Juan Simón Obando Zapata

Characterization of Bamboo along its Culm for

the Production of Bamboo Laminated Beams

Dissertação de Mestrado

Dissertation presented to the Programa de Pós-Graduação em Engenharia Civil of the Departamento de Engenharia Civil, PUC-Rio as partial fulfillment of the requirements for the degree of Mestre em Engenharia Civil.

Advisor: Khosrow Ghavami

Rio de Janeiro April 2015

Juan Simón Obando Zapata

Characterization of Bamboo along its Culm for the Production of Bamboo Laminated Beams

Dissertationn presented to the Programa de Pós-Graduação em Engenharia Civil of the Departamento de Engenharia Civil do Centro Técnico Científico da PUC-Rio, as partial fulfillment of the requirements for the degree of Mestre.

Prof. Khosrow Ghavami Advisor

Departamento de Engenharia Civil – PUC-Rio

Prof. Omar Pandoli Departamento de Química – PUC-Rio

Prof. Fathi Aref Ibrahim Darwish Universidade Federal Fluminense

Prof. José Eugenio Leal Coordinator of the Centro Técnico Científico da PUC-Rio

Rio de Janeiro, April 10th, 2015.

All rights reserved.

Juan Simón Obando Zapata

Graduou-se em Engenharia Civil pela Universidad de Los Andes em 2012. Possui cursos na área de Gerenciamento de projetos da construção, 2011; Gestão da inovação em tecnologias da construção (Lean Manufacturing), 2011; e Administração de projetos de construção sustentável (Leed technologies) 2011.

Ficha Catalográfica

CDD: 624

Obando, Juan Simón Zapata

Characterization of bamboo along its culm for the production of bamboo laminated beams / Juan Simón Obando Zapata; Adviser: Dr. Khosrow Ghavami; – Rio de Janeiro: PUC, Departamento de Engenharia Civil, 2015.

84 f. il (color) ; 30 cm Dissertação (mestrado) – Pontifícia

Universidade Católica do Rio de Janeiro, Departamento de Engenharia Civil, 2015.

Inclui referências bibliográficas.

1. Engenharia Civil – Teses. 2. Bamboo. 3.

Laminate Glued Bamboo LGB. 4. Bamboo-Laminated Beam. 5. Bamboo structural characterization. 6. Non-Conventional Materials. I Ghavami, Khosrow. II Pontifícia Universidade Católica do Rio de Janeiro. Departamento de Engenharia Civil. III Título.

To mom and dad: The masterly architects and thorough promoters

of my wonderful immense human adventure

Acknowledgments

Several months have been spent for the preparation of this dissertation, with the contributions of many people by giving me the support and the encouragement I needed. For this reason, I would like to acknowledge a few who have helped me with this research.

First, I want to thank my professor, advisor and companion Khosrow Ghavami, for his guidance, support and advises throughout this study. I thank very much the PhD student João Krause for his willingness and collaboration since the beginning of this work and professor Jose Jaime Garcia for his precise comments. I want to thank Juan Ossa for his invaluable work, especially with corrections and editing of the dissertation.

My thanks are also to PUC-Rio staff for their hospitality and to CAPES for financial supports during my staying time in Brazil. I would like to give special thanks to lab technicians Victor, Adrian and Anderson from ITUC, Jose and Euclides from Civil Engineering laboratory and Messias from architecture workshop for their time and diligence in the development of this work.

I also want to thank to my brothers, Cesar and Daniel for their unconditional friendship, to Rhaissa for her constant support and motivation and to Erika for always making me feel at home.

Finally, I want to thank my beloved mom, the strongest being in the world, my dad the greatest partner, my family “the big treasure” especially the couple of inspiring Antonias, for always encouraging to dream and supporting me throughout.

Abstract

Zapata, Juan Simon Obando; Ghavami, Khosrow (Advisor); Characterization of bamboo along its culm for the production of bamboo laminated beams. Rio de Janeiro, 2015. 84 p. MSc. Dissertation. Departamento de Engenharia Civil, Pontifícia Universidade Católica do Rio de Janeiro.

Laminated bamboo was created to standardize the raw material in order to

increase its strength, control its shape and develop sustainable and innovative

structural elements. Bamboo is a Functionally Graded Material (FGM) due to the

progressive distribution of the fibers across its wall thickness. This research

presents the results of an experimental investigation series in which bamboo culm,

of Dendrocalamus giganteus, was divided into 6 segments of analysis. Three

divisions along its length, bottom, middle and top, and then two divisions across

its wall thickness, inner and outer. In the first series, the specimens of each

segment were tested separately to establish their tensile modulus of elasticity Et.

Six types of bamboo uniaxial-laminated beam specimens of 2.5 cm width, 5cm

height and 50 cm length were assembled with layers from each particular segment

of bamboo culm, using resin of mamona adhesive. Four point bending tests were

conducted on beam specimens to establish the bending modulus of elasticity Eb.

Experimental values of both specimen groups were compared to those of

theoretical values, applying solid mechanics theory. The results provide

information to improve the segment arrangement of bamboo-laminated beams

upon subjection to bending loads. Based on the results, it is also possible to

introduce equivalent values for the analysis of the mechanical properties of the

beams, using solid mechanics theory.

Keywords

Bamboo; Laminate Glue Bamboo (LGB); Laminated beam; Bamboo characterization; Non-conventional materials.

Resumo

Zapata, Juan Simon Obando; Ghavami, Khosrow. (Orientador). Caracterização do bambu ao longo do colmo para a produção de vigas de bambu laminado. Rio de Janeiro, 2015. 84 p. MSc. Dissertação de Mestrado. Departamento de Engenharia Civil, Pontifícia Universidade Católica do Rio de Janeiro. As lâminas de bambu foram criadas para padronização da matéria prima de

modo a aumentar sua resistência, controlar sua forma e desenvolver elementos

estruturais sustentáveis e inovadores. O bambu é um material gradualmente

funcional (FGM) devido a sua progressiva distribuição de fibras por toda a

espessura de sua parede. Esta pesquisa apresenta os resultados de uma série de

investigaçóes experimentais em que o colmo de bambu (Dendrocalamus

giganteus) foi dividido em 6 segmentos de análise. Três divisões ao longo do seu

comprimento, em sua porção baixa, média e alta, e, em seguida, duas divisões de

sua espessura, interior e exterior. Na primeira série, os espécimes de cada

segmento foram testados separadamente para estabelecer o seu módulo de

elasticidade à tração Et. Seis tipos de vigas de bambu uniaxial-laminados, de 2,5

cm de largura, altura 5 centímetros e 50 cm de comprimento, foram montadas com

camadas de cada segmento específico do colmo do bambu, utilizando resina

adesiva de mamona. Quatro ensaios de flexão pontual foram realizados em

amostras de viga para estabelecer o módulo de elasticidade em flexão, Eb. Os

valores experimentais de ambos os grupos de amostra foram comparados com os

valores teóricos, aplicando a teoria da mecânica dos sólidos. Os resultados

forneceram informações para melhorar o arranjo dos segmentos das vigas de

lâminas de bambu sujeitas a cargas de flexão. Baseado nos resultados, também é

possível introduzir valores equivalentes para análises das propriedades mecânicas

das vigas usando a teoria da mecânica de sólidos.

Palavras chave

Bambu; Laminate Glue Bamboo (LGB); viga laminada; caracterização do bambu; materiais não convencionais.

Table of contents

1 Introduction 14

1.1 Thesis objectives 16

2 Literature review 18

2.1. General introduction 18

2.1.1. Environmental context 19

2.1.2. Bamboo for construction 20

2.2. Bamboo treatment 22

2.2.1. Weather, altitude and soil conditions 23

2.2.2. Curing process 23

2.2.3. Laminated bamboo 24

2.3. Bamboo as functionally graded material 26

2.4. General Mechanical and Physical Properties 27

2.4.1. Micro-mechanical Analysis 28

2.4.2. Macro-mechanical Analysis 31

2.4.3. Beam analysis by mechanics of materials. 32

2.4.4. Failure analysis 35

2.5. Experimental procedures 37

3 Materials and Experimental Procedures 40

3.1. Material used 40

3.1.1. Density and specific gravity 41

3.1.2. Humidity 41

3.1.3. Roughness 41

3.2. Equipment 41

3.2.1. Table saw 42

3.2.2. Planner thicknesser 42

3.2.3. Materials testing machines 43

3.3. Samples 45

3.4. Test specimens 45

3.5. Determination of tensile modulus of elasticity Et 47

3.6. Determination of shear modulus G 48

3.7. Beam specimens - Laminated Glued Bamboo (LGB) 49

3.8. Determination of bending modulus of elasticity Eb 50

3.9. Mamona resin adhesive 52

4 Results 54

4.1. Density and specific gravity 54

4.2. Moisture 55

4.3. Roughness 55

4.4. Test specimens analysis 56

4.4.1. Statistical analysis of test specimen results 62

4.5. Beam analysis 68

4.5.1. Statistics bending data analysis 71

4.6. Failure analysis 75

5 Conclusion 78

6 Reference 80

List of figure

Figure 1 - Global map of available bamboo species (Laroque, 2007) 20

Figure - 2 Stress/strain diagram comparing different structural materials

(Rittironk & Elnieiri, 2008) 21

Figure 3 Variation of fiber volume fraction across bamboo wall

(Ghavami & Marinho, 2003) 26

Figure 4 Relationship between volume fraction and location on bamboo

wall thickness (Ghavami et al, 2003) 29

Figure 5 Layering segmentation on bamboo wall thickness 30

Figure 6. Volume fraction vs. normalized modulus of elasticity for

Em and Ef1 calculus (Ghavami, 1990) 30

Figure 7 Element of a laminated beam before and after the application of a

bending moment (Gibson, 1994). 33

Figure 8 Types of fracture fragile fracture and ductile fracture (Rusinque

Guatibonza, 2009). 35

Figure 9 Simple tension failure 36

Figure 10 Cross-grain tension failure 36

Figure 11 Splintering tension failure 36

Figure 12 Brash tension failure 36

Figure 13 Compression failure 37

Figure 14 Horizontal shear failure 37

Figure 15 Segments of analysis depending on the longitudinal and cross

section location. 40

Figure 16 Table saw. 42

Figure 17 Planner thicknesser. 43

Figure 18 Hydraulic machine testing Instron 5500R 43

Figure 19 Hydraulic test machine Amsler 57/497 44

Figure 20 Strip obtaining process, from bamboo culm to final composite

(inner-outer) strip 46

Figure 21 Splitting longitudinally bamboo culm to obtain strips 46

Figure 22 Thicknesser process to reduce and flatten strips into test

specimens 47

Figure 23 Sample scheme for modulus of elasticity determination tests. 47

Figure 24 Tensile test for modulus of elasticity determination (a)

detailed strain and clip gage location before rupture in straight shape (b)

sample rupture. 48

Figure 25 Samples dimensions and opposite transverse cuts A and B

made on specimen to define shear zone approximately of 40mm

long and 3mm width. 49

Figure 26 Tensile test for shear modulus determination (a) detailed clip

gage location before rupture in straight shape and opposite transversal

cuts (b) sample rupture along the shear line. 49

Figure 27 (a) 3mm thick bamboo mats with a coat of mamona’s resin (b)

strips stacked arranged for stick (c) final beams casted after adhesive

drying and polishing edges. 50

Figure 28 Set up of 4 point bending test 51

Figure 29 Picture of a 4 points bending test arrangement showing

the load and supporting conditions 51

Figure 30 Image of mamona compnents Polyol and Pre-polyme and its

respective proportions 53

Figure 31 Specific Gravity of inner and outer segments along the culm

length 54

Figure 32 Profile of final polished bamboo laminas surface. 55

Figure 33 Surfaces of final layers used to obtain test specimens and

assemble beams. 56

Figure 34 Shear modulus of inner and outer walls vs longitudinal

location 57

Figure 35 Tensile modulus of elasticity of inner and outer walls vs

longitudinal location 58

Figure 36 Tensile modulus of elasticity found for all segments of

analysis 59

Figure 37 Tensile modulus of elasticity of inner segments 59

Figure 38 Tensile modulus of elasticity of outer segments 60

Figure 39 Marginal values of tensile MOE of segments along the length 60

Figure 40 Marginal values of tensile MOE on wall thickness 61

Figure 41 Residue graph 64

Figure 42 Estimated marginal averages of MOE along the length 67

Figure 43 Estimated marginal averages of MOE along the wall

thickness 67

Figure 44 Longitudinal inner profile vs modulus of elasticity 70

Figure 45 Longitudinal outer profile vs modulus of elasticity 70

Figure 46 Wall thickness profile of middle section vs modulus of

elasticity 71

Figure 47 Wall thickness profile of top section vs modulus of

elasticity 71

Figure 48 Square residual for beam data analysis 73

Figure 49 Limits of average MOE for segments 74

Figure 50 Estimated marginal averages of MOE for segments of

analysis 75

Figure 51 Fracture on beam specimen 3 by splintering tension and

horizontal shear 76

Figure 52 fracture on specimen 17 by brash tension and inner

compression 77

Figure 53 Fracture on specimen 8 by simple tension and inner

compression. 77

List of Tables

Table 1 Tensile modulus of elasticity Et and τ tensile strength of some

bamboo species ....................................................................................... 15

Table 3 Relation between σt, γ and energy consumed and strength over

volume of some construction materials (Ghavami, 1992) ......................... 16

Table 4 Tensile properties of laminae of Dendrocalamus strictus

(Verma & Chariar, 2013) .......................................................................... 39

Table 5 Mamona’s resin properties .......................................................... 53

Table 6 Density and specific gravity for bottom and middle segments ..... 54

Table 7 Moisture of bamboo used for test specimens and beams ........... 55

Table 8 Tensile modulus of elasticity Et and shear modulus G of test

specimens ................................................................................................ 56

Table 9 Bamboo tensile modulus of elasticity Et and bending modulus of

elasticity Eb of different culm segments for different species. ................... 62

Table 10 Homogeneity of variances proof for longitudinal segments as

dependent variable ................................................................................... 63

Table 11 Homogeneity of variances for cross section segments as

dependent variable. .................................................................................. 63

Table 12 Normality proof .......................................................................... 64

Table 13 Inter-subjected effects proof ANOVA table ................................ 65

Table 14 HSD Turkey table ...................................................................... 66

Table 15 multiple segments comparison by HDS Turkey and DMS ......... 66

Table 16 Bending modulus of elasticity obtained by four different

methodologies. ......................................................................................... 69

Table 17 r averages for modulus of elasticity regarding tensile modulus . 69

Table 18 Equality Levene proof of error variances ................................... 72

Table 19 Normality proof. ......................................................................... 72

Table 20 Inter-subjects effects proof ANOVA table .................................. 73

Table 21 MOE averages for segments ..................................................... 74

Table 22 Types of primary and secondary failures on the beams and

surface fracture. ....................................................................................... 76

1 Introduction

This dissertation continues a research program on non-conventional

building materials, which has been developed since 1979 at the Civil Engineering

Department of the Pontifical Catholic University of Rio de Janeiro – PUC-Rio,

under the leadership of Professor Khosrow Ghavami. Scientific research on

bamboo, oriented towards its physical, mechanical and microstructural properties

study, has fostered its large-scale use as an engineering material. Based on its

performance, there is a growing interest to make it available in shapes more

suitable to current structural applications. Previous studies on this topic

Sulastiningsih & Nurwati, 2009; Mahdavi et al, 2012; Correal & Lopez, 2008; Liu

& Yang et al, 2008 assessed bamboo laminated boards made of strips taken

indiscriminately from along the culm. However, bamboo is an anisotropic

material as its properties vary in all directions. This condition restricts the analysis

via traditional solid mechanics theory, and transmits bamboo heterogeneity to the

laminate composite. Based on a pattern of property variation, it is possible to

suggest divisions along the longitudinal axis initially, then across the wall in order

to obtain less heterogeneous segments. Based on this observation it is possible to

obtain groups of segments with similar properties and simultaneously

heterogeneous among them. Generally, the composite materials theory addresses

laminated board analysis, in which layers orientation and bonding turn out to be

significant factors. However, while unidirectional layers arrangement has

commonly poor transverse properties, for bamboo subjected to bending loads,

alignment of fibers parallel to grain has proven to be the best orientation

(Ghavami & Marinho, 1990).

Lamination solves shape and some anisotropic issues of bamboo culm but

also increases the cost, labor and equipment, which generate obstacles for local

and decentralized production. Furthermore, variation of properties between

different species requires considerable research for structural applications. This

demands detailed investigation on local environments and restricts the use of

15

worldwide information almost as benchmark only. The discriminate segments

arrangement of strips on bamboo-laminated beams reduces the anisotropic

variation. Moreover, stable properties of those segments leads to maintain strip

properties into laminated beam. Table 1 presents tensile modulus of elasticity (Et)

and tensile strength (τ) obtained by different authors for different bamboo species.

Bamboo species and source Et (GPa) τ (MPa)

Bambusa blumeana (Liese 1985) 4,1 4,5Dendrocalamus asper (Liese 1985) 6,3 5,4Guadua angustifolia (Ghavami & Marinho 2003) 15,1 NAPhyllostachya pubescens Eb (Chung & Yu 2002) 11,4 NADendrocalamus giganteus (Guatibonza 2009) 11,3 3,7Dendrocalamus giganteus (Culzoni 1985) 13,1 NADendrocalamus giganteus (Ghavami & Marinho 2001) 17,5 3,5

Table 1 Tensile modulus of elasticity Et and τ tensile strength of some bamboo species.

Table 2 presents results of the investigations carried out by several

researches on laminated bamboo arrangements tensile modulus of elasticity and

the shear strength subjected to four points bending specimens. They allow

establishing a range of values for both variables despite being of different species.

Type and source Bamboo species Et (GPa) τ (MPa)

Glued Laminated Guadua (Correal, Ramirez & Yamin 2009)

Guadua angustifolia

19,14 9,32

Glued laminated Timber (Liu, Yang, Dong & Jiang 2008)

Standard timber 9,70 NA

Laminated bamboo lumber H-Beam (Nugroho & Ando 2001)

Phyllostachys pubescens Mazel

10,10 NA

Laminated bamboo lumber V-Beam (Nugroho & Ando 2001)

Phyllostachys pubescens Mazel

11,57 NA

Bamboo and tallow fiberboard (Li 2004)

Phyllostachys pubescens

2,19 NA

Table 2 Bending modulus of elasticity Eb and tensile strength τ of some laminated wood arrangements.

16

Length and wall division arises as an alternative to produce bamboo-

laminated beams, which could improve its bending properties by strips

arrangement and their place of origin. This provides a deep characterization on

local species Dendrocalamus giganteus. Bamboo has turned out to be a suitable

structural material due to its mechanical properties, principally regarding its

specific weight and energy consumption, as collated by Ghavami, see Table 3.

Where σt is the tensile strength, γ is the specific weight and R relates σt over γ.

Then relating R with Rsteel results an efficiency strength-weight indicator and the

last columns shows energy consumed and tensile strength over volume.

Material σt [MPa]γ

[N/mm³x10¯ ²] R=(σt/γ)*10² R/Rsteel MJ/m³*MPa

Steel 500 7,83 0,64 1,00 1500Aluminium 304 2,70 1,13 1,76 240Pig iron 281 7,20 0,39 0,61 80Bamboo 140 0,80 1,75 2,73 30

Table 3 Relation between σt, γ and energy consumed and strength over volume of some construction materials (Ghavami, 1992).

Research on non-conventional materials involves interdisciplinary work

oriented towards characterization, procedures establishment, structural elements

production, environmental impact analysis, durability, performance and failure

mechanisms assessment. This interaction involves the creation of parameters for

research on non-conventional materials, including sustainability, strength and

durability concepts.

1.1. Thesis objectives

It was carried out a segmented characterization as the culm was cut along

the length (bottom, middle and top) and then those strips obtained by radial cut of

cross section were divided across the wall thickness (inner and outer),

theoretically properties of those segments will be less heterogeneous than whole

culm. This fact allows introducing the solid mechanics theory to analyze segments

and beam assembled exclusively by a type of them. This enables to link properties

of strips with beam element and assemble elements according applied bending

loads. This research project has the following objectives.

17

• Determine tensile modulus of elasticity of test specimens and

bending modulus of elasticity of beams specimens.

• Relate mechanical properties of individual test specimens with

beams elements.

• Suggest segments arrangement for bamboo-laminated beams

assembly subjected to bending loads.

• Determine the viability and accuracy of solid mechanics theory

analyzing the test results of bamboo-laminated beams.

2 Literature review

2.1. General introduction

Bamboo is the most important and abundant non-wood forest product,

which grows in most tropical and sub-tropical zones around the world (Chaowana,

2013). This plant is a giant perennial grass with large woody stem, which belongs

to the taxonomic family Poaceae and subfamily Bambusoideae. It encompasses

about 1,800 species within 50 genera (Chapman, 1996). While bamboo attains

maturity in 3-5 years, wood takes more than 20 years. It grows faster than any

other plant, some moso bamboo species can achieve 20m in only 3 months,

therefore, cutting down this timber substitute may not affect the ecological

balance at all (Khalil et al, 2012).

It has a superior adaptability to most climatic and edaphic conditions than

other fast-growing woods. Moreover, it has straight grain, smooth surface,

toughness and excellent abrasion resistance (Chaowana, 2013). Due to its hollow

section and circular configuration, bamboo is very light, handleable and easy to

transport and store, allowing rapid construction of structures. Bamboo has

diaphragm along the culm that makes it rigid and crack resistant when it bends;

therefore, it has proved to be an ideal material for anti-seismic construction

(Gonzales, 1999). However, bamboo presents some limitations, which until

present time considerably restrict its widespread and large-scale use. Once it is

cut, for example, insects, fungi and pests attack its structure weakening it. For this

reason, untreated bamboo structures are viewed as temporary. Similarly, bamboo

structures, as timber, must be fire proofed or protected from fire. Finally, it does

not have a regular shape along its body and its variable width causes difficulties in

the construction process. Due to this, the building industry does not fully regard

engineering bamboo as a suitable, economically viable and green alternative for

construction.

19

2.1.1. Environmental context

Recently, energy awareness has caught the attention of people all around the

globe, as the world is simply running out of fossil fuels. This fact will contribute

to energy shortages and supplying problems to big industries, which has brought

the attention of governments in many countries. In the aim of construction field to

incorporate healthier methods, innovating building and preserving resources,

bamboo surges as a large-scale alternative construction material. Particularly

when improved building development and energy use, conform the high standards

of environmental friendliness: to be lighter and stronger, to be efficient, to be

cheaper, to be sustainable (Rittironk & Elnieiri, 2008).

It is estimated that by 2011, more than 1 billion people were living in

informal settlements and over the next 25 years 2 billion people will be added to

this number (United Nations Human Settlements Programme UN-HABITAT,

2011). Dickson 2002, estimates this number in 9 billion people by 2050, and adds

that socio-economical gap between advanced and non-advanced societies will

raise as well (Dickson, 2002). Besides that, Rand Corporation presented in a

recent report (Silberglitt et al, 2006), an increasing technical-scientific gap

between scientifically advanced, proficient, developing and lagging countries.

Additionally, the report anticipates a similar widening gap between urban and

rural populations throughout the globe. On the other hand, diminishing wood

resources and restrictions imposed on natural forests, mainly in the tropic, have

centered world attention on the need to identify new renewable, green and locally

available materials (Sharma, 2010) in the same line of environmental friendliness

standards. Due to the development of the world economy, and population

explosion, the overall demand for wood and wood-based composites is rising

sharply. Meanwhile the available wood supply will decrease due to the global

biomass demands for green energy generation (Chaowana, 2013).

In rural areas, bamboo is called the poor man’s timber due to the entire

aspects of bamboo utilization in human life (Chaowana, 2013). Bamboo grows in

tropical and subtropical developing countries as can be seen on the Figure below.

20

Figure 1 Global map of available bamboo species (Laroque, 2007).

Latin America shelters 6% of total world population (Latouche, 2006), so it

turns its energy and resource problems more tractable comparing with super-

populated and other developing regions in the world. Nevertheless, there is also a

big need for adequate housing and infrastructure. The accelerated urbanization

throughout the world is challenging provision of adequate dwelling, because it has

forced many people to live in non-engineered or marginally engineered informal

settlements (Richard, 2013). This makes reconsidering the real objectives of

developing countries, which have followed the same relative consumption

requirements as industrialized countries. However, by contextualizing local

industries and giving way to other alternatives, some socio-economic problems

and supply demands could be mitigated without excess production and pollution.

Facing such energy, resource and social issues, bamboo growing in Latin America

comes out as a resource to address those problems in the construction industry.

Using these sustainable and friendly alternative solutions also helps to continue

using traditional materials. Therefore, innovation and knowledge about local

environment becomes a key factor to achieve a suitable balance between using

sustainable and industrialized materials.

2.1.2. Bamboo for construction

Structural use of bamboo offers potential advances on “reducing homeless

rates, bridging the growing socio-economical gap and mitigating damage caused

by natural disasters” (Richard, 2013). Bamboo is a fast-growing and renewable

resource therefore; these features have turned bamboo culms into a suitable raw

21

material used in building applications beyond housing, such as flooring, ceiling,

walls, furniture, roofs, trusses and rafters. It is also used in construction as

structural materials for bridges, water-transportation facilities and skyscraper

scaffoldings. However, low-cost native materials like bamboo are often replaced

for large-scale building materials due to lack of information about its

implementation. As a result, it has been principally used in non-engineered,

temporary and vernacular constructions (Richard, 2013).

Bamboo has similar properties to some timber and wood composites,

therefore, Chaowana considered it an ecological viable substitute for them

(Chaowana, 2013). After maturity, tensile strength of bamboo is comparable to

mild steel (Correal et al, 2009). Moreover, the ratio of strength over density of

bamboo pole, which indicates material efficiency, is 2,5 times higher than wood

and 3 times than steel (Rittironk & Elnieiri, 2008). This shows how bamboo is

extremely efficient due to its lightness and high strength. Figure 2. shows

stress/strain diagram of some of the most used structural materials.

Figure 2 Stress/strain diagram comparing different structural materials (Rittironk & Elnieiri, 2008).

Ghavami reported that its strength and stiffness is suitable for construction

and design of thinner structural elements than those made of wood (Ghavami et al,

2003). Its structural importance was seen, iamong others in Armenia, a city part of

the Colombian Coffee Region devastated by 1999 earthquake. Bamboo came out

rapidly as raw material for temporary shelters, permanent houses and public and

institutional building reconstruction (Sharma, 2010).

The use of bamboo fibers as reinforcement in composite materials has

increased sharply. “The amalgamation of matrix and natural fibers yield

composite possessing best properties of each component” (Khalil et al, 2012). The

22

exploitation of bamboo fibers in various applications has opened up new

opportunities for both academicals as well as industrials to design a sustainable

module for future use of bamboo fibers. However, in order to fully exploit the

potential of bamboo as a construction material according Khalil (Khalil et al

2012), it results fundamental to increase knowledge on areas of preservation,

joints, structural design and codification.

Khare reported an acceptable and feasible performance of bamboo used as a

potential reinforcement in concrete structural members (Khare, 2005). Khare also

concluded that bamboo is a potential substitute of steel reinforcement, even more

in regions where availability of steel is limited and plain concrete members are

commonly being used. Bamboo genre Dendrocalamus studied on this paper

presents the better performance among other species groups with excellent

bending properties and has great potential to be used as a load-carrying member

(Korde, 2008). Scientists have already researched on bamboo-based composites

but more research is still required to overcome potential challenges ahead. “These

facts will make life easier for both urban as well as rural people who are more

dependent on synthetic based composites in a big scale,” conclude Abdul (Abdul

et al, 2012).

2.2. Bamboo treatment

Bamboo strength is greater than most timber products, which is

advantageous, but it has approximately half of steel tensile strength. Bamboo is

easily accessible as it grows in almost every tropical and subtropical region. This

fact reduces the cost of construction and increases the strength of the buildings

that would otherwise be unreinforced. One major problem with bamboo is that it

is more prone to insects than other trees and grasses because it has a high content

of nutrients. On its raw state, it is vulnerable too, to fungi and plague attacks. In

order to address this problem, it becomes necessary to treat bamboo to protect it

from the environment. Steel does not have this problem but it also needs to be

coated to protect it from rusting. In addition, bamboo is light in a strength-weight

context compared to steel. Due to its low modulus of elasticity, bamboo can crack

and deflect more than steel reinforcement under the same conditions. These

23

properties, suggest that bamboo will make a fine addition to the current selection

of materials, but it is necessary to be more familiar with its strengths and

weaknesses.

For the current study, bamboo was not treated, but specimens and beams

were tested three months after cutting the poles, which remained until outdoor

assembling. Therefore, the effects of treated bamboo and its durability are not

within the scope of this study.

2.2.1. Weather, altitude and soil conditions

In order to get suitable bamboo culms there are some conditions to consider

regarding its growing and harvesting. As it was previously said, the grass grows

in tropical and subtropical regions and the ideal altitude ranges between 400 and

2000 MASL. Regarding weather conditions, temperature should be between 18

and 28 degrees Celsius with precipitations rainfall rates higher than 1200 mm. In

terms of soils, it should be a well-drained and fertile clayey sandy loam. Soils

must be moist, permeable and preferably rich in organic matter and protected from

floods (Chara, 2014). They should not have obstacles, stones, old roots and

undergrowth. It has had some indications about the certain period to cut bamboos,

but some literature demonstrated that it has not significant factor (Ghavami &

Marinho, 2003). They also suggested bamboo culms should be cut between three

and six years after it has reached its highest level of maturation and culms are

completely lignified.

2.2.2. Curing process

After harvesting, green poles should be cured in order to protect them from

plagues and fungi. Proper poles storage is a determinant fact to preserve its

properties and keep the performance (Chiozzini, 2007). Moreover, there are plenty

of methods to cure and seal poles however, some chemical treatments have

presented similar results than natural ones (Chiozzini, 2007). Chiozzini also found

that long-term treatments not always result more effective than short-term ones.

Most of these are some curing methods that make use of a mixture of saline

24

solutions (Chara, 2014). This study, in order hold a sustainable scope, addresses

natural treatments implemented by local bamboo builders in Nariño, Colombia

which are presented below:

Vertical: nodes are broken through the pole, except for the last one. Then,

bamboo hollows are filled with immunizing during 3 to 5 days for liquid

penetrates, and then it is rotated and refilled to the top according to the volume

absorbed. After the 8th to 10th day, liquid is removed and poles are dried vertically.

The solution requires, for 100 liters of water –preferably warmed-, 12 kg of borax

and 12kg of boric acid. If possible, it is recommended to add 1 liter of salvia

extract to improve the solution and red powdered pepper for fumigating it.

Immersion: poles are submerged during 12 hours in a solution composed by

1kg of borax, 1kg of boric acid and 50 liters of water. In this case it is

recommended to drill internally the nodes as in the vertical treatment.

Injection: due to results experienced by small producers, this method is no

longer used, however it uses between 5 to 20 cm3 of immersion solution which is

injected in each bamboo conduit in a zig-zag pattern from its cross section.

Smoke dried: is performed by a poly-woody acid, produced by condensation

of tar-saturated smoke. Poles must be kept within a tightly closed oven for a

period not less than 3 weeks.

After curing process, bamboo is ready to be employed in construction

process.

2.2.3. Laminated bamboo

Laminated bamboo has become a way to standardize and foster its use, since

it can be designed in many geometrical sections as required by structural

applications. In wood composite manufactures, adhesives are required to bond

wood elements together. Adhesives are not only a significant cost factor in wood

composite production but also they are the key factor for some of the product

properties. In bamboo, adhesive capacity is influenced by its surface properties,

such as wettability, roughness, pH value, buffering capacity among others

(Ahmad & Kamke, 2003). Availability of appropriate equipment for culm

25

transformation into regular pieces is one of the principal limiting factors for the

local production.

Laminated bamboo cannot replace entirely the use of traditional structural

materials, but its use can lead to more suitable balance in many constructive

aspects. Bamboo culm heterogeneity becomes a problem for standard housing

processes even in developing countries in medium and big scale production.

However, lamination comes out as a good opportunity to generate innovative

solutions by people involved on the industry. Therefore, it is a challenge to young

generations to achieve the balance between traditional industry and sustainable

and decentralized production, even more in the Latin American context. In Brazil,

many exotic bamboo species suitable for fabrication of Laminated Glued Bamboo

grow naturally. Among them stand the Dendrocalamus giganteus and Bambusa

vulgaris (Beraldo, Rivero, & Azzini, 2003). In this study, the wood-based

composite assembled was a Laminated Glued Bamboo Lumber made from

Dendrocalamus giganteus layers. Plies of bamboo were stacked in order to glue

them and produce beams, aimed to continue the research on those materials.

At the same density level, strength properties of fiberboard increased with

greater levels of resin content. Age had a significant effect on board properties.

Fiberboard made with one-year-old bamboo at 8% resin content level had the

highest modulus of rupture (MOR) and elasticity (MOE) among the bamboo

panels, which is largely due to a higher percentage of larger fiber size. Fiberboard

made with five-year-old bamboo at 8% resin level had the highest internal bond

strength, which was largely attributed to the higher resin recovery on old bamboo

fibers (Nugroho & Ando, 2001). Bamboo fiberboards showed comparable

physical and mechanical properties with tallow wood fiberboards. The

dimensional stability of bamboo fiberboard was not satisfactory. Wax was

recommended to improve the dimensional stability. On the other hand, spread

glue rates appeared to be a significant variable for the internal bond strength on

two-ply. Moreover, orientation of glue line in the vertical direction demonstrated

to maximize the ultimate strength of Laminated Bamboo Lumber LBL (Nugroho

& Ando, 2001).

Chaowana stated that bamboo-based composites will become a highly

competitive alternative to wood-based composites and will become an important

forest based product in the future (Chaowana, 2013). However, in Brazil,

26

Laminated Bamboo Lumber process is practically restricted to university research

(Beraldo et al, 2003). Nevertheless, since the 20th century, bamboo has received

increasing attention for industrial applications on regional markets, especially as a

raw material for wood-based composites such as: particleboard (PB), medium

density fiberboard (MDF), hard fiberboard (HB), laminate glued bamboo (LGB),

plywood, oriented strand board (OSB), Glue-Laminated Lumber (GLL),

laminated bamboo lumber (LBL), Laminated Veneer Lumber (LVL) and oriented

strand lumber (OSL) (Chaowana, 2013).

2.3. Bamboo as functionally graded material

Bamboo is a functionally graded composite material “constituted by long

and aligned cellulose fiber embedded in a lignin matrix” (Ghavami et al, 2003).

Fiber distribution is variable through its wall thickness, arising from center

outwards (Ghavami et al, 2003). The variation on fiber distribution prevents the

direct application of traditional solid mechanics equations, as they assume perfect

bonding between fiber and matrix and uniform distribution of fibers along the

wall thickness. This fact raised the need to establish how this variation occurs and

therefore modified basic equations for composite materials. Ghavami states the

importance of analyzing bamboo culms through DIA (Digital Image Analysis)

aimed to establish the variation of the volume fraction of the cellulose fibers on

the cross section. To the naked eye, it can be observed in Figure 3 how its

constitution changes along its cross-section. In fact, this allows great application

of rule of mixtures by adjusting variability of its fibers.

Figure 3 Variation of fiber volume fraction across bamboo wall (Ghavami & Marinho, 2003).

27

Rule of mixtures achieves a preliminary assessment of the mechanical

behavior of composite materials in elastic range. This rule is a group of equations

that assign values of mechanical properties to composites based on individual

mechanical properties and volume fraction. In this way, Ghavami put forward an

example of how to establish the composite modulus of elasticity knowing the

modulus of elasticity and volume fraction of both components.

Ec = EfVf + EmVm = EfVf + Em (1− Vf ) (2.1)

Where Ec is the composite modulus of elasticity

Ef and Vf are fiber modulus of elasticity and volume fraction respectively.

Em and Vm are matrix modulus of elasticity and volume fraction

respectively.

However, this procedure assumes perfect bonding between components,

thus a more suitable approach would be necessary to obtain bamboo components

properties. Furthermore, Nogata & Takahashi suggested investing more time and

resources on developing functionally graded materials, which are governed by

uniform strength as could be bamboo, rather than developing materials with high-

stiffness (Nogata & Takahashi, 1995).

For instance, bamboo wall is composite by bundles of more than one

hundred elementary fibers. Elementary fibers consist of layers of crystalized

cellulose nano-fibrils aligned with many angles with respect to the fiber on the

longitudinal direction and are embedded with hemi-cellulose and lignin (Fuentes

et al, 2011).

2.4. General Mechanical and Physical Properties

Taking Bamboo as giant timber and a potential composite of layered

structural material requires more knowledge about its mechanical and physical

properties. Despite the bamboo culm presents some excellent features such as

rapid growth rate, short rotation age, excellent flexibility and high tensile strength,

it also has some drawbacks. These disadvantages refer mainly to its natural

28

composition and structure, and this means that it is fundamental to understand its

physical and mechanical properties. As previous studies have demonstrated,

properties vary depending on the position in the culm, therefore, obtaining and

comparing these properties at different positions along the culms is a good start

point for the analysis.

In the first place, a micro and macro mechanical approach is presented, then,

the procedure to analyze laminated beams by composite materials theory and

elementary solid mechanics of materials is explained. Finally, a section covering

rupture mechanics is presented.

2.4.1. Micro-mechanical Analysis

Formulations for micro-mechanical analysis based on mechanic of materials

could be used in bamboo modeling as a natural composite material with aligned

elongated fibers. This is supported by studies of graded functionality of bamboo at

micro-structural level (Ghavami et al, 2003).

As bamboo fibers are not distributed uniformly throughout the thickness,

engineering constants cannot be obtained by the rule-of-mixtures, commonly used

for composites as shown below.

(2.2)

(2.3)

(2.4)

Where G12 is the composite shear modulus, Gm and Gf are the shear

modulus of matrix and fiber respectively

(2.5)

And ν12 is the composite Poisson coefficient, being νm and νf this coefficient

for matrix and fiber respectively.

To apply rule-of-mixtures in bamboo lumbers, it must determined a function

of volume fraction of fibers and thickness, assuming that fiber distribution is

symmetric to radial axis (arising from the inner wall outwards). Thereby, the

29

young modulus at main (longitudinal) axis could be indicated in a simplified

form in the following equation.

(2.6)

To determine it is necessary to implement digital images processing.

To achieve this, cross sections are digitalized and divided in little segments with

uniform fiber distributions. The function is defined after processing quantity of

fibers in each segment from the curve of volume fraction against the position on

x-axis. In this way, a regression of function for Dendrocalamus Giganteus

is obtained this is shown on Figure 4.

This function allows the use of rule-of-mixtures and to calculate bamboo

mechanical properties as a function of fiber matrix distribution. As it can be seen,

fiber and matrix form a unified compound; therefore, a composite analysis to

determine modulus of elasticity is done to assess the properties of these elements.

Figure 4 Relationship between volume fraction and location on bamboo

wall thickness (Ghavami et al, 2003).

The parabolic trend plotted shows a correlation index of 0,998 and evidence

the non-linear trend of fiber distribution. This parabolic behavior could allow

defining a trend between fiber and matrix concentration and issue about need to

use functional graded material methods instead of simpler rule-of-mixtures.

Figure 5 shows wall thickness division (a) and (b) in segments with uniform fiber

30

distribution (c). Modulus of elasticity is determined for each individual segment

by tensile tests.

Figure 5 Layering segmentation on bamboo wall thickness.

After that, each segment is analyzed through digital image process method

to calculate its volume fraction. It allows plotting a curve of volume fraction

against modulus of elasticity. Using a lineal regression it is possible to define

values for matrix and fiber modulus by extrapolating values from 0% and 100%

respectively as shown in Figure 6.

Figure 6. Volume fraction vs. normalized modulus of elasticity for Em and Ef1 calculus (Ghavami, 1990).

This methodology could be implemented to determine other elastic

properties and to establish separate properties of components, matrix and fibers.

31

2.4.2. Macro-mechanical Analysis

To characterize mechanical properties of bamboo is to analyze the structural

composite of whole. In this case, matrix and fiber properties are state in terms of a

new homogenous equivalent material. Average stresses replace real stresses.

As bamboo is a composite material with aligned fibers, whose wall

thickness is smaller compared to its diameter and length. It can be assumed as a

unidirectional lamina especially orthotropic under a plane stress state. This means

that there is not any stress in the z direction and there is only one in the plane

shear. Constitutive relation for these approach is shown on equations 2.7 – 2.18.

(2.7)

(2.8)

(2.9)

Where and are the components 1 and 2 deformations respectively. σ1

and σ2 are the 1 and 2 component tensile strengths. ν12 and ϒ12 the composite

modulus of Poisson and τ12 and G12 the composite shear strength and modulus.

Stress-deformation relation could be defined in a matrix form from

flexibility matrices and then, engineer constants can be defined as follows:

(2.10)

(2.11)

Thus, the matrix form is defined by:

(2.12)

Stresses on the lamina could also be expressed in terms of strain tensor,

where corresponds to the stiffness matrix elements of the lamina that is the

inverse of the flexibility matrix.

(2.13)

32

(2.14)

Where

(2.15)

(2.16)

(2.17)

(2.18)

2.4.3. Beam analysis by mechanics of materials

A theory of laminated beams in pure bending was developed from

Bernoulli-Euler theory of elementary mechanics of materials on Principles of

Composite Materials (Gibson, 1994). Although the application of this theory is

quite restricted, it provides considerable insight into the analysis of laminated

structures and introduces the general lamination theory.

Theory based on the analysis of Pagano (Pagano, 1967) for bidirectional

composites used the following assumptions:

1. Plane sections, which are initially normal to the longitudinal axis of the

beam, remain plane and normal during flexure.

2. The beam has both geometric and material property symmetry about the

neutral surface (the plies are symmetrically arranged over the xy plane).

3. Each ply is linearly elastic with no shear coupling (ply orientations are

either 0° or 90°).

4. The plies are perfectly bonded together, so that no slip occurs at ply

interfaces.

5. The only stress component present are σx and τxz

33

Figure 7 Element of a laminated beam before and after the application of a bending moment (Gibson, 1994).

Longitudinal normal strain at a distance z from the neutral surface is given

by the familiar equation from assumption 1.

(2.19)

Where ρ = radius of curvature of the neutral surface during flexure

ϕ = angle as defined on Figure 7

z = distance from neutral surface defined by the xy plane.

From assumption 3 the longitudinal stress in the jth ply is given by.

(2.20)

Static equilibrium requires that the applied bending moment M must be

related to the longitudinal stresses by

(2.21)

Recall that for a homogeneous, isotropic beam the moment-curvature

relation is given by

(2.22)

Where Iyy is the moment of inertia of cross section.

The effective flexural modulus of the laminated beam can be expressed

(2.23)

or for an even number of plies

(2.24)

34

Thus the bending modulus of laminated beam, unlike the modulus of

elasticity of the homogeneous isotropic beam, depends on the ply stacking

sequence and the ply moduli. “That is, if the properties do not change through the

thickness of a beam, the flexural modulus is the same as the Young’s modulus”

(Gibson, 1994). Due to lamination orientation and previous assumptions made by

Pagano (Pagano, 1967), an analysis by elementary solid mechanic could be

carried out. Considering LGB as a homogeneous and isotropic beam with ply

stacking unidirectionally. Elementary equation (2.25) for inertia moment of beam

cross-section (Hibbeler, 1997) was used to relate strain and moment of the beams

tests, and then solve for Et and Ec.

(2.25)

and then solving for σmax

(2.26)

(2.27)

where

σmax = maximum normal strength that occurs at the furthest point of the

cross section of the neutral axis

M = resulting internal moment determined by sections method and

equilibrium equations, it is calculated regarding neutral axis of cross

section.

I = moment of inertia of the cross section calculated regarding neutral axis.

c = perpendicular distance from neutral axis to the furthest point of y-axis

where σmax acts.

In most problems, bending stiffness remains constant along the beam.

Consequently, following equations for beam elastic curve was used to relate load,

shear and moment with E.

(2.28)

(2.29)

(2.30)

35

These equations are integrated to obtain deflection v of the elastic curve.

Each integration introduces an integration constant, which are solved by boundary

conditions and provides a unique solution for a particular problem.

2.4.4. Failure analysis

“The rupture of an element is separation or fragmentation due to external

loads, as result of process of creation of new rupture surfaces, which can origin

from a fissure existent” (Gonzales J. L., 2004). Gonzales also stated that fracture

process generally happens in little regions with strengths smaller than maximums

and he characterize them as a sudden, unexpected and catastrophic action.

Under behavior of materials standpoint, fracture divides in two sorts

depending on quantity of plastic deformation prior to failure. Figure 8 shows a

diagram of fragile and ductile fracture.

Figure 8 Types of fracture fragile fracture and ductile fracture (Rusinque Guatibonza, 2009).

Fragile fracture happens when deformation of the most of the body is

elastic, so that after fracture under small deformations, element fragments can be

jointed without big changes on geometric piece. On the other hand, ductile

fracture happens after a considerable plastic deformation and a stable propagation

of cracks. However, for static bending tests, ASTM classifies them in accordance

with the appearance of the fractured surface and the manner in which the failure

develops (ASTM D143, 2014). Those fracture surfaces may be roughly divided

into brash and fibrous regarding fragile and ductile types shown on Figure 8.

36

Figures 8 to 14 below present ASTM failure classifications that was used to

classify failures in present study.

Figure 9 Simple tension failure.

Figure 10 Cross-grain tension failure.

Figure 11 Splintering tension failure.

Figure 12 Brash tension failure.

37

Figure 13 Compression failure.

Figure 14 Horizontal shear failure.

2.5. Experimental procedures

Studies aimed to characterize bamboo properties in terms of location both

along its wall thickness and its culm as specific gravity, relative density, modulus

of elasticity and volume fraction are addressed in this section. Specific gravity and

bending properties of bamboo vary with age and height location as well as cross

the layer. They all increase from one-year-old bamboo to five-year-old bamboo,

as mentioned Ghavami referring to the age for cutting (Ghavami & Marinho,

2003). “The bamboo culm comprises about 50% parenchyma, 40% fibers and

10% vessels and sieve tubes” (Liese, 1985). The fibers contribute 60-70% of the

weight of the total culm tissue. They are long and tapered at their ends. Li stated

that outer layer had significantly higher SG and bending properties than the inner

layer, ratified by rising on E as shown on Figure 4 and 6 above. This because,

outer layer supports bamboo more than the inner layer. Bending strength had a

strong positive correlation with SG (Li, 2004) and so that with volume fraction.

Furthermore, height location of culms affects its physical and mechanical

properties (Lee, Bai, & Peralta, 1994) other studies about variation in mechanical

properties of moso bamboo established an equation for predicting the tensile

38

strength and modulus of elasticity from the position on the wall thickness (Xian,

Shen, & Ye, 1995) similar with interpolation established by Ghavami.

Yu et al found volume fraction of bamboo fibers denser in outer region (60–

65%), sparse (15–20%) in the inner region and increases linearly with height by

about 20–40%. For this reason, these studies focused in mechanical properties of

bamboo culms along and across the fiber direction. Experimental results indicate

that stiffness and strength under tensile loading of bamboo laminas is higher in

outer region and lower in inner region. To understand variations along the bamboo

wall, Yu et al conducted tests focused on that classificatory parameter. On their

work, bamboo specie was Phyllostachys pubescenes, which presented a relative

density ranging from 0,553 g/cm3 at internal edge to 1,006 g/cm3 at external one

(Yu, Jiang, Hse, & Shupe, 2008). The mean longitudinal tensile MOE ranged

from 8,987 to 27,397 GPa and mean longitudinal tensile strength ranged from

115.349 to 309.322 MPa, both from inner wall outwards. Relative density

decreases significantly from outer layer to the middle layer and the difference in

relative density between the layers toward the inner surface was not significant.

(Yu, Jiang, Hse, & Shupe, 2008)

Layer and height position have a significant effect on all of those studied

properties except for tensile strength. Relative density, tangential shrinkage,

tensile MOE and tensile strength of bamboo increase greatly from inner layer

outwards. Longitudinal shrinkage decreased greatly from the inner layer outwards,

relative density, tangential shrinkage and tensile MOE at 1,3m were less than

those are at 4,0m height (Li, 2004). One year old fibers showed a higher

percentage of larger fiber size, less percentage of fine fibers retained on sieves

higher than 60 meshes, and less lumpy fiber clumps than three and five year old

bamboo fibers due to the refinement process. Compression properties parallel to

the longitudinal direction are significantly higher than perpendicular to the

longitudinal direction therefore, it makes bamboo aligned longitudinally an

optimal structural material for compression strengths (Li, 2004).

Ghavami and Solorzano proposed first split bamboo wall in two ranges.

Both have a fiber distribution relatively uniform with 40 to 90% at outer face and

a 15 to 30% at inner face (Ghavami & Solorzano, 1995). Furthermore, Verma and

Chariar 2012, carried out a layered laminate bamboo composite study, analyzing

mechanical properties in segmented sector along the culm and from the center

39

outwards. Table 4 presents tensile properties of laminas of Dendrocalamus

strictus. It can be seen how stiffness and strength increase from lower internodes

to top and a considerable difference between inner and outer regions. Middle

regions in some cases have higher stiffness than outer region, but strength always

increase from center outwards. This presents orthotropic character of bamboo.

Nevertheless, it also lets assume that an assemblig based in segment location

could improve use of beams according applying loads and homogenize somehow

sections properties. Verma & Chariar, 2012 concludes that all laminas presented a

bi-linear stress-train curves and tensile strength and modulus of elasticity increase

from inner to outer region across any cross section and from bottom to top of

culms.

1 4 8 11 14 17

MOE [GPa] 4,6 5,9 6,4 5,23 6,93 8,9

Tensile Strength [MPa]

240 257 250 281 298 302

MOE [GPa] 4,63 6,2 6,3 6,6 6,3 7,56

Tensile Strength [MPa]

175 173 204 226 230 276

MOE [GPa] 2,1 2,5 2,7 3,63 3,7 4,66

Tensile Strength [MPa]

101 104 169 172 217 212

Outer Region

Middle region

Inner region

Specimen No.Bottom Middle Top

Table 4 Tensile properties of laminae of Dendrocalamus strictus (Verma & Chariar, 2013).

Verma and Chariar, 2013 found on their experimental results good

agreements between the estimated and predicted value for modulus of elasticity

and tensile strength, which are satisfactory agreement for initial design purposes

(Verma & Chariar, 2013).

3 Materials and Experimental Procedures

This research was developed in the Laboratorio de Ensaios Mecânicos ITUC

PUC – Rio with the objective of determining the values for Et, Gt and τt of six

types of test specimens and bending properties of unidirectional bamboo-

laminated beams.

3.1. Material used

For this dissertation the bamboo species used was Dendrocalamus giganteus

taken from the campus of PUC – Rio. 3 culms were cut in November 2013,

approximately 40 cm above ground level. After curing and drying, bamboo culm

was divided in three parts along its length (Bottom, Middle and Top)

approximately 2.5 to 3.5 m each part. Then transversal sections were split radially

obtaining 5 to 8 strips 3 to 4 cm width and cut longitudinally 120 cm length.

Those strips were processed in order to remove knots and irregular surfaces. All

the segments were labeled: Bottom-Outer (BO), Middle-Outer (MO), Top-Outer

(TO), Bottom-Inner (BI), Middle-Inner (MI) and Top-Inner (TI). Their

longitudinal labeling and cross section location are shown in Figure 15.

TI

MI

BI

TO

MO

BO

front view

cross section view

Figure 15 Segments of analysis depending on the longitudinal and cross section location.

41

3.1.1. Density and specific gravity

For calculating density and specific gravity, 4 internode samples were taken

from different longitudinal and cross section location. The internode was cut into

strips of approximately 22 cm long 3 cm wide and 0.3 cm thick. Mass, dimensions

and label were registered in order to obtain density and subsequently SG.

3.1.2. Humidity

Moisture content determination was made according to the standard

procedure ISO/TC 165 N135 dated: 2001-12-07. Five samples of approximately

25mm wide, 25mm length and height were prepared. Each sample was weighed

and taken to the oven at 110°C to be dried. The drying process took 24 hours and

at the end the weight of samples was read again.

Being m0 initial weight of each sample and m weight after drying, the

moisture M of each sample is calculated with equation:

(3.1)

3.1.3. Roughness

Surface roughness of mats was calculated in order to make sure that there

was an acceptable variation of the surface to allow an optimal performance of

adhesive. This calculation was performed with high accuracy roughness tester

Taylor Hobson 50. However, resulted dispensable essential because planner

thicknesser generated a finish seemed to a sanding process generating layers very

uniforms on thick.

3.2. Equipment

Process to get bamboo layers was carried out with a table saw in order to

divide the culm on strips, and a planner thicknesser was used to get suitable and

thin 3-5 mm thickness samples and laminas to assemble beams. Tests for

42

characterization and bending were carried out in a hydraulic testing machine,

using clip and strain gages for strain measure and load cells for load measures.

3.2.1. Table saw

The saw used was the Makita 2704 table saw 255mm (see Figure 16). The

machine saw table has high rigidity, and delivers accurate cutting work in order to

obtain strips with standard widths. This fact becomes important when optimizing

the material because all strips should have a standard width. Its motor enables

ripping 4"x8" wood with telescopic sub table.

Figure 16 Table saw.

3.2.2. Planner thicknesser

The thicknesser used was a compact thicknesser (see Figure 17) used for

dressing rough sawn of bamboo, it has a double-edged HSS blades and automatic

feed rollers, which push the material through at 8.5m per/min.

43

Figure 17 Planner thicknesser.

The machine allows adjusting thickness. After obtaining strips by sawing,

they were thinned until reaching required segment.

3.2.3. Materials testing machines

The properties of the tensile test segments were obtained by using a

hydraulic testing machine Instron 5500R (see Figure 18). The capacity was

100kN, for tensile, compression and bending tests. The range of velocity was

between 0,01 and 1000 mm/min.

Figure 18 Hydraulic machine testing Instron 5500R.

The machine was equipped with an automatic system reads load values and

vertical displacements, by means of an optical sensor built in. This equipment

44

allows choosing the load application procedure, as a function of load rate or rate

of displacement. For the characterization tests (tensile, shear and adhesive

strength), the test velocity was 1mm/min. The Instron 5500 machine used wedge-

sharped pincer clamps as shown on Figure 18, with a maximum capacity of

5000kgf, tighten by a screw system. Clamps held aluminum plates at ends of

samples to improve grip.

For the bending tests, an Amsler 57/497 was used to bring layered bamboo

beams to failure. Test machines had a load capacity of 20Ton, and are designed

for tensile, compression and bending tests. However, this machine presented a

wider effective span for bending tests since beams were approximately 55 cm

long. Despite test machine measured load, load cell were used in order to

synchronize all sources reads at acquisition system. A Linear Variable differential

transformer (LVDT) sensor located at the bottom of the sample beams was used to

measure vertical displacement in the middle of the sample. Test velocity was

2.4mm/min.

Figure 19 Hydraulic test machine Amsler 57/497.

Gadgets for bending test are shown on Figure 19, they have a maximum

spam length of 100cm. For the four point bending test, a distance of 16,7cm

between restrains was used as it can be seen on test arrangement.

45

3.3. Samples

This research used two types of specimens, test specimens and beam

specimens. Test specimens were thin individual layers 200 mm length to

determine tensile modulus of elasticity Et and shear modulus G for each segment

of analysis (BI, MI, TI, BO, MO and TO). Beams specimens were elements

composited by layers exclusively from a segment of analysis to determine bending

modulus of elasticity Eb.

3.4. Test specimens

There were obtained 18 test specimens for the modulus of elasticity and 18

more for shear modulus tests (3 samples for each segment of analysis), those were

obtained from bamboo culms by a radial-symmetrical cut in the cross section

along the culm. This provided strips with an accurate isosceles trapezium cross-

shape. As a first step, planner thicknesser was used to remove both curve parts in

order to get plane surfaces, as shown on the Figure 20. After that, the planner saw

polished layers edges, shaping a square form for the transversal section, as can be

seen in the final strip on Figure 20. The laminated vertically was used in this

research, applying loads on the stack direction.

Inner and outer segments compose the final strip. Outer layer was obtained

by sanding inner surface layer outwards until get 3mm thickness and the same

process was carried out for the outer wall. Final thickness of layers was

approximately 3mm (Figure 22), and from these layers to cut samples and layer to

assemble beams.

46

Figure 20 Strip obtaining process, from bamboo culm to final composite (inner-outer) strip.

In previous works, tensile tests carried out by Ghavami in bone shaped

samples with aluminum plates at edges, where the clamps act. In the following

tests, he suggested to use straight shapes due to the orthotropic nature of the

bamboo.

Figure 21 Splitting longitudinally bamboo culm to obtain strips.

47

Figure 22 Thicknesser process to reduce and flatten strips into test specimens.

3.5. Determination of tensile modulus of elasticity Et

Tensile modulus of elasticity was determined for each segment of analysis,

although according to standard ISO/DIS 22157, for simple tensile test parallel to

fibers, this should only be done with bottom culms. Deformations were obtained

by using one clip-gage placed at the center of the test specimens, and three of

them using both clip and strain-gages to calibrate readings. Three test specimens

of 200mm long, 100mm width and 3mm thick were obtained for each segment of

analysis. Ghavami suggested straight shape test specimens, as in almost all cases

shapes are narrow in the middle (known as bone shape) to force failing in this

area. However, those assumptions generate stress concentrations in fiber-matrix

composites that could alter the results. Samples were identified as UST

(unnotched simple traction). Sample shape and dimensions are shown below.

10

mm

3 m

m

200 mm

Figure 23 Sample scheme for modulus of elasticity determination tests.

48

Simple tensile test is shown on Figure 24, shows the location of strain-gage

in the middle of the sample. During the tests read load values, vertical

displacement and deformation were measured with the purpose of determining the

stress-deformation curve for each specimen. Rusinque suggested installing

corrugated aluminum plates with epoxy adhesives Sikadur in both sides of

samples, to improve grip with clamps (Rusinque, 2009).

3.6. Determination of shear modulus G

Shear tests were performed to calculate shear corrected modulus of

elasticity, indicated by ASTM D198. It was determined on pieces of

approximately 3 mm thick, 200 mm long and 20 mm width in order to establish

shear resistance and its variation regarding the volume fraction along the thickness

of the culm. The test procedure followed the steps proposed by Ghavami & Suoza,

which modify the sample indicated by standard ISO N134, suggesting a simple

test specimen as shown below in Figure 28 (Ghavami & Souza, 2000) Therefore,

shear test is led to failure as a simple tensile test..

Test specimens were cut with a scalpel and processed on the planner

thicknesser oriented to obtain constant thick. Thickness was measured with

(a) (b)

Figure 24 Tensile test for modulus of elasticity determination (a) detailed strain and clip gage location before rupture in straight shape (b) sample

rupture.

49

pachymeter along the sample in six different points to define an accurate average

thickness to calculate area under shear stresses.

15

mm

3 m

m

200 mm

40mm

Shear line

Shear surface

A

B

Figure 25 Samples dimensions and opposite transverse cuts A and B made on specimen to define shear zone approximately of 40mm long and 3mm width.

For this test, corrugated aluminum plates were attached at sample ends

with epoxy adhesive Sikadur to improve grip on clamps.

3.7. Beam specimens - Laminated Glued Bamboo (LGB)

There were used 18 beam specimens, 3 by each segment of analysis. They

were assembled stacking randomly 10 to 14 layers of 550 mm approximately and

Figure 26 Tensile test for shear modulus determination (a) detailed clip gage location before rupture in straight shape and opposite transversal cuts (b)

sample rupture along the shear line.

50

effective span of 500 mm. Layered bamboo arrangements glued with any kind of

adhesives have been named with many terms, depending on adhesives and the

types of wood arranging them. Layers obtained in previous steps were arranged in

sets with similar conditions, before being stacked using mamona resin as adhesive

laminator.

Strips were divided into groups of the same analysis segments, as seen on

Figure 23 (a). First layers were arranged to spread resin uniformly, then second

layers were placed aligned to the first ones, and this process was until having a

stack of 8 to 12 pieces, as can be seen on Figure Figure 23 (b). As the chemical

reaction involved is exothermic, the drying process does not need heating.

However, a pressure ranging between 15 to 20 kPa was applied during 24 hours

after applying the adhesive. Blocks were polished in order to remove resin

excesses and to shape longitudinal and cross-sections. Final beams ready to test

are shown on Figure 23 (c).

(a) (b) (c)

Figure 27 (a) 3mm thick bamboo mats with a coat of mamona’s resin (b) strips stacked arranged for stick (c) final beams casted after adhesive

drying and polishing edges.

51

3.8. Determination of bending modulus of elasticity Eb

Beams were instrumented with upper and lower strain gages in the

midpoint of the beam to measure strains. A LVDT sensor was located in the

middle to read vertical displacement and loads applied by the load applicator. All

sensors were connected to acquisition system, which recorded values of each one

during the test period. The Figure 24 shows the test arrangement for a 4 points

bend test, which is set up in this way to generate pure bending moment at the

middle-span.

500mm

167mm 166mm 167mm

Load pins

LVDT

Lower and upper strain gages

167mm

Supporting pins

Figure 28 Set up of 4 point bending test.

Figure 29 Picture of a 4 points bending test arrangement showing the load and supporting conditions.

52

Tests were carried out until failure although strain gages and LVDT in

almost all cases were exceeded. However, information recorded was enough to

determine the modulus of elasticity and shear modulus for the LBL casted.

Different methodologies were used to establish bending modulus of

elasticity. In the first place, modulus was established based on elastic curve

equations. Then a methodology based on upper and lower strains on the beams by

using strain gages. Finally, the ASTM provides equations to calculate directly the

apparent modulus of elasticity and shear corrected modulus (ASTM D198, 2014)

on static test for lumber in structural sizes.

3.9. Mamona resin adhesive

The adhesive used was resin of Mamona. This is a mixture composed by

Mamona oil, known as castor oil, extracted from mamona fruit (Ricinus communis

L.) a popular bush mainly grown in tropical regions. It is used for obtaining a

polymer known as Polyurethane, which presents favorable features in terms of

strength and sustainability. Due to this, the resin of mamona emerged as an

optimal adhesive to use on this research, both for its mechanical performance and

biomaterial condition, as it was recognized in (Marques & Rossinoli Martins,

2009).

Mamona’s resin is a bi-component material made of a mixture, in a

proportion 2:1, of a Polyol (alcohol) and a Pre-polymer (Isocyanate) respectively,

as can be seen on Figure 30 Image of mamona components Polyol and Pre-

polymer and its respective proportions. Polymerization reaction occurs between

an isocyanate and an alcohol; it liberates about 24 kcal/mol of Urethane, in an

exothermic reaction. A dense solution was the result, which was applied

uniformly in layers of approximately 1 to 0,7 mm over the entire surface stuck.

The application had to be done immediately after the alcohol and the isocyanate

were mixed, due to its fast drying properties.

The experimental density of the composite was calculated by measuring the

weight of 142 ml of resin. The result was

Therefore, its experimental

specific gravity is 0,92, which conforms the specifications of the supplier

53

(Proquinor Produtos Quimicos do Nordeste Ltda) who states a range of 0,9 – 1,0

g/cm3.

Figure 30 Image of mamona components Polyol and Pre-polymer and its respective proportions.

In preliminary studies about polyurethanes derived from Mamona oil aimed

to obtain mechanical and physical properties as a biomaterial developed for

medicinal elements and prosthesis (Loureiro et al, 1998) obtained the following

values.

max load [N]

tensile rupture [KPa]

elongation [%]

Modulus of Elasticity [MPa]

Mamona's resin 8 335,75 105,27 0,36

Table 5 Mamona’s resin properties.

4 Results

4.1. Density and specific gravity

Density and specific gravity of samples, from inner, outer, bottom and

middle sections of the culm are presented on Table 6. Bottom SG was around 0,63

– 0,64 while the middle one was between 0,74 and 0,86. Values allow plotting

SG, as suggested by Ghavami, 1995 relation to the position along the culm length

for both inner and outer sides.

Specimen mass [gr]

sample's dimensions density [gr/cm³]

Especific Gravity lenght [mm] wide [mm] thick [mm]

1 Middle-Outer 26,304 227 36,76 3,67 0,86 0,86 2 Bottom-Outer 12,918 229 34,84 2,58 0,63 0,63 3 Middle-Inner 27,116 228 40,78 3,94 0,74 0,74 4 Bottom-Inner 16,333 225 39,095 2,91 0,64 0,64

Table 6 Density and specific gravity for bottom and middle segments.

Figure 31 Specific Gravity of inner and outer segments along the culm length.

55

4.2. Moisture

For moisture calculations, five samples were taken from different locations

along the culm, results are presented below on Table 7. The average value of

moisture was 11,11%.

Sample m₀ [gr] m [gr] Humidity [%] 1 16,85 15,12 11,44% 2 13,61 12,23 11,28% 3 21,17 19,06 11,07% 4 9,42 8,47 11,22% 5 7,66 6,93 10,53%

Average 11,11%

Table 7 Moisture of bamboo used for test specimens and beams.

4.3. Roughness

Results for roughness measurements are shown in Figure 33. The range of

readings were 9,55 mm for X-axis and 168,18 µm for Y-axis. Results had an

outstanding accuracy as the machine has a precision ranges of µm, however, the

bamboo roughness values were around of 40,78 µm shown in the Figure 33.

Figure 32 Profile of final polished bamboo laminas surface.

The curve shown in the lower right corner of Figure 33 provides the surface

profile of the segment shown in Figure 34. This was done, mainly to verify an

56

acceptable roughness value to allow optimal adhesion between layers, despite it

looks considerably flat at first glance. Surfaces were found to be sufficiently flat

and smooth to ensure adherence, when compared with benchmarks from other

laminated bamboo studies.

4.4. Test specimens analysis

The measurements presented were obtained using clip gages for both

tensile and shear tests, and running three of them equipped with strain gages to

check values. The variability between results is attributed to the differences in

testing parameters, as summarized previously, and the multiple operators used to

obtain the data. Standards for timber analysis suggest the use of reference values,

however these values do not exist for bamboo properties. The generally accepted

method for assessing bamboo data is to compare obtained values with published

data. Table 8 presents values of average tensile modulus of elasticity and shear

modulus for the six segments of analysis and their standard deviation (s).

n s % s of n s % s of BI 3 79,84 26,94 34% 3 7470,00 1313,80 18%MI 3 60,75 48,35 80% 3 16278,53 6714,67 41%TI 3 42,27 10,90 26% 3 12061,03 8263,40 69%BO 3 75,83 23,99 32% 3 7853,83 3315,94 42%MO 3 105,55 5,10 5% 3 16168,33 7144,57 44%TO 3 52,20 27,19 52% 3 18385,67 11872,36 65%

segmentShear modulus [MPa] Modulus of elasticity [MPa]

Table 8 Tensile modulus of elasticity Et and shear modulus G of test specimens.

Figure 33 Surfaces of final layers used to obtain test specimens and assemble beams.

57

Standard deviation values as a percentage of averages show the high

variability between samples, which ranges from 5% to 80%. This variability can

be attributed to multiple sources, but is often a result of the material itself.

However, the limited number of tests for each segment tends to increase the range

of variability. This variability can be seen graphically on Figures 35 and 36 where

modulus values are plotted with respect to longitudinal location, inner wall results

are located over outer wall ones, to help visualizations the differences. However,

those ranges show some trend in terms of longitudinal and wall divisions.

Figure 34 Shear modulus of inner and outer walls vs longitudinal location.

While Figure 35 presents an apparent random distribution of shear modulus

both for longitudinal and radial location, Figure 26 presents a slight tendency to

increase MOE as it goes from bottom to top.

58

Figure 35 Tensile modulus of elasticity of inner and outer walls vs longitudinal location.

The standard deviation of the modulus of elasticity confirms wide

variability resulting from heterogeneous and orthotropic materials as bamboo. In

addition, the few numbers of trials of each segment makes it impossible to

determine outlier spots as random errors. While Verma & Chariar, 2012

concluded that MOE increases from inner wall outwards and from bottom to the

top. For this bamboo species and test there is only a marked trend of increasing

from bottom to middle segment. And a soft trend of increasing from inner to outer

region. Opposite to their conclusions, inner top segment resulted to have a minor

MOE than both middle segments but it was the region where the increasing from

inner outwards was more visible.

59

Figure 36 Tensile modulus of elasticity found for all segments of analysis.

Figure 37 Tensile modulus of elasticity of inner segments.

It turns necessary to analyze inner and outer wall segments separately in

order to determine some behavior patterns for individual segments. Figures 38 and

39 present tensile modulus of elasticity for inner and outer wall respectively.

A separate analysis of inner wall segments indicates a top strength for

middle sections, moreover, outer wall segments show an increasing trend as some

literature has suggested for some bamboo species. Addressing inner and outer

regions separately, it can be said that outer regions support Verma & Chariar

findings, while inner region states middle region as the higher stiffness one.

60

Figure 38 Tensile modulus of elasticity of outer segments.

Figure 40 and Figure 41 plot average values and the variance along the

length and across the wall. Figure 40 establishes a clear trend in bottom segments

compared to middle and top ones, confirming previous investigations, which

established that bamboo bottom was the weakest section. However, for the middle

and the top it cannot determine a defined trend, as the middle sections appears to

have higher modulus than top.

Figure 39 Marginal values of tensile MOE of segments along the length.

61

For marginal values of inner and outer sections on Figure 41, do not allow

to determine a strong pattern across the wall thickness. However, it can be seen

that outer segments seem to have higher values of MOE.

Figure 40 Marginal values of tensile MOE on wall thickness.

Previous studies encompassed bamboo culm analysis based on divisions

along the culm and across the wall let to compare obtained values with relatives of

other bamboo species (see Table 9). Both Verma & Chariar, 2012 and Li, 2004

found increasing values from bottom to top and from inner to outer wall for elastic

constants. However, values for top sections obtained in this research do not

correspond to those of literature as middle sections presented higher elastic

constants.

62

Bamboo Et and Eb along the culm [Gpa]

Across the wall thickness

Source Bamboo species Along the length

Bottom Middle Top

Inner

Et Obando & Ghavami 2015 Dendrocalamus giganteus 7,47 16,28 7,30

Eb Obando & Ghavami 2015 Dendrocalamus giganteus NA 11,11 4,71

Et Verma & Chariar 2013 Dendrocalamus strictus 2,10 2,70 4,66

Eb Li 2004 Phyllostachys pubescens 9,17 9,25 9,52

Outer

Et Obando & Ghavami 2015 Dendrocalamus giganteus 7,85 16,17 18,39

Eb Obando & Ghavami 2015 Dendrocalamus giganteus 4,70 9,32 8,29

Et Verma & Chariar 2013 Dendrocalamus strictus 4,60 6,40 8,90

Eb Li 2004 Phyllostachys pubescens 16,32 16,40 16,68

Table 9 Bamboo tensile modulus of elasticity Et and bending modulus of elasticity Eb of different culm segments for different species.

4.4.1. Statistical analysis of test specimen results

Data analysis demands determining statistical differences to classify and

analyzing results. Due to high degree of dispersion of data comes highly probably

do nor determine those differences, however, analysis let to generate marginal

values as average values with confidence intervals based on variances so that

ANOVA analysis was made for both test specimens and beam specimens. In this

case, an ANOVA model for fixed effect is ineffective because longitudinal and

radial position of segments turn out to be two different and independent factors, at

least in this case of study. Therefore, it becomes necessary an ANOVA model of

factorial design for two independent factors, in order to study the effect of each

one of them for each trial. This methodology analyzes the effect along the culm

and across the wall location on the response variable independently. It also

provides objective results to determine if there is a choice at factor longitudinal

location, which, independently of radial location, generates a better response, and

vice versa. Finally, this statistical method determines what combination of both

factors provides a better response, in this case, which one has better strength

performance.

63

In a factorial design facts, as well as interaction between them are equally

important for analysis. It leads to proof some hypothesis to validate ANOVA

analysis:

1. Equality of the effects on longitudinal location treatment.

2. Equality of the effects on radial location treatment

3. Interaction between longitudinal and radial locations.

In this way, the first hypothesis of homoscedasticity can be accepted or

rejected by using the Levene proof, which determines if variance of error remains

constant along the cases. Table 10 presents Levene contrast for equality of the

error variances, with longitudinal location as dependent variable. Sig. value is

0,000 therefore it is less than the significance level α=0,05. This rejects the null

hypothesis and then the assumption of homoscedasticity is unsatisfied. However,

for radial location the Sig. value is higher than significance level, therefore, null

hypothesis is accepted and the assumption of homoscedasticity is satisfied.

Table 10 Homogeneity of variances proof for longitudinal segments as dependent variable.

Table 11 Homogeneity of variances for cross section segments as dependent variable.

Summarizes, this means that values of MOE on wall thickness measured

maintain the error of the variance and on the other hand, values along the length

do not. It can be seen in Figure 38 above where inner profile reaches it maximum

value on middle segment and outer Figure 39, reaches it on top segment.

Normality assumption should be rectified by Shapiro-Wilk proof. Table 12 shows

Sig. values of 0,365 and 0,830 therefore the null hypothesis of data, which states

that it comes from a normal distribution, is accepted and normality assumption is

satisfied too. In other words, this indicates that values present a normal

distribution.

64

Table 12 Normality proof.

Finally, the residue graph Figure in 42 was generated. This Figure analyzes

intersections of residue vs observed values, identifying some linear or defined

pattern. The absence of any pattern shows independence, and allows accepting the

assumption.

Figure 41 Residue graph.

After verifying the required assumptions, the ANOVA analysis allows

concluding about the existence of significant differences between segments of

analysis. However, the Sig. values on Table 13 for longitudinal and wall location

are 0,187 and 0,567. Those values are higher than the significance level (α=0,05),

therefore null hypothesis cannot be rejected and it can be stated objectively that

there are significant differences. Nevertheless, it provides evidence that shows

65

that longitudinal segments vary less than wall division segments. Although it is

possible to determine an objective difference between groups, a 0,187 Sig. value

allows to assume a closeness to significance level 0,05.

Table 13 Inter-subjected effects proof ANOVA table.

On the ANOVA table it can be determine the optimal statistic method for

analyzing data by comparing average quadratic errors from longitudinal and cross

sectional divisions. If quadratic average error is less than quadratic errors of

factors (longitudinal and cross sectional), a factorial design analysis by blocks can

be carried out. In this case, longitudinal level presented a better performance that

can be grouped, even when no level presented significant differences.

66

Table 14 HSD Turkey table.

According to HSD Turkey analysis, longitudinal location levels are similar,

despite of visible difference of values at first glance. However, there is a relevant

fact in Table 14 that indicates a higher MOE value for middle segments. Table 15

shows a statistical analysis of relationships of each level with others. On the Sig.

values it can be seen the trend of M as the highest section, and the close

relationship between middle and top, and the trend to decrease values of B

sections.

Table 15 multiple segments comparison by HDS Turkey and DMS.

67

Statistical analysis provides marginal MOE values for both along the length

and wall thickness. Figure 43 plots MOE marginal averages for longitudinal

segments. It presents a clear sameness between inner and outer MOE of bottom

and middle sections, rising from bottom upwards. However, for the top section it

results in different values for inner and outer parts, being outer one higher than

middle average and the inner one lower.

Figure 42 Estimated marginal averages of MOE along the length.

On the other hand, marginal measures along the wall thickness evidence

small differences between inner and outer parts for bottom and middle sections. In

addition, it marks a defined rising trend for the top segment from inner outwards.

Figure 43 Estimated marginal averages of MOE along the wall thickness.

68

4.5. Beam analysis

Bending test provides numerous ways to obtain mechanical properties of

materials and beams as well. Available methodologies generate results, which

depending on what it is being measured, turn out to be the suitable or not. In this

case, four different ways to obtain modulus of elasticity were used and the results

are presented on Table 16. Those results are compared with control data, tensile

modulus of elasticity, obtained in order to determine any pattern on behavior of

segments of analysis and beams.

Displacement modulus of elasticity was obtained by solving the integration

method, for beam analysis of mechanical of materials using LVDT readings.

Strain modulus of elasticity was calculated by strain gage readings located at the

upper and lower surface of beam mid-span. Apparent modulus and shear corrected

were obtained using formulas suggested by ASTM D198 for statics tests of

lumber in structural sizes. Data for segment Bottom-Inner BI was lost due to fails

on the acquisition system. Consequently, lack of information hinders any analysis

involving this segment.

69

BI MI TI BO MO TO

n 3 3 3 3 3 37470,00 16278,53 12061,03 7853,83 16168,33 18385,67

s 1313,80 6714,67 8263,40 3315,94 7144,57 11872,36% s of 18% 41% 69% 42% 44% 65%

controln 0 3 3 3 3 3

NA 11109,00 4708,33 4698,00 9317,00 8287,00s NA 2752,93 182,56 795,56 3959,16 548,34

% s of NA 25% 4% 17% 42% 7%r NA 0,85 -0,99 0,99 0,94 -0,83n 0 3 3 3 3 3

NA 31388,00 13583,00 40681,33 822858,00 245302,67s NA 3330,27 1962,39 37527,17 780949,68 263598,94

% s of NA 11% 14% 92% 95% 107%r NA 0,49 -0,65 -0,94 0,97 -0,87n 0 3 3 3 3 3

NA 19887,40 6465,75 5216,88 12881,08 9710,54s NA 7465,66 1231,93 464,44 3005,88 1128,70

% s of NA 38% 19% 9% 23% 12%r NA 0,30 -0,98 1,00 0,68 0,58n 0 3,00 3,00 3,00 3,00 3,00

NA 1936,58 1318,48 2395,20 3188,40 1845,05s NA 107,51 78,56 194,83 550,14 331,03

% s of NA 6% 6% 8% 17% 18%r NA 0,92 -0,81 -0,95 -0,99 -0,82

Dis

pla

cem

en

t M

od

ulu

s o

f e

last

icity

MP

a

Str

ain

Mo

du

lus

of

ela

stic

ity

MP

a

Ap

pa

ren

t M

od

ulu

s o

f e

last

icity

MP

a

Sh

ea

r co

rre

cte

d

Mo

du

lus

of

ela

stic

ity M

Pa

Bending Modulus of elasticity acquisitions

segment

Te

nsi

le

Mo

du

lus

of

ela

stic

ity M

Pa

Table 16 Bending modulus of elasticity obtained by four different methodologies.

Strain modulus of elasticity presented several outliers values. This could be

due to random and procedure errors caused by issues relative to the data

acquisition system, strain gage operation and surface characteristics. Therefore,

Table 17 presents averages of r values in order to select suitable data for analysis.

Thus, Table 15 confirm assumptions that strain modulus should be discarded.

Moreover, shear corrected modulus has values substantially small compared to

others. This may be due to the shear values experimentally obtained, which affect

the corrected value and differences between standard lumber used and bamboo.

r averages 0,19 -0,20 0,32 -0,53

Strain Modulus of elasticity MPa

Apparent Modulus of elasticity MPa

Shear corrected Modulus of elasticity

Displacement Modulus of elasticity MPa

Table 17 r averages for modulus of elasticity regarding tensile modulus.

70

Coefficient r of correlation describes similarity between two data groups,

when it is close to one, both data groups are more correlated. However, both the

apparent and the displacement methods are considerably far from one, but are

closer than the shear corrected and strain modulus. Figures 45 and Figure 46 show

longitudinal and wall profiles in order to compare graphically different modulus

methodologies and then choose suitable data groups to carry out statistical

analysis.

Figure 44 Longitudinal inner profile vs modulus of elasticity.

Figure 45 Longitudinal outer profile vs modulus of elasticity.

Figure 45 and Figure 46 show the displacement and apparent modulus as the

curves that better fit to tensile modulus of elasticity.

71

Figure 46 Wall thickness profile of middle section vs modulus of elasticity.

Figure 47 Wall thickness profile of top section vs modulus of elasticity.

4.5.1. Statistics bending data analysis

To compare experimental tensile modulus with displacement and apparent

modulus it is necessary to carry out another statistic analysis as variability and

heterogeneity are strictly linked to the results of the response variable. Therefore,

it should be determined if the difference between the two experimental units

subjected to different treatments (method of modulus acquisition), is due to a real

difference between treatment effects or due to heterogeneity of samples.

Randomized block design is the method used for this statistical analysis.

72

Segments of analysis compose blocks, and the treatments are assigned randomly

to the blocks. This design strategy improves accuracy when compared to reducing

residual variability. All treatments run into each block, which implies a restriction

over randomization.

Levene proof verifies variances equality. Sig. value in this case is 0,04, as

shown in Table 18, which is close to a significance level of 0,05. This rejects

homoscedasticity assumption and the null hypothesis, however, for further

analysis the low range of difference between Sig. value and significance level

could be determinant. Despite Sig. value rejects hypothesis, it is very close to

significance value, even more in the case of anisotropic materials analysis.

Table 18 Equality Levene proof of error variances.

Normality verification of data requires Shapiro-Wilk proof. For this proof

all Sig. values in Table 19 are higher than 0,05 except for the TI. Therefore, it can

be said that normality assumption is met for most of the segments of analysis,

except for TI segment.

Table 19 Normality proof.

73

Figure 48 Square residual for beam data analysis.

The independence assumption is verified by identifying some defined

patterns at square residual vs prediction as shown in Figure 49. At first glance,

there are not any patterns so the assumption is accepted.

Variable dependiente: MOE

Origen

Tipo III de suma

de cuadrados gl

Cuadrático

promedio F Sig.

Modelo corregido 890003419,822a 6 148333903,304 5,814 ,000

Interceptación 5315647493,88

9 1

5315647493,88

9 208,354 ,000

segment 570591349,111 4 142647837,278 5,591 ,001

method 319412070,711 2 159706035,356 6,260 ,004

Error 969478947,289 38 25512603,876

Total 7175129861,00

0 45

Total corregido 1859482367,11

1 44

a. R al cuadrado = ,479 (R al cuadrado ajustada = ,396)

Table 20 Inter-subjects effects proof ANOVA table.

74

Differences between methods were clear since r coefficient averages were

between 0,19 and 0,32 (displacement and apparent), regarding the tensile

modulus. Moreover, according to ANOVA results in Table 20 there are significant

differences among segments too. Sig. values are between 0,001 and 0,004 both

lower than significance level 0,05.

Table 21 presents averages values and limits for each segment of analysis,

and Figure 50 shows them graphically. Those limits confirm the difference

between segments and put forward middle segment as the strongest of all.

Table 21 MOE averages for segments.

Figure 49 Limits of average MOE for segments.

When comparing both experimental and more accurate methods for

obtaining modulus with tensile test, it can be said that all three methods fit on a

range relatively thin regarding difference between specimens and beams,

experimental and random errors and number of trials. Estimated marginal values

75

for MOE in Figure 51 defines middle section as strongest section, and presents an

evident fall from middle to top. Bottom section remains as the one with the lowest

values.

Figure 50 Estimated marginal averages of MOE for segments of analysis

4.6. Failure analysis

ASTM D143 – 14 for specimens of timber, explains the types of failure in

static bending, as it was presented in the second chapter. However, in terms of

fracture surfaces, bamboo may be roughly divided into brash and fibrous. The

term brash indicates abrupt failure and fibrous indicates a fracture showing

splinters. Moisture content is an essential factor to determine the type of fracture.

Table 22 shows types of failure of each laminated bamboo beam. Moreover,

it presents an alternative secondary cause of failure, related to failures that

preceded the initial fracture during the tests. Another classification in terms of

surface fracture is included as well. The results presented a marked trend to

fibrous surface fracture on the inner specimens and brash surface fracture for

outer ones. Inner specimens failed due to tensions strengths considered simple,

splintering and brash tension with a great presence of horizontal shear and inner

compression strengths as secondary causes of failure. Outer specimens presented a

76

predominant horizontal shear and brash tension as primary cause of failure, and

compression with horizontal strengths as secondary cause for inner specimens.

Specimen Primary type of failure Secondary type of failure Surface fracture1 BI simple tension horizontal shear fibrous2 BI simple tension horizontal shear fibrous3 BI splintering tension horizontal shear fibrous4 MI splintering tension inner compression fibrous5 MI splintering tension inner compression fibrous6 MI splintering tension inner compression fibrous7 TI simple tension inner compression brash8 TI simple tension inner compression brash9 TI brash tension inner compression brash10 BO horizontal shear compression fibrous11 BO horizontal shear compression fibrous12 BO brash tension horizontal shear brash13 MO horizontal shear compression brash14 MO horizontal shear compression brash15 MO horizontal shear compression brash16 TO brash tension horizontal shear brash17 TO brash tension inner compression brash18 TO brash tension inner compression fibrous

Table 22 Types of primary and secondary failures on the beams and surface fracture.

Figures below show different type of fracture on beam specimens.

Figure 51 Fracture on beam specimen 3 by splintering tension and horizontal shear.

77

Figure 52 fracture on specimen 17 by brash tension and inner compression.

Figure 53 Fracture on specimen 8 by simple tension and inner compression.

5 Conclusion

This research established the tensile modulus of elasticity Et and bending

modulus of elasticity Eb, for 6 groups of specimens taken from defined segments

along the culm and across the wall thickness of Dendrocalamus Ginganteus

species. It was found that bottom section had the lowest Et (7,47 GPa and 7,85

GPa, inner and outer respectively). Then values for middle section were (1,62 GPa

and 1,61 GPa) and for top were (1,2 GPa and 1,8 GPa). Outer segments were

found to have higher values than inner ones, as literature (Vema & Chariar, 2012

and Li, 2004) has established for elastic constants on micromechanics of bamboo.

However, top sections values were found to be lower than middle section ones

dissenting from literature. Bending modulus of elasticity Eb, calculated for 6 types

of beams assembled by layers from each segment, were 19,88 GPa and 12,88 GPa

for middle section which presented higher values, followed by top section (6,46

GPa and 9,71GPa) and bottom section (5,2 GPa) which presented the lowest

values.

Although a statistical analysis showed no significant differences among

segments, it provided marginal values for elastic constants based on data

dispersion. Those values allowed introducing a relation between Et and Eb, (by

apparent MOE methodology), which could introduce equivalent values for the

bending properties using the solid mechanics theory. This is principally because

division in segments reduced the variation of properties along the culm, making

group properties more homogeneous while they are still heterogeneous within the

section. In addition, as laminated analysis theory assumes perfect bonding,

material properties and layers orientation, by using adhesive with strength higher

than τ, homogenized sections aligned in the same direction let introduce a solid

mechanics discretization.

Divergences on trend of top section with literature could be attributed to

experimental errors and low number of trials. However, difference between

regions and species, could be important facts to explain those differences. Based

79

on the results, it can be suggested that middle sections segments, both inner and

outer, would generate best beams subjected to bending loads. Top segments, are

proposed to use the whole layer without splitting, because there were not

significant differences among them to make it worthwhile and divergences of their

elastic constants with literature values. Secondly, bamboo walls reduce as it rises

from bottom to top; therefore layers resulting from top sections are not

sufficiently thin to carry out a proper division. Bottom segments are suggested to

compose beams subjected to lower bending loads or compose axially loaded

elements, as bottom section has the highest compressive stress than middle and

top according Li, 2004. For bottom and middle sections, it is recommended to

split them in half when it is necessary improving design accuracy or reduce

properties variation on the element.

Accurate equivalences introduced using solid mechanics approach require a

wide and segmented characterization of materials, however; bamboo anisotropy

makes this harder as it depends on factors beyond what can be determined.

Therefore, for a local and decentralized production this study demonstrates that

re-arranging beams assembly, bending design and beams performance could be

improved.

Further research is required to include factor such as ply orientation on

lamination, adhesive used, layered combination, and moisture content, to enhance

the approach presented and allow scaling-up to small scale commercial

manufacture.

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