Feasibility of strengthening glulam beams with prestressed basalt fibre reinforced polymers Master of Science Thesis in the Master’s Programme Structural Engineering and Building Performance Design ZACHARY CHRISTIAN KAVAN SHEBLI Department of Civil and Environmental Engineering Division of Structural Engineering Steel and Timber Structures CHALMERS UNIVERSITY OF TECHNOLOGY Göteborg, Sweden 2012 Master’s Thesis 2012:90 MASTER’S THESIS 2012:90 Feasibility of strengthening glulam beams with prestressed basalt fibre reinforced polymers Master of Science Thesis in the Master’s Programme Structural Engineering and Building Performance Design ZACHARY CHRISTIAN KAVAN SHEBLI Department of Civil and Environmental Engineering Division of Structural Engineering Steel and Timber Structures CHALMERS UNIVERSITY OF TECHNOLOGY Göteborg, Sweden 2012 Feasibility of strengthening glulam beams with prestressed basalt fibre reinforced polymers Master of Science Thesis in the Master’s Programme Structural Engineering and Building Performance Design ZACHARY CHRISTIAN KAVAN SHEBLI © ZACHARY CHRISTIAN, KAVAN SHEBLI, 2012 Examensarbete/Institutionen för bygg- och miljöteknik, Chalmers tekniska högskola2012:90 Department of Civil and Environmental Engineering Division of Structural Engineering Steel and Timber Structures Chalmers University of Technology SE-412 96 Göteborg Sweden Telephone: + 46 (0)31-772 1000 Cover: Left: 10mm x 10mm BFRP mesh (Smarter Building Solutions, USA); Right: 120 mm wide BFRP fabric (TEXBAS, Poland) Chalmers Reproservice / Department of Civil and Environmental Engineering Göteborg, Sweden 2012 CHALMERS Civil and Environmental Engineering, Master’s Thesis 2012:90 I Feasibility of strengthening glulam beams with prestressed basalt fibre reinforced polymers Master of Science Thesis in the Master’s Programme Structural Engineering and Building Performance Design ZACHARY CHRISTIAN KAVAN SHEBLI Department of Civil and Environmental Engineering Division of Structural Engineering Steel and Timber Structures Chalmers University of Technology Abstract With the relatively recent emergence of basalt fibre reinforced polymer products (BFRPs), the previously prohibitive issues to the introduction of FRP products to strengthen glulam beams initially seem to be addressed. The current thesis is a pilot study of the feasibility of prestressing glulam beams with BFRP materials. The principal issues facing the introduction of prestressed BFRP products in glulam beams are addressed and analysed through laboratory testing, finite element analysis and a theoretical analysis. From the observations and results of these investigations, possible production methods are considered in order to attempt to develop a plausible manufacturing technique. The aim of the laboratory testing and FE modelling was to examine the BFRP-adhesive-wood connection with various BFRP product and adhesive combinations. The expected results were: ultimate strength, failure mode and slippage of the connection. Unfortunately, no usable results could be obtained from laboratory tests due to premature failure of the BFRP materials. The FE results show that out of all of the tested arrangements, the most appropriate was the fabric BFRP with PUR adhesive. However, the shear strength of the connection still proved to be fairly low, highlighting the need for a complicated variable prestressing solution with several small steps. Based on current knowledge and technology, it was hypothesized that the most reasonable solution to actual production of glulam beams prestressed with BFRP products would best be performed with a variable radiation curing and prestressing system. Because this system is not currently developed, large investments and investigations would be presumably needed, and it is questionable whether potential benefits from such a product would outweigh the initial efforts to develop and implement an appropriate production system. Though the results from a theoretical analysis prove that potential for glulam beam height reduction is great, it is obvious from the work of the present thesis that a large number of challenges still exist before glulam beams prestressed with BFRP products is feasible. Key words: prestressed glulam beams, basalt fibre reinforced polymers (BFRP), anchorage length of FRPs in glulam, delamination of FRPs in glulam, prestressed glulam production, variable prestressing II CHALMERS Civil and Environmental Engineering, Master’s Thesis 2012:90 CHALMERS Civil and Environmental Engineering, Master’s Thesis 2012:90 III Contents Abstract ....................................................................................................................................... I Preface ....................................................................................................................................... V Nomenclature ........................................................................................................................... VI 1 Introduction ......................................................................................................................... 1 1.1 Background .................................................................................................................. 1 1.2 Objectives .................................................................................................................... 3 1.3 Methodology ................................................................................................................ 4 1.4 Limitations ................................................................................................................... 4 2 Introduction to materials ..................................................................................................... 6 2.1 Glulam ......................................................................................................................... 6 2.1.1 Benefits of using glulam ...................................................................................... 6 2.1.2 Manufacturing process ......................................................................................... 7 2.1.3 Fast curing of glulam beams .............................................................................. 11 2.2 Basalt ......................................................................................................................... 11 2.3.1 Melamine-urea-formaldehyde (MUF) ................................................................ 15 2.3.2 Polyurethane (PUR) ........................................................................................... 17 2.3.3 Epoxy ................................................................................................................. 19 3 Introduction to prestressing in composite members ......................................................... 20 3.1 History of prestressing ............................................................................................... 20 3.2 Prestressed FRPs in structural members .................................................................... 20 3.2.1 Unreinforced beam ............................................................................................. 21 3.2.2 Prestressed beam ................................................................................................ 24 3.3 Considerations with FRP attachment ........................................................................ 27 3.3.1 Basics of step-wise prestressing ......................................................................... 28 3.4 Previous studies ......................................................................................................... 29 3.4.1 Pre-cambering .................................................................................................... 29 3.4.2 Pre-tensioning ..................................................................................................... 30 3.4.3 Variable pre-tensioning ...................................................................................... 30 4 Investigations .................................................................................................................... 32 4.1 Laboratory tests ......................................................................................................... 32 4.1.1 Objectives ........................................................................................................... 32 IV CHALMERS Civil and Environmental Engineering, Master’s Thesis 2012:90 4.1.2 Materials and methods ....................................................................................... 32 4.1.3 Test configuration .............................................................................................. 34 4.1.4 Test procedure .................................................................................................... 37 4.1.5 Results and observations .................................................................................... 38 4.1.6 Conclusions ........................................................................................................ 44 4.2 FE analysis of anchorage ........................................................................................... 47 4.2.1 Objectives ........................................................................................................... 47 4.2.2 FE models ........................................................................................................... 47 4.2.3 Overall results and conclusions .......................................................................... 61 4.3 Case-study, Moelven ................................................................................................. 62 4.3.1 Objectives ........................................................................................................... 62 4.3.2 Materials ............................................................................................................. 63 4.3.3 Loads .................................................................................................................. 64 4.3.4 Methodology ...................................................................................................... 64 4.3.5 Graphic user interface ........................................................................................ 67 4.3.6 Results and conclusions ..................................................................................... 70 5 Application of investigative results .................................................................................. 72 5.1 Overall conclusions from investigations ................................................................... 72 5.2 Proposed prestressing methods .................................................................................. 73 5.2.1 Precambering ...................................................................................................... 73 5.2.2 Slippage between clamps during curing ............................................................. 75 5.2.3 Variable radiation curing .................................................................................... 76 6 Conclusions ....................................................................................................................... 80 6.1 Concluding remarks ................................................................................................... 80 6.2 Recommendations for further research ...................................................................... 82 7 References ......................................................................................................................... 83 Appendix A: Case-study, unreinforced beam design .............................................................. 86 Appendix B: Matlab code for case-study ................................................................................ 90 CHALMERS Civil and Environmental Engineering, Master’s Thesis 2012:90 V Preface The following Master’s thesis analyses the feasibility of prestressing glulam beams with basalt fibre reinforced polymer products (BFRPs). The work was carried out between January 2012 to July 2012 at the Division of Structural Engineering within the Department of Civil and Environmental Engineering at Chalmers University of Technology. This thesis would not have been possible without the help and support of several people. First and foremost, we would like to thank our Examiner, Professor Robert Kliger for his time and effort in guiding our work and for providing his invaluable insight. Our sincere thanks go to our Advisor, Dr. Reza Haghani. His constant help and guidance was key to the completion of this thesis. Furthermore, our sincere thanks to Mohsen Heshmati for sharing his valuable Abaqus knowledge, Professor Mohammad Al-Emrani for his help during testing, and Julia Folkesson and Sandra Watkinson for their efforts as our opponents. Finally, we would like to thank our families and significant others’ for their continued love and support. Göteborg, July 2012 Zachary Christian Kavan Shebli VI CHALMERS Civil and Environmental Engineering, Master’s Thesis 2012:90 Nomenclature E Modulus of Elasticity E1 Modulus of Elasticity in longitudinal direction E2 Modulus of Elasticity in transversal direction E3 Modulus of Elasticity in radial direction ௅ Modulus of Elasticity of Glulam beamீܧ ிோ௉ܧ Modulus of Elasticity of FRP ν Poisson’s ratio Nu12 Poisson’s ratio in longitudinal direction Nu13 Poisson’s ratio in transversal direction Nu23 Poisson’s ratio in radial direction G12 Shear Modulus in longitudinal direction G13 Shear Modulus in transversal direction G23 Shear Modulus in radial direction ௩݂ Shear capacity ௥݂ Rolling shear capacity ܾ Width of the beam ݄ Height of the beam ܣ Cross-section area ௟ீܣ Cross-section area of Glulam beam ௖ଵܣ Cross-section area of compressive rectangular zone for the glulam beam ௖ଶܣ Cross-section area of compressive triangular zone for the glulam beam ௧ܣ Cross-section area of tensile zone for the glulam beam ிோ௉,௧ Cross-section area FRPܣ ௕ܰ௥௘௔௞ Tensile force required for yielding ௧݂,ீ௟ Tensile capacity of glulam beam ܨீ ௟.௖ଵ Force from compressive rectangular zone for the glulam ܨீ ௟.௖ଶ Force from compressive triangular zone for the glulam ܨீ ௟.௧ Force from tensile zone for the glulam CHALMERS Civil and Environmental Engineering, Master’s Thesis 2012:90 VII ி௥௣,௧ Force from tensile zone for the reinforcementܨ ܰ Pre-stressing force ௖ Strain in compression sideߝ ௧ Strain in tension sideߝ ௖,௘ Maximum compressive elastic strain in glulamߝ ௖,௧ߝ Maximum tensile elastic strain in glulam Tensile strain in the FRP ிோ௉,௧ߝ ௣଴ஶ The strain due to the pre-stressing forceߝ Height of the plasticising ݔ ௣௟ Height of neutral axis in plastic phaseݔ ܼ Navier’s lever arm from centre of gravity ௧ Neutral axis of Glulam beam in tension sideݖ ிோ௉,௧ Neutral axis of FRPݖ ௖ Neutral axis of Glulam beam in compression sideݖ ݁ Lever arm from the pre-stressed reinforcement Moment of inertia ܫ Moment capacity ܯ VIII CHALMERS Civil and Environmental Engineering, Master’s Thesis 2012:90 CHALMERS Civil and Environmental Engineering, Master’s Thesis 2012:90 1 1 Introduction Fibre reinforced polymers (FRPs) have become increasingly more studied and utilized in the reinforcement and prestressing of structural members. However, most of the FRP materials to date have at least some type of inherent drawback which prevents them from becoming more widely utilized for structural applications. FRPs composed primarily of carbon (CFRP) for instance, demonstrate exceptional structural characteristics such as high Elastic Modulus and relatively good tensile strength. However, their performance under fire testing is less than desirable and its cost is prohibitive to its use in most applications. Another common FPR is fiberglass (GFRP). GFRPs exhibit good mechanical characteristics, but again serviceability concerns and cost (though considerably less than CFRPs) make it somewhat prohibitive in its implementation in real-world applications. The relatively new development of an FRP composed of fibres of melted basalt rock (basalt fibre reinforced polymers, BFRP) is beginning to create excitement within the construction industry as a viable FRP alternative to CFRPs and GFRPs. Basalt is naturally occurring and is one of the most abundant materials on Earth. Though early investigations were performed in the United States in the 1920s about production methods for an FRP composed of basalt, successful and large scale production was not achieved until the 1980s in what was then the Soviet Union. Up until 1995, production methods were kept secret, and its use was solely for militaristic purposes. Within the past two decades however, BFRP research and production methods have been declassified, and are now produced for civilian purposes with mechanical properties similar to those of GFRPs or CFRPs, but with generally better serviceability characteristics and at a significantly lower cost. Currently, there are two promising applications of BFRPs within the construction industry. The first is replacement of steel reinforcement in concrete members, thereby eliminating the risk and design complications associated with the corrosion of steel. The second application, and of greater interest to the following thesis, is its use as prestressing in engineered wood products such as glulam beams. Previously, prestressing of wood products with FRP materials was considered cost prohibitive. Additionally, concerns were raised about response of other FRPs during fire loading. However, based on the reported characteristics of basalt FRPs, not only would mechanical properties similar to previous FRPs be achieved, but concerns related to response during fire would be eliminated due to basalt’s extremely high thermal resistance. 1.1 Background The benefits of prestressing engineered wood products, and more specifically glulam, are great. Often in simply-supported glulam beams, the determining factor in design is deflection criteria. Therefore, a reduction in deflection due to prestressing can potentially reduce the beam cross section height – reducing material usage and necessary floor or building height. 2 CHALMERS Civil and Environmental Engineering, Master’s Thesis 2012:90 Furthermore, the allowable design strength of timber is limited by its high variability with regard to mechanical properties. Through gluing of timber into products such as glulam, variability is to some extent reduced simply by the inclusion of several different timber pieces. Further reduction can be achieved by the addition of a more standardized, man-made material such as an FRP due to greater control during production, obtaining less variability with increasing structural responsibility of the FRP in the member. Therefore, not only does prestressing greatly improve the response in serviceability, but it also further homogenizes a particularly variable product such as timber. The task, however, has been to find a cost effective material which not only exhibits the mechanical properties necessary to provide an ample prestressing force, but also performs well in serviceability situations such as fire loading. According to previous research and data provided about current Basalt Fibre Reinforced Polymers, an appropriate BFRP product should achieve this goal. In prestressing of structural members, prestressing calculations can either be performed by considering full interaction between the prestressing member and the structural member, or by considering partial or no interaction between the members – such as if the prestressing member were enclosed in a tube. However, for purposes of more efficiently integrating the prestressing material into glulam production, full interaction is desired so that it acts essentially as an additional lamella, thereby creating what is referred to as a composite member. When considering composite structural members (those whose cross section is composed of two or more materials), one of the main concerns is adhesive strength between the two materials. The adhesive strength determines which sections along the beam may or may not be considered to act according to classic beam theory as described by linear elastic beam theory. The adhesion between the two materials also determines the anchorage length of the prestressing material, which is the length required for full interaction between the prestressing material and primary beam material. At this point along the beam, all of the prestressing force has been transferred to the section from the prestressing material, and the section can be accurately described according to linear elastic beam theory. Accordingly, the interaction between the adhesive, prestressing material and structural material are of great interest. Therefore, in order to obtain better interaction and additionally to protect the adhesive which connects the BFRP to the glulam from possible fire damage, the BFRP is considered here to be embedded at a distance of one lamella away from the tensile edge under service loading. An additional concern to be considered in the prestressing of glulam beams is the inherent material properties of the glulam itself. One of the greatest challenges when attempting to introduce a prestressed material into a timber product is its relatively low “rolling shear” strength. Rolling shear is the case in which both shear components are perpendicular to the grain. Therefore, when considering a force acting axially such as prestressing, the force must be limited in some way in order to not exceed the rolling shear capacity of the glulam. One method of achieving this while still being able to attain the benefits of a high prestressing force is through variable prestressing. In such a case, the prestressing force is increased step- wise from zero at the ends of the beam to a maximum force towards the middle of the beam, where each step should be equal to or greater than a distance twice that of the anchorage CHALMERS Civil and Environmental Engineering, Master’s Thesis 2012:90 3 length to assure that full interaction is achieved across each step and prevent the accumulation of stresses between steps. 1.2 Objectives The aim of the current thesis is to determine the feasibility of strengthening glulam beams with prestressed BFRP products. This will be achieved through investigating the following in order to address the previously described concerns:  Adhesives: The effect of choice of different types of commonly used adhesives and their effectiveness in adhering to BFRP products will be studied. Three main adhesives will be considered – polyurethane (PUR), melamine- urea-formaldehyde (MUF) and a mixed-use structural epoxy.  BFRP product type/arrangement: Two different types of BFRP products will be examined and compared. One is a strip of BFRP fabric, while the second is a fish-net style mesh, with thicker BFRP strands in the longitudinal direction.  Current glulam production methods: Current glulam production methods will be explained and analysed in order to attempt to develop a prestressing method that most suitably corresponds to current manufacturing methods of unreinforced glulam beams, thereby saving extra labour and machine costs.  Possible manufacturing methods: In order to determine possible efficient production methods for introduction of prestressed BFRP products in glulam beams.  Strength limitations of materials and connections 4 CHALMERS Civil and Environmental Engineering, Master’s Thesis 2012:90 1.3 Methodology The previously described objectives will be obtained by means of four separate investigations.  Experimental testing of anchorage length and slip of adhesive joints: Physical test specimens will be manufactured which will then be tested through loading. Results of the testing will be collected and analysed in order to attempt determine connection strength, anchorage length and slippage between materials for different proposed material and product combinations.  FE analysis of anchorage lengths through use of the commercial software, Abaqus CAE: A finite element analysis will be performed on models which attempt to simulate the experimental testing. Results will be utilized to compare with experimental results; thereby mutually confirming experimental and FE models in addition to allowing for a more detailed analysis of connection behaviour than solely from experimental results.  Case-study in order to determine potential benefits: A computer program will be developed which theoretically determines the possible savings of a prestressed glulam beam with BFRP versus a glulam beam designed with no prestressing. Through use of the developed program, a previously designed glulam beam will be reanalysed to determine possible benefits from the introduction of prestressed BFRP products.  Development of proposed manufacturing methods: Based on the results of previous studies, efficient manufacturing methods for the introduction of prestressed BFRP in glulam beams will be proposed and briefly analysed through rough FE analysis and calculations. 1.4 Limitations Limitations to the current study are as follow:  The study primarily examines the case of a simply-supported prestressed beam. CHALMERS Civil and Environmental Engineering, Master’s Thesis 2012:90 5  Creep of the timber is considered only in the developed computer program, and as a modification factor applied when time is equal to infinity.  Possible relaxation of the BFRP material is not considered.  Only two possible BFRP products were studied – a fabric and a net-like mesh, and only two different adhesives are considered for each of these products (PUR and Epoxy in the fabric, and MUF and PUR in the mesh). 6 CHALMERS Civil and Environmental Engineering, Master’s Thesis 2012:90 2 Introduction to materials 2.1 Glulam Glulam is an engineered timber product which was first developed in Germany in the end of 19th century, and became in use in Scandinavian countries beginning in the 20th century. In Sweden, the first glulam was manufactured in 1919 in Töreboda. Glulam is manufactured from wood laminations bonded together with adhesive, parallel to the longitudinal grain direction. The thickness of the lamellae depends on the design and stress range. In Sweden, for regular straight applications the thickness of each lamella is typically 45 mm. For curved applications, however, the thickness can depend on the radius of curvature. Glulam beams are manufactured with the strongest lamellae in the outer edges of the beam, where the compression and tension stresses are maximal. This allows lumber with different grades to be used more efficiently by placing higher graded lumbers in zones with higher stress and lower graded lumbers in lower stress zones. 2.1.1 Benefits of using glulam The benefits of using glulam beams as opposed to other more ”conventional” construction materials are many, and are outlined in the following (Engineered Wood Systems – APA EWS 2000):  Strength: Glulam is one of the strongest structural materials per unit weight, compared with steel or concrete.  Environment concerns: The raw material is renewable. Laminated timber can be reused or recycled.  Aesthetics: The choice of glulam allows the design of a building and its structural members to suit the function and use those structural members without protection or cladding.  Energy saving: Energy consumption during glulam manufacturing is much lower compared to other materials.  Corrosion resistance: Glued laminated timber can withstand aggressive environments better than many other construction materials and will never corrode due to high resistance to chemical attack and aggressive environments.  Dimensional stability: Glulam neither twists nor curls as opposed to non-engineered wood products.  Superior fire resistance: Glulam has a high and predictable resistance to fire. CHALMERS Civil and Environmental Engineering, Master’s Thesis 2012:90 7  Price: Total cost of a glulam structure is often lower than other materials.  Large spans: Glulam can be used for large span constructions of up to 50 meters. The limitations are commonly governmental restrictions on transportation to construction site. 2.1.2 Manufacturing process Glulam production is typically performed in a similar manner, regardless of the factory and country. Figure 2.1 shows a schematic outline of the manufacturing process. Figure 2.1: Glulam Manufacturing. (Moelven Töreboda AB Corporate Website) The initial raw material is graded timber; in Nordic countries this is usually spruce, but for structures that are expected to be exposed to long-term, high moisture conditions, pine compreg could also be used. According to standards, lumber must be strength graded and dried after delivery from the sawmill. The moisture content of lumber must be 8-15% when they are glued together, where differential moisture content of adjacent lamellae cannot exceed 4%. The 4% differential moisture content restriction insures that the adhesive is able to cure properly and that cracks do not develop. Glulam cross-sections could potentially be made up of lamellae having approximately the same strength, resulting in a “homogeneous laminate”. However, in order to use timber strength more efficiently, lumber with higher quality are often placed towards the outer edges of the cross-section, where the stresses are normally larger. This type of manufacturing glulam is called combined cross-section. Figure 2.2 shows a combined glulam cross-section. 8 CHALMERS Civil and Environmental Engineering, Master’s Thesis 2012:90 Figure 2.2: Lay-up of Homogeneous Glulam and Combined Glulam (Moelven et al.) Finger joints are utilized in order to first join individual timber pieces together lengthwise. The finger joints are sawn, glued and planed to a standardized size. The joined lamella is then sawn to the required length for the eventual glulam. Adhesive is then applied and the lamellae are combined to form the glulam beams. In order to reduce the internal stresses the lamellae are turned so that the core part is in the same direction throughout the cross section. Care should be taken, however, that the outermost lamellae are always turned so that the core side faces outwards to prevent any potential delamination between grains (See Figure 2.7). Finally, pressure is applied until the adhesive is cured. As will later be discussed, the adhesive can either be cured naturally on gluing racks (as depicted in Figure 2.3), or a fast-cure process involving micro-wave radiation may be utilized. Figure 2.3: Applying pressure while curing oversized glulams The entire operation must be completed before the glue starts to cure, which takes place within an hour (for room-temperature curing) - the exact time depends on the type of adhesive and the temperature of the room. In addition to standard straight beams, the lamellae could be bent to produce an arc or frame shape during curing (Figure 2.4). CHALMERS Civil and Environmental Engineering, Master’s Thesis 2012:90 9 Figure 2.4: Curved glulam beams The adhesive is then cured under controlled humidity and temperature conditions, or optionally with application of heat. Straight beams may instead be cured in a continuous high frequency curing, through use of microwave radiation as previously mentioned. Figure 2.5: Stacked lamellae waiting to be cured by the radiation machine in the background 10 CHALMERS Civil and Environmental Engineering, Master’s Thesis 2012:90 Afterward, the final machining process of the elements is performed, including cutting the edges, drilling holes, etc. When the glulam manufacturing process is complete, the beams are wrapped in thin plastic and stored before the delivery to ensure a suitable moisture content upon delivery (Svenskt Limträ AB 2001). Figure 2.6: Wrapped glulams waiting to be shipped Figure 2.7: Finished glulam cross-section CHALMERS Civil and Environmental Engineering, Master’s Thesis 2012:90 11 2.1.3 Fast curing of glulam beams There are generally two ways for fast curing glulam beams; radio frequencies (RF) and microwave frequencies (µW). The first method (RF) involves the application of radio frequencies to heat the beam which consequently cures the adhesive. Radio frequencies for fast curing of glulam beams has been investigated and tested in wood industry but it has not yet been properly understood or used. The second method (µW) involves the application of microwave frequencies to pre-heat the beam and thus cure the glue. When the glued lamellae enter the microwave, molecules in the adhesive which are initially already polar start to vibrate and consequently heat up, polymerize and bond to the wood. The water molecules in the glue will also heat up due to the effects of the microwave radiation; however this is not the main process which facilitates adhesion. Microwave radiation, in contrast to radio frequencies, has been developed further and has become a standard commercial product in the wood industry. Moelven in Töreboda, Sweden for instance, which was visited as part of the investigations of the present master’s thesis, is currently using microwave radiation technology. However, this production method is currently limited to standard glulam beams, and additional types of beams such as those which are oversized or curved must be cured instead using the previously mentioned curing racks at room temperature (Testa 2012). 2.2 Basalt Basalt is a naturally occurring material, produced from the solidification of volcanic lava. It is composed primarily of SiO2, and is the most abundant rock found in the Earth’s crust. Russia has nearly endless reserves, though with only 30 active quarries. Other countries with volcanic areas also contain basalt reserves – the United States for instance has thousands of square kilometres of easily accessible basalt in places such as Washington, Oregon and Idaho (Parnas et al. 2007). However, as chemical content differs by location, one of the greatest challenges of use of basalt materials is a relatively high variation in mechanical properties. In order to produce a usable form of basalt, fibres are extruded and spun from molten basalt rock at temperatures of between 1300-1700°C, with diameters generally of 13 to 20 µm (Patnaik 2009, Parnas et al. 2007). Later, the basalt fibres are then normally combined with a resin polymer to form the final desired product – basalt fibre reinforced polymers (BFRPs). Mechanical properties of the basalt fibres depend on the circumstances during formation in addition to variation in chemical content. Generally, however, the material properties of interest can be assumed as follow: 12 CHALMERS Civil and Environmental Engineering, Master’s Thesis 2012:90 Table 2.1: FRP Properties (unit) Basalt (a) Fiberglass (a) Carbon (b) Density g/cm3 2.75 2.6 1.75-1.95 Thermal Expansion Coefficient ppm/°C 8.0 5.4 (-0.1)-(-1.6) (c) Tensile Strength MPa 4840 3450 2500-6000 Elastic Modulus GPa 89 77 200-800 Maximum Application Temperature °C 982 650 500 (d) (a): (Smarter Building Systems 2010), (b): (Carolin 2003), (c): (Adhikari 2009), (d): (Chowdhury et al. 2007) In the Table 2.1, the mechanical characteristics of basalt are compared to those of other common FRPs. As can be seen, basalt presents characteristics similar to those of fiberglass, but with much higher resistance to fire due to its high thermal coefficient - an important consideration in timber structures. An even greater difference can be seen in performance at high temperatures between basalt and carbon FRPs, with the average temperature of fire reaching well above the temperature at which mechanical properties of carbon are affected. Therefore, any possible benefit achieved from the higher modulus of elasticity of carbon as opposed to the more brittle basalt, must be carefully weighed against risks associated with fire response. Because basalt fibre’s Elastic Modulus is less than half that of typical reinforcement materials such as steel or carbon FRPs, it is generally assumed here that any benefits of introduction of basalt merely as reinforcement (without prestressing) would have little to modest improvements. Therefore, in the current thesis only pretensioning of basalt is considered in order to strengthen glulam beams. Additional properties of interest for use in the construction industry are basalt’s high resistance to alkalis and acids which eliminates the risk of corrosion as is the case of steel (most notably steel rebar cast in concrete). With regard to environmental and health concerns, basalt is a “sustainable” product in that it comes from natural sources. Additionally, it is free from carcinogens and other health hazards, posing no risk to humans or nature (Adhikari 2009). FRP products in general are not a new phenomenon. Fiberglass, carbon and aramid FRPs have been used for decades in various industries with great success. Within the construction industry, FRPs have shown great potential but have generally proven to be cost-restrictive, especially in the case of timber structures. However, basalt seems to overcome previous restrictions in that it not only demonstrates strength characteristics similar to the other FRPs, but does so at a much lower cost. In the current project, two types of Basalt FRPs are investigated. It was initially hypothesized that a “net-like arrangement” (hereby known as the “mesh BFRP”) would allow for easier incorporation of a prestressed BFRP product in typical glulam production. It was assumed CHALMERS Civil and Environmental Engineering, Master’s Thesis 2012:90 13 that a connection strength similar to that of a timber-to-timber connection could be obtained, while employing commonly utilized timber-to-timber adhesives, through timber-to-timber connection at the voids in the material. The material examined in the current thesis is the 10mm x 10mm Basalt mesh from Smarter Building Systems in Rhode Island, USA. The product specific material data is depicted in Figure 2.8 as provided by said company. It should be noted that Figure 2.7 depicts solely the strength characteristics per basalt fibre, while the following are more product specific results. Therefore as can be seen in the difference in strength characteristics, due to the presence of resin, the strength of the basalt fibre cannot be directly taken as the tensile strength of basalt fibres by the cross-sectional area of the strand by number of strands. As it became clear during testing, the actual proportion of basalt fibres to resin is relatively low. It should also be noted from the provided testing results that there is a relatively high standard deviation of ultimate strength. Table 2.2: Tensile strength tests of mesh BFRP (Smarter et al. 2010) Sample Maximum Load [N] 1 2725,71 2 2720,00 3 2685,71 4 2885,71 5 2811.43 Average 2765.71 Standard Deviation 81.52 Sample size: 25 mm x 25 mm Figure 2.8: Mesh BFRP The second product investigated is a fabric BFRP. A 120mm wide fabric was provided by the manufacturer TEXBAS, based in Warsaw, Poland. However, for the use during testing, the fabric was cut to a width of 90 mm, thereby giving an assumed ultimate tensile load of 177 kN through interpolation. 14 CHALMERS Civil and Environmental Engineering, Master’s Thesis 2012:90 Table 2.3: Fabric BFRP product information (TEXBAS TM 2012) Size Thickness Width Number of strands Ultimate Load [mm x mm] [mm] [mm] per width [kN] 0.4 x 15 0.4 + 0.025 15 +/- 1 32 +/- 2 29 0.4 x 17 0.4 + 0.025 17 +/- 1 36 +/- 2 33 0.4 x 25 0.4 + 0.025 25 +/- 1 66 +/- 2 49 0.4 x 50 0.4 + 0.025 50 +/- 1 132 +/- 2 98 0.4 x 55 0.4 + 0.025 55 +/- 1 145 +/- 2 108 0.4 x 120 0.4 + 0.025 120 +/- 1 187 +/- 2 237 Figure 2.9: Fabric BFRP With regard to long-term mechanical characteristics, no specific values could be found. However, it is stated by several sources that creep and shrinkage of the BFRP can be taken as negligible due to its material properties. 2.3 Adhesives ”Adhesion refers to the interaction of the adhesive surface with the substrate surface.” (Frihart 2005). Generally, there are three main steps involved in the process of adhesive bonding (Frihart 2005):  Preparation of the surfaces to be adhered: in order to provide optimal interaction between adhesive and surface  Contact of adhesive with surfaces: wetting and penetration  Setting: solidification and or curing of the adhesive Possibly the most important considerations when investigating adhesion are the wetting and penetration characteristics between the adhesive and material, especially for water-borne adhesives such as Melamine-urea-formaldehyde (MUF). Wetting is controlled by several factors, most notably the relative surface energies of the adhesive and substrate. Adhesives CHALMERS Civil and Environmental Engineering, Master’s Thesis 2012:90 15 with high surface tensions (due to being water-borne) have difficulty properly wetting substrates with low surface energy. Other adhesion considerations which affect the bonding, such as flow and penetration of the adhesive into the substrate material, are also dependent upon surface energies. For these reasons, FRPs with low surface energies generally are difficult to adhere using wood adhesives with high surface energies. Epoxies on the other hand do not rely on surface tensions and are therefore considered more of a multi-purpose adhesive. Even though wood bonding is one of the oldest adhesive applications, wood is still one of the most complicated materials to bond due to its inherent material properties which greatly influence adhesive interaction and the wetting process. The anisotropic nature of wood due to the elongation of cells in the longitudinal direction in addition to difference between radial and tangential properties causes difficulties when trying to predict adhesion behaviour. As has been previously mentioned, two different BFRP configurations are to be tested. One, a fabric-like product, allows for no wood-to-wood bonding and therefore requires more multi- purpose adhesives. Thus, two common multi-purpose adhesives [epoxy and polyurethane (PUR)] have been chosen to be tested in conjunction with this BFRP product. The second BFRP product is that of a mesh-like arrangement with large voids, allowing for wood-to- wood contact. It was hypothesized initially that by maintaining wood-to-wood contact, the BFRP would be able to be more easily introduced to current manufacturing processes. Thus, for this configuration, the most common purely wood-to-wood adhesive was chosen (MUF) in addition to the stronger PUR used as a control. The adhesives investigated and their corresponding mechanical properties of interest are summarized in Table 2.4. Table 2.4: Summary of mechanical properties of adhesives (Konnerth et al. 2005) Elastic Modulus (E) Poisson's Ratio (ν) GPa - MUF 6.3 0.34 PUR 0.47 0.23 Epoxy 3.2 0.36 2.3.1 Melamine-urea-formaldehyde (MUF) Melamine-urea-formaldehyde (MUF) resins are aminoplastic thermoset resins primarily used in structural or non-structural glued timber products for exterior and semi-exterior uses, and are among one of the most commonly used adhesives for these purposes (Pizzi 2003, Trada 1992). Another common adhesive with similar properties and uses is phenol-resorcinol- formaldehyde (PRF), representing (along with MUF) the most commonly used adhesives in glulam production due to their high structural capacities and water resistance. Usage of these 16 CHALMERS Civil and Environmental Engineering, Master’s Thesis 2012:90 adhesives has limitations, however, when bonded with non-wood products due to being water-borne. MUF is white when cured, and is almost invisible from longer distances. Therefore, a glulam beam utilized as a ceiling support would appear as a continuous wood product. In stark contrast, PRF is nearly black when cured, accenting the connections between laminates even from a far distance. Due to this aesthetic difference, architects and builders have requested MUF over PRF so frequently that many glulam manufacturers such as Moelven use almost exclusively MUF in glulam production. Specifications for Use: In use with timber products, the product specifications as provided by Akzo Nobel for Melamine-urea Adhesive 1247 (Hardener 2526) are as follows during application:  Temperature range for mixing: 17-25°C  Temperature of wood during application: above 20°C  Recommended moisture content of wood during application: 10-12%  Plane wood surface before application Specifications during curing are as follows:  Temperature above 20°C  Application of Pressure of at least 0.8 MPa  Pressing time of at least 5.75 hours for 100:20 (adhesive : hardener) mix at 20°C Upon proper application and curing of MUF, the following mechanical properties of interest are developed. Mechanical properties, MUF (Konnerth et al. 2005):  Elastic Modulus (E): 6.3 GPa  Poisson’s ratio (ν): 0.34 Figure 2.10: MUF product and application CHALMERS Civil and Environmental Engineering, Master’s Thesis 2012:90 17 2.3.2 Polyurethane (PUR) Polyurethane adhesive was produced in the early 1930s at Bayer in Germany. Polyurethane adhesives are normally defined as those adhesives that contain a number of urethane groups in the molecular backbone or are formed during use, regardless of the chemical composition of the rest of the chain. Thus a typical urethane adhesive may contain, in addition to urethane linkages, aliphatic and aromatic hydrocarbons, esters, ethers, amides, urea and allophanate groups. (Eling et al. 2012). There are two types of polyurethanes which include:  2-component: One component is a hydroxyl compound. The second (hardener) is isocyanate. Both are solvent-free components and react with each other during the formation of polyurethane.  1-component: Consists of isocyanate. Isocyanate reacts with moisture from the material or the air to form amine. In the reaction of carbon dioxide emitted. The amine reacts with the isocyanate to form a polyurea band with similar binding properties as polyurethane. 1-component PUR adhesive is one of the latest adhesives on the market. These adhesives can bond with most materials such as textile fibres, metals, plastics, wood, glass, ceramics, rubber and leather. They are also known for their excellent adhesion, elasticity, high cohesive strength and rapid hardening without heat. Releasing of carbon dioxide causes the glue foam to expand. If this is process is done without control (pressing time, pressing pressure, air and material humidity), the glue joint becomes too thick and the adhesive strength is reduced. 1-component polyurethane adhesive can also be used for highly relatively moist wood, up to about 20%. Moreover, one and two component polyurethane adhesive have similar characteristics. The advantages of this solvent glue are both its processing and product character. Processing advantages:  Curing without heat input.  More pressure capacity through shorter press times, which can provide larger flows and reduce bottlenecks in production compared to conventional adhesives.  Less adhesive consumption.  No time needed for mixing of the adhesive.  Less time for cleaning the adhesive equipment.  Less waste of adhesive.  Less sensitivity to varying moisture content of glued materials.  Higher speed during the cutting operation of final products.  Gluing can be performed with wetter wood (Collano 8-40%).  Less tool wear. Product advantages:  Strong and weather-resistant glue joints. 18 CHALMERS Civil and Environmental Engineering, Master’s Thesis 2012:90  Light glue line.  No formaldehyde emissions Disadvantages of using polyurethane: Isocyanate is one of the main substances in Polyurethane, which is widely used because of its reactivity with groups that contain reactive hydrogen, such as amine and alcohol groups at room temperature. This allows high flexibility in the types of products, because they can self- polymerize or react with many other monomers. A disadvantage of using isocyanate is that isocyanate will react rapidly with water that is present in most wood products. This water can reduce the effective molecular weight by altering the stoichiometry and can compete with desired reactions with the wood, such as the hydroxyl groups in the cellulose and hemicellulose fractions as well as the phenols and hydroxyl groups in the lignin domains. But the most important disadvantage is that they can react rapidly with many compounds present in human bodies. These reactions are rapid under physiological conditions and are not readily reversible which means that safety of handling isocyanate is a concern. The concern is greatest during the manufacturing stage when low molecular weight and volatile isocyanate are still present; once these react, the resulting ureas and esters are quite safe. An exception is that the heat of combustion causes the formation of free isocyanate groups. Isocyanates used in wood bonding are not as hazardous as some other isocyanates in that they generally have higher molecular weight so their volatility and the number of free isocyanate groups are diminished. (Frihart 2005). Therefore, great care must be taken during production involving PUR adhesives. Mechanical properties, PUR (Konnerth et al. 2005):  Elastic Modulus (E): 0.47 GPa  Poisson’s ratio (ν): 0.23 Figure 2.11: PUR product and application CHALMERS Civil and Environmental Engineering, Master’s Thesis 2012:90 19 2.3.3 Epoxy Epoxy adhesives are multi-purpose structural adhesives which have the ability to bond to a wide variety of surfaces such as wood, metals, plastics, ceramics and concrete. Although epoxies are generally considered to have strong and durable bonds, this does not hold true in all conditions. Some research suggests that durability is greatly reduced under wet conditions, and therefore many standards limit its use for load bearing applications. Further testing of the durability of epoxy when exposed to wet loading should be performed before consideration in wet environments in the context of this thesis. Additional limitations of epoxies are their cost, which is much higher than commonly used wood bonding adhesives, time and health risks involved during application. When specifically considering glulam production, application of epoxy would not be able to utilize the existing automated process for applying the adhesive, requiring much more time and labour or initial costs if new machinery is added. An advantage of using epoxy however, especially when considering FRP attachment, is that wood-wood connections are not required. However, similar to PUR, considerable health risks exist and great care must be taken during handling. Allergic reactions can be easily developed from skin contact causing permanent allergies to epoxy products. Mechanical properties, Epoxy (Konnerth et al. 2005):  Elastic Modulus (E): 3.2 GPa  Poisson’s ratio (ν): 0.36 Figure 2.12: Epoxy product and application 20 CHALMERS Civil and Environmental Engineering, Master’s Thesis 2012:90 3 Introduction to prestressing in composite members 3.1 History of prestressing The basic goal of prestressing a structure is to create a negative moment in the construction to improve its serviceability under loading (Nordin 2005). A prestressed structure can therefore be made much thinner than a structure with unprestressed reinforcement. However, since prestressing often is more costly, it is mainly used on larger structures or for structures which demands small deformations during loading. The first attempts to prestress structural members were in concrete structures with normal strength steel in the late 1800’s to early 1900’s. However, these attempts were unsuccessful, due to low strength of normal steel at the time. In 1928 though, prestressing of concrete members became practical after Eugene Freyssinet, a French civil engineer, incorporated the use high-strength steel wires for prestressing (Collins et al. 1991). Significant development of prestressed concrete was possible after T.Y. Lin’s load-balancing method of design (Dinges 2009). Since that time, prestressing concrete members with steel has developed considerably and has become a common occurrence. More recently, new research and applications involving various different materials has been under development; most notably with prestressing components composed of fibre reinforced polymers. 3.2 Prestressed FRPs in structural members In the recent two decades, use of FRPs for strengthening and repairing structures has increased widely due to relatively good mechanical properties such as high stiffness, high strength, good durability and light weight. The benefits of using FRP may be increased further by prestressing the FRP before bonding to the structure (Haghani 2010). Due to their increasing development and therefore benefits, strengthening of structural members with FRPs has begun to be analysed for applications with all of the major construction materials – concrete, steel and timber. The benefits for using prestressed FRPs for concrete structures include: reduction in deformations due to live loads, increased performance of the structure in serviceability limit state, reduced crack width on the tensile part of the structure and thus increasing the durability of the members, and providing a negative moment to counteract the dead load. (Haghani 2010). With regard to steel structures reinforced with prestressed FRPs, the main advantages are: increased fatigue life of the members and prevention of fatigue crack deformation or propagation in the steel structures (Haghani 2010). Of more interest to the current thesis, timber structural members have also been analysed for potential benefits from the addition of prestressed FRPs. Since deflection is typically the controlling design limitation in timber members, the primary benefit of using prestressed CHALMERS Civil and Environmental Engineering, Master’s Thesis 2012:90 21 FRPs for timber structures is in decreasing the deflection in the serviceability limit state. By using prestressed FRPs in timber structures, a negative moment would be applied to the member which would enhance the resistance to live loads, thus reducing the necessary beam height under the same loads. Another benefit of prestressing timber is from a change of the failure mode from a brittle mode to a more ductile mode by decreasing the stresses in the tension side of the beam and thereby generally limiting failure to the more plastic compressive side (Balsiero et al. 2010). In this manner, if failure were to occur, it would be a longer more visually notable failure, providing ample time for repair or escape as opposed to a sudden breakage of the beam which would be the case given a more brittle tensile failure. The following explains theoretically how the aforementioned benefits from prestressing timber are achieved. 3.2.1 Unreinforced beam As is demonstrated in Figure 3.1, when a glulam beam is subjected purely to a tensile force, it will resist the stresses up to a maximum tensile capacity inherent to the timber comprising the beam, ( ௧݂,ீ௟ሻ. When the stress exceeds the maximum tensile capacity, the glulam breaks in a tensile failure. The failure load can be calculated as Equation (3.1): ௕ܰ௥௘௔௞ ൌ ௧݂,ீ௟. ௟ (3.1)ீܣ Figure 3.1: Glulam beam in pure tension 3.2.1.1 Elastic phase When a typical glulam beam with a geometrically symmetric cross-section is subjected to a bending moment, the neutral axis and centre of gravity will be located in the centre of the 22 CHALMERS Civil and Environmental Engineering, Master’s Thesis 2012:90 beam’s cross section. Therefore, due to the neutral axis’ location at the geometric centre, the outermost tensile and compressive strains become equal. Since the case which is currently being considered is in within the bounds of elastic analysis, strain compatibility can be implemented implying that material properties can be taken as behaving linearly. Theoretically, in linear elastic analysis failure occurs in bending, induced in the tension side since the tensile capacity of timber products is inherently lower than that in compression (for example: in CE L40c glulam, tensile limit of 17.6 MPa compared to a compressive limit of 25.4 MPa). However, it should be noted that in reality other failure modes might occur, due to possible defects along the beam. Figure 3.2: Unreinforced beam, elastic phase (Persson et al. 2011) In the elastic phase: ௖ߝ ൌ ௧ (3.2)ߝ The moment capacity (ܯሻ can therefore be calculated as: ܯ ൌ .௖ߝ .ܧ ܾ. ݄ଶ 12 ൅ .௧ߝ .ܧ ܾ. ݄ଶ 12 (3.3) By in inserting (3.2) in (3.3), to obtain the moment capacity of the section: ܯ ൌ .ߝ .ܧ ܾ. ݄ଶ 6 (3.4) 3.2.1.2 Plastic phase Unreinforced glulam beams rarely reach the plastic phase, since the elastic compressive yield limit is often higher than tensile yield limits as was previously explained. Plastification of CHALMERS Civil and Environmental Engineering, Master’s Thesis 2012:90 23 timber may develop however if the elastic compressive yield limit is reached. Plastification occurs when strains above the elastic yield are obtained, and are redistributed within the compressive zone. The plastified section of the compressive zone increases with increasing strain. Further stresses cannot be carried during plastification and the neutral axis will therefore be shifted towards the tensile side. The strain can continue until it reaches the ultimate strain capacity and failure occurs. During the plastification phase, Navier’s formula no longer applies and therefore a strain compatibility approach must instead be employed. It has been determined by previous research that the ultimate plastic strain in wood can be assumed as being three times the ultimate elastic strain (Edlund 1995). The existence of plasticity in compression in timber can be explained by the following phenomena (Barlow & Woodhouse 1992):  Gross buckling of cell walls  Sliding of cell layers over each other  Pulling apart of adjacent cell walls  Macroscopic buckling which causes in localized plastic hinges Allowing for plastification of the compressive side for a beam subjected to a uniform flexural moment can therefore be seen in Figure 3.3. Figure 3.3: Unreinforced beam, plastic phase (Persson et al. 2011) ܨீ ௟.௖ଵ ൅ ܨீ ௟.௖ଶ ൌ ܨீ ௟.௧ (3.5) ܨீ ௟.௖ଵ ൌ .௖ଵܣ ܾ. .௅ீܧ ௖,௘ (3.6)ߝ ܨீ ௟.௖ଶ ൌ .௖ଶܣ ܾ. .௅ீܧ ௖,௘ (3.7)ߝ ܨீ ௟.௧ ൌ .௧ܣ ܾ. .௅ீܧ ௧ (3.8)ߝ 24 CHALMERS Civil and Environmental Engineering, Master’s Thesis 2012:90 As previously mentioned, when a glulam starts to plasticize, the stress distribution will be limited and begin to produce a rectangular pattern due to constant stress given increasing strains above the elastic strain limit (ߝ௖,௘ሻ. The height of the plasticized region is indicated as ."௣௟ݔ"in the figure. The new height of compressive zone is defined as "ݔ" The moment capacity in plasticized glulam can thus be calculated as: ܯ ൌ ܨீ ௟.௖ଵ. ቀ ݔ௣௟ െ ݔ 2 ቁ ൅ 2 3 . ܨீ ௟.௖ଶ. ൫ݔ௣௟ െ ൯ݔ ൅ 2 3 . ܨீ ௟.௧. ൫݄ െ ௣௟൯ (3.9)ݔ Where: ݔ ൌ ௖ߝ െ ௖,௘ߝ ௖ߝ . ௣௟ݔ (3.10) ௧ߝ ൌ ݄ െ ௣௟ݔ ௣௟ݔ . ௖ (3.11)ߝ ఌ೎,೐ߝ ൌ ௣௟ݔ െ ݔ ௣௟ݔ . ௖ (3.12)ߝ 3.2.2 Prestressed beam For the purposes considered in the current thesis, a prestressed glulam beam is considered with the FRP material located in the tension side, a distance of one lamella away from the outer edge. The axial prestressing force applied by the FRP material therefore will cause a negative moment in the beam after releasing the force due to eccentricity. This negative moment produces an upward cambering of the beam. The applied axial stress is limited by the tensile strength of the FRP in addition to the rolling shear in the wood. Additionally, the moment due to prestressing is also limited by the tensile and compressive strength of the glulam beam (taken here as conservative as opposed to the “bending strength” of timber). 3.2.2.1 Elastic phase The effect of prestressing causes an axial force and initial moment in the beam. The stresses and strains due to prestressing alone are shown in Figure 3.4. Figure 3.5 illustrates possible strain distributions after application of loading along the length of the beam. CHALMERS Civil and Environmental Engineering, Master’s Thesis 2012:90 25 Figure 3.4: Prestressed beam, stresses due to prestressing (Persson et al. 2011) Figure 3.5: Prestressed beam, elastic phase (Persson et al. 2011) After applying prestressing, the upper zone of the beam will be subjected to a tensile stress and the bottom zone of the beam will be subjected to a compressive stress. During service loading, the strain distribution may be taken as one of the previously depicted solutions seen in Figure 3.5, where the tensile and compressive sides may appear at either edge of the cross- section. To calculate the moment capacity in elastic phase, Navier’s formula can be considered. .௖ߝ ௅ீܧ ൌ ܰ ܣ ൅ ܰ. ݁ ൅ ܯ ܫ . ܼ (3.13) ܯ ൌ ሺீܧ௅. .௖ߝ ܣ െ ܰሻ. ܫ .ܣ ܼ െ ܰ. ݁ (3.14) When the resulting moment is found by Navier’s formula, the strains in the wood and FRP can then be determined as follows. ௧ߝ ൌ ܯ .௅ீܧ ܫ . ௧ݖ (3.15) ௖ߝ ൌ ܯ .௅ீܧ ܫ . ௖ݖ (3.16) 26 CHALMERS Civil and Environmental Engineering, Master’s Thesis 2012:90 ிோ௉,௧ߝ ൌ ܯ .௅ீܧ ܫ . ிோ௉,௧ (3.17)ݖ 3.2.2.2 Plastic phase When the strain in the compressive zone reaches the maximum elastic strain, the beam begins to plasticize in the compressive zone and results in stress redistribution within the cross- section. This redistribution acts in the same manner as the case of an unreinforced beam during the plastic phase. Figure 3.6 shows stress and strain distribution for a beam in the plastic phase. Figure 3.6: Prestressed beam, plastic phase (Persson et al. 2011) The strain ߝ௣଴ஶ is the pre-stressing strain in the prestressed FRP due to the prestressing force. By considering this additional force, the force equilibrium can be calculated as: ܨீ ௟,௖ଵ ൅ ܨீ ௟,௖ଶ ൌ ܨீ ௟,௧ ൅ ி௥௣,௧ (3.18)ܨ Where: ܨீ ௟,௖ଵ ൌ .௖ଵܣ ܾ. .௅ீܧ ௖,௘ (3.19)ߝ ܨீ ௟,௖ଶ ൌ .௖ଶܣ ܾ. .௅ீܧ ௖,௘ (3.20)ߝ ܨீ ௟,௧ ൌ .௧ܣ ܾ. .௅ீܧ ௖,௧ (3.21)ߝ ிோ௉,௧ܨ ൌ .ிோ௉,௧ܣ .ிோ௉ܧ ிோ௉,௧ (3.22)ߝ CHALMERS Civil and Environmental Engineering, Master’s Thesis 2012:90 27 By using the equilibrium condition and considering that ߝ௖ is always known, the height of neutral axis in the plastic phase (ݔ௣௟ሻ can be calculated if the strains are defined with εୡ . ݔ ൌ ௖ߝ െ ௖,௘ߝ ௖ߝ . ௣௟ݔ (3.23) ிோ௉,௧ߝ ൌ ݄ െ ௣௟ݔ െ ௧ݖ ௣௟ݔ . ௖ߝ ൅ ௣଴ஶ (3.24)ߝ ௧ߝ ൌ ݄ െ ௣௟ݔ ௣௟ݔ . ௖ (3.25)ߝ ௖,௘ߝ ൌ ௣௟ݔ െ ݔ ௣௟ݔ . ௖ (3.26)ߝ When the functions above are determined, the plastic moment capacity of the section can then be found as: ܯ ൌ ܨீ ௟.௖ଵ. ቀ ݔ௣௟ െ ௫ ଶ ቁ ൅ ଶ ଷ . ܨீ ௟.௖ଶ. ൫ݔ௣௟ െ ൯ݔ ൅ ଶ ଷ . ܨீ ௟.௧. ൫݄ െ ௣௟൯ݔ ൅ .ி௥௣,௧ܨ ሺ݄ െ ௣௟ݔ െ ௧ሻݖ (3.27) 3.3 Considerations with FRP attachment Prestressing FRP laminates for strengthening and repair of structures presents several challenges, due primarily to difficulties which can occur due to the bonding of prestressed FRPs to glulam beams. One of the greatest challenges encountered is development of high shear stresses at the ends of the prestressed FRP which can easily exceed the strength of the adhesive. Conventional adhesives used in composite structures such as epoxy resins normally withstand 20-25 MPa, whereas the shear stress at the ends can typically reach values of around 40-50 MPa. These high shear stresses in the ends of the prestressed FRP may result in delamination or debonding of the FRP laminate from the structural member (Al-Emrani et al. 2007). Another challenge more specific to prestressing glulam beams is the low rolling shear capacity in timber, which is generally taken as one third of the shear capacity of timber. ௥݂ ൌ ௙ೡ ଷ ൌ 1 (3.28) ܽܲܯ If the shear stress in bonding exceeds this limit, failure may occur due to very small prestressing loads in a timber structure. A further challenge is the potential risk of delamination. In the present master’s thesis however, for simplification purposes and lack of information we assume full interaction between adhesives and BFRP. Furthermore, the effect 28 CHALMERS Civil and Environmental Engineering, Master’s Thesis 2012:90 of the relaxation is not considered since little to no relaxation is assumed to occur in BFRP products. The most appropriate solution to overcome these previously outlined challenges is through implementing step-wise prestressing of FRP laminate. Through this method, the desired axial force can be applied to the FRP in several steps in order to limit the shear stress development by the rolling shear capacity of the wood. The following further describes this method. 3.3.1 Basics of step-wise prestressing The purpose of step-wise prestressing is to delay the axial force development, thereby transferring the axial force over an extended amount of time instead of suddenly as would be expected without step-wise implementation. The slower axial force transference in return transforms the shear stress development curve from one with a sudden initial peak, to several smaller “steps,” corresponding directly to the axial step size. Consequently, accumulation of shear stress is prevented, and by controlling the length and magnitude of the axial “steps,” the shear stress development can be limited to a set value. It should be noted that despite the overall change of the shear stress relationship, the areas under the normal and step-wise curves are the same as an equal axial force is eventually transferred to the section in both cases. Figure 3.7: Variable prestressing versus traditional prestressing (Haghani 2010) CHALMERS Civil and Environmental Engineering, Master’s Thesis 2012:90 29 Through implementation of this method, the application of the axial force can be controlled by the rolling shear capacity of the wood and length of the steps, which can be determined by the anchorage length determined for the traditional method. In order to achieve the previously described results, the anchorage length must first be defined. Through previous research, it was found that the anchorage length can be reasonably considered as the point along the non-variably prestressed curve which corresponds to 1% of the maximum shear stress at the edge. The “step-size” can then be found as twice this length, so as to avoid cumulative effects along the stress development curve. Additionally, the allowable axial load per step can then be found by determining the load which produces a stress peak within the defined limits for a case of non-variably applied axial force (Haghani 2010). 3.4 Previous studies Several methods to prestress glulam beams with FRPs have been investigated in recent decades. These investigations are summarized below: 3.4.1 Pre-cambering One method of prestressing of introducing a prestressed FRP has been the “indirect” method of pre-cambering, in which a beam is initially pre-cambered, the FRP is adhered and then the cambering released in order to pre-tension the FRP. In one study (Balsiero et al. 2010) adhered CFRP (Carbon fibre reinforced polymer) to a pre-cambered beam by cambering the beam to its maximum curvature limit and then bonding a non-tensioned CFRP product to the bottom face of a glulam beam. The cambering procedure is not very complicated and requires very light equipment. The following results were noted:  Low increase in strength due to small percentage of reinforcements causes a small change in the strength.  Small degree of cambering and curvature should be imposed to the beam to not damage the beam during cambering. The result was the stress in the FRP caused by cambering was very low. Another study (El-Hachal et al. 2001) strengthened an existing concrete bridge by means of a prestressed FRP through use of a cambering effect. A vertical load was applied on two points under the beam with hydraulic jacks to produce the camber. Then FRP was placed under the concrete beam. After curing the adhesive the jacks were removed and the FRP was released. The observations were as follows:  A low level of prestress could be induced to the beam after releasing the jacks. 30 CHALMERS Civil and Environmental Engineering, Master’s Thesis 2012:90  “Inefficient use of material and could damage and overstress the strengthened beam.” Thus, as can be seen by the previous research, pre-cambering risks damage to the beam while producing minimal improvements both in the case of strengthening a new beam as well as in situations involving pre-existing construction. 3.4.2 Pre-tensioning A second method of prestressing a glulam beam is through direct application of a pretensioned FRP member. One group of investigators (Dolan et al. 2012) tested glulam beams with the addition of Kevlar FRPs in both as pure un-tensioned reinforcement as well as a prestressed member in order to analyse the benefits of prestressing the glulam. The Kevlar FRP was placed between the two outermost lamellae. The results of interest were those of the flexural strength tests as well as the shear tests of the connections. With respect to the flexural strength tests, the results did not agree well with the expected results, with premature failure which the authors attributed to inherent defects in the glulam. From the shear tests of the connections, it was noted that with increasing prestress of the Kevlar FRP, a decrease in shear strength occurred. Additionally, it can be seen that relatively high standard deviation exists in the data, suggesting unreliable results. Another group (Guan et al. 2005) placed a prestressed GFRP a distance of 1 lamella from the tensile edge of a glulam beam and subjected to a bending force. Only FE models are analysed – no experimental tests were performed. Additionally, it should be noted that the allowable shear stress was limited by the average shear strength of the timber considered, instead of the rolling shear. A similar study was conducted by another team of investigators (Brady et al. 2012); however in this instance only theoretical calculations were performed – no experimental testing or FEM analysis. As is demonstrated by the previous work, an increase in bending capacity is plausible due to the introduction of prestressed FRP products in glulam beams. However, due to the limited scope of the studies and what are considered here to be inaccurate assumptions (most specifically the choice of average strength over the rolling shear to limit the prestressing force), no real conclusions beyond its plausibility can safely be made. 3.4.3 Variable pre-tensioning A third prestressing method of glulam beams involves the more challenging technique of achieving variable prestressing. However, despite the challenges, as it is seen during the present thesis, the results are more appropriate when prestressing glulam beams. In one study (Davids et al. 2010, Strengthening…) developed a technique of achieving variable prestressing through the release of the prestressing force on the FRP after clamping but before CHALMERS Civil and Environmental Engineering, Master’s Thesis 2012:90 31 the adhesive was cured. Thus, the friction produced from the clamping forces allowed for a more gradual transfer of the prestressing force from the FRP to the section. A 95% strength improvement in bending was noted over unreinforced beams and no delamination or anchorage failures were observed. In a second study (Brunner et al. 2005); variable prestressing was achieved through use of an anchoring device with the addition of alternative curing of the adhesive by heating. In this manner, no delamination was noted for prestressing forces of up to 60 kN, and currently further investigations are being performed at higher forces. Though the previous studies demonstrate promising results, it should also be noted that both techniques present unique challenges. In the first, where variable prestressing is achieved by release of the prestressing force during curing, predicting the actual results is extremely complicated. A model must be developed which accurately takes into account the frictional forces between all of the materials and the rate of curing of the adhesives. The second method presents more predictable results. However, due to the considerable time required during heat-curing of adhesives, the additional adhesive not intended to be cured during the initial steps would have already begun curing by the time that curing should theoretically begin in those steps. 32 CHALMERS Civil and Environmental Engineering, Master’s Thesis 2012:90 4 Investigations In the following section, the three primary investigations undertaken in the current thesis are outline and discussed. The investigations are as follows:  Laboratory Tests  FE Analysis of Anchorage  Case-Study and Optimization Program Development The results from the three investigations are studied and the overall knowledge gained is applied in the Section 5 where possible production methods are analysed. 4.1 Laboratory tests 4.1.1 Objectives In the laboratory testing, specimens are made and tested in order to:  Determine the experimental anchorage length of several different adhesive and BFRP configurations.  Determine the failure modes of the connections.  Determine the ultimate strength of the connections.  Determine the slippage of the connection, if any. 4.1.2 Materials and methods Specimens were cut from previously tested, but structurally sound, CE L40c Glulam beams. For ease of sample construction, lamellae of the same size as those in the existing Glulam beams were chosen. Therefore, the sample cross section will be taken as 45 mm high by 90 mm wide. It should be noted that in order to maintain the 45 mm height, samples were cut where the previous adhesive line lies in the middle of the new “lamellae.” In this manner, samples can still be cut at 45 mm while not having to consider removal of the adhesive. Additionally, a sample length of 300 mm is chosen in order to provide enough length for BFRP attachment as well as to prevent crushing of the timber in compression at the support. All specimens were examined for defects in the wood prior to gluing, and unacceptable specimens were discarded. Therefore, the specimens tested are free from compression wood, large knots, or other defects. CHALMERS Civil and Environmental Engineering, Master’s Thesis 2012:90 33 In preparation for gluing, the wood was planed and cleaned. All gluing specifications for the three adhesives were adhered to during production and curing of the specimens, with an ambient temperature of 21°C and an average moisture content of the wood measured of 11.17% (with range 10.37%-12.76%) during production. Adhesives were mixed as follows, with the second value representing the proportion of hardener: 100:25 for MUF, 100:100 for the two-component epoxy and 100:70 for PUR. Pressure was applied as recommended for the MUF and PUR (1 MPa for 24+ hours), and although no pressure is technically required for the epoxy, small lead weights were placed over adhesive sections as shown in Figure 4.1. Additionally, the BFRP was also cleaned in preparation for gluing with acetone. A total of 32 samples were produced in this manner. The fabric BFRP was tested using alternatively PUR or epoxy, with 50 and 100 mm embedment of the fabric within the sample. Similarly, the mesh BFRP was tested with 50 and 100 mm embedment, with MUF and PUR. Therefore, 4 samples of each BFRP-embedment-adhesive arrangement were produced (as depicted in Table 4.1). Figure 4.1: Specimen geometry 34 CHALMERS Civil and Environmental Engineering, Master’s Thesis 2012:90 Table 4.1: Specimens produced BFRP Type Embedment Length Adhesive Type Number of [mm] Samples F ab ri c 50 PUR 4 Epoxy 4 100 PUR 4 Epoxy 4 M es h 50 MUF 4 PUR 4 100 MUF 4 PUR 4 The fabric BFRP utilized was originally in 120 mm wide strips. However, in order to try to reduce any influence from potential stress concentrations, the fabric was cut to 90 mm prior to testing. The mesh BFRP was placed so that 9 longitudinal strands were attached within the 90 mm width of the specimen (at each strand placed every 10 mm). 4.1.3 Test configuration Originally, testing was to be performed using an Alpha Testing Machine, where the BFRP would be attached in one end and a steel attachment would be used to attach the wood end. However, due to machine usage restrictions, an alternative testing method to that which had been originally planned for had to be developed. Three of the biggest challenges involved in test design were the elimination of eccentricities, attachment of the BFRP to be pulled and measuring techniques. The final test design utilized a prestressing device developed by Reza Haghani and Mohammad Al-Emrani at Chalmers University of Technology, with load applied using a hydraulic jack (See Figures 4.2-4.6). CHALMERS Civil and Environmental Engineering, Master’s Thesis 2012:90 35 Figure 4.2: Testing method As is seen in Figure 4.2, load is applied to the rebar, which in turn pulls the connected “loading blocks” along the static outer rods. Eccentricities were reduced due to the connections chosen at both of the sample ends. In the wood specimen, a ø25mm rebar is used to restrain only horizontal movements. Again, calculations were performed in order to verify that no deformations due to compressive crushing of the wood were present at the expected load levels. Attachment of the BFRP proved to be fairly difficult. Initial trials involving direct clamping of the BFRP in between two steel edges were unsuccessful, where the BFRP either slipped due to too little clamping force or was sliced at the edges of the steel clamps due to too high of a clamping force. The final solution involved gluing of the BFRP between two steel plates using epoxy and slight pressure during curing. The size of the steel plates was increased from the initial tests to better distribute the clamping forces and prevent “slicing” of the BFRP. No slippage or slicing of the BFRP was observed after this method was implemented. Unfortunately however, seven samples were destroyed during this “learning process.” Again, good attachment was desired while avoiding eccentricities. Therefore, the glued plates containing the BFRPs were attached by drilling a hole in the plate-BFRP composite and attaching by use of a high strength steel bolt. Again, in this way, only horizontal movement is restricted. The prestressing system was supported vertically and horizontally by clamping (See Figure 4.5). Four steel clamping blocks were used to restrict movement of the two large longitudinal bars and also to provide vertical support to the loading system. The final test set-up can be seen in Figures 4.3-4.6. 36 CHALMERS Civil and Environmental Engineering, Master’s Thesis 2012:90 Figure 4.3: Test set-up Figure 4.4: Load application by hydraulic jack CHALMERS Civil and Environmental Engineering, Master’s Thesis 2012:90 37 Figure 4.5: Support system Figure 4.6: Measurements by lasers 4.1.4 Test procedure As previously mentioned, load is applied manually by a hydraulic jack. During loading, the load is monitored through use of a load cell, rated for a maximum of 50 kN. 38 CHALMERS Civil and Environmental Engineering, Master’s Thesis 2012:90 Figure 4.7: Monitoring of deformations Deformations were monitored using three lasers, measuring the deformation at the following points:  (1) At the edge of the moving portion of the loading device in order to monitor overall deformation.  (2) At the edge of the wood specimen to monitor any movements of the specimen due to possible influence from compression in the wood (though theoretically there should be none).  (3) At a point in the BFRP very close to the connection in order to examine slippage. Readings were collected every second during loading both in the lasers and concurrently in the load cell (through use of the data collection software associated with the lasers). Therefore, an output of load versus deformation can be easily and accurately obtained. Of course, since loading was done manually, loading at a constant rate could not be achieved. However, it is believed that this is not important as a good load versus deformation relationship can still be obtained and plotted. 4.1.5 Results and observations As mentioned previously, 7 specimens were destroyed during the development of the testing method. In the specimens that remained, the testing method seemed to perform well with no slippage or cutting of the BFRP. However, in all of the tests (in both the fabric and mesh BFRPs), failure occurred prematurely in the BFRP. The resulting ultimate loads are as follows: CHALMERS Civil and Environmental Engineering, Master’s Thesis 2012:90 39 Table 4.2: Test results FABRIC BFRP MESH BFRP Ultimate Load Ultimate Load [N] [N] P U R 50 6513.15 M U F 50 1188.56 50 5742.06 50 1736.08 50 6983.10 50 2089.68 100 6488.05 100 2742.14 100 9875.81 100 5753.47 100 8039.35 100 2488.91 100 5641.69 100 1263.84 E p ox y 50 8963.28 P U R 50 3672.91 50 7811.22 50 4861.48 100 8025.66 50 6237.11 100 8415.77 100 285.16* 100 7669.78 100 4218.15 100 5422.68 Average: 7514.08 [N] Average: 3472.92 [N] * Value excluded due to breakage prior to testing Due to a much larger cross-sectional area of the fabric BFRP versus the mesh BFRP, a higher ultimate strength was to be expected in the fabric. However, in comparison to the material capacities previously identified in the material descriptions, the experimental ultimate load capacity of both BFRPs is significantly lower than reported. Therefore, breakage always occurred in the BFRP material prior to the expected failure load of the connection due to rolling shear failure in the wood. The failure types presented in Figures 4.8-4.11 are typical for all of the specimens, in the fabric and mesh, respectively. 40 CHALMERS Civil and Environmental Engineering, Master’s Thesis 2012:90 Figure 4.8: Typical results - fabric BFRP Figure 4.9: Typical results - fabric BFRP, close-up CHALMERS Civil and Environmental Engineering, Master’s Thesis 2012:90 41 Figure 4.10: Typical results - mesh BFRP Figure 4.11: Typical results - mesh BFRP, close-up Premature failure in the BFRP obviously inhibits the ability to examine the connection’s ultimate strength and failure mode. Therefore, no results were recorded with regard to these considerations. However, BFRP failure does not necessarily mean that the slippage results obtained from the laser measurements are invalidated as well. 42 CHALMERS Civil and Environmental Engineering, Master’s Thesis 2012:90 Accordingly, the elongation of the specimen as a whole shows good results, with a fairly linear load versus deformation relationship, with clearly defined points of interest such as beginning of breakage and full breakage in specimens which broke rapidly. Figure 4.12: Typical elongation results In Figure 4.12, the following characteristics can be noted:  An initial “tightening” of the fabric BFRP  Linear deformations  A slight indication where the load was briefly released at half-way  A sudden, brittle failure of the BFRP Next, in attempting to isolate the slippage of the connection, the deformation measured by laser 2 and a percentage of the movement at laser 1 (to remove influence of elongation of the BFRP) are subtracted from the deformation measured by laser 3. According to the results, a slippage of the connection of around 3mm before failure was recorded by the lasers. This could not be confirmed visually, as no movement could be seen either by visual inspection or by photographs. 0 1000 2000 3000 4000 5000 6000 7000 8000 0 2 4 6 8 10 12 14 16 L oa d [ N ] Deformation [mm] Elongation - Fabric, PUR, 50mm CHALMERS Civil and Environmental Engineering, Master’s Thesis 2012:90 43 Figure 4.13: Typical slippage results Now, by removing the outliers (due to initial tightening of the fabric and extreme deformations after breakage), a relationship can be developed as follows. Figure 4.14: Typical slippage relationship 0 1000 2000 3000 4000 5000 6000 7000 8000 0 1 2 3 4 5 6 7 L oa d [ N ] Deformation [mm] Slippage - Fabric, PUR, 50mm y = 0,2367x + 0,0199 0 0,05 0,1 0,15 0,2 0,25 0,3 0,35 0,4 0,45 0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6 1,8 S tr es s [M P a] Deformation [mm] Slippage - Fabric, PUR, 50mm 44 CHALMERS Civil and Environmental Engineering, Master’s Thesis 2012:90 The slope, 0.2367, is noted for this particular test, with results for the all tests depicted in Table 4.3. Table 4.3: Slippage results FABRIC BFRP MESH BFRP Slippage Slippage [MPa/mm] [MPa/mm] P U R 50 0,2624 M U F 50 No Result 50 0,1556 50 0,1411 50 0,2367 50 0,1253 100 0,0463 100 0,0649 100 0,0338 100 0,049 100 0,0916 100 0,037 100 0,1192 100 0,0149 E p ox y 50 0,2298 P U R 50 0,1044 50 0,0952 50 0,24 100 0,0798 50 0,1543 100 0,079 100 0,0002 100 0,123 100 0,0941 100 0,1262 However, as can be seen by the results, no relationship could be determined and any averaged value would be inaccurate due to such high variability. 4.1.6 Conclusions Due to the unexpectedly premature failure of both of the BFRPs, no conclusions could be made with regard to the strength of the connection and connection failure type. It is unclear why the BFRP failed so early. Even if eccentricities were present in the system, such a large difference (for example in the fabric – 7.51 kN as compared to the expected 177 kN) could not be produced by eccentricities alone, even if very large (which none were noted during testing). An additional thought is that there was “slicing” of the BFRP as was noted in the previous tests. However, as can be seen by the previous photos, failure was generally found far enough away from the connections for this to be the cause. Due to its brittle behaviour, we believe that damage could have occurred in the BFRPs during handling. This was extremely evident in the mesh BFRP, as folding of the mesh or other slight movements visually caused discoloration, suggesting a fatigue-like failure in the individual strands. Additionally, it is unclear whether manufacturers are only investigating basalt fibres on a micro scale and later extrapolating the results to a larger cross-section through assuming that size and amount of fibres do not affect the overall result, which the presented results prove is incorrect. With regard to the mesh, strength properties provided publicly on the CHALMERS Civil and Environmental Engineering, Master’s Thesis 2012:90 45 manufacturer’s website solely describe the mechanical properties of a single basalt fibre. Still, even the 25mm x 25mm specimens tested independently (Table 2.2) suggested much higher load capacity than was obtained in the current study, again suggesting that overall strength decreases with increasing specimen size. Furthermore, large variability in strength is seen not only in the current study, but also in the independent study as well. Additionally, these observations have been noted during other investigations as well (Czigány 2005). The authors of the cited study suggest that the type and amount of resin used in BFRP production may greatly influence its mechanical properties. Furthermore, some variability is to be expected since BFRP is composed primarily only of basalt fibres and thus the material properties of each product may not only depend on geographic location, but also on location within the quarry – with basalt from one side of the quarry potentially having very different properties to basalt from the other side. Because of the unexpectedly low capacity of the mesh BFRP, strands were also tested individually by hanging weight. Table 4.4 illustrates the results. 46 CHALMERS Civil and Environmental Engineering, Master’s Thesis 2012:90 Figure 4.15: Testing of individual mesh BFRP strands Table 4.4: Results of tensile testing of individual mesh BFRP strands Specimen Ultimate Load Tensile Capacity [N] [MPa] 1 487.27 487.27 2 551.49 551.49 3 424.52 424.52 4 477.55 477.55 5 504.36 504.36 The tensile capacity was extrapolated based on the measured cross-section of each strand. Therefore, this includes any kind of binding or outer coatings of resin. The average strength CHALMERS Civil and Environmental Engineering, Master’s Thesis 2012:90 47 was thus calculated as 489 N per strand, or tensile capacity of 489 MPa, again suggesting that capacity decreases with increasing amount of material and also that the actual amount of basalt fibres must be relatively low. As far as the inconclusive slippage results are concerned, it can be expected that results would not be extremely accurate, despite the lasers being accurate to +/- 0.015 – 0.2 mm. Attachment of the surface to be measured on the BFRP was not ideal, as any movement of the BFRP beyond the linear path measured by the laser would affect the readings. This effect can be seen in several of the slippage results. Additionally, the failure of the BFRP may have developed too early for enough slippage to be accurately measured in the connection. Finally, large variability could also be attributed to the limited number of samples tested per BFRP- adhesive-embedment arrangement. 4.2 FE analysis of anchorage 4.2.1 Objectives The aim of the finite element (FE) analysis (FEA) is to determine the anchorage length of different proposed combinations of adhesives and BFRP materials. Simultaneously, the maximum load per step can be determined for all combinations based on the limiting rolling shear capacity of timber. The FE analysis should serve to verify the experimental procedures previously identified, as well as to better understand and extrapolate experimental results. Therefore, care should be taken in depicting the experimental procedures as accurately as possible while simultaneously simplifying the model for practical purposes such as run-time, file size, etc. The models which follow were determined based on these requirements. As previously mentioned, the FE models are utilized here to examine and verify the same cases as were tested previously. Therefore, eight model arrangements are investigated – one of each configuration tested in the laboratory testing, as are previously identified in Table 4.1: Specimens producedTable 4.1. 4.2.2 FE models Due to the specific challenges presented by modelling the fabric and mesh arrangements, two different models are developed for each case. The following work was performed using the commercial software, Abaqus CAE. 48 CHALMERS Civil and Environmental Engineering, Master’s Thesis 2012:90 4.2.2.1 Materials The materials modelled are representative of those used in the laboratory testing. The following properties for the isotropic materials were assigned in the models: Table 4.5: Material data Material Elastic Modulus (E) Poisson’s Ratio [GPa] (ν) Fabric BFRP 85000 0.3 Mesh BFRP 89000 0.3 PUR 0.47 0.3 MUF 6.3 0.34 Epoxy 3.2 0.36 Due to the anisotropic nature of wood, different material models were used depending on whether it was modelled in 2 or 3 dimensions. Additionally, it should be noted that the timber specimens are modelled according to mechanical properties specified for C24 grade timber instead of the corresponding glulam properties (CE L40c). This is due to the small size of the specimens, thereby prohibiting the corresponding strength increase allowed by glulams owing to reduction of risk of variability despite being composed of the previously stated timber grade. In the 2D models, the timber material was modelled as a “laminate,” with material properties as follows: Table 4.6: Two dimensional timber properties E1 E2 Nu12 G12 G13 G23 11000 370 0.04 690 353 27 In the 3D models, the timber material was modelled as an “engineering constant,” with material properties as follows: Table 4.7: Three dimensional timber properties E1 E2 E3 Nu12 Nu13 Nu23 G12 G13 G23 11000 370 370 0.04 0.04 0.04 690 353 27 In Tables 4.6 - 4.7, values are given in MPa, since units are defined in the models as N and mm. As can be seen from the material properties, materials are taken as linear, where the non- linear nature of wood in compression is ignored in the following models. Due to the nature of CHALMERS Civil and Environmental Engineering, Master’s Thesis 2012:90 49 the testing configuration, only the portions of wood near the supports would be in compression. Therefore, modelling wood in compression non-linearly would provide almost no additional precision while greatly increasing computation time. 4.2.2.2 FE model – fabric BFRP In the first model type, the configurations consisting of the fabric BFRP are tested. Here, the following combinations are modelled: Table 4.8: Fabric BFRP, configurations modelled BFRP Type Embedment Length Adhesive Type [mm] F ab ri c 50 PUR Epoxy 100 PUR Epoxy 4.2.2.2.1 Geometry Due to the homogeneity in the transversal direction, a 2D model is developed through use of shell elements. In order to best compare the FEA results with those from the laboratory testing, the models are created using the same geometry as the experimental specimens. Figure 4.16: Fabric BFRP model geometry, horizontal dimensions 50 CHALMERS Civil and Environmental Engineering, Master’s Thesis 2012:90 Figure 4.17: Fabric BFRP model geometry, vertical dimensions 4.2.2.2.2 Boundary conditions and loads The boundary conditions and loads can be seen in Figure 4.18. Figure 4.18: Fabric BFRP, boundary conditions and loads Loading is performed as a negative pressure along the edge of the BFRP material. Depending on whether the embedment length of the BFRP is 50 or 100 mm, the applied pressure is either 225 or 450 MPa, respectively. However, as will be explained later, the load is insignificant. The boundary conditions are placed along the upper and lower edge of the end opposite to the BFRP embedment and are taken as fixed – with all movement and rotation fixed. 4.2.2.2.3 Meshing The model was meshed in a manner so that a fine mesh is present along lines and points of interest, while the areas of lesser interest are meshed using a coarser mesh. In Figure 4.18, a typical meshing pattern is presented, where areas of greater concern (i.e. stress concentration points) are highlighted to be meshed with a finer mesh and are surrounded by transition zones CHALMERS Civil and Environmental Engineering, Master’s Thesis 2012:90 51 in order to achieve a more congruent mesh between areas of finer and coarser mesh. The resulting meshing pattern is seen in Figure 4.19, using a quadratic, structured mesh. Figure 4.19: Fabric BFRP, mesh At the areas of interest (most specifically along the embedment of the BFRP), an element size of 0.025 mm is used, with transition zones of varying element size until a maximum element size of 5 mm is smoothly obtained at the outer edges of the model. The model with 50 mm embedment of the BFRP is similar to the previously described 100 mm embedment model. 4.2.2.2.4 Results The results of interest (shear along the 1-2 direction – representing the direction of rolling shear) are shown in Figure 4.20 along with the deformed shape. Figure 4.20: Fabric BFRP, S12 results Figure 4.20 represents the results of the model with 50 mm of embedded BFRP and epoxy as the adhesive; however results of all combinations appear similar visually. The areas of stress concentration (dark red and blue as shown here) are of primary interest – more specifically at the level where the wood meets the adhesive. However, in order to view congruent results, 52 CHALMERS Civil and Environmental Engineering, Master’s Thesis 2012:90 path lines must be taken away from material intersections. Therefore, the following results are taken at the middle of the adhesive layers in order to achieve consistent and conservative results. In order to determine the anchorage length of the BFRP in each model, a path line was drawn along the middle of the adhesive layer as previously explained and the shear in the 1-2 direction (in the x-direction, along the y-face of the element) is recorded along the length. Typical results can be