KEVOS® MAKEOS · Mechanics
Wire Rope on Sheaves and Drums (Radial Pressure, Bending Stress and Load, Drum Capacity)
For a wire rope running over a sheave and onto a drum, is the radial pressure within the sheave material's limit, how much does bending add to the rope load, what factor remains against breaking, and will the drum hold the rope I need?
Check of a wire rope on its sheaves and drum by the handbook formulas: the radial pressure the rope exerts on the sheave tread from the tension, tread diameter and rope diameter against the allowable pressure for the sheave material; the bending stress in the outer wires from the rope modulus, wire diameter and sheave diameter, the rope's metal area and the equivalent bending load that adds to the direct tension; the factor of the rope's minimum breaking force over the tension plus bending load; and the length of rope a flanged drum or reel holds from its barrel, flange and width and the rope factor K.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Rope | ||
| Rope diameter | mm | Nominal diameter of the wire rope, from the rope certificate. |
| Outer wire diameter as a share of rope diameter | Diameter of an outer wire divided by the rope diameter; the handbook gives typical values by construction, for example 0.063 for 6 × 19 rope. | |
| Metal area factor Q (area = Q d²) | Factor that gives the rope's metal area as Q × d², which depends on the construction and core; the handbook lists values, for example 0.405 for 6 × 19 fibre core. | |
| Rope modulus of elasticity | MPa | Modulus of elasticity of the rope as a whole, lower than that of the wire; the handbook gives 69 000 to 97 000 MPa (10 to 14 million psi) with 83 000 MPa often used. |
| Rope tension | N | Direct tension in the rope where it runs over the sheave, including the load and any reeving friction. |
| Rope minimum breaking force | kN | Minimum breaking force of the rope, from the rope certificate or maker's catalogue. |
| Least factor required against breaking | Least factor of safety your application, code or standard requires for the rope. | |
| Sheave | ||
| Sheave tread (pitch) diameter | mm | Diameter of the sheave or drum at the bottom of the groove, where the rope bears. |
| Allowable radial pressure for the sheave material | MPa | Largest radial pressure recommended for the sheave or drum material and rope type, from the handbook's table or the sheave maker. |
| Drum | ||
| Drum barrel diameter | mm | Diameter of the drum or reel barrel the first layer winds on. |
| Drum flange diameter | mm | Outside diameter of the drum or reel flanges. |
| Width between flanges | mm | Clear width between the flanges. |
| Depth left unfilled below the flange rim | mm | Depth of the flange you leave unfilled to keep the rope from spilling over; zero for a full drum. |
| Rope factor K for this rope size (handbook Table 8) | ft/in³ | Factor from the handbook's drum and reel capacity table for the rope size, in feet of rope per cubic inch of winding space as tabulated; the tool converts units. |
| Rope length the drum must hold | m | Length of rope the drum or reel must store, including dead wraps. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
Rope
What this means: Rope diameter
- What it is
- Nominal diameter of the wire rope.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.5 mm to 200 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 14.2875 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger rope lowers the radial pressure for the same tension but raises the bending load.
- Get it right
- Use the catalogue size; 9/16 in is 14.29 mm.
What this means: Outer wire diameter as a share of rope diameter
- What it is
- Outer wire diameter divided by the rope diameter, which depends on the rope construction.
- Units and format
- Enter a plain number with no unit. The form accepts 0.005 to 0.3. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.063 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Thicker wires raise the bending stress and load.
- Get it right
- The handbook gives 0.106 for 6 × 7, 0.063 for 6 × 19, 0.045 for 6 × 37 and 0.050 for 8 × 19 rope.
What this means: Metal area factor Q (area = Q d²)
- What it is
- Factor that gives the metal area of the rope as Q × d².
- Units and format
- Enter a plain number with no unit. The form accepts 0.1 to 0.8. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.405 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Scales the equivalent bending load.
- Get it right
- The handbook lists values by construction and core, for example 0.405 for 6 × 19 fibre core and 0.475 for 6 × 19 IWRC.
What this means: Rope modulus of elasticity
- What it is
- Modulus of elasticity of the rope as a whole.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 1000 MPa to 300000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 82700 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Scales the bending stress and load.
- Get it right
- The handbook gives 10 to 14 million psi (about 69 000 to 97 000 MPa), with 12 million psi (about 83 000 MPa) often used.
What this means: Rope tension
- What it is
- Direct tension in the rope where it passes over the sheave.
- Units and format
- Enter a number in N: newtons. The form accepts 0.000001 N to 100000000 N. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 12000 N as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Raises the radial pressure and lowers the factor against breaking.
- Get it right
- Include the load share on this part of line and any reeving friction.
What this means: Rope minimum breaking force
- What it is
- Minimum breaking force of the rope.
- Units and format
- Enter a number in kN: kilonewtons (1 kN = 1000 N). The form accepts 0.000001 kN to 1000000 kN. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 150 kN as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Only changes the factor against breaking.
- Get it right
- Take it from the rope certificate, not a nominal catalogue figure for another grade.
What this means: Least factor required against breaking
- What it is
- Least factor of safety the rope must keep against breaking.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 50. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 5 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Only moves the pass or fail line.
- Get it right
- From the code or standard for your lifting application.
Sheave
What this means: Sheave tread (pitch) diameter
- What it is
- Diameter of the sheave or drum at the bottom of the rope groove.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 609.6 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger sheave lowers both the radial pressure and the bending load.
- Get it right
- Measure in the groove, not over the flanges.
What this means: Allowable radial pressure for the sheave materi…
- What it is
- Largest radial pressure the sheave or drum material should carry for this rope type.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.01 MPa to 1000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3.4 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Only moves the pressure check.
- Get it right
- The handbook gives maximums by material and rope; cast iron is lowest and manganese steel highest.
Drum
What this means: Drum barrel diameter
- What it is
- Diameter of the drum or reel barrel.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 457.2 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger barrel holds more rope per layer.
- Get it right
- Measure the barrel the first layer winds on.
What this means: Drum flange diameter
- What it is
- Outside diameter of the drum or reel flanges.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 762 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Larger flanges give a deeper winding space and much more capacity.
- Get it right
- Measure across the flange rims.
What this means: Width between flanges
- What it is
- Clear width between the drum or reel flanges.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 609.6 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Capacity rises in proportion to the width.
- Get it right
- Measure inside the flanges at the barrel.
What this means: Depth left unfilled below the flange rim
- What it is
- Depth below the flange rim left empty so the rope cannot spill over.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Reduces the winding depth and the capacity.
- Get it right
- Use zero for a full reel; leave a margin on working drums.
What this means: Rope factor K for this rope size (handbook Tabl…
- What it is
- Drum capacity factor for the rope size, in feet of rope per cubic inch of winding space, as the handbook tabulates it.
- Units and format
- Enter a number in ft/in³: ft/in³. The form accepts 0.001 ft/in³ to 100 ft/in³. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.741 ft/in³ as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Capacity is directly proportional to K.
- Get it right
- Read it from the handbook's drum and reel capacity table for your rope size; the tool converts the units.
What this means: Rope length the drum must hold
- What it is
- Length of rope the drum or reel must store.
- Units and format
- Enter a number in m: metres. The form accepts 0.000001 m to 1000000 m. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 600 m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Only moves the capacity check.
- Get it right
- Include dead wraps left on the drum and any spare length.
Method and formulas
- Radial pressure p = 2T ÷ (D d), with D the tread diameter and d the rope diameter.
- Outer wire diameter d_w = share × d; bending stress s_b = E d_w ÷ D; metal area A = Q d²; equivalent bending load P_b = s_b A.
- Factor against breaking = minimum breaking force ÷ (T + P_b).
- Winding depth A = (H − D − 2Y) ÷ 2; rope length L = (A + D) × A × B × K with dimensions in inches and L in feet, converted to metres.
- Example: 2.7556 MPa on the sheave against 3.4 MPa; bending adds 10.095 kN, leaving a factor of 6.7887, and the drum holds 780.56 m.
Limitations
- The drum capacity assumes even winding with the same number of wraps in each layer; uneven winding or spooling tension changes it.
- Allowable pressures, rope factors and moduli vary with rope construction, lay and condition; take them from the rope and sheave makers where you can.
- Fatigue life of the rope over sheaves is not estimated.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check a sheave or drum material against rope pressure
- Allow for bending when checking a rope around small sheaves
- Find whether a drum or reel holds the length of rope needed
Who it is for
- Lifting equipment designers
- Maintenance engineers
- Riggers and crane technicians
What you get
- Radial pressure on the sheave against the allowable
- Outer wire diameter, bending stress, metal area and equivalent bending load
- Factor against breaking on tension plus bending load
- Drum winding depth and rope capacity against the length needed
- Sheave-to-rope diameter ratio
Interpreting the result
- Radial pressure falls in proportion to sheave diameter, so a larger sheave protects both the groove and the rope.
- Bending load can be a large share of the tension on small sheaves; it is why rope makers set minimum sheave-to-rope ratios.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 3432–3435. Topic reference; no source tables or recommended settings are reproduced.
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