Kształtowanie Wytrzymałościowe Belki Wspornikowej - Brandt, A.; Ignaczak, J. (Engineering Transactions, 1958)
The object of this paper is the determination of the height of a cantilever beam subjected to its own weight and a useful load. The paper is a generalization to prestressed structures of the problem stated by Galileo and his successons. The aim of the present consideration is to obtain the form of a beam having minimum elastic potential for the same material volume, which is connected with obtaining uniform extremum normal stresses along the beam.In the first case, the form of the beam is determined for a straight cable parallel to the upper surface of the beam, the beam height being variable along the beam span.The second case concerns a beam with two unknown functions determining the beam height and the line of the internal force.The method described enables us to obtain. considerable reduction of material (concrete and cable) and bending moments due to the weight of the beam itself. These economies are important for large-span beams and high loads. The solutions obtained are in general in agreement with the intuitive choice of the form of a cantilever beam and that of cable axis.The accurate solution in the form of an elliptic integral andapproximate methods enabling easy determination of the functions required are described.