# Pulling force

Calculations of pulling forces 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 the force 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 pulling force 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.

The approximate results display only the pulling forces at the end of the respective sections, while the forwand and backward direction tabs display the pulling forces all along the route. The approximate results also use a simplified equation for bends, which does not consider the gravitational forces or the vertical elevations.

Symbol
$F_{pull}$
Unit
N
Formulae
 $F_{pull}+F_g L_{leg} \left(sin\left(\phi_{el}\right)+K_{dyn} cos\left(\phi_{el}\right)\right)$ Straight section $F_{pull} e^{K_{dyn} \phi_{arc}}$ Bend (approximation) $F_{pull} cosh\left(K_{dyn} \phi_{arc}\right)+sinh\left(K_{dyn} \phi_{arc}\right) \sqrt{{F_{pull}}^2+\left(F_g r_{arc}\right)^2}$ Horizontal bend $F_{pull} e^{K_{dyn} \phi_{arc}}-\frac{F_g r_{arc}}{1+{K_{dyn}}^2} \left(2K_{dyn} sin\left(\phi_{arc}\right)-\left(1-{K_{dyn}}^2\right) \left(e^{K_{dyn} \phi_{arc}}-cos\left(\phi_{arc}\right)\right)\right)$ Vertical upward bend, pulling up $F_{pull} e^{K_{dyn} \phi_{arc}}+\frac{F_g r_{arc}}{1+{K_{dyn}}^2} \left(2K_{dyn} e^{K_{dyn} \phi_{arc}} sin\left(\phi_{arc}\right)+\left(1-{K_{dyn}}^2\right) \left(1-e^{K_{dyn} \phi_{arc}} cos\left(\phi_{arc}\right)\right)\right)$ Vertical downward bend, pulling up $F_{pull} e^{K_{dyn} \phi_{arc}}+\frac{F_g r_{arc}}{1+{K_{dyn}}^2} \left(2K_{dyn} sin\left(\phi_{arc}\right)-\left(1-{K_{dyn}}^2\right) \left(e^{K_{dyn} \phi_{arc}}-cos\left(\phi_{arc}\right)\right)\right)$ Vertical downward bend, pulling down $F_{pull} e^{K_{dyn} \phi_{arc}}-\frac{F_g r_{arc}}{1+{K_{dyn}}^2} \left(2K_{dyn} e^{K_{dyn} \phi_{arc}} sin\left(\phi_{arc}\right)+\left(1-{K_{dyn}}^2\right) \left(1-e^{K_{dyn} \phi_{arc}} cos\left(\phi_{arc}\right)\right)\right)$ Vertical upward bend, pulling down
Related
$L_{leg}$
$\phi_{arc}$
$\phi_{el}$
$r_{arc}$
Used in
$F_{rad}$