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Bending of helically twisted cables
under variable bending stiffness
due to internal friction, tensile
force and cable curvature

Konstantin O. Papailiou

DISS

ETH

No. 11057

DISS

ETH

No. 11057

Bending of helically twisted cables
under variable bending stiffness
due to internal friction, tensile
force and cable curvature
DISSERTATION
for obtaining the title ofDOKTOR DER TECHNISCHEN WISSENSCHAFTEN
[DOCTOR OF TECHNICAL SCIENCES]
of the
EIDGENÖSSISCHE TECHNISCHE HOCHSCHULE ZURICH
presented by

Konstantin O. Papailiou
Dipl. El.-Ing. TH Braunschweig
Dipl. Bau-Ing. Universität Stuttgart
born on 3.7.1946
in Athens, Greece

Accepted on application by:

Prof. Dr. H.-R. Meyer-Piening, Supervisor
Prof. Dr. G. Oplatka, Co-Supervisor
Dr. V. Esslinger,Co-Supervisor
1995

For my father

Summary

The bending of helically twisted cable is a severe loading case for these important structural
components. During bending of such cables, slippage takes place between the individual wires of the
cable, which is greatly influenced by the frictional forces acting at the inter-wire contacts. Because of
this slippage, the cross-sections of thecable do not necessarily remain plane, which has to be
considered in the formulation of the bending stiffness of the cable.
The main subject of this work is to develop, based on generally accepted principles for bending of
cables, an adequate model to quantify the bending behaviour of multilayered helically twisted cables.
This model leads, under consideration of internal friction, to avariable effective bending stiffness which
depends on the cable curvature and the tensile load acting on the cable. With this information it is now
possible to calculate the deflection, curvature and the various components of stress in the wires of the
cable analytically. With the newly developed “cable scanner”, the catenary and curvature of the cable
axis can be determined by scanning the cablesurface. The agreement between theory and
measurement is quite good.
The model is extended to cover also ACSR (Aluminium conductor, steel reinforced), a conductor which
is widely used in overhead transmission lines, and is validated through corresponding measurements.
An important application of this work is the calculation of dynamic bending stresses in the individual
wires of suchconductors, under wind induced (aeolian) vibrations. These calculations consider the
ordinary alternating bending stresses plus the secondary tensile stresses (“zusatz” stresses) caused by
interlayer friction between wires, which together constitute the longitudinal fatigue stress. The theory
resolves a known discrepancy between measured stresses and stresses predicted by simpler
conductor models inuse today, which assume a constant bending stiffness. It also settles the long
outstanding uncertainty on the proper choice of effective bending stiffness for vibrating conductors. This
opens up a new way of determining the stress limits for such conductors under vibrating conditions.

Zusammenfassung

Die Seilbiegung stellt einen wichtigen Betriebszustand von Spiralseilen dar. Während desBiegevorganges verschieben sich die Drähte des Seiles gegenseitig, wobei die Reibung zwischen den
einzelnen Drähten eine entscheidende Rolle spielt. Durch die Biegeverformung bleiben auch die
Querschnitte für das gesamte Seil nicht notwendigerweise eben. Dies muss in der Formulierung des
Ansatzes für die Biegesteifigkeit des Seiles berücksichtigt werden.
Unter Beachtung von allgemeinanerkannten Grundsätzen für die Seilbiegung, wird im Rahmen dieser
Arbeit ein Modell für mehrlagige Spiralseile vorgestellt, dass auf einer, durch die innere Reibung
veränderlichen und von der Seilkrümmung und von der Seilzugkraft abhängigen, effektiven
Biegesteifigkeit basiert. Damit werden die Seillinie, die Seilkrümmung und die verschiedenen
Komponenten der in den einzelnen Drähten des Seiles...
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