Davalos, J., Qiao, P., Wang, J., Salim, H. and Schlussel, J. (2002). Shear Moduli of ... Sastra, H., Siregar, J., Sapuan, S. and Hamdan, M. (2006). Tensile ...
DETERMINATION OF ELASTIC CONSTANTS OF PULTRUDED FIBRE REINFORCED POLYMER CLOSED SECTIONS – EXPERIMENTAL CAMPAIGN
By Ibrahim Khyaam Arshad
April, 2015 Faculty of Engineering and Computing Coventry University
Dissertation submitted to the department of Civil Engineering, Architecture and Building, Coventry University in partial fulfilment of the requirements for the degree award of Bachelor of Engineering in Civil Engineering
ABSTRACT Fibre reinforced polymer (FRP) hollow section are classified as composite materials and have been used for various applications throughout history, initially developed for military applications and aerospace industry. Only recently has the material entered the civil engineering and construction industry as a stand-alone or hybrid structural material. A review has been undertaken to establish the level of research and practical application this material has witnessed over the recent years, the overall history of structural applications is minimal but increasingly growing. The need for imperative research into the material is apparent, being a new class of construction materials, FRP composites necessitate a new set of challenges. This study attempts to utilise experimental tests to determine the elastics constant of two 100 mm x 100 mm tubular hollow section having a thickness of 4 mm and the other 6 mm. The elastic constants determined were:
In-Plane Shear Moduli Longitudinal Flexural Moduli Transverse Flexural Moduli Poisson’s Ratio Longitudinal Compressive Moduli Longitudinal Compressive Strength
Experimental test protocols were used in accordance with standards or previous research methods, the data obtained for these elastic constants were examined in terms of reliability and upper or lower bound solutions. A range of 2.5 GPa to 2.6 GPa was determined from a full section profile test (Timoshenko beam) which was found to be a lower bound solution, the test also gave a upper bound solution for the longitudinal flexural modulus which ranged from 23 GPa to 25 GPa. A lower bound solution for the longitudinal flexural modulus was also determined from a standard three-point bending test, which gave a range between 12 GPa to 18 GPa. The transverse flexural modulus was determined by a C-channel test, a range of 8 GPa to 16 GPa was determined, resulting in both upper and lower bound results. A compressive strength and modulus test was carried out in order to determine the three elastics constants for Poisson’s ratio, longitudinal compressive modulus and longitudinal compressive strength. A range of 0.2 to 0.43 was determined for the major Poisson’s ratio and a range of 13 GPa to 50 GPa was observed for the compressive modulus. For the compressive strength a range of 60 MPa to 160 MPa was determined, these values were found to be substantially low and were much lower than published lower bound results. For the classification of hollow section under axial compression a strong relation was established between varying profile cross-sections, the correlation showed that the member thickness and cross-section had an effect on the classification of the profile. It was classified that the plate was slender for the 4 mm sample and intermediate for the 6 mm sample, the wall was classified for an effective length of 100 mm to 2000 mm with both columns resulting in intermediate classification at 2000 mm.
KEYWORDS:
fibre reinforced polymer composites, elastic constants, compression column classification, pultruded FRP hollow profiles, shear moduli, flexural moduli, Poisson’s ratio, compressive moduli.
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DEDICATION
I would like to dedicate this thesis to the two most inspirational people in my life, my parents:
Arshad Mohammed & Sajida Arshad Whom without I would not be here today, I cannot thank them enough for the love, care and support they have given me.
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ACKNOWLEDGEMENT
First and foremost the author would like to thank God for this opportunity and blessing. The author would like to express his upmost gratitude to Mr Alfred Kofi Gand, who has provided essential support, guidance, knowledge and time throughout this project and has aided immensely in the successes and completion of this project. The author would also like to express his appreciation and gratitude to the technicians; Kieran, Ian and Chris from the department of Civil Engineering, Architecture and Building, who have provided their time in fabricating material and aiding in experimental tests. Also the author would like to thank Dr Eoin Coakley, for taking time in aiding in this project. Finally the author would like to thank his family and friends for their support whilst undertaking this project and other members of staff who supported the project.
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TABLE OF CONTENTS ABSTRACT ............................................................................................................................ i DEDICATION .........................................................................................................................ii ACKNOWLEDGEMENT ........................................................................................................ iii ABBREVIATIONS / ACRONYMS ..........................................................................................vi LIST OF FIGURES .............................................................................................................. vii LIST OF TABLES..................................................................................................................ix 1. INTRODUCTION ............................................................................................................... 1 1.1 Introduction.................................................................................................................. 1 1.2 Aims ............................................................................................................................ 1 1.3 Objectives.................................................................................................................... 2 1.4 Research Constraints .................................................................................................. 2 1.5 Structure of Dissertation .............................................................................................. 2 2. BACKGROUND REVIEW .................................................................................................. 4 2.0 Introduction.................................................................................................................. 4 2.1 Structural Applications ................................................................................................. 4 2.2 Advantages ................................................................................................................. 8 2.3 Limitations ................................................................................................................... 9 2.3 Pultruded Glass Fibre Reinforced Profiles ................................................................... 9 2.4 Profiles and Geometry ............................................................................................... 10 2.5 Pultrusion Process..................................................................................................... 11 3. REVIEW OF TEST STANDARD AND PROTOCOLS ...................................................... 12 3.0 Introduction................................................................................................................ 12 3.1 In- Plane Shear Modulus (GLT)................................................................................... 12 3.1.1 Iosipescu Test ..................................................................................................... 12 3.1.2 ± 45° off-axis Tensile Test ................................................................................... 13 3.1.3 Full Section Profile Test (Timoshenko Beam) ...................................................... 14 3.1.4 10° off-axis Tensile Test ...................................................................................... 14 3.2 Longitudinal Flexural Modulus (Ef,L) ........................................................................... 15 3.3 Transverse Flexural Modulus (Ef,T) ............................................................................ 15 3.4 Poisson’s Ratio (V12 and V21) ...................................................................................... 16 3.5 Longitudinal Compressive Modulus (Ec,L) .................................................................. 16 4. EXPERIMENTAL TEST PROGRAMME .......................................................................... 18 4.0 Introduction................................................................................................................ 18
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4.1 Full Section Profile Test (Timoshenko Beam) ............................................................ 18 4.2 Three-Point Coupon Bending Tests ........................................................................... 20 4.3 Determination of Transverse Flexural Modulus .......................................................... 22 4.4 Compression Strength and Modulus Tests ................................................................ 23 4.5 10° off-axis Tensile Tests .......................................................................................... 25 5. ANALYSIS AND DISCUSSION OF TEST RESULTS ...................................................... 27 5.1 Full Section Profile Test (Timoshenko Beam) ............................................................ 27 5.2 Three-Point Coupon Bending Tests ........................................................................... 31 5.3 Determination of Transverse Flexural Modulus .......................................................... 36 5.4 Compression Strength and Modulus Tests ................................................................ 38 5.5 Discussion of Results ................................................................................................ 45 5.5.1 In-Plane Shear Modulus GLT ............................................................................... 45 5.5.2 Longitudinal and Transverse Flexural Modulus Ef,L & Ef,T .................................... 46 5.5.3 Poisson’s Ratio V12 and V21 ................................................................................. 47 5.5.4 Longitudinal Compressive Modulus and Strength EL,c and FL,c ............................ 48 6. CLASSIFICATION OF HOLLOW SECTIONS UNDER AXIAL COMPRESSION .............. 49 6.0 Introduction................................................................................................................ 49 6.1 Material Properties .................................................................................................... 49 6.2 Closed Form Equations ............................................................................................. 50 6.2 Compression Column Classification .......................................................................... 51 6.3 Classifying Various Profiles from Pultruders .............................................................. 53 6.4 Worked Example ....................................................................................................... 56 7. CONCLUSIONS AND RECOMMENDATIONS FOR FURTHER WORK .......................... 58 7.1 Conclusion................................................................................................................. 58 7.2 Recommendation for Further Work ............................................................................ 59 REFERENCES ................................................................................................................... 60 APPENDICES ..................................................................................................................... 65
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ABBREVIATIONS / ACRONYMS FRP – Fibre Reinforced Polymer GFRP – Glass Fibre Reinforced Polymer UD – Unidirectional (Fibres) ASTM – American Society for Testing and Materials BS EN – British Standard European Norm RDP – Rack Distribution Panel SH – Short IN – Intermediate SL – Slender CP - Compact
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LIST OF FIGURES Figure 2.1 – Britannia Bridge rectangular square hollow sections, UK (Dixon 2006) ............. 4 Figure 2.2 – Eyecatcher Building, Switzerland (Mosallam et al. 2013) .................................. 5 Figure 2.3 – Aberfeldy Pedestrian Footbridge, Scotland (Lynch 2012) .................................. 6 Figure 2.4 – Lleida Bridge, Spain (Pulido 2001) .................................................................... 6 Figure 2.5 – Pontresina Bridge, Switzerland (Fiberline.com 2008) ........................................ 7 Figure 2.6 – Fibre reinforced polymer material layers (Aamanet.org, 2013) ........................ 10 Figure 2.7 – GFRP Common Pultruded Profiles (Mosallam et al. 2013) .............................. 10 Figure 2.8 – Pultrusion Process Diagram (creativepultrusions.com 2015) ........................... 11 Figure 3.1 – Iosipescu Test Apparatus and Diagram (Cardoso 2014) ................................. 13 Figure 3.2 – (ASTM D 3518) ± 45° off-axis Tensile Test (Cardoso 2014) ............................ 14 Figure 3.3 – Channel Test for Transverse Flexural Modulus (Cardoso 2014) ...................... 16 Figure 3.4 – ASTM Standard fixtures for Compressive Modulus (Adams 2005) .................. 17 Figure 4.1 – Fabricated 1200 mm Timoshenko beams........................................................ 18 Figure 4.2 – Schematic representation of test ..................................................................... 19 Figure 4.3 – Full section profile test setup ........................................................................... 19 Figure 4.4 – Methods of analysis for full section profile test data......................................... 20 Figure 4.5 – Three-point bending samples .......................................................................... 20 Figure 4.6 – JJ Lloyd three-point bending test ..................................................................... 21 Figure 4.7 – Schematic representation of three-point bending test to ASTM D790 .............. 21 Figure 4.8 – Channel test for transverse flexural modulus ................................................... 22 Figure 4.9 – Schematic representation of channel test for transverse flexural modulus....... 22 Figure 4.10 – Coupon compression test to determine Poisson’s ratio ................................. 23 Figure 4.11 – Avery-Denison 2000 kN Capacity Compression Machine .............................. 24 Figure 4.12 – Schematic representation of coupon compression test .................................. 24 Figure 4.13 – Schematic representation of 10° off-axis tensile test ..................................... 25 Figure 5.1 – Full section profile test 4 mm yellow sample based on first method of analysis 27 Figure 5.2 – Full section profile test 4 mm yellow sample based on second method of analysis ............................................................................................................................... 28 Figure 5.3 – Full section profile test 4 mm yellow sample based on third method of analysis ........................................................................................................................................... 28 Figure 5.4 – Full section profile test 6 mm grey sample based on first method of analysis .. 29
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Figure 5.5 – Full section profile test 6 mm grey sample based on second method of analysis ........................................................................................................................................... 29 Figure 5.6 – Full section profile test 6 mm grey sample based on third method of analysis . 30 Figure 5.7 – Three-point bending test for 4 mm yellow coupons (1a) .................................. 31 Figure 5.8 – Three point bending test for 4 mm yellow coupons (2a) .................................. 32 Figure 5.9 – Three-point bending test for 4 mm yellow coupons (1b) .................................. 32 Figure 5.10 – Three-point bending test for 4 mm yellow coupons (2b) ................................ 33 Figure 5.11 – Three-point bending test for 6 mm grey coupons (1a) ................................... 33 Figure 5.12 – Three-point bending test for 6 mm grey coupons (2a) ................................... 34 Figure 5.13 – Three-point bending test for 6 mm grey coupons (1b) ................................... 34 Figure 5.14 – Three-point bending test for 6 mm grey coupons (2b) ................................... 35 Figure 5.15 – Channel test for 4 mm yellow channels ......................................................... 36 Figure 5.16 – Channel test 6 mm grey channels ................................................................. 37 Figure 5.17 – Coupon compression test for 4 mm yellow longitudinal coupon (A3) ............. 38 Figure 5.18 – Coupon compression test for 4 mm yellow transverse coupon (B1) .............. 39 Figure 5.19 – Coupon compression test for 4 mm yellow transverse coupon (B2) .............. 39 Figure 5.20 – Coupon compression test for 4 mm yellow transverse coupon (B3) .............. 40 Figure 5.21 – Coupon compression test for 6 mm grey transverse coupon (C1) ................. 40 Figure 5.22 – Coupon compression test for 6 mm grey transverse coupon (C2) ................. 41 Figure 5.23 – Coupon compression test for 6 mm grey longitudinal coupon (D1) ................ 41 Figure 5.24 – Coupon compression test for 6 mm grey longitudinal coupon (D2) ................ 42 Figure 5.25 – Coupon compression test for 6 mm grey longitudinal coupon (D3) ................ 42 Figure 6.1 – Column classification chart using data from Table 6.4 ..................................... 52
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LIST OF TABLES Table 2.1 – Comparison and rating of FRP and Steel Merits/Advantages (GangaRao et al. 2010) .................................................................................................................................... 8 Table 5.1 – Comparison between Timoshenko analysis methods ....................................... 30 Table 5.2 – Longitudinal Flexural Modulus from three-point bending test ............................ 35 Table 5.3 – Transverse flexural modulus from channel test ................................................ 37 Table 5.4 – Longitudinal and transverse compressive modulus from coupon compression test ...................................................................................................................................... 43 Table 5.5 – Calculated Poisson’s ratio from coupon compression test ................................ 43 Table 5.6 – Calculated Minor Poisson’s ratio from coupon compression test ...................... 43 Table 5.7 – Longitudinal and transverse compressive strength from coupon test ................ 44 Table 5.8 – In-plane shear modulus results from various sources ....................................... 45 Table 5.9 – Longitudinal flexural modulus from various sources ......................................... 46 Table 5.10 – Poisson’s ratio review from various authors and manufacturers ..................... 47 Table 5.11 – Longitudinal compressive modulus and strength comparison from various sources ............................................................................................................................... 48 Table 6.1 – Material properties used in compression column classification ......................... 49 Table 6.2 – Column classification range .............................................................................. 51 Table 6.3 – Plate Classification ........................................................................................... 51 Table 6.4 – Compression column classification for 4mm and 6mm samples ....................... 52 Table 6.5 – Exel Composites LTD plate classification ......................................................... 53 Table 6.6 – RBJ Plastics LTD plate classification ................................................................ 54 Table 6.7 – Exel Composites LTD Compression Wall Column Classification ...................... 55 Table 6.8 – RBJ Plastics LTD Compression Wall Column Classification ............................. 55
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1 INTRODUCTION 1.1 Introduction Fibre reinforced polymer (FRP) composites were introduced around the 1940’s; initially developed for military applications during the second world war (Cardoso 2014), and has only recently begun to flourish as a structural composite due to the superior properties it holds compared to other common construction materials. Within the early stages of introducing FRP to the construction industry, the manufacturing process was expensive therefore limiting its potential. However around the 1990’s large importance was placed on FRP composites and manufacturing expenses reduced, opening the material to vast structural applications (Bakis et al. 2002). The pultrusion process aided the reduction to the manufacturing cost of FRP composites, invented by W. Brant Goldsworthy within the 1950s, it enabled a continuous fabrication process that impregnated reinforcing fibres with thermosetting matrix that are drawn into heated die to form the composite profiles (Fairuz 2014 and Cardoso 2014). Elastic constants are crucial for understanding mechanical properties, the need for reliable experimental investigation in determining these elastic properties is essential for development of FRP composites. “It is imperative that for engineers and the construction industry to fully embrace this efficient and novel material, in-depth understanding of the structural behaviour of pultruded FRP elements is needed.” (Gand et al. 2013) The novel material has had little research in comparison to other common structural materials, with researchers placing large importance on the need understanding this material. A unique material with high strength to weight ratio, high durability and corrosion resistance, is sufficient in becoming a primary structural material. There is an imperative need for determination of elastic constants, to determine the mechanical properties of the material. The unique properties of FRP composites entail varying fibre architecture and characteristics, unlike steel which is common among varying geometries and profile. Therefore determination of FRP elastic constants is complex, and there is need for extensive research to be conducted. The certain drawbacks with FRP composites are the lack of research undertaken to determine the properties of the material, essentially which leads to the lack of consensual design codes, that can be easily accessible by engineers and equipped in designing FRP structures (Gand et al. 2013). This study attempts to determine elastics constants using experimental methods, to review the reliability of standard and non-standard methods in determining these elastic constants. The elastic constants are important in classifying compression columns and for numerical modelling, the determined values will then be examined in terms of what previous researchers have established.
1.2 Aims The aims of the project are to determine the elastic constants of pultruded GFRP hollow sections, by undertaking a series of experimental investigations. This will facilitate the understanding of mechanical properties of the material, which also will allow for the analysis of compression member classification.
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1.3 Objectives In order to achieve the aims of the project, a review and analysis will be undertaken on experimental methods to determine elastic constants for FRP composite. The specific objects for these aims are:
Investigate previous history of FRP composite as a structural material and review background on the material.
Review test methods that are capable of determining elastics constants.
Use experimental methods to determine elastic constants of two tubular hollow profiles with varying thicknesses and from different pultruders.
Analyse data obtained from tests, to calculate elastic constants, report on the reliability and success of experimental methods.
Use data obtained from test to classify compression columns, produce a list of classification for varying lengths for samples tested.
1.4 Research Constraints The project was subjected to numerous research constraints, these affected the productivity of the planned test programmes. Experimental investigations were limited to what was suitable to be conducted with test equipment available at Coventry University. Therefore initial investigation was carried out to assess which experimental procedures could be conduct. Material supply was also short, therefore every possible method to economically recycle material from non-destructive tests was carried out.
1.5 Structure of Dissertation The structure of this dissertation has been organised to cover all major topics covered in this project, the structure of this dissertation is as follows: In chapter 2 – BACKGROUND REVIEW, a general background review is given on FRP composites, this chapter focusses on providing general information to the reader and provide an insight on what FRP composites are. A background review is given on structural applications, material fabrication and pros and cons of the material. In chapter 3 – REVIEW OF TEST STANDARD AND PROTOCOLS is where various test standard and protocols are reviewed in terms of what is available and what previous authors have conducted. The test methods discussed coincide with what tests were conducted in this project, standards tested and non-standard test are reviewed and their advantages and limitations are described. In chapter 4 – EXPERIMENTAL TEST PROGRAMME, all tests conducted in the project are discussed and corresponding figures and schematics illustrations are presented. The chapter is split into sub-headings to differentiate the tests conducted, for each sub-heading the procedure conducted and analysis methods are discussed, pictures of tests and apparatuses used are presented in this chapter. In chapter 5 – ANALYSIS AND DISCUSSION OF TEST RESULTS is where all tests results and findings are presented, graphs and tables have been utilized in this chapter. Issues and Page | 2
problems that arose from tests are outlined in this chapter, a general discussion of results are displayed. In chapter 6 – CLASSIFICATION OF HOLLOW SECTIONS UNDER AXIAL COMPRESSION a closed form equation is used to determine the compression member classification is presented. Data obtained from chapter 5 are presented in this chapter to be used in the closed form equation, tables are provided with the classification of the composite profiles used in the project. In chapter 7 – CONCLUSIONS AND RECOMMENDATIONS FOR FURTHER WORK is where the dissertation is concluded and key findings are discussed, also a general insight on possible further research work that may be needed to enhance the knowledge on FRP composites is provided.
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2 BACKGROUND REVIEW 2.0 Introduction Global interest have increased for structural application of FRP composites within recent years, the composite has been around since the early 1940’s however only became appealing as a structural material within early 1990’s. Initially large popularity was placed in using FRP composites as seismic repairs and retrofitting applications and was successful as a lightweight, durable repair alternative (GangaRao et al. 2010). Although 100% composite structures are still very rare, there have been numerous cases of FRP composites being utilised as a primary structural material, with majority of noted case within North America (Gand et al. 2013). The large increase in applications has been down to various factors, such as a large decrease in cost and manufacturing process, alongside the advantages properties of the material such as lightweight to strength ratio, UV and Corrosion resistances and low maintenance, all these factors will be reviewed in this chapter.
2.1 Structural Applications Over recent years FRP composites have gained interest due to its advantageous structural properties and abilities as structural material. Only within the 1980’s did the composite enter the civil engineering construction industry, and was only after this when research began to establish its use as a structural material (Domone et al. 2010). However FRP composites have been used in structural applications around the world, and have been applied for bridge repairs, bridge design, mooring cables, structural strengthening and stand-alone components (Gand et al. 2013). Structural hollow sections are widely used within the civil engineering industry, the Britannia Bridge shown in Figure 2.1, was among the first major civil engineering application to use rectangular hollow sections for the main skeleton (Gardner et al. 2010). This introduced the hollow sections to the civil engineering industry, and became more popular for structural applications.
Figure 2.1 – Britannia Bridge rectangular square hollow sections, UK (Dixon 2006)
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Primarily FRP composites made an appearance within the construction industry as small component for buildings, it was apparent that the light-weight and durability properties meant they were well suited for this role. With applications such as canopies, domes, dormer windows, cupolas and cladding, the Mondial House in London built in 1974 was cladded entirely with glass fibre reinforced polymer (GFRP) panels (Kendall n.d). It was only within the 1990’s where FRP materials were used as primary load bearing structural systems began to increase, with applications such as bridge decks and pedestrian footbridges (Cardoso 2014). It became increasing apparent that FRP composites inhibited the ability to be used for primary load bearing materials, however due to the nature and properties of the material it was preferred for uses in tension/compression rather than for flexure. Some early examples of FRP structural applications date back around 20 years, such as the Eyecatcher Building in Switzerland built in 1998. The 5 storey building at a height of 15m was constructed with trapezoidal GFRP load bearing A-frames (Gand et al. 2013). Pultruded FRP members were bonded using high strength epoxy and were bolted together, this structure was among the first residential/office building to incorporate load bearing FRP materials (Mosallam et al. 2013).
Figure 2.2 – Eyecatcher Building, Switzerland (Mosallam et al. 2013)
Another early example of FRP composites utilised within the civil engineering sector is the pedestrian footbridge in Scotland. The Aberfeldy footbridge (Figure 2.3) constructed in 1992 is a 113m long cable-stayed bridge, composed of pultruded FRP members interlocked to form the bridge deck and towers. With a mid-span of 63m, the Aberfeldy bridge is the longest span composite bridge in the world (Steve 2013). A structural system was adopted in constructing the bridge, the advance composite construction system (ACCS) is a method of erecting the towers and bridge deck without the aid of cranes. This was made possible because of the lightweight characteristics of FRP composites, and overall the cost of the project was low due to smaller foundation and speedy erection of the bridge (Bakis et al. 2002). Page | 5
Figure 2.3 – Aberfeldy Pedestrian Footbridge, Scotland (Lynch 2012)
The use of FRP composite for bridge design has increased globally, the well suited abilities of FRP composite used as the primary material for constructing these bridges is shown in many cases around the world. The Lleida footbridge in Spain was constructed in 2001 and is composed of all FRP elements (Gand et al. 22013). The footbridge which took approximate only three months to construct is a prime example of how FRP composite can be manipulated and provide various benefits. The footbridge has a 38m span and only weighs 19kg, the bridge is composed of a double tied arch, 3m deck and 6.2 rise, which crosses the high-speed rail line and existing roadway. Rectangular hollow profiles were used to construct the arches and bridge deck girders, two U-profiles were glued together to form the rectangular sections.
Figure 2.4 – Lleida Bridge, Spain (Pulido 2001)
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Another example of a bridge that encompasses FRP composites is the Pontresina Bridge (Figure 2.5) in Switzerland, two combined bridges spanning 12.5m long with an internal depth of 1.5m. The bridges were composed of truss girders to support the loads induced on the bridge deck, one of the bridge structural connection were bolted together, whilst the other was boned together using a strong epoxy resin based adhesive. Every year the bridge is removed during spring and brought back during winter, the harsh environments meant the best suitable material for the footbridge was FRP due to its light-weight, high strength and corrosion resistance (Keller 2004).
Figure 2.5 – Pontresina Bridge, Switzerland (Fiberline.com 2008)
There are numerous other structural applications that are composed of FRP composites, however it is apparent that many application to-date are footbridges and bridge decks. The use of FRP composite for bridges is down to its advantageous properties, the light-weight to high strength ability and low maintenance means it has been adopted for this use globally. Further acceptance is required for FRP composite to increase the structural applications, Bakis et al. (2002) reports three important factors that need to addressed to increase the potential of FRP composite being used in structures. These were, a general acceptance of the material to allow further research to determine the material properties to aid designers, producing design codes similar to those of structural steel and concrete and reduction in pultruded members cost which at the moment is non-competitive. These factors amongst others need to be addressed to allow further structural application, although the number of reported application have been growing in recent years, there is still a need for further investigation to understand the boundaries in terms of structural applications for this material.
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2.2 Advantages The global interest in FRP materials has increased since the material advantages have become apparent, further research and development for this novel material means the advantages the material holds are increasingly growing. The advantages in regards to structural applications and as a civil engineering material are stated below:
GFRP has a high strength-to-weight ratio and considered to have higher or similar compressive strength as mild structural steel (Cardoso 2014). However on a pound for pound basis, GFRP is much stronger then structural steel (Aamanet.org, 2014).
Lightweight material, therefore transport and handling is much more economical than other structural materials (i.e. structural steel, concrete). Complete GFRP columns/beams can be fitted without the aid of cranes, complete structures can be prefabricated off-site and transported to be installed.
Pultruded GFRP members are a non-corrosive material, the composite is insusceptible to a broad range of corrosion and rot elements. Thus the material is well suited for application such as coastal areas, where constant maintenance of either structural steel or concrete is required.
Among the variety FRP composites, Glass-fibre reinforced polymers are electrically non-conductive, and have low thermal conductivity. The composite is also transparent to electromagnetic waves, such as radio waves and microwaves.
Profiles can be fabricated to majority desired shapes and sizes, the pultruded structural members can be designed to almost all standing structural steel profiles.
Have excellent low temperature capabilities, GFRP composites are known to have higher tensile strength in lower temperatures. Therefore the composite is well-suited for countries with low average temperatures, the material works well for temperatures from -70°F to +80°F.
Low maintenance cost of material, initial manufacturing cost is high. However assessing complete structural cost, such as transport, installation and maintenance, the cost is substantially lower compared to other structural materials.
Table 2.1 – Comparison and rating of FRP and Steel Merits/Advantages (GangaRao et al. 2010)
Property (Parameter) Strength/stiffness Weight Corrosion resistance/ Environmental Durability Ease of field construction Ease of repair Fire Transportation/handling Toughness Acceptance Maintenance
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Merit/Advantage (Rating) FRP Steel 4-5 4 5 2 4-5 3 5 4-5 3-5 5 4 2-3 5
3-4 3-5 4 3 4 5 3
Rating Scale 1: Very Low 2: Low 3: Medium 4: High 5: Very High
GangaRao et al. (2010) investigated the various merits of FRP and Steel and produced a comparison list, as shown in Table 2.1. As it can be seen, FRP outweighs steel on numerous advantages however the only downside for the material is the overall acceptance, this is due to the lack of knowledge and design guidance in the material compared to steel.
2.3 Limitations GFRP composites have historically been relatively expensive to manufacture, however this reduced after the introduction of the pultrusion process. Never the less the initial manufacturing cost is high compared to those of other structural materials (Bakis et al. 2002). The brittle nature of GFRP composites is also a disadvantage, sudden failure occurs and preliminary failure signs are rarely shown with FRP materials. Also the fire resistance of GFRP materials is rather low, with harmful gases exposed from burning composites. A key disadvantage of the composite material is the lack of research and design standards, emphasis is placed on a need for design standards and codes for the use of FRP composites in structural applications. The lack of knowledge means there a limited design professional and contractors who are experienced in working with the composite (GangoRao et al. 2010).
2.3 Pultruded Glass Fibre Reinforced Profiles Fibre reinforced polymers are a relatively new material, and has recently emerged as a practical material for structural applications. FRP commonly referred to as composites are a combination of numerous materials, which are combined on a macroscopic scale to enhance physical and mechanical properties of the materials (Gand et al. 2013). “The combination of high-strength, high-stiffness structural fibres with low-cost, lightweight, environmentally resistant polymers resulted in composite materials with mechanical properties and durability better than either of the constituents alone.” (Bakis et al. 2002) The composite consists of reinforcing fibres within a polymeric matrix, where both are combined to form the composite. Common reinforcing fibres used with the construction industry are glass fibres, carbon fibres and aramid fibres. There are four types of glass fibres these are E-glass, A-glass, AR-glass and high strength glass fibres. Glass fibres are widely used due to its low cost, however glass fibres have low elastic modulus and display affects in durability when exposed to alkaline environments (Gand et al. 2013). There are also three types of carbon fibres, which can be used with glass fibres to increase the stiffness of the material. Aramid fibres can also be used to increase stiffness of the material, however has low compressive and shear strength in comparison to other fibres. Polymers are used for resins, there are two common resins used, these are thermosets and thermoplastics. Thermosets polymers are generally used within the construction industry, these are polyesters and epoxides (Ngcc.org.uk 2015). Fibres control the strength and stiffness, whereas the resin is what combines the fibres to protect it and form the shape of the member. FRP consists of various layers, these are the veil, mat (resin) and roving (fibres) as shown in Figure 2.6.
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Figure 2.6 – Fibre reinforced polymer material layers (Aamanet.org, 2013)
Each layer has some significance in the structural behaviour of the composite, the veil is what protects the fibres and provides corrosion and UV resistances. The roving is what provides the composite with strength and stability, with the combination of unidirectional fibres in the pultrusion direction. The mat is what provides traversal strength and shear resistances, the combination of layers increase the structural properties of the material and each compliments each other to form the composite (Sidhu 2014).
2.4 Profiles and Geometry GFRP composites come in various shapes and sizes, many of which mimic current structural steel profiles. Pre 1970’s many FRP profiles were small sized and were used for nonstructural purposes, however introducing the pultrusion process meant FRP profiles could be further manipulated and used to fabricate large structural members (Bakis et al. 2002). The profile geometry is set within the pultrusion process, forms which eject the polymer matrix is what coordinates the profiles geometry. Common GFRP structural profiles are closed-web tubular members with rectangular, round, square profiles and open-web such as I-beam and channels as shown in Figure 2.7.
Figure 2.7 – GFRP Common Pultruded Profiles (Mosallam et al. 2013)
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2.5 Pultrusion Process Invented by W. Brant Goldsworthy as a method of making fishing rods, the pultrusion technique is a fundamental method of manufacturing fibre reinforced composites. “Pultrusion technique has become one of the important fibre reinforced polymer composite manufacturing techniques in the recent years and it is reported that it is the most cost effective technique for fabricating structural composite profile.” (Fairuz et al 2014:1798) The pultrusion process is a quick and efficient manufacturing method, where reinforcing fibres are impregnated with thermosetting matrix. The raw fibres are pulled through a resin bath, these impregnated fibres are then pulled through a heated die and cured which is known as polymerization, thus hardening the polymer matrix to form the composite profiles as shown in Figure 2.8. Relative to other manufacturing techniques, the pultrusion process shows enhancement in composite properties. The process of fibre being pulled in tension when cured resulted in advance of mechanical and thermal properties of the composite, according to Latere et al. (2014). Various aspects of the pultrusion process can directly affect the properties of composites, these factors are the pulling speed, die temperature, resin viscosity and resin polymerization. In order to produce consistent and quality composites, the pultrusion process parameters must be controlled (Fairuz et al. 2014).
Figure 2.8 – Pultrusion Process Diagram (creativepultrusions.com 2015)
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3 REVIEW OF TEST STANDARD AND PROTOCOLS 3.0 Introduction “The design and application of an FRP composite structure requires an understanding and knowledge of the physical and mechanical properties of the FRP materials.” (Gand et al. 2013) It is apparent that there is a need for extensive research into this novel material, and understanding the characteristics of the composite. Determining the elastic constant will aid further research, and supplement the application of the composite as a structural material. Mechanical properties of the GFRP are nominally supplied by manufacturers, however to predict accurate elastic constants experimental procedures were adopted. There are numerous authors who have used both standard and non-standard test methods to determine these elastic constants. Standard test methods such as the American Society for Testing and Materials (ASTM International) are a common standards organisation used to determine elastic constants of FRP composites. The International Organisation for Standards (ISO) and British Standards (BS) are also adopted, however ASTM have a larger variety of standards for testing FRP composites. There is also an abundant of non-standard test methods used by authors to determine elastic constants of FRP composites, commonly adopted due to not being capable of relating to requirements set by the standard test. There are various elastic constants that can be determined for GFRP composites, however only the elastic constant sufficing the compression member classification in chapter 6 are investigated. These are the in-plane shear modulus, longitudinal flexural modulus, transverse flexural modulus, Poisson’s ratio and the longitudinal compressive modulus.
3.1 In- Plane Shear Modulus (GLT) Determining the in-plane shear modulus is significant in understanding the shear deformation of the material, however among the other elastic constant, the in-plane shear modulus is the hardest to determine. Although there are numerous experimental procedures available to determine the in-plane shear modulus, it can be difficult to acquire accurate results as reported by Davalos et al. (2002) considerable discrepancies can be found in results. Due to this it is recommended that sufficient material is subjected to pure shearing and recommended experimental procedures are adopted. There are numerous standard and non-standard test methods to determine the in-plane shear modulus, with popular standard test methods such as: the Iosipescu (ASTM D5379. 2012), the V-notched rail shear test (ASTM D7078. 2012), the ±45° tensile test (ASTM D3518. 2013) and the plate twist method (BS EN 15310. 2005). Other non-standard test that are also popular and recommended by various authors are: the Timoshenko beam test, the 10° off-axis tensile test, the torsion test and resin burn of. All test methods have been recommended and been utilised by numerous authors, however some test methods have been known to be more reliable and sufficient in determining the in-plane shear modulus. 3.1.1 Iosipescu Test Developed by Nicholi Iosipescu, the Iosipescu test method is among the preferred method to determine the in-plane shear modulus. In 1993 it was standardised by ASTM as a method of determining shear properties for composite materials (ASTM D5379-12), with the ability to determine both in-plane shear modulus (GLT) and shear strength (𝜏u). The method generally applied to isotropic materials, subjects the material to direct shear and causes coupon to fail Page | 12
due to pure shearing. Although the Iosipescu test method is both accurate and ranked among top three test method by Lee & Munro (1986), there are various disadvantages of this test method. The method requires specialist test apparatus as shown in Figure 3.1, also coupon shape is complex and needs to be fabricated with sufficient accuracy for reliable results. Loading of coupon may result in side edge crushing causing inconsistencies in gauge readings, specimen size is relatively small with gauge length being approximately 12mm (Nguyen 2014). Numerous authors have adopted this method, Cardoso 2014 reports his finding from these authors. It was found that from this method a range of 2.4 to 5.7 GPa was obtained for the in-plane shear modulus, with sections 6.4 mm to 12.7 mm thick, 19 mm to 38.1 mm wide and 76.2 mm to 203 mm long coupons.
Figure 3.1 – Iosipescu Test Apparatus and Diagram (Cardoso 2014)
3.1.2 ± 45° off-axis Tensile Test The ± 45° off-axis tensile test (ASTM D3518) is a highly recommended test procedure to determine the in-plane shear modulus of laminate composites, a simple method that is a reliable alternative to the Iosipescu method if the Iosipescu apparatus is not available. This method following standards requires coupons fabricated whereby fibre directions are at ± 45°, thus acquiring shear stress-strain responses by mounting biaxial strain gauges at 0° and 90° as shown in Figure 3.2. There are various advantages of adopting this method, such as simplicity of test procedure and reproducibility, conventional tensile test with no special apparatus required and economical in material usage (Lee et al. 1986). However according to Lee (1989) tensile forces result in minimal tensile strains, these strains although minimal have an effect on the shear strength and may cause reductions in ultimate shear strength. According to ASTM standard D3518 (2013) to avoid deformation due to end constraints, a minimum length of 230 mm must be applied (Cardoso 2014), however non-standard approaches have been taken by Cardoso (2014) whereby samples of 6.4 mm x 12.7 mm x 119 mm with a gauge length of 81 mm were tested. It was concluded that end-constraints effects were minimal due to the number of samples tested, and final in-plane shear modulus was found to be between 4.1 to 4.7 GPa.
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Figure 3.2 – (ASTM D 3518) ± 45° off-axis Tensile Test (Cardoso 2014)
3.1.3 Full Section Profile Test (Timoshenko Beam) The full section profile test is amongst the simplest and easiest test to replicate, the nonstandard test requires minimal fabrication and a simple test setup. The full section profile test determines both the in-plane shear modulus and longitudinal flexural modulus. Whereby various authors such as Cardoso (2014) and Wolfenden et al. (1989) have used the Timoshenko beam test to obtain the in-plane shear modulus. The test requires a full section profile to be subject to three-point bending, thus the material fabrication is very simple and testing is not done to failure making the test method economical compared to others. It was also noted that the shear modulus obtained from the full section profile test often resulted in lower values compared to other test methods (Cardoso 2014). Variables arising from using complete profile section have an effect on final in-plane shear modulus. The British standard BS EN 13706-2 (2002) can be adopted when testing the full section profile test, the standard gives test parameters such as when deflection reaches L/200 loading should be stopped. The full section profile test was conducted and findings are reported in chapter 5, from conducting the experiment it was exaggerated that support deflections are present and proposed methods to record and mitigate these deflection are done to acquire reliable data from the experiment. 3.1.4 10° off-axis Tensile Test The 10° off-axis tensile test is very similar to the 45° off-axis tensile test, where unidirectional fibres are orientated 10° off tensile loading axis. Similarly to the 45° off-axis tensile test, no special apparatus is required and material fabrication is both economical and straightforward, rectangular coupons are clamped and tensile loads are applied to determine in-plane shear modulus and shear strength. When applying uniaxial tensile loading to specimen with fibre orientation at 10° a biaxial stress state occurs, these stresses are transverse, longitudinal and in-plane shear along the 10° plane. Lee et al. (1986) concludes that adopting the 10° off-axis tensile test results in samples reaching critical shear strength, thus recommending this test procedure for in-plane shear strength and modulus. There are various advantages of adopting this test method, such as specimen has uniform shear stresses through thickness, simplicity and accuracy of test and in-plane shear strain approaches or meets critical/maximum theoretical value (Lee et al. 1986). An extensive comparison between test methods used to determine shear constants of composites was conducted by Yeow (Lee et al. 1986), he concluded that the 10° off-axis tensile test is the best method for ply or lamina composites. Page | 14
In order to acquire accurate data, Lee et al. (1986) states any misorientation errors must be avoided due to the sensitivity of the test. It was recommended that fibre direction, load alignment and strain gauge positioning is at minimum ±1° to eliminate issues that may arise from misorientation errors. Nguyen (2014) states “Because the test data can be sensitive to the angle between the principal axis of the UD fibres and the tensile loading axis special care is given to the machining of the rectangular coupons.”
3.2 Longitudinal Flexural Modulus (Ef,L) Understanding the longitudinal flexural modulus is important to identify resistance the composite has against deformation, as the material is known to being brittle, further importance is placed on determining reliable test methods to acquire the flexural modulus. Commonly the standard three-point bending test is applied to determine longitudinal flexural modulus of materials, however there are also other approaches such as the full section profile which has been used by Wolfenden et al. (1989) to determine both flexural modulus and in-plane shear modulus. The three-point bending test (ASTM D790) is a standard method of determining the longitudinal flexural modulus of composite materials. The test procedure is very simple and requires rectangular coupons to be subjected to three-point bending, deformation should be internally or externally measured to determine the longitudinal flexural modulus. ASTM D790 (2010) states a typical span to depth ratio of 16:1 must be taken, however this should be increased for laminated materials such as FRP. Either a span to depth ratio of 32:1 or 40:1 are recommended for laminated thermosetting materials, failure must occur in outer fibres due to bending thus the need to increase the span-to depth ratio. For high-strength reinforced composites such as GFRP a recommended span to depth ratio of 60:1 must be adopted, this is to eliminate shear effects from data acquired. A minimum of five test specimens must be tested to eliminate any anomalies and errors, overall the three-point bending test is a reliable test method to acquire the longitudinal flexural modulus, and should be adopted according to ASTM D790. The full section profile test as outlined above is a non-standard method of determining longitudinal flexural modulus. Unlike the three-point bending test, the full section profile test uses full profile samples to be subjected to three-point bending to acquire load against deflection thus determining the flexural modulus. This test procedure is good in reviewing effects of complete profile flexural modulus, a comparison between the ASTM D790 test method and the full section profile test can be made.
3.3 Transverse Flexural Modulus (Ef,T) The transverse flexural modulus is difficult to determine with standard flexural modulus test methods, this is due to the limitations of profile dimensions. The non-standard approach adopted by Cardoso (2014) was to fabricate C-channels from square hollow sections, by cutting one wall of the profile out. Load was applied at the top of the channel, subjecting the mid-plate to transversal flexure, strain gauges mounted on both faces were used to measure transverse flexural strains, as shown in Figure 3.3. Due to the nature of FRP materials, other methods are difficult to adopt for transverse flexural modulus, only specimens with larger cross-sections can be adopted to some standardised flexural test methods. However this is uncommon and not economical therefore the channel test is the most appropriate test method of determining the transverse flexural modulus.
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Figure 3.3 – Channel Test for Transverse Flexural Modulus (Cardoso 2014)
3.4 Poisson’s Ratio (V12 and V21) The Poisson’s ratio is a ratio between longitudinal and transverse elastics modulus, where the ratio is determined by conducting compressive tests on samples in both longitudinal and transverse directions and using appropriate methods to record strains and stress of the material. Determining the Poisson’s ratio can be difficult in terms of specific accuracy and repeatability, therefore it is crucial that standard and recommended test methods are followed. Cardoso (2014) adopted the ‘dog bone’ tensile test to acquire both Poisson’s ratio and tensile modulus, the method is an ASTM standard (ASTM D638 2014) for tensile testing and acquiring Poisson’s ratio. To acquire the Poisson’s ratio from the tensile test, biaxial strain gauges are used to measure both longitudinal and transverse strains. Another method of determining the Poisson’s ratio is by fabricating rectangular coupons with fibre orientation in longitudinal and transverse direction, to then compress the coupons and measure the strain development on the specimen. This method requires no special apparatus and is a simple compression test, however it should be noted that coupon buckling may affect strain readings therefore this must be considered when analysing data. The test method provides both Poisson’s ratio and compressive strength of the material. A minimum of six coupons should be tested to eliminate any anomalies. Strain gauges can be applied to both sides of coupon to increase the accuracy of the test.
3.5 Longitudinal Compressive Modulus (Ec,L) The longitudinal compressive modulus is a key mechanical property, and determining it can aid in understanding the compressive strength of the material. There are numerous methods for determining the compressive modulus of composite materials, such as the ASTM D695 (2010) which is a standard test method for obtaining compressive properties of rigid plastics. This test method involves testing small coupons, to subject them to pure compressive loading. The test method requires a special apparatus, also small coupons are used to prevent any buckling. ASTM D3410 (2008) is also another standard test method of determining compressive modulus, by applying shear loading to coupon specimens. Both methods require a special apparatus, however disadvantages of possibility of end crushing and slippage may occur in both test method mentioned above. To alleviate this issue, a combination of both test methods can be used, which is also an ASTM standard test procedure (ASTM D6641. 2009). This method uses combined loading compression fixture that prevents coupons from end crushing or slippage. The apparent disadvantage of Page | 16
adopting these methods is a special fixture is required as shown in Figure 3.4, also ASTM standard parameters must be met, however authors have adopted this method and successfully obtained reliable compressive module from the experiments. There are also non-standard test methods are simpler than the standard methods, the main advantages of adopting a non-standard test method is no fixtures are required. However without special fixtures, various issues can arise such as buckling and end crushing of specimens, clamps and supports can be used to avoid these issues. Cardoso (2014) adopted the non-standard approach of testing stub-columns and subjecting them to axial compressive loads, strain gauges mounted on two faces were used to monitor longitudinal compressive strain. The non-standard approach is much simpler to carry out, however various controls must be taken to ensure the accuracy of the test.
a) ASTM D695 Fixture
b) ASTM D3410 Fixture
c) ASTM D6641 Fixture
Figure 3.4 – ASTM Standard fixtures for Compressive Modulus (Adams 2005)
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4 EXPERIMENTAL TEST PROGRAMME 4.0 Introduction Two specimens were tested, one with a nominal thickness of 4 mm and the other 6 mm. The 4 mm section manufactured by Exel Composites LTD (Exelcomposites.com 2015) will be referred to as the ‘Yellow Specimen’, the 6 mm section manufactured by RBJ Reinforced Plastics LTD (RBJ Plastics 2015) will be referred to as the ‘Grey Specimen’. Test specimens were accurately measured to acquire cross-section dimensions using a Vernier calliper and measuring tape.
4.1 Full Section Profile Test (Timoshenko Beam) To determine the in-plane shear modulus and the longitudinal flexural modulus, the full section profile test was adopted according to the method carried out by Cardoso (2014). Two specimens with cross-sections of 100 mm x 100 mm x 6 mm (Grey section) and 100 mm x 100 mm x 4 mm (Yellow section) where fabricated to a length of 1200 mm, as shown in Figure 4.1.
Figure 4.1 – Fabricated 1200 mm Timoshenko beams
The response for a three-point bending test is determined by: 4𝐴𝑤 𝑃𝐿
=
1 12𝐸𝐿,𝑐
𝐿 2
𝑛
(𝑟 ) + 𝐺 𝑠
𝐿𝑇
Equation 4.1
Where 𝐴 is the cross-sectional area, 𝑤 is the net deflection at mid-span. 𝑃 is the point load at mid-span, 𝐿 is the span length, 𝑟 is the radius of gyration and 𝑛𝑠 is the shear form factor. A typical three-point bending machine was used, with a point load at mid-span, supports were placed from 950 mm to 450 mm with 100 mm intervals. Trial tests were carried out to assess the magnitude of point loads to be applied, this was in order to prevent localized crushing. For the yellow specimen two loads of 2.75 kN and 3.5 kN were applied, for the grey specimen two loads of 5 kN and 10k N were applied. To obtain the true deflection, a net deflection was taken for mid-span deflection, which accounted for material settlement over supports. Mid-span deflection was measured using a digital dial gauge, LVTD were also used but were showing signs of inconsistencies. To determine support deflection, digital dial gauge were also used, before loading dial gauges were zeroed. Figure 4.2 illustrates the schematics of the test, Figure 4.3 shows the experimental setup and apparatus used.
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Figure 4.2 – Schematic representation of test
Mid-Span Point Load
Digital Dial Gauge
Support Span Intervals Supports LVDT
Figure 4.3 – Full section profile test setup
There are three unique methods of determining both in-plane shear modulus and longitudinal flexural modulus from obtained data. Figure 4.4 illustrate the three methods that can be used from the general Timoshenko beam expression. The first method used which was also adopted by Cardoso (2014) is where (4𝐴𝑤/𝑃𝐿) is plotted against (𝐿/𝑟) ², a straight line of fit is made between all corresponding points. From this in the in-plane shear modulus is determined by (1/𝐼𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡), the longitudinal flexural modulus is determined by (1/12 × 𝑆𝑙𝑜𝑝𝑒). The second method is by plotting (𝑤/𝑃𝐿) against (𝐿2 ), where the in-plane shear modulus is determined by (1/4 × 𝐼𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡 × 𝐴𝑟𝑒𝑎) and the longitudinal flexural modlus is determined by (1/48 × 𝑆𝑙𝑜𝑝𝑒 × 𝐼 (𝑀𝑜𝑚𝑒𝑛𝑡 𝑜𝑓 𝐼𝑛𝑒𝑟𝑡𝑖𝑎)). The third method is where (𝑤/𝑃𝐿3 ) is plotted against (1/𝐿2 ), the in-plane shear modulus is determined by (1/48 × 𝑆𝑙𝑜𝑝𝑒 × 𝐴𝑟𝑒𝑎) and the longitudinal flexural modulus is determined by (1/48 × 𝐼𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡 × 𝐼).
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Figure 4.4 – Methods of analysis for full section profile test data
The British standard BS EN 13706-2 (2002) is a standard method of testing a full section profile, the standard uses the same approach taken in the experiment however specifies various parameters that must be met. A maximum deflection parameter is given to be L/200 and loading must stop once beam reaches this deflection. Also the standard states a minimum of 5 span intervals must be tested, the standard method was adopted by M09BE students at Coventry University, the data obtained gives a larger range and loading interval that can be picked through the test.
4.2 Three-Point Coupon Bending Tests To determine the longitudinal flexural modulus, the ASTM D790 standard three-point bending test was adopted. For the two different samples a support span-to-depth ratio of 60:1 was taken according to standard requirements, the yellow specimen having a span 𝐿 of 240 mm and the grey specimen with a span 𝐿 of 360 mm. A total of eight samples were tested for both specimens as shown in Figure 4.5 (minimum of five samples required according to ASTM D790), with the “Yellow” samples having thickness varying from 3.30 mm to 4.59 mm, the “Grey” samples having thicknesses ranges from 5.82 mm to 6.97 mm. The “Yellow” samples having a nominal width of 37 mm and the “Grey” samples having a nominal width of 40 mm.
Figure 4.5 – Three-point bending samples
Standard requirements were followed for three-point bending apparatus, “for specimens 3.2 mm or greater in depth, the radius of the supports may be up to 1.6 time the specimen depth” (ASTM D790 2010). The radius of the loading nose was 3.5 mm and meets the requirements of minimum 3.2 mm radius set by ASTM standard, support radius were 4.5 mm. Testing was carried out using the 100 kN capacity JJ Lloyd machine (Figure 4.6), and Page | 20
conducted according to ASTM D790 standard. A loading rate of 25 mm/min was used in accordance with standard, a load of 100 N was set for the yellow sample and a load of 150 N for the grey sample. Deflection was measured using the JJ Lloyd internal interface extension meter.
JJ Lloyd 100 kN Capacity Machine
Loading Nose
Support
GFRP Coupon
Figure 4.6 – JJ Lloyd three-point bending test
Figure 4.7 – Schematic representation of three-point bending test to ASTM D790
To determine the longitudinal flexural modulus, (𝑃) is plotted against (4𝛿𝑏𝑡 3 /𝐿3 ). Where 𝑃 is the load applied in N, where 𝛿 is the mid-span deflection, 𝑏 being the breath of the sample, 𝑡 being the thickness of the sample and where 𝐿 is the support span. The slope of the best line of fit is equal to the longitudinal flexural modulus. To avoid any errors during first test, the test method was repeated with an increase of loading. Page | 21
4.3 Determination of Transverse Flexural Modulus The channel test was adopted to determine the transverse flexural modulus, the nonstandard approach was adopted according to the method carried out by Cardoso (2014). The test was carried out on six channels for both yellow and grey samples, the channels were extracted from complete tubular members and a single plate was removed to form the channel profile. The channels were fabricated to a length of 124 mm, two strain gauges were glued to either side of the channel. The channel was clamped securely to a flat surface using a G-clamp, a plastic cylinder with a flat surface was used to apply eccentric load (𝑃𝑒) at the top of the flange, as shown in Figure 4.8 and Figure 4.9. Free weights were applied to the top of the flange, with loads of 0.5 kg to 4 kg for the yellow sample with 0.5 kg interval and loads of 1kg to 8kg for the grey sample with 1kg intervals. Strain gauges mounted on the wall subject to transverse flexure were connected to a RDP rack. At each interval of applying loads, strain readings were recorded manually.
Weights
G - Clamp
Strain Gauges
Figure 4.8 – Channel test for transverse flexural modulus
Figure 4.9 – Schematic representation of channel test for transverse flexural modulus
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To obtain the transverse flexural modulus, (𝑃𝑒/𝑍) was plotted against ((𝜀1 − 𝜀2 )/2), where the slope of the straight line of fit is equal to the transverse flexural modulus. Where 𝑃 is the load applied and 𝑒 is the eccentric position of the load, 𝑍 is the elastic section modulus of the face wall tested, which is calculated by 𝐿𝑡 2 /6 where 𝐿 is the length of the specimen and 𝑡 is the thickness of the specimen. Where 𝜀1 and 𝜀2 are the inner and outer strain readings of the faces of the web wall.
4.4 Compression Strength and Modulus Tests The method used to obtain both Poisson’s ratio and longitudinal compressive modulus was the coupon compression test. A total of six coupons for both the yellow and grey sample were tested for both transverse and longitudinal direction, with nominal dimension of 90 mm x 63 mm x 4 mm and 6 mm respectively. A total of 3 samples were strain gauged to determine longitudinal and transverse compressive strain, with one sample having strain gauges attached to both faces, as shown in Figure 4.10. The remaining 3 samples were tested without strain gauges to determine the compressive strength of the material.
GFRP Coupons Strain Gauges
Figure 4.10 – Coupon compression test to determine Poisson’s ratio
The Avery-Denison 2000 kN capacity compression machine was used to test coupons, the machine and setup is shown in Figure 4.11 Samples were placed in apparatus, and levelled to ensure no premature buckling occurs. All specimens were tested until failure, a datalogger (Si-plan) was used to record loading increments and corresponding strain readings, Figure 4.12 illustrates the schematic representation of the test procedure. Concerns with strain readings became apparent whilst testing, although correct calibration procedures were taken some strain readings were void and not measuring.
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Figure 4.11 – Avery-Denison 2000 kN Capacity Compression Machine
Figure 4.12 – Schematic representation of coupon compression test
Once data was obtained from test, the compressive stress (𝜎𝑐 ) was plotted against the compressive strain (𝜀𝑐 ) for both longitudinal and transverse direction, where the slope of the line gave us the longitudinal compressive moduli (𝐸𝐿,𝑐 ) and transverse compressive moduli (𝐸𝑇,𝑐 ). To obtain the Poisson’s ration from the determine properties, the transverse compressive modulus is divided by the longitudinal compressive modulus. To obtain the compressive strength of the material, maximum load is divided by the cross-sectional area to determine compressive stress (𝜎𝑐 ) which correspond to the compressive strength.
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4.5 10° off-axis Tensile Tests The 10° off-axis tensile test can be adopted to determine an upper or mid-bound range of inplane shear modulus, material was fabricated however various issues arose from this test and data could not be obtained. Due to the time scale the problems could not be resolved in time to be analysed and reported, therefore experimental method and fabrication processes will be described. The method also adopted by Nguyen (2014) is a more accurate method to determine inplane shear modulus, a total of six coupons were fabricated at an off-axis of 10°. Although the test does not have any corresponding standard, BS EN 527-5 (2009) can be adopted for test parameters for tensile loading, therefore sample dimensions were adopted according to the standard and method adopted by Nguyen (2014). Samples had dimensions of 300 mm x 25 mm x 4 mm and 6 mm respectively, with a clamping length of 75 mm either side, allowing a gauge length of 150 mm. Biaxial stress state occurs when loading direction does not coincide with either transverse or longitudinal direction, therefore three in-plane stresses occur. These are in the longitudinal direction (𝜎11), transverse direction (𝜎22) and shear stress (𝜎12). To measure the corresponding strain, ‘rosette’ strain gauges orientated at 0°, 45° and 90° corresponding to tensile loading direction, as illustrated in Figure 4.13.
Figure 4.13 – Schematic representation of 10° off-axis tensile test
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Once values for stress and strain are obtained from the test, the raw data can be used to determine the in-plane shear modulus. Various complex expressions are used in determining the in-plane shear modulus from the 10° off-axis tensile test, however Nguyen (2014) derives these complex equation to form a general expression, as shown below:
𝐺12 =
𝜎12 𝛾12
=
0.17𝜎𝑥𝑥 1.88𝜀45 −1.28𝜀0 −0.60𝜀90
Equation 4.2
Where (𝜎𝑥𝑥 ) is stress measure in the longitudinal direction, where (𝜀0 ) is the strain measured at angle 0°, (𝜀45 ) is the strain measured at 45° and (𝜀90 ) is strain measured at 90°. Upon conducting the test procedure it was found that strain reading receptors were faulty and not measuring strains, multiple attempts were made to resolve the issue however due to time limit and testing restraints, it was not possible to conduct the experiment. Therefore chapter 6 values obtained from full section profile test will be used for in-plane shear modulus.
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5 ANALYSIS AND DISCUSSION OF TEST RESULTS Test results obtained from experiments were analysed to determine the elastic constants from raw data, the raw data is presented in appendix. Tables were created to represent all calculated values from tests, anomalies were discontinued when averaging the data obtained.
5.1 Full Section Profile Test (Timoshenko Beam) Within chapter 4 the three unique methods of analysing full section profile test data shown in Figure 4.4 were used to determine in the in-plane shear modulus and longitudinal flexural modulus. Figure 5.1 to Figure 5.6 represent the analysis of data obtained from test.
Timoshenko 4mm Yellow Section
3500
4Aω/PL (mm²/N) x 10⁶
3000 2500 2000 1500
2.75kN
1000
3.5kN y = 3.9163x + 362.83
Linear (2.75kN)
y = 3.4687x + 449.55
Linear (3.5kN)
500 0 0
100
200
300
400
500
600
(L/r)² Figure 5.1 – Full section profile test 4 mm yellow sample based on first method of analysis
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700
Timoshenko 4mm Yellow Section
6.00E-07
5.00E-07
ω/PL (N)
4.00E-07
3.00E-07 2.75kN 2.00E-07
3.5kN
1.00E-07
y = 4.3553E-13x + 6.2235E-08
Linear (2.75kN)
y = 3.8575E-13x + 7.7110E-08
Linear (3.5kN)
0.00E+00 0
200000
400000
L²
600000
800000
1000000
(mm2)
Figure 5.2 – Full section profile test 4 mm yellow sample based on second method of analysis
Timoshenko 4mm Yellow Section
1.20E-12
1.00E-12
ω/PL ³ (N)
8.00E-13
6.00E-13 2.75kN 4.00E-13
3.5kN
2.00E-13
y = 1.2220E-07x + 3.0522E-13
Linear (2.75kN)
y = 1.1315E-07x + 3.0759E-13
Linear (3.5kN)
0.00E+00 0
0.000001
0.000002
0.000003
0.000004
0.000005
0.000006
1/L² (mm-2) Figure 5.3 – Full section profile test 4 mm yellow sample based on third method of analysis
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Timoshenko 6mm Grey Section
3000
4Aω/PL (mm²/N) x 10⁶
2500
2000
1500 5kN 1000
10kN
500
y = 3.4099x + 362.03
Linear (5kN)
y = 3.3208x + 396.07
Linear (10kN)
0 0
100
200
300
400
500
600
700
(L/r)² Figure 5.4 – Full section profile test 6 mm grey sample based on first method of analysis
Timoshenko 6mm Grey Section
3.00E-07
2.50E-07
ω/PL (N)
2.00E-07
1.50E-07 5kN
1.00E-07
10kN
5.00E-08
y = 2.3772E-13x + 3.8149E-08
Linear (5kN)
y = 2.3151E-13x + 4.1736E-08
Linear (10kN)
0.00E+00 0
200000
400000
L²
600000
800000
1000000
(mm2)
Figure 5.5 – Full section profile test 6 mm grey sample based on second method of analysis
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Timoshenko 6mm Grey Section
5.00E-13
4.00E-13
ω/PL ³ (N)
3.00E-13
5kN
2.00E-13
10kN 1.00E-13
y = 3.6936E-08x + 2.4010E-13
Linear (5kN)
y = 3.8333E-08x + 2.3898E-13
Linear (10kN)
0.00E+00 0
0.000001
0.000002
0.000003
1/L²
0.000004
0.000005
0.000006
(mm-2)
Figure 5.6 – Full section profile test 6 mm grey sample based on third method of analysis Table 5.1 – Comparison between Timoshenko analysis methods
Method
4Aw/PL vs (L/r)²
w/PL vs L²
w/PL³ vs 1/L²
Elastic Property
4 mm Yellow Sample
6 mm Grey Sample
2.75 kN
3.5 kN
Average
5 kN
10 kN
Average
In-plane Shear Modulus (GLT) MPa
2756
2224
2490
2762
2525
2644
Longitudinal Flexural Modulus (Ef,L) MPa
21279
24024
22651
24439
25094
24766
In-plane Shear Modulus (GLT) MPa
2756
2224
2490
2762
2525
2643
Longitudinal Flexural Modulus (Ef,L) MPa
21279
24024
22651
24438
25094
24766
In-plane Shear Modulus (GLT) MPa
1404
1516
1460
2853
2749
2801
Longitudinal Flexural Modulus (Ef,L) MPa
30363
30129
30246
24196
24309
24253
From Table 5.1 the first two methods are near enough identical, however the third method of 𝑤/𝑃𝐿3 vs 1/𝐿2 shows a variation in both determined values, therefore it can be considered that the first two methods of analysing the full section profile test data are reliable. For the 4 mm yellow sample the third method displayed an increase of 34% compared to the first two methods for the longitudinal flexural modulus, whilst the 6 mm grey sample displayed a decrease of 2%. The third method showed a decrease of 57% for the 4 mm yellow sample and an increase of 6% for the 6 mm grey sample for the in-plane shear modulus. Page | 30
5.2 Three-Point Coupon Bending Tests Using the JJ Lloyd machine the three-point bending test was done to acquire the longitudinal flexural modulus, the load 𝑃 vs 4𝛿𝑏𝑡 3 /𝐿3 was plotted, the slope of the line is equal to the longitudinal flexural modulus, as shown in Figure 5.7 to Figure 5.13.
Three-Point Bending 4mm Yellow (1a) 100
A1
90
A2
80
A3
Load P (N)
70
A4
60 y = 13437x
Linear (A1)
y = 14402x
Linear (A2)
30
y = 14764x
Linear (A3)
20
y = 12090x
Linear (A4)
50 40
10 0 0
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
4δbt³/L³ (mm²) Figure 5.7 – Three-point bending test for 4 mm yellow coupons (1a)
Page | 31
Three-Point Bending 4mm Yellow (2a)
A5
100 A6
90 80
A7
Load P (N)
70 A8
60 50
y = 15662x
Linear (A5)
y = 15639x
Linear (A6)
20
y = 17008x
Linear (A7)
10
y = 17080x
Linear (A8)
40 30
0 0
0.001
0.002
0.003
0.004
0.005
0.006
4δbt³/L³ (mm²) Figure 5.8 – Three point bending test for 4 mm yellow coupons (2a)
Three-Point Bending Test 4mm Yellow (1b)
A1
120 A2
100 A3
Load P (N)
80
A4
60
y = 15188x
Linear (A1)
40
y = 13406x
Linear (A2)
y = 13248x
Linear (A3)
20
Linear (A4)
y = 11752x
0 0
0.002
0.004 0.006 4δbt³/L³ (mm²)
0.008
0.01
Figure 5.9 – Three-point bending test for 4 mm yellow coupons (1b)
Page | 32
A5
Three-Point Bending Test 4mm Yellow (2b) 120
A6
100
A7
Load P (N)
80
A8
60 40
y = 15528x
Linear (A5)
y = 16413x
Linear (A6)
y = 16357x
Linear (A7)
y = 16065x
Linear (A8)
20 0 0
0.001
0.002
0.003 0.004 4δbt³/L³ (mm²)
0.005
0.006
0.007
Figure 5.10 – Three-point bending test for 4 mm yellow coupons (2b)
Three-Point Bending Test 6mm Grey (1a)
B1
160 B2
140 B3
Load P (N)
120 B4
100 80
y = 16185x
Linear (B1)
60
y = 16983x
Linear (B2)
40
y = 15906x
Linear (B3)
y = 15897x
Linear (B4)
20 0 0
0.002
0.004 0.006 4δbt³/L³ (mm²)
0.008
0.01
Figure 5.11 – Three-point bending test for 6 mm grey coupons (1a)
Page | 33
Three-Point Bending Test 6mm Grey (2a)
B5
160 B6
140 B7
120 Load P (N)
B8
100 80
y = 15921x
Linear (B5)
60
y = 18016x
Linear (B6)
40
y = 17251x
Linear (B7)
y = 17243x
Linear (B8)
20
0 0
0.002
0.004 0.006 4δbt³/L³ (mm²)
0.008
0.01
Figure 5.12 – Three-point bending test for 6 mm grey coupons (2a)
Three-Point Bending Test 6mm Grey (1b)
B1
600 B2
500
B3
Load P (N)
400
B4
300
y = 15007x
Linear (B1)
y = 15580x
Linear (B2)
y = 15334x
Linear (B3)
y = 14409x
Linear (B4)
200 100 0 0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
4δbt³/L³ (mm²) Figure 5.13 – Three-point bending test for 6 mm grey coupons (1b)
Page | 34
Three-Point Bending Test 6mm Grey (2b)
B5
600 B6
500
B7
Load P (N)
400
B8
300
y = 14116x
Linear (B5)
y = 16310x
Linear (B6)
y = 16380x
Linear (B7)
y = 16210x
Linear (B8)
200 100 0 0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
4δbt³/L³ (mm²) Figure 5.14 – Three-point bending test for 6 mm grey coupons (2b) Table 5.2 – Longitudinal Flexural Modulus from three-point bending test
Longitudinal Flexural Modulus Ef,L (MPa) 4 mm Yellow Coupons
6 mm Grey Coupons
Test A
Test B
Average
Test A
Test B
Average
Sample 1
13437
15188
14313
16185
15007
15596
Sample 2
14402
13406
13904
16983
15580
16282
Sample 3
14764
13248
14006
15906
15334
15620
Sample 4
12090
11752
11921
15897
14409
15153
Sample 5
15662
15528
15595
15921
14116
15019
Sample 6
15639
16413
16026
18016
16310
17163
Sample 7
17008
16357
16683
17251
16380
16816
Sample 8
17080
16065
16573
17243
16210
16727
Average
15010
14745
14878
16675
15418
16047
Determined longitudinal flexural modulus are shown in Table 5.2. The average of both test for each sample was taken, then a complete average to determine the longitudinal flexural modulus for the material. From Table 5.2, the various samples had uncommon values for the longitudinal flexural modulus, this may have been due to the variations in thickness. The 6 mm grey coupons showed an increase of 8% in comparison to those of the 4 mm yellow sample, although the thicker 6 mm sample resulted in a higher longitudinal flexural modulus, the differences are not substantial Page | 35
5.3 Determination of Transverse Flexural Modulus Using the channel test method as shown in Figure 4.8, data was obtained and flexural stress was plotted against flexural strain as shown in Figure 5.15 and Figure 5.16. The slope is equal to the transverse flexural modulus, a total of eight data points were determined from tests, these are distinguished in Figure 5.15 and Figure 5.16.
Channel Test 4mm Yellow Sample A1
10
A2
Flexural Stress σ = Pe/Z (N/mm²)
9
A3
8
A4
7
A5
6
A6
5 4 3 2 1
y = 8098x
Linear (A1)
y = 7803.9x
Linear (A2)
y = 7750.7x
Linear (A3)
y = 7798.6x
Linear (A4)
y = 7649.2x
Linear (A5)
y = 15665x
Linear (A6)
0 0
0.0002
0.0004
0.0006
0.0008
0.001
Flexural Strain ε = (ε₁ - ε₂)/2 Figure 5.15 – Channel test for 4 mm yellow channels
Page | 36
0.0012
Channel Test 6mm Grey Sample B1
Flexural Stress σ = Pe/Z (N/mm²)
9
B2
8
B3 7
B4
6
B5 B6
5 y = 15136x
Linear (B1)
4
y = 15998x
Linear (B2)
3
y = 7255.3x
Linear (B3)
y = 10202x
Linear (B4)
y = 14652x
Linear (B5)
y = 16360x
Linear (B6)
2 1 0 0
0.0002
0.0004
0.0006
0.0008
0.001
0.0012
Flexural Strain ε = (ε₁ - ε₂)/2 Figure 5.16 – Channel test 6 mm grey channels Table 5.3 – Transverse flexural modulus from channel test
Samples
Transverse Flexural Modulus Ef,T (MPa) 4mm Yellow Channels
6mm Grey Channels
Channel 1 (A1, B1)
8098
15136
Channel 2 (A2, B2)
7804
15998
Channel 3 (A3, B3)
7751
7255
Channel 4 (A4, B4)
7799
10202
Channel 5 (A5, B5)
7649
14652
Channel 6 (A6, B6)
15665
16360
Average
7820
15567
As shown in Table 5.3, some inconsistencies are shown between channel tests. Therefore the final average taken to determine the transverse flexural modulus does not include the anomalies. The inconsistencies shown may be due to various factors such as issues in strain gauges or receptors, a repeat test could have been carried out, as samples are not tested to failure.
Page | 37
5.4 Compression Strength and Modulus Tests Compressive strain was plotted against compressive stress for both transverse and longitudinal directions, from this the longitudinal and transverse compressive modulus was obtained. From the total of 3 coupons, only one was successful in measuring strain readings for the 4 mm yellow longitudinal coupon, this issue also occurred with one of the transverse 6 mm grey coupons. Therefore the remaining samples will be used to determine the Poisson’s ratios, however all coupon failure loads were recorded therefore compressive modulus will be presented. Issues with strain gauges were present with various tests, for the coupons compression test the initial coupons tested did not measure strain readings. Later this issue was resolved and testing commenced to obtain strain readings for other coupons. Also technical issues occurred when attempting to record two strain readings simultaneously, this was required to determine any buckling strain of coupons.
Coupon Compression Test 4mm Yellow Longitudinal (A3) 80 70
σL (N/mm²)
60 50 40 30
Slope = 12.746 kN/mm²
20 10 0 0
1000
2000
3000
4000
5000
εL (x
10-6
6000
7000
8000
9000
)
Figure 5.17 – Coupon compression test for 4 mm yellow longitudinal coupon (A3)
Page | 38
10000
Coupon Compression Test 4mm Yellow Transverse (B1) 35 30
σT (N/mm²)
25
20 Slope = 10.101 kN/mm²
15 10 5 0 0
1000
2000
3000 εT (x 10-6 )
4000
5000
6000
Figure 5.18 – Coupon compression test for 4 mm yellow transverse coupon (B1)
Coupon Compression Test 4mm Yellow Transverse (B2) 40 35
σT (N/mm²)
30 25 20
Slope = 4.104 kN/mm²
15 10 5 0 0
1000
2000
3000
4000
5000
6000
7000
8000
εT (x 10-6 ) Figure 5.19 – Coupon compression test for 4 mm yellow transverse coupon (B2)
Page | 39
9000
Coupon Compression Test 4mm Yellow Transverse (B3) 45 40 35
σT (N/mm²)
30 25 20
Slope = 5.587 kN/mm²
15 10 5 0 0
1000
2000
3000
4000
5000
εT (x 10-6 )
6000
7000
8000
9000
10000
Figure 5.20 – Coupon compression test for 4 mm yellow transverse coupon (B3)
Coupon Compression Test 6mm Grey Transverse (C1)
90 80 70
σT (N/mm²)
60 50 40 30 Slope = 13.118 kN/mm² 20 10 0 0
500
1000
1500
2000
2500
3000
3500
εT (x 10-6 ) Figure 5.21 – Coupon compression test for 6 mm grey transverse coupon (C1)
Page | 40
4000
Coupon Compression Test 6mm Grey Transverse (C2)
90 80 70
σT (N/mm²)
60
50 40 30 Slope = 15.792 kN/mm²
20 10 0 0
500
1000
1500
2000
2500
3000
3500
εT (x 10-6 ) Figure 5.22 – Coupon compression test for 6 mm grey transverse coupon (C2)
Coupon Compression Test 6mm Grey Longitudinal (D1)
120 100
σL (N/mm²)
80 60 40 Slope = 90.287 kN/mm²
20 0 0
1000
2000
3000
4000
5000
εL (x 10-6 ) Figure 5.23 – Coupon compression test for 6 mm grey longitudinal coupon (D1)
Page | 41
6000
Coupon Compression Test 6mm Grey Longitudinal (D2)
160 140
σL (N/mm²)
120 100 80 Slope = 50.776 kN/mm²
60 40 20 0 0
1000
2000
3000
4000
5000
6000
εL (x 10-6 ) Figure 5.24 – Coupon compression test for 6 mm grey longitudinal coupon (D2)
Coupon Compression Test 6mm Grey Longitudinal (D3)
160 140
σL (N/mm²)
120 100 80 60 40
Slope = 66.466 kN/mm²
20 0 0
100
200
300
400
500
600
700
800
εL (x 10-6 ) Figure 5.25 – Coupon compression test for 6 mm grey longitudinal coupon (D3)
Page | 42
900
All compressive moduli are presented in Table 5.4, the values obtained will be cross-divided to obtain the ratio’s that will be used to determine minor Poisson’ ratio, all possible divisions will be used to see the various responses and ranges of Poisson’s ratio obtained. Table 5.4 – Longitudinal and transverse compressive modulus from coupon compression test
Compressive Modulus 𝑬𝒄 (MPa) Samples
4mm Yellow Coupons
6mm Grey Coupons
Longitudinal
Transverse
Ratio Ec,L/Ec,T
Longitudinal
Transverse
Ratio Ec,L/Ec,T
Coupons 1
-
10101
1.26
90286
13118
6.88
Coupons 2
-
4104
3.11
50776
15792
3.22
Coupons 3
12746
5587
2.28
66466
-
4.20
Average
2.22
4.77
In Table 5.4 all compressive modulus are determined, these values will be used to determine the minor Poisson’s ratio. The ratio’s determined between the longitudinal and transverse compressive modulus were also determined, the average of the values were taken and the final ratios are shown in Table 5.4. Table 5.5 – Calculated Poisson’s ratio from coupon compression test
Major Poisson’s Ratio (V12) Coupons
B1
B2
B3
Coupons
C1
C2
C3
A1
-
-
-
D1
0.49
0.40
-
A2
-
-
-
D2
0.26
0.23
-
A3
0.51
0.35
0.34
D3
0.22
0.25
-
From Table 5.5, it can be seen that various major Poisson’s ratios do not coincide with corresponding ratio for the same material, there anomalies will be discontinued and values obtained that are close to those found by previous tests will be used. Table 5.6 – Calculated Minor Poisson’s ratio from coupon compression test
Minor Poisson’s Ratio (V21) Coupons
B1
B2
B3
Coupons
C1
C2
C3
A1
-
-
-
D1
0.07
0.07
-
A2
-
-
-
D2
0.07
0.07
-
A3
0.40
0.11
0.15
D3
0.04
0.06
-
From Table 5.6 the ratio between transverse compressive modulus and longitudinal compressive modulus is found and multiplied by the major Poisson’s ratio to determine the minor Poisson’s ratio. As shown in Table 5.6, there is a large variation between Poisson’s ratio between samples and the ratio’s determined for the 6 mm grey coupon seem to be substantially smaller than those determined for the 4 mm sample. Page | 43
From the coupon compression test the compressive strength was obtained, both longitudinal and transverse compressive strength were determined, these values are presented in Table 5.7. Table 5.7 – Longitudinal and transverse compressive strength from coupon test
Compressive Strength 𝑭𝒄 (MPa) Sample
Longitudinal
Transverse
Ratio Fc,L/Fc,T
4 mm Yellow
6 mm Grey
4 mm Yellow
6 mm Grey
4 mm
6 mm
1
-
110.51
33.06
79.21
-
1.40
2
70.36
146.65
36.26
85.05
1.94
1.72
3
76.02
163.69
43.94
77.30
1.73
2.12
4
35.20
186.28
35.60
78.92
0.99
2.36
5
44.65
175.92
27.82
66.24
1.60
2.56
6
71.53
159.50
25.95
77.86
2.76
2.05
Average
59.55
157.09
33.77
77.43
1.80
2.04
A ratio between longitudinal and transverse compressive strength is determined in Table 5.7, from all ratios an average is taken and for the yellow 4 mm sample an average ratio of 1.80 was determined. For the grey 6 mm sample an average of 2.04 was determined, these ratios are between compressive strength in both directions.
Page | 44
5.5 Discussion of Results Data obtained from experimental tests require analysis to determine the reliability of results, a generalisation of test needs to be made in order to determine if solutions from tests results are lower bound, mid-bound or upper bound results. 5.5.1 In-Plane Shear Modulus GLT For the in-plane shear modulus values of 2490 MPa for the 4 mm yellow sample and 2644 MPa were determined from the full section profile test. From Figure 5.1 and Figure 5.2 similar response from the variation in Timoshenko analysis methods can be observed. However from Figure 5.3 a larger variation is observed, these variations in in-plane shear modulus are shown in Table 5.1. The full section profile test is found to provide a lower bound value for in-plane shear modulus, which is relative to those provided by manufacturers. However authors have presented that other solution methods such as the 10° off-axis tensile test is sufficient in providing an upper or mid bound for in-plane shear modulus, as shown in Table 5.8. Table 5.8 – In-plane shear modulus results from various sources Author/ Manufacturer
In-plane shear modulus 𝑮𝑳𝑻 (GPa)
Profile type
Test Method
Cardoso (2014)
2 – 2.8
Box Section
Timoshenko Beam Test
4.2 – 4.8
Plates/Coupons
10° off-axis tensile test
3.5 – 4.8
I Section & Box Sections
Three-point bending
Exel Composites LTD
2.93
All
-
Totry et al. (2009)
3.7
-
V-Notched Test
Bank (1990)
2.4 – 2.8
I Sections
Iosipescu Test
Davalos et al. (2002)
3.8
-
Torsion Test
4.23 – 4.25
-
Plate Twist
5–7
-
Modified Iosipescu Test
4
-
V-Notched Test
Lane (2002)
3.7
-
Resin Burn-off Test
Author
2.5 – 2.7
Box Section
Timoshenko Beam Test
Nguyen (2014)
Buchanan et al. (2012)
Analysing in-plane shear modulus obtained from various other authors proves that the Timoshenko beam test is although sufficient in providing shear modulus, but results in lower bound modulus. The data obtained from the test theoretical provide similar in-plane shear modulus from varying loads, however from Figure 5.1, Figure 5.2 and Figure 5.4 large variations in interception of best line of fit are observed. Ideally further loadings increments should have been taken to assess a wider range of loads corresponding to in-plane shear modulus. Higher loads could have been achieved, however it was ideal that load does not exceed the limit of localised crushing of the beam.
Page | 45
5.5.2 Longitudinal and Transverse Flexural Modulus Ef,L & Ef,T Determination for longitudinal flexural modulus, both the three-point bending test and full section profile test resulted in a range of flexural modulus. As seen in Table 5.2 and Table 5.1, the three-point bending test resulted in a lower bound of flexural modulus, whilst the full section profile test resulted in an upper bound modulus. The three-point bending test concentrates on actual material flexural strength, whilst the full section profile test includes the whole profile in determining the flexural modulus. In terms of reliability both results are similar to those published by other authors, as shown in Table 5.9. However the ASTM D790 three-point bending test is known to be a more accurate method of determining the flexural modulus. Table 5.9 – Longitudinal flexural modulus from various sources Author/Manufacturer
Longitudinal Flexural Modulus (GPa)
Test Method
Cardoso (2014)
11 – 25
Three-point Bending Test ASTM D790
Exel Composites LTD
11.0
Three-point Bending Test ASTM D790
Wolfenden et al. (1989)
22
Timoshenko Beam Test
Creative Pultrusion (2004)
11
Three-point Bending Test ASTM D790
23 – 25
Timoshenko Beam Test
15 - 16
Three-point Bending Test ASTM D790
Author
From Table 5.2, a variation in flexural modulus is shown for coupons from the same sample. Theoretically these samples should result in flexural modulus with slight variations, however variations exceed 5 GPa, similarly variations in repeat test were shown. These variations indicate that thicker samples result in larger flexural modulus, this is due to the possibility of deviations in the positioning of inner and outer roving layers. The thicker 6 mm grey sample shows larger flexural modulus, supporting the state that roving layers impact the flexural modulus and any misalignments could in affect the stiffness of the material (Cardoso 2014), thus causing variations between similar samples. The thicker 6 mm grey sample induced higher load capacity indicating that the thickness increases flexural strength, although some authors have indicated increased thickness reduces flexural modulus (Babukiran et al. 2008), in both the full section profile test and three-point bending test it can be observed that an increase in longitudinal flexural modulus between the varying sample thicknesses. Three-point bending test carried out by Singh et al. (2013) reports “flexural strength is greatly influenced by the fiber content/ weight fraction of reinforcement in matrix.” Although the variation are not substantial, it is examined that from the three-point bending test a 6 mm coupon achieved flexural modulus of 18 GPa whilst the maximum reached for the 4 mm coupon was 17 GPa, as shown in Table 5.2. Determination for the transversal flexural modulus was challenging due to the complexity of fibre orientation, the method used has only been reported by Cardoso (2014). The data obtained shows transverse flexural modulus ranging from 8 GPa to 16 GPa for the 4 mm yellow specimen and 6mm grey specimen respectively. Cardoso (2014) reports range of 10 GPa to 15 GPa for samples with various cross-sections sizes, a comparison between values determined by Cardoso (2014) we can see similarities between the range justifying values Page | 46
obtained from the test. Exel composites gave a lower bound range of 5.53 GPa for transverse flexural modulus, using the three-point bending test ASTM D790, a similar value of 5.5 GPa is reported by Creative Pultrusion (2004). The channel test therefore provides an upper-bound of transverse flexural modulus. Referring to Figure 5.15 and Figure 5.16 some samples resulted in large variations compared to other samples, it was apparent whilst testing that strain gauges were causing some issues, therefore these large variants may be due to this delinquency. In comparison between the varying thickness of 4 mm and 6 mm samples there is a large difference between results, with the 4 mm averaging 8 GPa and 6 mm averaging 16 GPa. In comparison to other elastic constants the transverse flexural modulus shows the largest variation between thicknesses, as shown in Table 5.3 Again as the thickness, fibre content and fibre misalignments caused variations between the longitudinal flexural modulus, the same variables can affect the transverse flexural modulus. As the anomalies were great, the final average transverse flexural modulus was taken from values that were consistent through the test. 5.5.3 Poisson’s Ratio V12 and V21 From the coupon compression test a range of Poisson’s ratio was determined, a large variation between determined values were shown. The elastic modulus determined from the coupons had significant variations, therefore affecting calculated poison’s ratios. It has been confirmed by various authors that FRP composites have a major Poisson’s ratio of around 0.3 and minor Poisson ratio of around 0.15, values obtained from authors are shown in Table 5.10. From Figure 5.25 it was observed that once members began buckling and began to reach failure, strain readings were affected and readings began to reverse therefore indicating member buckling. The differences in Poisson’s ratio determined were significant, variables such as the strain gauge issues may have had an effect on this, however from the test it was notes that loading rate was too high for some tests, resulting in large incremental increases in strain readings. This had an effect on strain vs stress graphs as some plots showed signs of large increases between values. Table 5.10 – Poisson’s ratio review from various authors and manufacturers Author/Manufacturer
Major Poisson’s Ratio 𝑽𝟏𝟐
Minor Poisson’s Ratio 𝑽𝟐𝟏
Test Method
Exel Composites LTD
0.33
-
Tensile Test ASTM D3039
Creative Pultrusion (2004)
0.35
0.15
Tensile Test ASTM D3039
Cardoso (2014)
0.36 – 0.49
-
Tensile Test ASTM D3039
Nguyen (2014)
0.225 – 0.237
0.08 – 0.085
Bank et al. (1996)
0.33
-
Seracino (2005)
0.22
-
-
Haj-Ali et al. (2003)
0.3
-
-
0.22 – 0.51
0.07 – 0.15
Coupon Compression Test
Author
Page | 47
Tensile Test BS EN 527- 5 Coupon Compression Test
5.5.4 Longitudinal Compressive Modulus and Strength EL,c and FL,c Both the longitudinal compressive modulus and compressive strength was determined from the coupon compression test, although it is recommended to obtain this from compression test of complete stub column profiles, a range was determined from the coupon test. Buckling failure was seen through various coupons, therefore in determination of data the slope was taken from start/mid range of the graph. Bai et al. (2009) reports that delamination may also affect determination of compressive strength. The longitudinal compressive modulus was determined by stress-strain graphs shown in Figure 5.17 to Figure 5.25, the range of compressive modulus determined from coupon test are depicted in Table 5.4. For the 4 mm yellow sample there was only one coupon that successful recorded, therefore it was unreliable as a comparison could not be made between the other two coupons. However for the 6 mm grey coupons, a large variation in determined moduli is observed, these values have a difference around 40 GPa for same samples. Similarly for the compressive strength variations were seen between coupons, with the 4 mm coupons having a difference of 40 MPa and the 6 mm having a difference of 19 MPa. Compressive behaviour is affected by various factors, such as manufacturing method and quality, small defects present in profile, fibre quality and alignment of fibres, also testing accuracy which can in effect result in variations with results (Cardoso 2014). These issues may have been present in testing of coupons as variations are present between results. Although a comparison made between previous works conducted by authors shows some similarities with the longitudinal compressive modulus, however the compressive strength is relatively lower to what other authors have determined, as shown in Table 5.11. As the coupon compression test is not ideal for determining the compressive strength, it can be seen that values obtained are much lower, this is due to authors testing complete profiles instead of single coupon plates. Table 5.11 – Longitudinal compressive modulus and strength comparison from various sources Longitudinal Compressive Modulus 𝑬𝑳,𝒄 (GPa)
Longitudinal Compressive Strength 𝑭𝑳,𝒄 (MPa)
Test Method
Cardoso (2014)
20 – 30
200 – 350
Stub Column Compression Test
Exel Composites
17.2
207
Compression Test ASTM D695
20
226
Compression Test ASTM D695
30 - 33
-
Longitudinal Tensile Test
19.3
-
-
Author/Manufacturer
Creative Pultrusion (2004) Nguyen (2014) Haj-Ali et al. (2003) Bank et al. (1996) Author
24 13 – 50
Coupon Test 60 – 160
Coupon Compression Test
Comparison between the two thickness shows that increase thickness results in higher compressive strength and modulus. This is expected as increasing fibres increase crosssectional area, therefore allowing the material to sustain higher loads. Although the differences are not substantial, variations would be expected to be higher if stub column test was carried or coupon fixtures were used.
Page | 48
6 CLASSIFICATION OF HOLLOW UNDER AXIAL COMPRESSION
SECTIONS
6.0 Introduction Classifying compression members requires all elastic constant determined in chapter 5, these values will be used in various expression to determine if columns are short, intermediate or slender depending on the length and thickness of samples.
6.1 Material Properties Material properties to determine the classification of compression members are stated below: 𝑬𝟏 = 𝑬𝑳,𝒄 = Longitudinal Modulus of Elasticity (MPa) 𝑬𝒑𝒃𝟏 = 𝑬𝒇,𝑳 = Longitudinal Flexural Modulus (MPa) 𝑬𝒑𝒃𝟐 = 𝑬𝒇,𝑻 = Transverse Flexural Modulus (MPa) 𝑮𝟏𝟐 = 𝑮𝟏𝟑 = 𝑮𝟐𝟑 = 𝑮𝑳𝑻 = In-plane Shear Modulus (MPa) 𝑽𝟏𝟐 = Major Poisson’s Ratio 𝑽𝟐𝟏 = Minor Poisson’s Ratio 𝑭𝒄 = 𝑭𝑳,𝒄 = Longitudinal Compressive Strength (MPa) Material properties used in determination of compression column classification are presented in Table 6.1. Unreliable values that were determined from the experimental test will not be used, therefore values will be sourced from literature. Table 6.1 – Material properties used in compression column classification
Properties
4mm Yellow Columns
6mm Grey Columns
𝑬𝟏
17000¤
30000
𝑬𝒑𝒃𝟏
22000
25000
𝑬𝒑𝒃𝟐
7900
16000
𝑮𝟏𝟐
2500
2600
𝑽𝟏𝟐
¤
0.33
0.33¤
𝑽𝟐𝟏
0.15¤
0.15¤
𝑭𝒄
207¤
250¤
Values labelled with superscript ¤ represents values obtained from manufacturer or author, values used from literature are sourced to be the closest to values of the material used in this project. Page | 49
6.2 Closed Form Equations Step 1 – Determining Local and Global Buckling:
𝑭𝒄𝒓𝒍 = 0.9
𝜋 2 𝐸𝑝𝑏1 12(1−𝑉12 𝑉21
𝑡 2
𝐸𝑝𝑏2
𝑏
𝐸𝑝𝑏1
( ) [1 + (1 + 2𝑉12 ) )
+ 4(1 − 𝑉12 𝑉21 )
𝐺12 𝐸𝑝𝑏1
]
Equation 6.1
Step 2 – Determining Global and Local Slenderness
𝝀= √
𝑚𝑖𝑛 (𝐹𝑐 ;𝐹𝑐𝑟𝑙 )
Equation 6.2
𝐹𝑐𝑟
𝐹
𝝀𝒑 = √ 𝑐 𝐹
Equation 6.3
𝑐𝑟𝑙
𝑭𝒄𝒓 =
𝑭𝒆 =
4𝑛𝑠 𝐹𝑒 −1) 𝐺12 2𝑛 (𝐺 𝑠 ) 12
Equation 6.4
2
Equation 6.5
(√1+
𝜋2 𝐸1 (𝑘𝑙⁄𝑟 )
𝑘𝑙 = Column Effective Length 𝑟 = Radius of Gyration = √𝐼⁄𝐴 𝑛𝑠 = 2.0 for SHS Step 3 – Determine the plate strength reduction factor:
𝜸𝟏 =
𝛾𝑝 𝛾𝑝𝑜
2
=
(1+∝𝑝𝑒 +𝜆2𝑝 −√(1+∝𝑝𝑒 +𝜆2𝑝 ) −4𝜆2𝑝 ⁄2𝜆2𝑝 2 (1+𝜆2𝑝 −√(1+𝜆2𝑝 ) −4𝜆2𝑝 ⁄2𝜆2𝑝
∝𝑝𝑒 = 0.015 Step 4 – Determining the normalized column strength: Page | 50
Equation 6.6
2
𝜸𝟐 =
1+∝+𝜆2𝑝 × 𝛾1 −√(1+∝+𝜆2𝑝 ×𝛾1 ) −4×𝜆2𝑝 ×𝛾1 Equation 6.7
2𝜆2𝑝
∝ = 0.34 Step 5 – Determining nominal compressive strength
𝑷𝒏 = 𝛾2 (𝐴 × 𝑚𝑖𝑛 (𝐹𝑐 ; 𝐹𝑐𝑟𝑙 )
Equation 6.8
6.2 Compression Column Classification To classify the compression columns a range is given, as shown in Table 6.2. This range will allow the classification on the various lengths for the columns and determine if the columns are short, intermediate or slender. The classification is split into columns and plates, therefore both columns and wall plates can be classified. A excel spreadsheet was developed to automatically calculate slenderness from inputting parameters manually, the table produce is represented in appendices Table A9.8. Table 6.2 – Column classification range
Columns
Plate
𝝀 ≤ 𝟎. 𝟕
=
Short (SH)
𝝀𝒑 ≤ 𝟎. 𝟕
=
Compact (CP)
𝟎. 𝟕 ≤ 𝝀 < 𝟏. 𝟑
=
Intermediate (IN)
𝟎. 𝟕 ≤ 𝝀𝒑 < 𝟏. 𝟑
=
Intermediate (IN)
𝟏. 𝟑 ≤ 𝝀
=
Slender (SL)
𝟏. 𝟑 ≤ 𝝀𝒑
=
Slender (SL)
Table 6.3 – Plate Classification
Thickness
𝝀𝒑
Classification
4 mm Yellow
1.89
Slender
6 mm Grey
1.14
Intermediate
Classifying the plate, we can see that the 4 mm sample is classified as slender, whilst the 6mm sample is classified as intermediate. This is expected as the thinner sample taking a similar compressive strength, will result in the 4 mm sample being slender. A further analysis is required to determine how the varying thicknesses can affect the plate slenderness ration.
Page | 51
Table 6.4 – Compression column classification for 4mm and 6mm samples
4mm Yellow
6mm Grey
Effective Length (mm)
𝝀
Classification
Effective Length (mm)
𝝀
Classification
100
0.30
Short
100
0.27
Short
200
0.43
Short
200
0.38
Short
400
0.60
Short
400
0.54
Short
600
0.72
Intermediate
600
0.66
Short
800
0.82
Intermediate
800
0.76
Intermediate
1000
0.90
Intermediate
1000
0.85
Intermediate
1200
0.97
Intermediate
1200
0.93
Intermediate
1500
1.05
Intermediate
1500
1.03
Intermediate
2000
1.14
Intermediate
2000
1.19
Intermediate
From Table 6.4 we can see that both columns exceed 2 m without being classified as slender, from reviewing these numbers and using elastic constants from manufacturers, values still classify within the same range. It is possible that the larger 100 mm x 100 mm cross-section induces the columns to be classified at larger spans then expected as intermediate or short. What also can be depicted from the Table 6.4 is that the 6 mm grey sample has a slightly larger length before being classified as intermediate, this is also expected as the 6 mm section will allow for a higher bearing capacity than the 4 mm yellow sample.
Column Classification 1.3 1.2 1.1 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
4 mm Yellow Column
λ
6 mm Grey Column
100
200
400
600 800 1,000 1,200 Column Effective Length (mm)
1,500
Figure 6.1 – Column classification chart using data from Table 6.4
Page | 52
2,000
Figure 6.1 represents values taken from Table 6.4, the line at 0.7λ represents the change from short to intermediate columns, therefore all column lengths below are short. The line at 1.3λ represents the change from intermediate to slender, from the graph it is observed that no columns exceed the slender line, therefore at 2 m no columns are slender.
6.3 Classifying Various Profiles from Pultruders Using the data obtained in experimental tests and using profile sizes supplied by manufacturers Exel Composites LTD and RBJ Plastics, a classification will be made to determine at what lengths columns are short, intermediate or slender for varying profile sizes. Table 6.5 – Exel Composites LTD plate classification
Exel Composites LTD Column Size (mm)
𝝀𝒑
Classification
80x30x2.5
0.91
Intermediate
80x20x5
0.3
Compact
51x51x6.5
0.59
Compact
51x51x3.2
1.21
Intermediate
44x44x6
0.56
Compact
44x44x3
1.11
Intermediate
42x10x2.5
1.27
Intermediate
42x30x2.5
1.27
Intermediate
30x30x2
1.14
Intermediate
25x25x3
0.63
Compact
Page | 53
Table 6.6 – RBJ Plastics LTD plate classification
RBJ Plastics LTD Column Size (mm)
𝝀𝒑
Classification
100x50x8
0.85
Intermediate
50x20x4
0.85
Intermediate
60x60x4.5
0.91
Intermediate
50x50x4.5
0.76
Intermediate
40x30x5
0.55
Compact
40x30x3
0.91
Intermediate
38x38x5
0.52
Compact
30x30x2
1.02
Intermediate
22x27x2.5
0.60
Compact
15x15x2.5
0.41
Compact
Page | 54
Table 6.7 – Exel Composites LTD Compression Wall Column Classification
Column Length (mm) 100 200 400 600 800 1000 1200 1500 2000
Exel Composites LTD 80x30x2.5 𝝀 0.38 0.54 0.76 0.93 1.07 1.20 1.30 1.44 1.64
Class
SH SH IN IN IN IN SL SL SL
80x20x5 𝝀 0.40 0.57 0.80 0.98 1.13 1.25 1.36 1.51 1.71
Class
SH SH IN IN IN IN SL SL SL
51x51x6.5
51x51x3.2
42x10x2.5
42x30x2.5
𝝀 0.47 0.66 0.93 1.14 1.31 1.45 1.57 1.72 1.92
𝝀 0.38 0.53 0.75 0.91 1.05 1.16 1.26 1.39 1.55
𝝀 0.82 1.14 1.51 1.71 1.82 1.89 1.93 1.97 2.00
𝝀 0.46 0.65 0.91 1.10 1.25 1.37 1.47 1.59 1.72
Class
SH SH IN IN SL SL SL SL SL
Class
SH SH IN IN IN IN IN SL SL
Class
IN IN SL SL SL SL SL SL SL
Class
SH SH IN IN IN SL SL SL SL
44x44x6 𝝀 0.51 0.72 1.01 1.23 1.40 1.55 1.68 1.83 2.02
Class
SH IN IN IN SL SL SL SL SL
44x44x3 𝝀 0.44 0.62 0.88 1.07 1.22 1.36 1.47 1.61 1.78
Class
SH SH IN IN IN SL SL SL SL
30x30x2 𝝀 0.52 0.74 1.03 1.25 1.42 1.56 1.67 1.80 1.94
Class
SH IN IN IN SL SL SL SL SL
25x25x3 𝝀 0.67 0.94 1.31 1.58 1.78 1.93 2.05 2.18 2.32
Class
SH IN SL SL SL SL SL SL SL
Table 6.8 – RBJ Plastics LTD Compression Wall Column Classification
Column Length (mm) 100 200 400 600 800 1000 1200 1500 2000
Page | 55
RBJ Plastics LTD 100x50x8
50x20x4
60x60x4.5
50x50x4.5
40x30x5
40x30x3
38x38x5
30x30x2
22x27x2.5
15x15x2.5
𝝀
Class
𝝀
Class
𝝀
Class
𝝀
Class
𝝀
Class
𝝀
Class
𝝀
Class
𝝀
Class
𝝀
Class
𝝀
Class
0.44 0.62 0.87 1.06 1.22 1.36 1.48 1.64 1.86
SH SH IN IN IN SL SL SL SL
0.70 0.98 1.37 1.66 1.87 2.04 2.17 2.32 2.49
IN IN SL SL SL SL SL SL SL
0.40 0.56 0.80 0.97 1.12 1.25 1.36 1.51 1.72
SH SH IN IN IN IN SL SL SL
0.44 0.62 0.88 1.07 1.23 1.37 1.49 1.65 1.87
SH SH IN IN IN SL SL SL SL
0.58 0.82 1.15 1.39 1.59 1.76 1.89 2.06 2.26
SH IN IN SL SL SL SL SL SL
0.56 0.79 1.11 1.35 1.55 1.71 1.85 2.01 2.22
SH IN IN SL SL SL SL SL SL
0.51 0.73 1.02 1.25 1.43 1.59 1.72 1.89 2.10
SH IN IN IN SL SL SL SL SL
0.55 0.77 1.09 1.32 1.51 1.67 1.80 1.97 2.17
SH IN IN SL SL SL SL SL SL
0.61 0.86 1.20 1.46 1.66 1.83 1.97 2.13 2.33
SH IN IN SL SL SL SL SL SL
0.83 1.17 1.62 1.92 2.13 2.29 2.40 2.52 2.63
IN IN SL SL SL SL SL SL SL
From Table 6.5 and Table 6.6 it can be observed that the various profiles geometries the manufacturers supply and there corresponding plate classification. From the tables it can be assumed clearly the factor that affects the plate classification is plate thickness, if a comparison is made between varying thicknesses in Table 6.5 from Exel composites, its is observed that an increase in plate thickness reduces the slenderness ratio, therefore classifying the column as compact rather than slender. Column sizes 60 mm x 60 mm x 4.5 mm and 50 mm x 50 mm x 4.5 mm have slight variation in column breadth and depth, however the slenderness ratio is affected with the 60 mm x 60 mm x 4.5 mm having a higher ratio than that of the 50 mm x 50 mm x 4.5 mm profile. The two factors that can indefinitely be determined from this examination of profiles are; 1) Profile thickness will decrease plate slenderness ratio if thickness is increased, 2) Profile cross-section dimension will increase plate slenderness ratio if they are increased. From Table 6.7 and Table 6.8 a comparison is made between various standard profile dimensions supplied by manufactures Exel Composites LTD and RBJ Plastics LTD, columns were classified to a length of 2 m. A variety of responses were determined, with some columns ranging from short to slender, whilst others did not classify as short but were between intermediate and slender. From Table 6.7 we can see that profile cross section affects the classification more than the thickness, column 80 mm x 30 mm x 2.5 mm and 42 mm x 10 mm x 2.5 mm show a large difference in slenderness ratio although thicknesses are similar. For the 80 mm x 30 mm x 2.5 mm column is classified as short up to around 200 mm, however the 42 mm x 10 mm x 2.5 mm column is intermediate at 100 mm. This indicates that the cross-sectional dimensions have a large effect on the column classification. Examining the varying thicknesses we can see from Table 6.8 columns 40 mm x 30 mm x 5 mm and 40 mm x 40 mm x 3 mm have a 2 mm variation in thickness, this variation in thickness has a minute effect on the slenderness ratio. Analysing the classification range, it is determined that the major factor affecting the wall classification is the cross-sectional dimensions, also the thickness does have effect but these a negligible.
6.4 Worked Example For the 100 mm x 100 mm x 6 mm grey section used in the project, a worked example is carried out in order to demonstrate the method of calculating the slenderness ratio for plate and wall of the column for a column length of 1200 mm, data used is presented in Table 6.1. Step 1 – Determining Local and Global Buckling using Equation 6.1
𝐅𝐜𝐫𝐥 = 0.9
π2 × 25000 6 2 16000 2600 ( ) [1 + (1 + 2 × 0.33) + 4(1 − 0.33 × 0.15) ] 12(1 − 0.33 × 0.15) 100 25000 25000
𝐅𝐜𝐫𝐥 = 192.84 MPa
Page | 56
Step 2 – Determining Global and Local Slenderness using Equations 6.2 – 6.5
𝐅𝐞 =
π2 × 30000 (1200⁄38.45)
( √1 + 𝐅𝐜𝐫 =
𝛌= √
2
= 303.73 𝑀𝑃𝑎
4 × 2 × 303.73 − 1) 2600 = 224.35 𝑀𝑃𝑎 < 𝑭𝒄 = 250 𝑀𝑃𝑎 2×2 (2600)
(192.84) = 0.93 = 𝐼𝑛𝑡𝑒𝑟𝑚𝑒𝑑𝑖𝑎𝑡𝑒 224.35
250 𝛌𝐩 = √ = 1.14 = 𝐼𝑛𝑡𝑒𝑟𝑚𝑒𝑑𝑖𝑎𝑡𝑒 192.84
Step 3 – Determining Plate Strength Reduction Factor using Equation 6.6
𝛄𝟏 =
γp (1 + 0.015 + 1.142 − √(1 + 0.015 + 1.142 )2 − 4 × 1.142⁄2 × 1.142 = = 0.98 γpo (1 + 1.142 − √(1 + 1.142 )2 − 4 × 1.142⁄2 × 1.142
Step 4 – Determining Normalised Column Strength using Equation 6.7
𝛄𝟐 =
1 + 0.34 + 1.142 × 0.98 − √(1 + 0.34 + 1.142 × 0.98)2 − 4 × 1.142 × 0.98 = 0.49 2 × 1.142
Step 5 – Determining Nominal Compressive Strength using Equation 6.8
𝐏𝐧 = 0.49 × (2256 × 192.84) = 214.50 𝑀𝑃𝑎
Page | 57
7 CONCLUSIONS AND RECOMMENDATIONS FOR FURTHER WORK 7.1 Conclusion Determination of elastic constants for FRP composites is difficult to achieve with accuracy and reliability. Although there are some standards available, authors have used methods that are non-standard. The ranges of elastics constant varies a lot in FRP composites, unlike steel, which normally has similar elastic constants to varying manufacturers or profile geometry, FRP composites elastic constant can vary substantial due to variation in fibres and manufacturers. This is why accurate and reliable methods are needed to be established in order to provide a basis for researcher to adopt. It was determined that the fibre architectures affect the elastics constants of FRP composites, the varying thicknesses and inconsistencies in FRP materials places a challenge for determining elastic constants, especially to elastic constants such as the inplane shear modulus (Nguyen 2014). Although the full section profile test was sufficient in providing a range of elastic modulus between 2.5 GPa and 2.7 GPa, it was found that the determined values were close to a lower-bound solution, similar to those given by manufacturers. Nguyen (2014) recommends using the 10° off-axis tensile test to be adopted for determining the in-lane shear modulus, the results obtain from this test are found to be more suitable for numerical modelling and design purpose, although conservative values such as manufacturers results can be used, however this is considered to be too safe. Longitudinal flexural modulus was found to be very similar to those published by manufacturers, using the three-point bending test (ASTM D790). The full section profile test also gave a range of flexural modulus, which was found to be an upper-bound in comparison to values obtained from the three-point bending test. Both values are verified by conducting a comparison between previous published values, although the ASTM standard test is a more appropriate test to determine flexural modulus, the full section profile test is also reliable but sufficient in providing an upper-bound solution. The flexural modulus obtained from both the three-point bending and full section profile test shows slight variation between the varying thickness, it is appropriate to say although the thickness affects the flexural modulus, it does not do so substantially and longitudinal flexural modulus is relatively constant through varying materials. Determination of the transverse flexural moduli is among the most difficult elastic constant to determine, due to the nature of fibre directions. The channel test was found to be a good method of determining this elastic constant, however it was found that any faults with strain gauges can result in unreliable test results. Therefore it is imperative to ensure accuracy of strain gauges an eccentric loading when testing channels. A range of 8 GPa to 16 GPa was determined from the test, the lower-bound given by manufacturers is 5.5 GPa. Therefore for design purposes, the channel test is sufficient in determining an upper-bound range to be used in numerical modelling and other purposes. The coupon compression test was again problematic due to strain gauge issues, although the test has been recommended and is easy to conduct; there are various variables that must be considered. The range of compressive strength determined from the test was substantially lower than those published by authors and manufacturers, however it is recommended that a stub column test is adopted in order to determine the compressive strength. A special fixture that fixes coupon ends to reduce gauge length would have further Page | 58
increased the reliability of the test, and compression strength would have increased. In coupon test it was found that failure of coupons was due to buckling or flexure, therefore decreasing the obtained compressive strength. In future it would be recommended that a fixture is used or an ASTM standard apparatus fixture to increase the reliability of the coupon compression test. The column classification was an interesting analysis of how varying thicknesses and profile cross-section geometry affects the classification, a strong variation in thickness was shown in plate classification, whilst for the column wall classification, the cross-section had a large effect. For the profiles used in the project, both columns were classified as intermediate at 2000 mm, the plate was classified as slender for the 4 mm specimen and intermediate for the 6 mm specimen.
7.2 Recommendation for Further Work There is imperative need to further investigate this novel material; there are certain gaps in knowledge that will aid the development of this material.
The effects of corner fillets on tubular hollow sections when determining elastic constant and compressive strength. Do the corner fillets have an effect of compressive strength of tubular columns, and what are the differences between plate strength and column strength?
Accuracy of experimental procedures to determine in-plane shear modulus for FRP composites. Analysis between full section profile test and other experimental procedures to determine which test method provides lower-bound or upper-bound solutions.
Investigation into elastic constants for varying tubular cross-sections and sizes, to determine if profile size has an effect on any of the elastic constants determined in the project.
Determine a relationship between elastic constant, does any increase or decrease in one elastic constant have an effect on other elastic constant?
Is the channel test a reliable method of determination for transverse flexural modulus, can a comparison be made between other tests methods and which one provides upper or lower bound solutions?
Using the column classification data, what failure modes are shown for short, intermediate or slender columns, examine the intermediate range further as more knowledge is required for failure modes of intermediate columns.
These are few of many recommendations for further research work, as stated by various authors there is substantial need for further test in various areas for this material.
Page | 59
REFERENCES Aamanet.org, (2013). When push comes to pull | how the pultrusion process delivers a high performing product. [Online] Available at: http://www.aamanet.org/news/3/10/0/all/982/whenpush-comes-to-pull-how-the-pultrusion-process-delivers-a-high-performing-product [Accessed 14 Mar. 2015].
Adams, D. (2005). Current compression test methods. [Online] Compositesworld.com. Available
at:
http://www.compositesworld.com/articles/current-compression-test-methods
[Accessed 21 Mar. 2015].
ASTM D3410 / D3410M-03 (2008), Standard Test Method for Compressive Properties of Polymer Matrix Composite Materials with Unsupported Gage Section by Shear Loading, ASTM International, West Conshohocken, PA,
ASTM Standard D3518 (2013), Standard Test Method for In-Plane Shear Response of Polymer Matrix Composite Materials by Tensile Test of a ±45° Laminate, ASTM International, West Conshohocken, PA
ASTM Standard D5379 (2012), Standard Test Method for Shear Properties of Composite Materials by the V-Notched Beam Method, American Society for Testing and Materials, West Conshohocken, PA
ASTM Standard D638 (2014), Standard Test Method for Tensile Properties of Plastics, ASTM International, West Conshohocken, PA,
ASTM D6641 / D6641M-14 (2014), Standard Test Method for Compressive Properties of Polymer Matrix Composite Materials Using a Combined Loading Compression (CLC) Test Fixture, ASTM International, West Conshohocken, PA,
ASTM D695 (2010), Standard Test Method for Compressive Properties of Rigid Plastics, ASTM International, West Conshohocken, PA,
ASTM Standard D7078 (2012), Standard Test Method for Shear Properties of Composite Materials by V-Notched Rail Shear Method, ASTM International, West Conshohocken, PA,
Page | 60
ASTM Standard D790 (2010), Standard Test Methods for Flexural Properties of Unreinforced
and
Reinforced
Plastics
and
Electrical
Insulating
Materials,
ASTM
International, West Conshohocken, PA,
Babukiran, B. and Harish, G. (2008). Influence of Resin and thickness of Laminate on Flexural Properties of Laminated Composites. International Journal of Engineering Science and Innovative Technology, 3(1), pp.280-286.
Bakis, C., Bank, L., Brown, V., Cosenza, E., Davalos, J., Lesko, J., Machida, A., Rizkalla, S. and Triantafillou, T. (2002). Fiber-Reinforced Polymer Composites for Construction—Stateof-the-Art Review. Journal of Composites for Construction, 6(2), pp.73-87.
Bai, Y., Vallée, T. and Keller, T. (2009). Delamination of pultruded glass fiber-reinforced polymer composites subjected to axial compression. Composite Structures, 91(1), pp.66-73.
Bank, L. (1990). Shear Properties of Pultruded Glass FRP Materials. J. Mater. Civ. Eng., 2(2), pp.118-122.
Bank, L. and Yin, J. (1996). Buckling of orthotropic plates with free and rotationally restrained unloaded edges. Thin-Walled Structures, 24(1), pp.83-96.
Buchanan, S., Archer, E., Townsend, D., Jenkins, S., McIlhagger, A. and Quinn, J. (2012). Determination of in-plane shear modulus of 3D woven composites with large repeat unit cells. Plastics, Rubber and Composites, 41(4/5), pp.194-198.
BS EN 13706-2 (2002), Reinforced plastics composites - Specifications for pultruded profiles, British Standard Institution, London, UK
BS EN 15310 (2005), Reinforced plastics - Determination of the in-plane shear modulus by the plate twist method, British Standard Institution, London, UK
BS EN 527-5 (2009), Plastics -- Determination of tensile properties -- Part 5: Test conditions for unidirectional fiber-reinforced plastic composites, British Standard Institution, London, UK Cardoso. D.T.C, (2014), ‘Compressive Strength of Pultruded Glass-Fiber Reinforced Polymer (GFRP) Columns’, Federal University of Rio de Janeiro. Brazil. PhD Thesis.
Page | 61
Creative Pultrusion, (2004). The Pultex Pultrusion Design Manual of Standard and Custom Fiber Reinforced Polymer Structural Profiles. 4(9), p.21.
Creativepultrusions.com, (2015). Pultrusion Process - Creative Pultrusion. [Online] Available at: http://www.creativepultrusions.com/products-solutions/pultrusion-process/ [Accessed 14 Mar. 2015].
Davalos, J., Qiao, P., Wang, J., Salim, H. and Schlussel, J. (2002). Shear Moduli of Structural Composites from Torsion Tests. Journal of Composite Materials, 36(10), pp.11511173.
Dixon,
A.
(2006).
Brittania
Bridge
Train
crossing.
[image]
Available
http://commons.wikimedia.org/wiki/File:Brittania_Bridge_Train_crossing_3.JPG
at:
[Accessed
21 Jan. 2015].
Domone, P. and Illston, J. (2010). Their nature and behavior. London: Taylor & Francis Ltd. 348 – 355 Exelcomposites.com, (2015). Exel Composites – Advanced Pultrusion and Pull winding Technologies. [online] Available at: http://www.exelcomposites.com/ [Accessed 25 Mar. 2015].
Fairuz, A., Sapuan, S., Zainudin, E. and Jaafar, C. (2014). Polymer Composites Manufcaturing using a Pultrusion Process: A Review. American Journal of Applied Sciences, 11(10), pp.1798-1810.
Fiberline.com, (2008). Pontresina bridge, Switzerland | Fiberline Composites. [online] Available at: http://fiberline.com/pontresina-bridge-switzerland [Accessed 24 Mar. 2015].
Gand, A., Chan, T. and Mottram, J. (2013). Civil and structural engineering applications, recent trends, research and developments on pultruded fiber reinforced polymer closed sections: a review. Frontiers of Structural and Civil Engineering, 7(3), pp.227-244.
GangaRao, H. and Vijay, P. (2010). Feasibility Review of FRP Materials for Structural Applications. Morgantown: West Virginia University, pp.5-8.
Page | 62
Gardner, L., Chan, T. and Law, K. (2010). Structural design of elliptical hollow sections: a review. Proceedings of the ICE - Structures and Buildings, 163(6), pp.391-402.
Haj-Ali, R. and Kilic, H. (2003). Nonlinear constitutive models for pultruded FRP composites. Mechanics of Materials, 35(8), pp.791-801.
Keller, T. (2004). Influences of Adavanced Composite Materials on Structural Concepts for Bridges and Buildings. Swiss Federal Institute of Technology, Lausanne, Switzerland, pp.12.
Kendall, D. (n.d.). Fibre Reinforced Polymer (FRP) Composite Buildings - Future Oppportunities. Opportunities in Construction, p.3.
Lane A. (2002). An experimental investigation of buckling mode interaction in PFRP columns. PhD Thesis. University of Warwick
Latere Dwan'isa, J., Mohanty, A., Misra, M., Drzal, L. and Kazemizadeh, M. (2004). Biobased polyurethane and its composite with glass fiber. Journal of Materials Science, 39(6), pp.2081-2087.
Lee, S. (1989). Reference book for composites technology. Lancaster, Pa., U.S.A.: Technomic Pub. Co.
Lee, S. and Munro, M. (1986). Evaluation of in-plane shear test methods for advanced composite materials by the decision analysis technique. Composites, 17(1), pp.13-22.
Lynch,
D.
(2012).
No.13
Aberfeldy
footbridge.
[online]
Nce.co.uk.
Available
at:
http://www.nce.co.uk/features/nce-40-years/no13-aberfeldy-footbridge/8630564.article [Accessed 24 Mar. 2015].
Mosallam, A., Bayraktar, A., Elmikaw, M., Pul, S. and Adanur, S. (2013). Polymer Composites in Construction: An Overview. [online] Symbiosisonlinepublishing.com. Available at:
http://symbiosisonlinepublishing.com/materialsscience-engineering/materialsscience-
engineering07.php [Accessed 8 Mar. 2015].
Ngcc.org.uk, (2015). What are fibre reinforced polymers?. [online] Available at: http://www.ngcc.org.uk/Information/Introduction/Overview.aspx [Accessed 14 Mar. 2015]. Page | 63
Nguyen, T. (2014). Lateral-torsional buckling resistance of pultruded fibre reinforced polymer shapes. Ph.D. University of Warwick.
Pulido, M. (2001). Lleida Footbridge (Lleida, 2001) | Structurae. [online] Structurae. Available at: http://structurae.net/structures/lleida-footbridge [Accessed 24 Mar. 2015].
RBJ Plastics, (2015). RBJ Plastics. [online] Available at: http://www.rbjplastics.com/ [Accessed 25 Mar. 2015].
Sastra, H., Siregar, J., Sapuan, S. and Hamdan, M. (2006). Tensile Properties of Arenga pinnata Fiber-Reinforced Epoxy Composites. Polymer-Plastics Technology and Engineering, 45(1), pp.149-155.
Seracino, R. (2005). FRP Composites in Civil Engineering, CICE 2004. Leiden: A.A. Balkema.
Sidhu, H. (2014). An Experimental Investigation into Reciprocally Supported and Configured Modules (RSCM) of GFRP hollow square sections. Undergraduate. Coventry University.
Singh, S., Kumar, P. and Jain, S. (2013). An experimental and numerical investigation of mechanical properties of glass fiber reinforced epoxy composites. Advanced Material Letters, 4(7), pp.567-572.
Steve, A. (2013). The Aberfeldy Footbridge at 20. [online] Compositesandarchitecture.com. Available at: http://compositesandarchitecture.com/?p=2398 [Accessed 24 Mar. 2015].
Sundarraja, M., Sriram, P. and Ganesh Prabhu, G. (2014). Strengthening of Hollow Square Sections under Compression Using FRP Composites. Advances in Materials Science and Engineering, 2014, pp.1-19.
Totry,E., Gonzalez, C. and Llorca, J. (2009). Mechanical Behaviour of composite materials in shear: Experiments and Simulations. 1, pp. 187-188.
Wolfenden, A. and Bank, L. (1989). Flexural and Shear Moduli of Full-Section Fiber Reinforced Plastic (FRP) Pultruded Beams. J. Test. Eval., 17(1), p.40.
Page | 64
APPENDICES Table A9.1 – Timoshenko Experimental Specimen Dimensions 100x100x4mm Yellow Section (Timoshenko Beam) Left TOP
BOTTOM
Middle
Right
Face Average
North
3.93
4
4.17
4.03
East
3.04
3.29
3.26
3.20
South
3.23
3.3
3.53
3.35
West
4.46
4.39
4.45
4.43
North
4.03
4.03
3.96
4.01
East
3.25
3.24
3.04
3.18
South
3.66
3.51
3.39
3.52
West
4.65 4.56 4.6 Section Measured Average Thickness:
Side Average
3.75
3.83
4.60 3.79
WIDTH Top
Middle
Bottom
Average
N-S Face (Breth)
99.76
100.31
99.77
99.95
E-W Face (Depth)
100.06
99.84
99.84
99.91
THICKNESS 100x100x6mm Grey Section (Timoshenko Beam)
TOP
BOTTOM
Left
Middle
Right
Face Average
North
5.84
5.84
5.63
5.77
East
6.32
6.31
6.21
6.28
South
6.68
6.86
6.61
6.72
West
6.15
6.1
6.02
6.09
North
5.78
5.95
5.87
5.87
East
6.3
6.27
6.62
6.40
South
6.64
6.84
6.65
6.71
West
5.99 6.06 6.1 Section Measured Thickness:
Side Average
6.21
6.26
6.05 6.235
WIDTH Top
Middle
Bottom
Average
N-S Face (Breth)
101.07
101.28
101.11
101.15
E-W Face (Depth)
101.29
101.27
101.31
101.29
Page | 65
Table A9.2 – Timoshenko Experimental Data 100 x 100 x 4mm Yellow Sample Recorded Deflections Left
Middle
LVDT
Right
δ₁
δ₂
δ₁
δ₂
δ₁
δ₂
δ₁
δ₂
LOAD (N)
0.43
0.48
1.58
1.74
1.723
2.14
0.43
0.48
2750
0.48
0.5
1.95
2.04
1.77
2.13
0.44
0.42
3500
0.54
0.52
1.32
1.26
1.4
1.36
0.56
0.58
2750
0.62
0.57
1.64
1.57
1.73
1.67
0.65
0.64
3500
0.54
0.55
1
1.02
1.07
1.08
0.45
0.48
2750
0.71
0.65
1.3
1.22
1.39
1.32
0.66
0.55
3500
0.57
0.58
0.88
0.92
0.98
1.01
0.43
0.45
2750
0.66
0.7
1.08
1.1
1.17
1.2
0.49
0.55
3500
0.63
0.52
0.72
0.67
0.83
0.78
0.43
0.39
2750
0.7
0.68
0.82
0.82
0.94
0.94
0.39
0.31
3500
0.46
0.42
0.78
0.73
0.78
0.73
0.54
0.59
2750
0.59
0.4
0.88
0.81
0.95
0.81
0.67
0.62
3500
100 x 100 x 6mm Grey Sample Recorded Deflections Left SPAN (mm) 950 850 750 650 550 450
Page | 66
Middle
Right
δ₁
δ₂
δ₁
δ₂
δ₁
δ₂
LOAD (N)
0.23
0.2
1.41
1.36
0.18
0.19
5000
0.42
0.38
2.77
2.7
0.36
0.36
10000
0.22
0.21
1.1
1.09
0.2
0.18
5000
0.41
0.38
2.21
2.17
0.4
0.38
10000
0.28
0.21
0.9
0.9
0.22
0.2
5000
0.5
0.43
1.77
1.71
0.42
0.4
10000
0.2
0.19
0.64
0.63
0.17
0.18
5000
0.38
0.37
1.27
1.25
0.35
0.35
10000
0.2
0.19
0.49
0.47
0.19
0.18
5000
0.3
0.27
0.96
0.93
0.35
0.32
10000
0.2
0.19
0.4
0.34
0.16
0.15
5000
0.38
0.33
0.68
0.66
0.24
0.2
10000
Table A9.3 – Three-Point Bending Experimental Specimen Dimensions SECTION
THICKNESS
AVERAGE
1
2
3
4
5
THICKNESS
A1
4.44
4.48
4.45
4.48
4.43
4.46
A2
3.98
4.01
3.98
3.96
3.92
3.97
A3
4.12
4.17
4.15
4.16
4.16
4.15
A4
4.57
4.54
4.65
4.55
4.62
4.59
A5
3.44
3.43
3.41
3.43
3.44
3.43
A6
3.31
3.3
3.3
3.28
3.3
3.30
A7
3.68
3.65
3.57
3.67
3.68
3.65
A8
3.5
3.41
3.42
3.4
3.5
3.45
B1
6.65
6.33
6.36
6.34
6.38
6.41
B2
6.2
6.08
6.08
6.08
6.15
6.12
B3
6.31
6.14
6.14
6.16
6.36
6.22
B4
6.01
5.8
5.83
5.8
5.88
5.86
B5
6.29
6.41
6.35
6.32
6.29
6.33
B6
5.82
5.76
5.86
5.79
5.89
5.82
B7
7.02
6.94
6.96
6.95
6.99
6.97
B8
6.87
6.75
6.76
6.79
6.85
6.80
SECTION
WIDTH
AVERAGE
1
2
3
4
5
WIDTH
A1
37.04
37.03
36.78
37.14
37.14
37.03
A2
36.84
37.02
36.8
36.88
37.03
36.91
A3
37.02
36.98
37.09
37.1
37.19
37.08
A4
36.95
37.06
36.91
37.05
36.99
36.99
A5
36.84
36.83
36.74
36.63
36.74
36.76
A6
36.67
36.71
36.83
36.74
36.92
36.77
A7
36.94
36.8
36.5
36.52
36.54
36.66
A8
36.99
36.82
36.48
36.79
36.55
36.73
B1
39.93
40.09
40.13
39.97
40.02
40.03
B2
39.81
39.84
39.85
39.91
39.81
39.84
B3
39.97
40.19
40.1
40.23
40.17
40.13
B4
39.96
40.04
39.71
39.99
40.07
39.95
B5
40.15
39.85
39.91
40.04
40.02
39.99
B6
39.94
39.82
39.87
39.74
40.31
39.94
B7
40.07
39.9
39.74
39.61
40.39
39.94
B8
39.55
39.62
39.81
40.16
40.19
39.87
Page | 67
Table A9.4 – Three-Point Bending Test Data A1
A2
A4
A3
Load (N) 0.0281
Extension (mm) 3.3E-05
Load (N) 0.1425
Extension (mm) -3E-05
Load (N) 0.5326
Extension (mm) 4.1E-05
4.6732
-0.0154
0.77617
-0.0376
6.0739
-0.0727
4.3184
-0.0394
0.40982
-0.0059
6.6153
-0.0723
3.9636
-0.0392
0.04347
0.07821
7.1566
-0.0724
3.6088
-0.0389
0.92093
0.41275
7.698
0.07805
3.254
-0.0387
4.0143
0.72679
8.2394
0.30516
2.8991
0.01555
7.1077
1.038
8.7807
0.52336
2.5443
0.19056
10.201
1.1988
9.3221
0.57602
2.1895
0.38356
13.232
1.4846
9.8634
0.81947
2.752
0.49935
16.264
1.8002
10.405
1.0414
4.3526
0.66093
19.295
1.9362
10.604
1.1072
5.9533
0.85812
22.327
2.2619
10.694
1.3142
7.554
1.0518
24.608
2.5743
10.785
1.5381
9.1547
1.2442
26.587
2.885
13.168
1.7554
10.755
1.4366
28.566
3.1957
16.175
1.9721
12.356
1.4928
30.546
3.5064
19.181
2.188
13.957
1.6355
32.525
3.6169
21.656
2.4039
15.557
1.8383
34.504
3.9544
23.299
2.6199
17.158
2.0336
36.707
4.268
24.943
2.8358
18.759
2.2258
38.992
4.5788
26.586
3.0518
20.359
2.418
41.277
4.8895
28.229
3.1671
21.96
2.6028
43.108
5.0549
29.872
3.269
23.561
2.6014
44.502
5.348
31.411
3.5009
25.161
2.8051
45.896
5.6632
32.908
3.5535
26.762
3.0047
47.291
5.9745
34.406
3.7229
28.363
3.199
48.685
6.0905
35.903
3.9482
29.963
3.3533
50.08
6.4195
37.4
4.1665
31.564
3.4407
51.474
6.7314
38.898
4.3826
33.165
3.6494
52.868
7.0425
40.395
4.5986
34.766
3.8455
54.676
7.3532
41.892
4.8147
36.366
4.0386
56.657
7.6639
43.39
5.0306
37.967
4.2311
58.638
7.7799
44.887
5.2466
39.568
4.4231
60.619
8.1132
46.385
5.4625
41.168
4.5914
62.6
8.4257
47.882
5.6417
42.769
4.5984
64.581
8.7364
49.379
5.7168
44.37
4.8152
66.562
9.047
50.877
5.9515
45.97
5.0137
68.544
9.3074
52.374
6.1714
47.571
5.2079
70.534
9.4381
53.871
6.3885
49.172
5.4001
72.532
9.6546
55.369
6.6045
50.772
5.5921
74.53
9.973
56.866
6.8204
52.373
5.7841
76.528
10.285
58.363
7.0364
53.974
5.8705
78.526
10.595
59.51
7.2216
Page | 68
A5
Load (N)
Extension (mm)
Load (N)
Extension (mm)
0.4553 5.4869 5.5184 5.55 5.5816 5.6131 5.6447 5.9631 6.6431 7.3232 8.0033 8.6833 9.8776 11.483 13.089 14.695 16.301 17.907 19.513 21.118 22.724 24.33 25.936 27.542 29.148 30.753 34.985 36.283 37.582 38.88 40.179 41.525 42.981 44.437 45.893 58.801 58.748 58.695 58.642 59.301 61.338 63.374
2.71E-20 2.71E-20 2.3E-05 0.00028 0.00494 0.0524 0.27227 0.39969 0.47326 0.68976 0.89168 1.0902 1.2885 1.4864 1.584 1.7075 1.9178 2.119 2.3175 2.5158 2.7137 2.9116 2.9973 3.1387 3.3476 3.549 3.5938 3.7383 3.9484 4.1478 4.3468 4.5447 4.7426 4.9406 4.9943 5.1704 5.378 5.5779 5.7765 5.7824 5.9876 6.1931
3.2411 4.3926 5.5441 6.6956 7.8471 8.9986 10.15 11.302 12.453 13.605 14.756 15.908 15.896 18.992 22.262 23.451 24.639 25.827 27.016 30.909 29.841 32.19 34.54 36.89 39.249 41.935 44.622 47.308 49.994 39.798 44.803 44.042 45.322 46.603 47.883 49.163 50.444 51.724 53.005 54.285 55.566 56.846
2.71E-20 -0.0043 0.0918 0.37115 0.69115 0.93851 1.1319 1.4563 1.7722 2.0872 2.402 2.7168 3.0317 3.1476 3.4882 3.8054 4.1205 4.4354 4.7367 4.889 5.2167 5.5331 5.8479 6.1628 6.4777 6.7927 7.1075 7.2377 7.5725 7.8893 8.2046 8.5195 8.8344 9.0455 9.2989 9.6202 9.9357 10.251 10.566 10.88 11.05 11.264
55.574
5.9858
80.524
10.906
57.794
7.3437
57.175
6.1903
82.522
11.217
56.078
7.5803
58.776
6.386
84.52
11.527
71.083
7.7874
60.376
6.5786
86.518
11.838
73.019
8.0071
75.053
6.6934
87.803
11.846
74.955
8.2233
77.183
6.7932
85.262
11.511
76.891
8.4396
79.313
7.0009
82.72
11.198
78.827
8.6555
81.443
7.1965
80.178
10.887
80.763
8.8712
83.573
7.389
78.708
10.576
82.699
8.8982
85.703
7.4147
78.168
10.266
84.635
9.1425
87.833
7.631
77.629
9.955
86.571
9.3638
89.963
7.8296
76.352
9.6444
88.507
9.581
92.092
8.0235
73.814
9.3338
90.315
9.7972
94.222
8.2157
71.276
9.0232
91.867
10.013
96.352
8.4078
68.738
8.7126
93.42
10.16
98.482
8.5367
66.2
8.402
94.973
10.03
98.692
8.4436
63.662
8.0914
77.599
9.8015
92.457
8.2354
61.125
7.7808
75.813
9.5829
87.774
8.0394
58.587
7.4702
74.027
9.3661
85.82
7.8469
55.101
7.1596
72.242
9.1501
83.865
7.6545
48.118
6.849
70.456
8.9342
81.911
7.4624
44.298
6.5384
68.671
8.7182
79.809
7.2705
40.734
6.2278
66.885
8.5023
77.62
7.0785
41.936
5.9171
65.094
8.2864
75.431
6.8866
40.295
5.6065
63.232
8.0705
73.242
6.6947
38.654
5.2959
61.37
7.8546
71.053
6.5028
37.013
4.9853
59.508
7.6387
68.864
6.3108
35.372
4.6747
57.646
7.4228
66.675
6.1189
33.731
4.3641
55.784
7.2069
64.486
5.927
32.089
4.0535
53.922
6.991
62.297
5.7351
30.067
3.7429
52.06
6.7751
60.109
5.5431
27.878
3.4324
50.198
6.5592
57.92
5.3512
25.689
3.1218
48.336
6.3432
55.731
5.1593
23.501
2.8112
46.473
6.1273
53.542
4.9674
21.312
2.5006
44.611
5.9114
51.353
4.7755
19.123
2.19
42.749
5.6955
49.164
4.5835
16.934
1.8794
40.887
5.4796
46.975
4.3916
14.746
1.5688
39.025
5.2637
44.786
4.1997
12.557
1.2582
37.163
5.0478
42.389
4.0078
35.301
4.8319
39.971
3.8158
33.488
4.616
37.554
3.6239
31.732
4.4001
35.137
3.432
29.975
4.1842
32.719
3.2401
28.219
3.9683
30.302
3.0481
26.463
3.7523
27.884
2.8562
24.706
3.5364
Page | 69
65.411 67.447 69.484 71.521 73.341 74.169 74.997 75.826 76.654 77.482 78.311 79.139 79.967 81.211 82.561 83.912 85.262 85.494 85.571 88.016 85.808 83.599 81.391 79.183 76.974 74.766 72.557 70.349 68.14 65.932 63.724 61.515 59.307 57.098 54.89 46.868 45.027 43.186 41.344 39.503 37.662 35.821 33.979 32.138 30.297 28.456
6.3924 6.5909 6.789 6.9868 7.0429 7.2637 7.4668 7.5841 7.6846 7.8983 8.0997 8.2987 8.4968 8.6947 8.8927 8.9311 8.7325 8.5267 8.3276 8.129 7.9311 7.7333 7.5355 7.3377 7.1399 6.9421 6.7443 6.5465 6.3487 6.1508 5.953 5.7552 5.5574 5.3596 5.1618 4.964 4.7662 4.5684 4.3705 4.1727 3.9749 3.7771 3.5793 3.3815 3.1837 2.9859
58.127 59.407 60.688 61.968 63.249 70.514 71.773 73.033 74.293 75.553 76.813 78.073 79.333 76.674 73.33 69.986 66.642 63.298 73.325 71.108 68.891 66.675 64.375 61.818 59.261 57.079 55.574 54.069 52.564 51.058 49.553 48.048 46.543 45.037 43.532 42.027 40.522 39.016 37.511 35.62 33.463 32.011 30.617 29.222 27.827 26.433
11.586 11.902 12.217 12.532 12.847 13.162 13.375 13.699 14.015 14.33 14.645 14.817 15.149 15.286 14.952 14.635 14.319 14.005 13.69 13.375 13.06 12.745 12.431 12.116 11.801 11.486 11.171 10.857 10.542 10.226 9.9116 9.5968 9.282 8.9672 8.6524 8.3376 8.0228 7.7079 7.3931 7.0783 6.7635 6.4486 6.1338 5.819 5.5042 5.1894
25.641
2.6643
22.95
3.3205
23.47
2.4724
21.193
3.1046
21.299
2.2805
19.437
2.8887
19.129
2.0886
17.68
2.6728
16.958
1.8967
21.339
2.4569
14.788
1.7048
21.276
2.241
12.617
1.5128
18.835
2.025
10.446
1.3209
16.395
1.8091
8.2758
1.129
11.856
1.5932
6.1052
0.93709
9.4306
1.3773
A6
A7
A8
Load (N)
Extension (mm)
Load (N)
Extension (mm)
Load (N)
Extension (mm)
3.881 4.6986 5.5161 6.3337 7.1512 7.9688 8.7863 9.7128 11.03 12.347 13.664 14.981 16.297 17.614 18.931 20.248 21.565 22.882 24.199 25.516 26.833 28.15 30.591 41.365 42.569 43.772 44.976 46.179 47.382 48.586 49.947 51.52
-0.0085 -0.012 0.0618 0.41671 0.78468 1.0054 1.3977 1.7678 2.1359 2.5038 2.8716 3.2394 3.6073 3.8047 4.1927 4.5614 4.9295 5.2974 5.4991 5.8981 6.268 6.6359 7.0038 7.3717 7.7397 8.1077 8.3808 8.7602 9.1294 9.4973 9.7214 10.08
2.7953 4.7914 6.7876 8.3642 9.894 11.424 12.954 14.484 16.013 17.543 19.073 20.603 22.133 20.559 22.468 24.377 26.286 28.195 30.104 32.013 33.923 35.832 37.741 39.512 40.876 42.239 43.602 44.965 46.329 47.692 49.055 50.491
2.71E-20 -0.0092 -0.0088 0.07037 0.36551 0.6433 0.9187 1.0254 1.2803 1.5613 1.8373 2.1126 2.31 2.4767 2.7626 3.0392 3.3148 3.5901 3.8654 4.1406 4.4159 4.6825 4.7756 4.9114 5.181 5.4627 5.7392 6.0146 6.2899 6.5653 6.8406 7.1158
6.1743 6.7747 7.3751 7.9755 8.5759 9.1763 9.7767 10.377 10.978 11.578 12.528 13.667 14.805 15.943 17.081 18.219 19.358 20.496 21.634 22.772 23.911 24.182 31.933 34.483 37.032 39.582 41.079 42.145 43.211 44.277 45.343 46.409
5.3E-05 -0.0266 0.0013 0.126 0.43813 0.51276 0.83282 1.1309 1.4272 1.7231 2.019 2.3149 2.5695 2.7233 3.0311 3.3285 3.6245 3.9205 4.0274 4.3515 4.6507 4.9467 5.2427 5.5387 5.8346 6.1305 6.4264 6.6047 6.8744 7.1761 7.4726 7.7686
Page | 70
26.614 24.773 22.932 21.091 19.423 19.477 18.699 17.635 17.37 18.01
2.7881 2.5902 2.3924 2.1946 1.9968 1.799 1.6012 1.4034 1.2054 1.0075
25.038 19.208 18.702 18.196 17.638 17.08 16.523 15.965 16.181 16.746
4.8746 4.5598 4.245 3.9302 3.6154 3.3006 2.9858 2.671 2.3562 2.0413
53.092 54.665 56.237 57.81 57.502 56.606 57.308 58.011 58.713 59.416 60.033 60.6 61.167 61.733 70.647 73.489 75.337 77.186 79.034 80.882 82.73 84.579 86.427 88.275 85.344 78.939 75.252 79.132 78.362 77.468 75.664 73.859 72.055 70.25 68.445 66.729 65.016 63.303 61.591 59.878 58.166 56.453 54.741 53.028 51.316 44.144 Page | 71
10.452 10.82 11.187 11.555 11.923 12.291 12.659 13.027 13.203 13.599 13.968 14.336 14.704 14.919 15.298 15.667 15.859 16.24 16.608 16.976 17.344 17.712 18.08 18.438 18.248 17.87 17.501 17.133 16.765 16.397 16.03 15.662 15.294 14.926 14.558 14.19 13.822 13.455 13.087 12.719 12.351 11.983 11.615 11.247 10.88 10.512
51.955 53.419 54.883 56.347 57.811 59.275 60.739 62.203 63.667 65.131 66.595 68.059 69.523 70.987 72.451 73.915 75.379 76.843 78.307 79.771 81.235 82.699 73.974 79.769 83.287 82.142 80.997 79.852 78.707 77.562 76.417 75.272 74.127 62.441 61.991 61.464 60.937 60.41 59.883 58.59 57.291 55.991 54.692 53.393 44.476 42.465
7.3911 7.587 7.8048 8.0875 8.3637 8.6393 8.9146 9.1898 9.4651 9.6003 9.7738 10.06 10.337 10.613 10.869 11.002 11.29 11.568 11.844 12.119 12.394 12.636 12.767 13 12.817 12.532 12.256 11.98 11.705 11.429 11.154 10.879 10.604 10.328 10.053 9.7777 9.5025 9.2271 8.9518 8.6766 8.4013 8.1261 7.8508 7.5756 7.3003 7.0251
47.475 48.541 49.9 51.457 53.014 54.571 56.127 57.684 59.241 60.797 62.354 63.911 65.467 67.024 68.581 70.137 71.713 73.467 75.222 76.976 78.731 80.486 82.24 73.988 71.568 69.148 66.727 64.307 61.887 59.466 57.046 65.616 64.404 63.192 61.979 60.767 59.555 58.342 57.13 55.917 54.705 53.493 52.28 52.293 52.325 47.411
8.0645 8.3605 8.493 8.8078 9.1075 9.4035 9.6994 9.9954 10.144 10.439 10.738 11.034 11.33 11.625 11.921 12.115 12.214 12.528 12.826 13.122 13.418 13.714 14.01 14.154 14.265 13.956 13.656 13.359 13.063 12.767 12.471 12.175 11.879 11.583 11.287 10.991 10.696 10.4 10.104 9.8079 9.5121 9.2162 8.9203 8.6244 8.3285 8.0327
40.559 37.388 35.492 33.596 31.7 29.804 27.908 38.552 35.197 32.942 30.688 28.433 26.178 21.166 24.201 24.417 23.927 22.581 21.235 19.89
10.144 9.7761 9.4082 9.0404 8.6726 8.3047 7.9369 7.569 7.2012 6.8333 6.4655 6.0975 5.7297 5.3618 4.994 4.6261 4.2583 3.8904 3.5226 3.1547
40.454 38.443 36.432 34.421 32.41 30.399 28.634 26.891 25.149 23.406 21.664 19.921 18.179 16.436 14.694 12.951 11.209 9.4666 7.7241 10.774
B1
6.7498 6.4745 6.1993 5.924 5.6488 5.3735 5.0983 4.823 4.5478 4.2726 3.9973 3.7221 3.4469 3.1716 2.8964 2.6211 2.3459 2.0707 1.7955 1.5201
41.603 40.864 40.125 39.386 38.647 37.908 37.169 36.06 34.309 32.557 30.806 29.055 27.303 25.552 22.281 18.57 15.512 14.886 14.261 13.635
B2
7.7368 7.4409 7.145 6.8492 6.5533 6.2574 5.9615 5.6656 5.3697 5.0738 4.7779 4.4821 4.1862 3.8903 3.5944 3.2986 3.0027 2.7068 2.4109 2.115
B3
B4
Load (N) 8.6867
Extensio n (mm) 3.03E-05
Load (N) 1.8355
Extensio n (mm) 8.73E-05
Load (N) 3.9708
Extensio n (mm) 4.05E-05
8.6539
-0.00439
2.5003
-0.03747
2.5072
-0.01847
8.6211
0.014277
3.1651
-0.03731
1.0435
-0.01153
8.5883
0.014183
3.83
0.19948
2.4668
0.000694
8.5555
0.15501
4.4948
0.24116
3.9457
0.099311
8.8792
0.39304
5.1596
0.4983
5.4245
0.34529
9.4668
0.54059
5.8244
0.73584
6.9034
0.50501
10.054
0.66944
7.2993
0.8161
8.3822
0.59111
10.642
0.90592
10.508
1.0375
9.861
0.83964
12.633
1.1324
17.712
1.2765
11.34
1.0734
14.745
1.2109
21.405
1.3364
13.183
1.2137
23.976
1.4195
24.125
1.573
15.467
1.3666
27.712
1.6512
26.844
1.8124
17.752
1.6077
33.161
1.8763
29.563
2.0467
20.037
1.8405
40.711
2.1002
32.282
2.2796
22.321
2.0711
42.52
2.3202
35.001
2.5125
24.606
2.1723
44.329
2.3462
37.631
2.6787
26.89
2.3534
46.137
2.5948
39.895
2.8255
35.799
2.5934
47.946
2.6716
42.158
3.0557
38.033
2.8257
38.301
2.8544
44.422
3.2899
40.266
2.9648
42.729
3.0866
46.685
3.5242
42.551
3.0952
47.157
3.3117
48.948
3.7577
45.166
3.3381
Page | 72
Load (N)
Extensio n (mm)
4.2151 4.215 4.215 4.215 4.7994 7.9129 11.026 14.14 17.253 20.367 23.48 26.594 29.707 35.457 35.833 38.757 41.68 44.604 47.527 50.451 53.374 56.298
-7.7E-03 -5.7E-02 -0.0571 0.13469 0.46942 0.79573 0.99368 1.2704 1.4677 1.7675 2.0969 2.4224 2.7479 2.9122 3.2631 3.5907 3.7561 4.1046 4.4336 4.5624 4.9195 5.2476
B5 Load (N)
Extension (mm)
3.9403 -7.43E-02 3.8854 -0.05241 3.8306 0.10211 4.4555 0.42476 9.5283 0.53577 13.656 0.86841 17.445 0.97344 21.234 1.3076 25.05 1.6205 28.873 1.9311 32.695 2.0321 36.517 2.3698 40.339 2.6831 43.594 2.9811 46.849 3.1588 50.103 3.4795 53.358 3.6893 57.216 3.9128 61.865 4.2318 66.513 4.5426 71.162 4.853 75.811 5.0259
51.087
3.536
51.212
3.9907
47.78
3.5715
54.584
3.7267
53.475
4.0619
50.394
3.802
58.081
3.8321
55.739
4.3123
53.008
4.0325
61.578
4.0675
58.002
4.551
55.622
4.1564
65.075
4.2939
60.265
4.6107
58.237
4.3502
68.571
4.5177
62.529
4.8694
60.851
4.5863
72.068
4.6916
64.792
5.1063
63.465
4.8176
75.565
4.7179
67.13
5.3408
65.195
4.873
79.062
4.7427
69.636
5.4911
62.738
5.0967
69.681
4.8197
72.143
5.6107
64.411
5.3351
72.939
5.062
74.649
5.857
67.483
5.409
76.197
5.2889
81.405
6.0931
70.555
5.6608
79.455
5.3205
87.214
6.1521
73.627
5.8962
81.932
5.5609
90.067
6.4116
85.151
6.0229
84.278
5.791
92.919
6.4763
85.177
6.2093
86.623
6.0166
95.772
6.7178
84.877
6.4488
88.968
6.1086
98.624
6.9576
84.354
6.6572
91.314
6.2896
101.48
7.1907
83.831
6.7137
93.659
6.5226
104.33
7.4238
86.999
6.9666
96.004
6.7481
107.18
7.6065
94.246
7.1998
98.35
6.9722
110.03
7.7076
96.809
7.4311
100.69
7.0084
112.89
7.9567
99.373
7.4782
103.12
7.2589
115.74
8.169
101.94
7.7321
105.83
7.4878
118.59
8.2378
104.5
7.9666
108.53
7.6603
121.44
8.4804
107.06
8.198
111.24
7.7808
124.3
8.516
109.63
8.2735
113.94
8.0192
127.03
8.7729
112.19
8.4913
116.64
8.0866
129.66
9.0107
114.75
8.7292
120.54
8.3317
132.29
9.2442
119.99
8.8738
124.83
8.5604
133.86
9.4774
122.17
9.0134
129.12
8.7845
135.3
9.6778
124.36
9.2567
133.81
9.0087
136.75
9.7771
126.54
9.4885
132.96
9.0679
138.2
10.026
128.72
9.6705
134.51
9.317
138.58
10.262
130.91
9.7621
137.92
9.5447
138.51
10.335
133.09
10.01
141.33
9.7421
137.62
10.097
135.28
10.085
144.21
9.6337
134.56
9.8573
134.61
9.8612
139.56
9.3942
131.51
9.6229
130.98
9.6234
134.9
9.1687
128.45
9.3901
128.3
9.3914
130.25
8.9443
125.4
9.1573
127.12
9.1611
125.65
8.7208
122.34
8.9245
123.01
8.9309
121.08
8.4973
119.29
8.6917
118.89
8.7006
116.51
8.2739
116.11
8.459
114.77
8.4703
116.25
8.0504
111.99
8.2262
110.66
8.2401
115.6
7.8269
107.88
7.9934
106.1
8.0098
112.21
7.6034
104.26
7.7606
99.797
7.7793
Page | 73
59.222 62.145 65.069 67.992 70.916 67.577 70.874 74.171 77.468 80.764 84.061 87.358 90.655 93.952 102.02 110.36 113.23 116.09 118.95 121.81 124.67 127.53 130.39 133.25 136.11 138.98 137.14 132.07 127 121.93 117.76 114.52 116.74 116.85 113.13 109.4 105.68 101.95 98.23 94.507 90.783 80.025 76.284 72.543 68.803 65.062
5.4942 5.7192 6.0528 6.3786 6.6283 6.8457 7.0182 7.3535 7.6798 8.006 8.1415 8.496 8.6758 9.0131 9.34 9.6653 9.8728 10.161 10.491 10.652 10.984 11.314 11.639 11.832 12.173 12.499 12.733 12.445 12.116 11.79 11.464 11.139 10.814 10.488 10.163 9.8377 9.5124 9.1871 8.8615 8.5361 8.2108 7.8855 7.5601 7.2348 6.9095 6.5841
63.034 63.315 79.661 80.948 85.067 89.186 93.166 96.682 100.2 103.71 107.23 110.75 114.26 117.78 121.35 125.72 130.09 134.45 138.82 143.19 138.37 133.76 129.15 124.55 119.94 115.33 110.72 106.11 101.5 96.892 91.818 86.7 81.582 76.464 80.909 81.248 78.401 72.285 66.17 54.868 50.097 45.938 42.521 39.104 35.688 32.271
5.3195 5.4428 5.6452 5.9473 6.2623 6.573 6.7429 7.0391 7.276 7.5239 7.8408 8.1524 8.2817 8.616 8.7622 9.1028 9.4155 9.7265 9.923 10.171 10.406 10.178 9.8605 9.5489 9.2384 8.9281 8.6179 8.3077 7.9975 7.6873 7.3771 7.0669 6.7566 6.4462 6.1359 5.8257 5.5155 5.2053 4.8951 4.5849 4.2746 3.9644 3.6542 3.344 3.0338 2.7236
108.82
7.3799
100.82
7.5278
95.797
7.5491
105.44
7.1564
97.368
7.2951
92.551
7.3189
102.05
6.9329
93.92
7.0618
89.306
7.0886
98.663
6.7094
90.472
6.829
85.965
6.8584
95.277
6.486
90.649
6.5962
78.928
6.6282
91.89
6.2625
94.074
6.3635
73.94
6.398
88.504
6.039
92.745
6.1307
70.455
6.1677
85.117
5.8155
88.625
5.8979
66.969
5.9375
81.731
5.592
84.505
5.6651
63.484
5.7073
78.344
5.3685
80.384
5.4323
59.999
5.4771
74.958
5.1447
76.264
5.1996
56.513
5.2469
71.571
4.9212
72.143
4.9668
61.448
5.0167
68.184
4.6977
68.023
4.734
58.245
4.7864
62.205
4.4742
63.903
4.5012
55.041
4.5562
61.588
4.2507
58.927
4.2685
51.838
4.326
57.946
4.0273
51.425
4.0357
48.635
4.0957
54.305
3.8038
48.241
3.8029
45.431
3.8655
50.663
3.5803
45.389
3.5701
42.228
3.6353
47.022
3.3568
42.537
3.3373
39.024
3.4051
43.1
3.1333
39.685
3.1046
35.821
3.1749
38.744
2.9099
36.833
2.8718
32.618
2.9447
34.387
2.6864
33.981
2.639
29.485
2.7145
30.031
2.4629
31.13
2.4063
26.561
2.4842
26.508
2.2394
28.278
2.1735
23.637
2.254
23.666
2.0159
25.426
1.9408
20.713
2.0238
20.824
1.7925
22.574
1.708
17.789
1.7936
17.982
1.569
19.722
1.4752
15.586
1.5633
61.321 57.581 53.84 50.099 46.359 42.618 38.877 35.137 31.396 27.937 24.65 21.364 18.077 14.79 11.503 8.216 4.9292
15.14
1.3455
16.87
1.2424
13.654
1.3331
12.298
1.122
14.018
1.0097
11.721
1.1029
8.5219
0.89851
11.167
0.77689
9.787 8
0.87268
9.378 8
0.61401
B6
B7
B8
Load (N)
Extension (mm)
Load (N)
Extension (mm)
Load (N)
Extension (mm)
5.1493
0.034305
11.311
7.51E-02
4.4842
0.009014
5.6305
0.13011
13.753
0.091793
4.0919
0.023711
6.1116
0.40791
16.196
0.34229
3.6997
0.099345
6.5927
0.66882
18.638
0.57084
3.3558
0.31815
8.2773
0.92765
21.081
0.60247
5.6104
0.32796
10.481
1.0105
23.523
0.85159
7.8649
0.54677
12.684
1.2972
25.966
0.92222
10.119
0.75347
14.887
1.4345
15.412
1.1196
12.374
0.9557
17.09
1.6468
19.847
1.3521
14.629
1.0456
19.293
1.9137
24.282
1.4176
16.883
1.1684
Page | 74
6.2588 5.9334 5.6081 5.2828 4.9574 4.6321 4.3068 3.9814 3.6561 3.3307 3.0054 2.6801 2.3547 2.0294 1.704 1.3787 1.0533
28.854 25.437 22.021 18.604 15.187 11.77 8.3537
2.4133 2.1031 1.7929 1.4827 1.1725 0.86229 0.6097
21.497
2.1728
28.717
1.6317
26.624
1.3815
23.7
2.4318
32.917
1.8628
26.75
1.4949
25.903
2.5639
36.734
1.9799
28.518
1.5876
28.106
2.806
40.551
2.1347
30.285
1.8039
30.31
3.0671
44.369
2.368
32.173
2.0074
32.513
3.326
48.186
2.5929
34.48
2.2086
34.716
3.369
52.003
2.6799
36.788
2.2493
36.919
3.655
55.448
2.8799
46.063
2.4708
39.122
3.9174
58.829
3.1114
48.622
2.6784
41.326
4.1765
62.209
3.3271
51.181
2.6848
48.276
4.2593
65.59
3.3637
53.74
2.889
51.386
4.5449
62.951
3.5396
56.299
3.0974
54.497
4.8078
73.535
3.6822
58.859
3.2055
57.607
4.9267
77.435
3.9187
61.418
3.3202
60.718
5.1636
81.334
4.1447
63.977
3.5349
63.828
5.4281
85.233
4.2465
66.536
3.6798
66.664
5.6879
89.132
4.4565
69.532
3.7561
69.269
5.8859
93.032
4.5613
76.844
3.957
71.875
6.0366
96.931
4.7368
69.263
3.9713
74.481
6.2533
100.75
4.9701
85.323
4.1967
77.087
6.3973
104.46
5.0295
92.839
4.4024
79.642
6.6691
108.16
5.263
94.291
4.6038
82.194
6.9288
111.87
5.4932
95.742
4.8043
84.745
7.1881
115.57
5.6432
97.194
4.8791
87.297
7.4466
119.28
5.7605
98.645
5.0097
89.848
7.7052
124.04
5.9979
101.58
5.2219
92.4
7.7924
129.8
6.1479
104.99
5.4244
94.952
8.069
123.02
6.2763
108.4
5.6251
97.503
8.32
124.26
6.5142
111.81
5.6706
101.79
8.4098
125.51
6.5539
115.15
5.8778
107.81
8.6861
139.29
6.7895
111.18
5.9444
110.89
8.9475
141.22
7.0201
113.04
6.1155
113.97
9.2064
143.15
7.1361
114.89
6.3241
117.05
9.2985
141.73
6.9503
117.13
6.516
120.13
9.5801
135.33
6.7184
119.44
6.5667
123.02
9.8434
128.96
6.4945
121.74
6.7879
125.78
10.02
122.72
6.2706
124.04
6.8581
128.54
10.177
116.48
6.0473
126.34
7.0325
131.29
10.447
111.92
5.8242
128.64
7.2417
134.05
10.707
107.68
5.6012
130.95
7.4444
136.81
10.966
103.43
5.3781
133.25
7.5546
139.57
11.225
99.188
5.1551
135.55
7.4151
142.33
11.325
94.942
4.932
132.36
7.2043
145.09
11.601
90.697
4.7089
128.91
7.0025
147.84
11.749
86.452
4.4859
125.46
6.8015
136.77
11.524
82.207
4.2628
122.02
6.6014
Page | 75
134.24
11.258
77.962
4.0398
118.57
6.4013
131.71
10.998
75.082
3.8167
115.13
6.2013
129.17
10.739
72.925
3.5936
111.68
6.0014
126.64
10.481
70.769
3.3706
108.24
5.8015
124.11
10.222
67.39
3.1475
104.79
5.6016
121.42
9.964
62.863
2.9245
101.35
5.4017
118.49
9.7055
58.336
2.7014
97.901
5.2017
115.56
9.4471
53.809
2.4784
94.455
5.0018
112.62
9.1887
49.283
2.2553
90.813
4.8019
109.69
8.9303
44.756
2.0322
87.049
4.602
106.76
8.6719
40.229
1.8092
83.286
4.4021
103.83
8.4135
35.702
1.5861
79.522
4.2022
100.9
8.1551
31.651
1.363
75.758
4.0023
97.964
7.8966
27.635
1.14
71.994
3.8023
95.033
7.6382
23.619
0.91692
68.23
3.6024
88.808
7.3798
19.603
0.69386
64.466
3.4025
81.723
7.1214
15.586
0.47079
60.702
3.2026
78.671
6.863
11.57
0.24773
56.939
3.0027
75.619
6.6044
53.175
2.8028
72.567
6.346
49.411
2.6029
69.515
6.0876
45.647
2.403
66.463
5.8292
41.883
2.203
63.411
5.5708
38.119
2.0031
60.359
5.3123
34.355
1.8032
57.307
5.0539
30.592
1.6033
54.255
4.7955
26.62
1.4034
51.202
4.5371
22.34
1.2035
48.15
4.2787
18.06
1.0036
45.098
4.0202
13.78
0.80365
42.046
3.7618
9.4994
0.60373
38.994
3.5034
38.054
3.245
35.228
2.9866
32.402
2.7281
29.576
2.4697
26.751
2.2113
23.925
1.9529
Page | 76
Table A9.5 – Channel Test Data YELLOW 4MM
GREY 6MM STRAIN READINGS
SPECIMEN
A1
A2
A3
A4
A5
A6
Page | 77
LOAD (Kg)
STRAIN READINGS SPECIMEN
LOAD (Kg)
ε₁
ε₂
ε₁
ε₂
0.5
109
-122
1.0
46
-62
1.0
221
-246
2.0
105
-117
1.5
345
-375
3.0
168
-174
2.0
464
-501
4.0
227
-231
2.5
594
-641
5.0
294
-294
3.0
730
-788
6.0
363
-359
3.5
876
-947
7.0
440
-428
4.0
1021
-1106
8.0
514
-497
0.5
119
-124
1.0
56
-48
1.0
236
-252
2.0
113
-83
1.5
366
-388
3.0
176
-137
2.0
493
-561
4.0
239
-193
B1
B2
2.5
629
-651
5.0
309
-251
3.0
765
-782
6.0
376
-309
3.5
917
-984
7.0
448
-371
4.0
1072
-1121
8.0
524
-437
0.5
124
-120
1.0
124
-84
1.0
245
-240
2.0
259
-210
1.5
375
-371
3.0
394
-334
2.0
510
-502
4.0
529
-564
5.0
673
-621
B3
2.5
651
-649
3.0
799
-787
6.0
820
-711
3.5
958
-944
7.0
974
-799
4.0
1115
-1105
8.0
1137
-874
0.5
108
-129
1.0
77
-87
1.0
222
-260
2.0
158
-173
1.5
342
-400
3.0
241
-261
2.0
461
-539
4.0
332
-364
5.0
425
-467
B4
2.5
590
-696
3.0
726
-855
6.0
490
-572
3.5
872
-1022
7.0
595
-680
4.0
1018
-1188
8.0
701
-799
0.5
122
-122
1.0
63
-55
1.0
244
-242
2.0
128
-110
1.5
381
-370
3.0
196
-167
2.0
523
-504
4.0
261
-223
5.0
333
-281
B5
2.5
671
-642
3.0
819
-784
6.0
407
-343
3.5
981
-941
7.0
480
-407
4.0
1154
-1107
8.0
561
-475
0.5
103
-47
1.0
22
-54
B6
Page | 78
1.0
170
-101
2.0
85
-107
1.5
240
-163
3.0
144
-164
2.0
282
-229
4.0
196
-220
2.5
357
-294
5.0
260
-280
3.0
429
-360
6.0
327
-342
3.5
508
-422
7.0
399
-409
4.0
587
-487
8.0
467
-475
Table A9.6 – Coupons Compression Test Data 4 mm Yellow Coupons A3
B1
B2
B3
Load (N)
Strain
Load (N)
Strain
Load (N)
Strain
Load (N)
Strain
122.07
-26.55
671.39
25.33
61.035
-19.836
-122.07
2.1362
61.035
-26.55
549.32
28.381
0
-23.193
-122.07
2.4414
-61.035
-25.94
549.32
28.076
61.035
-26.245
-61.035
3.6621
61.035
-23.804
671.39
27.771
0
-26.855
-244.14
2.7466
-732.42
-25.33
610.35
26.855
0
-27.771
-183.11
4.2725
122.07
-21.973
610.35
27.161
183.11
-30.518
366.21
2.7466
122.07
-21.667
610.35
27.161
0
-35.706
-122.07
5.4932
61.035
-20.752
488.28
27.466
-183.11
-36.926
-122.07
2.1362
122.07
-31.128
549.32
28.687
122.07
-36.316
-183.11
-4.2725
-61.035
-43.335
549.32
28.687
-61.035
-43.03
-122.07
-17.09
1220.7
-48.523
549.32
28.076
122.07
-49.133
-122.07
-54.321
244.14
-54.932
488.28
28.381
244.14
-65.308
0
-110.17
244.14
-60.12
671.39
29.297
244.14
-96.436
244.14
-195.31
305.18
-65.918
732.42
29.297
61.035
-144.04
427.25
-303.04
244.14
-68.359
854.49
34.79
549.32
-209.05
610.35
-416.56
122.07
-73.547
915.53
42.114
793.46
-281.98
732.42
-535.28
183.11
-76.599
1159.7
53.406
854.49
-368.35
1098.6
-644.23
183.11
-81.482
1342.8
70.496
1098.6
-458.07
1098.6
-740.97
366.21
-91.858
1342.8
91.858
1281.7
-552.67
1464.8
-845.95
488.28
-116.88
1525.9
118.71
1586.9
-650.02
1709
-949.71
305.18
-157.47
1342.8
151.67
1709
-751.65
1892.1
-1059
976.56
-208.44
1892.1
191.35
1770
-835.57
2136.2
-1170.3
915.53
-267.03
1892.1
232.54
2502.4
-918.27
2197.3
-1280.2
1159.7
-331.73
2685.5
281.98
2746.6
-981.14
2380.4
-1391.6
1281.7
-403.44
2929.7
335.08
2990.7
-1072.1
2746.6
-1505.1
1647.9
-476.07
2868.7
399.17
2746.6
-1204.8
3356.9
-1620.5
1892.1
-548.4
2563.5
465.09
2624.5
-1389.2
3234.9
-1734.3
2014.2
-617.98
3173.8
527.65
2441.4
-1593
3295.9
-1850
2136.2
-695.5
3967.3
599.98
3662.1
-1708.7
3845.2
-1967.2
2380.4
-766.91
3540
678.71
3967.3
-1815.8
3723.1
-2082.8
2563.5
-832.82
3784.2
758.97
3845.2
-1901.2
3967.3
-2196.4
3112.8
-893.25
4028.3
842.9
4028.3
-2007.4
4089.4
-2317.2
2929.7
-944.82
3845.2
932.62
4272.5
-2107.5
4455.6
-2432.3
3295.9
-993.35
4394.5
1026.9
4333.5
-2211.6
4638.7
-2549.4
3418
-1049.5
4516.6
1123.4
5004.9
-2332.8
4699.7
-2664.8
3662.1
-1107.2
4760.7
1228
4943.8
-2453.3
4943.8
-2789
3845.2
-1167
5188
1337.3
4943.8
-2582.4
5432.1
-2917.2
4028.3
-1225.3
5249
1456.3
5188
-2724
4882.8
-3045.3
4211.4
-1286.3
5493.2
1586.6
5432.1
-2865.6
5737.3
-3175.7
4455.6
-1348
5737.3
1731.9
5310.1
-3006.9
5737.3
-3305.7
4577.6
-1408.1
6164.6
1897.3
5737.3
-3159.8
5981.4
-3443.9
Page | 79
4882.8
-1467.3
6042.5
2080.4
6103.5
-3315.4
6164.6
-3584.9
5127
-1526.2
5371.1
2291.9
6042.5
-3473.2
6408.7
-3729.2
5615.2
-1582.9
6347.7
2541.2
6164.6
-3636.8
6469.7
-3877
5371.1
-1644
6591.8
2850.6
6652.8
-3824.8
6713.9
-4033.2
5859.4
-1702
6713.9
3241
6774.9
-4012.5
6958
-4195.3
5859.4
-1757.8
6347.7
3791.8
7324.2
-4210.5
7141.1
-4362.5
6225.6
-1816.1
7141.1
4943.2
7141.1
-4417.4
7141.1
-4539.8
6347.7
-1875
5798.3
8103
7263.2
-4633.5
7629.4
-4717.1
6713.9
-1930.8
4638.7
9497.1
7629.4
-4861.1
7690.4
-4906.3
6713.9
-1984.9
-244.14
1781.9
7751.5
-5113.2
7995.6
-5091.9
6897
-2042.5
-1098.6
1614.4
7812.5
-5370.8
8117.7
-5287.2
7141.1
-2101.1
-488.28
1529.5
8239.7
-5670.5
8789.1
-5493.5
7385.3
-2151.8
-1159.7
1384.6
8239.7
-5982.7
8667
-5718.1
6652.8
-2207.9
-1281.7
1258.5
8483.9
-6346.1
8728
-5943.3
7751.5
-2261.4
-1220.7
1167.6
8667
-6751.7
8789.1
-6187.4
7751.5
-2315.1
-1342.8
1047.7
8789.1
-7223.5
9155.3
-6440.4
8117.7
-2369.1
-915.53
905.46
8422.9
-7800.3
9399.4
-6713
8361.8
-2421.9
-1159.7
725.71
9094.2
-8531.8
10071
-7004.7
8667
-2476.5
-1342.8
536.19
9033.2
-9695.7
9277.3
-7332.5
8728
-2526.6
-1220.7
558.17
5432.1
6405
9948.7
-7684
8850.1
-2579.3
-1220.7
546.57
2746.6
6403.2
10071
-8063
9216.3
-2629.7
-1159.7
541.99
2990.7
6405.3
10254
-8482.7
9338.4
-2684.6
-1281.7
533.75
-1220.7
735.78
10437
-8951.1
9582.5
-2734.7
-1159.7
527.34
-2197.3
862.43
10620
-9494.6
9704.6
-2783.8
-1342.8
520.63
-2258.3
917.97
10986
9838.3
10010
-2832.6
-1159.7
512.08
-1586.9
951.54
11047
8962.7
10071
-2883.3
-1159.7
505.37
-2441.4
973.51
10620
7774
10437
-2935.5
-2136.2
497.44
-1709
989.69
4821.8
7764
10559
-2988
-1281.7
492.55
-2075.2
1005.2
122.07
-9309.4
10437
-3042
-2014.2
1015.6
-1159.7
-9626.5
11230
-3095.1
-1709
1024.8
-1159.7
-8981.9
11230
-3150.9
-2014.2
1032.4
-1037.6
-7963.3
11414
-3201.3
-2075.2
1040.6
-1037.6
-6803.3
11597
-3255.3
-2014.2
1046.4
-976.56
-5520
11841
-3308.4
-732.42
-3923
12268
-3367.9
11902
-3425.6
12573
-3483.6
12573
-3541.3
12939
-3597.7
12939
-3659.1
13000
-3716.7
13550
-3775.6
13489
-3834.8
13123
-3900.8
13550
-3965.1
Page | 80
14160
-4033.2
14343
-4094.2
14587
-4166
14832
-4232.5
14893
-4303.6
14587
-4376.2
15320
-4449.5
15259
-4523
15930
-4606.6
15991
-4682.9
16113
-4756.8
16418
-4839.8
16479
-4929.2
16785
-5018
17029
-5104.7
17334
-5191
17395
-5287.2
17761
-5381.8
17761
-5492.6
18005
-5598.1
18188
-5705.9
18494
-5813.9
18616
-5921.6
18738
-6042.8
18982
-6160.3
19287
-6287.5
19714
-6428.8
19592
-6565.6
19775
-6715.1
19958
-6871
20081
-7034
20447
-7201.2
20569
-7384
20752
-7591.9
20874
-7802.4
21179
-8034.4
21301
-8295.6
21423
-8588.9
21729
-8932.5
21790
-9401.2
21790
9953
21423
8465.6
13489
6642.8
11230
6642.2
6713.9
6640.3
4943.8
6642.8
Page | 81
1831.1
-2247.9
-732.42
-147.71
-976.56
100.1
-854.49
131.84
-854.49
150.76
-854.49
164.18
-732.42
174.56
-732.42
184.33
-854.49
186.77
-1770
194.4
-793.46
198.67
-671.39
202.64
-671.39
205.99
-671.39
209.35
-671.39
211.49
-793.46
215.45
-671.39
217.29
-793.46
220.34
-1037.6
220.64
-793.46
223.08 6 mm Grey Coupons
C2
C3
D1
D2
D3
Load (N)
Strain
Load (N)
Strain
Load (N)
Strain
Load (N)
Strain
Load (N)
Strain
0 -122.07 -122.07 -122.07 0 -122.07 -122.07 -671.39 0 -122.07 -183.11 0 -183.11 -61.035 61.035 366.21 732.42 1098.6 1403.8 1892.1 2319.3 2563.5
-12.817 -8.8501 -7.9346 -6.1035 -4.8828 -6.7139 -7.9346 -7.019 -5.7983 -3.6621 -4.2725 -7.6294 -3.3569 -3.9673 -0.6103 -2.4414 -5.188 -11.597 -17.7 -42.725 -65.002 -104.98
610.35 671.39 671.39 671.39 732.42 671.39 854.49 732.42 244.14 671.39 488.28 854.49 976.56 793.46 1525.9 1831.1 2258.3 2685.5 2868.7 3479 4150.4 3601.1
3.6621 2.7466 3.3569 3.3569 3.0518 2.7466 3.6621 1.5259 3.6621 3.9673 3.6621 3.3569 0 -11.597 -22.583 -38.147 -54.321 -72.632 -94.91 -124.21 -161.13 -201.72
-183.11 -427.25 -183.11 -183.11 -915.53 0 -732.42 -244.14 366.21 -183.11 122.07 61.035 122.07 -671.39 427.25 488.28 976.56 1220.7 1770 2319.3 2380.4 3234.9
-6.7139 -7.6294 -9.4604 -8.2397 -11.902 -7.6294 -8.5449 -10.071 -9.7656 -9.4604 -10.071 -11.902 -12.512 -18.005 -29.602 -51.575 -81.482 -117.8 -157.78 -199.28 -241.39 -278.93
122.07 61.035 -61.035 -366.21 -427.25 61.035 183.11 122.07 61.035 183.11 183.11 549.32 244.14 976.56 1464.8 2258.3 2380.4 2746.6 3295.9 3662.1 4211.4 5554.2
7.019 9.1553 10.986 13.428 11.597 16.479 16.479 18.005 19.226 19.531 23.499 26.855 34.18 40.894 50.964 69.885 89.722 107.42 127.26 143.74 166.32 186.16
1831.1 1525.9 1770 1709 1831.1 1953.1 1831.1 1770 2319.3 3112.8 3173.8 3295.9 3845.2 4333.5 4699.7 4943.8 5615.2 6042.5 6286.6 6713.9 7263.2 7507.3
56.458 56.763 57.373 56.458 57.373 53.406 51.88 54.932 58.594 63.782 72.937 82.092 93.384 101.93 110.78 119.63 126.34 129.09 134.89 137.94 136.41 134.58
Page | 82
3051.8 3479 3906.2 4272.5 4699.7 5310.1 5432.1 6042.5 6347.7 6774.9 7141.1 7629.4 8117.7 8667 9155.3 9338.4 9643.6 10071 10498 10803 11963 11780 12146 12573 13123 13428 14526 13855 14526 14954 15381 15686 16174 16479 17029 17395 17700 18127 18616 18921 19409 19653 20020 20630 20996 21423 Page | 83
-144.35 -191.04 -248.11 -307.62 -372.31 -443.12 -517.58 -597.53 -673.22 -763.24 -847.47 -939.33 -1029.1 -1122.1 -1214.6 -1307.1 -1399.2 -1489 -1582.9 -1674.5 -1766.7 -1853.3 -1939.7 -2026.7 -2114.9 -2194.5 -2276.3 -2357.2 -2434.7 -2516.8 -2589.1 -2664.8 -2739.3 -2807 -2874.1 -2939.1 -2999.6 -3066.4 -3124.7 -3185.7 -3234.9 -3287.4 -3332.5 -3369.1 -3407 -3441.8
4638.7 5188 5554.2 5065.9 6408.7 6835.9 7019 8422.9 7995.6 8422.9 8911.1 9216.3 9521.5 10376 9826.7 10803 11169 11658 12085 12512 12756 13672 13977 13977 14343 14832 15259 15625 15259 16479 16235 17151 17883 18127 19104 18860 19226 19592 20020 20569 20752 21362 21729 22339 22705 23315
-247.19 -299.99 -357.97 -419.92 -482.79 -548.4 -609.44 -676.27 -740.66 -811.16 -878.3 -947.27 -1016.5 -1083.1 -1154.5 -1221 -1291.2 -1359.6 -1429.7 -1492 -1563.7 -1630.2 -1698 -1763.9 -1825.9 -1890.9 -1953.7 -2012.6 -2072.1 -2129.8 -2185.7 -2238.8 -2294.3 -2345 -2389.2 -2436.5 -2481.1 -2522.9 -2563.2 -2601.9 -2636.1 -2670.6 -2703.2 -2728.6 -2752.4 -2776.5
3540 4211.4 4455.6 4943.8 5371.1 5859.4 6225.6 6713.9 7019 7568.4 7751.5 8300.8 8728 9216.3 9277.3 9826.7 10254 11353 11108 11658 12024 12573 12695 13184 13489 13855 14343 14771 15198 15808 15991 16296 16785 17090 17517 15930 18616 17639 18799 19409 19897 20081 20813 21423 21912 21362
-323.18 -367.13 -419.92 -466.61 -516.05 -562.74 -611.57 -657.04 -703.12 -762.33 -812.07 -865.78 -917.05 -971.68 -1025.4 -1083.7 -1135.6 -1192.6 -1246.6 -1302.8 -1368.7 -1431 -1494.8 -1564.6 -1632.7 -1709.6 -1783.4 -1864 -1943.1 -2026.4 -2102.7 -2183.5 -2267.8 -2341.3 -2428.3 -2048.6 -2265.6 -1848.1 -1637 -1511.8 -1481.6 -1457.2 -1435.2 -1420 -1405.9 -1393.7
5554.2 5371.1 5981.4 6286.6 6774.9 7080.1 7446.3 7812.5 8117.7 8789.1 9155.3 9582.5 10010 10803 10803 11230 11658 12024 12695 12878 13123 13550 14038 14587 14954 15259 15259 16174 16541 17395 17334 17700 18066 18921 18982 19348 19653 20142 20386 20935 21301 22278 22156 22400 22888 23315
202.33 220.03 232.24 242.31 249.94 261.54 270.69 281.07 286.56 299.99 306.4 313.11 325.01 333.86 343.02 349.43 356.14 364.38 370.18 380.55 383.3 393.68 403.14 410.46 418.4 426.64 433.96 443.42 452.58 460.51 472.41 478.82 491.03 496.83 506.9 518.19 529.48 542.6 552.06 567.32 581.67 596.92 609.44 629.58 648.19 667.42
7873.5 8544.9 8728 9277.3 9521.5 9765.6 10254 10681 11108 11658 12085 13550 12817 13184 13489 13977 14099 13855 15564 15625 16541 16357 16785 17029 17639 18799 18555 18799 19043 19531 20020 20386 20752 21118 21667 21912 22522 22888 23254 23865 24048 24353 24780 25146 25818 25940
132.14 125.73 119.63 111.08 99.182 86.975 73.242 60.73 44.861 31.128 14.954 -0.610 -16.17 -34.79 -54.93 -69.88 -85.14 -107.4 -125.7 -142.2 -162.0 -180.3 -197.4 -214.5 -232.2 -252.6 -267.6 -284. -300.9 -319.8 -335.0 -353.3 -370.7 -388.7 -401.9 -419.6 -435.7 -450.1 -467.5 -479.7 -495.3 -511.4 -524.2 -540.47 -555.42 -567.93
21851 22095 22461 22949 23254 23743 24109 24536 24902 25085 25696 26062 26428 26855 27771 27832 28076 28564 29114 29297 29663 30029 30457 29602 31128 244.14 -1098.6 -1892.1 -2014.2 -2075.2 -1525.9 -1831.1 -1953.1
Page | 84
-3471.1 -3498.5 -3519 -3541 -3552.6 -3541 -3535.8 -3538.2 -3507.4 -3494.6 -3476.3 -3458.3 -3432.3 -3384.4 -3343.5 -3295 -3221.4 -3139 -3026.1 -2911.4 -2815.6 -2651.7 -2313.5 -1925 -1373.6 -46.082 -10.986 -39.368 -90.027 -104.98 -111.08 -112.61 -105.29
23254 23621 24353 24414 24719 25208 25635 26062 26306 27222 27161 27527 27893 28259 28503 28931 29114 29236 4394.5 -2014.2 -2929.7 -2990.7 -2868.7 -2990.7 -3479 -2868.7 -2990.7 -2990.7 -2929.7 -3173.8 -2868.7 -3356.9 -2929.7 -2868.7 -2929.7 -2807.6 -2807.6 -2868.7 -2929.7 -2807.6 -2868.7 -3418 -2868.7 -2868.7
-2798.5 -2814.6 -2828.1 -2845.2 -2857.1 -2860.4 -2860.4 -2861.9 -2850.6 -2830.2 -2876 -2873.8 -2837.5 -2829.3 -2718.8 -2675.2 -2433.8 -2142.3 -2068.2 -1284.8 -302.12 -151.37 -103.45 -78.735 -60.73 -47.607 -37.537 -28.381 -19.836 -12.817 -6.4087 -0.6103 1.2207 7.019 11.292 15.869 17.395 49.133 27.771 72.021 224.3 1769.1 1027.2 6509.7
22400 22766 23193 23499 24048 24231 24841 25146 25513 25940 27039 26794 27283 27893 27893 28198 28870 29236 29541 29968 30334 30823 31189 31433 31921 32288 32959 33081 33508 33691 34241 34973 35095 35400 35950 36255 36743 37109 37598 38208 38147 38269 38757 38818 39185 39490
-1386.4 -1377.3 -1373.6 -1369.3 -1362.3 -1351.3 -1344.9 -1334.5 -1322.6 -1308.9 -1297 -1285.7 -1273.5 -1259.5 -1248.2 -1236.3 -1228.3 -1219.2 -1208.2 -1200.3 -1187.7 -1169.7 -1147.2 -1116.3 -1080.6 -1034.5 -977.78 -900.88 -810.55 -714.72 -613.1 -512.08 -403.44 -289.61 -173.95 -56.763 70.19 222.78 421.45 674.74 977.48 1368.7 1939.1 2673 3592.2 4605.7
23682 23987 24475 24902 25269 25757 26489 26367 26855 27405 27710 28381 28381 28870 29236 29541 30151 30518 30579 31372 31677 32043 32410 32898 33203 33630 33997 34485 34790 35339 35706 35950 35645 37109 37292 37781 37781 38574 38940 39185 39673 40161 40527 41016 41260 41626
686.65 711.98 731.2 757.14 782.17 808.41 834.35 863.95 892.64 925.29 958.25 988.46 1019 1053.5 1086.1 1118.2 1147.5 1178.9 1206.4 1230.8 1256.4 1274.7 1291.5 1310.7 1327.5 1343.7 1358.6 1373.9 1388.5 1404.7 1418.2 1433.1 1448.1 1464.8 1481.3 1497.2 1514.3 1531.1 1552.7 1574.7 1599.7 1621.4 1650.4 1673.9 1699.5 1727.3
26489 26672 27222 27771 28015 28320 28198 28809 29602 29907 30396 30762 31189 31738 31982 32227 32715 33142 33630 33569 34424 34851 35156 35583 36072 36316 36255 37170 37354 38025 38696 38391 39001 39551 39856 40344 41077 41199 41626 41626 42358 42725 43274 43396 44006 44373
-582.28 -594.18 -606.99 -618.9 -628.36 -644.53 -653.99 -665.59 -677.19 -686.04 -696.72 -706.79 -716.86 -722.66 -734.25 -741.58 -749.82 -756.84 -761.72 -769.35 -774.84 -780.94 -786.74 -790.71 -793.15 -794.68 -795.9 -797.73 -797.42 -797.42 -795.9 -792.85 -787.35 -783.39 -776.67 -771.18 -765.38 -760.8 -754.39 -747.68 -737.92 -731.81 -723.27 -715.03 -704.04 -693.36
39673 40894 41260 40588 41443 8606 1281.7 -488.28 -976.56 -549.32 -854.49 -793.46 -732.42
Page | 85
5783.7 6872.6 7412.4 8028 8885.8 9533.4 3502.5 969.54 553.89 510.86 486.45 470.28 460.82
41992 42542 42847 43213 43640 44067 44312 44861 45105 45654 46143 46509 47058 47302 47668 48157 48401 49316 49316 49500 49622 51025 50537 51147 51758 51941 52429 52734 53101 53162 52490 4089.4 671.39 -1159.7 -1220.7 -1342.8 -1220.7
1758.4 1788.3 1823.4 1863.7 1900.3 1938.2 1980.9 2024.5 2068.8 2117 2172.5 2229 2285.5 2347.1 2414.2 2482.9 2570.2 2653.2 2741.1 2831.7 2937 3044.4 3162.8 3290.7 3464.4 3661.8 3903.2 4171.8 4500.7 5133.1 6612.2 7884.2 3080.1 632.93 363.16 333.86 311.89
44739 45105 45776 46326 45532 46814 47119 46997 47974 48279 48706 49194 49561 49927 50415 50781 51086 51392 51880 52307 52795 53650 53467 53894 54321 54626 55237 55786 56152 56335 56702 57007 57617 57983 58289 58533 60120 59509 59937 60242 60730 61279 61462 61646 62378 62561
-679.02 -661.01 -646.67 -628.05 -608.52 -583.5 -551.76 -521.85 -487.67 -453.8 -420.23 -390.93 -357.06 -320.43 -284.12 -245.97 -205.69 -165.41 -122.07 -75.989 -29.907 19.226 68.665 124.82 180.97 242.61 304.57 369.87 440.06 512.08 593.26 673.52 754.7 849 944.21 1041.9 1149.9 1267.7 1392.2 1521.3 1657.7 1805.4 1969 2152.1 2352.3 2572
62988 63293 63599 64209 64331 64453 1831.1 -671.39 -3906.2 -5188 -5737.3 -5981.4 -5920.4 -5920.4
Page | 86
2815.2 3089 3419.2 3860.8 4467.8 5388.5 -48.218 1535.9 -350.65 -185.85 -197.14 -213.93 -234.38 -233.76
Table A9.7 – JJ Lloyd Loading Script 4mm Yellow Coupons
6mm Grey Coupons
Stage [0N], [25mm/min]
Stage [0N], [25mm/min]
Result "load at 0N", Load
Result "load at 0N", Load
Stage [10N], [25mm/min]
Stage [10N], [25mm/min]
Result "load at 10N", Load
Result "load at 10N", Load
Stage [20N], [25mm/min]
Stage [20N], [25mm/min]
Result "load at 20N", Load
Result "load at 20N", Load
Stage [30N], [25mm/min]
Stage [30N], [25mm/min]
Result "load at 30N", Load
Result "load at 30N", Load
Stage [40N], [25mm/min]
Stage [40N], [25mm/min]
Result "load at 40N", Load
Result "load at 40N", Load
Stage [50N], [25mm/min]
Stage [50N], [25mm/min]
Result "load at 50N", Load
Result "load at 50N", Load
Stage [60N], [25mm/min]
Stage [60N], [25mm/min]
Result "load at 60N", Load
Result "load at 60N", Load
Stage [70N], [25mm/min]
Stage [70N], [25mm/min]
Result "load at 70N", Load
Result "load at 70N", Load
Stage [80N], [25mm/min]
Stage [80N], [25mm/min]
Result "load at 80N", Load
Result "load at 80N", Load
Stage [90N], [25mm/min]
Stage [90N], [25mm/min]
Result "load at 90N", Load
Result "load at 90N", Load
Stage [100N], [25mm/min] Result "load at 100N", Load Stage [0N], [25mm/min]
Stage [100N], [25mm/min] Result "load at 100N", Load Stage [110N], [25mm/min] Result "load at 110N", Load Stage [120N], [25mm/min] Result "load at 120N", Load Stage [130N], [25mm/min] Result "load at 130N", Load Stage [140N], [25mm/min] Result "load at 140N", Load Stage [150N], [25mm/min] Result "load at 150N", Load Stage [0N], [25mm/min]
Result "load at 0N", Load
Result "load at 0N", Load
Page | 87
Table A9.8 – Column Classification Excel Spreadsheet Fcrl
Fe
Fcr
λ
Classification
λp
Classification
ϒ1
ϒ2
Pn (N)
Pn (kN)
L (mm) = L (mm) =
2500 100
57.63 57.63
41.26 85.94 25790.08 2007.64
0.82 0.17
Intermediate Short
1.90 1.90
Slender Slender
0.99 0.99
0.25 0.25
21872.83 21872.83
21.87 21.87
L (mm) =
200
57.63
6447.52
1004.17
0.24
Short
1.90
Slender
0.99
0.25
21872.83
21.87
L (mm) =
300
57.63
2865.56
669.84
0.29
Short
1.90
Slender
0.99
0.25
21872.83
21.87
L (mm) =
400
57.63
1611.88
502.79
0.34
Short
1.90
Slender
0.99
0.25
21872.83
21.87
L (mm) =
500
57.63
1031.60
402.65
0.38
Short
1.90
Slender
0.99
0.25
21872.83
21.87
L (mm) =
600
57.63
716.39
335.97
0.41
Short
1.90
Slender
0.99
0.25
21872.83
21.87
L (mm) =
700
57.63
526.33
288.40
0.45
Short
1.90
Slender
0.99
0.25
21872.83
21.87
L (mm) = L (mm) = L (mm) = L (mm) = L (mm) = L (mm) = L (mm) = L (mm) = L (mm) = L (mm) = L (mm) = L (mm) = L (mm) =
800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000
57.63 57.63 57.63 57.63 57.63 57.63 57.63 57.63 57.63 57.63 57.63 57.63 57.63
402.97 318.40 257.90 213.14 179.10 152.60 131.58 114.62 100.74 89.24 79.60 71.44 64.48
252.79 225.14 203.06 185.04 170.06 157.42 146.62 137.29 129.15 121.99 115.65 110.00 104.94
0.48 0.51 0.53 0.56 0.58 0.61 0.63 0.65 0.67 0.69 0.71 0.72 0.74
Short Short Short Short Short Short Short Short Short Short Intermediate Intermediate Intermediate
1.90 1.90 1.90 1.90 1.90 1.90 1.90 1.90 1.90 1.90 1.90 1.90 1.90
Slender Slender Slender Slender Slender Slender Slender Slender Slender Slender Slender Slender Slender
0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99
0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25
21872.83 21872.83 21872.83 21872.83 21872.83 21872.83 21872.83 21872.83 21872.83 21872.83 21872.83 21872.83 21872.83
21.87 21.87 21.87 21.87 21.87 21.87 21.87 21.87 21.87 21.87 21.87 21.87 21.87
Page | 88
