Tendon Control of Cable Structures

Introduction

Cable structures are used extensively in civil engineering: suspended bridges, cable-stayed bridges, guyed towers, roofs in large public buildings and stadiums. The main span of current cable-stayed bridges (Fig.15.1) can reach more than $850 \ m$ (e.g. Normandy bridge, near Le Havre, in France). These structures are very flexible, because the strength of high performance materials increases faster than their stiffness; as a result, they become more sensitive to wind and traffic induced vibrations. Large bridges are also sensitive to flutter which, in most cases, is associated with the aeroelastic damping coefficient in torsion becoming negative above a critical velocity (Scanlan, 1974). The situation can be improved either by changing the aerodynamic shape of the deck, or by increasing the stiffness and damping in the system; the difficulty in active damping of cable structures lies in the strongly nonlinear behavior of the cables, particularly when the gravity loads introduce some sag (typical sag to length ratio is 0.5% for a cable-stayed bridge). The structure and the cables interact with linear terms (at the natural frequency of the cable ω _i ) and quadratic terms resulting from stretching (at 2 ω _i ); the latter may produce parametric resonance if some tuning conditions are satisfied (parametric excitation has indeed been identified as the source of vibration in several existing cable-stayed bridges).