Experimental Test and Analytical Calculation on Residual Strength of Prestressed Concrete T-Beams After Fire

Abstract

High temperatures during a fire can lead to the evaporation of moisture and the degradation of hydration products within concrete, consequently compromising its mechanical properties. This paper thoroughly investigates the effect of fire-induced high temperatures on the residual load-bearing capacity of concrete structures, with a focus on prestressed concrete T-beams. By conducting constant temperature tests and residual load-bearing capacity tests, complemented by finite element modeling, this study examines the degradation of mechanical properties in prestressed concrete T-beams due to fire exposure and its impact on post-fire residual load-bearing capacity. Additionally, an equivalent concrete compressive strength method was employed to propose a calculation method for concrete material degradation under high temperatures and a corresponding concrete strength reduction factor. Simplified calculations were also performed for the high-temperature damage to reinforcement and prestressed tendons, leading to the derivation of a simplified formula for the residual load-bearing capacity of post-fire prestressed concrete T-beams. The results indicate that in prestressed concrete T-beams exposed to fire, an increase in holding time results in more severe damage modes, accelerated crack propagation, and wider crack widths during bending failure. Under the same load, a longer holding time corresponds to a more pronounced reduction in deflection. At holding times of 60 min, 120 min, and 180 min, the prestress losses were 48.17%, 85.16%, and 93.26%, respectively. The cracking load decreased by 15%, 27%, and 42%, while the residual load-bearing capacity decreased by 11%, 21%, and 28%. Comparison with experimental data demonstrates that both the finite element model and the simplified calculation formula exhibit high accuracy, offering a reliable reference for the performance evaluation of post-fire prestressed concrete T-beams.

1. Introduction

Over the past three decades, both domestic and international scholars have conducted extensive research on the fire resistance of concrete beams, yielding significant results [1,2]. However, studies examining the residual mechanical properties of concrete T-beams after disasters remain relatively scarce, particularly in the context of prestressed concrete T-beams [3]. Prestressed concrete T-beams offer numerous advantages over ordinary concrete beams, including superior performance, reduced structural weight, enhanced deformation capacity, and increased resistance to lateral seismic forces [4]. Consequently, they have been widely utilized in various applications, such as the Comprehensive Training Hall of Hainan Provincial Sports Center and the Chengdu Fuhua Bridge. Prestressing tendons play a crucial role in the load-bearing capacity of a given structure; however, exposure to high temperatures during a fire can lead to a more rapid degradation of their ultimate tensile strength. Furthermore, the flange and web of T-shaped beams are relatively thin, rendering them more susceptible to structural instability and instantaneous failure when subjected to the high temperatures of a fire [5].

Research on fire resistance in structural engineering began in the late 19th century, while China initiated its studies in this area in the 1970s. The 1980s marked a period of vigorous development in fire protection design research. Kodur et al. [6] conducted a multi-parameter study on the fire resistance of rectangular concrete beams and established expressions for the fire resistance limits of reinforced concrete beams under various conditions. Tan et al. [7] proposed a simplified fire resistance formula applicable to different fire-exposed surfaces based on experimental tests of reinforced concrete (RC) columns under fire conditions. Wang Yuzhuo et al. [8] investigated the temperature field distribution of reinforced concrete beams at various fire resistance durations, noting that the temperature distribution pattern differs between heating and cooling periods. However, the incorporation of prestressing tendons results in significant differences in fire resistance performance between prestressed concrete structures and conventional reinforced concrete structures [9]. Bamonte P et al. [10] found that existing fire design codes for concrete beams are not applicable to prestressed concrete beams, indicating the need for the establishment of assessment methods specifically for the fire resistance performance of prestressed concrete beams. Selamet et al. [11] analyzed the variation of various mechanical properties of prestressed steel cables with changes in temperature. Khalaf et al. [12] developed a novel analytical model to predict the bond stress slip between prestressing tendons and concrete under fire conditions. Zhang Gang et al. [13] discovered, through experimental research, that a cross-sectional shape significantly influences fire resistance performance.

In addition to the necessity of investigating the fire resistance of building structures, the safety issues pertaining to these structures after experiencing a fire are of greater significance. This specifically involves evaluating the extent of damage to structural components to facilitate informed decision-making regarding appropriate remediation strategies. Consequently, it is imperative to conduct research on the residual load-bearing capacity of structures following a fire incident. Yu et al. [14] found that as the duration of the fire increases, the ductility and flexural stiffness of prestressed concrete beams exhibit significant deterioration. Liu et al. [15] established a comprehensive sample database grounded in refined numerical analysis models and proposed several predictive methods for assessing residual flexural load-bearing capacity following fire exposure. Zhang et al. [16] formulated a theoretical computational model to assess the residual load-bearing capacity of SP-PCBs post-fire; however, the resulting data proved to be somewhat conservative.

Despite significant progress, there are still considerable gaps in the current research landscape. Existing studies predominantly focus on non-prestressed concrete structures, leaving the behavior of prestressed concrete T-beams under fire exposure less understood. Although computational models simulate fire damage in concrete structures, only a few specifically address the residual load-bearing capacity of prestressed T-beams, particularly with varying fire exposure durations and intensities. Research on fire resistance in prestressed beams exists, but key limitations remain. A major challenge is the variation in mechanical performance between different cross-sectional shapes, particularly T-shaped prestressed beams, whose fire resistance and residual load-bearing capacity are underexplored. Additionally, there is a notable lack of validated computational methods to assess the residual capacity of T-shaped prestressed beams after fire.

In response to these gaps, this study conducts thermal retention and residual load-bearing capacity tests on T-shaped prestressed concrete beams subjected to elevated temperatures. The aim is to evaluate the residual capacity post-fire. Using the experimental data, a nonlinear finite element analysis was conducted, resulting in the development of a computational formula applicable to T-shaped prestressed beams exposed to high temperatures. This study addresses the limitations of previous research and proposes a simplified calculation method based on experimental findings. The method offers practical guidance for engineers evaluating fire-damaged structures and contributes to both theoretical understanding and real-world applications in the fire resistance of prestressed concrete beams.

2. Overview of Experimental Methodology

2.1. Design and Materials of Experimental Specimens

2.1.1. Workflow for Specimen Design

This study constructed four T-shaped prestressed concrete beams, all of which share identical geometric dimensions. The specific dimensions and reinforcement details are illustrated in Figure 1. Each experimental T-beam has a total length of 2000 mm and a height of 250 mm, with a flange thickness of 600 mm, a web width of 150 mm, and a cover thickness set at 25 mm. The concrete design strength of the experimental T-beams is classified as C40, utilizing HRB400-grade reinforcement bars manufactured by Xiangtan Steel Group Co., Ltd., located in Xiangtan, China. The longitudinal reinforcement for the flange and web consists of ribbed bars with diameters of 8 mm and 12 mm, respectively. Additionally, 8 mm smooth round bars are used for stirrups, spaced at 100 mm, while the prestressing tendons are composed of 1860-grade 1 × 7 stranded wire.

The casting process for the experimental T-beams is depicted in Figure 2. The concrete is mixed using a concrete mixer and poured into the prepared beam molds once it achieves adequate workability. Subsequently, a vibratory probe is employed to ensure proper compaction of the concrete, followed by leveling the surface. The beams are then covered with plastic sheeting and cured at room temperature, during which appropriate watering is conducted. Once curing is complete, the molds are removed. Prestressing is applied to the experimental T-beams with straight reinforcement, employing a post-tensioning method for bonded prestressing tendons.

2.1.2. Mechanical Properties of Materials

All materials used for the experimental beam specimens were sourced from the same batch, with the concrete strength designed according to a C40 mix ratio. During the concrete casting process, a set of 150 mm × 150 mm × 150 mm cubic specimens was also prepared to determine the compressive strength of the concrete. The weight mix ratio of the concrete and the measured compressive strength of the standard cubes are presented in

Table 1. Concrete mix proportions and strength test results.

Weight Proportioning Ratio				Cube Identification Number	Compressive Strength of Cubes (MPa)
Cement	Water	Sand	Gravel	1	40.2
				2	41.6
1	0.390	1.906	2.951	3	40.8

. Tests were conducted on the reinforcement used in the experimental beams, with the mechanical properties of the reinforcing bars detailed in

Table 2. Mechanical properties of steel bars.

Materials	Diameter of Reinforcing Steel Bars (mm)	Yield Strength (MPa)	Tensile Strength (MPa)
Plain round steel bar	8	462.9	586.6
Deformed steel bar	8	464.1	598.8
Deformed steel bar	12	470.2	611.4

.

2.2. Experimental Design and Measurement Protocols

2.2.1. Experimental Protocol

This study conducted two distinct experimental phases: thermal retention tests and residual load-bearing capacity tests. The experiments were designed to incorporate three different fire exposure durations: 60 min, 120 min, and 180 min. Additionally, a prestressed concrete T-beam maintained at ambient temperature was established as a control group. For the purpose of statistical analysis, a standardized numbering system was employed, where “PTL” denotes prestressed concrete T-beams. The subsequent numbers indicate the fire exposure duration: “0” represents no exposure to fire, “60” indicates an exposure duration of 60 min, “120” represents 120 min, and “180” signifies 180 min of exposure.

The simulated fire temperature increase and thermal retention tests were conducted at the Fire Laboratory of Central South University, utilizing a horizontal fire testing furnace. Temperature elevation was controlled according to the ISO-834 standard temperature-time curve (JGJ369-2016) [17], initially raising the temperature to 800 °C, which was then maintained constant for three specified durations: 60 min, 120 min, and 180 min. The experimental beams were subjected to a three-sided fire exposure configuration. Initially, the beams were suspended in the testing furnace, with the pre-installed thermocouple leads connected to the measuring instruments. Fire-resistant rock wool was placed on top of the beams, and the cover of the high-temperature furnace was securely fastened before commencing the heating process. The specific arrangement for the fire simulation test is illustrated in Figure 3. Upon completion of the thermal retention test, the high-temperature furnace and the experimental beams were allowed to cool naturally to ambient temperature. Subsequently, the beams were removed for comparative observation.

The residual load-bearing capacity tests were conducted using a high-precision microcomputer-controlled electro-hydraulic servo long-column pressure testing machine. A four-point loading configuration was employed, with the boundary conditions set for a simply supported beam. The loading and measurement apparatus are illustrated in Figure 4. Prior to the commencement of the test, a preloading procedure was conducted, initially applying a load of 5 kN to verify the proper functioning of the testing apparatus. Subsequently, the load was reduced to 0 kN, followed by a zeroing process for the measurement instruments.

2.2.2. Testing Parameters

To analyze the temperature variation patterns within the cross-section of the experimental T-beams, K-type thermocouples were strategically placed at mid-span to measure temperature. The selected thermocouples were WRNK01K type, manufactured by Shanghai Yibai Automation Instrument Co., Ltd. in Shanghai, China, consist of nickel–chromium and nickel–silicon materials with a length of 2 m. Five temperature measurement points were established on the experimental beams to specifically monitor the temperatures of the tensile reinforcement (Point 1), prestressed reinforcement (Point 2), and the internal compressive reinforcement of the flange (Points 3, 4, and 5). The precise locations of these measurement points are illustrated in Figure 5.

In the residual load-bearing capacity tests, a single displacement device was symmetrically positioned at the bottom mid-span of the experimental T-beams to obtain data on the variation in bending deflection. The displacement device had a measurement range of 200 mm, with the specific arrangement as illustrated in Figure 6.

3. Analysis of Experimental Phenomena and Results

3.1. Experimental Observations

3.1.1. Post-Fire Test Visual Manifestations

Figure 7 illustrates the structural response of concrete beams to high temperatures. The black charred areas indicate thermal degradation, correlating with longer exposure times and highlighting the need for improved fire-resistance measures in concrete. Minor spalling on the bottom surfaces, caused by internal pressures from moisture vaporization, suggests potential structural integrity issues. The fine diagonal cracks reflect complex stress distributions due to differential thermal expansion between the exposed and cooler regions.

The test beam subjected to a duration of 60 min exhibited no significant damage, with the area of the black regions on the concrete surface being relatively limited; however, as the duration increased, the area of the black regions progressively expanded. Upon reaching a duration of 120 min, the black regions on the surface effectively encompassed the entire concrete surface. Moreover, as a result of the substantial evaporation of moisture within the concrete, white stripes and spots emerged on the surface. At a duration of 180 min, the black regions on the surface fully covered the entire concrete area and the coloration deepened, accompanied by a notable increase in the number of white stripes and spots. These visual indicators, including color changes and surface damage, are critical for assessing the structural performance of concrete after fire exposure. They reinforce the theoretical understanding of thermal effects on concrete and support the study’s conclusions on fire-induced damage. Visual analysis thus plays a vital role in evaluating the resilience and safety of concrete structures under extreme thermal conditions.

3.1.2. Observations of Residual Load-Bearing Capacity Test

Residual load-bearing capacity tests were conducted on both the experimental beams at ambient temperature and those subjected to high temperatures from fire exposure. The overall failure modes and crack development of the experimental beams are illustrated in Figure 8, while the cracking behavior in the pure bending region is detailed in Figure 9. All experimental T-beams exhibited significant deformations, and the incremental stress levels were relatively high. When the stress levels exceeded the flexural strength of the concrete, this could lead to crack formation, subsequently resulting in spalling. The experimental beams experienced flexural failure, with the ultimate failure mode characterized by the crushing of the concrete in the compression zone of the top flange. Cracks in the experimental T-beams were primarily concentrated in the pure bending region, predominantly manifesting as vertical cracks, with negligible occurrence of diagonal cracks.

As the load increased, cracking was observed in the flange of the pure bending region of the experimental beams, accompanied by slight audible sounds. With further load application, new cracks emerged, extending upward to the mid-height of the beam, which corresponds to the location of the neutral axis. The width of these cracks also increased. When the load reached ultimate load capacity, no new cracks were formed; instead, the widths of the existing cracks continued to expand until cracking occurred in the concrete of the compression zone, as shown in Figure 10. As the duration of fire exposure increased, the extent of damage to the experimental beams escalated, resulting in earlier crack formation, accelerated crack propagation, and widening of the cracks. In the experimental T-beam PTL-180, a distinct “bang” was heard, coinciding with the occurrence of cracking and fragmentation of the concrete at the anchorage end of the prestressing strands, as illustrated in Figure 11.

3.2. Results and Analysis of Experimental Findings

3.2.1. Measured Cross-Section Temperature Profiles

The temperature increase followed the ISO-834 standard heating curve, as shown in Figure 12. Three exposure durations were tested: 60, 120, and 180 min. The measured temperature profiles closely matched the ISO-834 standard, with a rapid temperature increase in the first 30 min, followed by a slower rise. However, the measured peak temperatures were lower than the ISO-834 curve due to the distance between the furnace measuring rods and flame nozzles, as well as insufficient furnace airtightness.

From the figure, it is evident that the temperature at Measurement Point 1 exceeds that of Measurement Points 2, 3, 4, and 5, and that the temperature at Point 1 rises at a significantly faster rate. As the thermal retention time increased from 60 min to 120 min, the temperature at Measurement Point 1 reached 800 °C, with heat continuing to conduct inward. When the retention time extended to 180 min, the temperature at Point 1 remained at 800 °C, while the internal concrete temperature continued to rise.

If an accelerant like gasoline had been used, the residual load-bearing capacity would have likely decreased more than the observed 28% after 180 min. Gasoline would produce higher peak temperatures, leading to accelerated degradation, severe spalling, microcracking, and greater tendon relaxation. The resulting steeper thermal gradients would cause more uneven heating and internal damage, further reducing the residual load-bearing capacity beyond what was observed under the ISO-834 standard.

3.2.2. Prestress Loss After Constant Temperature Test

After the test beam naturally cooled to ambient temperature, the prestress in the tendons was measured using pressure sensors at the anchorage ends, and the corresponding prestress loss was calculated, as shown in

Table 3. Loads, bending moment, and prestress loss in test beams.

Experimental Beam Identification Number σlt1	Cracking Load (kN)	Cracking Moment (kN·m)	Ultimate Load (kN)	Ultimate Bending Moment (kN·m)	Application of Prestressing (MPa)	Residual Prestressing (MPa)	Prestressing Loss Ratio (%)
PTL-0	21.15	7.05	141.34	47.11	1395	1395	0
PTL-60	17.88	5.96	125.47	41.82	1395	723	48.17
PTL-120	15.46	5.15	111.24	37.08	1395	207	85.16
PTL-180	12.22	4.07	102.14	34.05	1395	94	93.26

. Fire exposure causes deformation and material degradation in prestressed concrete T-beams, leading to significant prestress loss. Previous studies, including those by Yuan Guanglin et al. [18], identified the following key factors as contributing to prestress loss: the relaxation and creep of prestressing steel tendons, high-temperature creep in concrete, and differential thermal expansion between tendons and concrete. The corresponding equation is presented as:

$${\sigma }_{lt}={\sigma }_{lt1}+{\sigma }_{lt2}+{\sigma }_{lt3},$$

(1)

In the equation, ${\sigma }_{lt1}$ represents the prestress loss in prestressed steel tendons induced by high-temperature creep, ${\sigma }_{lt2}$ denotes the prestress loss in concrete attributable to high-temperature creep, and ${\sigma }_{lt3}$ signifies the prestress loss resulting from the differential thermal expansion between the steel tendons and concrete.

The relaxation of prestressing strands at high temperatures significantly affects beam deformation. Elevated temperatures can alter the material properties of the prestressing strands, particularly resulting in a reduction of their strength, which in turn exacerbates prestress loss. At high temperatures, prestressing strands may undergo plastic deformation, thereby reducing the effective prestress level applied. At temperatures of 800 °C, degradation of the concrete matrix weakens the bond between the tendons and concrete, further reducing tensile strength. Microcracking, caused by the breakdown of calcium silicate hydrate (C-S-H) and evaporation of chemically bound water, worsens this loss of bond strength. In our tests, prestress losses after 60, 120, and 180 min of fire exposure were 48.17%, 85.16%, and 93.26%, respectively (Table 3), indicating progressive damage to the tendons with prolonged exposure.

While environmental factors like moisture during cooling may promote rehydration of the concrete matrix, their effect on restoring prestress loss is minimal. The primary cause of these losses—plastic deformation and thermal relaxation of the steel tendons—is largely irreversible, regardless of cooling conditions. Therefore, moisture may improve concrete’s post-fire properties, but has little impact on tendon prestress recovery.

3.2.3. Residual Load-Bearing Capacity After Constant Temperature Test

The thermal retention tests simulating fire exposure were conducted prior to the residual load-bearing capacity tests. The experimentally measured cracking loads, cracking moments, as well as ultimate loads and ultimate moments for the experimental T-beams are summarized in Table 3, where the residual load-bearing capacity is represented by the ultimate load and moment. The reductions in cracking load observed for the prestressed concrete T-beams after 60, 120, and 180 min of fire exposure (15%, 27%, and 42%, respectively) align with trends reported in studies on non-prestressed beams under similar conditions. However, in prestressed beams, the presence of tendons introduces additional internal stresses, accelerating the reduction in cracking load compared to non-prestressed beams. Similar findings on cracking load reductions in non-prestressed beams under fire exposure were reported by Kodur et al. [6] and Yu et al. [14], though the greater reduction observed in our prestressed beams can be attributed to tendon relaxation and the thermal weakening of the prestressing steel.

Correspondingly, the ultimate loads, which represent the residual load-bearing capacities, decreased by 11%, 21%, and 28%. The relaxation of prestressing strands at elevated temperatures can result in a reduction of the residual load-bearing capacity of the beams. As the prestress in the strands decreases, the flexural capacity of the beams diminishes, potentially leading to excessive deformations and a risk of structural failure.

3.2.4. Midspan Deflection Variation Curves

Figure 13 shows the relationship between mid-span deflection and residual load-bearing capacity during the loading test. The curve has three phases: the uncracked elastic phase, where prestress counteracts the applied load; the cracked nonlinear phase, where increasing loads reduce prestress and lead to concrete cracking; and the ultimate phase, where the prestressing tendons approach their limit as the load increases. Although the curve lacks a clear inflection point, the rate of load increase slows until reaching the maximum load. Prolonged exposure to high temperatures significantly reduces beam stiffness. Increased holding time correlates with greater mid-span deflection, indicating that extended exposure exacerbates damage and diminishes residual load-bearing capacity.

In practice, material aging and environmental factors must be considered when evaluating prestressed concrete beams. Over time, concrete and steel degrade due to creep, shrinkage, and corrosion, which affect their mechanical properties. Environmental conditions like temperature fluctuations, moisture, and freeze–thaw cycles further accelerate these processes. These factors lead to increased cracking and reduced load-bearing capacity, emphasizing the need for structural assessments that account for material aging and environmental impacts to ensure long-term safety and durability.

Although the experimental results provide valuable insights, the sample size was limited due to practical constraints. Ideally, performing at least three tests per thermal step would enhance the statistical robustness. Additionally, future studies will incorporate statistical methods to evaluate the degree of uncertainty and potential measurement errors, offering a more comprehensive understanding of the reliability of the results.

4. Finite Element Analysis Model

4.1. Establishment of the Finite Element Analysis Model

In this study, the residual load-bearing capacity of prestressed concrete T-beams after fire exposure was determined using ABAQUS 2021 finite element software with a thermomechanical coupled analysis method. The model’s accuracy was validated against experimental data, ensuring its reliability for future predictive simulations. Besides the Finite Element Method (FEM), other numerical methods such as the Finite Difference Method (FDM) [19] and the Bezier Multi-Step Method [20] offer alternative solutions for simulating the behavior of fire-exposed prestressed concrete T-beams, providing valuable insights.

Based on the temperature field model, the mechanical properties of the materials post-fire are incorporated, followed by a static analysis [21]. The material properties were defined based on thermal and mechanical parameters, with the principal values outlined in

Table 4. Key material parameters.

Construction Materials	Density (kg/m3)	Elastic Modulus (MPa)	Coefficient of Thermal Expansion	Poisson’s Ratio
Concrete	2400	3.16 × 104	7.24 × 10−6	0.2
Reinforcing steel	7850	2.01 × 104	1.52 × 10−5	0.3
Prestressing tendon	7930	1.95 × 105	1.40 × 10−5	0.3

. A 0.02 m mesh grid of C3D8R eight-node linear hexahedral elements was used for the concrete, while the reinforcement utilized a 0.04 m grid of T3D2 two-node linear truss elements. Two analysis steps were performed: Step 1 applied prestress through a cooling method, with a maximum increment of 100 steps and an initial increment of 0.001; Step 2 is established to compute the load-displacement curve of the prestressed UHPC-T beam under load post-fire, independent of time, thus defining a unit duration analysis step with a maximum increment of 100 steps, an initial increment of 0.001, and a maximum increment of 0.1. The constraints between the reinforcement and concrete used an embedded region, with tie constraints established between the loading block and the T-beam. Coupling constraints were applied between loading points RP-1, RP-2, and the loading pads.

The loading block was constrained using mechanical displacement boundary conditions (U1 = U2 = U3 = UR1 = UR3 = 0), while UR2 was free due to rotation at the supporting pads. A displacement load was applied at RP-1 and RP-2, with U2 set to a specific value. The prestress, applied using a cooling method, was adjusted with a total duration of 1 and a maximum increment of 100 steps. The bottom of the prestressed concrete T-beam was exposed to fire on three sides, with heat exchange and surface radiation modeled according to the ISO-834 temperature curve [17]. The fire-exposed surface had an initial temperature of 20 °C, a convective heat exchange coefficient of 40 W/(m² × K), and a radiation coefficient of 0.5. The non-fire-exposed surface had a convective heat exchange coefficient of 20 W/(m² × K) and a radiation coefficient of 1.0.

4.2. Validation of the Temperature Field Model

This study uses the experimental beam PTL-180 as a case example to extract node temperatures and plot the temperature rise curve. Additionally, the temperature values at each node are compared with the temperature values recorded at various measurement points of the T-beam subjected to 180 min of fire exposure, as illustrated in Figure 14. The figure indicates that the temperature–time curves of the simulated points closely align with those of the experimental points. The parameters, interactions, and mesh discretization choices for the temperature field model of the prestressed concrete T-beam proposed in this study are deemed appropriate. The computational results obtained from the established temperature field model are consistent with the experimental findings.

At temperatures of 900 °C or 1000 °C, the residual capacity of prestressed concrete T-beams would decrease further compared to the results obtained at 800 °C. Higher temperatures accelerate the degradation of concrete, particularly due to the decomposition of calcium silicate hydrate (C-S-H) and more extensive dehydration. This results in a more significant loss of compressive strength and increased internal damage such as spalling and microcracking. The prestressing tendons would experience greater plastic deformation and relaxation, leading to a further reduction in effective prestress and overall structural stiffness. Additionally, crack propagation would be more severe at these higher temperatures, with cracks forming earlier and penetrating deeper into the concrete. The higher thermal gradients would result in more brittle failure modes, and the increased crack width would further compromise the structural integrity of the beam. Consequently, both the residual load-bearing capacity and the structural behavior would be significantly impacted at fire temperatures of 900 °C or 1000 °C.

4.3. Validation of Prestress Loss

The 1.66% discrepancy between the experimental prestress loss (85.16%) and the calculated prestress loss (83.5%) after 120 min of fire exposure can be attributed to several factors in the material modeling and numerical simulation process. First, the finite element model uses approximations for the nonlinear thermal degradation of both concrete and steel, which may not fully capture the real-world behavior of these materials at elevated temperatures. Additionally, slight differences in boundary conditions, such as support constraints or load application methods, between the experimental setup and the numerical model can affect stress distribution and prestress loss. Prestress relaxation, which tends to increase under high-temperature conditions, might also be more pronounced in reality than predicted by the model. Finally, the level of mesh refinement could contribute to slight inaccuracies in capturing stress gradients. Despite these factors, the 1.66% discrepancy is within a reasonable range for complex simulations.

In the finite element analysis using ABAQUS, mesh refinement and node placement, particularly at the tendon-concrete interface, play a significant role in determining the accuracy of prestress loss calculations. A finer mesh at this interface allows for a more accurate representation of the stress distribution and bond–slip behavior, which directly impacts the accuracy of prestress loss predictions. In our model, a trade-off was made between computational efficiency and accuracy, which resulted in a 5% error in prestress loss calculations. Further refinement of the mesh and optimization of node placement could reduce this error by improving the representation of stress transfer mechanisms at the interface. This adjustment would enhance the convergence behavior of the model and lead to more precise results.

4.4. Validation of Residual Load-Bearing Capacity

Figure 15 compares the load–midspan displacement curves for four experimental beams. The results show that the experimental curve values are slightly higher than those obtained from finite element simulations, with a simulation error of approximately 5%, which is acceptable. Several factors contribute to this error: (1) discrepancies between the design and actual material parameters, where tensile stress-induced concrete fractures in actual components are not accurately simulated in finite element models; and (2) the complexity of prestress loss under high temperatures, as prestressing strands experience elevated stress and exhibit nonlinear temperature–stress relationships. Despite these challenges, the finite element model provides a reasonable approximation of the residual load-bearing capacity of prestressed concrete T-beams post-fire.

In this study, the bond–slip behavior between reinforcement and concrete was incorporated using the embedded region method in ABAQUS, allowing for relative slip between the two materials. This approach captures the interaction between concrete and prestressing tendons, including potential slip under thermal loads. In future work, we plan to refine the model further by integrating the effects of differential thermal expansion between steel and concrete during cooling phases, which can significantly influence bond–slip behavior and the residual strength of fire-exposed structures.

To refine our model further, we plan to implement cohesive interface models to simulate bond–slip under thermal stress more accurately, as recommended by Rabinovitch [22] and Funari et al. [23]. These studies highlight improved debonding simulation, especially under dynamic conditions. Additionally, to enhance the model’s ability to simulate crack propagation at elevated temperatures, future work will reference methods from Lonetti [24] and Fabbrocino et al. [25], which address delamination and crack growth dynamics in composite materials. Further research is also encouraged to integrate advanced debonding models under thermal effects, as examined in recent studies on composite and FRP-strengthened beams [26]; this would allow for a more detailed representation of reinforced material interactions under fire conditions, ultimately improving the model’s accuracy and applicability in high-stress environments.

5. Calculation of Residual Load-Bearing Capacity After High Temperature

5.1. Fundamental Assumptions

Based on the experimental results, the following computational assumptions are established for analyzing the residual load-bearing capacity of prestressed concrete T-beams under thermal–structural coupling effects:

(1)

The section of the prestressed concrete T-beam after fire exposure conforms to the plane cross-section assumption.

(2)

There is no relative slip between the internal reinforcement and the concrete of the prestressed concrete T-beam following fire exposure.

(3)

The tensile contribution of the concrete in the tensile zone of the prestressed concrete T-beam is neglected.

5.2. Concrete Strength Reduction Factor

During a fire, the concrete within the cross-section of prestressed concrete T-beams is affected by the flame from varying distances, resulting in differing degrees of high-temperature damage. Based on the extent of damage, the cross-section can be categorized into three layers: the damaged layer, the impaired layer, and the undamaged layer. Research indicates that concrete loses nearly all of its compressive strength when temperatures exceed 900 °C, and that its compressive strength declines sharply upon reaching 600 °C, signifying severe degradation that significantly impacts the load-bearing capacity of the structural element.

In calculating the residual load-bearing capacity, the following simplifications are applied based on the temperature of the concrete: When the temperature of the concrete exceeds 600 °C, its compressive strength is considered to be zero; When the temperature is below 300 °C, the compressive strength is taken to be the value at ambient conditions; In the temperature range from 300 °C to 600 °C, the compressive strength is determined based on the maximum compressive strength at the highest temperature within that range. A simplified representation of the compressive strength of concrete post-fire is illustrated in Figure 16.

To facilitate the calculation of the residual load-bearing capacity of prestressed concrete T-beams following a fire, this study employs an equivalent concrete compressive strength approach. The specific calculation steps are as follows:

(1)

The temperature field distribution of prestressed concrete T-beams during a fire is simulated using the finite element software ABAQUS;

(2)

Isotherms representing the temperature distribution across the cross-section of the component are drawn based on the temperature field distribution cloud map, as illustrated in Figure 17;

(3)

The areas $A_i$ of each segment are calculated based on the temperature isotherms;

(4)

The component is divided into the flange and web sections according to the following equation, and the equivalent strength reduction coefficients are calculated for each section separately.

$$k_{cY}={\displaystyle \frac{{\displaystyle \sum f_{ci}{A}_i}}{f_c{A}_Y}},$$

(2)

$$k_{cB}={\displaystyle \frac{{\displaystyle \sum f_{ci}{A}_i}}{f_c{A}_B}},$$

(3)

In this equation, $k_{cY}$ and $k_{cB}$ represent the equivalent compressive strength reduction coefficients for the flange and web of the prestressed concrete T-beam after exposure to fire; $f_{ci}$ denotes the compressive strength experienced by each region after exposure to intermediate temperatures; $f_c$ represents the compressive strength of concrete at ambient temperature; $A_Y$ and $A_B$ refer to the cross-sectional areas of the flange and web of the prestressed concrete T-beam, respectively.

Figure 17. Isothermal distribution in prestressed concrete T-beam cross-section.

Figure 17. Isothermal distribution in prestressed concrete T-beam cross-section.

5.3. Simplified Calculation of Steel Strength After High Temperature

According to the literature [27], the simplified strength model for reinforcement and prestressing tendons following a fire is illustrated in Figure 18.

The expression for calculating the strength of reinforcement following a fire is as follows:

$${\displaystyle \frac{f_y^T}{f_y}}=\left\{\begin{array}{cc}1.0& \hfill T\le 400 °\mathrm{C}\\ 1.15-0.000375T& \hfill 400 °\mathrm{C}<T\le 800 °\mathrm{C}\end{array}\right.,$$

(4)

The expression for calculating the strength of prestressing tendons following a fire is as follows:

$${\displaystyle \frac{f_{py}^T}{f_p}}=\left\{\begin{array}{cc}1.0& \hfill T\le 300 °\mathrm{C}\\ 1.3-0.001T& \hfill 300 °\mathrm{C}<T\le 800 °\mathrm{C}\end{array}\right.,$$

(5)

5.4. Fundamental Equations

According to the “Code for Design of Concrete Structures”, the limit height of the compression zone in bending members is defined as the height at which the concrete in the compression zone reaches its ultimate compressive strain, corresponding to the yield strength of the longitudinal tensile reinforcement [28]. Consequently, the height of the compression zone in T-shaped bending members is determined using the following formula.

If the bending member is classified as a Type I T-beam, its corresponding calculation diagram is illustrated in Figure 19.

From the equilibrium condition ${\displaystyle \sum N=0}$, the following can be derived:

$$K_{cY}{f}_c{b}_{f}x-f_y^T{A}_S-f_{py}^T{A}_p=0,$$

(6)

The following is derived from Equation (6):

$$x={\displaystyle \frac{f_y^T{A}_S+f_{py}^T{A}_p}{K_{cY}{f}_c{b}_f}},$$

(7)

The following expression is obtained based on the moment equilibrium condition:

$$M_u^T=K_{cY}{f}_c{b}_{f}x(h_0-{\displaystyle \frac{x}{2}})-f_{py}^T{A}_p(h_0-h_p),$$

(8)

Alternatively,

$$M_u^T=f_{py}^T{A}_p(h_p-{\displaystyle \frac{x}{2}})+f_y^T{A}_y(h_0-{\displaystyle \frac{x}{2}}),$$

(9)

If the bending member is classified as a Type II T-beam, its corresponding calculation diagram is illustrated in Figure 20.

From the equilibrium condition ${\displaystyle \sum N=0}$, the following can be derived:

$$K_{cY}{f}_c{b}_f{h}_f+K_{cb}{f}_{c}b(x-h_f)-f_y^T{A}_S-f_{py}^T{A}_p=0,$$

(10)

The following is derived from Equation (10):

$$x={\displaystyle \frac{f_y^T{A}_S-f_{py}^T{A}_p-K_{cY}{f}_c{b}_f{h}_f}{K_{cb}{f}_{c}b}}+h_f,$$

(11)

The following expression is obtained based on the moment equilibrium condition:

$$M_u^T=K_{cY}{f}_c{b}_f{h}_f(x-{\displaystyle \frac{h_f}{2}})+K_{cb}{f}_{c}b(x-h_f)(h_0-{\displaystyle \frac{x-h_f}{2}}),$$

(12)

5.5. Validation of Results

Utilizing the aforementioned method, the residual bearing capacity of the experimental T-beam after the fire was calculated. The T-beam used in this study conforms to the specifications of a Type I T-beam, and the values derived from the calculation formulas are presented in

Table 5. Assessment of residual bearing capacity calculation Formula.

Specimen Identification Number	Experimental Value (kN)	Calculated Value from Formulas (kN)	Calculated Values from Formulas/Experimental Values
PTL-0	141.43	121.13	0.86
PTL-60	125.47	117.05	0.93
PTL-120	111.24	103.27	0.93
PTL-180	102.14	94.25	0.92
		AVE (Average value)	0.91
		STD (Standard deviation)	0.04

. As illustrated in the table, the average ratio of the calculated values to the experimental values was found to be 0.91, indicating that the calculated results are, on average, 91% of the experimental values. This suggests a strong correlation between the computational predictions and the observed results, reflecting the model’s accuracy in simulating the behavior of prestressed concrete T-beams under fire exposure. The standard deviation of 0.04 signifies low variability among the calculated values, which fall consistently close to the average. A ratio near 1.0, coupled with a low standard deviation, is indicative of good agreement between theoretical predictions and experimental outcomes, further supporting the reliability of the proposed computational method. This indicates a strong agreement between the computed results and the measured experimental data.

While the simplified formula provides a conservative estimate of residual load-bearing capacity, particularly at room temperature with a difference of 14%, the discrepancy reduces to 7–8% at higher temperatures. This indicates that the formula offers a closer approximation under elevated temperature conditions. However, this conservatism could lead to oversizing structural elements, resulting in inefficient material use. To address this, scaled models of 52 experimental beams were developed for comparative calculations of their residual load-bearing capacity, though detailed descriptions are omitted here due to space constraints. The calculated results were compared with the experimental measurements and finite element simulation values, as shown in Figure 21. The error between the experimental, simulated, and formula-derived values of the residual load-bearing capacity of the test beams was within 15%. Thus, the method proposed in this study proves to be effective for calculating the residual load-bearing capacity of prestressed concrete T-beams after fire exposure.

6. Conclusions

This study conducted high-temperature tests on prestressed concrete T-beams and residual load-bearing capacity tests post-fire, successfully acquiring data on the residual load-bearing capacity of these beams following fire exposure. Utilizing finite element simulations, the degradation of material properties under fire exposure was analyzed, leading to the proposal of a computational method for determining the residual load-bearing capacity of prestressed concrete T-beams post-fire. The following key conclusions have been drawn:

• The duration of high temperatures during a fire significantly influences the damage extent to prestressed concrete T-beams. As the duration of high temperatures increases, both the concrete and reinforcement bars experience thermal damage, exacerbating the high-temperature degradation of prestressed tendons and consequently affecting their residual load-bearing capacity. When the duration of high temperatures is 60, 120, and 180 min, the prestress losses are observed to reach 48.17%, 85.16%, and 93.26%, respectively.
• After a fire, as prestressed concrete T-beams are subjected to bending loads, the rate of crack propagation and the rate of deflection decrease accelerate with increasing duration of high temperatures, leading to wider cracks at failure and a significant reduction in residual load-bearing capacity. When the duration of high temperatures is 60, 120, and 180 min, the cracking loads decrease by 15%, 27%, and 42%, respectively, while the residual load-bearing capacities decline by 11%, 21%, and 28%.
• This study established a finite element analysis model for the residual load-bearing capacity of prestressed concrete T-beams post-fire, and experimentally validated the model’s high degree of fit and accuracy.
• Considering the damage to concrete, reinforcement, and prestressing tendons under high temperatures, a simplified computational formula for the residual load-bearing capacity of prestressed concrete T-beams post-fire was proposed. By comparing the results with experimental data, the reliability of the computational formula was validated, providing a dependable reference for assessing the residual performance of prestressed concrete T-beams in practical engineering applications following fire exposure.