Analysis of the Single Cable Segment

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Abstract:

An extensive analytical treatment of the static characteristics of the single cable segment is presented. The fundamental catenary description is developed and generalized to formulate equations which relate the forces in a segment to its anchor geometry, length, and weight per unit length. The variety of associated mathematical problems are stated precisely and categorized. Three categories are identified. Category I includes six problems for which direct solutions are possible because the important catenary parameter is known. Category II includes three other problems for which direct solutions are available. Those problems which retain the transcendental nature of the catenary relationships and for which direct solutions are not available are included in Category III. There are seven such problems, and the application of three iterative algorithms to their solution is discussed. The Newton and the secant methods are two common approaches which are applied in the paper. A third, nonstandard method, sometimes identified as the "Rigid Link" approach, is discussed also. Many details pertaining to convergence of these methods are brought out in the discussion. The paper's purpose is to expand the coverage of cable statics analysis to provide a broader foundation for investigations of the more complex, multisegmented skyline configurations. Forest Sci. 23:238-252.

Keywords: Catenary; mathematical analysis

Document Type: Journal Article

Affiliations: Mechanical Engineer, Forest Engineering Systems, Pacific Northwest Forest and Range Experiment Station, USDA, Forest Service, Portland, Oregon 97208

Publication date: June 1, 1977

More about this publication?
  • Forest Science is a peer-reviewed journal publishing fundamental and applied research that explores all aspects of natural and social sciences as they apply to the function and management of the forested ecosystems of the world. Topics include silviculture, forest management, biometrics, economics, entomology & pathology, fire & fuels management, forest ecology, genetics & tree improvement, geospatial technologies, harvesting & utilization, landscape ecology, operations research, forest policy, physiology, recreation, social sciences, soils & hydrology, and wildlife management.
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