Slings and hitches
Sling leg tension from load and leg angle
- where
- tension in each leg (t)
- load including rigging below the sling (t)
- number of legs taking the load
- leg angle to the vertical (°)
- leg tension as a force (kN)
Explain this equation
Works out how hard each sling leg is pulling when the legs lean out from the hook. Use it to check a leg, a shackle or a lifting lug against its WLL before a multi-leg lift.
W is everything hanging below the sling. n is how many legs genuinely share it. β is the angle each leg makes with the vertical, which is half the angle between opposite legs. T is the result in tonnes; T_kN is the same pull as a force, using 9.81 kN per tonne.
Each leg must hold up its share of the weight vertically. A leaning leg only supplies cos β of its pull upwards, so the total pull has to rise by 1/cos β to give the same lift. That is why the tension grows quickly as the legs spread.
Sense check: two legs at 30° on a 4 t load pull about 2.3 t each. At 45° the factor is 1.41, and at 60° it is 2, so each leg of a two-leg sling then carries the whole load.
Watch out: for a four-leg sling enter n = 3, because uneven leg lengths usually leave one leg slack. An off-centre centre of gravity loads the steeper leg more than this shows.
Works out the pull in each sling leg when legs are inclined. The load is shared between the legs, but each leg has to pull harder the further it leans from the vertical.
Enter your values to see the result.
Good to know
β is measured from the vertical (half the included angle between opposite legs). At 30° each leg carries 1.155 × its share; at 45°, 1.414 ×; at 60°, 2 ×. For a four-leg sling, enter n = 3 unless you are certain all four legs share equally: the LEEA uniform load method assumes only three legs carry the load because of uneven leg lengths and load stiffness. Enter the load in tonnes; 1 t = 9.81 kN.
Common mistake
Using the included angle (the angle between the legs) instead of the angle to the vertical, which doubles β and badly overstates the tension; or assuming all four legs of a four-leg sling share the load.
Limits
Assumes legs of equal length, symmetrically placed in plan, with the hook directly over the centre of gravity. Unequal legs or an offset CoG put more load in the steeper (more vertical) leg. Static load only; no dynamic allowance. For planning only: this does not replace a lift plan prepared by a competent person under LOLER 1998 (reg. 8) and BS 7121, and the manufacturer’s WLL markings, load charts and data always govern over this result.
Sources
- LEEA COPSULE Ed. 10, 1.A5.4 Principles for the selection of slings (uniform load method: 2-leg 0–45° ×1.4, 45–60° ×1.0; 3- and 4-leg 0–45° ×2.1, 45–60° ×1.5; 4-leg rated as 3-leg; trigonometric method 2·cos β, 3·cos β, 4·cos β)
- LEEA COPSULE Ed. 10, 14.5.2 Chain slings (BS EN 818-4), method of use: choke hitch ×0.8 of the marked SWL, basket hitch 0–45°, legs equally disposed
- The Lifting Operations and Lifting Equipment Regulations 1998 (SI 1998/2307), reg. 8: every lifting operation properly planned by a competent person, appropriately supervised and carried out safely
- HSE L113 Safe use of lifting equipment. Lifting Operations and Lifting Equipment Regulations 1998. Approved Code of Practice and guidance
Results are calculations from the published methods and figures shown, and depend on the data you enter. For planning and checking only. Scaffolds must be erected to NASC TG20 or a bespoke design by competent persons, and lifting operations planned under LOLER by a competent person. Never rely on these results instead of a design, a lift plan or manufacturer ratings.