Shackle selection and the pin-hole fit on a lifting lug

The lift statics run twice. The lug, its welds and the shell are checked on W_L = K_L·W_E, with K_L the overall factor for impact and safety, 1.5 to 2.0 by Moss. The shackle is compared on W_E, unfactored. Its maker's design factor, 5:1 or 6:1, already carries impact. Factoring the load again for the shackle would count the same allowance twice.

For a tailing lug the load compared is the lug resultant. For a lifting lug it is the sling load including its spread, combined with the side load: √(sling² + lateral²).

The lug load used is the largest over the lift's angle steps, since a lug's load changes as the vessel rises. In the default lift the tail lug is worst late in the lift, when the tail carries most of the weight, and the top lugs at the first pick. The shackle has to suit the worst step, not the step at which the lift starts.

• Pin through the hole: D_pin ≤ D_hole. A pin that does not pass is the plain failure; a pin much smaller than the hole bears on a narrow strip of the hole and raises the bearing stress the lug check reads.
• Plate in the jaw: the lug plate with its cheek plates, t + 2·t_p, no wider than the jaw. A plate that is too thick cannot be rigged.
• Bow over the lug top: R − D_pin/2 no more than the inside length, the metal above the hole fitting inside the bow, with room left for the sling or hook.
• Load within the working load limit, on W_E.

Each fit is reported as a ratio, like a stress check, so the tightest one shows at a glance. A ratio near 1 on the pin means a close fit in the hole; a ratio near 1 on the jaw or the bow means the next size of plate or cheek plate will not go in.

Once the shackle is chosen, its pin diameter and the hole size feed the lug plate checks on W_L. The hole diameter D1 sets the net section beside the hole and the shear above it. The pin diameter D2 sets the bearing area.

• Net section: P / ((A − D1)·t) ≤ 0.45·F_y.
• Shear above the hole: P / ((R − D1/2)·t) ≤ 0.4·F_y.
• Bearing: P / (D2·t) ≤ 0.9·F_y.

This is where the shackle choice and the lug design meet. A larger shackle has a larger pin, which needs a larger hole, which takes metal from the section above it. In the example, shear above the hole already governs at 0.96. Cheek plates add to t at the hole, which lowers all three stresses without a wider lug, as long as the plate with its cheek plates still fits the jaw.