Backcalculation of residual tensile strength of regular and high performance fiber reinforced concrete from flexural tests

•Closed form equations for measuring tensile constitutive response from flexural tests.•Parameters obtained from routine experimental data can be used for design of FRC elements.•Correlation of backcalculated tensile data from flexural and direct tension tests.•Comparison of nature of the stress distribution under the two tension and flexural tests.•Residual tensile strength, and post crack stiffness correlated with the fiber type and content. The tensile stress–strain response of a fiber reinforced concrete dominates the performance under many loading conditions and applications. To represent this property as an average equivalent response, a back-calculation process from flexural testing is employed. The procedure is performed by model fitting of the three-point and four-point bending load deflection data on two types of macro synthetic polymeric fibers, one type of steel fiber and one type of Alkali Resistant (AR) glass fiber. A strain softening tensile model is used to simulate the behavior of different FRC types and obtain the experimental flexural response. The stress–strain model for each age, fiber type and dosage rate is simulated by means of the inverse analysis procedure, using closed-form moment–curvature relationship and load–deflection response of the piecewise-linear material. The method of approach is further applied to one external data set for High Performance Fiber Reinforced Concrete (HPFRC) with two different types of steel fibers and validated by tensile test results reported. Results of back-calculation of stress–strain responses by tri-linear tensile model for all mixtures are compared and correlated with the corresponding standard method parameters used for post crack behavior characterization and a regression analysis for comparative evaluation of test data is presented.