Sling geometry and forces matter11 June 2009
In the first of a series of articles on complex rigging situations, Derrick Bailes looks at the slinging arrangements required to lift awkward loads.
The simplest slinging operation is one where a single leg sling can be hooked directly into a suitable lifting point on the load and a classic example of this is to lift an electric motor which has an eyebolt screwed into the motor frame. Using this simple situation as a starting point, I will go through increasingly complex multi-leg slinging arrangements explaining what is happening and what the rigger must take account of.
The eyebolt hole in our motor is positioned directly above the centre of gravity so that the weight of the motor is balanced and it will lift level. However when the motor is lifted out for maintenance, it often has one half of a hefty coupling on the end of the shaft causing it to tilt.
A solution to the problem is to use a second sling leg connected to the shaft just behind the coupling. A roundsling choked around the shaft is a good way of making the connection and, with suitable adjustment, this arrangement will enable you to lift the load level.
However as the majority of the weight will be that of the motor, the sling leg connected to the eyebolt will be much nearer to the vertical than the one connected to the roundsling. This lack of symmetry is often encountered when lifting irregular shaped loads.
Their shape and the location of the possible lifting points dictates the geometry of the sling arrangement. The important point to understand is how the load is shared between the components of the slinging system and therefore the forces arising in each.
In a two leg sling, if both legs are at the same angle to the vertical, then the load will be shared equally and the force in each leg will be the same. The amount of force will depend upon the angle. The greater the angle to the vertical, the greater the force. The reason is simply that the force in the leg can be resolved into a vertical component and a horizontal component. The bigger the angle, the smaller the vertical component and the larger the horizontal component. Therefore for a given load, the bigger the angle, the greater the force required in the leg to provide the required vertical component.
This is why slings are generally rated for an angle range of 0-45 degrees and, if a greater angle is needed, they have a lower rating for the range of 45-60 degrees. Above 60 degrees, the force increases more rapidly and at 90 degrees it is infinite, hence the upper limit of 60 degrees for general purpose slings.
The same principle applies if two single leg slings are used instead of a two leg sling. The point to remember in that case is that the slings will be rated for a straight pull and the user will have to make the appropriate allowances for the angles.
Having understood how increasing the angle of the leg to the vertical increases the force in the leg, many people confuse it with what happens when the legs are not at the same angle. In this situation, the load is not equally shared. In fact the leg making the smaller angle to the vertical takes a greater share of the load and that making the larger angle takes a lesser share. If the load tilts to the point where one leg is vertical, it will take all the load and the other leg will have none.
At first sight, this appears to be the opposite of what happens when the angles are equal. The reason is as before, that the force in each leg can be resolved into a vertical component and a horizontal component. When the load is suspended, the horizontal components of the two legs must be equal and opposite, for example, they must cancel each other out.
The bigger the angle, the bigger the horizontal component as a proportion of the force in the leg. Hence to make the horizontal components equal, the force in the leg making the larger angle must be less than that making the smaller angle. By the way, if the load is not lifted from directly above its centre of gravity, the horizontal compenents will not be equal and opposite and the load will tilt until they are.
A word of caution when using a sling with both legs close to the vertical. When the angles to the vertical are small, any difference in angle has a proportionately greater effect than when the angles to the vertical are larger. Therefore such difference will cause a greater difference in the share of the load taken.
If you are proficient in trigonometry, and can measure or accurately estimate the angle of each leg, you can easily calculate the forces in the legs. A simple alternative is to draw a force diagram to a convenient scale and measure the forces from it.
The situation becomes a little more complex when using three and four leg arrangements. In these, as well as considering the angle between the legs and the vertical, the user must also take account of how they are disposed when viewed in plan.
The standard rating for a three leg sling assumes that the legs are equally disposed in plan, for example, at 120 degrees to each other. However if the load is not symmetrical, it is likely that two legs will be closer together. The closer they get, the nearer the arrangement approaches that of a two leg sling. The two legs which are closest will effectively act as one leg of a two leg arrangement and the third leg will act as the other. Therefore, if they are all at the same angle to the vertical, the third leg will take half the load.
For a three leg arrangement to be stable, the centre of gravity must lie within the triangle formed by the three attachment points. However if it is within the triangle but close to one of its sides, the arrangement is again approaching that of a two leg, with the two legs forming that side taking most of the weight and the third leg providing only a small balancing force.
With a four leg arrangement, the way the load is shared becomes still more complex. The standard rating for a four leg sling is the same as that for a three leg as it is assumed that there will usually be some inequality in the share of the load which each takes. This arises from the tolerances on leg lengths, the position of the lifting points and the rigidity of the load.
The standard rating assumes that attachment points will form a square or a shallow rectangle. If the rectangle is too long and thin, then the two legs at each end will form a very small angle to the longitudinal axis of the load. The effect is the same as that previously mentioned in the context of the two leg arrangement, for example, any difference between their angles will have a greater effect on their share of the load. It is also assumed that the centre of gravity of the load will lie in the centre of the rectangle. If the load is rigid, then one pair of diametrically opposite legs will take all the weight and the other pair will provide only a small balancing force. Effectively it is a two leg arrangement.
It would be unrealistic to expect every load to be symmetrical and every slinging arrangement to share the load uniformly. In practice the standard rating of general purpose slings does allow for some variation. As a general guide for practical purposes, the sling loading can be assumed to be symmetrical if the following conditions are met:
(a) all sling legs are in use;
(b) the load is less than 80% of the marked WLL;
(c) none of the sling legs exceeds the maximum permitted angle to the vertical for that WLL;
(d) all sling legs are at least 15 degrees to the vertical;
(e) all sling leg angles to the vertical are within 15 degrees to each other;
(f) in the case of three and four leg slings, the plan angles are all within 15 degrees of each other.
In all of the arrangements referred to, if the load is not great and the choice of slings and accessories is good, then the simplest solution is to select equipment of more than adequate capacity. Nevertheless riggers should understand the factors involved so that when circumstances dictate, they can accurately assess what is required and do the necessary calculations.