Tangent geometric stiffness of inclined cables under self-weight

An exact formula is derived for the tangent geometric stiffness of inclined cables under self-weight. Comparisons are made with the well-known approximate formula by Ernst. It is found that the accuracy of Ernst's formula deteriorates with increasing cable slackness and inclination. The error can be significant for certain configurations of the cable that are commonly used in such structures as cable-stayed bridges, guyed towers, electric transmission lines, and conductor cables connecting electrical substation equipment. An accurate and simple approximate formula is developed, which is applicable to a wide range of parameter values.