# Pulling force at end of a section

Calculations of pulling force or pulling tensions for cable trays are similar to those for pulling cable in conduit, adjusting the coefficient of friction to reflect using rollers and sheaves.

If the sheaves in the bends in cable trays are well-maintained, they will not have the multiplying effect on tension that bends in conduit have. The sheaves will turn with the cable, allowing the coefficient of friction to be assumed zero. This results in the commonly-used approximation for conduit bend equation becoming one. Even though cable tray bends produce no multiplying effect, it is essential for heavier cables to include the force required to bend the cable around the sheave. If the sheaves are not well-maintained, the bend will have a multiplying effect. The tension in the pull must then be calculated using the same equations used for installations in conduit.

Pulling lubricants must be compatible with cable components and be applied while the cable is being pulled. Pre-lubrication of the conduit is recommended by some lubricant manufacturers.

Symbol
$F_{out}$
Unit
daN
Formulae
 $L_{p} \mu_{p} w_{p} + T_{in}$ Horizontal straight section $L_{p} w_{p} \left(\mu_{p} \cos{\left(\theta_{p} \right)} + \sin{\left(\theta_{p} \right)}\right) + T_{in}$ Inclined straight section, pulling up $- L_{p} w_{p} \left(- \mu_{p} \cos{\left(\theta_{p} \right)} + \sin{\left(\theta_{p} \right)}\right) + T_{in}$ Inclined straight section, pulling down $L_{p} w_{p} + T_{in}$ Pulling straight up $- L_{p} w_{p} + T_{in}$ Pulling straight down $T_{in} \cosh{\left(\mu_{p} \phi_{p} w_{p} \right)} + \sqrt{R_{p}^{2} m^{2} + T_{in}^{2}} \sinh{\left(\mu_{p} \phi_{p} w_{p} \right)}$ Horizontal bend section $- \frac{R_{p} m \left(2 \mu_{p} w_{p} \sin{\left(\phi_{p} \right)} + \left(\mu_{p}^{2} w_{p}^{2} - 1\right) \left(e^{\mu_{p} \phi_{p} w_{p}} - \cos{\left(\phi_{p} \right)}\right)\right)}{\mu_{p}^{2} w_{p}^{2} + 1} + T_{in} e^{\mu_{p} \phi_{p} w_{p}}$ Vertical concave up bend, pulling up $- \frac{R_{p} m \left(2 \mu_{p} w_{p} e^{\mu_{p} \phi_{p} w_{p}} \sin{\left(\phi_{p} \right)} + \left(\mu_{p}^{2} w_{p}^{2} - 1\right) \left(e^{\mu_{p} \phi_{p} w_{p}} \cos{\left(\phi_{p} \right)} - 1\right)\right)}{\mu_{p}^{2} w_{p}^{2} + 1} + T_{in} e^{\mu_{p} \phi_{p} w_{p}}$ Vertical concave up bend, pulling down $\frac{R_{p} m \left(2 \mu_{p} w_{p} e^{\mu_{p} \phi_{p} w_{p}} \sin{\left(\phi_{p} \right)} + \left(\mu_{p}^{2} w_{p}^{2} - 1\right) \left(e^{\mu_{p} \phi_{p} w_{p}} \cos{\left(\phi_{p} \right)} - 1\right)\right)}{\mu_{p}^{2} w_{p}^{2} + 1} + T_{in} e^{\mu_{p} \phi_{p} w_{p}}$ Vertical concave down bend, pulling up $\frac{R_{p} m \left(2 \mu_{p} w_{p} \sin{\left(\phi_{p} \right)} + \left(\mu_{p}^{2} w_{p}^{2} - 1\right) \left(e^{\mu_{p} \phi_{p} w_{p}} - \cos{\left(\phi_{p} \right)}\right)\right)}{\mu_{p}^{2} w_{p}^{2} + 1} + T_{in} e^{\mu_{p} \phi_{p} w_{p}}$ Vertical concave down bend, pulling down $T_{in} e^{\mu_{p} \phi_{p} w_{p}}$ Approximation for bends
Related
$L_{p}$
$m$
$\phi_{p}$
$R_{p}$
$\theta_{p}$
Used in
$F_{cable}$
$s_{roll}$
$SP_{p}$