A general formulation framework for an age-dependent constitutive equation of concrete is presented to account for the development of the elastic modulus at an early age. This is achieved by expanding the total stress vs. strain relation with respect to the time-varying elastic modulus. Two types of constitutive formulation frameworks are derived depending on whether (or not) the time-varying effect of the elastic modulus was taken into account in the linearized series expansion. The causes for the age-dependent deformations under sustained loads are defined in the formulation based on the two internal mechanisms of delayed elasticity and the ageing phenomenon. The ageing phenomenon is incorporated in a conventional delayed strain concept in terms of the variable elastic modulus with time. Four cases of age-dependent constitutive equations are formulated within the presented formulation framework by employing different types of creep models. The mechanical characteristics of the terms that comprise the various constitutive equations are examined and compared. Numerical application of the time-dependent test results of cylindrical specimens indicate that the creep formulation that considered the elastic modulus development showed a good agreement with the experimental result while the formulation that did not consider the elastic modulus development underestimated the result by 15%.

Three types of creep experiments of compression, tension, and bending were implemented to identify quantitative relations among the three types of creep under drying atmospheric conditions. In case of the bending creep experiment, two types of unreinforced concrete beams with similar dimensions were cast for use in the beam creep and shrinkage tests. The variations in the shrinkage strain within the beam depth were measured to evaluate the effect of the shrinkage variations on the bending creep strain. The beam creep strain measured within the beam depth was composed of uniform and skewed parts. The skewed parts of the creep strain were found to be dominant whereas the uniform parts were small enough to be neglected in the bending creep evaluation. This indicated that the compressive bending creep at the top surface was close to the tensile bending creep at the bottom surface. The ratios of tensile and bending creep strains to compressive creep strain were approximately 2.9 and 2.3, respectively, and the ratio of bending creep strain to tensile creep strain was approximately 0.8. Particular attention is laid on the close agreement between tensile and compressive bending creep strains even if the creep in tension is 2.9 times larger than the creep strain in compression.