For a catenary segment with nonlinear axial stiffness, as a standard input data format the nonlinear axial stiffness property is defined in the form of

(9–31)

in the range .

From the above definition, the tension on the cable can be expressed as

(9–32)

Numerically, the series form of the strain function with respect to the tension can be derived from Equation 9–32:

(9–33)

in the range , where .

An intermediate tension is introduced here, which is

(9–34)

where

An equivalent nonlinear tension is also introduced:

(9–35)

where

in which

In addition, the equivalent tension is denoted as

(9–36)

where

Finally, the bottom left-hand positions and extension of the nonlinear axial stiffness catenary line segment can be expressed as

(9–37)

where , and the equivalent nonlinear stiffness is defined as

(9–38)