FIGURE 33. Stresses in bottom fiber along half-span.This procedure illustrates the following principles relevant to a beam with straight ten-
dons carrying a uniform load: At transfer, the critical stresses occur at the supports; under
full design load, the critical stresses occur at midspan if the allowable final stresses ex-
ceed j] times the allowable initial stresses in absolute value.
The primary objective in prestressed-concrete design is to maximize the capacity of a
given beam by maximizing the absolute values of the prestresses at the section having the
greatest superimposed-load stresses. The three procedures that follow, when taken as a
unit, illustrate the manner in which the allowable prestresses may be increased numerical-
ly by taking advantage of the beam-weight stresses, which are opposite in character to the
prestresses. The next procedure will also demonstrate that when a beam is not in balanced
design, there is a range of values of F 1 that will enable the member to carry this maximum
allowable load. In summary, the objective is to maximize the capacity of a given beam
and to provide the minimum prestressing force associated with this capacity.DETERMINATION OF CAPACITY
AND PRESTRESSING FORCE FOR A BEAM
WITH STRAIGHT TENDONS
An 8 x 10 in (203.2 x 254 mm) rectangular beam, simply supported on a 20-ft (6.1-m)
span, is to be prestressed by means of straight tendons. The allowable stresses are: initial,
- 2400 and - 190 lb/in^2 (+16,548 and -1310.1 kPa); final + 2250 and -425 lb/in^2
(+15,513.8 and - 2930.3 kPa). Evaluate the allowable unit superimposed load, the maxi-
mum and minimum prestressing force associated with this load, and the corresponding
eccentricities.
Calculation Procedure:
- Compute the beam properties
Here A = 80 in^2 (516.16 cm^2 ); S= 133 in^2 (858.1 cm^2 ); ww = 83 Ib/lin ft (1211.3 N/m).