Relationship between compressive strength and modulus of elasticity of High-Strength Concrete

Modulus of elasticity of concrete is frequently expressed in terms of compressive strength. While many empirical equations for predicting modulus of elasticity have been proposed by many investigators, few equations are considered to cover the entire data. The reason is considered to be that the mechanical properties of concrete are highly dependent on the properties and proportions of binders and aggregates. This investigation was carried out as a part of the work of the Research Committee on High-strength Concrete of the Architectural Institute of Japan (AIJ) and National Research and Development Project, called New RC Project, sponsored by the Ministry of Construction. More than 3,000 data, obtained by many investigators using various materials, on the relationship between compressive strengths and modulus of elasticity were collected and analyzed statistically. The compressive strength of investigated concretes ranged from 20 to 160 MPa. As a result, a practical and universal equation is proposed, which takes into consideration types of coarse aggregates and types of mineral admixtures. producing concrete, mix proportioning, unit weight and air content of fresh concrete, method and temperature of curing, and age. 2.1 Estimation of the Unit Weight Out of the 3000 experimental data collected, only one third included measured unit weight of specimens, γ. In order to express modulus of elasticity as a function of compressive strength and unit weight, the unit weights of hardened concrete had to be estimated when measured unit weights were not available from the data on materials used, mix proportioning, curing conditions, and age. 3 EQUATION FOR MODULUS OF ELASTICITY 3.1 Evaluation of Exponent b of Compressive Strength, σB As compressive strength increases, Eq. 1 overestimates the modulus of elasticity. It is therefore, considered appropriate to reduce the value of exponent b of the compressive strength, σB, to less than 1⁄2 in order to make it compatible to the measured values. Firstly, range of possible values of exponent b in Eq. 2 was investigated evaluating 166 sets of data, each set of which had been obtained from identical materials and curing conditions by the same researcher. Figure. 2 shows the relationship between the ultimate compressive strengths and the estimated exponent b. Similarly, Figure. 3 shows the relationship between the exponent b and the ranges of compressive strengths in the sets of data. In Figures. 2 and 3, while the estimated values of exponent b vary widely, the values show a tendency to decrease from around 0.5 to around 0.3, as the maximum compressive strengths increase and the ranges of compressive strength widens. In other words, whereas modulus of elasticity of normal-strength concrete has been predictable from the compressive strength with exponent b of 0.4 to 0.5, the values of 0.3 to 0.4 are more appropriate a general-purpose equation to estimate modulus of elasticity for a wide range of concretes from normal to high-strength. Consequently, the 1/3 is proposed as the value of exponent b.