CSI Software enables the calculation of creep behavior in frame and shell objects. Creep contributions include external loading, internal nonlinear effects, and internal redistribution of stresses within redundant structures.

The time domain is controlled by setting the number of output steps in the staged-construction case. Each stage should have several steps. Stage lengths should be of increasing duration, each about as long as the sum of all previous stages. No internal time increment (dt) is necessary. Smaller time steps should be taken when the solution is not monotonic. Further, because calculation uses forward differences, smaller time steps should also be taken in younger materials and at the beginning of loading, when creep occurs more rapidly.

Formulation uses two Gauss points for frames, and a 2x2 quadrature for shells. Stress increments are computed at each analysis step. Nonzero stress increments then contribute to creep strain. Each stress increment initiates a new creep history which is cumulative with the previous histories at a material point. These are then summed over the total history of the material. The exact method stores each history separately, causing the material-point state-information size go grow as analysis proceeds. As an alternative to this cumulative method, to prevent the slowing of long analyses for larger structures, a fixed-size Dirichlet series may be specified within the material creep properties. This represents the creep state as a set of Kelvin-Voigt elements with different relaxation times. To account for a new stress increment, the state of each Kelvin-Voigt element is modified to capture the effect of multiple stress increments. This works very well with approximately 10 terms in the series. Different numbers of terms may be tested against the exact solution.

For informational purposes, material definition enables the creep curve to be plotted for different Age at Loading conditions. Please note that this has no effect on material behavior. The actual Age at Loading used during analysis is the material age at which each individual load increment is applied.

Tips

• Creep formulation is a function of mesh size. The influence of meshing upon results should be tested before deciding upon discretization.

References

• Ghali, A., Favre, R., Elbadry, M. (2002). Concrete Structures: Stresses and Deformations: Analysis and Design for Serviceability (3rd ed.). London, England: Spon Press.