The effect of shearing stress on the span calculations of a suspended cable

Abstract

The paper presents the complete equation of a suspended cable, taking into account its density, elasticity and rigidity, and determines the extent to which the effect of shearing stress should be considered for practical span calculations. The criterion of the importance of flexural rigidity can be written in the form e=100 × 2γ=100Ed 2 D 3 /ρ(S/2) 6 per cent where γ is the percentage error caused by neglecting flexural rigidity in calculating the span from the usual formulae, and γ=w 2 0 EI 0 /T 3 0 . Here d is the diameter of the wire, ρ the volume density, ω 0 the linear density, I 0 the moment of inertia of the section, all in the unstretched condition, E Young's modulus, T0 the lowest tension, D the deflection and S the span. The ordinary catenary equation is sufficiently accurate for most practical purposes, but when λ <2γ and with the lower tension, where λ=T 0 /EQ and Q is the cross-sectional area, the effect of flexural rigidity is more important than that of elasticity.