loading for all four groups of specimens, irrespective ofwhich direction they are loaded or whether they have internaljoints. However, the load-displacement responses for the speci-mens from the group NNCH and the group NV are not as consistentas those for the specimens from the group NH and the group NNCVafter yield. There is no obvious reason for this. It is also interestingthat group NNCV gives best consistency for both the load-displacement responses and the ultimate load, but again there isno obvious reason for this superior performance.

3.5. Test results

The test results for the beam specimens are presented in Table 3.Mt and Mc are the test value and the calculation value of ultimatebending moment for the beam, respectively; wt and wc are the testvalue and the calculation value of ultimate middle bending deflec-tions, respectively; Error1 (%) is calculated as 100 � (Mt �Mc)/Mt,and Error2 (%) is calculated as 100 � (wt � wc)/wt. Fmaxis the max-imum bending load; fm is the bending strength; the modulus ofelasticity (MOE) and the bending strength of the beam were calcu-lated by using the following Eqs. (3) and (4), respectively

MOE ¼ aDF48IDw

ð3L2 � 4a2Þ ð3Þ

fm ¼ 3Fmaxa

bh2 ð4Þ

Here a is the distance between the loading support and the loadingpoints; DF is the load increment in the elastic stage; Dw is thedeflection of the middle span point under DF; L is the span of thebeam; I is the moment of inertia of the beam; fm is the bendingstrength of the beam;Fmax is the maximum bending load; b is thewidth; and h is the height of the beam cross-section.

As can be seen from Table 3, the presence of internal jointsincreased the stiffness (as measured by the MOE) and reducedthe failure load for both bending directions. The increased stiffnessmay be attributed to the additional glue along the bending axisenhancing the stiffness, while the reduced failure load may bedue to the internal joints acting as crack initiators.

These effects were more prominent in the transverse bendingdirection, where each individual internal joint spanned a greaterdepth across the direction of bending. In this case the reductionin the characteristic value of the failure load was almost 20% andthe increase in the mean MOE was 12.5%.

(a) Side surface for NNCH-2 (b) Bottom surface for NNCH-2

(c) Side surface for NH-1 (d) Bottom surface for NH-1

(e) Side surface for NV-2 (f) Bottom surface for NV-2

(g) Side surface for NNCV-4 (h) Bottom surface for NNCV-4

Fig. 8. Failure mode 2.

370 H. Li et al. / Construction and Building Materials 160 (2018) 365–375

Although for loading in the radial direction internal joints theMOE increased by about 5% and the mean failure load reducedby slightly less than 2%, from a design point of view these changesare less significant. These tests suggest that the effect of internaljoints is far more significant for loading in the tangential bendingdirection.

3.6. Strain analysis for the mid-span cross-section

Fig. 10 plots the typical strain profile through the loading for themid-span cross-section of the beams. No matter which directionthe bending occurs or whether or not internal joints are present,all the strain profiles show the same form, as shown in Fig. 10.The strain across the cross-section of the laminated bamboo beamis basically linear throughout the loading process, following theassumptions of standard beam theory. However, during the load-ing process, the neutral axis moves downwards from the centreof the beam, particularly during the latter part of the process,which can be seen clearly from the figures. This indicates thatthe fibres at the top of the beam have yielded in compression areundergoing plastic deformation.

Fig. 11 plots the load against the top and bottom strain at themid-span cross-section for four typical specimens. The slope valuesfor both the elastic stage under tension and compression are equalto each, other as shown by the marked black line. These figuresshow that the initial elastic moduli for both compression and ten-sion are equal.

3.7. Stress-strain model for laminated bamboo lumber beam

Although nonlinear behaviour appeared in the tension zone forsome specimens, as shown in Fig. 11, the amount of non-linearityin tension was far less than that which occurred in compression,and consequently it is not considered in the beam stress-strainmodel shown in Fig. 3a. As the elastic moduli for compressionand tension of the LBL beam were equal as proved in Fig. 11, thestrain-stress model for LBL beams can be shown as in Fig. 12 whichcan also be expressed through the following equations.

r ¼Ee ð�ecy 6 e 6 etuÞrcy þ kcepEðe� ecyÞ ð�ec0 6 �e 6 �ecyÞrc0 ð�ecu 6 �e 6 �ec0Þ

8><>: ð5Þ

Here E is the modulus of elasticity, and the other parameters havethe same meaning as in Eqs. (1) and (2).

4. Calculation formula for the ultimate state

Based on the strain-stress relationship for laminated bamboo,three possible failure modes for laminated bamboo lumber beamscan be identified. Firstly, all bamboo fibres in compressive zonemay are still be in the elastic stage when the beam fails (Mode I).Secondly, some bamboo fibres in compressive zone may be inthe plastic-elastic stage and some may be in the elastic stagewhen the beam fails (Mode II). Thirdly, some bamboo fibres in

(a) Group NNCH (b) Group NH

(c) Group NNCV (d) Group NV

Fig. 9. Load-displacement responses for beam specimens.

H. Li et al. / Construction and Building Materials 160 (2018) 365–375 371

compressive zone may be in the fully plastic stage, some in theelastic-plastic stage and some in the elastic stage when the beamfails (Mode III).

4.1. Ultimate bending moment

4.1.1. Mode IAll the bamboo fibres in both the compressive zone and the ten-

sile zone are in the elastic stage when the beam fails in Mode I.Although test specimens NNCV-5 and NV-3 were in this state whenthey failed, they do not belong to this mode as they failed throughhorizontal shear failure rather than through tensile failure at theextreme tensile fibre.

Fig. 13 plots the strain-stress distribution at the ultimate failurestate for Mode I. M is the bending moment of the beam; rce is thecompressive elastic stress value; rt is the tensile stress value; et isthe tensile strain value; ece is the compressive elastic strain value;h is the cross-section height of the beam; a is the height coefficientfor the tension zone in the beam cross-section; and b is the heightcoefficient for the elastic compressive zone in the beam cross-section. Based on the plane-section assumption, the strain andthe curvature can be expressed as the following

e ¼ �yd2wdx2

¼ ky ð6Þ

Here k is the curvature and y is the distance between the strainpoint and neutral axis.

The following equations can be obtained from Fig. 13.

a ¼ etece þ et

ð7Þ

b ¼ eceece þ et

ð8Þ

The ultimate bending moment for the beam can then be calcu-lated by the follow equation:

M ¼ bZ ah

�bhrðyÞydy ð9Þ

Here b is the width of the beam cross-section.Based on the above equations, the ultimate bending moment for

the LBL beams can be failing under Mode I can be obtained asfollows:

M ¼ bh2Eeta3 þ b3

3að10Þ

4.1.2. Mode IIThe compressive zone for Mode II can be divided into two parts,

an elastic area and an elastic-plastic area. All the test specimensthat failed in bending rather than horizontal shear failed in thismode.

Fig. 14 plots the strain-stress distribution at the ultimate failurestate for Mode II. c is the height coefficient for the elastic-plasticcompressive zone in the beam cross-section. Based on the plane-section assumption, the height coefficients a, b and c can beexpressed as follows:

a ¼ etet þ eep

ð11Þ

b ¼ ecyet þ eep

ð12Þ

Table 3Results for beams.

Specimen Fmax/kN fm/MPa wt /mm MOE /MPa Mode Mt/kN.m Mc/kN.m Error1 % wc /mm Error2 %

NNCH-1 29.97 79.61 69.0 8936 2 8.99 8.27 �8.00 65.6 �5.00NNCH-2 34.95 92.84 70.5 10138 2 10.5 9.98 �4.86 71.5 1.35NNCH-3 31.74 84.32 68.3 9450 2 9.52 8.73 �8.33 67.9 �0.63NNCH-4 35.46 94.2 81.0 9387 2 10.6 9.35 �12.1 83.3 2.88

Mean 33.03 87.74 72.2 9478 – – – – – –SDV 2.62 6.97 5.94 496 – – – – – –COV 0.079 0.079 0.082 0.052 – – – – – –CHV 28.72 76.29 62.43 8661 – – – – – –

NNCV-1 31.48 83.62 68.6 8146 2 9.44 8.78 �7.06 61.0 �11.1NNCV-2 31.74 84.32 72.3 8764 2 9.52 8.94 �6.09 62.4 �13.7NNCV-3 32.22 85.59 71.2 9008 2 9.67 8.87 �8.22 72.3 1.52NNCV-4 31.99 84.98 71.3 8476 2 9.6 10.2 5.83 64.2 �9.94NNCV-5 12.13 – 24.7 – 1 – – – – –NNCV-6 33.97 90.24 75.9 9253 2 10.2 9.41 �7.67 73.1 �3.71

Mean 32.28 85.75 71.9 8730 – – – – – –SDV 0.984 2.62 2.64 435.2 – – – – – –COV 0.030 0.030 0.037 0.050 – – – – – –CHV 30.66 81.45 67.56 8014 – – – – – –

NH-1 32.47 86.25 64.9 10107 2 9.74 9.53 �2.16 63.3 �2.52NH-2 28.98 76.98 56.9 9736 2 8.69 8.12 �6.66 63.0 10.79NH-3 33.72 89.57 67.3 10052 2 10.1 10.20 1.20 68.8 2.25NH-4 34.45 91.51 70.7 10142 2 10.3 8.93 �13.6 70.4 �0.38

Mean 32.41 86.08 64.9 10009 – – – – – –SDV 2.43 6.44 5.87 185.9 – – – – – –COV 0.075 0.075 0.090 0.019 – – – – – –CHV 28.42 75.48 55.24 9703 – – – – – –

NV-1 27.74 73.69 52.4 9757 2 8.32 7.81 �6.16 53.1 1.25NV-2 29.73 78.98 61.9 9433 2 8.92 8.74 �2.04 66.2 6.93NV-3 15.12 – 25.6 – 1 – – – – –NV-4 25.28 67.15 51.6 9494 1 – – – – –NV-5 30.98 82.3 59.1 10331 2 9.29 8.97 �3.46 55.4 �6.21NV-6 31.73 84.29 62.6 10088 2 9.52 9.48 �0.39 64.7 3.32

Mean 29.09 77.28 57.52 9821 – – – – – –SDV 2.61 6.94 5.21 385 – – – – – –COV 0.090 0.090 0.091 0.039 – – – – – –CHV 24.80 65.87 48.94 9187 – – – – – –

Note: Considering the failure mode, specimens NV-3 and NNCV-5 weren’t used when calculating the mean, SDV, COV, CHV values.

372 H. Li et al. / Construction and Building Materials 160 (2018) 365–375

c ¼ eep � ecyet þ eep

ð13Þ

The ultimate bending moment for the beam can be calculatedby the following equation:

M ¼ bZ ah

�ðbhþchÞrðyÞydy ð14Þ

Based on the equations above, the ultimate bending moment forthe LBL beams failing in Mode II can be obtained as follows:

M ¼ bh2

6aEetð2a3 þ 2b3 � 6b2c� 3bc2 þ 12kcepb2cþ 9bkcepc2

þ 2kcepc3Þ ð15Þ

4.1.3. Mode IIIThe compressive zone for Mode III can be divided into three

parts, an elastic area, an elastic-plastic area and a plastic area. Nonespecimens tested in this paper failed in this mode, but Mode III willoccur in a certain situations. As before, the strain-stress relation-ship for the laminated bamboo is expressed by Eqs. (2) and (5).

Fig. 15 plots the strain-stress distribution at the ultimate failurestate for Mode III. d is the height coefficient for the plastic compres-sion zone in the beam cross-section. Based on the plane-sectionassumption, the height coefficients a, b, c and d can be expressedas follows:

a ¼ etet þ ecu

ð16Þ

b ¼ ecyet þ ecu

ð17Þ

c ¼ eep � ecyet þ ecu

ð18Þ

d ¼ ecu � eepet þ ecu

ð19Þ

The ultimate bending moment for the beam can be calculatedby the following equation:

M ¼ bZ ah

�ðbhþchÞrðyÞydyþ dbhrcu bhþ chþ 1

2dh

� �ð20Þ

Based on the equations above, the ultimate bending moment forthe LBL beams failing in Mode III can be obtained as follows:

M ¼ bh2

6aEetð2a3 þ 2b3 � 6b2c� 3bc2 þ 12kcepb2cþ 9bkcepc2

þ 2kcepc3Þ þ dbh2rcu bþ cþ 12d

� �ð21Þ

(a) Specimen NNCH-1 (b) Specimen NH-1

(c) Specimen NNCV-1 (d) Specimen NV-1

Fig. 10. Typical strain profile development for the mid-span cross-section.

(a) Specimen NNCH-2 (b) Specimen NH-1

(c) Specimen NNCV-1 (d) Specimen NV-1

Fig. 11. Typical load-strain curves for the mid-span cross-section.

H. Li et al. / Construction and Building Materials 160 (2018) 365–375 373

tu

tu

cy

cy

c0

c0

cu ---

--

tE

cEep-

ep-

Fig. 12. Strain-stress model of laminated bamboo lumber under bending.

ce

t t

ce

hM

y

0x

Elastic compressivearea

Elastic tensile area

Neutral axis

h

h

Fig. 13. Strain-stress distribution at the ultimate failure state for Mode I.

ep

cy

t t

cy

ep

Elastic compressive area

Elastic tensile area

Elastic-plasticcompressive area

hM

y

0Neutral axis

x

h

h

h

Fig. 14. Strain-stress distribution at the ultimate failure state for Mode II.

ep

cy

tu tu

cy

cu

hM

y

0x

cu

ep

Plastic compressive area

Elastic compressive area

Elastic tensile area

Elastic-plasticcompressive area

Neutral axish

h

hh

Fig. 15. Strain-stress distribution at the ultimate failure state for Mode III.

374 H. Li et al. / Construction and Building Materials 160 (2018) 365–375

4.2. Ultimate bending deflection

For each of the three failure modes the bending deflection atultimate load can be calculated by applying the principles of struc-

tural mechanics, calculating the curvature at each cross-sectionfrom the bending moment and the stress-strain relationship, inte-grating over the length of the beam and applying the boundaryconditions.

The comparison between the test results and calculation resultscan be seen in Table 3. As this table showed, the calculations givegood agreement with the test results.

5. Conclusions

In order to evaluate the bending capacity for laminated bamboolumber beams, both material performance tests and beam testshave been carried out. Based on the experimental results and the-oretical analysis of the specimens, the following conclusions can bedrawn.

(1) Based on the material performance test results, the meanultimate tensile strength is 84.53 MPa, giving a CHV(expected to be exceeded by 95% of specimens) of 68.77MPa and the mean tensile modulus of elasticity is 7007MPa, giving a characteristic value (CHV) of 104 MPa. Themean tensile Position’s ratio is 0.27, giving a CHV of 0.23.

(2) The average ultimate compressive strength of 30 specimensis 68.8 MPa, giving a CHV of 64.8 MPa. The mean compres-sive modulus of elasticity is 9393 MPa giving a CHV of8677 MPa while the mean compressive Position’s ratio is0.29 giving a CHV of 0.27.

(3) A simplified tri-linear strain-stress relationship was pro-posed based on the compression and tensile tests parallelto the grain.

(4) Two failure modes can be identified from the location of thecracks occurring in the test beams. In one mode a horizontalcrack appeared along the neutral axis and the beam splithorizontally into two parts (a horizontal shear failure), andin the other failure mode the specimens failed at the bottomsurface near the mid-span, and split up through the depth ofthe beam with no evident failure occurring on the com-pressed face at the top of the specimen near the mid-span(a tensile bending failure).

(5) Bending direction and the presence of internal joints havesome influence on the mechanical properties of the LBLbeams. Internal joints have more influence on specimensunder tangential bending (where the culms are bent acrosstheir width) than those under radial bending (where theculms are bent across their thickness).

(6) Irrespective of the bending directions, the strain across thecross-section of the laminated bamboo beam is linearthroughout the test process, following standard beam the-ory. Based on the theory and the proposed simplifiedstrain-stress relationship for the beam, the calculation for-mula for the ultimate bending moment and an approachfor calculating the ultimate bending deflections were pro-posed for three bending failure modes which give goodagreement with the test results.

Acknowledgments

The material presented in this paper is based upon work sup-ported by the National Natural Science Foundation of China(51308301), the Natural Science Foundation of Jiang-su Province(No. BK20130978), the Postdoctoral Science Foundation of China(2015 M580382), Jiangsu Postdoctoral Science Foundation Project(1501037A), Open Fund Project from Key Laboratory of Concreteand Pre-stressed Concrete Structure of Ministry of Education

H. Li et al. / Construction and Building Materials 160 (2018) 365–375 375

(Southeast university) and a Project Funded by the Priority Aca-demic Program Development of Jiangsu Higher Education Institu-tions. Any opinions, findings, and conclusions orrecommendations expressed in this material are those of the wri-ter(s) and do not necessarily reflect the views of the foundations.The writers gratefully acknowledge Nian-qiang ZHOU, Zhen CAO,Zhongjin HAN, Yunfei Fu, Yulin Li and others from the Nanjing For-estry University for helping with the tests.

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