Two-Leg Bridle With an Off-Center Load
A 6,200 lb, 24 ft pipe spool with a 30 in. OD is to be lifted horizontally by a two-leg bridle from a single hook. The center of gravity is 10 ft from the west end. Sling attachment points are 4 ft in from each end, so the west point is 6 ft from the CG and the east point is 10 ft from it; the span between attachment points is 16 ft. The hook is plumb above the CG, 6 ft above the pipe centerline. Slings are 1/2 in. 6×19 EIPS wire rope, vertical capacity 5.6 tons per leg, with correct thimbles and shackles. The site rigging standard prohibits sling angles below 45° from horizontal and requires the hook to be over the CG.
1. Calculate the tension in each leg and state whether the site standard is met.
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Geometry
With the hook over the CG: west leg horizontal run 6 ft, vertical 6 ft, so θ_w = 45°. East leg horizontal run 10 ft, vertical 6 ft, so θ_e = atan(6/10) = 31.0°.
Solve equilibrium
- Horizontal: T_w cos45° = T_e cos31° → 0.7071 T_w = 0.8572 T_e → T_w = 1.212 T_e.
- Vertical: T_w sin45° + T_e sin31° = 6,200 → 0.7071 T_w + 0.5150 T_e = 6,200.
- Substitute: 0.7071(1.212 T_e) + 0.5150 T_e = 0.8570 T_e + 0.5150 T_e = 1.372 T_e = 6,200 → T_e ≈ 4,520 lb, T_w ≈ 5,480 lb.
- Check: vertical components 3,873 + 2,328 = 6,201 lb. Good.
Verdict
- Capacity is 5.6 tons = 11,200 lb per leg, so both legs are within strength.
- The east leg at 31° is below the 45° minimum. Standard not met, even though nothing is overloaded on paper. The 45° rule exists to limit tension and to keep the horizontal squeeze on the load down; a 31° leg is doing both badly.
- Note the trap: computing with equal angles on both legs would have understated the west leg. The leg nearer the CG carries more, and it is also the steeper one.
2. Propose a fix that satisfies the standard without changing the slings, and verify it numerically.
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Option 1 - raise the hook (preferred, no new hardware)
With the hook still plumb over the CG, raising it to 10 ft above the pipe centerline gives θ_w = atan(10/6) = 59.0° and θ_e = atan(10/10) = 45.0°.
- Horizontal: T_w cos59° = T_e cos45° → 0.5150 T_w = 0.7071 T_e → T_w = 1.373 T_e.
- Vertical: 0.8572 T_w + 0.7071 T_e = 6,200 → 0.8572(1.373 T_e) + 0.7071 T_e = 1.884 T_e = 6,200.
- T_e ≈ 3,290 lb, T_w ≈ 4,520 lb. Both legs over 45°, both well under 11,200 lb, and the peak tension dropped from 5,480 to 4,520 lb.
Option 2 - spreader beam
Fit a spreader rated for the load and the 16 ft span so the legs hang vertically from the spreader ends. Leg tensions then fall to about 3,875 lb west and 2,325 lb east (the vertical reactions, from moment balance about the east point: V_w × 16 = 6,200 × 10). This also removes the horizontal squeeze on the spool and is the better answer if the spool has a thin wall or a bolted flange that should not be side-loaded.
Either way, do not solve this by adding a third leg at random - it changes the load share and usually makes the near-CG leg worse unless it is analysed.
3. The crane chart shows 6,800 lb capacity at the required radius on outriggers on asphalt. Is the lift acceptable? What else governs before you proceed?
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Capacity check
Gross load is the 6,200 lb spool plus slings, shackles and any spreader - call it 6,400 lb. That is 94% of the 6,800 lb chart value at radius. Being inside the chart is not the same as being a good plan: chart values already include a design margin, but the operator still needs a lift plan, and a lift at 94% of chart leaves nothing for dynamic load, wind or a radius increase during the pick.
What else governs
- Radius control: any boom-down or swing that increases radius reduces capacity quickly on a small chart window. Mark the swing path and keep the load inside it.
- Ground bearing: outrigger floats on asphalt in summer can punch through. Use mats sized to the outrigger load, and confirm nothing (culvert, trench, basement wall) is under the floats.
- Load control: two tag lines, and no one under or beside the load during the pick.
- Load integrity: confirm the spool's lift lugs or the sling wrap point can take the load without crushing a thin wall or slipping on the pipe.
- Communication: a designated signal person with the operator's line of sight; stop the lift if any of these change.
If the radius cannot be held, or the ground bearing cannot be confirmed, the lift is not acceptable at 94% of chart regardless of the numbers on paper.