A NUMERICAL APPROACH FOR EVALUATING FIRE RESISTANCE OF FRP- STRENGTHENED PRESTRESSED CONCRETE BEAMS By Tejeswar Rayala A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of Civil Engineering – Master of Science 2025 ABSTRACT In recent years, the demand for repair and strengthening of concrete structures has been increasing due to aging infrastructure, increased service loads, changes in functional use, design deficiencies, updates in building codes, and environmental deterioration. To address these challenges, Fiber- Reinforced Polymer (FRP) composites have emerged as a popular and efficient method for strengthening concrete structures. Due to their light weight, high strength, durability against corrosion, and ease of installation, FRP composites are considered an efficient and reliable option for strengthening both reinforced and prestressed concrete elements. However, despite these advantages, FRP systems are thermally sensitive. At elevated temperatures, the polymer matrix and adhesive bonds deteriorate rapidly, leading to a significant reduction in strength, stiffness, and bond capacity. This vulnerability limits the performance of FRP-strengthened members under fire conditions. As a result, the application of FRP systems in prestressed concrete beams remains limited due to the lack of comprehensive design guidelines and experimental data related to fire exposure. To address this limitation, a rational approach is proposed for evaluating the fire resistance of FRP-strengthened prestressed concrete (PC) beams. This approach expands on conventional fire design principles for PC beams, while incorporating the effects of FRP reinforcement and fire insulation into strength calculations under fire exposure. Simplified equations are utilized to evaluate the cross-sectional temperature distribution in fire exposed FRP-strengthened PC beams, considering both uninsulated and insulated scenarios. These cross-sectional temperature profiles are then utilized to evaluate the reduction in strength of concrete, prestressing steel, and FRP based on their temperature-dependent mechanical properties. The moment capacity of the FRP- strengthened PC beams is determined at various fire exposure durations by applying force equilibrium and strain compatibility principles. The proposed approach is validated by comparing analysis results with available fire test data from FRP-strengthened reinforced concrete (RC) beams. The results show that, without supplementary fire insulation, FRP-strengthened PC beams experience a significant reduction in moment capacity early into fire exposure and can experience failure in 75 min. In contrast, with adequate fire insulation, these beams retain a substantial portion of their load-bearing capacity for up to 3 hours during fire exposure. I dedicate this work to my father, Shree Satyanarayana Rayala, and my mother, Smt. Rajyalakshmi Rayala, whose unconditional love, support, and sacrifices have been the foundation of my journey and accomplishments. I also dedicate this work to those who have lost their lives to fire-related tragedies, with the hope that this research may contribute in some way to improving safety and protecting lives in the future. iii ACKNOWLEDGMENTS I would like to express my sincere gratitude to my advisor, Professor Venkatesh Kodur, for his exceptional mentorship, unwavering support, and invaluable guidance throughout the course of my graduate studies. His deep knowledge and dedication to advancing the field of structural fire engineering have profoundly influenced my academic journey. Professor Kodur’s encouragement, constructive feedback, and commitment to excellence consistently motivated me to challenge myself and pursue my work with diligence and integrity. I am truly fortunate to have had the opportunity to learn from him, and I deeply appreciate the time and effort he invested in my academic and professional growth. I would also like to extend my sincere thanks to the members of my thesis committee, Dr. Qingxu Jin and Dr. Nizar Lajnef, for their valuable time, insightful feedback, and thoughtful suggestions that greatly contributed to shaping and refining this thesis .Furthermore, I am deeply thankful to the administrative staff of the Department of Civil and Environmental Engineering at Michigan State University for their unwavering support throughout my time at the university. In particular, I would like to acknowledge Dr. Peter Savolainen, Laura Post, Shelly Harbenski, and Bailey Weber for their consistent support and prompt assistance throughout my graduate journey. A heartfelt thanks to my friends and colleagues, Dr. Augusto Masiero Gil, Manish Kumar Sah, and Ankush Jha, whose friendship, encouragement, and countless late-night discussions provided both academic and emotional support throughout this journey. Their support, willingness to share ideas, and encouragement during tough times played an important role in making my graduate experience meaningful. Moreover, their presence has made this experience not only productive but also enjoyable and memorable. I also extend my sincere gratitude to Dr. B. Kesava Rao from R.V.R. & J.C. College of Engineering, India, whose early guidance and encouragement sparked my interest in research and laid the foundation for my academic journey. Lastly, I would like to acknowledge my parents, Satyanarayana and Rajyalakshmi, my sister, Homai, and all my family members for their unconditional love, constant encouragement, and unwavering belief in me throughout this journey. Their sacrifices, emotional support, and values have been the foundation of my personal and academic growth. Without their blessings and motivation, this achievement would not have been possible. iv TABLE OF CONTENTS CHAPTER 1 INTRODUCTION ..................................................................................................1 1.1 Background ...........................................................................................................................1 1.2 FRP Strengthening Methods for Concrete Structures ...........................................................3 1.3 Behavior of Reinforced and Prestressed Concrete Beams under Fire Exposure ..................4 1.4 Fire Resistance of FRP-Strengthened RC Beams .................................................................5 1.5 Significance of Current Research ..........................................................................................7 1.6 Methodology for Fire Resistance Evaluation ........................................................................8 1.7 Objectives ..............................................................................................................................8 1.8 Outline ...................................................................................................................................9 CHAPTER 2 STATE-OF-THE-ART REVIEW .......................................................................15 2.1 General ................................................................................................................................15 2.2 Overview of FRP Composites .............................................................................................16 2.3 Flexural Behavior of FRP-Strengthened PC Members Under Ambient Condition ............19 2.4 Properties of Materials at High Temperatures .....................................................................19 2.5 Rational Approach for Evaluating Fire Resistance of FRP-Strengthened RC Beam ..........27 2.6 Research Gaps .....................................................................................................................27 CHAPTER 3 RATIONAL APPROACH ...................................................................................39 3.1 General .................................................................................................................................39 3.2 Rational Approach for Evaluating Fire Resistance of FRP-Strengthened PC Beams ..........40 3.3 Validation of the Rational Approach ....................................................................................48 3.4 Summary ..............................................................................................................................51 CHAPTER 4 NUMERICAL STUDY ........................................................................................59 4.1 General .................................................................................................................................59 4.2 Fire Resistance of CFRP-Strengthened PC-T Beams ..........................................................59 4.3 Comparative Study on Fire Endurance of CFRP-Strengthened RC and PC Beams ............63 CHAPTER 5 CONCLUSIONS ..................................................................................................70 5.1 General .................................................................................................................................70 5.2 Limitations of Rational Approach ........................................................................................71 5.3 Key Findings ........................................................................................................................72 5.4 Recommendations for Future Work .....................................................................................73 REFERENCES ............................................................................................................................74 APPENDIX : DESIGN EXAMPLE ...........................................................................................79 v CHAPTER 1 INTRODUCTION 1.1 Background Prestressed concrete (PC) is an advanced form of construction developed to enhance the performance of traditional reinforced concrete. Introduced in the early 20th century, it involves applying internal stresses to concrete elements to partially mitigate the effects of external loading. This approach significantly improves the concrete resistance to cracking, enhances durability and service life. There are two main techniques for prestressing concrete: pre-tensioning and post- tensioning. In pre-tensioning, steel wires or tendons are stretched before concrete is poured around them. After the concrete hardens and achieves sufficient strength, the tension in the tendons is released, compressing the concrete and making it stronger and more resistant to external loads. Alternatively, post-tensioning involves placing steel tendons inside special ducts within the hardened concrete, which are then stretched and securely anchored, creating compression in the concrete. Both methods effectively strengthen the concrete by introducing beneficial compressive stresses. Prestressed concrete provides significant advantages in construction, such as higher cracking resistance, material efficiency, and the ability to span longer distances with reduced cross-sectional dimensions. These characteristics make it particularly suitable for structures like bridges, buildings, parking garages, and various infrastructure projects, resulting in cost savings and optimized space utilization. However, over time, these structures experience strength degradation caused by factors such as loss of prestress, poor maintenance, corrosion of prestressing steel strands, concrete aging, and exposure to aggressive environmental conditions. Figure 1.1 illustrates the capacity timeline of a structure, showing its gradual deterioration and the need for repair and strengthening [1]. Structural issues arise from three main causes: construction deficiencies such as design errors or missing reinforcements, external damage from impacts or fires, and functional changes that increase load-bearing requirements. As these factors continue to impact aging structures, the necessity for proactive maintenance, rehabilitation, and effective strengthening solutions becomes essential to sustain their safety, functionality, and longevity. A significant portion of infrastructure across the United States was constructed during the early to mid-20th century, leading to widespread deterioration or structures approaching the end of their 1 designed lifespan. According to the latest infrastructure assessment by the American Society of Civil Engineers (ASCE, 2021), the overall condition of the nation's infrastructure received a grade of C-, indicating a need for substantial improvements and ongoing maintenance. The report emphasizes that approximately $2.59 trillion must be invested over the next ten years to effectively rehabilitate and upgrade critical infrastructure components. Considering these challenges, it is crucial to develop feasible and cost-effective retrofitting and strengthening techniques capable of enhancing structural performance, preserving original dimensions, minimizing long-term maintenance expenses, and extending the lifespan of concrete structures. Traditional strengthening methods for concrete structures, which gained popularity in the early 2000s, include enlarging concrete sections, applying steel jackets, bonding steel plates, and using external post-tensioning with steel tendons [2 - 4], as shown in Figure 1.2. While these techniques have proven effective in enhancing structural capacity and extending service life, they present several challenges that limit their practicality. Increasing the size of concrete sections adds considerable weight and alters the original geometry of the structure, potentially affecting its functionality. Similarly, bonding steel plates and using steel jackets improve strength and stiffness but are highly susceptible to corrosion, leading to increased maintenance costs and long-term durability concerns. Additionally, these methods often require skilled workers, specialized installation processes, and extended construction time, making them less efficient for large-scale or urgent strengthening applications. In response to these drawbacks, the construction industry has increasingly shifted towards using fiber-reinforced polymer (FRP) for strengthening concrete structures. FRP composites are materials made by combining strong fibers like carbon, glass, or aramid with a polymer matrix. Originally developed in the mid-20th century, they were first used in aerospace and automotive industries because of their lightweight and high-strength properties. Over time, their use expanded to marine, defense, and eventually construction applications, where they became a reliable option for strengthening and repairing structures. FRP composites are now widely used in infrastructure projects to reinforce beams, columns, slabs, and bridges as a durable and long-lasting alternative to traditional materials. Unlike conventional strengthening methods that add weight or require extensive modifications, FRP provides an effective solution without significantly altering the structure. Its high strength-to-weight ratio, resistance to corrosion, and 2 easy installation make it a practical choice for improving structural performance while preserving the original design [5]. 1.2 FRP Strengthening Methods for Concrete Structures Strengthening of concrete structures using FRP is primarily achieved through externally bonded (EB) FRP and near-surface mounted (NSM) FRP techniques. These methods are widely implemented to enhance flexural and shear strength, leading to improved structural performance under increased loading conditions or material degradation. The choice of the appropriate strengthening method depends on factors such as structural needs, environmental conditions, and the extent of required reinforcement. Flexural strengthening is typically required in beams and slabs subjected to excessive bending stress due to increased load demands, structural aging, or design modifications. This can be achieved through both EB FRP and NSM FRP techniques, as illustrated in Figure 1.3 and Figure 1.4. In EB FRP strengthening, FRP sheets or laminates are attached to the tension face of concrete elements using adhesive resins, effectively increasing their load-carrying capacity. The bonded FRP layers serve as additional reinforcement, reducing tensile stresses and improving flexural strength. However, the effectiveness of this method largely depends on proper surface preparation and adhesive bonding, as inadequate adhesion can lead to premature debonding. Although EB FRP is easy to apply, its exposure to environmental conditions such as moisture, temperature variations, and mechanical impact may affect long-term performance. Alternatively, NSM FRP strengthening is a technique where FRP bars or strips are embedded into shallow grooves cut into the concrete surface and secured with adhesive. This approach provides better protection against environmental exposure and mechanical damage compared to externally bonded FRP, as the reinforcement is embedded within the structure rather than exposed. NSM FRP provides improved bond performance and a more effective transfer of stress between the FRP and the concrete substrate. As a result, it is often preferred for applications requiring long- term durability and higher resistance to external factors. Shear strengthening is another important application of FRP reinforcement, mainly used in beams and columns to enhance resistance against shear forces. This is achieved by attaching FRP laminates to the sides of structural members in vertical, inclined, or U-wrap configurations. These FRP sheets help control crack propagation and improve shear strength by confining the concrete and redistributing stresses. The effectiveness of shear strengthening depends on the placement and 3 orientation of the FRP laminates, ensuring optimal resistance against shear failure. In addition, the use of U-wrap configurations in beams and columns provides additional confinement, further enhancing the overall load-carrying capacity. 1.3 Behavior of Reinforced and Prestressed Concrete Beams under Fire Exposure Beams are essential structural elements that transfer loads from floor systems to columns and form a critical part of a building's load-resisting system. When exposed to fire, the structural performance of both RC and PC beams is significantly affected due to the increase in temperature within the section. The rise in temperature within these beams occurs through a combination of convective and radiative heat transfer from the surrounding environment and conductive heat flow within the concrete mass. The extent of heat penetration depends on the thermal properties of the materials, such as thermal conductivity, specific heat, and density of both concrete and reinforcement. As these properties change notably at elevated temperatures, they lead to highly uneven and nonlinear temperature distributions within the cross-section of beam during fire exposure. Although RC and PC beams differ in design and load-resisting mechanisms, their thermal response under fire is generally similar, as both utilize concrete and steel materials that have comparable thermal behavior. However, their mechanical performance under high temperatures differs considerably due to the distinct roles of reinforcement in each system. As the temperature increases, the mechanical properties of concrete and steel degrade. Concrete experiences a reduction in stiffness and compressive strength due to moisture loss, microcracking, and thermal expansion. Steel reinforcement, whether conventional rebars in RC beams or high-strength prestressing strands in PC beams, also suffers a loss of yield strength and elastic modulus as the temperature rises. In RC beams, the steel reinforcement typically degrades at a slower pace. With adequate concrete cover, the steel remains insulated for a longer period, allowing the beam to retain some load-bearing capacity even as the fire continues. Consequently, RC beams tend to show a more gradual decline in strength and increased deflection over time, which may provide warning signs before failure occurs. In contrast, PC beams respond more critically under fire conditions. The high-strength prestressing strands used in these beams are more sensitive to heat, losing about 54% of their yield strength at 400°C and nearly 90% at 600°C. Although the modulus of elasticity 4 decreases more gradually than in conventional rebars, the rapid strength loss in prestressing steel severely reduces the structural capacity of PC beams, as illustrated in Figure 1.5. The deflection behavior of PC and RC beams under fire conditions demonstrates a clear difference in their structural behavior as the fire progresses. As shown in Figure 1.6, both beams initially demonstrate similar deflection responses during the first 50 minutes of fire exposure. This early similarity is due to the comparable thermal behavior of concrete and steel reinforcement at moderate temperatures. However, beyond this point, the deflection in the PC beam begins to rise rapidly, leading to failure at approximately 112 minutes. In contrast, the RC beam shows a slower, more gradual increase in deflection and withstands fire exposure for a significantly longer duration, ultimately failing at around 212 minutes. The earlier failure of the PC beam is primarily due to the rapid degradation of prestressing strands when exposed to elevated temperatures. As the reinforcement temperature approaches 400°C, the strands begin to lose their yield strength much faster than the conventional rebars used in RC beams. Since PC beams rely on the initial prestressing force to resist applied loads and control deflections, this rapid loss of strength leads to a sharp decline in structural capacity. Additionally, PC beams are more prone to concrete spalling, which can expose the prestressing steel directly to fire, accelerating its deterioration. On the other hand, RC beams, with slower degrading reinforcement and typically greater concrete cover, can retain their load-carrying capacity for a longer period, resulting in a more stable deflection profile under the same fire conditions. Since PC beams are highly vulnerable to rapid strength and stiffness loss during fire, they require special attention in design, detailing, and fire protection to ensure adequate structural safety. 1.4 Fire Resistance of FRP-Strengthened RC Beams The fire resistance of RC beams strengthened with FRP mainly depends on the behavior of the materials when exposed to high temperatures. This includes the thermal degradation of concrete, steel reinforcement, and particularly FRP composites. While concrete and steel reinforcement generally maintain their properties better under fire conditions due to their high heat capacity and slower rate of degradation, FRP materials are much more vulnerable. The poor performance of FRP at elevated temperatures is mainly due to the nature of the polymer matrix, which begins to soften and degrade beyond its glass transition temperature (𝑇𝑔), typically in the range of 80°C to 5 150°C. Once this threshold is exceeded, both the mechanical properties of FRP and its bond with concrete deteriorate rapidly. During fire exposure, the bending capacity of FRP-strengthened and un-strengthened RC beams shows distinct behavior over time, as illustrated in Figure 1.7. Both beams are subjected to 50% of their original load-bearing capacity at ambient temperature. The FRP-strengthened beam initially supports a greater load due to the contribution of the FRP, but its capacity begins to decrease rapidly as temperatures rise. This is primarily due to the loss of strength in the FRP material and the weakening of the adhesive bond with the concrete. In contrast, the un-strengthened RC beam retains its capacity for a longer duration, showing a slower and more gradual decline in performance, which is due to the low thermal conductivity and higher thermal stability of concrete and steel reinforcement during fire exposure. As fire exposure continues, the FRP-strengthened beam experiences a sharp decline in performance, failing much earlier than its un-strengthened beam. The rapid softening of the polymer matrix in FRP, combined with the temperature-induced breakdown of epoxy adhesives, leads to debonding and loss of composite action. Once the bond strength falls below the applied shear stress at the interface, effective stress transfer is no longer possible, and the FRP no longer contributes to the beam’s capacity. As a result, even though the beam was originally designed to carry a higher load, it fails sooner due to the inability of the degraded FRP to sustain the applied moment. This highlights the need for fire protection measures if FRP systems are to be used in applications where fire exposure is a concern. To address this issue, external fire insulation is usually recommended. Protective insulation delays the rise in temperature at the FRP-concrete interface, which helps to maintain both the mechanical strength of the FRP and the adhesive bond [6-8]. However, achieving sufficient insulation effectiveness is challenging. A thin layer may not provide adequate protection, while an overly thick layer can delaminate due to its own weight, leaving the beam exposed. Even with fire insulation, maintaining interface temperatures below 𝑇𝑔 for extended fire durations remains challenging. Over time, the effectiveness of the FRP system is lost, and the beam performs as an un-strengthened RC member under continued fire exposure. This emphasizes the need for careful consideration of insulation type, thickness, and application technique to ensure sufficient fire resistance. Extensive experimental and numerical research has enhanced the understanding of FRP- strengthened RC beams under fire and led to effective design strategies. However, there is limited 6 research on the fire resistance of FRP-strengthened PC beams, highlighting the need for further investigation in this area. 1.5 Significance of Current Research PC beams are widely used in buildings, bridges, parking structures, and other infrastructure due to their high efficiency. In recent years FRP composites have become a popular method for strengthening deteriorated PC elements. However, the fire performance of these strengthened systems is a growing concern. Both FRP materials and prestressing tendons are extremely susceptible to elevated temperatures. Under fire conditions, the polymer matrix in FRP systems deteriorates, leading to a severe loss of strength, stiffness, and bond with the concrete surface. Likewise, prestressing steel also experiences a decline in mechanical performance when subjected to high temperatures, which affects the beam's ability to maintain its designed load-carrying capacity. Since both prestressing tendons and FRP composites are vulnerable to high temperature, their combined use in PC beams poses significant challenges under fire conditions. The simultaneous degradation of the FRP strengthening system and the loss of prestressing steel strength can lead to an excessive loss in the flexural capacity of the beam when it is subjected to fire. This loss compromises structural stability and may cause premature failure, particularly in load-carrying elements that rely heavily on both prestress and external strengthening for performance. The situation is even worse when there is no adequate fire protection system, as the heat can easily reach the tendons and the FRP layer, degrading both components within a short period. Despite these concerns, research specifically addressing the fire resistance of FRP- strengthened PC beams remains limited. The majority of the current studies have focused on the performance of such beams under ambient conditions, focusing primarily on load-deflection behavior, crack control, and long-term durability. These studies have demonstrated the effectiveness of FRP in enhancing flexural and shear capacities, but they do not capture the complex interaction between thermal degradation and structural performance during fire exposure. As a result, there is a lack of experimental and analytical data that can guide the safe use of FRP in prestressed systems subjected to elevated temperatures. To fill this gap, further research is required to evaluate the fire resistance of FRP-strengthened PC beams. This includes understanding failure mechanisms, evaluating residual capacity after fire exposure, and determining the effectiveness of protective strategies. Such studies are essential for developing 7 fire-safe design practices and updating building codes to ensure the reliable use of FRP in prestressed concrete structures exposed to fire. 1.6 Methodology for Fire Resistance Evaluation The fire resistance of FRP-strengthened PC structural elements is normally established following the prescribed standardized test procedure such as ASTM E119 [9] or ISO 834 [10]. However, these testing methods come with several practical limitations. Challenges include constraints related to testing equipment, loading mechanisms, specimen dimensions, and the availability of sensors capable of measuring critical response parameters under elevated temperatures. Furthermore, conducting fire resistance tests is expensive, time-consuming, and labor-intensive. Being the limitations, it is not feasible to experimentally evaluate a wide range of FRP-strengthened concrete flexural members with varying insulation configurations, thicknesses, and applied load levels through fire testing. Current design guidelines for FRP-strengthened PC structures contain strength-calculating equations intended for ambient conditions. However, these standards lack specific equations or methodologies for assessing fire resistance. It generally advises ignoring the FRP's contribution during fire exposure and suggests using the fire resistance of an un-strengthened PC member. To overcome these limitations, recent studies by Kodur and Yu (2016) [11], and Gao et al. (2018) [12], have proposed simplified design methods for predicting the fire performance of FRP- strengthened reinforced RC beams. These methods consider key factors that affect fire resistance. The current research builds upon the rational approach previously developed for FRP-strengthened RC beams, extending its application to evaluate the fire resistance of FRP-strengthened PC beams. The study specifically focuses on analyzing PC beams strengthened with externally bonded (EB) FRP systems. 1.7 Objectives Based on the above discussion, it is clear that a more comprehensive understanding of FRP- strengthened PC beam behavior is needed under fire conditions, both at the material level and within the structural system. To address this need, the present study develops a simplified approach for evaluating the fire resistance of FRP-strengthened PC beams exposed to elevated temperatures. The specific objectives of this study are listed below: • Conduct a comprehensive state-of-the-art review on the high-temperature behavior of FRP materials, including their strength and stiffness, as well as the thermal and mechanical 8 properties of prestressing steel. Additionally, explore the fire response of FRP-strengthened reinforced RC beams to develop a clear understanding of their performance under elevated temperature. • Develop a rational approach and validate it using the FRP-strengthened RC beam through FEA results and extend this approach to evaluate the fire resistance of FRP-strengthened PC beams. • Develop a fire protection strategy through the application of thermal insulation on FRP- strengthened PC beams, compare the fire performance with that of uninsulated beams, and conduct a parametric study to identify the effective insulation thickness required to achieve the desired level of fire resistance. • Recommend strategies to enhance the fire resistance of FRP-strengthened PC beam and demonstrate the rational approach application through a detailed design example of a typical FRP-strengthened PC beam. 1.8 Outline This thesis is structured into five main chapters, each addressing a critical component of the research. Chapter 1 provides an introduction to the study, outlining the background, motivation, objectives, and methodology, along with the overall significance of evaluating the fire resistance of FRP-strengthened prestressed concrete (PC) beams. Chapter 2 presents a comprehensive review of the existing literature related to the thermal and mechanical behavior of constituent materials such as concrete, prestressing steel, and FRP composites at elevated temperatures. It also discusses the flexural performance of FRP-strengthened PC beams under ambient conditions and highlights existing research gaps, with particular attention to the limitations of current fire resistance design methods. Chapter 3 introduces a rational approach developed to evaluate the fire resistance of FRP-strengthened PC beams. This chapter explains the step-by-step methodology, including cross- sectional temperature analysis, effective concrete width estimation, and calculation of moment capacity under fire exposure, followed by validation of the approach using available test data and numerical results. Chapter 4 applies the rational approach in a detailed parametric study that investigates the fire resistance performance of CFRP-strengthened PC-T beams under different configurations. This chapter also includes a comparative study between CFRP-strengthened RC and PC beams to better understand their relative performance under fire. Chapter 5 summarizes the key conclusions drawn from the study, identifies practical limitations of the rational approach, 9 and provides recommendations for future research. The document concludes with a design example illustrating the application of the proposed method to a CFRP-strengthened PC beam with fire insulation. 10 Figures Figure 1.1: Repair/Strengthening philosophy [1] horseen.com/steel-plate-bonding theconstructor.org/jacketing freyssinet.co.uk/post-tensioning horseen.com/enlargement-section Figure 1.2: Various strengthening techniques for concrete structures (a) steel plate strengthening, (b) steel jacketing, (c) external post-tensioning, (d) concrete section enlargement 11 constrofacilitator.com/frp-repair structuremag.org/frp-strengthening Figure 1.3: EB FRP strengthening: (a) schematic of EB FRP beam layout, (b) cross-section of flexural strengthening in T-beam, (c) cross-section of shear strengthening in T-beam, (d) application of EB FRP on beam, (e) U-wrap FRP for shear strengthening 12 Figure 1.4: NSM FRP strengthening: (a) NSM FRP layout in beam, (b) cross-section of flexural strengthening with NSM FRP strips, (c) cross-section with NSM FRP rods Figure 1.5: Temperature-dependent reduction in strength and modulus of prestressing strands and steel rebars [13] 13 Figure 1.6: Time-dependent deflection behavior of PC and equivalent RC beams under fire exposure [13] Figure 1.7: Comparison of moment capacity between un-strengthened and FRP-strengthened reinforced concrete beams under fire exposure [73] 14 CHAPTER 2 STATE-OF-THE-ART REVIEW 2.1 General The development of fiber-reinforced polymer (FRP) composites began in the early 20th century, with significant progress made in the 1930s when glass fibers were combined with synthetic resins. During World War II, FRP was mostly used in military and aerospace applications since it was very strong and resistant to corrosion. In the following decades, especially from the 1950s to the 1970s, FRP became popular in industries such as automotive, marine, and manufacturing. It was commonly used in products like boat hulls, automobile parts, and industrial containers. The construction industry started using FRP in the 1970s, mostly for non-structural purposes, such as architectural panels, cladding, and other decorative elements. Its resistance to environmental damage made it especially suitable for harsh conditions. In the 1980s and 1990s, attention shifted to its use in structural applications, especially for strengthening and repairing reinforced concrete structures that had deteriorated due to age, corrosion, or increased loading demands. During this time, externally bonded FRP systems were developed to improve the flexural and shear performance of concrete beams, columns, and slabs. By the 1990s, there were several successful strengthening projects using FRP were completed in countries such as Japan, the United States, and in Europe. These projects demonstrated the effectiveness of FRP in real-world applications, leading to increased research and the creation of design guidelines, including ACI 440 in the United States and FIB bulletin 14 in Europe. These guidelines encouraged the safe and reliable use of FRP in construction. In the 2000s, advancements in materials and installation techniques further improved FRP systems, including the use of carbon, aramid, and basalt fibers, as well as better bonding methods and anchorage systems. Despite significant advancements and widespread use in structural applications, the performance of FRP composites under fire remains a major concern. FRP materials are sensitive to high temperatures, which can reduce their effectiveness and may create safety concerns. Over the past few decades, researchers have conducted numerous studies to investigate the behavior of FRP at elevated temperatures, both in structural applications and at the material level. These studies have increased understanding about the way fire influences the mechanical properties of FRP and the performance of FRP-strengthened members. 15 This chapter provides a comprehensive review of existing research related to the behavior of FRP composites and FRP-strengthened prestressed concrete members under fire conditions. It begins with an overview of FRP composites, including their constituent materials such as fibers and resins, and discusses their typical applications in structural engineering. The chapter then examines the flexural behavior of FRP-strengthened prestressed concrete members under ambient conditions. Following this, it presents a detailed review of the temperature-dependent properties of key materials involved in these systems, including concrete, prestressing steel, FRP composites, and fire insulation materials. The chapter also outlines a rational approach for evaluating the fire resistance of FRP-strengthened members and highlights its advantages over conventional design methods. In conclusion, the chapter identifies the main gaps in current literature and emphasizes the need for further research to ensure the safe and efficient application of FRP in fire-exposed structures. 2.2 Overview of FRP Composites Fiber-Reinforced Polymer (FRP) composites are engineered materials made by combining high-strength fibers with a polymer matrix. The fibers, which are typically made from materials such as carbon, glass, or aramid, provide the composite with tensile strength and stiffness. The polymer matrix, commonly epoxy, vinyl ester, or polyester, holds the fibers in place, facilitates load transfer, and protects the material from environmental effects. Together, these components form a lightweight and durable material with a high strength-to-weight ratio and excellent resistance to corrosion. These characteristics make FRP composites suitable for a wide range of structural applications in industries such as construction, aerospace, automotive, and marine. 2.1.1 Constituent Materials: Fibers and Resins Fiber Reinforced Polymer (FRP) materials are commonly classified into four main types based on the type of fiber used: carbon fiber reinforced polymer (CFRP), glass fiber reinforced polymer (GFRP), basalt fiber reinforced polymer (BFRP), and aramid fiber reinforced polymer (AFRP), with AFRP being the least frequently used. Among these, CFRP is the most widely used due to its superior strength, stiffness, and lightweight characteristics, making it highly suitable for strengthening and retrofitting applications in structural engineering. Carbon fibers, typically 5–10 µm in diameter, have a crystalline structure aligned along their length, which contributes to their remarkable strength-to-weight ratio and modulus similar to steel [15,16]. Although CFRP is more expensive than traditional materials, its reduced weight (about 50–60% less than steel) can lead to 16 overall cost advantages in structural applications [17]. CFRP also offers excellent performance under sustained and cyclic loads, showing minimal strain over extended durations [18]. It is commonly used to retrofit and strengthen deficient structures, helping to improve load capacity and stiffness without requiring complete replacement of damaged structure [16]. Additionally, CFRP materials are available in various configurations such as sheets, strips, laminates, and bars, offering flexibility for different design requirements. However, one major drawback of CFRP is its high cost compared to other FRP types, which can limit its use in projects where budget constraints are a concern. BFRP is a composite material composed of basalt fibers, typically ranging from 10 to 20 µm in diameter, embedded within a polymer matrix. These fibers are produced from volcanic rock containing minerals such as plagioclase, pyroxene, and olivine [19-21]. BFRP is considered a lower-cost option compared to CFRP [22] and is characterized by its tensile strength, resistance to alkaline environments, and ability to function in various environmental conditions. The polymer matrix supports its strength retention and thermal properties, while the stiffness of the material depends on the composition and structure of the individual basalt fibers. Strength retention studies show that BFRP can maintain between 71% and 92% of its strength over a 50-year period in dry, moist, and saturated environments with typical annual temperatures between 5 °C and 35 °C [23]. It is suitable for use in structural reinforced concrete elements and automotive components, especially when combined with epoxy, due to its strength and flexibility [23-25]. However, BFRP has a relatively lower tensile modulus compared to CFRP, which can lead to a more brittle response after reaching peak strength [26]. GFRP is a composite material composed of glass fibers embedded within a polymer matrix, with fiber content typically ranging from 0.5% to 2.0% by weight [27]. The presence of glass fibers significantly improves the mechanical properties of the plastic matrix, particularly in terms of strength and stiffness [28], as illustrated in Table 2.1. GFRP has been in use within the civil engineering sector since the 1930s, primarily due to its economic feasibility and widespread availability [29]. The performance of GFRP composites depends on several factors, including the type of polymer matrix, fiber volume, fiber orientation, and the quality of the bond between the fibers and the matrix [30]. GFRP exhibits good resistance to environmental conditions, chemicals, heat, and saline exposure, and has a relatively high strength-to-weight ratio, typically ranging between 9.67 to 19.52 kg/m². It is also known for its insulating properties and affordability, making 17 it suitable for use in a variety of applications. Studies have indicated that the creep strain of GFRP can range from 0.3% to 1%, while increases in plate thickness beyond 6.35 mm [31], when combined with proper anchorage at the ends, can improve its strength by up to 100%. Additionally, the application of externally bonded GFRP sheets has been shown to extend the fatigue life of reinforced concrete beams under cyclic loading [18]. GFRP is commonly used in secondary structural applications such as bridge components, domes, building frames, and masonry walls. Its primary advantage lies in its low cost compared to other fiber-reinforced polymers. However, a notable limitation is its relatively low tensile modulus, which makes it unsuitable for use as primary reinforcement in load-bearing structural members [32]. AFRP is a composite material made from synthetic fibers that provide high mechanical and thermal performance. The polymer chains in aramid fibers are arranged in an organized structure, which contributes to their high tensile strength, stiffness, and resistance to heat [33,34]. AFRP has a lower density than many other fiber-reinforced materials, approximately 40% less than that of glass fiber GFRP, as illustrated in Table 2.1. It also offers better resistance to alkaline environments and is generally more economical than CFRP in certain applications [20]. Studies show that AFRP performs well under cyclic loading, with a strength reduction of around 13%, which is lower compared to other FRP types. The creep strain of AFRP typically ranges between 0.15% and 1%, indicating that it maintains dimensional stability under long-term loading [34]. Despite these advantages, the use of AFRP in heavily loaded structural elements is limited due to its low compressive strength [15,35]. Moreover, aramid fibers can degrade when exposed to ultraviolet (UV) light unless they are coated properly [36]. Therefore, AFRP is primarily applied in situations that require high tensile strength and where compressive stresses are minimal. In FRP composites, the resin plays a crucial role by acting as the matrix that binds the reinforcing fibers and transfers stress between them. This component significantly influences the overall mechanical and thermal behavior of the composite. The most commonly used types of resins in FRP systems are thermosetting and thermoplastic polymers [24]. Thermosetting resins, such as epoxy, vinyl ester, and polyester, are more commonly used in civil engineering applications because they offer better thermal stability, chemical resistance, and reduced creep and stress relaxation [15], see Table 2.2. These characteristics make them suitable for structural applications where long-term performance is essential. On the other hand, thermoplastic resins tend to have lower resistance to heat and creep, which limits their effectiveness in structural environments. 18 2.3 Flexural Behavior of FRP-Strengthened PC Members Under Ambient Condition The application of FRP composites for strengthening PC members has gained significant attention due to their high strength-to-weight ratio, corrosion resistance, and ease of installation. These advantages make FRP systems particularly attractive for the rehabilitation and retrofitting of existing prestressed structures. Several experimental investigations have been conducted to evaluate the flexural behavior of FRP-strengthened PC members under ambient conditions. Hassan and Rizkalla (2002) [37] conducted experimental studies on the strengthening of prestressed bridge slabs using five different FRP systems, including near-surface mounted (NSM) bars and externally bonded CFRP laminates. Their findings indicated that CFRP reinforcement effectively increased the stiffness and enhanced the ultimate load-carrying capacity of the slabs by up to 50%. Similarly, Rosenboom et al. (2006, 2007) [1,38] carried out experimental testing on prestressed concrete bridge girders and reported up to a 73% improvement in flexural capacity due to CFRP strengthening, while maintaining adequate ductility. Moreover, the application of CFRP was shown to significantly reduce crack spacing and crack widths, with crack widths decreasing by as much as 400% when compared to un-strengthened girders (See Figure 2.3). Furthermore, De Waal et al. (2017) [39] carried out an experimental study on the strengthening of 60-year-old PC bridge deck units using adhesively bonded CFRP plates. The results demonstrated a 10% increase in load capacity at the serviceability limit and a 54% improvement in ultimate strength. Subsequently, Di Ludovico et al. (2010) [40] experimentally tested five full- scale PC girders with varying levels of tendon damage and CFRP strengthening. The study found that 17% and 33% strand loss led to 20% and 26% reductions in flexural capacity, respectively. CFRP laminates with U-wrap anchorage restored up to 16% of capacity but resulted in brittle failure. These experimental findings confirm the significant benefits of CFRP systems in restoring and enhancing the flexural performance of prestressed concrete elements. However, there remains a noticeable gap in research concerning the behavior of such strengthened members when exposed to elevated temperatures. 2.4 Properties of Materials at High Temperatures The fire resistance of FRP-strengthened PC structural members is primarily influenced by the thermal and mechanical properties of the constituent materials, as well as the bond behavior at the FRP–concrete interface. Thermal properties, including thermal conductivity, specific heat, and density, play a critical role in governing heat transfer through the cross-section. Thermal 19 conductivity controls the rate at which heat is conducted through materials; specific heat determines the amount of energy required to raise the temperature of a unit mass; and density affects the thermal inertia of the material. Together, these properties influence the temperature distribution and thermal gradients that develop during fire exposure. Mechanical properties, including tensile strength and elastic modulus, are essential in determining a material's ability to resist applied loads and maintain structural integrity under elevated temperatures. The tensile strength indicates the maximum stress a material can withstand before failure, while the elastic modulus reflects its stiffness and ability to deform under load. In addition, the bond between the FRP and concrete governs the efficiency of stress transfer between materials, significantly impacting the overall performance of the strengthened system. These thermal, mechanical, and bond-related characteristics are all highly sensitive to temperature and undergo considerable changes when exposed to fire. The temperature-dependent behavior of concrete, prestressing steel, FRP, and insulation materials is discussed in detail in the following sections. 2.4.1 Concrete Concrete is a non-combustible and heterogeneous material composed of cement, coarse aggregates, fine aggregates such as sand, water, and various admixtures like plasticizers. The behavior of each constituent changes when subjected to elevated temperatures, leading to complex thermo-physical responses in the material. As concrete is heated, it undergoes a series of physical and chemical transformations that influence its overall properties. These changes are largely dependent on the type and proportion of materials used in the mix. Extensive research has been conducted to understand the variation of concrete’s thermal and mechanical properties under high- temperature conditions. Several empirical models have also been proposed in technical literature and standards, such as the ASCE manual [41]and Eurocode 2 [42], to represent these temperature- dependent changes. These models typically categorize concrete based on aggregate type (e.g., siliceous, carbonaceous, or lightweight) or concrete strength (normal-strength concrete, NSC; or high-strength concrete, HSC). The ASCE manual provides relations specifically for NSC with compressive strength less than 50 MPa, whereas Eurocode 2 includes formulations suitable for both NSC and HSC with compressive strength exceeding 70 MPa. As FRP strengthening is most often applied to NSC elements in structural applications, the focus here is primarily on evaluating the high-temperature properties of NSC incorporating siliceous and carbonaceous aggregates. 20 The thermal properties of concrete, primarily thermal conductivity and specific heat, significantly affect the temperature rise within concrete flexural members exposed to elevated temperatures. Over recent decades, various studies [43-50] have investigated these properties experimentally, and considerable variability exists in the reported data due to differences in testing methodologies and measurement techniques [51]. Despite such variations, it is generally agreed that the thermal properties depend primarily on the type of coarse aggregate used, such as siliceous, carbonate, or lightweight aggregates. Additionally, the concrete strength and moisture content influence these thermal characteristics. Empirical relationships for the temperature-dependent thermal properties of concrete have been presented in standards such as Eurocode 2 and the ASCE manual. Figure 2.4 compares the thermal conductivity variations provided by these standards. Siliceous aggregate concrete initially exhibits higher thermal conductivity, which decreases rapidly as temperature increases, while carbonate aggregate concrete starts with lower thermal conductivity and experiences a gradual reduction with rising temperature. Lightweight aggregate concrete maintains relatively stable thermal conductivity values over a broad temperature range. Similar differences are evident in the specific heat relations provided by both standards, as illustrated in Figure 2.5. Eurocode 2 presents a single conservative relationship for siliceous and carbonate aggregates and explicitly considers moisture content. In contrast, the ASCE manual provides separate relationships based on aggregate types, notably capturing a significant rise in specific heat between 600°C and 800°C associated with endothermic reactions in carbonate aggregates. Apart from this temperature range, specific heat values across different aggregate types remain similar, except near 700°C, where carbonate aggregates have higher values. Overall, concrete with carbonate aggregates, characterized by a higher specific heat and lower thermal conductivity, is generally recommended for improved fire resistance performance [51]. The mechanical properties of concrete, including compressive strength, tensile strength, elastic modulus, and stress-strain behavior, are significantly affected by temperature. These properties directly influence the fire resistance of FRP-strengthened prestressed concrete flexural members. Compared to thermal characteristics, temperature effects on mechanical properties have been more extensively studied. Consequently, a considerable amount of data is available for normal strength concrete (NSC) made with various aggregate types. Figure 2.6 presents the normalized variation of compressive and tensile strength of NSC with temperature. Experimental results show considerable variation, which is attributed to differences in heating rates, loading conditions, 21 testing procedures, specimen age, curing method, and moisture content. Several researchers have developed constitutive models to describe compressive strength degradation with temperature [51]. Among these, the ASCE Manual [41] and Eurocode 2 [42] are the most widely accepted. According to Figure 2.6, there is minimal reduction in compressive strength up to 300°C. Beyond 400°C, strength declines rapidly due to structural changes within the concrete. The ASCE model generally reflects the upper range of test data, while Eurocode 2 represents the lower range. A key distinction is that the ASCE model does not consider the effect of aggregate type. Despite this, numerical studies indicate that both models provide conservative estimates of fire resistance, with the ASCE model offering better predictive accuracy. Tensile strength also decreases with rising temperature, although fewer studies are available compared to compressive strength. It is generally accepted that tensile strength deteriorates more rapidly, particularly below 400°C. Eurocode 2 is the only standard that provides a relationship for this degradation, as illustrated in Figure 2.6. It shows a linear decrease in tensile strength beyond 100°C. Figure 2.7 illustrates the normalized reduction in elastic modulus for concrete with different aggregates. Unlike compressive strength, the elastic modulus begins to decline immediately with increasing temperature. For both siliceous and carbonate aggregates, it reduces by approximately 50 to 60 percent from its value at room temperature. Carbonate-based concrete shows slightly better retention, likely due to greater thermal resistance of the aggregates. Lightweight concrete exhibits slower deterioration, which is possibly due to lower aggregate content and reduced internal voids. 2.4.2 Prestressing Steel The proportion of prestressing steel in a prestressed concrete member is relatively small when compared to the total cross-sectional area of the concrete. Consequently, the thermal properties of prestressing steel have limited effect on the overall temperature distribution within the structural member during fire exposure. However, the mechanical behavior of prestressing steel at elevated temperatures is a critical factor influencing the fire resistance of prestressed concrete elements, especially in flexural applications. Prestressing steel exhibits significant changes in its mechanical characteristics when subjected to high temperatures, including reductions in strength, stiffness, and prestressing force due to thermal relaxation. These changes can compromise the structural integrity and serviceability of prestressed members under fire conditions. As a result, considerable research has been carried out to examine the high-temperature performance of prestressing steel. Studies 22 have focused on key aspects such as the variation of yield and ultimate strength, modulus of elasticity, and the rate of stress relaxation with increasing temperature. At room temperature, the thermal properties of prestressing steel, such as thermal conductivity and specific heat, are mainly influenced by the type and composition of the steel. As the temperature rises, these properties become more dependent on the temperature the steel reaches during exposure. Since steel is a good heat conductor, prestressing tendons allow heat to spread quickly along their length, much faster than in concrete. However, because the cross-sectional area of prestressing steel is relatively small compared to that of the surrounding concrete, its impact on the overall temperature rise of the structural member is minimal. Figure 2.8 shows the variation in thermal conductivity and specific heat of prestressing steel with temperature, based on ASCE guidelines [41]. Thermal conductivity decreases almost linearly up to about 800°C and remains fairly constant afterward up to 1000°C. On the other hand, specific heat increases gradually with temperature and shows a sharp peak between 700°C and 800°C. This peak is caused by the phase change in the steel. After this point, specific heat reduces slightly and remains approximately stable. The mechanical properties of prestressing steel, particularly ultimate tensile strength and modulus of elasticity are critical in determining the performance of prestressed concrete structures. Under normal conditions, prestressing steel exhibits a high level of strength and stiffness, with a linear elastic behavior up to failure and no distinct yield point. However, these mechanical properties are highly susceptible to degradation when exposed to elevated temperatures. Recent research has shown that high temperatures can significantly reduce both the strength and stiffness of prestressing steel, leading to early material failure and a reduction in structural capacity. For example, Hou et al. (2014) conducted experimental studies and reported that prestressing steel undergoes approximately a 50% reduction in tensile strength between 300°C and 500°C, resulting in early failure and a significant decrease in load-bearing capacity. In a similar context, Shakya and Kodur (2016) [52] conducted a comprehensive experimental study to examine the mechanical properties of low relaxation seven-wire prestressing strands under elevated temperatures ranging from 20°C to 800°C. Their results demonstrated that prestressing strands experience a greater reduction in strength compared to conventional reinforcing bars throughout the tested temperature range. When subjected to an initial stress of 50%, the rate of strength degradation increased slightly beyond 450°C. Additionally, the rupture strain remained 23 largely unchanged up to 200°C but decreased between 200°C and 500°C due to blue brittleness. Beyond 500°C, rupture strain increased significantly as a result of enhanced ductility. The influence of initial stress on yield and ultimate strength was minimal up to 450°C but became more significant at higher temperatures due to thermal creep effects. Furthermore, Zhang Li, et al. (2017) [53] conducted an experimental study to examine the mechanical properties of prestressing steel at high temperatures and after cooling. Central wires from seven-wire strands were tested for more reliable results, along with strands recovered from fire-tested concrete slabs. The study used grade 1860 strands based on Chinese and British standards. Findings showed that Young’s modulus mostly recovers after cooling, while yield and ultimate strength undergo permanent reduction. Greater strength loss was observed in fire-exposed strands, likely due to corrosion and uneven heating. Empirical formulas were proposed to predict property degradation. Figure 2.9 illustrates the temperature-dependent mechanical properties of low relaxation prestressing steel, as specified in Eurocode 2. The figure includes data for cold-worked (cw) strands, classified into Class A and Class B, as well as quenched and tempered (q & t) strands. In the comparison, it is evident that cold-worked prestressing steel in both Class A and Class B exhibits a faster reduction in strength with increasing temperature compared to quenched and tempered steel. This difference in degradation behavior can be due to the manufacturing process. Cold-worked steel is strengthened through plastic deformation at room temperature, which improves strength but also introduces residual stresses and microstructural changes that reduce its thermal stability. In contrast, quenched and tempered steel undergoes a heat treatment process that results in a more stable microstructure at elevated temperatures, providing better resistance to thermal softening. This factor adjusts the mechanical properties relative to their original values at ambient temperature, allowing for a consistent comparison across material types and conditions. Although numerous studies have developed constitutive models to describe the degradation of strength and stiffness of prestressing steel under high temperatures, Eurocode 2 reduction factors are widely adopted for evaluating the fire resistance. For this current study, Class B cold-worked prestressing steel was used for evaluating the fire resistance of prestressed concrete beams. 2.4.3 FRP Composites FRP composites are widely used in structural, aerospace, and marine applications due to their high strength-to-weight ratio and excellent resistance to corrosion. These materials are composed of various combinations of fibers and polymer matrices, and even minor changes in their 24 composition can significantly affect their behavior at elevated temperatures. As a result, the thermal and mechanical performance of FRP composites can vary considerably across different products. Due to this variability, it is challenging to review all forms of FRP materials in a single study. Therefore, the present review focuses specifically on the high-temperature behavior of selected carbon fiber-reinforced polymer (CFRP) composites. Since CFRP is one of the most commonly used FRP types in structural strengthening applications, its thermal and mechanical properties under elevated temperatures are discussed in the following The thermal properties of FRP composites, such as thermal conductivity and specific heat, change significantly at elevated temperatures. These properties are important for evaluating the fire resistance of prestressed concrete members strengthened with FRP. However, there is limited research specifically focused on the thermal behavior of CFRP under high-temperature conditions. Figure 2.10 presents experimental data on thermal conductivity and specific heat of FRP reported by various researchers. Griffis et al. (1981) [54] observed a continuous decrease in thermal conductivity with increasing temperature, extending up to 800°C. In contrast, other studies, including those by Miller and Weaver (2003) [55], Scoot and Beck (1992) [56], and Sweeting and Liu (2004) [57], reported values only up to 200°C, with slight increases or stable trends. These differences are mainly due to variations in polymer matrices, fiber types, orientations, and volume fractions used in each test. Most tests were stopped below 200°C to avoid polymer decomposition. The data on specific heat shows more consistent trends. Griffis et al. (1981) [54] reported a sharp increase in specific heat between 350°C and 510°C, followed by a plateau, which is attributed to heat absorption during polymer matrix degradation. Other studies, limited to lower temperatures, showed gradual increase. The mechanical properties of FRP composites, particularly tensile strength, degrade significantly at elevated temperatures due to the thermal sensitivity of the polymer matrix. This degradation is crucial to consider when evaluating the fire resistance of FRP-strengthened structures. Figure 2.11 presents normalized strength data for CFRP and GFRP composites from various studies. Among the CFRP data, Dai et al (2015) [58]. report a gradual reduction in strength, maintaining relatively high values even beyond 500°C. In contrast, Basby et al.(2005) [59], Wang et al.[(2017)[39], and Yu and Kodur(2014) [61] show more rapid decreases, with strength dropping below 20% by 600°C. Nguyen et al.(2017) [62] observe moderate degradation until 400°C, followed by a sharper decline, while Saafi (2002) [63] reports significant strength loss beginning 25 around 200°C.For GFRP, both Saafi and Basby et al. show rapid degradation. Saafi’s results indicate a steep drop, with strength nearing zero by 400°C. Basby et al. observe a more gradual decline, but with similarly low values at higher temperatures. This trend continues in the stiffness behavior of FRP composites, as shown in Figure 2.12, which presents normalized modulus values across a range of temperatures. Most studies indicate a progressive reduction in stiffness, with GFRP showing more severe losses than CFRP. Dai et al. (2015) [58] report minimal reduction in modulus, maintaining high values up to 600°C, which suggests the use of a thermally stable matrix. In contrast, Basby et al. .(2005) [59], Yu and Kodur(2014) [61], and Saafi (2002) [63] report more pronounced degradation, with stiffness values dropping below 30% by 600°C. Wang et al.(2017) [39] show moderate loss, while Nguyen et al. [62] present consistently high modulus values throughout, likely due to differences in test procedures or material configuration. For GFRP, both Saafi and Basby et al. report substantial stiffness degradation, with Saafi’s data showing near-complete loss by 400°C. For the current study, the model proposed by Bisby et al. is adopted. They compiled the available experimental data on high-temperature strength properties of CFRP and introduced a sigmoid function to define the variation in both strength and stiffness with temperature. Strength reduction factor: 𝑓𝑓,𝑇 = 𝑓𝑓,20°𝑐 [( 1 − 𝑎𝜎 2 ) tanh(−𝑏𝜎(𝑇 − 𝑐𝜎)) + ( 1 + 𝑎𝜎 2 )] For CFRP 𝑎𝜎 = 0.1; 𝑏𝜎 = 5.83 × 10−3; 𝑐𝜎 = 339.54 Elastic modulus reduction factor: 𝐸𝑓,𝑇 = 𝐸𝑓,20°𝑐 [( 1 − 𝑎𝐸 2 ) tanh(−𝑏𝐸(𝑇 − 𝑐𝐸)) + ( 1 + 𝑎𝐸 2 )] 𝑎𝐸 = 0.05; 𝑏𝐸 = 8.68 × 10−3; 𝑐𝐸 = 367.41 Where 𝑓𝑓,20°𝑐 and 𝐸𝑓,20°𝑐 are FRP tensile strength and modulus at ambient temperature. 2.4.3 Insulation Properties The thermal properties of fire insulation, particularly thermal conductivity and heat capacity are critical for accurately assessing the fire resistance of insulated FRP-strengthened prestressed concrete (PC) beams. These properties are influenced by the composition and type of insulation material used. In this study, spray-applied fire-resistive materials (SFRMs) are considered, and 26 their behavior under elevated temperatures is shown in Figure 2.13, based on data from previous research [64-67]. Figure 2.13 illustrates that the thermal properties of SFRMs vary significantly with temperature. Initially, a decrease in thermal conductivity was observed between 100°C and 200°C, mainly due to moisture evaporation. However, at higher temperatures, conductivity increases, likely influenced by gypsum crystallization [67]. Similarly, the heat capacity of SFRMs rises at lower temperatures due to moisture loss, remains relatively stable until 400°C, and then increases again beyond 500°C due to the release of chemically bound water [67]. 2.5 Rational Approach for Evaluating Fire Resistance of FRP-Strengthened RC Beam A rational approach is a systematic method used to evaluate the fire resistance of FRP- strengthened concrete beams. It combines thermal and structural analysis to assess how the beam performs under fire conditions over time. Compared to detailed finite element analysis (FEA) and full-scale fire tests are expensive and time-consuming, the rational approach offers a reliable and cost-effective alternative. Kodur and Yu (2016) [11] proposed a rational approach, as illustrated in figure 2.14, to evaluate the fire resistance of FRP-strengthened concrete beams. This method integrates conventional RC beam fire design procedures with the contribution of FRP reinforcement and fire insulation. The methodology is based on two main steps: first, estimating cross-sectional temperatures of concrete, steel, and FRP using simplified equations; and second, using these temperatures to determine the reduction in material properties and calculate the moment capacity over time. The approach applies strain compatibility and force equilibrium principles to identify when the moment capacity falls below the applied fire-induced moment, which marks beam failure and defines fire resistance. Validation of the proposed model was conducted through comparisons with both experimental test data and finite element analysis results, showing a margin of error within 10%, confirming its applicability and reliability for structural fire design. The study found that FRP-strengthened beams without fire protection rapidly lose their flexural capacity, typically failing within 20 minutes. However, the use of fire insulation significantly extended fire resistance, in some cases maintaining structural capacity for up to two hours or more. 2.6 Research Gaps After reviewing the state-of-the-art literature, it is evident that several studies have addressed the effects of elevated temperatures on key construction materials such as concrete, prestressing steel, and FRP composites. In addition, many investigations have examined the behavior of FRP- 27 strengthened prestressed concrete (PC) members under ambient conditions. However, there is a clear lack of research focused on the fire performance of FRP-strengthened PC beams, despite the fact that both FRP and prestressing steel are more sensitive to high temperatures than conventional steel reinforcement. While rational approaches have been developed and successfully applied to FRP-strengthened reinforced concrete (RC) beams, to date, these models have not been extended or applied to prestressed concrete systems. To address this gap, the current research aims to extend the rational method to evaluate the fire resistance of FRP-strengthened PC beams and to provide effective fire protection strategies that can enhance their performance under elevated temperature conditions. 28 Tables Table 2.1: Comparison of mechanical properties of steel and various FRP types [68,69] Material Yield Density Tensile Specific Elastic Strain at Type Strength (g/cm³) Strength Gravity Modulus Break (%) (MPa) (MPa) Steel 500 7.70–8.10 350–450 7.8 (GPa) 200 0.2 AFRP 1700–2500 1.28–2.60 1720–2540 1.38–1.39 41–125 1.9–4.4 GFRP 600–1400 2.11–2.70 480–1600 1.5–2.5 BFRP 1000–1600 2.15–2.70 1035–1650 2.7–2.89 35–51 45–59 1.2–3.1 1.6–3.0 Table 2.2: Properties of thermosetting resins used in FRP composites [15, 24] Resin Specific Gravity Epoxy Vinyl Ester Polyester 1.2–1.3 73–81 1.1–1.4 Tensile Strength (MPa) 55–130 1.12–1.32 Tensile Modulus (GPa) 2.75–4.1 3–3.35 Cure Shrinkage (%) 1–5 5.4–10.3 34.5–103.5 2.1–3.45 5–12 29 Figures Figure 2.1: Various types of FRP materials: (a) CFRP laminates, (b) BFRP laminates, (c) GFRP laminates, (d) AFRP laminates, (e) CFRP rebars, (f) BFRP rebars, (g) GFRP rebars, (h) AFRP rebars, and (i) FRP fibers embedded in polymer matrix 30 Figure 2.2: Stress–strain behavior of various fibers and reinforcing steels at ambient temperature [15] Figure 2.3: Average crack width at midspan for prestressed concrete I-girder [38] 31 Figure 2.4: Thermal conductivity of concrete at elevated temperatures for different aggregate types Figure 2.5: Variation of specific heat of concrete with temperature for different aggregate types 32 Figure 2.6: Temperature-dependent normalized compressive and tensile strength for various aggregates Figure 2.7: Temperature-dependent normalized elastic modulus for various aggregates 33 Figure 2.8: Variation of thermal conductivity and specific heat of steel with temperature (Eurocode 2) Figure 2.9: Temperature-based reduction factors for prestressing steel (Eurocode 2) 34 Figure 2.10: Thermal conductivity and specific heat of CFRP composites 35 Figure 2.11: Temperature-dependent normalized strength degradation of CFRP and GFRP composites Figure 2.12: Temperature-dependent normalized modulus degradation of CFRP and GFRP composites 36 Figure 2.13: Thermal properties of various SFRM insulation materials 37 Figure 2.14: Flowchart of the rational approach for evaluating fire resistance of FRP- strengthened concrete beams (Kodur and Yu, 2016) [11] 38 CHAPTER 3 RATIONAL APPROACH 3.1 General A rational approach is a structured and logical method used to solve engineering problems by applying fundamental principles and realistic assumptions. It simplifies complex processes by breaking them down into manageable parts, allowing for practical and accurate evaluation without relying on overly conservative or highly complex methods. As highlighted in Chapter 2, there remains a noticeable gap in the literature regarding the fire performance of FRP-strengthened prestressed concrete (PC) beams. Although several studies have investigated the behavior of FRP-strengthened members under ambient conditions, limited attention has been given to their performance in fire. Existing design codes, including ACI 440.2R (2017) [70] and FIB Bulletin 14 (2007) [71], advise excluding the role of FRP in structural capacity under fire exposure, primarily due to its susceptibility to high temperatures. This often results in conservative designs that may not reflect the actual performance of FRP-strengthened members. To address this issue, this chapter introduces a simplified methodology to estimate the fire performance of FRP-strengthened prestressed concrete beams. The approach builds upon existing fire design procedure used for prestressed concrete members, enhancing them by incorporating the thermal and mechanical behavior of FRP materials and the protective effect of fire insulation. The proposed method involves two major phases. The first focuses on estimating the temperature distribution within concrete, FRP reinforcement, and prestressing tendons over a specified fire exposure time. The second phase calculates the corresponding flexural capacity of the member under these elevated temperatures. To facilitate this, simplified equations are introduced for predicting temperature profiles in the materials, followed by a step-by-step procedure for determining the flexural capacity of the beam under fire conditions. The accuracy of this simplified approach is verified by comparing its predictions with results from experimental fire tests and detailed numerical simulations. Furthermore, its practical use is demonstrated through design examples, highlighting its effectiveness as a reliable and efficient tool for assessing the fire resistance of FRP-strengthened PC beams. 39 3.2 Rational Approach for Evaluating Fire Resistance of FRP-Strengthened PC Beams Evaluating the fire resistance of FRP-strengthened prestressed concrete beams is challenging because both FRP and prestressing steel lose strength at high temperatures. Most current design guidelines simplify this by ignoring the contribution of FRP during fire, which can lead to conservative and less accurate results. To address this, a rational approach has been developed to provide a more realistic method of analysis. This approach uses a step-by-step process that combines simple heat transfer calculations with structural analysis to estimate how the beam behaves over time in a fire. As illustrated in Figure 3.1, the procedure begins with the selection of a fire exposure time. At each time step, the first objective is to estimate the temperature distribution within the concrete section, FRP reinforcement, and prestressing steel. This is accomplished using simplified heat transfer equations calibrated against test data. These temperatures are critical because material properties such as strength and stiffness significantly degrade with temperature. Once the temperatures are determined, the corresponding reductions in the mechanical properties of each material are evaluated. As outlined in Chapter 2, the compressive strength of concrete, along with the strength and stiffness of both FRP and prestressing steel, decrease progressively with rising temperature and are typically determined using empirical relationships or tabulated reduction factors. These reduced properties are then used to model the structural response of the member under fire conditions. The next stage of the approach involves structural analysis, where strain compatibility and internal force equilibrium are assessed. First, the strain at the bottom (soffit) of the beam is calculated. The behavior of the FRP is then evaluated, considering the possibility of debonding failure at high temperatures. An initial estimate is made for the position of the neutral axis, which separates the compression and tension zones of the cross- section. Using this estimate, the effective strains in the FRP and prestressing steel are determined, and the corresponding stresses are calculated based on temperature-dependent stress–strain relationships. After obtaining stress values, the internal force components within the beam cross-section are determined, including the compressive force in the concrete and the tensile forces in both the FRP reinforcement and prestressing steel. The next step is to verify if the internal forces are in equilibrium. If equilibrium is not achieved, the position of the neutral axis is adjusted, and the calculations are repeated. Once equilibrium is satisfied, the flexural capacity of the beam at the specified fire exposure time is calculated, considering the temperature-induced reduction in 40 material properties. Following this, the moment capacity of the beam during fire exposure is calculated. This includes the effects of dead and live loads that remain acting during the fire. The calculated moment demand is then compared with the reduced flexural capacity of the beam. If the capacity is greater than the demand, the beam is considered safe at that time step, and the analysis continues to the next stage of fire exposure. If the demand exceeds the capacity, the beam is assumed to have failed, and the corresponding time is taken as the fire resistance of the member. 3.2.1 Analysis of Cross-Sectional Temperatures The fire resistance of FRP-strengthened PC beam is significantly affected by the degradation of strength in the FRP reinforcement, prestressing steel, and concrete due to elevated temperatures. Therefore, precisely estimating the temperature distribution within the cross-section at a specific duration of fire exposure is critical for evaluating the structural behavior of the beam under fire conditions. For an uninsulated FRP-strengthened PC beam, the temperature distribution across the cross-section remains nearly the same as that of an un-strengthened PC beam. This is because externally bonded (EB) FRP reinforcement has a relatively small cross-sectional area compared to concrete, resulting in a minor impact on heat transfer within the beam. Kodur et al. (2013) [72] developed a set of simplified equations to estimate cross-sectional temperatures in RC members exposed to standard fire conditions. These equations have been validated through finite element analysis (FEA) results and fire test data, demonstrating accuracy within a ±10% margin, particularly for temperatures in the range of 300°C - 600°C. Since PC and RC beams exhibit similar thermal mechanisms, the same temperature prediction equations are applied in this study for FRP-strengthened PC beams. The temperature (𝑇𝑐) at any point within the cross-section of a concrete beam, represented by coordinates y and z in Figure 3.1, can be determined for a specified fire exposure duration using this method and the following equations. For one-dimensional heat transfer For two-dimensional (2D) heat transfer 𝑇𝑐 = 𝑐1 ∙ 𝜂𝑧 ∙ (𝑎𝑡𝑛) 𝑇𝑐 = 𝑐2[(−1.481 ∙ (𝜂𝑧 ∙ 𝜂𝑦) + 0.985 ∙ (𝜂𝑧 + 𝜂𝑦) + 0.017)](𝑎𝑡𝑛) where 𝜂𝑧 = 0.155 𝐼𝑛 𝑡 𝑧1.5 − 0.348√𝑧 − 0.371 41 (1) (2) (3) 𝜂𝑦 = 0.155 𝐼𝑛 𝑡 𝑦1.5 − 0.348√𝑦 − 0.371 (4) The parameter 𝑡 represents duration of fire exposure in hours, 𝑧 and 𝑦 indicate the distance from a given point within the concrete section to the fire-exposed surface (m), and 𝑎𝑡𝑛 represents the fire temperature according to ISO 834 (2012) or ASTM E119 (2012) standard fire conditions. The coefficients 𝑎, 𝑛, 𝑐₁, and 𝑐₂ used in the temperature prediction equations are taken from Table 3.1. Equations (1) to (4) are applicable for estimating cross-sectional temperatures in FRP- strengthened PC beams without fire insulation. For FRP-strengthened PC beams with fire insulation, the temperature in concrete, prestressing steel, and FRP reinforcement is significantly reduced due to the protective insulating effect of the insulation layer. In these beams, thermal behavior is primarily influenced by the properties of both insulation and the concrete. The temperature distribution within an insulated PC section can be determined using the same equations [Eqs. (1) - (2)] applied to uninsulated PC beams, by converting the insulation layer into an equivalent concrete layer to account for its thermal resistance. A U-shaped fire insulation layer is applied to a PC beam, as shown in Figure 3.3 (a), with insulation thicknesses 𝑧𝑖 on the sides and 𝑦𝑖on the bottom. When the insulation layer is substituted with an equivalent concrete layer of thickness 𝑧𝑒𝑐 on the sides and 𝑦𝑒𝑐 on the bottom, as illustrated in Figure 3.3 (b), the temperature distribution within the beam’s cross-section should remain unchanged. By applying fundamental heat transfer principles and one-dimensional heat transfer equations [Eq. (1)], the relationship between the fire insulation thickness and the corresponding equivalent concrete thickness can be derived (Yu 2013) [72]: 𝑍𝑒𝑐 𝑍𝑖 = √𝑡𝛼 𝛽 ∙ √( 𝑘𝑐 (𝜌𝑐)𝑐 ) ( (𝜌𝑐)𝑖 𝑘𝑖 ) (5) Where 𝛼 and 𝛽 are regression coefficients; 𝑘𝑐, (𝜌𝑐)𝑐and 𝑘𝑐, (𝜌𝑐)𝑐 are thermal conductivity and heat capacity of concrete and insulation respectively. Through nonlinear regression analysis of a comprehensive dataset generated using FEA, (Yu 2013) [72]: determined the regression coefficients α and β. The study identified the values of α and β as 4.5 and 1.75, respectively. The accuracy of these coefficients, obtained from regression analysis, falls within a 5–15% range, depending on the sectional dimensions of the beam and concrete properties. By applying the equivalent concrete depth method, the distance from the outer 42 edge of the insulation to the fire-exposed surface (𝑧𝑐 ′ and 𝑦𝑐 ′)can be determined using the following equations. ′ = 𝑧𝑐 + 𝑧𝑒𝑐 = 𝑧𝑐 + 𝑧𝑖 √𝑡 𝑧𝑐 4.5 ′ = 𝑦𝑐 + 𝑦𝑒𝑐 = 𝑦𝑐 + 𝑦𝑖 √𝑡 𝑦𝑐 4.5 1.75 ∙ √( 𝑘𝑐 (𝜌𝑐)𝑐 ) ( (𝜌𝑐)𝑖 𝑘𝑖 ) 1.75 ∙ √( 𝑘𝑐 (𝜌𝑐)𝑐 ) ( (𝜌𝑐)𝑖 𝑘𝑖 ) (6) (7) These equivalent concrete depths (𝑧𝑐 ′ and 𝑦𝑐 ′) can be substituted into Eqs (1) to (4) by replacing 𝑧 and 𝑦 to evaluate the cross-sectional temperature rise in an insulated PC member. 3.2.2 Effective Concrete Width Method Concrete exhibits good performance at elevated temperatures due to its low thermal conductivity and high heat capacity, which slows down heat penetration and delay strength loss. Unlike steel, concrete retains a significant portion of its mechanical properties under fire exposure, especially in its inner core, where temperatures rise more gradually. However, longer exposure to high temperatures leads to progressive strength degradation, particularly in the outer layers of concrete elements. To account for strength variation due to temperature exposure, Eurocode 2 introduces the effective concrete width approach. This method accounts only for the portion of the compression zone width where the temperature remains below 500°C, while the outer concrete layers exceeding 500°C are excluded in strength calculations. However, Eurocode 2 does not specify values for effective width reduction in PC T-beams, resulting in a lack of predefined reduction factors for these elements. Although simplified cross- sectional temperature equations [Eq (1) - (4)] are available, they were not used in this study because they provide temperature values only at specific points within the section, making it difficult to construct a complete temperature gradient curve throughout the cross-section of the beam. To address the limitations of simplified temperature prediction methods and obtain a more accurate representation of thermal behavior, a numerical analysis was conducted using ABAQUS to evaluate the temperature distribution within the cross-section of a PC T-beam. The analysis was conducted for a fire duration of four hours, based on the ASTM E119 standard fire curve, which simulates a realistic fire scenario typically used in structural fire resistance evaluations. The beam modeled in the study had a typical T-shaped cross-section, characterized by a flange width of 2220 43 mm, flange thickness of 105 mm, web width of 620 mm, and web height of 535 mm. These dimensions reflect a common configuration for PC floor beams used in practice. The beam was exposed to fire on three sides: the bottom and the two vertical sides of the web. The top surface of the flange was assumed to remain at a constant temperature of 20°C, representing ambient conditions. This boundary condition is justified by practical considerations, as the top surface of floor beams is usually covered by flooring materials, screed, or insulation, which act as protective layers and significantly delay heat transfer from above. As such, it is reasonable to assume minimal thermal exposure on the top surface during the early stages of a fire. In the ABAQUS thermal model, DC3D8 elements, which are 8-node linear brick elements designed for 3D heat transfer analysis, were used to discretize the beam cross-section. A uniform mesh size of 30 mm was chosen after careful consideration. This mesh size provided sufficient resolution to capture temperature gradients across the section while maintaining computational efficiency. Using a finer mesh could improve detail but would significantly increase computational time, while a coarser mesh might miss key thermal transitions near the fire-exposed surfaces. The resulting temperature distribution profile of the full T-beam after four hours of fire exposure is shown in Figure 3.4. This figure illustrates the temperature gradient across the entire beam, demonstrating how heat penetrates inward from the fire-exposed surfaces. Upon completion of the thermal simulation, temperature data were extracted at 15-minute intervals to capture the evolution of heat penetration throughout the cross-section. A Python-based post-processing script was utilized to extract the temperature data generated from the ABAQUS thermal analysis and to generate temperature gradient profiles across the depth of the T-beam cross-section at specified time intervals. The sectional temperature distribution used for evaluating concrete strength variation is presented in Figure 3.5(a), while the corresponding temperature contours used to identify the critical concrete regions within the compression zone are shown in Figure 3.5(b). Prior to using these gradients for effective width determination, it was necessary to establish the location of the neutral axis at each stage of fire exposure, as this governs the extent of the concrete compression zone. Initially, the full flange width was assumed to be effective, and the corresponding neutral axis depth was calculated using standard strain compatibility and equilibrium conditions. This calculation was repeated for each time step to capture the progressive changes in the position of the neutral axis as the temperature within the section evolved over time. 44 Once the neutral axis depth was identified, the region located above it, which represents the concrete in compression, was evaluated based on the extracted temperature data. In accordance with Eurocode 2 guidelines, any portion of concrete within the compression zone that reached temperatures exceeding 500°C was considered ineffective and was excluded from strength calculations. The effective compression width was thus determined by removing these outer, overheated layers from the total compression zone at each time step. Subsequently, reduction factors for the effective width were calculated by comparing the retained compression width to the original flange width. These reduction factors quantify the loss of usable concrete in the compression zone due to elevated temperature exposure and were used as key input parameters in the subsequent fire-resistance analysis. The calculated reduction factors for each time step are presented in Table 3.2. 3.2.3 Determining Moment Capacity at a specified Fire Exposure Duration By evaluating the temperature-induced degradation of material properties, including the yield stress(𝑓𝑦,𝑇),ultimate stress (𝑓𝑢,𝑇) and Young’s modulus (𝐸𝑝,𝑇)of prestressing steel, along with the ultimate stress (𝑓𝑓,𝑇) and Young’s modulus (𝐸𝑝,𝑇) of FRP reinforcement and 𝑓𝑐 ′ of concrete as discussed in Chapter 2, the flexural capacity of FRP-strengthened PC beams at a specific fire exposure time can be determined by using a methodology similar to that used for room- temperature conditions, as outlined in ACI 440.2R-17 (2017) [70]. According to ACI 440.2R-17, failure in an FRP-strengthened section at ambient temperature can occur through multiple mechanisms. These include concrete crushing in compression before the prestressing steel reaches its yield strength, yielding of the steel in tension followed by rupture of the FRP laminate, and yielding of the steel in tension leading to concrete crushing. Additionally, failure under fire exposure may result from shear or tensile delamination of the concrete cover, known as cover delamination, or debonding of the FRP reinforcement from the concrete substrate. These failure modes are incorporated in the analysis for calculating the flexural capacity of the beam. Initially, the strain in the concrete substrate (𝜀𝑏𝑖,𝑇) is determined and excluded from the effective strain in the FRP. This initial strain is obtained through an elastic analysis of the existing member, considering all loads present at the time of FRP installation. For this analysis, an uncracked section is assumed, considering only the dead load acting on the beam during FRP application, and the initial strain in the concrete substrate is calculated as: 45 εbi,T = −𝑃𝑒,𝑇 𝐸𝑐𝐴𝑐𝑔 (1 + 𝑒𝑦𝑏 𝑟2 ) + 𝑀𝐷𝐿𝑦𝑏 𝐸𝑐𝐼𝑔 (8) where 𝑃𝑒,𝑇= effective prestressing force depends on strength degradation of prestressing steel; 𝐸𝑐= modulus of elasticity of concrete; 𝐴𝑐𝑔 = gross cross-sectional area; 𝑒 = eccentricity of prestressing force; 𝑦𝑏 =distance from extreme bottom fiber to the section centroid; 𝑟 =radius of gyration; 𝑀𝐷𝐿 = moment due to dead load; and 𝐼𝑔 = gross moment of inertia. At the section where the externally bonded FRP reinforcement ends, failure due to FRP debonding may occur. To prevent intermediate crack-induced debonding, the effective strain in the FRP reinforcement should be restricted to the debonding strain(𝜀𝑓𝑑,𝑇 ) threshold, which is determined using the following calculation: 𝜀𝑓𝑑,𝑇 = 0.41√ ′ 𝑓𝑐 𝑛𝐸𝑓,𝑇𝑡𝑓 ≤ 0.9𝜀𝑓𝑢 (9) where 𝑓𝑐 ′ =compressive strength of concrete (MPa); 𝑛 =number of layers of FRP reinforcement; 𝑡𝑓 =thickness of FRP reinforcement; and 𝜀𝑓𝑢 =rupture strain of FRP reinforcement. The effective strain in the FRP reinforcement can be estimated using an initial approximation of the neutral axis depth. The maximum strain that can develop in the FRP reinforcement is governed by one of three failure conditions: the strain at which concrete crushing occurs, the strain at which FRP rupture happens, or the strain at which FRP debonding from the substrate takes place. The effective strain (𝜀𝑓𝑒,𝑇) in the FRP reinforcement at the ultimate limit state can be calculated as: 𝜀𝑓𝑒,𝑇 = 𝜀𝑐𝑢 ( ℎ − 𝑐 𝑐 ) − 𝜀𝑏𝑖,𝑇 ≤ 𝜀𝑓𝑑,𝑇 (10) where ℎ =effective depth of FRP reinforcement; 𝑐 =neutral axis depth (0.1 × ℎ); and 𝜀𝑐𝑢 = 0.003(Concrete crushing is considered to occur when the compressive strain in the concrete reaches its maximum allowable limit of 0.003) The strain in the prestressing steel can be determined using strain compatibility, calculated as: 𝜀𝑝𝑠,𝑇 = 𝜀𝑝𝑒,𝑇 + 𝑃𝑒,𝑇 𝐸𝑐𝐴𝑐𝑔 (1 + 𝑒2 𝑟2) + 𝜀𝑝𝑛𝑒𝑡 (11) 46 (12) (13) 𝑑𝑝 − 𝑐 𝑐 𝑑𝑝 − 𝑐 ℎ − 𝑐 where 𝜀𝑝𝑒,𝑇 =effective strain in the prestressing steel after losses; and 𝜀𝑝𝑛𝑒𝑡 = net tensile strain in the prestressing steel beyond decompression, at nominal strength, depends on the failure mode and is calculated as: 𝜀𝑝𝑛𝑒𝑡 = 0.003 ( ) for concrete crushing failure 𝜀𝑝𝑛𝑒𝑡 = (𝜀𝑓𝑒,𝑇 + 𝜀𝑏𝑖,𝑇) ( ) for FRP rupture or debonding failure The stress in the prestressing steel and FFP reinforcement is determined based on its temperature-dependent material properties. For a typical seven-wire low-relaxation prestressing strand, the stress-strain relation can be approximated using the following equations. 𝑓𝑝𝑠,𝑇 = { 𝑓𝑢,𝑇 − 𝐸𝑝,𝑇 ∙ 𝜀𝑝𝑠,𝑇 0.276 𝜀𝑝𝑠,𝑇 − 0.007 for 𝜀𝑝𝑠,𝑇 ≤ 0.0086 for 𝜀𝑝𝑠,𝑇 > 0.0086 } 𝑓𝑓𝑒,𝑇 = 𝐸𝑓,𝑇 ∙ 𝜀𝑝𝑒,𝑇 (14) (15) With the strain and stress in the FRP and prestressing steel determined for the assumed neutral axis depth, internal force equilibrium can be verified by equating compression and tensile forces. 𝛼1𝑓𝑐 ′𝛽1𝑏𝑇𝑐 = 𝐴𝑝𝑠𝑓𝑝𝑠,𝑇 + 𝐴𝑓𝑓𝑓𝑒,𝑇 (16) where 𝛼 and 𝛽1 are concrete stress block parameters, determined based on the parabolic stress- strain relationship for concrete, as specified in ACI 318. The neutral axis depth (𝑐) is computed using an iterative solution process. Initially, an estimated value of (𝑐) is assumed, and the corresponding stresses and strains are calculated using Eq (13) to (18). A revised neutral axis depth (𝑐) is then obtained using Eq (18), and its value is compared to the initial assumption. If the computed and assumed values of (𝑐) are consistent, the correct neutral axis depth is established. If they differ, a new (𝑐) value is selected, and the iteration continues until convergence is achieved. Once equilibrium is established, the nominal flexural strength of the FRP-strengthened PC beam under the specified fire exposure can be determined as follows: 𝛽1𝑐 2 where 𝜓𝑓= strength reduction factor for FRP is applied to improve the reliability of strength 𝑀𝑛,𝑇 = 𝐴𝑝𝑠𝑓𝑝𝑠,𝑇 (𝑑𝑝 − ) + 𝜓𝑓𝐴𝑓𝑓𝑓𝑒,𝑇 (ℎ − 𝛽1𝑐 2 (17) ) prediction and accounts for the different failure modes observed for FRP-strengthened members (delamination of FRP reinforcement). 47 The failure of an FRP-strengthened PC beam at a specified fire exposure duration is evaluated by comparing its reduced moment capacity [Eq (20)] to the applied moment due to external loading. According to ASCE 7 (ASCE 2010), the load level under fire conditions should be reduced below the maximum design loads used for ambient conditions, as fire is classified as an accidental event. The recommended loading for fire exposure is specified as: 𝑤𝑓𝑖𝑟𝑒 = 1.2𝐷 + 0.5𝐿 (18) where 𝑤𝑓𝑖𝑟𝑒 is the loading under fire exposure; and 𝐷 and 𝐿 are dead and live loading on the beam. Thus, the following criterion is applied to assess the failure of an FRP-strengthened PC beam: 𝑀𝑓𝑖𝑟𝑒 ≤ 𝑀𝑛,𝑇 (19) where 𝑀𝑓𝑖𝑟𝑒is the applied moment on the beam at the critical section during fire exposure. The moment capacity of an FRP-strengthened PC beam and the moment due to applied loading can be determined at any specified fire exposure duration using the previous set of equations. The beam is considered to have failed when the applied moment under fire conditions (𝑀𝑓𝑖𝑟𝑒) exceeds its moment capacity (𝑀𝑛,𝑇). The time at which this failure occurs defines the fire resistance of the FRP-strengthened PC beam. To further illustrate the application of this procedure, a design example evaluating the fire resistance of an externally FRP-strengthened PC beam is provided in Appendix. 3.3 Validation of the Rational Approach The validity of the rational approach is established by comparing the predicted results from the above approach with those of fire tests on FRP-strengthened RC beams as reported by Bhatt (2021) [14] and Kodur & Yu (2016) [11].The validation process includes analyzing a rectangular RC beam (350mm × 500mm) externally strengthened with CFRP, both with and without 38 mm VG insulation, and an externally strengthened CFRP RC-T beam, both insulated and uninsulated using 19 mm Spray-Applied Fire Resistive Material (SFRM). The use of different cross-sectional shapes and fire protection strategies provides comprehensive validation, ensuring that the rational approach accurately predicts fire-induced degradation, structural stability, and failure mechanisms before extending its application to FRP-strengthened PC beams. Figure 3.6 shows the geometry and cross-sectional details of CFRP-strengthened RC beams with and without VG insulation, based on the study by Kodur and Yu (2016) [11]. To assess the thermal behavior of these beams under fire conditions, simplified temperature prediction equations outlined in the preceding section were used to estimate temperatures at key locations: corner rebar, 48 middle rebar, and the average temperature of the externally bonded FRP. The results obtained using the rational approach were compared with finite element analysis (FEA) data to evaluate the accuracy of the simplified method. This comparison is presented in Figure 3.7. As observed in Figure 3.7, FEA and rational approach exhibit consistent temperature rise trends across all monitored locations within the beam over the 240-minute of ASTM E119 fire exposure. Among the three monitored positions, the average temperature in the FRP reinforcement shows the highest rise throughout the exposure duration. This is primarily due to the external placement of the FRP on the beam's soffit, directly exposed to fire, resulting in minimal thermal insulation and a faster heat transfer rate. In contrast, the corner and middle steel reinforcement experience significantly lower temperature elevations due to the presence of surrounding concrete, which acts as a thermal barrier. Specifically, the middle rebar, being more deeply embedded in the section, remains relatively cooler for a longer period compared to the corner rebar. The corner steel, though closer to the surface than the middle steel, still benefits from the effective concrete cover that delays heat penetration. Overall, the rational predictions align well with the FEA results across all monitoring points. Slight underestimations during the early stages of heating are observed in the rational model, which can be attributed to the use of simplified assumptions. Nevertheless, the rational approach effectively captures the key thermal trends and provides a reliable estimation of temperature distribution in CFRP-strengthened RC beams exposed to fire. The reduced moment capacity of CFRP-strengthened RC beams was determined by incorporating the temperature-dependent degradation of constituent material properties. The step- by-step process for this calculation, based on the rational approach, is illustrated in Figure 2.14. Figure 3.8 presents the time-dependent variation in moment capacity for CFRP-strengthened RC beams with and without 38 mm VG insulation under fire exposure. Results obtained from both the rational approach and FEA show a consistent trend. For the uninsulated beam, there is a sharp decline in moment capacity beginning at around 20 minutes of fire exposure. This rapid degradation is primarily due to the direct exposure of the externally bonded FRP to elevated temperatures. As the temperature exceeds the glass transition temperature (Tg) of the polymer matrix, the resin begins to soften and decompose, severely compromising the tensile contribution of the FRP to the beam’s flexural capacity. In contrast, the insulated beam exhibits a gradual decline in moment capacity over time. The presence of the 38 mm VG insulation layer significantly slows down the heat transfer to the FRP reinforcement, preserving its mechanical performance for a 49 longer duration. The moment capacity of the insulated beam remains relatively higher throughout the 240-minute fire exposure, highlighting the critical role of fire protection in enhancing structural resilience. The reliability of the rational approach was further demonstrated by comparing its predictions with the experimental and FEA results from Bhatt’s (2021) [14] study on CFRP-strengthened RC T-beams, which were tested with and without 19 mm spray-applied fire resistive material (SFRM) insulation. As shown in Figure 3.9, the beam geometry and cross-sectional details differ from those used in previous studies, with Bhatt employing narrower CFRP sheets (170 mm × 1 mm). When compared with the earlier study by Kodur and Yu (2016) [11] on rectangular RC beams strengthened with CFRP and protected by 38 mm VG insulation, both studies showed a similar pattern in time–temperature profiles. In each case, the rational method closely matched the FEA results, accurately capturing the rise in temperature across key reinforcement locations, including the FRP layer, corner rebar, and middle rebar, as illustrated in Figure 3.10. Despite the similar thermal trends, a noticeable difference was observed in the rate and extent of moment capacity degradation between the two beam types. This variation is primarily attributed to the difference in CFRP reinforcement size and placement. The analysis highlights the manner in which the narrower CFRP sheet used in Bhatt’s study contributed less flexural strength, leading to a more rapid decline in capacity once thermal degradation began. As the temperature exceeded the glass transition point of the CFRP’s polymer matrix, strength was lost abruptly, causing the uninsulated beam to lose most of its capacity within the first 5 minutes of fire exposure. Thereafter, it performed similarly to an un-strengthened beam. In contrast, the beam with SFRM insulation showed a slower and more gradual loss of capacity, as the insulation delayed the heat transfer and preserved the mechanical integrity of the CFRP for a longer duration. These results are shown in Figure 3.11. Together, the findings from both Bhatt (2021) [14] and Kodur & Yu (2016) [11] clearly demonstrate the effectiveness of the rational approach in estimating not only temperature evolution but also time-dependent structural degradation in CFRP-strengthened RC beams under fire conditions. These findings support the use of the rational method as a reliable tool not only for RC beams but also for its extension to FRP-strengthened PC beams, providing a practical and efficient means of evaluating fire resistance. 50 3.4 Summary This chapter introduces a rational approach for evaluating the fire resistance of FRP- strengthened prestressed concrete (PC) beams. The method integrates simplified heat transfer equations with structural analysis to assess beam performance under elevated temperatures. It consists of two main phases: first, estimating the temperature distribution in concrete, FRP, and prestressing steel; and second, calculating the corresponding moment capacity by accounting for temperature-induced degradation in material properties. For insulated beams, the thermal resistance of the insulation is modeled using an equivalent concrete depth approach. The analysis considers potential failure modes such as FRP debonding, rupture, and concrete crushing, and follows a step-by-step equilibrium-based procedure to determine moment capacity at different stages of fire exposure. The accuracy of this approach is validated through comparisons with experimental data and finite element analyses of FRP-strengthened RC beams. The results show that the rational method effectively captures both temperature profiles and flexural degradation over time. Case studies involving insulated and uninsulated beams underscore the importance of fire protection in maintaining structural performance. Overall, the rational approach demonstrates its reliability and practicality as an efficient tool for assessing the fire resistance of FRP- strengthened PC beam. 51 𝒂 𝒏 𝒄𝟏 𝒄𝟐 Table 3.1: Factors for temperature evaluation in concrete members [Kodur et al. (2013)] Tables Factor ASTM E119 910 0.148 ISO 834 935 0.168 NSC-carbonate NSC-silicate HSC-carbonate HSC-silicate 1.0 1.0 1.01 1.06 1.12 1.12 1.12 1.20 NSC-Normal-strength concrete HSC-High-Strength concrete Table 3.2: Effective width reduction factors of PC T-beam under ASTM E119 fire exposure Time (min) Time (min) Effective width factor Effective width factor 135 150 165 180 195 210 225 240 0.931 0.927 0.909 0.898 0.891 0.882 0.859 0.837 0 15 30 45 60 75 90 105 120 1.000 1.000 0.999 0.981 0.977 0.962 0.956 0.948 0.939 52 Figures Figure 3.1: Flowchart showing steps in the rational methodology for assessing fire resistance of FRP-strengthened PC beam 53 Figure 3.2: Fire-induced heat transfer mechanisms in a 3-sided exposed beam [11] Figure 3.3: -Equivalent concrete depth approach for predicting cross-sectional temperatures 54 Figure 3.4: Temperature distribution profile of the T-Beam after 4 hours of fire exposure (ABAQUS simulation) Figure 3.5: (a) Temperature distribution from ABAQUS and (b)Temperature contours of PC T- beam after 4 hours of ASTM E119 fire exposure 55 Figure 3.6: Geometry and cross-section details of CFRP-strengthened RC beams with and without VG insulation (Kodur & Yu, 2016) [11] Figure 3.7: Comparison of time–temperature curves from rational approach and FEA for insulated RC beam 56 Figure 3.8: Time-dependent moment capacity degradation of CFRP-strengthened RC beam with and without insulation Figure 3.9: Geometry and cross-section details of CFRP-strengthened RC T-beams with and without SFRM insulation (Bhatt, 2021) [14] 57 Figure 3.10: Comparison of time–temperature curves from rational approach and FEA for Insulated RC T-beam Figure 3.11: Time-dependent moment capacity degradation of CFRP-strengthened RC T-beam with and without insulation 58 CHAPTER 4 NUMERICAL STUDY 4.1 General As demonstrated in Chapter 3, the rational design approach proves to be a reliable and effective tool for evaluating the fire resistance of structural members. In this chapter, the same methodology is applied to analyze the fire performance of FRP-strengthened prestressed concrete (PC) T-beams, both with and without spray-applied fire resistive material (SFRM) insulation. The fire behavior of these members is influenced by several interrelated factors, including concrete cover and insulation thickness. These interdependencies make the fire resistance evaluation complex, and therefore, it is necessary to examine the effect of each parameter through a structured parametric study. Since conducting numerous fire tests is not feasible due to limitations in furnace size, loading equipment, and the high cost and time requirements, this chapter relies entirely on the rational approach to perform a comprehensive evaluation. The fire resistance of un-strengthened and FRP-strengthened PC T-beams is first assessed. To enhance the fire performance of the strengthened beams, fire protection in the form of insulation is introduced, and its effectiveness is analyzed. A parametric study is then carried out by varying concrete cover and insulation thickness to evaluate their impact on the fire resistance of the beams. The goal is to identify the optimal insulation configuration necessary to achieve the required fire rating. Additionally, for consistent comparison, a reference rectangular RC beam is selected, and a prestressed concrete beam with equivalent flexural capacity under ambient conditions is modeled to align with the RC reference. This allows for a direct and meaningful comparison between CFRP-strengthened RC and PC beams in terms of their fire performance. 4.2 Fire Resistance of CFRP-Strengthened PC-T Beams A CFRP-strengthened prestressed concrete (PC) T-beam, shown in Figure 4.1, was selected for this study. The beam configuration was based on a real structural member from an existing parking garage that was later repurposed into an office building. To enhance fire protection, a second case was considered by incorporating a 19 mm layer of Spray-Applied Fire Resistive Material (SFRM). Initially, however, the beam was analyzed without insulation to evaluate its baseline fire performance. The geometric configuration and room-temperature material properties of the beam 59 are summarized in Table 4.1. The fire resistance evaluation was conducted using the rational design approach, following the step-by-step methodology illustrated in Figure 3.1. As outlined in Section 3.2.1, the first step involved determining the temperature distribution within the beam’s cross- section, including the concrete, prestressing steel, and CFRP reinforcement. This was achieved using simplified temperature prediction equations at 1-minute intervals over the duration of the fire exposure. To accurately account for the thermal degradation of the concrete section, especially in the compression zone, ABAQUS simulations were conducted to model the temperature gradient across the beam's cross-section. These simulations were performed at 15-minute intervals using the standard ASTM E119 fire curve. At each time step, any layer of concrete in the compression zone that exceeded 500 °C was considered ineffective and excluded from the strength calculations. The corresponding effective width reduction factors were derived and are provided in Table 3.2. Figure 4.2 illustrates the temperature progression over time at various critical locations within the CFRP-strengthened PC beam subjected to ASTM E119 standard fire exposure without insulation. As shown, the temperature of the externally bonded FRP laminate rises rapidly and closely follows the ASTM E119 curve throughout the duration of fire exposure. This sharp increase in temperature is primarily due to the direct exposure of the FRP, which is positioned at the soffit of the beam i.e., the bottom surface that is fully exposed to fire. Moreover, because FRP materials have low thermal mass and limited insulating properties, they quickly absorb heat, leading to a rapid rise in temperature when unprotected. In contrast, the corner prestressing steel rebar, which is embedded within the concrete, initially maintains ambient temperature for the first 20 minutes of fire exposure. This delay is due to the thermal insulating capacity of the concrete cover, which significantly slows down heat penetration in the early stages. However, after 20 minutes, the temperature of the corner rebar begins to rise progressively as heat penetrates the concrete cover, and within 60 minutes, the temperature of the prestressing steel exceeds 300°C. The middle prestressing steel rebars, exhibit an even more delayed temperature increase. These rebars remain close to ambient temperature for the initial 60 minutes, after which the temperature begins to rise gradually due to the continued inward conduction of heat. Meanwhile, the center of the beam at mid-depth (d/2) experiences negligible temperature increase and remains near ambient conditions for the entire 240-minute duration of fire exposure. This is due to the low thermal conductivity and high heat capacity of concrete, which effectively limits heat penetration to the beam’s core, thereby preserving the internal temperature for a prolonged period. 60 In contrast to the uninsulated case presented in Figure 4.2, Figure 4.3 illustrates the temperature progression at critical locations within a CFRP-strengthened PC beam subjected to ASTM E119 fire exposure, but with the application of a 19 mm Spray-Applied Fire Resistive Material (SFRM) insulation layer. The presence of insulation significantly reduces the rate of heat transfer, acting as a thermal barrier that protects the internal components of the beam. The FRP laminate, which exhibited a rapid temperature rise in the uninsulated beam, shows a much slower progression in the insulated beam. It maintains ambient temperature for the first 10 minutes of fire exposure, and although the temperature gradually increases over time due to proximity to the fire-exposed surface, the peak temperature remains substantially lower than in the uninsulated case. This delayed thermal response helps in preserving the tensile properties of the FRP reinforcement for a longer duration during fire. The corner prestressing steel rebar also benefits from the insulation. Unlike the uninsulated condition where it began heating after 20 minutes, the insulated beam maintains near-ambient temperatures at this location for approximately 40 minutes. The temperature begins to rise thereafter, reaching around 300°C at approximately 100 minutes. This enhanced thermal resistance is a result of the combined protective effects of both the concrete cover and the external SFRM insulation. Similarly, the middle prestressing steel rebar experiences only a marginal temperature increase and remains close to ambient conditions throughout most of the fire exposure. The temperature at mid-depth (d/2) remains virtually unchanged for the full 240-minute duration, indicating that the core of the concrete section is effectively shielded from heat. Overall, the comparative results demonstrate that the insulated beam performs significantly better than its uninsulated beam in terms of thermal resistance. The use of SFRM insulation delays the temperature rise in critical structural components, reduces peak temperatures, and contributes to maintaining structural integrity under prolonged fire exposure. This highlights the importance and effectiveness of applying insulation in enhancing the fire endurance of CFRP-strengthened PC beams. Figure 4.4 illustrates the time-dependent degradation of moment capacity for three different PC T-beam configurations exposed to ASTM E119 standard fire conditions: an un-strengthened beam, a CFRP-strengthened beam without insulation, and a CFRP-strengthened beam with 19 mm Spray-Applied Fire Resistive Material (SFRM) insulation. The un-strengthened beam, which has the lowest initial moment capacity among the three, shows a steady reduction in capacity over time. Initially, it maintains its structural performance reasonably well, but after approximately 30 61 minutes, the degradation of prestressing steel and concrete due to rising temperatures causes an accelerated loss of capacity. The beam ultimately fails at around 86 minutes. In contrast, the CFRP- strengthened beam starts with a significantly higher moment capacity under ambient conditions. However, due to the direct exposure of the externally bonded CFRP laminate to fire, the beam undergoes a sharp strength reduction almost immediately. Within the first 5 minutes, a steep drop in capacity is observed, and its performance quickly approaches that of the un-strengthened beam. This rapid degradation is due to the thermal sensitivity of CFRP, particularly the softening and decomposition of the resin matrix as temperatures exceed the glass transition point. Despite this early deterioration, the strengthened beam retains slightly higher capacity than the un-strengthened beam due to the residual tensile contribution of the FRP in the early stages. Nonetheless, failure occurs at about 75 minutes, earlier than the un-strengthened beam, underscoring the vulnerability of unprotected CFRP under fire exposure. The best performance is observed in the CFRP- strengthened beam protected with 19 mm SFRM insulation. This configuration effectively delays heat penetration into both the CFRP and the internal steel reinforcement. As a result, the beam retains its structural capacity for a significantly extended period and fails only after approximately 160 minutes of fire exposure. The insulation slows the degradation of material properties, particularly of the thermally sensitive CFRP and prestressing steel, preserving the beam’s strength for a longer duration. This comparison clearly highlights the importance of insulation in fire-resistant design. While CFRP strengthening significantly enhances the initial load-carrying capacity of PC beams under ambient conditions, its effectiveness is drastically reduced under fire exposure without proper fire protection. On the other hand, un-strengthened beams, although starting with lower capacity, can exhibit superior fire endurance compared to unprotected CFRP-strengthened beams. The use of SFRM insulation bridges this gap, allowing CFRP-strengthened beams to achieve both high strength and prolonged fire resistance. These findings emphasize the necessity of incorporating fire protection strategies when designing CFRP-strengthened prestressed concrete elements for fire-prone environments. A parametric study was conducted to investigate the influence of effective concrete cover and insulation thickness on the fire performance of CFRP-strengthened prestressed concrete (PC) T- beams. These parameters were selected due to their significant effect on the thermal behavior and structural integrity of beams under fire exposure. The details of the study, including the variations 62 in cover and insulation thickness along with corresponding failure times, are summarized in Table 4.2. All cases were evaluated under the standard ASTM E119 fire exposure conditions. The results of the study reveal two key observations. First, increasing the effective concrete cover improves the fire resistance of both un-strengthened and strengthened beams. For example, increasing the cover from 50 mm to 64 mm, while maintaining the insulation thickness at 19 mm, resulted in a notable improvement in failure times. The un-strengthened beam’s failure time increased from 61 minutes to 86 minutes, while the CFRP-strengthened beam’s failure time increased from 54 minutes to 75 minutes. This improvement can be attributed to the increased thermal barrier provided by the additional concrete, which delays the heat penetration to the internal reinforcement. Second, the thickness of the fire insulation plays a critical role in the fire resistance of CFRP-strengthened beams. Without insulation, the strengthened beam failed at 75 minutes. However, with the addition of a 12.5 mm insulation layer, the failure time increased significantly to 124 minutes. Further increasing the insulation thickness to 16.7 mm and 25 mm extended the failure time to 147 minutes and 201 minutes, respectively. These results clearly demonstrate that the presence and thickness of insulation significantly enhance the fire endurance of the beam by protecting the externally bonded CFRP laminates from direct heat exposure. Overall, the findings from the parametric study confirm that both effective concrete cover and insulation thickness are crucial parameters for enhancing the fire resistance of CFRP-strengthened PC beams. While the increased concrete cover delays heat transfer to the internal steel reinforcement, the addition of insulation is especially effective in mitigating the thermal degradation of the CFRP reinforcement. Based on the results, it can be concluded that a minimum insulation thickness of 25 mm is required to achieve a fire resistance rating of approximately three hours, which is a common requirement in fire-resistant structural design. 4.3 Comparative Study on Fire Endurance of CFRP-Strengthened RC and PC Beams For a consistent comparison between the fire performance of CFRP-strengthened reinforced concrete (RC) beams and prestressed concrete (PC) beams, a rectangular RC beam was selected as the reference. To ensure uniformity in loading and mechanical characteristics, a rectangular prestressed PC beam with an equivalent flexural capacity under ambient conditions was chosen. Both beams were subjected to the same fire exposure and loading configurations. The geometric details, reinforcement layouts, and insulation configurations of both RC and PC beam specimens 63 are illustrated in Figure 4.5. The corresponding material properties used for CFRP-strengthened PC and RC beams are summarized in Table 4.3. Figure 4.6 presents the degradation in moment capacity over time for CFRP-strengthened and un-strengthened RC and PC beams subjected to ASTM E119 standard fire exposure. The un- strengthened RC beam demonstrates the highest fire endurance, maintaining its structural integrity for approximately 229 minutes before failure. In comparison, the CFRP-strengthened RC beam, while initially exhibiting a higher moment capacity due to the contribution of the FRP, fails slightly earlier at around 207 minutes. This earlier failure is primarily attributed to the vulnerability of CFRP laminates to elevated temperatures, which leads to a reduction in their tensile contribution as the polymer matrix degrades. In contrast, both CFRP-strengthened and un-strengthened PC beams exhibit lower fire resistance. The un-strengthened PC beam fails at around 99 minutes, while the CFRP-strengthened PC beam fails even earlier at approximately 90 minutes. The reduced performance of these prestressed beams is largely due to the higher sensitivity of prestressing steel and CFRP to temperature-induced strength degradation. However, when a 19 mm SFRM insulation layer is applied to the CFRP-strengthened PC beam, its fire resistance improves substantially, with failure delayed until approximately 229 minutes. This performance is comparable to that of the un- strengthened RC beam, highlighting the effectiveness of insulation in mitigating the rapid degradation of thermally sensitive materials and enhancing the overall fire endurance of CFRP- strengthened PC beams. 64 Table 4.1: Geometric dimensions and material properties of the PC T-beam Tables Length of the beam (𝑙) Effective flange width, (𝑏𝑓) Depth of prestressing steel (𝑑𝑝) Total depth of beam (ℎ) Flange thickness (ℎ𝑓) Concrete compressive strength (𝑓𝑐 ′) Effective prestress in tendon (𝑓𝑝𝑒) Yield strength of prestressing steel(𝑓𝑝𝑦) Ultimate strength of prestressing steel(𝑓𝑝𝑢) Modulus of elasticity of prestressing steel(𝐸𝑝) FRP dimensions Thickness of FRP Ultimate tensile strength of FRP (𝑓𝑓𝑢) Rupture strain of FRP (𝜀𝑓𝑢) Modulus of elasticity of FRP laminates (𝐸𝑓) Insulation thickness (𝑡𝑖) Insulation thermal conductivity (𝑘𝑖) Insulation specific heat (𝑐𝑖) Insulation density (𝜌𝑖) 8850mm 2220 mm 576mm 640mm 102 mm 41.4 MPa 1138 MPa 1586 MPa 1860 MPa 1.96 x 105 MPa 51mm x 8534 mm 1.2mm 2800 MPa 0.017 1600000 MPa 19mm 0.154 W/m-K 1.888 kJ/kg-K 425 kg/m3 65 Table 4.2: Parametric study on PC T-beam under ASTM E119 fire exposure S. No Effective cover (mm) Insulation (mm) Un- strengthened Beam Failure Time (min) Strengthened Beam Failure Time (min) Insulated Strengthened Beam Failure Time (min) 1 2 3 4 5 6 50 64 64 64 64 64 19.0 19.0 0.0 12.5 16.7 25.0 61 86 86 86 86 86 54 75 75 75 75 75 133 160 75 124 147 201 Table 4.3: Material Properties of CFRP-Strengthened PC and RC beams Material Parameter Concrete Prestressing steel ′) Compressive strength (𝑓𝑐 Modulus of elasticity (𝐸𝑐) Yield strength (𝑓𝑝𝑦) Effective prestress (𝑓𝑝𝑒) Ultimate strength (𝑓𝑝𝑢) Modulus of elasticity (𝐸𝑝) Reinforcing steel Yield strength (𝑓𝑦) Modulus of elasticity (𝐸𝑠) Value 34.5 MPa 27600 MPa 1586 MPa 1138 MPa 1860 MPa 2.0 x 105 MPa 415 MPa 2.0 x 105 MPa FRP laminates SFRM insulation Ultimate tensile strength (𝑓𝑓𝑢) Rupture strain of FRP (𝜀𝑓𝑢) Modulus of elasticity (𝐸𝑓) 621 MPa 0.015 mm/mm 37000 MPa Thermal conductivity (𝑘𝑖) Specific heat (𝑐𝑖) Density (𝜌𝑖) 0.154 W/m-K 1.888 kJ/kg-K 425 kg/m3 66 Figures (a) (b) (c) Figure 4.1: Details of CFRP-strengthened PC T-beam: (a) longitudinal layout, (b) cross-section without insulation, (c) cross-section with SFRM insulation Figure 4.2: Temperature progression in CFRP-strengthened PC beam under ASTM E119 fire exposure without insulation 67 Figure 4.3: Temperature progression in CFRP-strengthened PC beam under ASTM E119 fire exposure with insulation Figure 4.4: Comparison of moment capacity of PC T-beams under ASTM E119 fire exposure 68 (a) (b) (c) (d) - Figure 4.5: Geometric configuration of CFRP-strengthened RC and PC beams: (a) longitudinal layout; (b) cross-section of RC beam; (c) cross-section of PC beam; (d) cross-section of insulated PC beam Figure 4.6: moment capacity comparison of CFRP-strengthened and un-strengthened RC and PC beams under fire exposure with and without insulation 69 CHAPTER 5 CONCLUSIONS 5.1 General This thesis presents a comprehensive investigation into the fire performance of fiber-reinforced polymer (FRP) strengthened prestressed concrete (PC) beams when subjected to standard fire exposure conditions (ASTM E119). The study is motivated by the growing use of FRP systems in structural strengthening applications and the limited understanding of their performance under elevated temperatures, particularly within prestressed concrete systems. An extensive literature review was conducted to examine the thermal and mechanical behavior of key constituent materials, including concrete, prestressing steel, and FRP composites, under elevated temperature conditions. The review also investigated the flexural performance of FRP-strengthened prestressed concrete beams under ambient conditions. From this review, significant research gaps were identified, particularly concerning the behavior of strengthened prestressed concrete elements in fire. Most existing studies tend to neglect the contribution of FRP reinforcement at elevated temperatures due to its thermal sensitivity, and limited efforts have been made to develop strategies that enhance the fire resistance of these systems. This highlights the need for a comprehensive analytical framework that can account for temperature-dependent material degradation and evaluate the performance of FRP-strengthened prestressed concrete beams under fire exposure. To address these gaps, a rational mechanics-based approach was formulated to evaluate the fire resistance of FRP-strengthened PC beams. This method incorporates temperature-dependent material degradation, heat transfer analysis, and equilibrium-based mechanical modeling to simulate the progressive deterioration of structural performance under fire conditions. The approach was first applied to previously tested FRP-strengthened RC beams to assess its validity. The predicted results showed close agreement with available fire test data and finite element analyses, confirming the reliability of the method. Following successful validation, the approach was applied to FRP-strengthened PC beams. For consistent benchmarking, a rectangular PC beam with an equivalent ambient moment capacity to a reference RC beam was selected. Both beams were subjected to similar loading and fire conditions to facilitate meaningful comparison. The results highlighted the relatively higher vulnerability of PC beams, which is attributed to the thermal sensitivity of both prestressing steel and the externally bonded FRP system. A detailed 70 parametric study was then conducted to investigate the influence of various parameters, including effective concrete cover and insulation thickness, on the fire resistance of strengthened PC beams. The results demonstrated that applying appropriate insulation, such as spray-applied fire resistive material, significantly delays thermal degradation and enhances structural performance during fire exposure. Although the rational approach has proven to be effective and reliable for evaluating fire resistance, certain limitations exist. These include assumptions about simplified thermal gradients and simplified modeling of strain compatibility. These limitations are discussed to provide complete context for the results and to identify areas where further refinement is needed. This chapter summarizes the main outcomes of the study and outlines key conclusions. It also offers recommendations for future work aimed at expanding the scope and accuracy of the proposed rational design approach for evaluating the fire resistance of FRP-strengthened prestressed concrete members. 5.2 Limitations of Rational Approach The applicability of the rational approach is subject to certain limitations, as it is validated only for FRP-strengthened PC beams under specific conditions. • The rational approach assumes no relative slip between the external FRP reinforcement and the concrete; however, this assumption may not be valid in practical applications, where relative can slip occur under high temperature exposure. Thus, this limitation may not be critical in the core region of the beams. • Although the rational approach has been validated for various FRP-strengthened RC beams, further validation against fire test data of FRP-strengthened PC beams can enhance the validity of the model. • The rational method for temperature evaluation is restricted to standard fire scenarios, including ASTM E119 and ISO 834. These equations may have to be shortly revised to the real design fire conditions. • The temperature predictions for FRP-insulated PC beams do not account for uncertainties such as cracking, uneven insulation thickness, or moisture evaporation in concrete and insulation, which can have some minor influence on the actual cross-sectional temperature distribution. 71 • The rational approach does not consider the effect of fire-induced axial restraints in PC beams. In practical conditions, axial restraints can develop due to thermal expansion and boundary conditions, affecting structural response and fire resistance. • The rational approach does not account for creep in prestressing steel and FRP at elevated temperatures. However, its influence may be minimal, as fire exposure durations are typically short, and strength degradation tends to govern the structural response before significant creep effects develop. • Concrete spalling is not considered in the proposed approach. However, its impact is minimal, as spalling is less likely to occur in normal-strength concrete subjected to standard fire conditions. • The proposed rational approach is limited to normal-strength concrete and does not account for the fire behavior of high-strength concrete, which is more susceptible to spalling and may exhibit different thermal and mechanical degradation characteristics. 5.3 Key Findings Based on the findings of this study, the following conclusions can be drawn: • The proposed rational approach provides a reliable method for evaluating the fire resistance of CFRP-strengthened PC beams. Its predictions align closely with FEA results, with deviations within an acceptable range. • The methodology accounts for key parameters such as the presence of fire insulation and the degradation of material properties in prestressing steel, FRP, and concrete. This enables accurate evaluation of moment capacity at different fire exposure durations while considering various failure modes. • PC strengthened beams exhibit more rapid strength degradation due to the high thermal sensitivity of prestressing steel, resulting in an accelerated loss of structural capacity and earlier failure at 90 minutes, compared to RC strengthened beams that sustain structural integrity up to 207 minutes. • The fire-induced degradation of PC beams is influenced by the compressive strength of concrete, which is evaluated using the concept of "effective concrete width." A relationship for width reduction in PC T-beam sections is developed based on results obtained from numerical simulations performed using FEA in ABAQUS. 72 • The fire resistance of FRP-strengthened PC beams can be significantly enhanced through supplementary fire insulation. The parametric study reveals that at least 25 mm of insulation is required to achieve three hours of fire resistance for FRP-Strengthened PC beams. • The proposed rational design methodology for evaluating the fire resistance of CFRP- strengthened PC beams is demonstrated through a design example. Its simplicity and broad applicability make it a practical approach for structural fire design. 5.4 Recommendations for Future Work Future research should prioritize the experimental validation of FRP-strengthened PC beams under fire conditions. While the current study is based on numerical analysis and comparisons with data from RC members, fire testing of full-scale FRP-strengthened PC beams is essential to confirm the accuracy of the rational approach. These experiments should consider variations in beam geometry, FRP type and layout, and fire insulation strategies to better capture the unique behavior and failure mechanisms of prestressed systems under elevated temperatures. Furthermore, extending the rational approach to more realistic fire scenarios beyond standard fire curves such as ASTM E119 or ISO 834. In actual buildings, fires may be localized, move across spaces, or be affected by ventilation and suppression systems, all of which can alter thermal boundary conditions. Incorporating these factors into the rational framework would improve its relevance for practical design situations. In addition, future studies should address the post-fire condition of FRP-strengthened PC beams. This includes assessing the residual mechanical properties of concrete, prestressing steel, and FRP after fire exposure, as well as the bond behavior between FRP and concrete. Understanding these aspects is critical for developing reliable assessment methods and repair techniques for fire-damaged structures. 73 REFERENCES [1] [2] [3] [4] [5] [6] Rosenboom, O. A. (2006). Behavior of FRP repair/strengthening systems for prestressed concrete. North Carolina State University. 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The moment capacity of the fire- exposed beam is determined based on fire exposure duration, and its fire resistance is assessed under specified standard fire conditions and applied loading. The detailed solution is presented in the following subsections. i. Calculate the External Moment Applied on the Beam Based on ASCE 7 recommendations, external loads under fire conditions can be calculated as 𝑤𝑓𝑖𝑟𝑒 = 1.2𝐷𝐿 + 0.5𝐿𝐿 = 1.2 × 23.8 + 0.5 × 19.8 = 38.46 𝑁 𝑚𝑚 The maximum external moment applied at the beam midspan is calculated as 𝑀𝑓𝑖𝑟𝑒 = 𝑤𝑓𝑖𝑟𝑒𝑙2 8 = 38.48 × 88502 8 = 376.7 𝑘𝑁 ∙ 𝑚 (20) (21) ii. Calculate the Temperature in Prestressing steel and External FRP Laminates The temperatures in the prestressing steel and external FRP laminates are determined using the proposed 1D and 2D heat transfer equations. As the T-beam is protected with SFRM fire insulation, the insulation layer is converted into an equivalent concrete layer for thermal analysis. The thermal properties of concrete and SFRM insulation are adopted from the literature (Bhatt 2021; Bisby 2003) 𝑘𝑖 = 0.154 W/m ∙ K 𝑘𝑐 = 1.355 W/m ∙ K (𝜌𝑐)𝑖 = 802 kJ/m3 ∙ K (𝜌𝑐)𝑐 = 2566 kJ/m3 ∙ K Thickness of the equivalent concrete layer is calculated using Eq. (5): 𝑧𝑒𝑐 = 19 ∙ √14.5 1.75 ∙ √( 1.355 2.566 ) ( 0.802 0.154 ) = 33.86 𝑚𝑚 (22) 79 By determining the equivalent concrete layer for the SFRM fire insulation, the distance from the center of the corner prestressing steel to the fire exposure sides is calculated as 33.8+64=97. 86mm.Since 𝑧′ = 𝑦′ =97.86mm, the temperature at the corner rebar after 1 hour of fire exposure is calculated using Eqs. (2)-(4). 𝜂𝑧 = 𝜂𝑦 = 0.155 𝐼𝑛 1 0.09781.5 − 0.348√0.0978 − 0.371 = 0.061 𝑇𝑐 = 1[(−1.481 ∙ (0.061 ∙ 0.061) + 0.985 ∙ (0.061 + 0.061) + 0.017)] × (910 ∙ 10.148) = 120°𝐶 (23) (24) For the external FRP, the average temperature of the FRP laminates is determined at a point one-quarter of the FRP length from the fire-exposed surface. The distance from the fire-exposed surface to the FRP is calculated as 𝑧′ = 33.86 + 51 = 84.8mm and 𝑦′ = 33.86mm. Accordingly, the FRP laminate temperature is evaluated using Eqs. (2)-(4). 𝜂𝑧 = 0.155 𝐼𝑛 1 0.08481.5 − 0.348√0.0848 − 0.371 = 0.101 𝜂𝑦 = 0.155 𝐼𝑛 1 0.03381.5 − 0.348√0.0338 − 0.371 = 0.352 𝑇𝑐 = 1[(−1.481 ∙ (0.101 ∙ 0.352) + 0.985 ∙ (0.101 + 0.352) + 0.017)] × (910 ∙ 10.148) = 374°𝐶 (25) (26) (27) Using a Python program, the temperatures at different fire exposure times can be calculated following the same procedure. The resulting time-temperature progressions in prestressing steel and external FRP are plotted in Fig. 7(b). iii. Evaluate the Strength of Prestressing Steel and FRP By determining the temperature in the prestressing steel and external FRP, the residual strength of prestressing steel can be evaluated using the temperature-dependent properties specified in Eurocode 2 (CEN 2004), as listed in Fig. 4.After 1 hour of fire exposure, the strength of prestressing steel is reduced to 𝑓𝑝𝑦,𝑇 = 1535Mpa, 𝑓𝑝𝑢,𝑇 = 1800Mpa and 𝑓𝑝𝑒 = 1108Mpa. Meanwhile, the residual strength of the external FRP laminate is calculated using the empirical relationships proposed by Bisby et al. (2005) through Eqs. (10) and (10). 80 𝑓𝑓,𝑇 = 2800 [( ) tanh(−5.83 × 10−3(374 − 339.54)) + ( 1 − 0.1 2 1 + 0.1 2 )] = 1293𝑀𝑃𝑎 𝐸𝑓,𝑇 = 16 × 104 [( 1 − 0.05 2 ) tanh(−8.68 × 10−3(374 − 367.41)) + ( 1 + 0.05 2 )] = 79919𝑀𝑃𝑎 (28) (29) To determine the effective concrete width in the compression zone, the temperature distribution across the beam is calculated, and the effective width reduction factors listed for a PC T-beam in Table 3 are considered. For 1-hour fire exposure, the effective concrete width retains 97.7% of its original width. iv. Calculate the FRP-system design material properties To determine the design material properties of the FRP system, the beam is located in an interior space, and CFRP material is used. As per ACI 440.2R-17, an environmental reduction factor of 0.95 is applied. The design tensile strength (𝑓𝑓,𝑑) and design rupture strain (𝜀𝑓𝑢,𝑑) are calculated using the following equations: 𝑓𝑓,𝑇𝑑 = 𝐶𝐸 × 𝑓𝑓,𝑇 = 0.95 × 1290 = 1228𝑀𝑃𝑎 𝜀𝑓𝑢,𝑑 = 𝐶𝐸 × 𝜀𝑓𝑢 = 0.95 × 0.017 = 0.01615 (30) (31) v. Preliminary calculations The preliminary calculations are performed based on ACI 318-19 provisions and the principles of mechanics, as outlined below. Stress block parameter (𝛽1) Modulus of elasticity of concrete (𝐸𝑐) Area of Prestressing steel (𝐴𝑝𝑠) Area of FRP reinforcement (𝐴𝑓) Cross-sectional area (𝐴𝑐𝑔) Distance from top fiber to the section centroid (𝑦𝑡) Gross moment of inertia (𝐼𝑔) Radius of gyration (𝑟) Effective prestressing strain (𝜀𝑝𝑒,𝑇) 0.75 30.2 𝑘𝑁/𝑚𝑚2 594 𝑚𝑚2 245 𝑚𝑚2 564800 𝑚𝑚2 240.43 𝑚𝑚 2.21 × 1010𝑚𝑚4 198 𝑚𝑚 0.00576 81 Effective prestressing force (𝑃𝑒,𝑇) Eccentricity of prestressing force (𝑒) 653.853 𝑘𝑁 335.56 𝑚𝑚 vi. Calculate the existing state of strain on the beam soffit The existing strain state is assessed assuming the beam remains uncracked and is influenced only by dead loads, with calculations carried out using Eq. (9). Distance from extreme bottom fiber to the section centroid: 𝑦𝑏 = ℎ − 𝑦𝑡 = 640 − 240.43 = 400𝑚𝑚 (32) Initial strain in the beam soffit: εbi,T = + −653853 30200 × 564800 232 × 106 × 400 30200 × 2.21 × 1010 = −3.05 × 10−5 335.56 × 400 1982 (1 + ) (33) vii. Calculate the design strain of FRP system The design strain of FRP is calculated using Eq. (10) while accounting for the debonding failure mode. 𝜀𝑓𝑑,𝑇 = 0.41√ 41.4 1 × 79919 × 1.2 ≤ 0.9 × 0.01615 = 8.51 × 10−3 ≤ 0.0145 (34) Since the design strain is lower than the rupture strain, debonding governs the design of the FRP system. viii. Estimate the depth of the neutral axis An initial estimate for neutral axis depth (𝑐) is taken as 0.1h and is adjusted based on equilibrium verification. In this design example, the calculations were performed using a program that confirmed equilibrium, allowing 𝑐 to be used as the final value. 𝑐 = 50 𝑚𝑚 ix. Calculate the effective level of strain in the FRP reinforcement The effective strain level in the FRP reinforcement may be calculated using Eq. (12) 𝜀𝑓𝑒,𝑇 = 0.003 ( ) + 3.05 × 10−5 ≤ 8.51 × 10−3 640 − 50 50 = 0.0354 > 8.51 × 10−3 Failure is governed by FRP debonding: 𝜀𝑓𝑒,𝑇 = 𝜀𝑓𝑑,𝑇 = 8.51 × 10−3 82 (35) (36) (37) x. Calculate the strain in the existing prestressing steel The strain in the prestressing steel can be calculated using Eq.13 and Eq.15. 𝜀𝑝𝑛𝑒𝑡 = (8.51 × 10−3 + (−3.05 × 10−5)) ( 576 − 50 640 − 50 ) = 7.56 × 10−3 (38) 𝜀𝑝𝑠,𝑇 = 0.00576 + 653853 30200 × 564800 (1 + 335.562 1982 ) + 7.56 × 10−3 = 0.0134 (39) xi. Calculate the stress level in the prestressing steel and FRP The stresses are determined using Eq. (16) and Eq. (17). 𝑓𝑝𝑠,𝑇 = 1800 − 0.276 0.0134 − 0.007 𝑓𝑓𝑒,𝑇 = 79919 ∙ 8.51 × 10−3 = 680𝑀𝑃𝑎 = 1756 𝑀𝑃𝑎 (40) (41) xii. Calculate the equivalent concrete compressive stress block parameters 𝜶 and 𝜷𝟏 The strain in concrete at failure is determined using strain compatibility principles as follows. 𝜀𝑐 = (𝜀𝑓𝑒,𝑇 + εbi,T) ( 𝑐 ℎ − 𝑐 ) = (8.51 × 10−3 + (−3.05 × 10−5))( ′ = 𝜀𝑐 ′ 1.7 × 𝑓𝑐 𝐸𝑐 = 7.18 × 10−4 1.7 × 41.4 30200 = = 2.33 × 10−3 50 640 − 50 ) (42) (43) The concrete stress block factors are determined according to ACI 318. These factors are derived from the parabolic stress-strain relationship of concrete and are expressed as follows. 𝛽1 = 4𝜀𝑐 6𝜀𝑐 2 ′𝜀𝑐 − 𝜀𝑐 ′ 2 = 3𝛽1𝜀𝑐 3𝜀𝑐 𝛼 = ′ − 𝜀𝑐 ′ − 2𝜀𝑐 = 4 × 2.33 × 10−3 − 7.18 × 10−4 6 × 2.33 × 10−3 − 2 × 7.18 × 10−4 = 0.685 (44) 3 × 2.33 × 10−3 × 7.18 × 10−4 − (7.18 × 10−4)2 3 × 0.685 × (2.33 × 10−3)2 = 0.40 (45) xiii. Check for equilibrium The verification of force equilibrium is performed by comparing the initially estimated 𝑐 from Eq. (41) with the calculated value derived from Eq. (18). 𝑐 = (𝐴𝑝𝑠𝑓𝑝𝑠,𝑇 + 𝐴𝑓𝑓𝑓𝑒,𝑇) (𝛼𝑓𝑐 ′𝛽1𝑏𝑇) = 594 × 1756 + 245 × 680 0.40 × 0.685 × 41.4 × 0.977 × 2220 = 50 (46) Since the initially estimated (𝑐) value matches the calculated (𝑐) ,equilibrium is achieved. If equilibrium is not satisfied, the initial estimate is adjusted iteratively with different (𝑐) values until equilibrium is attained. 83 xiv. Calculate the moment capacity of external FRP-Strengthened PC beam The moment capacity is determined using Eq. (19), incorporating an additional reduction factor (𝜓𝑓 = 0.85) to account for the contribution of the FRP system. 𝑀𝑛,𝑇 = 594 × 1756 (576 − 0.685 × 50 2 𝑀𝑛,𝑇 = 671𝑘𝑁 ∙ 𝑚 ) + 0.85 × 245 × 680 (640 − 0.685 × 50 2 ) (47) Using a Python program, the moment capacity at different failure times is determined following the same procedure. The variation in moment capacity with fire exposure time is illustrated in Fig. 8. xv. Estimate failure time The moment capacity of the FRP-strengthened PC beam reaches 376 𝑘𝑁 · 𝑚 at 160 minutes. Beyond this point, continued fire exposure causes the moment capacity to fall below the applied external moment, leading to structural failure. Thus, the beam's fire resistance is determined to be 2 hours. 84