Formula reference

Two-leg bridles

• Leg length

  L = √(H² + V²)

  H = horizontal distance, V = vertical distance from beam point to apex.

  Subtract hardware (shackles, hook) to get the steel length.

  Practice:A5B4

• Symmetric bridle: tension per leg

  T = (W ÷ 2) × L ÷ V

  W = load.

  At a 120° included angle each leg carries the full load.

  Practice:A1A2B1

• Symmetric bridle: horizontal force on each beam

  F_H = (W ÷ 2) × H ÷ V

  Flat bridles pull the beams hard toward each other.

  Practice:B2

• Any two-leg bridle: leg tension

  T₁ = W·L₁·H₂ ÷ (V₁·H₂ + V₂·H₁)

  T₂ = W·L₂·H₁ ÷ (V₁·H₂ + V₂·H₁)

  1 and 2 are the two beam points; H and V are each leg's horizontal and vertical distances to the apex.

  Works for beams at different heights (high/low bridles).

  Practice:A3B3

• Any two-leg bridle: vertical force on each beam

  F_V1 = W·V₁·H₂ ÷ (V₁·H₂ + V₂·H₁)

  F_V2 = W·V₂·H₁ ÷ (V₁·H₂ + V₂·H₁)

  The two always add up to W.

  Practice:A4

• Any two-leg bridle: horizontal force

  F_H = W·H₁·H₂ ÷ (V₁·H₂ + V₂·H₁)

  Equal and opposite on the two beams.

• Included angle

  Included angle = 2 × arctan(H ÷ V)

  For a symmetric bridle.

  Keep it at or under 120°.

  Practice:B14

Beams, trusses and points

• Simple span, point load: reactions

  R_A = W × b ÷ S

  R_B = W × a ÷ S

  a = distance from A to the load, b = from the load to B, S = span.

  With several loads, add each load's share. The closer support carries more.

  Practice:A12A13B10

• Overhangs and cantilevers: take moments

  R₂ = Σ(W × d) ÷ S

  d = each load's distance from support 1, S = distance between the supports.

  Then R₁ = total load − R₂. A cantilever can unload the back point.

  Practice:B11

• Uniform load on a simple span

  R_A = R_B = total ÷ 2

  Practice:A13

• Continuous truss on 3 equal points, uniform load

  Ends = 3/16 of total each

  Center = 10/16 of total

  Treating it as two simple spans underestimates the center.

  Practice:A14

• Continuous truss on 4 equal points, uniform load

  Ends = 0.4·w·S each

  Inner = 1.1·w·S each

  w = load per foot, S = one span (total = 3·w·S).

  Practice:B12

• Center of gravity

  CG = Σ(W × x) ÷ ΣW

  x = each weight's distance from the same reference point.

  Practice:A15

Rope, slings and hardware

• Working load limit

  WLL = Breaking strength ÷ DF

  DF = design factor (8:1 is common for wire rope).

  Practice:A8B7

• With a termination

  WLL = Breaking strength × E ÷ DF

  E = termination efficiency (for example 0.80 for clips or a wedge socket).

  Apply the efficiency before the design factor.

  Practice:A9

• Breaking strength you need

  BS = WLL × DF ÷ E

  Practice:B8

• D/d ratio

  D/d = D ÷ d

  D = diameter of what the rope bends around, d = rope diameter.

  Lower ratios lose more strength at the bend.

  Practice:A10

• Two-leg sling, legs measured from horizontal

  T = (W ÷ 2) ÷ sin(angle)

  At 30° from horizontal each leg carries the full load.

  Practice:B15

Forces and angles

• Shock load

  F = W × (1 + D_F ÷ D_S)

  D_F = free-fall distance, D_S = stopping distance, in the same units.

  Practice:A11B9

• Breast line

  F_breast = W × H ÷ V

  T_line = W × L ÷ V

  H, V = how far the load is pulled sideways and how far it hangs below its suspension point; L = √(H² + V²).

  Practice:A16

• Fleet angle

  Fleet angle = arctan(offset ÷ distance)

  About 1.5° max for a smooth drum, 2° for grooved.

  Practice:A17B16

• Tilting a two-point object

  Height difference = d × sin(tilt)

  d = distance between the picks, measured along the object.

  With the CG below the picks, the higher pick takes more load.

  Practice:B13

Conversions

Not on the official sheet. Know these from memory.