Cable spring effect and its longitudinal restraint stiffness on towers

On cable-stayed or suspension bridges, the cable spring concept is used to describe the influence of the main cable on the deflection of the towers. A formula for the longitudinal constraint stiffness of a cable spring was derived based on the catenary equation and two examples (construction stage and completion stage) were assessed introduced for verification. The results showed that the proposed catenary stiffness formula provides satisfactory accuracy. The stiffness value is related to the horizontal and vertical components at one end of the main cable and the weight of the cable when the unstressed length is an invariant constant. Furthermore, the stiffness value is closely related to the sag–span ratio of one span. Thus, in a two-tower suspension bridge, the longitudinal restraint stiffness of a side-span cable to the tower is much larger than the corresponding stiffness of the mid-span. In a three-tower suspension bridge, with two main spans and two side-spans, the cable spring effect plays an important role in the total stiffness of the mid-tower. The developed equations can be used for preliminary estimates of longitudinal displacement.