Page 278 - Handbook of Civil Engineering Calculations, Second Edition

PRESTRESSED CONCRETE 2.63

PRESTRESSED-CONCRETE BEAM
DESIGN GUIDES

On the basis of the previous calculation procedures, what conclusions may be drawn that
will serve as guides in the design of prestressed-concrete beams?

Calculation Procedure:
1. Evaluate the results obtained with different forms of tendons
The capacity of a given member is increased by using deflected rather than straight ten-
dons, and the capacity is maximized by using parabolic tendons. (However, in the case of
a pretensioned beam, an economy analysis must also take into account the expense in-
curred in deflecting the tendons.)
2. Evaluate the prestressing force
For a given ratio of y b /y t , the prestressing force that is required to maximize the capacity
of a member is a function of the cross-sectional area and the allowable stresses. It is inde-
pendent of the form of the trajectory.
3. Determine the effect of section moduli
If the section moduli are in excess of the minimum required, the prestressing force is min-
imized by setting the critical values of f bf and f ti equal to their respective allowable values.
In this manner, points A and B in Fig. 34 are placed at their limiting positions to the left.
4. Determine the most economical short-span section
For a short-span member, an I section is most economical because it yields the required
section moduli with the minimum area. Moreover, since the required values of S b and S t
differ, the area should be disposed unsymmetrically about middepth to secure these
values.
5. Consider the calculated value of e
Since an increase in span causes a greater increase in the theoretical eccentricity than
in the depth, the calculated value of e is not attainable in a long-span member because
the centroid of the tendons would fall beyond the confines of the section. For this rea-
son, long-span members are generally constructed as T sections. The extensive flange
area elevates the centroidal axis, thus making it possible to secure a reasonably large
eccentricity.
6. Evaluate the effect of overload
A relatively small overload induces a disproportionately large increase in the tensile
stress in the beam and thus introduces the danger of cracking. Moreover, owing to the
presence of many variable quantities, there is not a set relationship between the beam ca-
pacity at allowable final stress and the capacity at incipient cracking. It is therefore imper-
ative that every prestressed-concrete beam be subjected to an ultimate-strength analysis to
ensure that the beam provides an adequate factor of safety.

KERN DISTANCES
2
The beam in Fig. 36 has the following properties: A 850 sq.in. (5484.2 cm ); S b
3
3
3
3
11,400 in (186,846.0 cm ); S t 14,400 in (236,016.0 cm ). A prestressing force of 630
kips (2802.2 kN) is applied with an eccentricity of 24 in. (609.6 mm) at the section under