Drawbridge - Force and Moment vs. Elevation

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/s²)

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/s²) (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

• Calculate maximum stress in drawbridge made as cantilever beam

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 a can be calculated.

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.

Temperature ^oC
K
^oF

Length m
km
in
ft
yards
miles
naut miles

Area m²
km²
in²
ft²
miles²
acres

Volume m³
liters
in³
ft³
us gal

Weight kg_f
N
lbf

Velocity m/s
km/h
ft/min
ft/s
mph
knots

Pressure Pa
bar
mm H₂O
kg/cm²
psi
inches H₂O

Flow m³/s
m³/h
US gpm
cfm