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 flat floor also applies, set by the number of suspension ropes. The required factor of safety is the greater of Formula (36) and the floor.

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. This is a limit on the formula's validity; the sheave-ratio requirement itself is a separate check, set out below.

Step 3 — the flat floor

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

For a two-rope system RopeFactor applies 16. ISO 8100-1 §4.5.2.2.3 permits 12 for two lifetime-tested ropes; RopeFactor does not apply that reduction and takes the stricter value. The certified-rope declaration below changes the sheave-ratio limit only, never the floor.

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

The sheave-ratio check, D_t/d_r

Separately from the safety factor, ISO 8100-1 §4.5.2.1 (Table 11) sets a minimum ratio of traction-sheave diameter to nominal rope diameter.

• Standard ropes: D_t/d_r ≥ 40.
• Lifetime-tested ropes: D_t/d_r ≥ 30, for a rope of 4 to under 8 mm nominal diameter carrying a fatigue-lifetime-test certificate per ISO 8100-1 §4.5.1.2.1 b) (Table 10). Table 10 lists no rope of 8 mm or more, so a larger rope stays at 40 whatever its certificate.

The lower limit is not applied automatically. The engineer declares it by setting Fatigue-tested / certified rope? to Yes on the ISO input form, and the report then prints the basis on the sheave-ratio line, for example:

PASS — D/d 36.0 accepted per lifetime-tested rope, ISO 8100-1 §4.5.2.1 Table 11 (limit 30)

Below 30 the check warns even for a certified rope. For a certified rope of 8 mm or more the declaration does not apply, and below 40 the sheave-ratio line warns and states the rope's diameter as the reason. The declaration has no effect on the flat floor or on Formula (36), which remains valid only at D_t/d_r ≥ 40; a certified rope between 30 and 40 passes the sheave-ratio check while its required safety factor is the flat floor.

Under ASME A17.1 the sheave ratio is a flat D_t/d ≥ 40 (§2.24.2.2) with no certified-rope provision, and the declaration is not shown.

The resulting minimum, by geometry

Computed from Formula (36) and the 12 floor (three or more ropes). The requirement is always the larger of the two. In the tinted cells the floor is the larger, so the floor is the requirement and the bracketed figure is what Formula (36) produced and 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 floor, the floor 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