Lifting and Rigging Loads: Method

Lifting and Rigging Loads

The tool does the arithmetic of a lift plan as the public rigging standards write it: the tension in each leg of a bridle, the sling angle and its load-angle factor, the hitch reductions, the rating the sling must carry, the share of a load between two cranes, the compression in a spreader bar or the bending in a lifting beam, the checks of a plate lifting lug, the derating of shackles, hooks and eyebolts under side loads, the crane chart check with its critical-lift threshold, and the tilt of a four-point lift. The sources are DOE-STD-1090 Hoisting and Rigging (the 2004 edition carries the tables and worked examples, the 2011 and 2020 editions the critical-lift rules), USACE EM 385-1-1, NAVFAC P-307 and the Army rigging manual TM 3-34.86, all U.S. government works; ASME B30.9, B30.20, B30.26 and BTH-1 are cited for the consensus design factors and categories, which the tool takes as entered inputs rather than reproducing their tables.

Bridle statics

The lift points lie in a plane on top of the load: two on the x axis for a two-leg bridle, a triangle for three legs, the corners of a rectangle for four. The hook is placed directly above the centre of gravity, which a level lift requires (DOE-STD-1090-2004 11.3.1.c–d: when the centre of gravity is closer to one attachment the slings must be of unequal length and the stresses unequal). Each leg runs from its lift point to the hook, so its length L, its horizontal run r and its angle with the horizontal θ follow from the hook height H; the load-angle factor of the leg is L/H = 1/sin θ, the table of DOE-STD-1090-2004 Figure 11-7 (1.000 at 90°, 1.155 at 60°, 1.414 at 45°, 2.000 at 30°), and the tension is the leg's vertical share times that factor, which is the TM 3-34.86 formula T = (W/N)(L/V).

With two legs the vertical shares follow the lever rule about the centre of gravity. Three legs meeting at the hook are statically determinate: the three equations of force equilibrium give the three tensions, and the moments about the hook vanish identically because every leg passes through the hook and the weight acts under it. Four legs are indeterminate, and DOE-STD-1090-2004 Figure 11-9 settles the design assumption: two legs carry the load while the other two balance it, so the capacity of a four-leg bridle is that of two legs, WLL × H/L × 2. The tool applies that rule to the worse diagonal pair with the centre of gravity projected onto the diagonal, and prints beside it the three-leg-carry alternative (each leg dropped in turn, keeping the solutions in which all three remaining tensions are positive) and the equal-share solution (the minimum-norm statics of four equally stiff legs), the latter a lower bound that the standard does not allow for design. Figure 11-8 gives the same two-leg rule for three-leg bridles unless a qualified rigger verifies the even distribution; the tool shows both.

The lifted weight is the load plus the rigging below the hook, multiplied by a dynamic factor the lift plan may require; the standards quoted do not fix one (ASME BTH-1, cited, handles dynamics through its design categories and service classes). TM 3-34.86 paragraph 3-33 calls the angle at which each leg carries the whole weight the critical angle, about 60°/N, and tells the rigger to stay above it; the BNL workbook says to avoid angles below 45°.

Hitches and the required rating

A vertical hitch uses the leg's vertical rating. A choker hitch reduces it by the angle of choke, the angle formed in the sling body where it passes through its eye (not the inclination of the load): DOE-STD-1090-2004 Figure 11-10 gives 100 % above 120°, 87 % from 90° to 120°, 74 % from 60° to 89°, 62 % from 30° to 59° and 49 % below 30° for wire rope; NAVFAC P-307 Table 14-3 gives 75 % from 121° to 135° (80 % for chain, web and round slings), 65, 55, 46 and 36 % in the lower bands, refuses angles above 135° as unstable, and leaves chain below 121° to the sling maker. EM 385-1-1 15.D.01.b(8) requires the reduction below 120°. A basket hitch carries the leg on two parts, so its rating is twice the vertical rating times the D/d efficiency of NAVFAC Table 14-2 (50 % at a bend of one rope diameter, 95 % at 40:1, 100 % above 40:1, the lower value between listed ratios). The required vertical rating of each leg is the largest tension over the hitch factor, and the breaking strength it implies is that rating times the design factor, 5 for wire-rope slings (DOE 11.3.2.d; NAVFAC 14.7.2.3.1 writes the rated load of an endless sling as NRS × efficiency × 2 / DF). An entered tag rating gives a margin as a working-load comparison; the design factor is already inside the rating.

Two cranes and unequal legs

Two pick points D apart carry a load whose centre of gravity is a from the first: with plumb hoist lines R₁ = W (D − a)/D and R₂ = W a/D. A hoist line that leans by d over a height h carries R/cos φ and pulls the crane sideways by R tan φ, which NAVFAC P-307 and DOE-STD-1090 prohibit as side loading of the boom; the tool reports the pulls so the plan can remove them. A lift with more than one crane is a critical lift under EM 385-1-1 16.H.01.c and DOE-STD-1090-2011 2.1.2.E, and the share of each crane moves as either hook is raised.

Spreader bars and lifting beams

A spreader bar carries the load on vertical slings at its end lugs and hangs from two inclined top slings that meet at the hook; the hook sits over the combined centre of gravity of load and bar, at the height set by the top-sling angle. Moments about the hook give the vertical components of the top slings, the tensions are those components over sin θ, and the horizontal components, equal by equilibrium, compress the bar. The bar is checked as a pinned column: Euler's π²E/(KL/r)² above the transition slenderness C_c = √(2π²E/F_y) and Johnson's parabola F_y − F_y²(KL/r)²/(4π²E) below it, divided by the entered design factor (3 on yield for structural lifting devices in DOE-STD-1090-2004 Appendix 4.1.1.b and ASME B30.20; ASME BTH-1, cited, names 2.0 for its Design Category A and 3.0 for Category B), with the self-weight bending wL²/8 added in a linear interaction. A lifting beam hangs from one lug and carries hanger loads in bending: the hook reaction is their sum, the beam hangs level only when the lug sits at the resultant, and the shear and moment diagrams follow from singularity functions; the bending stress M/S is compared with F_y/N_d and the average shear with 0.577 F_y/N_d. Lateral-torsional buckling of an open section, fatigue and impact are outside the tool (BTH-1 covers them).

Lifting lugs

A plate lug of thickness t with a hole D_h for a pin D_p, a radius R about the hole and a base b wide welded with fillets of leg w, loaded by P at α from the lug axis in its plane and β out of plane. The in-plane resultant P cos β loads the net section (2R − D_h) t, the projected bearing area D_p t and the two shear-out planes 2 t (R − D_h/2); the components at the base load the plate section b t directly and in bending through the height h of the hole, and the two weld lines (throat 0.707 w, b long, t apart) in direct stress, bending and shear, combined as a resultant on the throat against 0.6 F_EXX (the nominal fillet strength of AISC 360 J2, cited) over the weld design factor. The design factors are entered: 3 on yield (DOE Appendix 4.1.1.b, BTH-1 Category B), 5 on ultimate for the net section (the sling and rigging-hardware factor of DOE-STD-1090 and NAVFAC P-307 applied to the lifting interface), and a bearing allowable of k_br F_y/N_y with 1.25 cited from BTH-1. The Hertz line contact of the pin in the hole is reported as the peak pressure p₀ = 2 (P/t)/(π b), b = √(4 (P/t) R_e/(π E*)), R_e = r_p r_h/(r_h − r_p), as a measure of the pin fit, not as an allowable. The site's Lug Strength tool carries the AFFDL-TR-69-42 aerospace method with its curves and interaction equations.

Shackles, hooks and eyebolts

Hardware is selected for the resulting leg tension, not the weight of the load (NAVFAC P-307 14.8.3). DOE-STD-1090-2004 12.3.1.e requires shackles used at load angles other than 90° to be derated and 12.3.1.a says to avoid side pulls on the body; the public values are the BNL workbook's step table (no reduction to 5°, 30 % from 5° to 45°, 50 % from 45° to 90°, nothing beyond 90°) and the NAVFAC rule of 50 % for any side load on a screw-pin or bolt-type shackle (round-pin shackles may not be side loaded at all); the rated load also assumes an included angle of at most 120° between two legs in the bow. A hook is loaded in its bowl, never on the tip or sideways; the tool takes the maker's fraction for any other loading. A shoulder eyebolt, seated flush and loaded in the plane of its eye, keeps a fraction of its vertical rating that the tool interpolates between entered values at 90°, 60° and 30° (the defaults 0.5 and 0.3 are illustrative, from the ratios in the BNL table; the maker's chart governs) and is not loaded below 30°; a plain eyebolt takes vertical loads only; a swivel hoist ring needs no angular reduction, and the full leg tension is compared with its rating.

Crane capacity and critical lifts

The gross load is the lifted weight plus the rigging, the hook block and the other deductions the chart requires; its ratio to the chart capacity at the working radius is the percent of capacity. EM 385-1-1 16.H.01.e makes a lift at 75 % of the chart or more a critical lift, as do DOE-STD-1090-2011 2.1.2.E for steel erection and NAVFAC P-307 10.4.1.g; a critical lift needs a written plan (EM 385-1-1 16.H.02, Form 16-3; DOE-STD-1090-2011 Section 2). The other triggers, hazardous loads, personnel, more than one crane, a centre of gravity that could change and loads out of the operator's view, do not depend on the percentage.

Tilt and stability

With the legs taut the load and its slings rotate as one body about the hook. The hang is stable when the centre of gravity lies below the hook, h_s = H + d_cg > 0, and the load tilts until the centre of gravity is under the hook, tan φ = e/h_s; W e is the tipping moment the offset produces and W h_s the restoring moment per radian. The rigging manuals' rule to keep the lift points above the centre of gravity guards the moment a leg goes slack at pick-up or set-down, when the body pivots about the remaining attachments instead of the hook; the tool flags lift points below the centre of gravity and a centre of gravity outside the lift-point pattern.

Conventions and limits

Lengths, forces, stresses and moments go through the site's unit dictionary; angles are plain numbers in degrees. The figures are drawn from the computed geometry and the chart of leg tension against sling angle carries the DOE Figure 11-7 table scaled by the load. Five rows of that printed table (35°, 25°, 15°, 10° and 5°) differ from 1/sin θ in the third decimal; the tool uses the closed form and the test records the misprints. Not covered: slings over edges and corners (the D/d of the load), the weight of the slings themselves, uncertain centres of gravity, pin bending, lateral-torsional buckling, fatigue, wind on the load, ground bearing under outriggers, and the proof-load tests that the standards require of fabricated lifting devices and lugs.