Why do we take the same dimensions of the column for all the stories in a multi-storeyed building even when the loads coming on the lower column is higher than the loads on the upper storey practically.
It is not a necessity to always keep the size of columns the same in all floors, but practically it is better to reduce the amount of reinforcement rather than changing the size of column as we go to higher floors.
The reduction of amount of reinforcement in higher floors is always true if we only consider the gravity forces, but this condition sometimes changes when lateral forces come to action. In this case, the column design may be controlled either by gravity forces or biaxial moments. Since the gravity forces are low in higher floors, usually their behavior is controlled by the moments and, thus, you will see more amount of reinforcement in these columns than the columns in the lower floors in which the gravity forces are higher and thus design is controlled by axial forces. As a result, not only the gravity forces but also the lateral forces have great effect on column designs.
I doubt considering the same dimension for columns in different stories. Actually for practical issues (e.g. molding works in R.C buildings and splices in steel ones) they are tried to be classified normally in two or three stories. But due to designing columns based on axial load and bending moment (P-Mx-My) interaction and satisfying weak beam-strong column recommendation (in some ductility levels) their dimensions will differ. For example, you may assume a bracing frame where story shear increases as you go to lower stories, then the axial load at columns connected to brace by gusset plate will increase which results in greater dimensions.
It is not a necessity to always keep the size of columns the same in all floors, but practically it is better to reduce the amount of reinforcement rather than changing the size of column as we go to higher floors.
The reduction of amount of reinforcement in higher floors is always true if we only consider the gravity forces, but this condition sometimes changes when lateral forces come to action. In this case, the column design may be controlled either by gravity forces or biaxial moments. Since the gravity forces are low in higher floors, usually their behavior is controlled by the moments and, thus, you will see more amount of reinforcement in these columns than the columns in the lower floors in which the gravity forces are higher and thus design is controlled by axial forces. As a result, not only the gravity forces but also the lateral forces have great effect on column designs.
Value management may also be a factor, as reducing the variation in column sizes will inevitably save on the cost of formwork. This is where reinforced concrete structure is been considered.
That is right that the load of columns in multi-storey buildings change at the height (for sure longitudinal force decreases with increasing the height; and not necessarily the bending moments) - hence, it may seem natural to change the cross-section of the columns.
Often the reason for leaving the constant cross-section of the column are architectural considerations, rather than structural.
Quite frequently multi-storey buildings are office buildings with glass facades and architects would like to get line of visible, external columns of constant thickness.
Often, the real problem is construction of the lower storey columns with a small cross-section, and not a problem for a large cross-section of the upper columns.
Then you can perform concrete columns with high strength concrete or steel-concrete composite columns.