Depth of the section of a simply supported beam carrying a mid span point load
(Strength of Materials – by Er. R.K. Rajput)
Generally, the beams which carry the loads have the uniform section throughout their length but their bending moments that are loaded will vary section to section along their length. The stresses which are in the extreme fibers of the beams above and below the neutral axis will also vary section to section along the length of the beam. Therefore, all the extreme fibers which can be loaded up-to maximum permissible stress (sigma max) are not loaded to their capacity. So, to apply the maximum load in a beam’s material, one needs to calculate the depth of the cross section of the beam which is given by the above formula.