On stresses in in a rope when hoisting a load
Abstract
The strength calculation of a rope is in practice somewhat conditional. Specifically, one proceeds from the ratio of the breaking load to the static load, which is called the safety factor and whose minimum value is established by safety regulations for hoisting. Having set this factor and determined the number and diameter of wires with its help, a verification of the safety factor is then carried out, partly taking into account the actual stresses in the rope. However, since the latter are not fully accounted for, such verification cannot provide a sufficiently clear picture of the actual value of the safety factor. In the present study, we confine ourselves to small lifting heights, reducing the problem to the integration of an ordinary third-order differential equation.
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References
- On dynamic stresses in hoisting ropes, supplement to No. 12 of Gornyi zhurnal, 1929, (in Russian)
- A. P. German, Calculation of ropes, Shakhtnyi pod'yem, 1932, p.262, § 52 (in Russian)
- A. N. Dinnik. Collection "Prikladnaya matematika i mekhanika", 1933, v. 2. p. 335, § 7. (in Russian)
- N. Nielsen, Handbuch der Theorie der Cylinderfunctionen, 1904, p. 28.
- A. Sh. Lokshin. Mathematische Annalen, 1899, Vol. 52, pp. 271, 340.
- Goursat, Course d’Analyse Mathématique, 1929, t. II, No. 383.