Structural Fire Engineering Publications are listed below. They aim at understanding the behaviour of structures during or after exposure to fire and providing engineers with simplified tools that allow conducting performance-based design considering fire events. You can also check our engineering tools and/or submit your engineering inquiries.
Kuehnen R, Youssef MA, El-Fitiany, S, 2020, “Performance-based design of RC beams using an equivalent standard fire“, Journal of Structural Fire Engineering.
The design of buildings for fire events is essential to ensure occupant safety. Supplementary to simple prescriptive methods, performance-based fire design can be applied to achieve a greater level of safety and flexibility in design. To make performance-based fire design more accessible, a time-equivalent method can be used to approximate a given natural fire event using a single standard fire with a specific duration. Doing so allows for natural fire events to be linked to the wealth of existing data from the standard fire scenario. The purpose of this paper is to review and assess the application of an existing time-equivalent method in the performance-based design of reinforced concrete (RC) beams.
The assessment is established by computationally developing the moment-curvature response of RC beam sections during fire exposure. The sectional response due to natural fire and time equivalent fire are compared.
It is shown that the examined time equivalent method is able to predict the sectional response with suitable accuracy for performance-based design purposes.
The research is the first to provide a comprehensive evaluation of the moment-curvature diagram of RC beams using time-equivalent standard fire scenarios that model realistic fire scenarios.
Vedrtnama, A, Bedonb, C, Youssef, MA, Wamiqa, M, Sabsabi, A, Chaturvedia, S, 2020, “Experimental and Numerical Structural Assessment of Transparent and Tinted Glass during Fire Exposure”, Construction and Building Materials, 250: 118918.
Transparency, illumination, aesthetic and energy requirements have considerably increased the use of glass in modern high-rise buildings. During fire exposure, fracture and shattering of windows and facades accelerate the spread and severity of fire, which increases the risk for the occupants and the amount of structural damage. This paper aims at analyzing the effect of non-uniform thermal gradients on the flexural capacity of ordinary glass panels. Both transparent and tinted glass panels are considered to account for widely-used glass compositions. The bending response of fire-damaged glass panels is experimentally explored considering different durations of thermal exposure. The thermal breakage due to non-uniform temperature distributions over the height is also assessed. A finite element investigation is then conducted to further explore the experimental findings.
Kuehnen, RT, Youssef MA, El-Fitiany S.F., 2020, “Performance-Based Design of RC Columns using an Equivalent Standard Fire”, Fire Safety Journal, 111.
The extreme variability of natural compartment fires poses a significant challenge in the process of performance-based fire design. To reduce this variability, the severity of a natural fire can be related to that of a standard fire, known as a time equivalent (te). In this paper, the applicability of a time equivalent, previously derived based on the average internal temperature profile (AITP) that develops within reinforced concrete (RC) beams exposed to fire from three sides, is examined for RC columns exposed to fire from four sides. A parametric study is presented to examine the suitability of the existing AITP te in representing the internal temperatures of RC columns. The accuracy of the AITP te in approximating column performance, is judged based on the moment-curvature, axial load-axial strain, and bending moment-axial force relationships during fire exposure. Comparison with existing methods is provided to further demonstrate the superior suitability of the AITP te in representing natural fire severity for RC columns.
Kuehnen, RT, Youssef MA, 2019, “Equivalent Standard Fire Duration to Evaluate Internal Temperatures in Natural Fire Exposed RC Beams”, Fire Safety Journal. 108.
With the recent shift towards performance-based fire design, practical methods to account for natural fire loading when designing concrete structures are needed. Available design methods and analysis approaches are based on standard fire curves. To apply these methods, a natural fire event can be converted to a standard fire with a specific duration (time equivalent). However, existing time equivalents often ignore the influence of internal temperature gradients on the section behaviour, which is unacceptable for concrete structures.
This paper introduces a time equivalent method suitable for reinforced concrete (RC) beams exposed to natural fire. The method is based on the actual temperature gradient within a concrete section. To simplify analysis of RC beams exposed to fire, an average internal temperature profile (AITP) can be utilized, which records the average temperature variation along the height of a section. Two equations are provided such that a standard fire duration can be determined to accurately or conservatively represent the AITP of a beam section exposed to natural fire. Characteristics of the natural fire, as well as the influence of section dimensions are accounted for. The developed AITP time equivalent method is found to be superior to the existing methods and accurate in approximating the moment-curvature response for RC beam sections.
Ilomame, M, El-Fitiany, S, Youssef, MA, 2019, “Fire Temperature Distribution in Earthquake-Damaged RC Elements”, 12th Canadian Conference on Earthquake Engineering, Quebec, QC, June.
Post-earthquake fire hazards result in significant structural loss that, in some cases, exceed the initial damage due to earthquake itself. Although few research studies have addressed this topic, the fire performance of seismically-damaged Reinforced Concrete (RC) structures is not well understood. In addition, current building codes allow structural elements to undergo large plastic deformations and experience partial damage. This might increase the heat penetration inside the damaged cross-sections and leads to a fast-progressive collapse of the building. This paper utilizes a numerical approach to evaluate heat distribution in a seismically-cracked RC section. A cantilever-beam damaged under lateral cyclic load is chosen from the literature to be used as a case study. The strength and serviceability of the seismically-damaged beam are found to be highly affected by fire.
Kuehnen, RT, Youssef, MA, El-Fitiany, S, 2019, “Performance-Based Design of RC Beams Exposed to Natural Fire: A Case Study”, 7th International Conference on Engineering Mechanics and Materials, Laval, Quebec, June.
: In North America, the current practice for structural fire safety involves the implementation of prescriptive methods, requiring compliance with passive fire-resistance barriers and active suppression systems. Although this approach has been largely successful in delaying the propagation of fire, which allows for the safe evacuation of occupants, it provides limited knowledge about expected structural behavior during fire. To ensure structural integrity, the North American industry is moving towards performance-based structural fire design, focusing on structural elements that can achieve specific performance objectives during fire exposure. Buildings can thus be designed with greater flexibility, reduced construction costs, and improved occupancy safety. Given the intrinsic fire-resistant properties of concrete, performance-based design is particularly powerful in the case of reinforced concrete (RC) structures. In this paper, a case study is presented demonstrating a simplified approach to undertake performance-based flexural fire design of RC beams. The case study highlights the three main steps in the design process: (i) determination of the natural fire severity, (ii) calculation of element internal temperatures, and (iii) sectional flexure analysis. In each part, the process is performed using simplified analysis methods, which are validated against results obtained using experimental tests and finite element simulations. Using the approach, engineers can calculate the moment capacity of RC beams to withstand natural fire events..
Salah F. El-Fitiany, Maged A. Youssef, 2018, “Practical method to predict the axial capacity of RC columns exposed to standard fire“, Journal of Structural Fire Engineering, https://doi.org/10.1108/JSFE-08-2016-0015. Existing analytical methods for the evaluation of fire safety of Reinforced Concrete (RC) structures require extensive knowledge of heat transfer calculations and the finite element method. This paper proposes a rational method to predict the axial capacity of RC columns exposed to standard fire. The average temperature distribution along the section height is first predicted for a specific fire scenario. The corresponding distribution of the reduced concrete strength is then integrated to develop expressions to calculate the axial capacity of RC columns exposed to fire from four faces. These expressions provide structural engineers with a rational tool to satisfy the objective-based design clauses specified in the National Code of Canada in lieu of the traditional prescriptive methods.
Existing analytical methods for the evaluation of fire safety of Reinforced Concrete (RC) structures require extensive knowledge of heat transfer calculations and the finite element method. This paper proposes a rational method to predict the axial capacity of RC columns exposed to standard fire. The average temperature distribution along the section height is first predicted for a specific fire scenario. The corresponding distribution of the reduced concrete strength is then integrated to develop expressions to calculate the axial capacity of RC columns exposed to fire from four faces. These expressions provide structural engineers with a rational tool to satisfy the objective-based design clauses specified in the National Code of Canada in lieu of the traditional prescriptive methods.
El-Fitiany SF, Youssef MA, 2017, “Fire Performance of Reinforced Concrete Frames using Sectional Analysis”, Engineering Structures, 142: 165-181.
Global behavior of RC structures during fire events can be predicted using complex nonlinear thermal-structural numerical simulations. However, such simulations are computationally expensive, which limit their use by design engineers. A practical approach to track the performance of RC frames during fire exposure is proposed and validated in this paper. A previously developed simple heat transfer technique is used to calculate an average 1D temperature distribution for heated RC sections. Consequently, the flexural and axial stiffnesses as well as the unrestrained thermal deformations are evaluated using sectional analysis. Based on rational assumptions, simplified expressions are also driven to evaluate those values. The proposed method can be easily applied using available commercial linear structural analysis software to predict the fire performance of RC framed structures. Additional experimental and analytical work is required to validate the proposed method in non-standard fire scenarios.
Alhadid, MMN, Youssef, MA, 2016, “Residual Axial Behavior of Fire-Damaged Reinforced Concrete Columns“, CSCE 5th International Structural Specialty Conference, London, ON, Canada, Paper #898.
Engineers need a simplified procedure to predict the residual axial capacity and stiffness of Reinforced Concrete (RC) columns exposed to a complete heating-cooling cycle. Finite difference heat transfer and sectional analysis models are developed to determine the axial behavior of such columns with various end-restraint conditions at different fire durations. The influence of cooling phase on temperature distribution and residual mechanical properties are considered in the analysis. The ability of the model to predict the axial behavior of the damaged columns is validated in view of related experimental studies and shown to be in very good agreement. A parametric study is then conducted to assess the axial performance of fire-damaged RC columns. A procedure is proposed to determine the residual strength and stiffness of fire-damaged RC columns in typical frame structures.
Youssef M.A., Diab M.A., El-Fitiany S.F., 2015, “Shear Capacity of RC Beams at Elevated Temperatures”, Magazine of Concrete Research, 67(22): 1190-1203.
Fire safety is a critical criterion for designing reinforced concrete structures. With the introduction of performance-based design, structural engineers need design tools to assess the capacity of different elements during fire exposure. This paper proposes an analytical method to predict the shear capacity of reinforced concrete beams exposed to elevated temperatures. The proposed method extends the use of existing ambient temperature methods by accounting for the effect of elevated temperatures on material properties. It involves heat transfer analysis, evaluation of the material properties at elevated temperatures, and application of the modified compression field theory to estimate the shear capacity. The method is validated using experimental results by others. A parametric study is then conducted to investigate the effects of different parameters on the shear capacity of reinforced concrete beams exposed to fire.
Youssef M.A., 2014, “Fire Resistance of Reinforced Concrete Structures”, keynote speech, The Eighth Alexandria International Conference on Structural and Geotechnical Engineering (AICSGE8), Alexandria, Egypt, April 14-16. (Invited)
El-Fitiany SF, Youssef MA, 2014, “Interaction Diagrams for Fire-Exposed Reinforced Concrete Sections”, Engineering Structures, 70: 246-259.
Fire safety of Reinforced Concrete (RC) columns is an important design aspect to ensure the overall integrity of structures during fire events. Currently, fire ratings of RC sections are achieved using prescriptive methods. As new codes are moving towards performance based design, practitioners are in need of rational design tools to assess the capacity of heated sections. To construct the axial force-moment interaction diagram of a RC section using existing numerical methods, high computation demand and knowledge of heat transfer and stress analysis are required. This paper presents the derivation of a set of formulas that can be used to estimate the average temperature distribution within the concrete section and the corresponding internal forces. The utilization of these formulas to construct interaction diagrams of fire-exposed RC sections is then explained. The proposed formulas are validated by comparing their predictions with experimental and analytical results by others.
El-Fitiany S.F., Youssef M.A., 2014, “Simplified Method to Analyze Continuous Reinforced Concrete Beams during Fire Exposure”, ACI Structural Journal, 111(1): 145-155.
Structural engineers are in need of analytical tools to evaluate the performance of reinforced concrete (RC) structures during fire events. Existing numerical methods require extensive knowledge of heat transfer calculations and the finite element method. This paper proposes a rational method to track the fire performance of continuous RC beams during ASTM E119 standard fire exposure. The proposed method uses a simplified sectional analysis approach and is based on separating the effects of thermal deformations and vertical loads. The effective flexural stiffness and the thermal deformations of the beam are estimated using simple expressions that are developed based on a comprehensive parametric study.
Alhadid MMA, Youssef MA, 2013, “Structural Behavior of Jacketed Fire-Damaged Reinforced Concrete Members: A Review”, 3rd Specialty Conference on Disaster Prevention and Mitigation, May 29 to June 1, Montreal, QC, Canada, DIS-023, 10 pp, DOI: 10.13140/2.1.2612.4804.
The production of concrete as a superior building material led to a consequent civilian renaissance in construction. Unfortunately despite the enormous advantages of Reinforced Concrete (RC) structures, they deteriorate and loose part of their strength when exposed to fire. The mechanical properties of concrete and reinforcing steel as well as the interfacial behavior between them pass through several significant changes during the heating and cooling stages. Therefore, a detailed assessment strategy should be carried out to evaluate the overall performance of a fire-damaged structure. The main objective of this paper is to summarize the experimental and analytical research concerned with the behavior of retrofitted fire-damaged RC elements. The paper will present information about the residual strength of fire-damaged RC elements and the expected improvements in their capacities when retrofitted using RC jackets. The information gathered in this paper will provide a strong basis to identify future research needs for assessing the capacity and retrofitting of fire-damaged RC structures.
El-Fitiany SF, Youssef MA, 2013, “Unrestrained Thermal Deformations of Concrete Elements Exposed to Fire”, 3rd Specialty Conference on Disaster Prevention and Mitigation, May 29 to June 1, Montreal, QC, Canada, DIS-043, 10 pp, DOI: 10.13140/2.1.4709.6326.
Fire impacts Reinforced Concrete (RC) members by raising the temperature of the concrete mass. This rise in temperature dramatically reduces the mechanical properties of concrete and steel and induces new strains, thermal and transient creep. As a result, heated RC members undergo considerable thermal deformations during fire events. This paper presents a comprehensive parametric study to evaluate the unrestrained thermal deformation parameters, curvature and axial strain, for rectangular RC sections during ASTM-E119 fire exposure. These parameters describe the section’s free thermal expansion at different fire durations. The proposed expressions can be used by engineers to estimate the restraint effect in indeterminate RC structures exposed to fire.
Youssef MA, El-Fitiany SF, 2013, “Simplified Method for Predicting Deformations of RC Frames During Fire Exposure”, Application of Structural Fire Engineering (ASFE), April 19-20, Prague, Czech Republic, pp. 334-339, DOI: 10.13140/2.1.3205.3761.
Structural engineers are in need of analytical methods to assess the performance of Reinforced Concrete (RC) frames during fire events. Existing numerical methods require extensive knowledge of heat transfer calculations and the finite element method. This paper proposes a practical approach to track the fire performance of indeterminate RC frames during ASTME119 and ISO 834 standard fires exposure. The proposed method utilizes a finite difference method to predict the temperature distribution within the section of the RC frame. The predicted elevated temperatures are then used to conduct a sectional analysis. The effective flexural and axial stiffnesses are evaluated and used to predict the overall behavior of the structure during fire. The proposed approach is validated by comparing its predictions with analytical results by others.
Hayhoe W., Youssef M.A., El-Fitiany SF, 2013, “Reinforced Concrete Walls during Fire: Investigation of the Out-of-Plane Flexural Capacity”, Application of Structural Fire Engineering (ASFE), April 19-20, Prague, Czech Republic, pp. 352-357, DOI: 10.13140/2.1.4861.1845.
Current building codes address the design of concrete walls for fire by specifying minimum thicknesses and concrete covers based on required fire ratings. As building codes move towards performance-based design for fire, it is important to provide engineers with tools to design concrete walls to resist fire. The out-of-plane flexural capacity of a wall is critical to resist loads associated with the hose stream during fire-fighting efforts, wind loads, and movements perpendicular to the wall longitudinal axis. In this paper, a parametric study is conducted to evaluate the effect of different parameters on the out-of-plane flexural capacity. A simplified sectional analysis method is utilized to sketch the moment-curvature diagrams of different walls. Results are examined to assess the effect of each of the considered parameters on the wall out-of-plane performance and capacity.
Hayhoe WC, Youssef MA, 2013, “Structural Behaviour of Concrete Walls during or after Exposure to Fire: A Review”, CSCE 2013 General Conference, May 29 to June 1, Montreal, QC, Canada, GEN-182, 10 pp, DOI: 10.13140/2.1.4294.9126.
Reinforced concrete walls form an integral part of the structure of many buildings. They support both vertical and lateral loads and provide fire separation between different compartments within a building. During a fire, a concrete wall must: maintain its structural adequacy, provide temperature insulation between the building compartments, and remain free of excessive cracking or deformations that would allow the passage of flames. After a fire, it is critical to know the vertical and lateral capacity of the fire-damaged concrete wall to assess the safety of the building. Current building codes address the design of concrete walls for fire by specifying minimum thicknesses of walls based on required fire ratings. As building codes move towards performance-based design for fire, it is important to provide engineers with a performance-based method for designing concrete walls to resist fire. This paper summarizes and provides a critical review of existing experimental and analytical research addressing the effect of fire on concrete walls. The completeness, practicality, and accuracy of the existing literature is reviewed for the purpose of determining future research needs.
El-Fitiany SF, Youssef MA, 2012, “Evaluation of Flexural Stiffness of RC Beams during Fire Events”, 3rd International Structural Specialty Conference, CSCE, Edmonton, AB, Paper No STR-1103, 9 pp, DOI: 10.13140/2.1.2645.2486.
Analysis of Reinforced Concrete (RC) structures for fire safety is usually conducted at the research level rather than practical design applications. This limitation is due to the complexity of the fire problem and the need for comprehensive finite element tools. Fire performance of RC continuous beams can be predicted by superimposing the effects of thermal expansion and vertical loads. The free thermal rotation of RC sections during fire exposure can be described by the thermal curvature at different fire durations. On the other hand, the reduction in the material mechanical properties can be represented by the degradation in the flexural stiffness of the exposed cross-section. This paper presents a comprehensive parametric study on the reduction of the flexural stiffness for rectangular RC sections heated from three sides according to ASTME119 fire exposure. The effective flexural stiffness is determined as the secant slopes of the moment-curvature diagrams. These curves are constructed for heated RC sections at different axial load levels. Based on the results of the parametric study, the authors proposed equations to estimate the reduced flexural stiffness for RC beams at different fire durations up to 2.5 hrs. Structural engineers can use the proposed equations to check the structural fire safety of RC beams.
El-Fitiany S.F., Youssef M.A., 2011, “Stress-Block Parameters for Reinforced Concrete Beams during Fire Events”, ACI SP-279: Innovations in Fire Design of Concrete Structures, ACI-TMS Committee 216: Fire Resistance and Fire Protection of Structures, Paper No. 1: 1-39.
Fire safety is a critical criterion for designing reinforced concrete (RC) structures. As new design codes are moving towards performance-based design, analytical tools are needed to help engineers satisfy code criteria. These tools are also needed to assess the fire performance of critical structures. As full scale experiments and finite element simulations are usually expensive and time consuming options for designers to achieve specific fire performance, a simplified sectional analysis methodology that tracks the axial and flexural behavior of RC square sections subjected to elevated temperatures from their four sides was previously developed and validated by the authors. In the first part of this paper, the proposed methodology is extended to cover rectangular beams subjected to standard ASTM-E119 fire from three sides. An extensive parametric study is then conducted to study the distribution of the concrete compressive stresses at different ASTM-E119 fire durations. Based on the parametric study, simple equations expressing the equivalent stress-block parameters at elevated temperatures are presented. These equations can be utilized by designers to accurately estimate the flexure capacity of simply supported and continuous beams exposed to fire temperatures.
El-Fitiany S.F. and Youssef M.A., 2010, “A simplified sectional analysis approach for RC elements during fire events”, Structures in Fire – Proceedings of the Sixth International Conference, SiF’10, pp. 239-246, DOI: 10.13140/2.1.3180.8007.
Sectional analysis is widely used to assess the design of Reinforced Concrete (RC) members at ambient temperature. During fire exposure, a heat gradient is created within the concrete mass that induces non-uniform thermal and mechanical strains. These strains complicate using the same approach to predict the fire resistance of RC members. A simplified sectional analysis that tracks the axial and flexural behavior of RC elements during fire events is presented in this paper. The proposed method is based on using the Finite Difference (FD) analysis to estimate the temperature distribution within a concrete section. A rational approach is then proposed to convert the FD two-dimensional temperature distribution to one-dimensional distribution. This modification converts a complex problem to a simplified one and thus enables engineers to better understand the behavior and have higher confidence in the results. This paper covers the use of the simplified method for square columns subjected to fire from four sides and for rectangular beams exposed to fire from three sides. The validation of the proposed method is presented by comparing its predictions with other experimental and analytical results.
El-Fitiany S.F., Youssef M.A., 2009, “Assessing the Flexural and Axial Behaviour of Reinforced Concrete Members at Elevated Temperatures using Sectional Analysis”, Fire Safety Journal, 44(5): pp. 691-703.
Simplified, rational, and practical models that account for the effect of elevated temperature on concrete and steel properties are needed. These models will enable engineers to design and assess reinforced concrete (RC) structures to satisfy specific fire performance criteria. This paper introduces a simple method that predicts the flexural and axial behaviour of RC sections during exposure to elevated temperatures. The method is based on using finite difference analysis to estimate the temperature distribution within a concrete section and a modified version of the well-known sectional analysis approach to predict the axial and/or flexural behaviour. A rational approach is proposed to convert the two-dimensional temperature distribution to a one-dimensional distribution. This approach converts a complex problem to a simplified one and thus enables engineers to better understand the behaviour and have higher confidence in the results. The predictions of the proposed method are validated using experimental and analytical studies by others. Additional tests are needed to further validate and improve the proposed method.
Youssef M.A., El-Fitiany S.F., Elfeki M., 2008, “Flexural Behavior of Protected Concrete Slabs after Fire Exposure”, ACI SP-255: Designing Concrete Structures for Fire Safety, ACI-TMS Committee 216: Fire Resistance and Fire Protection of Structures, Paper No. 3: 47-74.
Fire is one of the common events that might occur during the lifetime of any concrete structure. At elevated temperatures, mechanical properties of concrete and reinforcing bars experience significant deterioration. Following a fire event, these properties improve with time toward their original values. The paper focuses on the flexural behavior of unreinforced or lightly reinforced siliceous concrete slabs after exposure to elevated temperatures. Such behavior is controlled by the concrete tensile behavior. Models to predict related concrete and steel mechanical properties during and after exposure to elevated temperatures are presented. When needed, new models are developed based on available experiments data. A case study involving flexural testing of 11 concrete slabs after 85 days from exposure to fire is presented. The slabs were protected by a thin sprayed liner (TSL). The case study allowed evaluating the presented models and assessing the effect of the TSL layer on the slabs’ behavior.
El-Fitiany S.F. and Youssef M.A. , 2008, “Behaviour of Axially Loaded Concrete Members During and Following Fire Events”, 2nd Canadian Conference on Effective Design of Structures CCEDS-II, Sustainability of Civil Engineering Structures, Hamilton, ON, Canada, pp. 487-496, DOI: 10.13140/2.1.4032.7687.
Effect of Fire on concrete structures is one of the research topics that have received noticeable attention from researchers in the last four decades. Concrete compressive strength, modulus of elasticity, and tensile strength experience significant deterioration during fire events. Following being exposed to fire, these properties were found to regain their original values with time. The same phenomenon was observed for reinforcing steel rebars. This recovery in material properties is expected to affect the overall behaviour of fire-damaged reinforced concrete elements. This paper reviews the available models proposed by different researchers to predict concrete mechanical properties during and after fire exposure. The investigated properties are those affecting the axial capacity of a compression member, concrete compressive strength, initial modulus of elasticity, and thermal induced strains. Steel tensile strength was also studied to account for its contribution to the capacity of axially loaded reinforced concrete sections. Based on the proposed models, an analytical study was conducted to assess the overall axial behaviour of a specific concrete section during and after experiencing an ASTM-E119 fire scenario for up to one hour.
Youssef M.A. and Moftah M., 2007, “General Stress-Strain Relationship for Concrete at Elevated Temperatures”, Engineering Structures, 29(10): 2618-2634.
A general stress–strain relationship for concrete when subjected to fire is needed, as it allows designing concrete structures to specific fire-performance criteria and improves the understanding of the behaviour of these structures during fire events. Existing relationships are developed based on fire tests of unconfined concrete specimens. They provide significantly different predictions because of uniqueness of each relationship and the existence of numerous formulations for calculating the governing parameters. In this paper, available formulations for estimating the parameters affecting the behaviour of unconfined and confined concrete are presented. These parameters are concrete compressive strength, concrete tensile strength, concrete compressive strain at peak stress, initial modulus of elasticity of concrete, transient creep strain, thermal strain, and yield stress and bond strength of reinforcing bars. Recommendations for choosing specific formulations are made based on accuracy, generality, and simplicity. Suitable compressive and tensile stress–strain relationships at elevated temperatures that utilize the recommended formulations are proposed based on well-established relationships for confined concrete at ambient temperature. The proposed relationships are compared to existing ones and to the available experimental data. They can capture changes in the mechanical properties of concrete resulting from temperature and confinement and are found to be superior to existing relationships. However, additional tests are needed to further validate and improve the proposed relationships.
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