ISO 8100-2 minimum rope safety factor

ISO 8100-2 determines the minimum suspension-rope factor of safety from the equivalent number of bends, N_equiv, and the traction sheave-to-rope diameter ratio. A separate minimum value applies based on the number of suspension ropes. The required factor of safety is the greater of Formula (36) and that minimum value.

Sf_min = max( Formula (36) , flat floor )

Step 1 — the equivalent number of bends, N_equiv

N_equiv accounts for the traction sheave and the deflector pulleys in the rope path. The calculation applies weighting factors based on groove geometry, pulley diameter and whether each rope bend is simple or reverse. It is the sum of a traction term and a pulley term.

N_equiv = N_equiv(t) + N_equiv(p)

The traction term comes from the groove form. A plain U-groove has N_equiv(t) = 1.0. Undercut U-grooves and V-grooves take higher values from their geometry. Intermediate angles are interpolated.

• Plain U-groove: N_equiv(t) = 1.0.
• Undercut below 75°: the value ramps linearly from 1.0 at 0° to 2.5 at 75°.
• Double wrap doubles the traction term and adds two simple bends to the pulley term, because the rope passes the sheave twice.

Deflector pulleys are added by diameter and bend type:

N_equiv(p) = (D_t / D_p)⁴ × (N_ps + 4 · N_pr)

Deflector pulley influence varies with the fourth power of the traction-sheave-to-deflector-pulley diameter ratio. Reverse bends are assigned four times the weighting of simple bends.

Step 2 — Formula (36)

Sf = 10^( 2.6834 − log₁₀( 695.85×10⁶ · N_equiv / (D_t/d_r)^8.567 ) / log₁₀( 77.09 · (D_t/d_r)^−2.894 ) )

The formula only applies at D_t/d_r ≥ 40. Below that it is out of range, and the flat floor is the requirement.

Step 3 — the minimum value

• 12 for three or more suspension ropes.
• 16 for two ropes.

The minimum value often governs when the traction sheave-to-rope diameter ratio is relatively large or N_equiv is low.

The resulting minimum, by geometry

Computed from Formula (36) and the 12 floor (three or more ropes). Greyed cells are where the floor governs; the figure in brackets is what Formula (36) actually produced. The requirement is always the larger of the two, so in those cells the floor applies and the calculated value is not usable.

The table shows the effect of both variables. Increasing the D_t/d_r ratio reduces the value produced by Formula (36); increasing N_equiv increases it. Where Formula (36) falls below the applicable minimum value, the minimum value governs — past approximately D_t/d_r 55 that is the case across almost the whole range.

That is the metric job in the worked calculation example, where the actual factor of safety comes out at 16.96 against this 13.88.

Check a job against this