Magnel Diagram Prestressed Concrete
11.4.5 Design of tendon profiles
Having obtained a value of prestress force which will permit all stress conditions to be satisfied at the critical section, it is necessary to determine the eccentricity at which this force must be provided, not only at the critical section but also throughout the length of the member.
At any section along the member, e is the only unknown term in the four equations 11.9 to 11.12 and these will yield two upper and two lower limits which must all be simultaneously satisfied. This requirement must be met at all sections throughout the member and will reflect both variations of moment, prestress force and section properties along the member.
The design expressions can be rewritten as:
At transfer e <
At service e >
Zb /minZh
Equations 11.2811.31 can be evaluated at any section to determine the range of eccentricities within which the resultant force Pt} must lie. The moments Mnm and Mmm are those relating to the section being considered.
For a member of constant crosssection, if minor changes in prestress force along the length are neglected, the terms in brackets in the above expressions are constant. Therefore the zone within which the centroid must lie is governed by the shape of the bending moment envelopes, as shown in ligure 11.14.
In the case of uniform loading the bending moment envelopes are parabolic, hence the usual practice is to provide parabolic tendon profiles if a straight profile will not fit within the zone. At the critical section, the zone is generally narrow and reduces to zero if the value of the prestress force is taken as the minimum value from the Magnel diagram. At sections away from the critical section, the zone becomes increasingly greater than the minimum required.
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