Spanned Cable Minimum Sag for a Tension Limit

Scoped_min = w L^2 / (8 sqrt(T_allow^2 - (w L / 2)^2)). A 100 ft span at 1 lb/ft held to a 502 lb rope WLL needs at least 2.5 ft of sag; pull it tighter and the tension climbs past the limit, because tension is inversely proportional to the sag. The allowable must exceed the w L / 2 support vertical reaction, or no sag can carry the load. Enter the rope WLL or anchor capacity with the design factor applied. A planning screen; the WLL, the anchors, and the head rigger govern.

Formula or tabled_min = (w L^2/8 + P L/4) / sqrt(T_allow^2 - (w L/2 + P/2)^2), the inverse of spanline-sag-tension with an optional midspan point load P; with P = 0 it is w L^2 / (8 sqrt(T_allow^2 - (w L/2)^2)).

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, allowable_tension_lb, min_sag_ft, horizontal_tension_lb

• Support-tension limit the allowable limits the support (anchor) tension and must exceed the w L / 2 vertical reaction; below that no sag can carry the loadcable statics
• Shallow parabola valid where the resulting sag is under about a tenth of the span; a deep sag trends toward the catenarycable statics
• Uniform load, level supports the load is uniform along the horizontal span and the two supports are at the same heightcable statics
• Estimate only the certified rope WLL, the anchor capacity, and the head rigger govern the actual pickASME B30.9