If the loads are sustained for longer duration than initial deflections increased very prominently because of the two major affects i.e., creep and shrinkage. These two effects are considered as combined in most of the cases during the calculation of deflection. Generally, creep becomes more prominent in many cases but, there are various types of members for which shrinkage deflections are large. For these types of members, a separate calculation is to be done.
Generally, creep deformations are considered as directly related to the compressive stress. In case of a reinforced concrete beams, the deflections due to long term loading are more complicated than for axially loaded concrete cylinders (used for compressive strength test). This is so because during the long term loading concrete creeps while, the steel does not.
During the long-term loading, strains at the top face of a beam increases because of the creep. While, the strains in the steel (tension zone) remain unchanged. Due to this neutral axis lower down to the bottom side and these results an increase in the compression area. So, now a less compressive stress will be required for an equilibrium with the tensile force T= Asfs.
This lowers the neutral axis which results in the less internal lever arm between the compression and the tension zone. Therefore, moments from the compression and tension side will no more remain the same. This situation demands an increase in stress and henceforth, strains in the steel no more remain constant as assumed initially.
Formula for Long-term Deflection
Due to such type of complexities, it is very important to calculate the additional time-dependent deflections of beams that occur because of creep and shrinkage. This can be done by using a very simple empirical relation. In this relation initial elastic deformations are multiplied by a factor λ. It depends on the data of long term deflections for reinforced concrete beams.