What Happens When the Hook Is Not Over the Center of Gravity

Why this matters

An off-centre hook produces three separate effects, and crews reliably notice one of them. The legs stop sharing, the load hangs tilted, and the load swings. Those are three different arithmetic problems with three different answers, and the one that hurts people is not the one that shows up in the sling calculation. Hoisting slowly does not remove any of the three. It removes the shock at pick-up, which is a fourth thing entirely.

Effect one: the legs stop sharing

For a rigid load on two pick points with both legs in tension, the share on each point is set by moments and by nothing else. Each point carries the total load multiplied by the distance from the centre of gravity to the other point, divided by the span between them.

That relationship holds while the load is rigid and both legs are taut. Where a leg goes slack, or where there are more than three legs, the split is no longer geometric and a sibling article covers what governs it instead.

Then the sling angle correction applies to whatever share each leg ended up with, per leg, individually. The angle convention is stated because half the trade quotes it the other way: all sling angles here are measured from HORIZONTAL, and leg tension is that leg's vertical share divided by the sine of its angle from horizontal.

Two corrections, applied in that order. Share first, angle second, per leg. A crew that takes half the load and applies the angle factor to it has skipped the first one and will be light on the heavy leg by exactly the amount the offset produced.

Effect two: the load tilts

A suspended rigid load rotates until its centre of gravity sits directly under the effective suspension point, which for a bridle is where the leg lines of action meet. The tilt angle is governed by two lengths: the horizontal distance from that suspension point down-line to the centre of gravity, and the vertical distance between them. The tangent of the tilt equals the horizontal offset divided by the vertical distance.

Read the shape of that before any numbers go into it. The vertical distance is in the denominator, so the further the suspension point sits above the centre of gravity, the less the load tilts for the same offset. Short legs on a load whose mass sits high produce a large tilt from a small offset. Long legs on a load whose mass sits low barely tilt at all.

This holds only while the suspension point is above the centre of gravity. Below it, the load does not tilt to an angle, it turns over, and a sibling article covers that boundary and how to check which side of it you are on.

Effect three: the swing, and why it travels twice the offset

              * hook
             /|\
            / | \
        L  /  |  \  L
          /   |   \
         /    |    \
        x     +     x
      start   |   far side
       CG   under
            hook

   |<-- d -->|<-- d -->|

If the load can slide, it drags along the ground toward the point under the hook and then lifts with no offset left. That is the benign case and it is not the common one. A load that is chocked, bolted, in a pocket, sitting on a high-friction surface, or heavy enough that it will not slide leaves the ground with its offset intact, and at that instant it is a pendulum released from rest.

A pendulum released from rest rises to the same height on the far side. So the centre of gravity does not stop under the hook; it passes through and reaches roughly the same distance past it. The travel is about twice the offset, and the exclusion zone has to be the load's own footprint plus that full travel, in the direction of the offset, not a comfortable-looking distance.

Two more figures fall out of the same geometry, and both are worth having because they contradict what the swing looks like.

The speed is modest and the momentum is not. The centre of gravity rises only a small fraction of an inch to reach the offset position, so its speed at the bottom of the swing is small. It is also an upper bound rather than a value, because air resistance, sling friction and any tag line take energy out: the peak speed is not more than the value the energy calculation gives.

The crossing is fast. For small swing amplitude, treating the load as a point mass hanging a distance L below the hook, the period is the standard pendulum relationship and the load reaches the bottom in a quarter of it. A rigid body swinging about the hook has a somewhat different period set by its own mass distribution, so the point-mass figure is an approximation and it is the one to use for planning where people stand rather than for anything structural.

One gate, two configurations

The gate: the hook is 1.0 ft off the centre of gravity, in the direction of the pick-point span, on a load taken as 6,000 lb for the walkthrough that is chocked and cannot slide. What does the offset cost?

Configuration A: single-point pick, long line. One lifting eye on the top of the load, one sling, one hook, with the hook sitting 20.0 ft above the centre of gravity and the eye 4.0 ft above the centre of gravity.

• Leg share: one attachment point, so the whole 6,000 lb.
• Tilt: horizontal offset 1.0 ft, vertical distance from the eye down to the centre of gravity 4.0 ft. Tangent of the tilt is 1.0 / 4.0 = 0.250, so the load hangs at about 14 degrees from level.
• Swing travel: about 2 x 1.0 = 2.0 ft of horizontal excursion for the centre of gravity.
• Rise of the centre of gravity at the offset: 20.0 minus the square root of 20.0 squared minus 1.0 squared, which is 20.000 - 19.975 = 0.025 ft.
• Peak speed at the bottom of the swing: not more than the square root of 2 x 32.2 x 0.025, which is 1.3 ft per second.
• Time from release to the bottom: a quarter of the period for a 20.0 ft pendulum, which is about 1.2 seconds.
• Sling tension at the bottom of the swing: the weight plus its own centripetal term, which here works out to about a quarter of one percent above the static 6,000 lb, so 6,015 lb.

Configuration B: two-point bridle, short legs. Same load, same 1.0 ft offset. Pick points 6.0 ft apart, legs at 60 degrees from horizontal, centre of gravity 2.0 ft below the plane of the pick points.

• Share, near point: 6,000 x 4.0 / 6.0 = 4,000 lb, because the centre of gravity is 4.0 ft from the far point.
• Share, far point: 6,000 x 2.0 / 6.0 = 2,000 lb.
• Leg tension, near: 4,000 / sin 60 = 4,000 / 0.866 = 4,619, carried as 4,620 lb because rounding a tension upward is the conservative direction.
• Leg tension, far: 2,000 / 0.866 = 2,309, carried as 2,310 lb.
• Apex height above the pick plane: 3.0 x tan 60 = 5.20 ft. Distance from apex down to the centre of gravity: 5.20 + 2.0 = 7.20 ft.
• Tilt: tangent is 1.0 / 7.20 = 0.139, so about 8 degrees from level.
• Swing travel: about 2.0 ft, the same as configuration A.
• Peak speed at the bottom: rise is 7.20 minus the square root of 7.20 squared minus 1.0 squared, so 7.200 - 7.130 = 0.070 ft, giving a speed of not more than 2.1 ft per second.
• Time to the bottom: a quarter period for a 7.20 ft pendulum, about 0.7 seconds.

Reading the two against each other, which is the point.

The same 1.0 ft offset resolved into completely different problems. In A the tension question barely moved: the sling carries 6,000 lb and the swing adds a quarter of a percent. What A got was a 14 degree tilt, which on a tall load is the difference between clearing a doorway and not. In B the tension question is the whole event: the near leg went from the 3,000 lb a centred hook would have given it to 4,000 lb, a 33 percent increase, and the two legs are carrying in a 2 to 1 ratio. B's tilt is half of A's, because B's suspension point sits 7.20 ft above the centre of gravity against A's 4.0 ft, and the vertical distance is in the denominator.

And the one figure that did not change: the swing travelled about 2.0 ft in both. The excursion is set by the offset, not by the rigging, not by the leg count, and not by the hoist. B swings faster and crosses sooner, which makes it harder to stay ahead of, but neither configuration lets anybody stand within 2.0 ft of where the load starts, plus the load's own extent, plus room for the tilt to put a corner somewhere the level drawing did not.

That is why the swing is not a capacity problem. Nothing in either configuration was overloaded by the swing itself. It is a struck-by problem, and a 6,000 lb load crossing at 1.3 ft per second in A, or 2.1 ft per second in the short-leg rig B that crews build far more often, is not something a person stops with their hands, arms or body. Nobody stands in the arc, nobody pushes a moving load by hand, and in construction the clearing duty for cranes and derricks sits at 29 CFR 1926.1425 while in general industry the load-handling requirements at 29 CFR 1910.179 carry it for overhead and gantry cranes.

Why hoisting slowly does not fix any of it

Hoisting slowly does one real thing: it removes the dynamic multiplier at pick-up. Taking up through slack applies a load nobody measured on top of the static weight, and shock loading is prohibited outright at 29 CFR 1910.184(c) in general industry with 29 CFR 1926.251 the construction home of the same duty. So slow take-up is correct and it is not optional.

What it does not do is change the offset. The swing excursion is set by where the centre of gravity started relative to the hook, and it will be the same 2.0 ft whether you got there in two seconds or in twenty. The tilt is set by geometry and does not care about hoist speed either. The share split is a moment balance and does not care at all.

Two things do fix it. Land the load, block it, and move the hook over the centre of gravity, which means re-spotting the crane or shifting the pick points with the rig fully slack, never by adjusting rigging on a suspended load. Or accept the offset knowingly, size the heavy leg on its actual share rather than on half the load, and set the exclusion zone on the full swing travel.

A tag line changes what the load does after it is airborne, and a sibling article covers what it can and cannot control. It is not a substitute for either fix, and holding one is not a reason to be standing anywhere near the arc.

How to verify you got this right

Take a pick you ran this month and ask three questions in order. Did the sizing use a share, or did it use half the load? If it used half the load, the offset was never in the arithmetic. Did the load hang level on the trial lift? If it did not, the tilt tells you the direction of the offset and roughly its size, and that information should have gone back into the share calculation before the pick continued. And where were people standing relative to twice the offset in the direction the load was going to swing?

The failure mode here is quiet, which is why it repeats. Nothing breaks. The load comes up crooked, somebody says it always does, the pick completes, and the heavy leg carried a third more than the plan said on a sling whose design factor absorbed it without complaint. That design factor was there for the things nobody measured, and it just got spent on something that could have been measured with a tape.

References

• 29 CFR 1910.184, Slings (general industry), safe operating practices at (c) including the shock loading prohibition, and 29 CFR 1926.251, Rigging equipment for material handling (construction)
• 29 CFR 1926.1425, Keeping clear of the load (construction cranes and derricks), and 29 CFR 1910.179 for general industry overhead and gantry cranes
• ASME B30.9, Slings, in the edition adopted by your jurisdiction, your contract or your employer's programme: sling rating basis and the effect of hitch and angle
• Sling manufacturer's tag and catalogue: vertical, choker and basket ratings for the specific sling in the rig
• See related: Why the Center of Gravity Decides the Whole Lift; How to Find a Load Center of Gravity Without a Drawing; Why a Load Rotates and What a Tag Line Actually Controls