Approximate expressions for the ageing coefficient and the relaxation function in the viscoelastic analysis of concrete structures

Creep analysis of concrete structures meets well-known computational difficulties when one needs to determine the relaxation function corresponding to a specified creep function through the inversion of Volterra's linear integral equation. For this reason, the recent proposals for the 1990 edition of the CEB Model Code introduce an approximate formulation of the relaxation function obtained from the expression of the ageing coefficient χ(t, t0) of the algebraic age-adjusted-effective modulus (AAEM) method assumed as a function of age at loading, t0, only. In the first part of this paper, an approximate algebraic expression, χ + ̃ for the ageing coefficient with reference to the MC 90 is presented. This formulation differs from previous proposals in that, in addition to the influence of t0, it also takes into account the influence of other parameters, such as relative humidity, characteristic strength of concrete and effective thickness. In the second part, this approximate algebraic expression of the ageing coefficient is used to obtain an approximate formulation for the relaxation function which is in very good agreement with the exact values of the relaxation function as obtained from the creep function through the solution of the basic integral equation. Finally, an example of structural calculation is provided (by applying the AAEM method and comparing the values obtained with those yielded by the general numerical method): the example clearly shows the advantages offered by the new approximate formulation of the ageing coefficient, χ + ̃, compared to the expression proposed in the CEB MC 90.