On the Compressive Fiber Strain of Concrete at the Flexural Failure of Reinforced Concrete Beam Section

Abstract

The flexural failure of reinforced concrete section is generally caused by crushing of concrete at the compression zone. For the calculation of ultimate flexural capacity or corresponding deformation of a beam, the compressive fiber strain of concrete at failure should be assumed. In practice, the empirical values, for instance, ε_cu=0.25∼0.35%, are being used in the calculation. However, these values are not always clearly defined from the theoretical viewpoint.
In this study, based on the stress-strain curve of concrete having the strain softening region, the theoretical estimation was made on the compressive fiber strain of concrete at the ultimate flexural capacity as well as that at the failure or the crushing of concrete in compression zone of the reinforced concrete rectangular beam section. The results obtained are as follows:
(1) The extreme compressive fiber strain to be used for ultimate flexural strength calculation is defined as the value at which the compressive stress brock coefficient, k₂/k₁k₃, obtained from the stress-strain curve of concrete becomes minimum, where k₁k₃ and k₂ denote the ratio of the average stress of stress-strain curve up to an arbitrary strain to the compressive strength and the ratio of the location of center of gravity of the corresponding area to the arbitrary strain, respectively.
(2) It is reasonable to assume that the compression failure of concrete in compression zone takes place primarily when the distance of neutral axis from compressive fiber becomes minimum. The corresponding compressive fiber strain can be defined from the stress-strain curve of concrete as the strain at the maximum value of stress brock coefficient, k₁k₃.
(3) Practically, the compressive strain at the failure of concrete described in (2) can be used for the calculation of ultimate flexural strength or deformation of beams.
(4) The increase of negative slope of the strain softening region in concrete stress-strain curve reduces the value of compressive fiber strains, especially that for the failure of concrete. On the contrary, the increase of strain at the peak stress (that is, at the compressive strength) in stress-strain curve results in much increase of the ultimate compressive fiber strains.