Algebraic Methods for Creep Analysis of Continuous Composite Beams

This interesting study is similar to the study by Bazant and Najjar (1973) [extensively reviewed in Section 5.5 of Bazant (1975)], which apparently escaped the attention of the authors. However, the conclusion in which the authors recommend the effective modulus method, is different. It appears unwarranted and conflicts with more extensive evidence. The authors dismiss the age-adjusted effective modulus method on the basis that it requires evaluation of the relaxation function. However, it must be pointed out that this function can be easily and quite accurately evaluated from an approximate formula by Bazant and Kim (1979), also reported in BaZant (1988) and other review works. Contrary to what the authors say, solution of the integral equation need not be carried out. (An accurate calculation of the relaxation function by a computer solution of the integral equation is nevertheless an almost trivial matter.) In a broad range of examples worked out by BaZant and Najjar (1973), including stress redistributions due to changes of the structural system, stress redistributions in composite cross sections, differential creep of a structure with concretes of different age, shrinkage stresses, effect of settlement of supports, creep buckling, etc., the age-adjusted effective modulus method gave results overall far closer to the exact solution according to the principle of superposition than other algebraic methods. The differences between various solutions happen to be for the problem considered by the authors, considerably less than in some other creep and shrinkage problems, e.g., those analyzed by BaZant and Najjar (1973). This means that the examples they considered are not the cases most sensitive to creep, and therefore not the cases most suitable for comparison of various methods. Furthermore, the accuracy of the application of the age-adjusted effective modulus method to shrinkage stresses in a concrete slab strongly depends on the shrinkage function. The function given by "CEB FIP Model Code 1990" (1988) is not quite realistic, showing a much higher overall deviation from the bulk of available test data than the B3 model (BaZant and Baweja 1995). The accuracy of the age-adjusted effective modulus method for shrinkage is high only when the average rate of shrinkage, compared to the long-term value, is roughly the same as the rate of creep, in which case the assumption that the shrinkage curve should be approximately a linear function of the compliance function for creep is a good approximation. Anyway, the authors would obtain very different conclusions if they studied a range of possible shrinkage curves, as predicted by the B3 model for concretes of different diffusivities and various thicknesses. It makes little sense to draw a general conclusion from an isolated example, especially if an unrealistic shrinkage function is used. Regarding the mean stress method, its apparently good performance for shrinkage problem must be due to the high rate of shrinkage, in their chosen shrinkage function. This rate var-