Engineering Transactions, 6, 1, pp. 169-180, 1958

Kształtowanie Wytrzymałościowe Belki Wspornikowej

A. Brandt
Instytut Podstawowych Problemów Techniki PAN

J. Ignaczak
Instytut Podstawowych Problemów Techniki PAN

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 and
approximate methods enabling easy determination of the functions required are described.

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Copyright © Polish Academy of Sciences & Institute of Fundamental Technological Research (IPPT PAN).


Galileo Galilei, Discorsi e dimonstrazioni matematiche interno a due scienze attenenti alla mecanica et i movimenti locali, 1638.

F. Blondel, Epistula ad P. Wurtius..., Data Parisiis 1661.

P. S. Girard, Traité analitique de la résistance des solides et des solides, d'égale résistance, 1798.

T. Young, Course of Lectures on Natural Philisophy, 1807.

W. S wida, Über die Form eines Pfeiters gleicher Festigkeit bei gleich- zeitiger Druck-und Biegebeanspruchung, Zeitschr. Ang. Math. Mech., 1934.

K. Ludwig, Über Früger mit Eigengewicht und gleichem Widerstand gegen Biegung, ZAMM, 1936.

Z. Wasiutyński, O ksztattowaniu wytrzymalosciowym, cz. I, II, III, Warszawa 1939.

Z. Wasiutyński, Podstawowe wiadomości o kształtowaniu wytrzymałościowym, Arch. Inzyn. Lad. 1 (1956).

Z. Wasiutyński, O formach budowlanych i ich kształtowaniu, Podst. Probl. Współcz. Techn., t. 1, PWN, Warszawa 1956.

A. Brandt i Z. Wasiutyński, Kształtowanie wytrzymałościowe płyt z betonu sprężonego, Inzyn. Bud. 2 (1957).

A. Brandt, Kształtowanie belek sprężonych, Inzyn. Bud. 1 (1958).