Spanned Cable Sag and Tension

ScopeH = w L^2 / (8 d), the support tension H sqrt(1 + (4d/L)^2), and the developed length. A 100 ft span at 1 lb/ft sagging 2.5 ft runs 500 lb; pull it to a 0.5 ft sag and the tension jumps to 2,500 lb - five times the tension for the same load, because tension is inversely proportional to the sag. Shallow parabola (sag under ~1/10 span), uniform load, level supports; a concentrated load is the sling-angle case. A planning screen; the rope WLL, the anchors, and the head rigger govern.

Formula or tableH = (w L^2/8 + P L/4)/d; V = w L/2 + P/2; T_support = sqrt(H^2 + V^2) (= H sqrt(1 + (4 d/L)^2) with P = 0); slack = [w^2 (L/2)^3/3 + w P (L/2)^2/2 + P^2 (L/2)/4]/H^2 (= 8 d^2/(3 L) with P = 0); length = L + slack; sag_ratio = d / L.

Source and editionShallow-cable parabola statics (by name) with ASME B30.9 / Wire Rope Users Manual rigging practice; first-principles, no edition cycle.

Free accessThe shallow-cable parabola (H = w L^2 / 8d) is a public statics result; ASME B30.9 governs sling and rigging practice. An ESTIMATE only; the certified rope WLL and the head rigger govern.

What governsEstimate. Head rigger and manufacturer working-load-limit charts govern. Inspect every piece of hardware before the show.

API field namesspan_ft, load_lb_per_ft, sag_ft, horizontal_tension_lb, support_tension_lb, cable_length_ft, sag_ratio

• Shallow parabola valid where the sag is under about a tenth of the span; a deep sag trends toward the catenarycable statics
• Uniform load the rope self-weight plus any evenly distributed load; a concentrated load is the sling-angle casecable statics
• Level supports the two supports are taken at the same heightcable statics
• Estimate only the certified rope WLL, the anchor capacity, and the head rigger govern the actual pickASME B30.9