Page 272 - Handbook of Civil Engineering Calculations, Second Edition

PRESTRESSED CONCRETE 2.57

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 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 i 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 10 in. (203.2 254 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/sq.in. ( 16,548 and 1310.1 kPa); final, 2250 and 425 lb/sq.in.
( 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:
1. Compute the beam properties
2
Here A 80 sq.in. (516.16 cm ); S 133 cu in (2179.9 cu cm); w w 83 lb/lin ft (1211.3
N/m).