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 tendons, 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 incurred in deflecting the tendons.)

2. Evaluate the prestressing force For a given ratio of yj/ye 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 independent 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 minimized by setting the critical values offbf and/, equal to their respective allowable values.

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 Sb and St 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 reason, 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 capacity at allowable final stress and the capacity at incipient cracking. It is therefore imperative that every prestressed-concrete beam be subjected to an ultimate-strength analysis to ensure that the beam provides an adequate factor of safety.

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