# Drawbridge - Force and Moment vs. Elevation

## Calculate the acting forces and moments when elevating drawbridges or beams.

### Horizontal Beam/Drawbridge

For a beam supported at one end - like a typical drawbridge - the resultant force acting on the bridge can be calculated as

*F = q L *

* = m g L (1)*

*where *

*F = resultant force or weight (N)*

*q = uniform distributed load or weight (N/m)*

*L = length of beam or bridge (m)*

*m = continuous distributed mass (kg/m)*

*g = acceleration of gravity (9.81 m/s ^{2})*

For an uniform distributed load the resultant force F will act in distance

*a = L / 2 (2)*

The moment acting in A can be calculated as

*M = F a (3)*

* = F L / 2 (3b)*

**Note!** The generic eq. 3 can be used for any combination of distributed or point loads.

#### Example - Moment with Horizontal Beam/Drawbridge

The total weight - or resultant force - of a *10 m* HE-B 340B steel beam with continuous mass *134 kg/m* can be calculated as

*F = (134 kg/m) (9.81 m/s ^{2}) (10 m) *

* = 13145 N*

The acting distance a for the resultant force or weight can be calculated as

*a = (10 m) / 2*

* = 5 m*

The moment acting in A can be calculated as

*M = (13145 N) (5 m)*

* = 65725 Nm*

### Elevated Beam/Drawbridge

For and elevated beam or drawbridge the distance between the action force F and the moment in A varies. For a lifting angle the distance can be calculated as

*a = cos(α) L / 2 (4)*

* where *

*α = lifting angle (degrees)*

Eq. 3 for the moment can be modified to

*M = F cos(α) L / 2 (5)*

#### Example - Moment for Elevated Beam/Drawbridge

The beam from the example above is lifted *30 degrees*. The moment in A can be calculated

*M = (13145 N) cos(30 degrees) (10 m) / 2 *

* = 56920 Nm*

### Elevation Beam/Drawbridge Calculator

Default values are from the examples above where a = L / 2 in horizontal position. The calculator is generic and can be used for any uniform or point load combination as long as the resultant force ** F** and point of action

**can be calculated.**

*a* *F - resultant force or weight (N)*

* a - distance between resultant force and A in horizontal position (m)*

#### Drawbridge Lifting Moment

Lifting moment (%) related to maximum start moment at elevation 0 degrees.