Tensile Stress-strain Relationship Research Articles

Effect of basalt fibers and silica fume on the mechanical properties, stress-strain behavior, and durability of alkali-activated slag-fly ash concrete

Previous investigations have shown that there is limited exploration into the combined mechanism of silica fume and basalt fibers of various lengths on the performance of alkali-activated concrete. Based on this, the primary focus of this study is to elucidate the current knowledge gaps concerning the mechanical properties and durability of basalt fiber-reinforced alkali-activated concrete, with a particular emphasis on its stress-strain behavior. The effects of basalt fiber content (i.e., 0.2%, 0.4%, and 0.6% Vf), basalt fiber length (i.e., 6 and 12 mm), mixing proportions of 6 mm and 12 mm basalt fibers (i.e., 75:25, 50:50, and 25:75) and silica fume content (i.e., 3%, 6%, and 9%) on the workability, mechanical properties, stress-strain behavior, and durability of alkali-activated concrete were investigated. Based on experimental results, predictive models were proposed for the splitting tensile strength, flexural tensile strength, elastic modulus, peak strain, and stress-strain relationship of basalt fiber-reinforced alkali-activated concrete, showing excellent predictive accuracy. Additionally, the durability properties of all samples, including shrinkage, carbonation depth, and chloride ion permeability, were also tested. The results indicate that the combined effect of fibers and silica fume can enhance the mechanical properties and durability of the concrete. Finally, the reinforcement mechanism of the synergistic action of fibers and silica fume is discussed.

Experimental investigation and numerical simulation on uniaxial tensile behavior of hybrid PVA-ECC

Engineered Cementitious Composites (ECC) with multiple cracking and strain-hardening characteristics can meet the high requirements of infrastructure for safety and durability, however, the high cost of oiled polyvinyl alcohol (PVA) fiber in ECC limits the extensive application of ECC. The price of regular unoiled PVA fiber is relatively lower, therefore, hybrid PVA-ECC with redesigned mix proportion of unoiled and oiled PVA fibers can reduce the cost of PVA-ECC, and it exhibits satisfactory mechanical properties at the same time, offering a wider application prospect than the oiled PVA-ECC. The tensile stress–strain relation of hybrid PVA-ECC is an important property for structural design, however, the lack of theoretical method for predicting tensile stress–strain relation of hybrid PVA-ECC hinders the application of hybrid PVA-ECC in practical engineering. Based on the micromechanical model of multiple cracking, the crack space calculation model, the series spring model and the random probability distribution model, the numerical simulation model for predicting tensile behavior of hybrid PVA-ECC was proposed. The mix proportion of hybrid PVA-ECC was redesigned based on the characteristics of different PVA fibers. The uniaxial tensile test was conducted to investigate the uniaxial tensile behavior of hybrid PVA-ECC and to provide a reference for validating the numerical model.

Tensile stress–strain relationship of fiber-reinforced concrete with different densities

This study aims to propose a rational model to establish the tensile stress–strain relationship of fiber-reinforced concrete (FRC) with different densities based on the general form described in the fib Model Code 2010. To determine the key parameters in the stress–strain model, the inverse analysis was conducted using the load–deflection curve obtained from 85 FRC beam specimens covering a wide range of the compressive strength between 22.0 and 96.5 MPa, concrete density between 1178 and 2306 kg/m3, and fiber reinforcing index (βf) between 0.22 and 5.79. The inverse analysis was iterated until an acceptable consistence was obtained between the experimental load–deflection curve and the prediction by the section lamina approach according to the variation of key parameters in the tensile stress–strain relationship. Subsequently, regression analyses were performed using the values of the key parameters determined in the inverse analysis of each beam. The reliability of the proposed model was examined through comparisons with 48 datasets for tensile stress–strain curves compiled from the uniaxial tensile specimens. The proposed model also assessed the correlation between tensile and flexural strengths of FRC. Moreover, the threshold of βf was identified to distinguish the hardening and softening responses in the stress–strain relationship. The proposed model consistently facilitates the tensile response of FRC, indicating that the normalized root-mean-square error values determined between experimental and predicted curves range between 0.175 and 0.071.

Viscoelastic tensile model of core/wrapped composite yarn with double filament

Viscoelastic models are typically employed to investigate the mechanical properties of yarn. In this study, a viscoelastic model was developed to predict the tensile stress–strain relationship of a core/wrapped composite yarn with double filaments. The tensile properties of the yarn were tested, and various stages of the tensile curve were analyzed. Moreover, based on the tensile fracture characteristics, a five-element nonlinear viscoelastic model comprising Kelvin element, Maxwell element, and linear springs was established. Furthermore, the tensile properties of the composite yarns were simulated and calculated using the developed model. Additionally, the stress–strain relationship was fitted using a polynomial on the basis of the established model. The results reveal that the tensile fracture curve of the composite yarn comprises three stages. They are a small strain linear stage, a large strain stage, and a strength fluctuation stage. The viscoelastic tensile model can decently explain the three-stage stress–strain characteristics of the composite yarn tensile curve. The theoretical results were consistent with the experimental results, and the correlation coefficient was greater than 0.999. Based on the results, the proposed model can be employed with high accuracy to predict the tensile properties of a core/wrapped composite yarn with a double filament.

Uniaxial tensile properties of multi-scale fiber reinforced rubberized concrete after exposure to elevated temperatures

With the rapid development of transportation and population growth, there is a surge hike in demand for automobile tires. Waste rubber disposal has become a big environmental concern worldwide due to the non-biodegradability of waste rubber. Based on the previous literature, waste rubber has great potential to make green concrete. However, the mechanical behavior of concrete, especially the tensile strength after being heated, will be reduced by adding waste crumb rubber. To improve the residual tensile behavior of rubberized concrete, steel fibers, PVA fibers (or PE fibers), and CaCO3 whiskers were added to make green concrete with better fire resistance. This study investigated the influences of the crumb rubber and multi-scale fibers on the failure mode, first cracking strength and strain, ultimate strength and strain, and the stress-strain relationships of MSFRRC subjected to elevated temperatures (up to 800 °C). In addition, the damage evolution of rubberized concrete under uniaxial tension was studied by the acoustic emission (AE) technique. Results show that specimens without fibers exhibited a single straight crack and a brittle failure. Adding crumb rubber could not improve the brittleness of concrete and eliminate explosive spalling. However, the brittleness of rubberized concrete could be improved and a multi-cracking behavior could be achieved by incorporating multi-scale fibers. Meanwhile, the ultimate strength decreased significantly when the crumb rubber volume replacement ratio increased from 0% to 30% since the increase in the porosity of the concrete specimen. The incorporation of multi-scale fibers could mitigate the strength loss and contribute to the first cracking strength, ultimate strength, and strain-hardening capability. The tensile strength of MSFRRC was enhanced by 54.4%–64.3% and the ultimate strain increased by 26.9–50.4 times. Nevertheless, the strain-hardening capability was eliminated owing to the weakened interfacial bond between the steel fiber and the matrix and the decomposition of PVA fibers when the temperature reached 400 °C. In addition, the large and medium capillary pores were reduced due to the additives of multi-scale fibers and the content of mesopores increased. Furthermore, the empirical formulas to predict the residual uniaxial tensile stress-strain relationship of MSFRRC considering parameters of crumb rubber, multi-scale fibers, and elevated temperatures were proposed based on the test results.

Tensile Properties and Prediction Model of Recombinant Bamboo at Different Temperatures

The destruction of recombinant bamboo depends on many factors, and the complex ambient temperature is an important factor affecting its basic mechanical properties. To investigate the failure mechanism and stress–strain relationship of recombinant bamboo at different temperatures, eighteen tensile specimens of recombinant bamboo were tested. The results showed that with increasing ambient temperature, the typical failure modes of recombinant bamboo were flush fracture, toothed failure, and serrated failure. The ultimate tensile strength, ultimate strain and elastic modulus of recombinant bamboo decreased with increasing temperature, and the ultimate tensile stress decreased from 154.07 to 96.55 MPa, a decrease of 37.33%, and the ultimate strain decreased from 0.011 to 0.008, a decrease of 26.57%. Based on the Ramberg-Osgood model and the pseudo‒elastic design method, a predictive model was established for the tensile stress–strain relationship of recombinant bamboo considering the temperature level. The model can accurately evaluate the tensile stress–strain relationship of recombinant bamboo under different temperature conditions.

Identification of probabilistic distribution parameters for the mesoscopic stochastic fracture model

As a kind of multiphase composite material, the basic mechanical behaviors of concrete are randomness and nonlinearity. The mesoscopic stochastic fracture model (MSFM) which can reflect the coupling effect of randomness and nonlinearity, has been widely used for the nonlinear analysis of concrete structures. In this paper, we proposed a new stochastic modeling principle to identify the probabilistic distribution parameters of MSFM. In order to reduce the modeling works, a dimension-reduced algorithm is proposed as well. In this paper, an overview of MSFM is firstly presented to introduce the background of the research. Then the stochastic harmonic function (SHF) representation is introduced to express the random field mentioned in the MSFM, and the probability density evolution method (PDEM) is applied to obtain the theoretical probability density function (PDF) of the stress–strain relationships. Furthermore, a stochastic modeling principle is proposed, in which minimizing the Kullback–Leibler divergence (KLD) is taken as the optimization object. Based on the framework of genetic algorithm, a dimension-reduced algorithm is proposed to identify the parameters with reference to the data from tested complete curves of uniaxial compressive and uniaxial tensile stress–strain relationship of concrete. The results indicate that the proposed principle and algorithm can be used to identify the parameters of MSFM accurately and efficiently.

Numerical Analysis of Splitting Tensile Strength of Steel Fibre Reinforced Concrete under Static Loading

This paper presents the study on the numerical analysis of splitting tensile strength test of steel fibre reinforced concrete under static loading. ABAQUS FEM software is used to model the test configuration for plain concrete and steel fibre reinforced concrete (SFRC) based on the experimental investigations that studied the effectiveness of adding steel fibres of 1.5% volume fraction into the concrete mix. Four 3D models are created which are brick concrete, brick SFRC, stone concrete and stone SFRC. The numerical analysis results are compared with the published experimental results in terms of splitting tensile strength, tensile stress-strain relationship and tensile damage. The splitting tensile strengths from horizontal stress output are found to be slightly lower compared to the experimental results with percentage difference of less than 15%. While the results from using analytical formula also underestimate the splitting tensile strength with percentage difference up to 22% when compared to the experimental results. Elastic modulus from tensile experimental results should be taken as Young’s modulus of the model since it gives results that are closer to experimental results. The Poisson’s ratio that gives the closest results to the experimental result is taken as the Poisson’s ratio of the concrete and SFRC. The adopted 3D model captured reasonably well the reaction of the concrete cylinders subjected to splitting tensile test. Numerical analysis displays a strong correlation with the experimental results after proper evaluations and realistic optimizations of the governing parameters through extensive analyses.

Tensile behavior analysis and prediction of steel fiber-reinforced-carbon/glass hybrid composite bars

This paper presents the uniaxial tensile experiment results and analysis of a new steel fiber-reinforced-carbon/glass hybrid composite bars (S-CG HCBs). The effects of carbon/glass ratio, steel fiber replacement ratio, fiber volume fraction and fiber arrangement over the cross section on the tensile properties of S-CG HCBs were investigated. In addition, a method for the tensile test of steel fiber was presented. Two damage modes of S-CG HCBs were analyzed based on carbon fiber fracture pattern. The results indicated that the tensile stress-strain relationship of S-CG HCBs could be modified by adding steel fiber. Meanwhile, the yield stress, rupture stress, failure stress, and stress drop at carbon fiber fracture could be controlled effectively by the changes of experimental variables. Finally, a tensile stress-strain model for S-CG HCBs was proposed considering the distribution pattern of carbon and steel fibers through a simple damage analysis.

Numerical Modelling of the Compressive and Tensile Behavior of Ultra-High Performance Concrete in Beams

INTRODUCTION Ultra-high performance concrete (UHPC) differs in its structural behavior from conventional concrete upon loading due to its high compressive and tensile strength, stiffness, toughness, and durability. Therefore, UHPC needs an appropriate constitutive model to simulate its mechanical properties in finite element analysis (FEA). METHOD In this study, numerical models were developed to trace the structural behavior of UHPC beams upon loading since beam behavior depends on the constituents' response to compression and tension. New numerical models were formulated to display the stress-strain relationships of UHPC in compression and tension by adopting a new methodology that depended on actual results. The compressive stress-strain relationship consisted of two portions; the ascending one for elastic and strain hardening up to compressive strength and a descending curve for the strain-softening until reaching a strain of 0.0062. RESULT A linear tensile stress-strain relation was applied for the elastic tensile behavior up to tensile strength. Then, a tri-linear relationship was applied for the stiffness degradation and crack propagation upon debonding fibers from the concrete matrix until fracture. These numerical models were used in Abaqus software to simulate the UHPC beam behavior. CONCLUSION The developed models were verified and approved for beams' behavior upon loading in flexure and shear. The results indicated that the models could predict the UHPC beams' response throughout the entire loading range from the beginning until failure. The verification included bear capacity, deflection, crack pattern, and stress distribution.

Mechanical behavior and models for porosity-free concrete reinforced with high amounts of steel fiber

• Mechanical properties of porosity free concrete were investigated in several material tests. • Compressive stress–strain curve and tension softening curve were modeled. • Equivalent characteristic length (average crack spacing) was obtained by numerical analysis. • Tensile stress–strain relationship was proposed by using equivalent characteristic length. A new cementitious composite characterized by an extremely high compressive strength (>400 MPa), known as porosity-free concrete (PFC), has been recently developed. Many tests have been conducted to formulate appropriate stress–strain laws for compression and tension. This study clarified that PFC has extremely high compressive strength and post-cracking toughness owing to the reinforcing fibers. In addition, the flexural strength of porosity-free concrete was investigated by combining experimental and numerical analyses. Furthermore, the formulation of the stress–strain law in tension introduced “equivalent characteristic lengths” to convert the crack width into an equivalent strain. (93 words)

Water loss and defects dependent strength and ductility of articular cartilage

Water loss and surface defects of articular cartilage extremely aggravate the risk of osteoarticular diseases. The effects of water content and surface defects on the mechanical properties of cartilage need to be taken into further account. By using a self-developed in-situ tensile tester, the tensile stress-strain relationship and real-time morphological changes under conditions of different water contents are obtained with and without a micro void. It is confirmed that tissue structure and permeability are the main factors affecting the strength and ductility of cartilage. The less water content contributes to the lower permeability, inducing higher strength but poorer plasticity. Raman spectroscopy analysis results directly reveal the transition from the bonding water with stronger hydrogen bonds to the free water with weaker hydrogen bonds in cartilage layer caused by both drying treatment and tensile deformation, which results in decreased permeability and enhanced resistance to deformation. Raman-based organic matrix content is negatively correlated with permeability but positively correlated with the strength of cartilage. The obtained experimental data may facilitate to predict cartilage damage and develop artificial cartilage materials.

An Experimental and Analytical Study on a Damage Constitutive Model of Engineered Cementitious Composites under Uniaxial Tension.

Engineered cementitious composites (ECC) exhibit ultra-high ductility and post-cracking resistance, which makes it an attractive material in civil engineering. First, a monotonic uniaxial tensile test was performed, considering the effects of polyvinyl alcohol (PVA) fiber volume content and water-binder ratio. Then, the effects of the above variables on the tensile characteristics including the tensile stress–strain relationship, deformation capacity, and fracture energy were investigated based on test results; and when the water-binder ratio is 0.28 and the fiber volume content is 2%, the deformation performance of ECC is improved most significantly. Next, combined with damage mechanics theory, the damage evolution mechanism of ECC in monotonic uniaxial tension was revealed, based on which the damage factor and damage evolution equation of ECC were developed and the expressions of model parameters were proposed. Moreover, the comparison between the proposed model and test results demonstrated the accuracy of the proposed model. Finally, to further verify the feasibility of the proposed model, a finite element (FE) simulation analysis of the tensile performance of high-strength stainless steel wire rope (HSSWR) reinforced ECC by adopting the proposed model was compared with test results and the simulation analysis results by using anther existing model, the “trilinear model of ECC”. The comparison shows that the proposed model in this paper can predict more accurately.

Mechanical characteristics of hardened basalt fiber expanded clay concrete cylinders

Concrete is a universal construction material, and it is one of the most widely used materials in civil engineering. Concrete is strong in compression but weak in tension, therefore exhibiting brittle material characteristics. Lightweight concrete (LWC) has a considerably lower density compared to normal concrete and this is associated with its brittle nature, thus affecting the strength, ductility, and durability of lightweight concrete. To improve these shortcomings and proffer solutions, this paper investigates the effects of dispersed chopped basalt fiber (BF) incorporation in concrete and basalt fiber reinforced polymer (BFRP) mesh for concrete confinement. An experimental investigation was conducted to determine the strength and toughness of BF reinforced lightweight expanded clay concrete (LWECC). This experiment was performed with eighteen (18) specimens of LWECC cylindrical column with 1.6% chopped BF mixed with lightweight ECC. To verify this experiment, three-dimensional finite element models (FEM) were created based on the experimental loading and accounted for tested material properties. A close agreement was achieved between the test and finite element analysis results, split tensile strength, compressive strength, and stress-strain relationship of cylindrical basalt fiber concrete was developed. The results proved the best porosity index, compressive strength and modulus of elasticity when expanded clay concrete was reinforced with BF and confined in BFRP mesh.

Evaluation of structural and mechanical strength of symmetric tilt interface in W/Fe composite laminate using molecular dynamics

In this work, a tungsten (W)/iron (Fe) composite laminate is constructed by joining two constituents W and Fe according to the symmetric tilt interface relationship. The performance of the newly built W/Fe symmetric tilt interfaces is evaluated by interface energy, tensile stress–strain relationship, and strength and then compared with semi-coherent W/Fe boundaries and W and Fe symmetric tilt grain boundaries. The results show that even though most W/Fe symmetric tilt interfaces have very high interface energy, some have interface energy comparable to those of semi-coherent W/Fe boundaries and W and Fe symmetric tilt grain boundaries, and thus should be considered for W/Fe composites. The mechanical properties for tensile deformation parallel to the interface of these stable W/Fe symmetric tilt interfaces outperform the estimated values from composite theory and even those of semi-coherent W/Fe boundaries. Our findings suggest that the symmetric tilt interfaces not only play an important role in the interface strength of W/Fe composite laminate, but also should be incorporated into future designs of W/Fe or other composites to circumvent the lattice, thermal, and mechanical mismatches between heterogeneous constituents.

The effect of tension stiffening in moment-curvature responses of prestressed concrete members

Although tensile resistance of concrete is often neglected in calculating the nominal flexural capacity of a concrete member, it needs to be taken into account to accurately trace the deformation response of concrete members as it affects pre- and post-cracking behavior. To adequately address tensile resistance contributed by concrete in moment–curvature analysis, it is necessary to exploit a proper concrete tensile stress–strain model. While constitutive stress–strain models of reinforced concrete in tension have been studied by many researchers and well documented, those of prestressed concrete have gained relatively less attention. There are also conflicting results on how prestressing force affects concrete tension stiffening. This study fills the gap in existing studies and suggests an appropriate and simple model capturing the concrete tensile stress–strain relationship of prestressed concrete in a moment–curvature analysis. Based on an inverse-engineering approach using experimental test data and nonlinear analysis results, the effect of concrete tension stiffening varied by the level of prestressing force is investigated. The results show that concrete tensile properties hardly affect the force–deformation response of beams with high-level prestressing. Additionally, several parameters related to concrete tension stiffening are examined in the parameter study. By comparing predicted moment–curvature responses with test data, ideal values for considered parameters are obtained. Based on the parameter study, simple equations are proposed that are expressed in concrete compressive strength to simulate the concrete tensile stress–strain responses of partially prestressed members. The proposed equations are demonstrated using several prestressed beam tests found in previous studies.

Theoretical modification of the laboratory-determined tensile stress–strain relationship of strain hardening cementitious composites (SHCCs) for large-scale specimens

Strain hardening cementitious composites (SHCCs) are a type of cementitious material reinforced with randomly distributed short fibers that exhibit tensile strain hardening behavior and prominent crack resistance. The tensile behavior of SHCCs could be significantly affected by the distribution of the fiber orientation. In large-scale specimens, the distribution of the fiber orientation is close to ideal three-dimensional uniform random distribution. However, fiber orientation distributions in laboratory SHCC specimens are influenced by the specimen dimensions (width and thickness) and casting process, resulting in neither ideal two-dimensional nor three-dimensional uniform random distribution. Therefore, the performance of large-scale SHCC specimens may be overestimated in analysis when directly using the tensile properties of SHCCs obtained from uniaxial tensile tests of small specimens. Since the uniaxial tensile tests of large-scale SHCC specimens are difficult to be conducted, theoretical evaluation of the tensile properties of mass SHCCs in large-scale specimens were conducted by modifying the uniaxial tensile test results of small specimens. In this paper, closed-form probability distribution models for fiber orientations that consider the influence of the specimen width and thickness were theoretically derived. The effects of the specimen width and thickness on the tensile properties of SHCCs were studied by applying the proposed method to the uniaxial tensile numerical model of SHCCs, while uniaxial tensile specimens with two different geometries and dimensions were tested for verification. Both the analytical and experimental results showed that, within a certain range, the width and thickness of the specimens significantly influenced their ultimate tensile strength and ultimate tensile strain. To relate the uniaxial tensile test results of laboratory-sized specimens to that of mass SHCC in large scale specimens, reduction factors for the stress–strain relationship of SHCCs obtained by traditional tensile test specimens were proposed to account for the specimen size effect based on the model analysis. The reduced tensile stress–strain relationship was applied to a finite element model of SHCC beams under four-point bending tests. It was found that the finite element analysis results obtained by using the reduced tension stress–strain relationship are in better agreement with the test results.

Determination of local constitutive behavior of AA6061–T6 friction stir welds using digital image correlation

The local constitutive behavior of aluminum alloy 6061–T6 friction stir welds was characterized by uniaxial tensile tests using digital image correlation. The global tensile stress–strain relations for friction stir weld specimens were determined using a conventional testing machine equipped with an extensometer. The digital image correlation method was simultaneously applied to measure the full-field strain distributions over a 30 mm gauge length of the friction stir weld specimens during loading. The global specimen strains over the gauge length were determined by superimposing local strains measured by digital image correlation using the “inverse rule of mixtures” for composites. The Hollomon and Ludwik constitutive models were used to describe the local flow curves for the weld zones. The global true stress–true strain curves obtained from uniaxial tensile tests were compared with those constructed by superimposing local strains measured using digital image correlation. Both the global mechanical responses were in good agreement with each other. It is shown that the global true stress–true strain curves can be constructed using the inverse rule of mixtures method from the local constitutive equations for the different weld zones determined by the uniaxial tensile tests using digital image correlation.

Effects of fibre orientation on tensile properties of ultra high performance fibre reinforced concrete based on meso-scale Monte Carlo simulations

The damage and fracture of ultra high performance fibre reinforced concrete (UHPFRC) is inherently dependent on fibre orientation and distribution. The effects of fibre orientation on the tensile properties of UHPFRC are investigated by meso-scale finite element (FE) simulations. The nonlinear bond-slip behaviour of fibre-mortar interfaces is explicitly modelled by zero-thickness cohesive elements with softening constitutive laws. After validation against existing experiments, extensive Monte Carlo simulations of FE models are conducted with different fibre volume fractions (1.5%, 2.0%, 2.5% and 3.0%) and orientation in the ranges of 0–90° (random), 0–30°, 30–60° and 60–90°, respectively. The fibre orientation is found to significantly influence tensile stress-strain relationships of UHPFRC, fracture patterns in the mortar, stress evolution in the fibres and bond-slip behaviour of the interfaces. Using more fibres is useful only when the fibres are reasonably oriented with respect to the tension direction, and a transition from brittle to ductile failure with strain hardening can be achieved by optimising the fibre orientation even for relatively low fibre content. Empirical equations are curve-fitted between the orientation number and key properties such as the elastic modulus, first-cracking stress and peak stress, which can be used to optimise tensile properties of UHPFRC members.

Design method of flexural capacity of BFRP bar reinforced ecological high ductility cementitious composites beam

Steel expansion joints are damaged under traffic loading, and bridge deck link slab made by basalt fiber reinforced polymer (BFRP) bar reinforced ecological high ductility cementitious composites (Eco-HDCC) can be used to replace the expansion joints. To provide the structural design guideline of bridge deck link slab, experimental study and theoretical analysis of BFRP bar reinforced Eco-HDCC bending beam were conducted. The diameter of BFRP bar and cover thickness were considered. Monotonic and cyclic loading modes were compared. When the diameter is within 8 mm ∼ 16 mm and the cover thickness is within 25 mm ∼ 35 mm, the peak load of beam increases as the diameter increases or the cover thickness decreases. Monotonic and cyclic loading regimes have little effects on the peak load. Before the beam cracks, diameter and cover thickness have little effects on the strain of BFRP bar and compressive strain of Eco-HDCC. After the beam cracks and under the same load, both the strain of BFRP bar and compressive strain of Eco-HDCC decrease as the diameter increases. Loading regime has little effect on the envelope curves of load-BFRP bar strain and load-Eco-HDCC compressive strain. Calculation formulas of flexural capacity for under-reinforced beam, balanced-reinforced beam and over-reinforced beam are established as the tensile stress–strain relationship of Eco-HDCC is involved. Compared with the test results, the calculation formulas of flexural capacity are feasible.