Size effect in unnotched concrete specimens in bending: An analytical approach

The size effect in unnotched concrete specimens in bending causes a higher modulus of rupture compared with its axial tensile strength. To determine the axial tensile strength of concrete from flexural tensile tests, size effect coefficients are, therefore, required. Analytical equations have been derived in the past by the application of nonlinear fracture mechanics and finite element parametric studies. However, the well-known equations from the Model Codes do not represent the correct asymptotic behavior of the size effect which is problematic for high values of fracture energy, for example, for fiber-reinforced concrete. Other equations known to the authors require knowledge of the characteristic length of the specimen, that is, their uniaxial tensile strength has to be known a priori. Therefore, this paper presents an analytical approach for the size effect in unnotched concrete specimens in bending that features correct asymptotic behavior and does not require a priori knowledge of the axial tensile strength. The comparison with finite element parametric studies and test results from the literature shows a very good agreement of the proposed equation from brittle to plastic behavior.