Cable & Span Parameters
Span Length L
200 m
Unit Weight w
15.0 N/m
ACSR 100 mm²: ~400 N/m / Telephone: 5–20 N/m
Horizontal Tension H
5000 N
Support Height Diff Δh
0 m
Additional Loading
Ice Thickness tice
0 mm
Cable Diameter Dc
20 mm
Wind Pressure pw
0 Pa
30 m/s wind ≈ 540 Pa
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Max Sag [m]
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Sag Ratio [%]
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Max Support Tension [N]
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Arc Length [m]
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Equiv. Load [N/m]
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Catenary Const. a [m]
Cable Profile — Catenary vs Parabolic Approximation
Catenary Equations
Catenary constant $a = H/w$, maximum sag:
$$y(x) = a\left[\cosh\!\left(\frac{x}{a}\right) - 1\right]$$ $$d_{max} = a\left[\cosh\!\left(\frac{L}{2a}\right) - 1\right]$$Parabolic approx. ($d \ll L$): $d \approx \dfrac{wL^2}{8H}$
Support tension: $T = \sqrt{H^2 + (wL/2)^2}$
Arc length approx.: $S \approx L + \dfrac{8d^2}{3L}$
CAE Note: FEM analysis of overhead lines uses cable or link elements that inherently handle large-deformation (geometric nonlinearity). The initial catenary shape must be set correctly as the pre-stressed configuration before applying additional loads. Suspension bridge analysis requires nonlinear static analysis to find cable geometry before dynamic modal analysis.
Sag & Tension by Load Case
Load Combination: Ice adds vertical load: w_ice = ρ_ice × π × t × (D_c + t) × g. Wind pressure gives horizontal load: w_wind = p_w × (D_c + 2t). Resultant: w_total = √(w_v² + w_h²) treated as equivalent vertical load.