Why a four-leg sling is designed on two legs

Put a rigid body on three supports and the reactions follow from statics alone. Sum of vertical forces, sum of moments about two horizontal axes: three equations, three unknowns, one answer. That answer is exact, and it does not depend on the material, the temperature or how carefully anything was made.

Put the same body on four supports and the equations do not change. There are still three of them, and now there are four unknowns. The system is statically indeterminate to the first degree, and the missing equation is a compatibility condition: the supports must deform in a way consistent with the body staying rigid.

That compatibility condition is where the difficulty lives, because it depends on things nobody knows to useful precision:

• The axial stiffness of each leg. A wire rope leg and a chain leg of the same length have different stiffnesses; two wire rope legs from different reels are not identical either.
• The as-made length of each leg. A sling manufactured to a nominal 6 m is somewhere near 6 m. A leg 10 mm shorter than its partner takes load first and keeps taking it until something yields or the load tilts.
• How level the hook is. The load hangs from a hook that finds its own equilibrium, and a load hung slightly out of level redistributes the shares immediately.
• The stiffness of the load itself. A rigid frame distributes nothing; a flexible skid distributes a great deal, and most real loads are neither.

None of those is a design input. All of them change from lift to lift with the same equipment.

The convention is one sentence, and the reasoning behind it is what tells you when it does not apply.

Two diagonally opposite legs carry the whole load. Each of those two legs carries half the vertical load, and the angle factor applies to that half.

Why the diagonal pair rather than an adjacent pair? Because the diagonal is the case that is stable. If the load hangs on two adjacent legs it is not in equilibrium about the axis through them, so it tilts until other legs pick up. If it hangs on a diagonal pair, the line between them passes under the centre of gravity, and the arrangement can sit there indefinitely. The diagonal is the distribution the load can actually adopt and stay in.

Two legs is the design case; the other two are what stop it tilting. They are not useless. They restrain the load about the diagonal it would otherwise be free to rotate on, they take up when the first pair stretches, and on a real lift they carry something. What they do not do is let you divide by four in a calculation.

The equal-share case is the unprovable one. To get four equal shares you need all four legs the same length to a tolerance nobody specifies, the same stiffness, a level hook, and a load rigid enough not to redistribute. Every one of those is an assumption you would have to defend, and none of them is checkable on site with the load in the air.

A 25 t skid on four corner lift points, slings at 60 degrees from horizontal. Each lift point is 20 mm plate in S355, 200 mm wide, with a 52 mm hole on a 50 mm pin, 60 mm from the hole centre to the top edge, and two 8 mm fillet welds 180 mm long with the pin 150 mm above the weld.

Turnbuckles, chain shorteners or hydraulic levellers in each leg change the problem. What they change is narrower than it looks.

What they fix. They remove the manufacturing-tolerance term. Four legs that can be adjusted to length can be brought to a condition where all four are taut and none is doing more than its neighbours, at the moment of adjustment.

What they do not fix. The compatibility condition still applies as soon as anything moves. The load lifts and deflects; the hook finds a different equilibrium; the load rotates a degree or two on the way up; a leg stretches under load by more than the adjustment resolution. All four legs stay engaged, but not equally.

The usual project position, and a defensible one, is to credit adjustable legs with a better distribution rather than an equal one. Something in the region of 30 percent to the worst leg rather than 25, or 60/40 between the pairs, is a claim you can support with an adjustment procedure and a tolerance. Crediting a true quarter each requires you to argue that nothing about the geometry changes between adjustment and lift, which is not true.

There is one arrangement that genuinely restores determinacy: make the four points into three. A pair of legs meeting at a common point above two lift points, or a spreader arrangement that resolves four points to three attachments at the hook, gives you a statically determinate system whose reactions follow from equilibrium alone. It costs headroom and hardware. It buys an answer you can prove.

Everything above assumes the centre of gravity sits centrally between the four points. Frequently it does not, and then the diagonal-pair rule has to be applied to the worse diagonal.

Work it in two steps.

Step one: split the load between the two diagonals. Take moments about the line joining one diagonal pair to find the vertical load the other diagonal has to carry. In practice, the pair nearer the centre of gravity carries more, in inverse proportion to distance in exactly the way a simple beam's reactions do.

Step two: apply the two-leg rule within the worse diagonal. The two legs of that diagonal share what it carries, split again by their distances from the centre of gravity along the diagonal.

Which direction the offset runs in matters more than its size. Move the centre of gravity a quarter of the length along one axis only, and the worst attachment goes from a quarter of the load to about 35 percent - uncomfortable, and still inside the half-share the two-leg rule gives you. Move it a quarter of the way along both axes, so it sits toward one corner, and that corner can carry three quarters of the total before any angle factor is applied. An offset toward a corner is the case to check.

Two practical consequences:

• Find the centre of gravity before sizing the lift points, not after. The share depends on it and the share is the largest single number in the load path.
• Give the centre of gravity a tolerance and check the worst position inside it. A centre of gravity known to plus or minus 300 mm is a range of load cases, and the governing one is at the edge of the range, not the middle.

The honest summary: a four-leg sling assembly may carry a four-leg rating, and the structure it lifts is still designed on two. Those two statements are not in conflict, because they are answers to different questions. The first is about the slings. The second is about your padeyes, and nobody rates those but you.

1. Dividing by four. It halves the design load on every lift point, and the worked example is what that costs.

2. Reading a four-leg sling rating as a distribution. The assembly's rating is about the slings, not about your load.

3. Assuming the diagonal pair is the symmetric one. On an off-centre load the two diagonals do not carry the same amount, and the governing one is the one nearer the centre of gravity.

4. Crediting adjustable legs with an equal split. Adjustment removes the manufacturing tolerance and does not remove the compatibility problem. Credit a better split with a procedure behind it, not an equal one.

5. Using a nominal centre of gravity. A centre of gravity with a tolerance is a range of load cases, and the governing case is at the edge.

6. Sizing the lift point and forgetting the structure under it. A padeye at 114 percent is visible. The plate it is welded to, carrying half the load rather than a quarter into a local region that was checked for a quarter, is not.