Engineering Transactions,
1, -, pp. 5-69, 1953
Dźwigary Załamane W Planie
This paper is based on the six treatises by the same author which are
listed in the introduction. Beams having a horizontal projection in the shape of a broken line, will be referred to in this paper, as broken line beams. A broken line beam is defined as beam whose axis represents, in non-deformed state, a broken line in the plane perpendicular to the direction of active forces.
An example of such a beams is shown in perspective in Fig. 1, and in horizontal projection in Fig. 2. It is subjected not only to bending but also to torsion, which is its main feature. Fig. 5 shows a broken line cantilever beam. Shearing forces as well as bending and twisting moments are expressed by Eas. (1)-(9). The deformations of various types of broken line beams can be reduced to those of ordinary cantilever beams, each point undergoing rotations, represented vectorially in Fig. 14, about the following axes: […].
For these angles of rotation the formulae of recurrence (16) - (25) are deduced. Thus the deflection at each point is represented by Eq. (13). The theory of finite differences provides a good calculation method for broken line beams. This problem is discussed in chapter III. Chapter IV deals with statically indeterminate broken line girders
represented by «balcony» and continuous girders, Figs. 33 and 37 respectively. In chapter V the equation of five successive twisting moments Di, (194), for a continuous girder is deduced. This facilitates the calculation of a continuous broken line girder in a similar manner, as the equation of three moments facilitates the calculation of a straight continuous beam.
This is a difference equation of the forth order. In chapter VI the author shows, that the calculation of beams curved in the horizontal plane can be replaced by one pertaining to broken line beams, the axes of which are inscribed or circumscribed or representing a broken line, part of which is inscribed and the rest circumscribed.
The considerations of each chapter are illustrated by numerous
examples.
listed in the introduction. Beams having a horizontal projection in the shape of a broken line, will be referred to in this paper, as broken line beams. A broken line beam is defined as beam whose axis represents, in non-deformed state, a broken line in the plane perpendicular to the direction of active forces.
An example of such a beams is shown in perspective in Fig. 1, and in horizontal projection in Fig. 2. It is subjected not only to bending but also to torsion, which is its main feature. Fig. 5 shows a broken line cantilever beam. Shearing forces as well as bending and twisting moments are expressed by Eas. (1)-(9). The deformations of various types of broken line beams can be reduced to those of ordinary cantilever beams, each point undergoing rotations, represented vectorially in Fig. 14, about the following axes: […].
For these angles of rotation the formulae of recurrence (16) - (25) are deduced. Thus the deflection at each point is represented by Eq. (13). The theory of finite differences provides a good calculation method for broken line beams. This problem is discussed in chapter III. Chapter IV deals with statically indeterminate broken line girders
represented by «balcony» and continuous girders, Figs. 33 and 37 respectively. In chapter V the equation of five successive twisting moments Di, (194), for a continuous girder is deduced. This facilitates the calculation of a continuous broken line girder in a similar manner, as the equation of three moments facilitates the calculation of a straight continuous beam.
This is a difference equation of the forth order. In chapter VI the author shows, that the calculation of beams curved in the horizontal plane can be replaced by one pertaining to broken line beams, the axes of which are inscribed or circumscribed or representing a broken line, part of which is inscribed and the rest circumscribed.
The considerations of each chapter are illustrated by numerous
examples.
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