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:
- 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.) - Evaluate the prestressing force
For a given ratio of yjy^ 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. - 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 offbf and/, 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. - 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 Sb and St
differ, the area should be disposed unsymmetrically about middepth to secure these val-
ues. - 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 reason,
long-span members are generally constructed as T sections. The extensive flange area el-
evates the centroidal axis, thus making it possible to secure a reasonably large eccentrici-
ty.
- 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
The beam in Fig. 36 has the following properties: A = 850 in
2
(5484.2 cm
2
); Sb = 11,400
in
3
(186,846.0 cm
3
); St = 14,400 in
3
(236,016.0 cm
3
). A prestressing force of 630 kips
(2802.2 kN) is applied with an eccentricity of 24 in (609.6 mm) at the section under in-