In this article various topics are discussed regarding cable pulling, specifically the usage of weight correction factors and sidewall bearing pressure factors for pulling up to 6 cables in a duct. And we discuss about the conduit jamming ratio and how it is considered according to different manuals.
Posted 2021-06-07
Categories: Theory
Transportation, handling, and installation of cables causes often more mechanical stress than what is actually experienced during operation. Therefore, it is important to carefully plan the cable installation, which can be done in Cableizers updated cable pulling module.
The conductors of the cable are generally the only members that can bear the pulling forces without damage. Do not use metallic shielding wires, tapes, braids or armor not designed for the purpose in pulling tension calculations.
Pulling different conductor sizes at the same time is not recommended if the conductor size or other cable characteristics are significantly different. If you must pull different size conductors, it must be done with care.
Pulling additional cables into an existing conduit system is generally not recommended. If this must be done, extreme caution must be taken. Of special concern is the cutting action of the tensioned pulling rope.
When multiple cables are pulled together, their mechanical configuration in the conduit is changing along the route which exposes them to uneven forces, an imbalance that is causing additional frictional drag. The weight correction factor $f_{wc}$ is taking this into account by increasing the weight of cable assemblies consisting of more than one single cable.
Formulas for weight correction factors are mostly limited for pulling of up to 3 cables. Some formulas exist for pulling cable assemblies of 4 cables, but they were not leading to consistent results. Cableizer has extended the formulas for cable assemblies of up to 6 cables.
The following examples are calculated with a cable with an outer diameter $D_e$ of 37 mm and a conduit with an inner diameter $Di_d$ of 150 mm. In addition, all calculations are also done on the example of a very large conduit ($Di_d$ = 10 m) for validation reasons. In this case, the cables lie next to each other and do not rub against each other, and the weight correction factor should be negligible (i.e. equal to 1.0). As can bee seen in the following table, this is the case except for 5/6 cables which have a constant weight correction factor independent of the cable and conduit dimensions. As a consequence, the pulling force calculation in Cableizer for large conduits is rather conservative (i.e. on the safe side).
| Configuration | Formula | fwc (Did = 150 mm) | fwc (Did = 10 m) |
|---|---|---|---|
| 1 single cable | 1.0 | 1.0 | 1.0 |
| 2 cables | $\frac{1}{\sqrt{- \frac{D_{e}^{2}}{\left(- D_{e} + Di_{d}\right)^{2}} + 1}}$ | 1.06 | 1.00 |
| 3 cables triangular/triplex | $\frac{1}{\sqrt{- \frac{D_{e}^{2}}{\left(- D_{e} + Di_{d}\right)^{2}} + 1}}$ | 1.06 | 1.00 |
| 3 cables cradled | $\frac{1.33 D_{e}^{2}}{\left(- D_{e} + Di_{d}\right)^{2}} + 1$ | 1.14 | 1.00 |
| 4 cables diamond/quadruplex | $\frac{1.33 D_{e}^{2}}{\left(- D_{e} + Di_{d}\right)^{2}} + 1$ | 1.14 | 1.00 |
| 4 cables cradled | $\frac{2 D_{e}^{2}}{\left(- D_{e} + Di_{d}\right)^{2}} + 1$ | 1.21 | 1.00 |
| 5 cables | 1.4 | 1.4 | 1.4 |
| 6 cables | 1.4 | 1.4 | 1.4 |
The above figures show that the weight correction factor is as expected incrasing with an incrasing number of cables pulled together. Cradled configurations do have higher weight correction factors than when the cables are more organized (3 cables triangular/triplex or 4 cables diamond/quadruplex). If you are close to or exceeding the pulling force limits, it can therefore be of interest to investigate if binding the cables together can be an option.
Generally, manufacturers do also consider the influence of the weight correction factor when calculating the sidewall bearing pressure. In Cableizer, this is considered with the sidewall bearing pressure factor $f_{rad}$, which can be optionally selected. Its calculations is always dependent on the weight correction factor, but it can be applied to the calculations independently of the weight correction factor. A normal use case is to either apply both $f_{wc}$ and $f_{rad}$ or none of them.
The following examples are calculated with a cable with an outer diameter of 37 mm and a conduit with an inner diameter of 150 mm. The sidewall bearing pressure $F_{rad}$ is proportional to the sidewall bearing pressure factor and the pulling force. The pulling force $F_{pull}$ itself is proportional to the weight correction factor and the gravitational force. The gravitational force $F_g$ itself is proportional to the number of cables $N_c$ being pulled together. As a consequence, the factor $f_{rad} \cdot f_{wc} \cdot N_c$ indicates to what extent the sidewall bearing pressure is increased as compared to the case where a single cable is being pulled.
| Configuration | Formula | frad | frad · fwc · Nc |
|---|---|---|---|
| 1 single cable | 1.0 | 1.00 | 1.00 |
| 2 cables | $\frac{f_{wc}}{2}$ | 0.53 | 1.12 |
| 3 cables cradled | $f_{wc} - \frac{2}{3}$ | 0.48 | 1.63 |
| 3 cables triangular/triplex | $\frac{f_{wc}}{2}$ | 0.53 | 1.68 |
| 4 cables cradled | $f_{wc} - \frac{3}{4}$ | 0.46 | 2.26 |
| 4 cables diamond/quadruplex | $\frac{f_{wc}}{2}$ | 0.57 | 2.61 |
| 5 cables | $f_{wc} - 1$ | 0.40 | 2.80 |
| 6 cables | $f_{wc} - 1$ | 0.40 | 3.36 |
The above figures show that the sidewall bearing pressure on the most exposed cable is increasing steadily with an increasing number of cables being pulled. As expected, cradled configurations do have lower sidewall bearing pressures than when the cables are more organized (3 cables triangular/triplex or 4 cables diamond/quadruplex).
Jamming is the wedging of three unbound cables when pulled into a conduit. This usually occurs because of crossovers when the cables twist or are pulled around bends. The conduit jamming ratio is the ratio of the conduit inner diameter $Di_d$ and the cable outside diameter $D_e$. When calculating jamming probabilities, a 5% factor is used to account for the oval cross-section of conduit bends. The cable diameters should be measured, since actual diameters may vary from the published nominal values.
Cableizer indicates the risk for jamming according to the following table. As shown, different references use different ranges for quantifying the jamming risk. Cableizer does only indicate the jamming ratio for Three cables unbound because even while jamming can occur when pulling four or more cables into a conduit, the probability is very low.
| Jamming ratio | 2.4 | 2.5 | 2.6 | 2.7 | 2.8 | 2.9 | 3.0 | 3.1 | 3.2 | |||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Cableizer / Southwire 1) | very small | small | moderate | significant | moderate | small | very small | |||||||||||||||||||||
| General Cable 2) | impossible | possible | probable | impossible | ||||||||||||||||||||||||
| IEEE Std 1185-2010 3) / Okonite 4) | ok | probable | ok | |||||||||||||||||||||||||
| Polywater 5) | ok | probable | ok | |||||||||||||||||||||||||
Always follow the instructions from the cable manufacturer when preparing your cable pull. While some manufacturers disregard the use of the weight correction factor (example from Brugg Cables), others include it in their calculations (example from Southwire). In Cableizer, both options can conveniently be calculated.
Cableizer specifically disclaims any warranties, including, but not limited to, the implied warranties of merchantability, accuracy, or fitness for any particular purpose of its calculation results.
