The strength of the cement paste (concrete without aggregate) is principally determined by age and density. The increase in strength with time follows the reaction processes. The initial strength is developed from the setting reaction where C3A is hydrated. However, the real strength is developed from the slower hardening reactions where C2S and C3S are hydrated.

 

 

The Young's modulus of the cement paste varies with density.

 

 

Here, ES and ρS are the modulus and density respectively of the solid tobomorite gel.

The addition of the aggregate, with a modulus three times that of the cement, will obviously have a significant effect on the overall modulus of the concrete. In this case the modulus can be calculated from composite theory.

 

 

Here, Va and Vp are the volume fractions of aggregate and cement paste respectively and Ea and Ep are the modulus of the aggregate and cement paste respectively.