LOAD

It cannot be derived because it is not theoretically correct. It is a conservative estimate of the load carried by beams which support rectangular slabs.

When S = L, m = 1 and the load on each beam is w*S²/3. The total load carried by all four beams is 4w*S²/3, one third more than the actual load.

When L = 2*S, m = 1/2 and the sum of loads on all four beams turns out to be 1.25w*S*L which is 25% more than actually exists.

When L > 2*S, you should treat it as a one way slab and omit beams in the short direction.

Two way rectangular panels are not used very much. Flat slabs or flat plates seem to be more popular because of the economy of the forms.

Thank you very much sir Bruce, a couple of year this hung up also. Now i realize that this conservative formula is applicable only to working stress design, actually im not using this one( why using the one that you dont know what it is). I know that the actual distribution of load to a supported beam( two way distribution) is triangular and trapezoidal( rectangular panel) but for simplier purposes we make it uniform.