Beam Loads  Support Force Calculator
Calculate beam load and supporting forces.
Online Beam Support Force Calculator
The calculator below can be used to calculate the support forces  R_{1} and R_{2}  for beams with up to 6 asymmetrically loads.
For a beam in balance loaded with weights (or other load forces) the reactions forces  R  at the supports equals the load forces  F. The force balance can be expressed as
F_{1} + F_{2} + .... + F_{n} = R_{1} + R_{2} (1)
where
F = force from load (N, lb_{f})
R = force from support (N, lb_{f})
In addition for a beam in balance the algebraic sum of moments equals zero. The moment balance can be expressed as
F_{1 }a_{f1} + F_{2 }a_{f2} + .... + F_{n }a_{fn} = R a_{r1} + R a_{r2 } (2)
where
a = the distance from the force to a common reference  usually the distance to one of the supports (m, ft)
Example  A beam with two symmetrical loads
A 10 m long beam with two supports is loaded with two equal and symmetrical loads F_{1} and F_{2}, each 500 kg. The support forces F_{3} and F_{4} can be calculated
(500 kg) (9.81 m/s^{2}) + (500 kg) (9.81 m/s^{2}) = R_{1} + R_{2}
=>
R_{1} + R_{2} = 9810 N
= 9.8 kN
Note! Load due to the weight of a mass  m  is mg Newton's  where g = 9.81 m/s^{2}.
With symmetrical and equal loads the support forces also will be symmetrical and equal. Using
R_{1} = R_{2}
the equation above can be simplified to
R_{1} = R_{2} = (9810 N) / 2
= 4905 N
= 4.9 kN
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Example  A beam with two not symmetrical loads
A 10 m long beam with two supports is loaded with two loads, 500 kg is located 1 m from the end (R_{1}), and the other load of 1000 kg is located 6 m from the same end. The balance of forces can be expressed as
(500 kg) (9.81 m/s^{2}) + (1000 kg) (9.81 m/s^{2}) = R_{1} + R_{2}
=>
R_{1} + R_{2} = 14715 N
= 14.7 kN
The algebraic sum of moments (2) can be expressed as
(500 kg) (9.81 m/s^{2}) (1 m) + (1000 kg) (9.81 m/s^{2}) (6 m) =?R_{1} (0 m) + R_{2} (10 m)
=>
R_{2} = 6377 (N)
= 6.4 kN
F_{3} can be calculated as:
R_{1}= (14715 N)  (6377 N)
= 8338 N
= 8.3 kN
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