Overhead rigging - Multiple points of failure vs safety factor of fewer
Hello all,
I am currently running the numbers for overhead rigging of some speakers for an installed PA system. The current point of contention is the WLL of some forged shoulder eye bolts and the angle at which they'll be loaded, which leads into a more general issue of a 3-point rig versus 2-point.
The speakers each weigh 40 lbs, and will be flown individually. Each of them came with 3 machinery-type forged shoulder eye bolts; two of them 3/8"-16 G5 for primary support, a third 1/4"-20 G5 for use in angle adjustment. The current plan is to use three slings of 1/8" 7x7 aircraft cable, with thimbles and wire clips at each end, which will then be anchored with similar eye bolts to an adjustable bracket, that will in turn be fastened with 3/8"x2" lag screws to the ceiling rafters.
My numbers on the slings are a worst-case breaking strength of 1500lbs for the cable itself, times .2 for a 5:1 safety factor, times .95^2 for use of two mechanical splices per sling, times .85^2 for use of two 8:1 D/d thimbles per sling, times cos(30)=.866 allowing a basket angle up to 30* from parallel to gravity, giving a max safe working load per cable of 169 lbs. That provides a safety factor of better than 4:1 against the WLL, over 20:1 against breaking strength. I think we're fine here.
Now, the original plan was to suspend the cabinet primarily from two provided anchor points at the top of the speaker, which are in a plane with the CG of the speakers parallel to the face; the cabinet would hang vertically when suspended by these anchors. The angle adjustment cable will be tied to the provided anchor point provided low on the rear face of the cabinet, forming a tripod basket sling. Each sling will then have its own anchor in the mounting bracket, providing multiple points of failure all the way through the rig.
The issue with this is the low center of gravity caused by the woofer's voice coil, basically a big lump of iron and ferrite magnet positioned low in the cabinet. Using these three anchor points, the angle adjustment cable would end up picking up most of the load (and at an angle somewhere significantly over 45*), and also shifting the CG of the entire rig backwards.
The primary anchor point on the speaker that provides the closest natural suspension angle to the angle we'll need is a single anchor at the top of the rear face of the cabinet. My colleague suggests using this one instead of the two top anchors, but I'm apprehensive. The natural hanging angle of the cabinet from this single anchor point is 39*, making the load angle on the eye bolt 51*, exceeding most manufacturer recommendations for load angle on a machinery eye bolt, this time on the primary load anchor and not an adjustment line.
I did see one reference saying machinery eye bolts can be used with a shear load, assuming that the load is still exerted in the plane of the eye and that a WLL of 25% of the eye bolt's straightline WLL is used for any angle over 45*. The nominal WLL rating (again with a 5:1 safety factor or better versus breaking strength) for a 3/8" machinery FSEB is 1000 lbs, giving this anchor point a max WLL of 250 lbs, still five times actual load. A 1/4" machinery eye bolt has a WLL of 500 lbs in straightline, so the worst-case shear WLL would be 125 lbs, only 3 times actual load (but with an overall safety factor of 15:1).
Even though the math seems to add up, I'm still apprehensive about trusting human safety to only two points of failure, and about subjecting a single primary anchor to essentially the full weight of the speaker at a high shear angle. Two points of failure is still better than one, but based on these calculations I would still prefer to use the two anchors on the top, because in that situation the most likely point of failure is the angle adjustment, and if it fails it would simply leave the speaker hanging vertically from its two primary anchors, each picking up a paltry 20 lbs against a 160lb max WLL for the cables (and not even close to the 1200lb straightline WLL of the eye bolts). Using the rear primary anchor to pick up almost all of the load, that cable and eye bolts now become the most likely point of failure, and if that fails, the only remaining tether is the angle adjustment cable and its anchors, which have the lowest overall worst-case safety factor. Such a failure would also be more violent, causing increased cantilevering of the lag screws holding the entire mount to the rafter.
Am I right to be apprehensive, or should I trust the relatively high safety factor inherent in the rigging calculations and go with the 2-point flying rig?
A third option would be to have an emergency tether, perhaps as beefy as 1/4", anchored to an unused primary anchor point and to the center of the mounting bracket (or, even better, independently attached to the rafter). It would calm my fears but might detract aesthetically, which is a concern as it usually is when trying to minimize the visual impact of big black boxes hanging in midair.
