The effects of the elastic moduli of the cement paste matrix and aggregate on the modulus of elasticity of concrete

Abstract

The general form of an equation has been derived which expresses the modulus of elasticity of concrete or mortar in terms of one empirical constant, the moduli of the matrix and aggregate constituents, and the mix proportions. If E (subscript c), E (subscript a), and E (subscript m) are the moduli of elasticity of the concrete, aggregate and matrix respectively, and if, V(subscript c), V (subscript a), and V (subscript m) are the volume of concrete, aggregate and matrix respectively, then [see PDF for diagram] and Z = an empirical constant. With the empirical constant, Z, tentatively evaluated as 0.785, the modulus values computed with this equation were shown to be in good agreement with laboratory data which covered an unusually wide range of variables. The average deviation was found to be within (plus or minus sign) 10%, and the maximum deviation was within (plus or minus sign) 35%. Laboratory tests were conducted to determine the effects of the water-cement ratio and of the age of cement paste on its elastic properties, compressive strength and tensile strength. Laboratory tests were also conducted to obtain data on the modules of elasticity of concrete. Several materials, each with a greatly different elastic moduli, were used as concrete aggregates in order that the effects of their elastic properties on the modulus of elasticity of concrete could be observed. The materials used as aggregates were steel punchings, crushed glass, lead drops, Ottawa sand, crushed limestone, and a calcareous-siliceous river gravel. In addition to these tests the pertinent data collected by other investigators in this field have been summarized, and all of these data were compared with the derived equation.