Suspension Bridge 2D — Parabolic Cable Sag & Tension

This 2D side-view companion to the 3D suspension bridge model draws the main cable, towers, deck and hangers in profile so the parabolic cable shape and the way tension builds up toward the towers are easy to read at a glance. Drag the traffic load, span, design sag ratio, hanger count or cable stiffness and the bridge redraws using the real elastic-cable equilibrium: the parabola y=4fx(L−x)/L² for cable shape, H=wL²/(8f) for horizontal tension, and T(x)=√(H²+w²(L/2−x)²) for the tension distribution that peaks at the towers. Because the cable's unstretched length is fixed, adding traffic load doesn't just raise tension — it forces the cable to stretch and sag lower to reach a new equilibrium, exactly as a real suspension bridge cable does.