Ultra-high-performance Fiber-reinforced Concrete Beams Research Articles

Detecting Multiple Damages in UHPFRC Beams through Modal Curvature Analysis

Curvature-based damage detection has been previously applied to identify damage in concrete structures, but little attention has been given to the capacity of this method to identify distributed damage in multiple damage zones. This study aims to apply for the first time an enhanced existing method based on modal curvature analysis combined with wavelet transform curvature (WTC) to identify zones and highlight the damage zones of a beam made of ultra-high-performance fiber-reinforced concrete (UHPFRC), a construction material that is emerging worldwide for its outstanding performance and durability. First, three beams with a 2 m span of UHPFRC material were cast, and damaged zones were created by sawing. A reference beam without cracks was also cast. The free vibration responses were measured by 12 accelerometers and calculated by operational modal analysis. Moreover, for the sake of comparison, a finite element model (FEM) was also applied to two identical beams to generate numerical acceleration without noise. Second, the modal curvature was calculated for different modes for both experimental and FEM-simulated acceleration after applying cubic spline interpolation. Finally, two damage identification methods were considered: (i) the damage index (DI), based on averaging the quadratic difference of the local curvature with respect to the reference beam, and (ii) the WTC method, applied to the quadratic difference of the local curvature with respect the reference beam. The results indicate that the developed coupled modal curvature WTC method can better identify the damaged zones of UHPFRC beams.

Characterization of crack-bridging and size effect on ultra-high performance fibre reinforced concrete under fatigue loading

The use of ultra-high performance fibre-reinforced concrete (UHPFRC) has become popular owing to its high strength, durability and toughness characteristics compared to conventional concrete. In this work, experimental investigations have been carried out to examine the fracture behaviour of UHPFRC beam specimens under static and fatigue loading with an emphasis on understanding the size effect. Experimental results of both monotonic and fatigue have been utilized to develop a mathematical formulation for predicting crack bridging degradation considering the fatigue loading history. Subsequently, the size effect behaviour on the crack-bridging strength of UHPFRC beams under fatigue loading conditions has been explored. An algorithm has been developed to predict crack propagation as a function of load cycles and to estimate the fatigue life corresponding to any load amplitude, accounting for the size effect. The crack-bridging strength has been observed to decrease with an increase in specimen size, lowering the fatigue life.

Experimental and numerical analyses of the effect of fibre content on the close-in blast performance of a UHPFRC beam

Limited research has been conducted on the influences of fiber content on close-in blasting characteristics for ultrahigh-performance fiber-reinforced concrete (UHPFRC) beams. This paper aims to address this knowledge gap through experimental and mesoscale numerical methods. Experiments were conducted on ten UHPFRC beams built with varying steel fiber volumetric fractions subjected to close-in explosive conditions. Additionally, this study considered other parameters, such as the longitudinal reinforcement type and ratio. In the case of UHPFRC beams featuring normal-strength longitudinal reinforcement of diameters Φ12, Φ16, and Φ20, a reduction in maximum displacement by magnitudes of 19.6%, 19.5%, and 17.4% was observed, respectively, as the volumetric fractions of fiber increased from 1.0% to 2.5%. In addition, increasing the longitudinal reinforcement ratio and using high-strength steel longitudinal reinforcement both significantly reduced the deformation characteristics and increase the blasting resistances of UHPFRC beams. However, the effects on the local crushing and spalling damage were not significant. A mesoscale finite element model, which considers the impacts of fiber parameters on UHPFRC beam behaviors, was also established and well correlated with the test findings. Nevertheless, parametric analyses were further conducted to examine the impacts of the steel fiber content and length and the hybrid effects of various types of microfibers and steel fibers on the blasting performance of UHPFRC beams.

Design oriented shear strength prediction model of UHPFRC beams

The application of Ultra-high performance fiber reinforced concrete (UHPFRC) to beams can effectively improve their strength and ductility properties. At present, there are more shear test studies on UHPFRC beams, but few theoretical studies on their strength calculation method. The fibers in UHPFRC can inhance the strength of the beams, and how to quantify the fibers’ contribution to the total strength is a research difficulty. Firstly, the shear strength database including 197 UHPFRC beam specimens is created. The key characteristics determining the shear strength, namely fiber volume fraction, stirrup configuration, and shear-span ratio, are determined by evaluating the test results. Then, considering the effects of the factors above, a truss-arch model is developed. The arch shear strength is determined by utilizing the shear deformation coordination of the arch compression structs and truss compression structs. Superimposing the shear strengths of the arch and truss models yields the shear strength of UHPFRC beams. Finally, the accuracy and reliability of the proposed method are assessed using the test database and compared to existing shear strength calculations. The study findings demonstrate that the mean value of the calculated to observed shear strength ratios produced by the suggested technique is 1.10, with a coefficient of variation of 0.28, indicating that the proposed method has superior calculation accuracy and reliability than existing methods.

Effectiveness of flange plates on torsional behaviors of ultra-high-performance fiber-reinforced concrete hollow beams

This study investigates the effectiveness of flanges with various types of stirrup and cross-sectional dimensions on the torsional behaviors of ultra-high-performance fiber-reinforced concrete (UHPFRC) hollow beams. A finite element model was developed and validated for simulating the torsional behavior. The impact of the essential parameters of flanges was investigated through experimental and numerical methodologies. The results showed that the inclusion of flanges substantially influenced the torsional strength of UHPFRC hollow beams, attributed to the section torsional plastic resistance moment and UHPFRC tensile capacity in flanges. The effectiveness of flange plates was considerably influenced by the web wall thickness. The stirrup type and the increase in flange reinforcement ratio, flange width, and thickness had a favorable effect on the torsional behaviors of thick-walled UHPFRC beams but minimal effect on thin-walled UHPFRC beams. The failure of thin-walled beams was determined by the web thickness and web reinforcements.

Experimental and Numerical Characterization of Non-Proprietary UHPFRC Beam—Parametric Analyses of Mechanical Properties

Fabrication of ultra-high-performance concrete (UHPC) is costly, especially when commercial materials are used. Additionally, in contrast to conventional concrete, numerical procedures to simulate the behaviour of ultra-high-performance fibre-reinforced concrete (UHPFRC) are very limited. To contribute to the foregoing issues in this field, local materials were used in the fabrication process, while accounting for environmental issues and costs. Micro steel fibres (L: 13 mm, d: 0.16 mm, and ft: 2600 MPa; L: length, d: diameter, ft: tensile strength) were used in 2% volumetric ratios. Compression and indirect tests were carried out on cylindrical and prismatic beams according to international standards. To further enrich the research and contribute to the limited simulation data on UHPFRC, and better comprehension of the parameters, numerical analyses were performed using the ATENA software. Finally, nonlinear regression analyses were employed to capture the deflection-flexural response of the beams. The results were promising, indicating cost-effective fabrication using local materials that met the minimum requirements of UHFRC in terms of compressive strength. Furthermore, inverse analysis proved to be an easy and efficient method for capturing the flexural response of UHPFRC beams.

Curing–dependent structural behavior of ultra-high-performance hybrid fiber-reinforced concrete beams

The application of ultra-high-performance fiber-reinforced concrete (UHP-FRC) is exceptionally versatile. However, a comprehensive understanding of UHP-FRC beam structural performance characteristics is lacking. The majority of research has concentrated on the behavior of structural members following standard water curing. This study investigated the impact of the curing regime on the structural performance of UHPC beams. The four different curing regimes used were standard, simulated hot arid weather, steam curing at various ages, and 5% sodium sulfate curing. Experimentally measured mechanical properties of UHP-FRC have been determined following ASTM guidelines, and the investigated beams have been tested under displacement-controlled four-point loading. Additionally, ACI 318 and FHWA-HIF codified formulas were employed in this study to predict the moment capacity of the tested beams. As a result of the various steam systems of varying ages, the load-carrying capacities of the beams were improved. By accelerating cement hydration, steam curing produces a stronger bond between fibers and the cementitious matrix, improving flexural strength. The control beam (under standard curing) showed a smaller maximum deflection, while all other beams showed similar deflection capacity. By accelerating the drying shrinkage, the beams under the 28-day standard with hot air curing were negatively impacted, with an average deflection value around 5% lower than control beams. The cured beams under simulated hot, arid conditions had the lowest flexural rigidity. A steam-cured beam had the highest moment-curvature performance, while a beam cured under simulated arid conditions had the lowest. Additionally, the ACI 318 design equation significantly underestimated beam maximum moments, while the FHWA approach marginally overestimated beam maximum moments with a predicted-to-tested average of 0.82.

Bayesian calibration and reliability analysis of ultra high-performance fibre reinforced concrete beams exposed to fire

A study of uncertainty quantification and reliability of ultra-high-performance fibre reinforced concrete (UHPFRC) beams exposed to fire is presented. The study sets forth two methodologies, the first involving the stochastic calibration of temperature-dependent thermal properties of UHPFRC via Bayesian inversion, and the second concerning the computation of the reliability of UHPFRC beams in fire via Monte Carlo Simulation (MCS). Using the calibrated posterior probability distributions of temperature-dependent thermal properties of UHPFRC in stochastic heat transfer analyses results in predictive temperature distributions that reasonably track (within 95% confidence interval) the temperature response reported on UHPFRC beams specimen subjected to 80 and 60 minutes standard fire. Stochastic temperature distributions based on the calibrated thermal properties were sequentially transferred via a time series surrogate model, into a structural-fire reliability analysis of UHPFRC beams designed to the specifications of the ACI 544. Reliability analysis is conducted and the obtained reliability index generally reduced with increasing fire exposure for the UHPFRC beam considered and fire resistance is estimated based on a reliability target of 0.7.

Shear capacity of UHPFRC deep beams with web openings

The shear capacity of Ultra-High Performance Fiber Reinforced Concrete (UHPFRC) deep beams with web openings located between the provided stirrups was investigated experimentally. All the tested beams were constructed from the same UHPFRC mix containing steel fibers volume fraction of 1.5 %. The test program included eight simply supported deep beams with the same cross-section and same longitudinal reinforcement. The principal studied parameters were opening height, width, location, and the stirrups ratio ρv %. The provided stirrups spacing sv was considerably more than the maximum stirrups spacing sv,max required by ACI 318 code for normal reinforced concrete, while sv,max required by the Egyptian code (ECP 203) were more or equal to sv. The equations used by French recommendations (AFGC) and Korea Concrete Institute (KCI) for the shear design of UHPFRC deep beams have been examined. The experimental results indicated that the shear capacity of UHPFRC deep beams is mainly controlled by opening height, width, and location. Square opening with a height of 20 % of the beam's overall height located at the natural load pass caused reduction of shear capacity by 43 % compared with the reference solid beam. Increasing the opening width by 75 % symmetrically around the natural load pass reduced the shear capacity of the UHPFRC beam by about 21 % while increasing the opening width by 125 % from one side out of the load pass caused a reduction by only 5 %. Increasing the stirrups ratio by 80 % for beams of similar opening size and location, increased the shear capacity by 17.1 %. Predicting the ultimate shear strength of the tested UHPFRC deep beams with openings of height 20 % and 40 % of the beam's total height using the equations of AFGC was just safe if these equations were calculated by deducting the height of opening from the beam effective depth. The equations used by KCI were also safe with a factor of safety about 6 % more than that of AFGC.

Numerical modelling, parametric analysis and design of UHPFRC beams exposed to fire

A non-linear sequentially-coupled thermal–mechanical finite element (FE) paradigm that reasonably tracks the coupled fire-structure response of ultra-high performance fibre reinforced concrete (UHPFRC) beams subjected to the ISO 834 fire is established and presented. A fire resistance parameter study is conducted on UHPFRC beams via the developed FE paradigm, and then flexural based fire-structural assessment is demonstrated, as an avenue to substantiate the viability of numerical performance-based structural fire design. The parameter study considered two variables, notably heating mechanism and load levels. Comparison of results revealed that the fire-structure response was more severe under the hydrocarbon than the ISO 834 heating mechanism and hydrocarbon fire resistance ratings estimation were found to be 30 minutes lower than those determined using the ISO 834 fire. Predicted failure of the beams under the ISO 834 and hydrocarbon fires was observed at load ratios exceeding 0.6 and 0.4, respectively. By reposing on ACI544’s analytical model for UHPFRC beams in flexure, and numerically acquired heat-transfer response, the time-variant reduced nominal moment capacities of UHPFRC beams were computed. Failure predicted via computed residual moment capacities was somewhat consistent with that reckoned by load ratio parameter study.

A numerical failure analysis of nano-filled ultra-high-performance fiber-reinforced concrete structures via a moving mesh approach

This work proposes a novel FE-based model for simulating crack propagation mechanisms in Ultra-High-Performance Fiber-Reinforced Concrete (UHPFRC) structures (typically exhibiting compressive strength over 150 MPa and tensile strength around 10 MPa) enhanced with nanofillers under general loading conditions. This model combines synergistically a Moving Mesh (MM) technique with the Interaction Integral (M-integral) method, and the R-curve concept. In particular, the MM technique, based on the Arbitrary Lagrangian-Eulerian formulation, is used for tracking geometry changes of the computational domain caused by crack advance, thus avoiding massive re-meshing operations. In particular, a mesh regularization technique based on proper rezoning equations is used to ensure that the mesh points move consistently. The M-integral method is used for extracting the crack front variables (i.e., the Stress Intensity Factors (SIFs)), required for the computation of the mixed-mode crack growth direction. Finally, the well-known R-curve concept allows the ductile behavior of nano-enhanced UHPFRC beams to be captured in a LEFM setting. In particular, the crack growth resistance, regarded as a function of the crack extension, is numerically derived via a calibration procedure starting from the available experimental data. In addition, to assess the reliability and effectiveness of the proposed approach, the results of numerical simulations are compared with experimental outcomes reported in the literature.

Replacement of Stirrups by Steel Fibers in Shear Dominant UHPFRC Beams

In the present study, the impacts of variety of fiber types and amounts on shear dominant Ultra High Performance Fiber Reinforced Concrete (UHPFRC) beams and the feasibility of fully replacement of stirrups by the steel fibers were investigated. Fifteen UHPFRC beams containing five different fiber types and three volume fractions were prepared without stirrup and were loaded under four-point loading. The influences of steel fiber were discussed in terms of the load-deflection behavior, cracking behavior, collapse modes, ultimate shear strength, nominal moment capacity and deflection ductility. The steel fiber use prominently increased the post-cracking stiffness and load capacity of the UHPFRC beams with the help of the fibers’ crack-bridging ability. Conversely, the steel fibers in different types didn’t have an importance on the collapse mode of the shear dominant UHPFRC beams. The use of straight steel fibers in the UHPFRC beams, even at very low volume fractions of 0.5 percent, changed the collapse condition from shear to flexure resulting in a ductile behavior. But the hooked fiber inclusion by 1.5 vol percent percent at least is needed to guarantee the flexural behavior regardless of hooked or multi hooked-end form.

Experimental and Numerical Investigation for Torsional Behavior of UHPFRC Shallow and Deep Beams

AbstractWith increasing the use of ultra-high performance fiber reinforced concrete (UHPFRC) in recent years, torsional design of UHPFRC beams has become of great importance. This paper presents an experimental and numerical study to investigate the torsional behavior of UHPFRC shallow and deep beams with fcu equal to 190.2 MPa. Ten UHPFRC beams with steel fibers volume fraction of 1.5% subjected to pure torsion were investigated. The provided torsional web reinforcement ratio, the area of longitudinal bars and the tested span to total height ratio (L/h = 6.0, 4.0, 2.0 and 1.0) were the studied parameters. A numerical model has been proposed to predict the torsional response of tested beams. Experimental results showed that increasing stirrups’ spacing for the beams of the same L/h ratio (to be 235% of the maximum given by ACI 318-2019 code), reduced the experimental ultimate torsional strength by only 6.7%. The torsional web reinforcement ratio of UHPFRC shallow and deep beams can be safely taken to be 40% of the minimum required by ACI 318-2019. The maximum stirrups spacing can be safely taken the lesser of twice the beam width or 300 mm. The equation used by ACI 318-2019 and ECP-203-2020 for calculating the cracking strength in torsion has been modified to be suitable for UHPFRC beams by taking into consideration the L/h ratio and steel fibers percent. The proposed 3-D numerical model showed good predictions for the torsional strength of tested UHPFRC shallow and deep beams.

Verification of the shear resistance of UHPFRC beams – Design method for the German DAfStb Guideline and database evaluation

This contribution focuses on the verification of the shear resistance of Ultra-High Performance Fiber-Reinforced Concrete (UHPFRC) beams. A verification method following Eurocode2 and the German DAfStbGuideline „Steel Fibre Reinforced Concrete“ is presented, which superimposes the shear resistance of a member without shear reinforcement, the shear resistance provided by stirrups, and the contribution of the fibers activated in the shear crack. With regard to the contribution of the fibers, the verification method differentiates between members with I-shaped and approximately rectangular solid cross section. This provides a more favorable design of members with I-shaped cross section. Reliability of the design approach is statistically evaluated by means of a total of 208 shear tests on UHPC and UHPFRC beams with different configuration. For 133 tests on beams with I-shaped cross section the ratio between ultimate shear force from experiment Vexp and theoretical shear resistance Vcal shows a mean value of X̅=1.48 and a 5 % quantile of Q0,05 = 0.94. For 75 tests on beams with approximately rectangular solid cross section the results are X̅=1.59 and Q0,05 = 0.94. For all 208 tests included in the database X̅=1.52 and Q0,05 = 0.94 are obtained. Based on the statistical parameters it is concluded that the prediction model is sufficiently reliable for being considered with the forthcoming German DAfStbGuideline on Ultra-High Performance Concrete.

Experimental study of the effects of using ultra-high strength reinforcing rebar and UHPFRC on cyclic behavior of reinforced concrete beams

Reinforced concrete beams made of ultra-high-performance fiber-reinforced concrete (UHPFRC) are good alternatives to ordinary concrete and reduce the density of reinforcement in the beam, leading to the desired structural behavior. In the present study, the effect of using ultra-high strength reinforcing rebar (UHRR) and UHPFRC on the cyclic behavior of the reinforced concrete beams has been studied experimentally. The current study aims to reduce the amount of UHPFRC and UHRR to achieve a beam with the desired mechanical properties. Nine specimens of real-scale laboratory beams (dimensions of 250 × 200 × 2200 mm) were made and tested by four-point bending with cyclic loading. The empirical study was performed for three volume fractions ratio of UHRR 0.5 %, 1 %, and 1.5 % on three configurations of UHPFRC in the beam: complete UHPFRC beam, beam reinforced with UHPFRC layers at the upper and lower surfaces with thicknesses of 40 mm and beam reinforced with UHPFRC in the longitudinal middle zone of ​​the beam. Parameters of different specimens' cracking patterns, strength capacity, flexural ductility, hysteresis response, energy dissipation, and ultimate strength are compared. The results show that, generally, specimens reinforced with UHPFRC at the upper and lower surfaces of the beam, using less UHPFRC, have better flexural performance than other specimens (even better than complete UHPFRC beam specimen) and are the most desirable condition.

Improving the shear design of steel-bar reinforced ultra high performance fibre reinforced concrete beams using mesoscale modelling

Understanding the failure mechanisms of steel-bar reinforced ultra high performance fibre reinforced concrete (UHPFRC) beams is crucial to improving their design but challenging because of the contrast between beam size and fibre size. We develop a 2D mesoscale finite element model with the fibres explicitly resolved to bridge this gap by simulating the damaging and fracturing processes of the beams. To make fibre distribution in the model mechanically representative, we propose a method to project the fibres from 3D to 2D. The continuum damaged plasticity model is used as the constitutive law for the UHPC matrix, and the zero-thickness cohesive elements with softening constitutive law are used to model the nonlinear bond-slip behaviour of the fibre- and bar-matrix interfaces. The models are validated against experimental data obtained from 3 and 4-point loading tests by comparing the simulated and measured fracturing processes, crack patterns and the load-displacement curves. The validated models are then used to analyse the sensitivity of the shear strength of the beams to fibre content, shear span-to-depth ratio, as well as shear and longitudinal reinforcement ratios in the beam, from which a shear strength equation is proposed to improve the design of reinforced UHPFRC beams. The improvement of the new equation over the AFGC equation is demonstrated against experimental data measured from 32 beams with various material properties.

Finite element analysis of shear performance of UHPFRC-encased steel composite beams: Parametric study

The shear response of ultra-high performance fiber reinforced concrete (UHPFRC)-encased H-shaped steel section composite beams is simulated using a three-dimensional (3D) non-linear finite element model (FEM) in the present study. The proposed FEM's accuracy is validated against experimental data from previously tested steel and UHPFRC beams available in the literature. Numerical results agreed well with the experimental findings in terms of load–deflection response and failure mode. Before conducting the parametric analysis, the influence of the model mesh size on the ultimate load capacity, as well as the initiation and propagation of cracks along the entire length of H-shaped steel and UHPFRC beams, is considered. The mesh sensitivity analysis, which was performed using three different mesh sizes of 50, 40, and 30 mm, revealed that all mesh sizes successfully predicted the ultimate load of the analyzed beams, while the lowest one (30 mm) was the best in predicting the distribution of shear and flexural cracks along the entire length of the steel and UHPFRC beams. The parametric study investigated the encasement effect as well as the shear-span-to-depth ratio and effective length of the steel beam on the ultimate load capacity, stiffness, ductility, and failure pattern of composite beams. The gain in ultimate load of the composite beam was 448 % and 278 % with respect to the bare steel and UHPFRC beams, respectively. Furthermore, the ultimate load reduction ratios for specimens with shear span-to-depth ratios of 2.1, 2.6, 3.1, and 3.6 were 20, 32, 38, and 41 %, respectively, with respect to the shear span-to-depth ratio of 1.6.

Modified softened membrane model for ultra-high-performance fiber-reinforced concrete solid and hollow beams under pure torsion

Limited research has focused on the development of rational theoretical models for evaluating the pure-torsional behavior of ultra-high-performance fiber-reinforced concrete (UHPFRC) beams. To fill this research gap, this study aimed to develop a modified softened membrane model for torsion (SMMT). Based on the direct tension force transfer model, a UHPFRC tensile constitutive model was derived by considering the fiber pull-out behavior. The proposed constitutive model was implemented in the SMMT, and the modified SMMT was found to be useful in predicting the pure-torsional behavior of UHPFRC beams with solid and hollow cross-sections. Moreover, the theoretical torsional responses were compared with the experimental results, and the experimental data reported in previous studies were used to verify the applicability of the proposed model. The results indicate that the estimated analytical responses matched well with the experimental outcomes, and the modified SMMT considered the influences of both the wall thickness and excellent UHPFRC material properties. The proposed model is expected to be effective for further investigation of the torsional mechanism and design methodology of UHPFRC members under pure torsion.

Machine Learning-Based Models for Shear Strength Prediction of UHPFRC Beams

Estimating shear strength is a crucial aspect of beam design. The goal of this research is to develop a shear strength calculation technique for ultra-high performance fiber reinforced concrete (UHPFRC) beams. To begin, a shear test database of 200 UHPFRC beam specimens is established. Then, random forest (RF) is used to evaluate the importance of influence factors for the shear strength of UHPFRC beams. Subsequently, three machine learning (ML)-based models, including artificial neural network (ANN), support vector regression (SVR), and eXtreme-gradient boosting (XGBoost), are proposed to compute shear strength. Results demonstrate that the area of longitudinal reinforcement has the greatest influence on the shear capacity of UHPFRC beams, and ten parameters with high importance (e.g., the area of longitudinal reinforcement, the stirrup strength, the cross-section area, the shear span ratio, fiber volume fraction, etc.) are selected as input parameters. The models of ANN, SVR, and XGBoost have close accuracy, and their R2 are 0.8825, 0.9016, and 0.8839, respectively, which are much larger than those of existing theoretical models. In addition, the average ratios of prediction values of ANN, SVR, and XGBoost models to experimental results are 1.08, 1.02, and 1.10, respectively; the coefficients of variation are 0.28, 0.21, and 0.28, respectively. The SVR model has the best accuracy and reliability. The accuracy and reliability of ML-based models are much better than those of existing models for calculating the shear strength of UHPFRC beams.

Nonlinear Inverse Analysis for Predicting the Tensile Properties of Strain-Softening and Strain-Hardening UHPFRC.

The tensile stress–strain response is considered to be the most important and fundamental mechanical property of ultra-high-performance fiber-reinforced concrete (UHPFRC). Nevertheless, it is still a challenging matter for researchers to determine the tensile properties of UHPFRC. As a simpler alternative to the direct tensile test, bending tests are widely performed to characterize the tensile behavior of UHPFRC, but require further consideration and a sophisticated inverse analysis procedure. In order to efficiently predict the tensile properties of UHPFRC, a nonlinear inverse method based on notched three-point bending tests (3PBT) was proposed in this paper. A total of fifteen UHPFRC beams were fabricated and tested to evaluate the sensitivity of the predicted tensile behavior to variations in fiber volume fraction. A segmented stress–strain model was used, which is capable of describing the various tensile properties of UHPFRC, including strain softening and strain hardening. A more approximate formulation was adopted to simulate the load–deflection response of UHPFRC beam specimens. The closed-form analytical solutions were validated by tensile test results and existing methods in literature. Finally, parametric studies were also conducted to investigate the robustness of the proposed method. The load–deflection responses obtained from notched 3PBT could be easily converted into tensile properties with this inverse method.