Analytical structural reliability analysis of a suspended cable

• Analytical solutions to the behaviour of a suspended cable are presented.
• Nonlinear performance functions are stated.
• Analytical expressions for the gradients of the performance function are developed.
• FOSM solutions are verified for a number of examples.
• Load cases including, wind, snow, and temperature variation are included.

Suspended cables, including transmission lines, suspension bridge cables, and edge cables of roof structures, feature in high profile and large span projects for architectural reasons, for their functional efficiency, and for ease of construction, particularly over large spans. A suspended cable predominantly reacts external loads by means of axial tension, and is, therefore, able to make full use of the material strength. Because of the slenderness of the suspended cable, the structural response is nonlinear, even if the material property is within the elastic range. From a mechanics perspective, therefore, these types of structure exhibit high levels of geometric non-linearity. For this reason, the nonlinear relationships between tension force, normal displacement, and the external loads need to be considered. In aiming to determine the structural safety of a suspended cable, and to understand which uncertainty features have the greatest influence, these relationships are written within a probabilistic framework.This article briefly sets the analysis of suspended cables within the context of geometrically nonlinear elastic structures and corresponding finite element analysis methodologies. Analytical solutions to the tension and normal displacement of a suspended cable subjected to external loading are presented. Nonlinear performance functions, in the form of either the cable tension or normal displacement are stated. Analytical expressions for the required gradients of the performance function of a suspended cable with respect to the basic variables under static loads are developed. The structural reliability of a suspended cable is studied using a first-order reliability method (FOSM) and verified by comparison with Monte Carlo simulation (MCS) and Monte Carlo simulation based optimization principles (MCOP) for a number of examples. Load cases including, wind, snow, and temperature variation are included.