Intro
Structural engineers often refer to uniform loadings but such ideal loadings apply, at best, to dead loads (slabs for example). Actual live loads are unlikely to be uniform. I tabulate maximum moments for several variations in simple beam loading, in each case using a unit total load magnitude but different load geometries.
I found my results slightly surprising.
RESULTS
For the ideal uniform load: 
Setting the total load
, we have 
For the single concentrated load:
(*) [2.0]
For the double concentrated load: 
(*) [1.33]
For the triple concentrated load: (*) [1.33]
For the quadruple concentrated load: 
(*) [1.20]
For the quintuple concentrated load: (*) [1.20]
For the N (N is odd) concentrated load:
For the N (N is even) concentrated load: 
For the sine function load:
(*) [1.27]
For the centered triangular load: (*) [1.33]
For the right side triangular load: 
(*) [1.03]
Setting the total load
, we have For the single concentrated load:
(*) [2.0]
For the double concentrated load: (*) [1.33]
For the triple concentrated load: (*) [1.33]
For the quadruple concentrated load: (*) [1.20]
For the quintuple concentrated load: (*) [1.20]Yes, there’s a pattern.
For the N (N is odd) concentrated load:
For the N (N is even) concentrated load: For the sine function load:
(*) [1.27]For the centered triangular load:
(*) [1.33]
For the right side triangular load: (*) [1.03]Conclusions
All of the loadings marked (*) produce a maximum moment that is larger than that of the unform load of equivalent magnitude.
The loadings marked [x.xx] produce a maximum moment that is this factor times that of the unform load of equivalent magnitude.
Calculations
