Why does elastic compression loss (e.g. loss of pre-stressing in previously grouted tendons due to stressing of further tendons) not appear in internal force results of structural elements?
The influence of prestressing losses in previously grouted tendons on the internal forces of the respective structural element is just pretended but in reality not existent when differences between the relevant cross-sections (concrete sections, composite sections) are properly considered. Let us show the relationship on behalf of a concentrically in 2 steps pre-stressed beam (the general validity also for bending, shear, multi-stage stressing is obvious):
Let us denote:
In principle, the two forces are related to 2 different cross-section areas and adding them is not allowed. However, in proof checking procedures we generally want to work with summation values applied to one relevant cross-section, normally the relevant composite section after grouting all tendons. I.e. for working with the final composite section Acomp we must adjust N1 accordingly.
Let us look at the concrete stresses after the two steps: σc = N1/A1 + Ncomp/Acomp. For working with the summation value N = N1+Ncomp and the composite section Acomp we must relate the value N1 to the composite section by N1* = N1*(Acomp/A1).