# 7. Choosing the Appropriate Section Shape

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)

Let’s define a new variable:

(2)

(3)

Similarly,

(4)

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)