The following simple illustration will walk us through formulas relating to beam load calculations or, more accurately, beam reactions:
Referring to the diagram alongside, let’s consider a beam being supported at its ends (left and right), denoted by the letters A and B respectively.
Let there be point loads acting on the beam over positions marked as W1, W2, and W3.
RA = Reaction at the end A of the beam.
RB = Reaction at the end B of the beam.
Now, there are primarily a couple of forces (turning effect) that’s acting over the beam ends A and B viz. clockwise and anti-clockwise moment of force.
Since the moment of force over a supported beam is equal to the product of Force (weight here) and its distance from the support or the pivot, total clockwise moment acting at point A may be given as:
W1.a + W2.b + W3.c,
Also, the anticlockwise moment of force acting over point B must be:
Now because the beam is in equilibrium, implies that the above two moments of force must be equal in magnitudes, therefore equating the two expressions gives:
W1.a + W2.b + W3.c = RB.l
RB =W1.a + W2.b + W3.c / l
The equilibrium with the beam also implies that:
RA + RB = W1.a + W2.b + W3.c
RA = ( W1.a + W2.b + W3.c) - RB
Now as per the conditions of equilibrium, the algebraic sum of all horizontal components in the above expression becomes immaterial and can be nullified (ƩH = 0.)
Therefore, the final equation becomes
RA = ( W1 + W2 + W3) - RB
The above formula may be used for finding out the reaction of a loaded beam about its end supports.