**8**, 2, pp. 233-252, 1960

### Kształtowanie Belek Sprężonych przez Wyrównywanie Skrajnych Naprężne

In the first case, the beam is subjected to the action of its load and the prestressing force. In the second state, the beam also carries a useful load.

The shape of the beam is determined from the condition of equal extreme values of the normal stresses along the span of the beam. These conditions, which are four in general, are not always all needed for the determination of the shape of the beam. This depends to a considerable degree on the ratio

of own weight to the useful load; it frequently suffices to use one or two conditions. In Sec. 8, it is shown that for beams of considerable span, where the dominating role is played by shape in the unloaded state. own weight, it is reasonable to determine the several problems are solved, showing the determination of the shape of the beams in cases where functions sought for are the beam. height a(x) and the ordinate of the prestressing force; the beam height a(x), with constant position of the prestressing force (Sec. 5); the variable width of the beam b(3e), the ordinate of the force constituting a given function y(x) (Sec. 6); the beam width b(x) and the ordinate of the prestressing force y(x), (Sec. 7). In addition, in Sec. 7, the convergence of the two methods is shown by equalizing the extreme values of the normal stresses and directly, from the condition of minimum potential of elastic strain for a constant volume of the material. This agreement is sometimes less distinct in view of additional limitations on the form following from the conditions imposed usually by practice. It is not maintained that the method of equalizing the stresses is the only possible for the determation of the shape of prestressed beams. A description is given only of the application of this method and its relation to question of verification of the strength.

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#### References

Z. WASIUTYŃSKI, O kształtowaniu wytrzymałościowym, Akademia Nauk Technicznych, Warszawa 1939.

J. R. ROBINSON, Cours de béton précontraint, Dunod, Paris 1959.

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