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Beam Loads - Support Force Calculator

Calculate beam load and supporting forces.

Beam - loads and support force

Online Beam Support Force Calculator

The calculator below can be used to calculate the support forces - R1 and R2 - 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

F1 + F2 + .... + Fn = R1 + R2                           (1)


F = force from load (N, lbf)

R = force from support (N, lbf)

In addition for a beam in balance the algebraic sum of moments equals zero. The moment balance can be expressed as

F1 af1 + F2 af2 + .... + Fn afn = R ar1 + R ar2                               (2)


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 F1 and F2, each 500 kg. The support forces F3 and F4 can be calculated

(500 kg) (9.81 m/s2) + (500 kg) (9.81 m/s2) = R1 + R2 


R1 + R2 = 9810 N

         = 9.8 kN

Note! Load due to the weight of a mass - m - is mg Newton's - where g = 9.81 m/s2.

With symmetrical and equal loads the support forces also will be symmetrical and equal. Using

R1 = R2

the equation above can be simplified to

R1 = R2 = (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 (R1), 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/s2) + (1000 kg) (9.81 m/s2) = R1 + R2 


R1 + R2 = 14715 N

       = 14.7 kN

The algebraic sum of moments (2) can be expressed as

(500 kg) (9.81 m/s2) (1 m) + (1000 kg) (9.81 m/s2) (6 m) =?R1 (0 m) + R2 (10 m)


R2 = 6377 (N)

    = 6.4 kN

F3 can be calculated as:

R1= (14715 N) - (6377 N)

    = 8338 N

    = 8.3 kN

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Related Topics

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  • Mechanics

    The relationships between forces, acceleration, displacement, vectors, motion, momentum, energy of objects and more.
  • Statics

    Forces acting on bodies at rest under equilibrium conditions - loads, forces and torque, beams and columns.

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