Civil Engineering Reference
In-Depth Information
the eccentricity of the prestress. In addition, there will be a moment due to the external
load, including the beam's own weight. The resulting stress at any point in the beam
caused by these three factors can be written as follows where
P
is the prestressing force:
P
A
Pec
I
Mc
I
f
In Figure 19.5, a stress diagram is drawn for each of these three items, and all three are
combined to give the final stress diagram.
The usual practice is to base the stress calculations in the elastic range on the proper-
ties of the gross concrete section. The gross section consists of the concrete external di-
mensions with no additions made for the transformed area of the steel tendons nor
subtractions made for the duct areas in posttensioning. This method is considered to give
satisfactory results because the changes in stresses obtained if net or transformed proper-
ties are used are usually not significant.
Example 19.1 illustrates the calculations needed to determine the stresses at various
points in a simple-span prestressed rectangular beam. It will be noted that, as there are no
moments at the ends of a simple beam due to the external loads or to the beams own
weight, the
Mc
/
I
part of the stress equation is zero there and the equation reduces to
P
A
Pec
I
f
EXAMPLE 19.1
Calculate the stresses in the top and bottom fibers at the centerline and ends of the beam shown in
Figure 19.6.
Figure 19.6
