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 .

(1)

where, results from all dead and service live loads

Let’s define a new variable:

(2)

(3)

Similarly,

(4)

where typically results from the dead load only

We can define

(5)

**Note**: we are neglecting crushing and making the simplification that

So,

(6)

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.

(7)

(8)

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.

Similarly,

(9)