A suspension bridge carries deck load through suspenders into main cables, towers and anchorages. The calculator below uses the standard ideal parabolic-cable relation for a symmetric span under a uniform load per unit horizontal length. It is preliminary statics, not a bridge design or cable-capacity check.
Suspension Bridge Interactive Calculator
Vary main span, uniform load per unit horizontal length and mid-span sag. Results use an ideal symmetric, perfectly flexible parabolic cable; they exclude cable self-weight, side spans, stiffness, live-load patterning, dynamics and all capacity checks.
Equation Used
- The main span is symmetric and the cable is perfectly flexible.
- The entered load is uniform per unit horizontal span and assigned to one modeled cable.
- Cable self-weight, side spans, deck stiffness, hanger elasticity and geometric nonlinearity are omitted.
- No member strength, fatigue, aerodynamics, foundation, anchorage, construction-stage or code compliance check is performed.
Idealized Suspension-bridge Load Path
FHWA's suspension-bridge cable primer identifies main cables, suspenders, towers, anchorages, side spans, the main span, and the stiffening truss and deck as the principal elements. Deck load reaches the main cable through suspenders; the cable carries tension, towers take vertical reaction, and anchorages resist cable force.
This calculator isolates one symmetric main span. Under uniform load per unit horizontal length, the ideal cable profile is parabolic and its horizontal tension component is constant.
Using the Animation and Calculator
The model is useful for checking the first-order relationship among span, load, sag and ideal cable-force components, and for seeing why smaller sag raises the horizontal component.
It is not suitable for design approval. Real suspension bridges require code-defined load combinations, nonlinear structural analysis, cable and deck self-weight, side-span interaction, hanger and deck stiffness, live-load patterning, temperature, wind and seismic response, fatigue, aerodynamics, foundations, anchorages, construction stages, deterioration and inspection.
Ideal Parabolic-cable Relations
For uniform load w per unit horizontal length, span L and sag f:
The main-span vertical contribution at each cable end is V = wL/2; this is not the total tower reaction including the side span. The ideal saddle resultant is T = square root of (H squared + V squared). The displayed sag ratio is L/f, written as 1:n.
FHWA's long-span bridge report gives a sag relation with an inclination factor cos(theta). For level cable ends, theta = 0, giving f = wL squared /(8H).
Worked Example: Entered Uniform-load Scenario
For L = 1000 m, w = 100 kN/m and f = 100 m, H = 125000 kN. The main-span vertical contribution at one cable end is 50000 kN, and the ideal saddle resultant is 134629 kN. The span-to-sag ratio is 10, displayed as 1:10.
These values are ideal force components for one entered load scenario. They do not specify cable area, allowable stress, tower or anchorage capacity, or a safe bridge.
What the Calculator Includes
- Calculated: ideal symmetric parabolic-cable force components and L/f.
- Strong sensitivity: H varies with L squared and inversely with f for fixed w.
- Not calculated: material or member capacity, deck response, side spans, foundations, anchorages, construction sequence, temperature, fatigue, corrosion, wind, flutter, seismic action or code compliance.
Frequently Asked Questions
Why is the modeled cable parabolic?
A perfectly flexible cable under uniform load per unit horizontal projection has an ideal parabolic profile. Cable self-weight and other effects alter a real bridge profile.
Is w the total load on the whole bridge?
No. It is the load per horizontal length assigned to the single modeled cable. Load sharing between real cables must be established separately.
What does H represent?
H is the constant horizontal component of ideal main-cable tension within this symmetric model.
What does the tower vertical result represent?
V = wL/2 is the main-span vertical contribution at one cable end from the assigned uniform load. It excludes side-span forces and is not the total tower reaction.
Is the saddle resultant a cable-capacity result?
No. T combines H and V at the ideal saddle. It does not compare stress with cable strength or account for deterioration.
Can this calculator design a suspension bridge?
No. It omits the many structural, geotechnical, aerodynamic, durability, construction and code checks required for design.
References
- Federal Highway Administration, Primer for the Inspection and Strength Evaluation of Suspension Bridge Cables, FHWA-IF-11-045: bridge components, cable load path and inspection context.
- Federal Highway Administration, Redundancy in Long-span Bridges for Risk Mitigation in a Multi-hazard Environment: ideal cable sag relation f = wL squared /(8H).
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