Since an ideal tendon profile determination is a design problem, it should be noted that the designers have been using a graphical design method which was developed by Magnel  in late forties.
In this article, it is shown that the ideal tendon profile in the posttensioned beam could be determined by automated computer inspection of the Magnel diagrams, in the various cross sections without drawing any quadrilateral on paper.
Since at x = 0.5L, the eccentricity is e(0.5 L) = [e.sub.DM] and in the supports e(L) = e(0) = [e.sub.DC], and then an ideal parabolic tendon profile could be computed by
And for linear tendon profile similar to Figure 1, we have
Another ideal tendon profile can also be achieved, if the Magnel diagram would be drawn in many cross sections (n [much greater than] 3), across the span.
Using [([e.sub.i]).sub.D], which resulted in nine points, by which a symmetric curve is produced and the tendon profile is displayed in Figure 7 by the point line, one can see that the simple linear profile in Figures 1(a) and 5 and the optimal profile in Figure 7 are very close, and in fact the parabolic and linear shape tendons can be ideal ones, if we use the expressions in (21)-(23) in this paper.
In this article, the ideal tendon profile in the posttensioned beams is investigated by multiple automatic examinations of the Magnel design diagrams.
Caption: Figure 7: Ideal tendon profile based on the Magnel diagram of 9 cross sections each L/8 apart.
First, parabolic and linear tendon profiles will be derived by using three cross sections.
The beam cross-section is shown in Figure 1, and the designed strength grade of concrete was C40; the prestressing steel was [[phi].sup.s] 15 steel strand, the tensile strength of which was [f.sub.ptk] = 1860 N/[mm.sup.2], the inner diameter of corrugated duct was 50 mm, and initial tensile stress [[sigma].sub.con] = 0.75/ptk; bonded tendons were used; the material grade of H-steel (H x B x [t.sub.1] x [t.sub.2] = 100 mm x 100 mm x 6 mm x 8 mm) was Q235, and H-steel was symmetrically arranged in beam cross-section; stirrups are [[phi]12@100 and material was HPB235; the tendon profile
is shown in Figure 2.