Prestressed Concrete - Design of Reinforced Concrete - page 579

Computing Stresses

(250)(4)(12)
13,824

P
A

Pec
I

250
288

f top

0.868 0.868 0

P

A Pec

f bottom 0.868 0.868 1.736 ksi

I

19.6 SHAPES OF PRESTRESSED SECTIONS

For simplicity in introducing prestressing theory, rectangular sections are used for most of
the examples of this chapter. From the viewpoint of formwork alone, rectangular sections
are the most economical, but more complicated shapes, such as I's and T's, will require
smaller quantities of concrete and prestressing steel to carry the same loads and, as a re-
sult, they frequently have the lowest overall costs.
If a member is to be made only one time, a cross section requiring simple formwork
(thus often rectangular) will probably be used. For instance, simple formwork is essential
for most cast-in-place work. Should, however, the forms be used a large number of times
to make many identical members, more complicated cross sections, such as I's and T's,
channels, or boxes, will be used. For such sections the cost of the formwork as a percent-
age of each member's total cost will be much reduced. Several types of commonly used
prestressed sections are shown in Figure 19.8. The same general theory used for the deter-
mination of stresses and flexural strengths applies to shapes such as these, as it does to
rectangular sections.
The usefulness of a particular section depends on the simplicity and reusability of the
formwork, the appearance of the sections, the degree of difficulty of placing the concrete,
and the theoretical properties of the cross section. The greater the amount of concrete lo-
cated near the extreme fibers of a beam, the greater will be the lever arm between the C
and T forces and thus the greater the resisting moment. Of course, there are some limita-
tions on the widths and thicknesses of the flanges. In addition, the webs must be suffi-
ciently large to resist shear and to allow the proper placement of the concrete and at the
same time be sufficiently thick to avoid buckling.
A prestressed T such as the one shown in Figure 19.8(a) is often a very economical
section because a large proportion of the concrete is placed in the compression flange,
where it is quite effective in resisting compressive forces. The double T shown in Figure
19.8(b) is used for schools, office buildings, stores, and so on and is probably the most
used prestressed section in the United States today. The total width of the flange provided
by a double T is in the range of about 5 to 8 ft, and spans of 30 to 50 ft are common. You
can see that a floor or roof system can be erected easily and quickly by placing a series of
precast double T's side by side . The sections serve as both the beams and

slabs for the floor or roof system. Single T's are normally used for heavier loads and
longer spans up to as high as 100 or 120 ft. Double T's for such spans would be very
heavy and difficult to handle. The single T is not used as much today as it was in the re-
cent past due to stability difficulties in both shipping and erection.
The I and box sections, shown in parts (c) and (d) of Figure 19.8, have a larger pro-
portion of their concrete placed in their flanges, with the result that larger moments of