How to Compute the Tension in Each Leg of a Bridle

Why this matters

Almost every bridle calculation that goes wrong goes wrong in the first line, not the last. The rigger divides the load weight by the number of legs, and everything downstream is arithmetic performed correctly on a wrong number. Weight divided by legs is true only when the hook sits over the centre of gravity, the legs are equal, and the load is flexible enough to let every leg take its share. A rigid steel frame on a four-leg bridle satisfies none of that, and the honest answer for the share can be twice what the division gave.

This procedure is a calculation sheet with twelve slots. It owns two things the rest of this group cites rather than re-derives: how many legs you are allowed to count, and how an off-centre centre of gravity re-bases the share before any angle correction touches it.

Nobody stands under the load or inside the arc it can swing to if a leg releases, and on a bridle that arc runs toward the surviving leg. All measuring below happens with the load on the ground and the slings hanging slack, so no hand is near a bight that has tension in it.

The sheet, slot by slot

Slot 1. Load weight and where it came from. A nameplate, a fabricator's drawing, a shipping document or a scale ticket. Not an estimate, not a guess from a similar unit. If none of those exist, the weight is unknown and that is the finding: stop and route it to the qualified person your employer designated, because there is no correction in this sheet that repairs a guessed weight. Adding margin to a guess makes you confident, not safe.

Slot 2. Centre of gravity and how you established it. Marked on the drawing, obvious by symmetry, or determined by a trial lift held a few inches clear with everyone outside the footprint. A load that tips on pick-up is telling you slot 2 was wrong.

Slot 3. How many legs you may count. On a two-leg bridle with the hook over the centre of gravity, count two. On a three- or four-leg bridle on a rigid load, count two, unless a qualified person has established otherwise for that specific rig. The extra legs are steadying the load, not sharing it: with rigid geometry and fixed-length legs, the two shortest legs take the weight and the others hang until something stretches or settles. Adjustable legs, turnbuckles or chain shorteners do not change the rule by themselves, because you cannot verify by eye that you tuned four legs into equal tension.

Slot 4. Vertical share per counted leg. With the hook over the centre of gravity and equal legs, this is the weight divided by the counted legs. With the centre of gravity off-centre between two pick points, share is inversely proportional to horizontal distance from the centre of gravity: the near lug carries the fraction of the weight given by the far lug's distance over the total spacing. The near leg always carries more, which is the opposite of most people's first instinct.

Slot 5. Measured leg length and measured vertical height, per leg. Not the sling's nominal size and not the height to the top of the load. Bearing length from hook to attachment, and vertical height from hook to attachment. Measure with the load landed and the slings slack.

Slot 6. Angle factor, per leg. Leg tension equals the share multiplied by leg length divided by vertical height. That ratio is one over the sine of the leg's angle from horizontal, and every angle in this sheet is from horizontal. Thirty degrees from horizontal is the floor most programmes set; below it the lift becomes a plan question rather than a field judgement, and the angle article in this group carries why the penalty accelerates down there.

Slot 7. Hitch. Read the column on the sling tag that matches how the sling is actually rigged. A leg running eye to lug is a vertical hitch and the factor is 1.00. Write the 1.00 down; a factor of one is a decision you made, not a step you skipped.

Slot 8. Bend severity at the bearing point. If the pin, saddle or lug the sling bends over is smaller than the sling manufacturer's stated minimum, re-base the number using that manufacturer's efficiency table. Re-base, not add: the published rating was derived at a stated minimum diameter, so you are moving it to your geometry rather than layering margin on it.

Slot 9. Required rated capacity per leg. The tension from slot 6, adjusted by slots 7 and 8. Round up to the next size the manufacturer publishes. Every rounding on this sheet goes in the direction that asks for more sling, because rounding a requirement down is the arithmetic that drops loads.

Slot 10. Sling actually selected. Tag legible, tag belongs to that sling, rating read off the right column, and the set matched in type and length.

Slot 11. Hardware in the load path. Shackles, master link, hook. Each carries its own marking and its own rated capacity, and each is checked against the force it actually sees, which for a master link is the whole load and for a shackle is one leg's tension. A shackle pin gets fully seated and secured before the strain comes on, because a pin that backs out under a rotating load releases the leg with no warning.

Slot 12. Who computed it and who checked it. One person's arithmetic on a lift sheet is a draft.

Worked example: a four-leg bridle on a rigid frame

A fabricated steel skid, weight 9,000 lb taken from the fabricator's drawing, four lift lugs, four equal-length legs to a master link. The centre of gravity is central by symmetry, confirmed on the drawing.

• Slot 1, weight: 9,000 lb, fabricator's drawing.
• Slot 2, centre of gravity: central, from the drawing.
• Slot 3, legs counted: 2 of 4, because the frame is rigid and the legs are fixed length.
• Slot 4, vertical share per counted leg: 9,000 / 2 = 4,500 lb.
• Slot 5, measured: leg length 10 ft 0 in, vertical height hook to lug 7 ft 6 in.
• Slot 6, angle factor: 10.0 / 7.5 = 1.333. Sine is 7.5 / 10.0 = 0.75, so about 48.6 degrees from horizontal, comfortably above the 30 degree floor. Leg tension = 4,500 x 1.333 = 6,000 lb.
• Slot 7, hitch: vertical, factor 1.00. Still 6,000 lb.
• Slot 8, bend severity: legs land on shackles whose pin diameter meets the sling manufacturer's stated minimum, factor 1.00. Still 6,000 lb.
• Slot 9, required per-leg rated capacity: 6,000 lb, rounded up to the next published size.
• Slot 10: sling tag vertical rating at or above that, four matched legs.
• Slot 11: each shackle rated at or above 6,000 lb on its own marking; master link rated for the full 9,000 lb assembly load per its own marking.

The counting rule in slot 3 is the whole example. A rigger who counts four legs gets a share of 9,000 / 4 = 2,250 lb, a tension of 2,250 x 1.333 = 3,000 lb, and selects a sling with exactly half the capacity the lift needs. Against the 5 to 1 design factor inside a wire rope, web or roundsling rating, that sling is working at an effective 2.5 to 1, and against the 4 to 1 commonly inside an alloy steel chain rating, 2.0 to 1. It will lift the skid. It will lift the skid every time, until the day the frame lands slightly nose-first and three legs go slack.

Worth noticing but not paying for twice: the horizontal component on each counted leg is 4,500 multiplied by the 6 ft 7 in horizontal offset over the 7 ft 6 in height, about 3,968 lb inward on each lug. That is a question for whoever designed the lugs, not for the sling.

Branch: the same sheet when the centre of gravity is off

A fabricated beam, weight 6,000 lb from the drawing, two lugs 12 ft 0 in apart, centre of gravity marked 4 ft 0 in from lug A. Two-leg pick, hook directly over the centre of gravity because a hook anywhere else tips the load on pick-up.

• Slot 4, using the inverse-distance rule: lug A carries 6,000 x 8 / 12 = 4,000 lb; lug B carries 6,000 x 4 / 12 = 2,000 lb. Those sum to 6,000 lb, which is the check that the share step closed.
• Slot 5, measured separately per leg because the hook is not centred between the lugs: leg A 6 ft 0 in long, leg B 9 ft 2 in long, both to a vertical height of 4 ft 6 in.
• Slot 6, leg A: 6.0 / 4.5 = 1.333, tension = 4,000 x 1.333 = 5,333 lb, sine 0.75, about 48.6 degrees from horizontal.
• Slot 6, leg B: 9.17 / 4.5 = 2.038, tension = 2,000 x 2.038 = 4,076 lb, sine 0.491, about 29 degrees from horizontal.
• Slots 7 and 8: vertical hitch and adequate bend diameter on both legs, both factors 1.00.
• Slot 9: leg A needs 5,333 lb and leg B needs 4,076 lb. If the pair is matched, both are selected against 5,333 lb, rounded up.

Two findings come out of that sheet, and only one of them is a number. Leg B carries half the vertical share and still ends up within a quarter of leg A's tension, because it is so much flatter, which is the sine relationship doing exactly what the angle article says it does. And leg B is sitting at about 29 degrees from horizontal, under the floor. That is not a rounding to shrug at: it is the trigger to raise the hook, lengthen leg A, or move the pick, and it is invisible to anyone who assumed the legs shared equally and never measured them separately.

How to verify you got this right

Add the vertical components back up. Each leg's share, not its tension, is what must sum to the load weight. In the branch case, 4,000 plus 2,000 equals 6,000 lb. If your shares do not sum to the weight, slot 4 is wrong and nothing after it is worth checking.

Re-read your own slot 3 against your own slot 4. Counting four legs and then dividing by two, or counting two and dividing by four, is the specific transcription error this sheet exists to prevent, and it survives a recheck of the arithmetic because the arithmetic is fine.

Check that every rounding made the requirement larger. Angle estimated rather than measured: round the angle toward horizontal. Height uncertain: use the smaller height. Required capacity: round up. If a rounding made the lift look easier, redo it in the other direction.

Then take the strain and hold the load a few inches clear with everyone outside the footprint and the swing arc, and look at what the rig actually did. Legs that were equal on the ground can settle unequal. A load that rotates as it lifts says the centre of gravity is not where slot 2 said. Set it down and rework the sheet rather than talking yourself past it in the air.

References

• 29 CFR 1910.184, slings, for general industry, and 29 CFR 1926.251, rigging equipment for material handling, for construction. Say which Part governs the job before quoting a requirement.
• 29 CFR 1926 Subpart CC, cranes and derricks in construction, where the machine's load chart governs and already contains the machine's own weight and often a rigging allowance.
• ASME B30.9 for slings and ASME B30.26 for rigging hardware such as shackles and links, in the editions your authority having jurisdiction, contract or employer programme has adopted.
• The sling and hardware manufacturers' rating tables and identification markings, which own every efficiency figure and minimum bearing diameter this sheet routes to.
• See related: Why Sling Angle Costs More Capacity Than Anyone Expects; What a Rated Capacity Actually Refers To.