Parameters
Bridge Type
Span L500 m
Sag f50.0 m
Deck load w30.0 kN/m
Pylon height H_p120 m
Side Span
—
Horizontal tension H [kN]
—
Max. cable tension [kN]
—
Sag ratio f/L
—
Cable arc length [m]
—
Tower top angle θ [°]
—
Hanger force (mid) [kN]
—
Vertical reaction V [kN]
—
Total deck load W [kN]
Bridge Profile
Parabolic Cable Theory
Cable shape under uniform deck load $w$ [kN/m]:
$$y(x) = \frac{w}{2H}x^2, \quad -\frac{L}{2} \leq x \leq \frac{L}{2}$$Horizontal tension: $H = \dfrac{wL^2}{8f}$, Maximum cable tension: $T_{max} = \dfrac{H}{\cos\theta_{max}}$, $\tan\theta_{max} = \dfrac{4f}{L}$
Parabola arc length: $S \approx L\left[1+\dfrac{8}{3}\left(\dfrac{f}{L}\right)^2 - \dfrac{32}{5}\left(\dfrac{f}{L}\right)^4 + \cdots\right]$
The catenary–parabola difference is within a few % when $f/L \ll 1$, so the parabolic approximation is sufficiently accurate.
CAE Applications: Initial geometry setup for cable finite elements (cable/truss element) in Ansys Mechanical / LS-DYNA. Static equilibrium and natural frequency pre-check for suspension and cable-stayed bridges. Reference comparison with the Akashi Kaikyo Bridge (L = 1991 m) and Rainbow Bridge (L = 570 m).