The diagram below illustrates the initial and final conditions, with the simplifying assumption that the concrete can take zero tension. At the initial stage, the applied moment is , and at the final stage, the applied moment is .
where, results from all dead and service live loads
Let’s define a new variable:
where typically results from the dead load only
We can define
Note: we are neglecting crushing and making the simplification that
We can see that large the section can resist large service loads AND will be able to resist a large prestressing force at the transfer stage (ignoring crushing in either case).
For a continuous beam, or a continuous slab (positive and negative moments), allowable variation may be as important as the value. For example, the hollow-core slab above could be as efficient as the box-girder, in such a scenario.
This is what we’ll use for actual design (rather than simply the choosing of section size), as we will see in detail in the following section.