EXTERNAL FORCES 43 



The older method was given for the reason that it is so frequently 

 met with in handbooks and trade papers, but the method of modern 

 text books is preferable and should be used by the student in his 

 work. 



Equivalent Distributed Loads 



A convenient method to use in figuring bending moments when 

 one or more concentrated loads must be considered in addition 

 to a uniformly distributed load, is to reduce the concentrated 

 loads to equivalent distributed loads. Suppose we take the ex- 

 pression last given for the effect of a concentrated load at some 

 point of the beam: 



Let M 



Li O 



The problem is to find the value of W, the uniformly distributed 

 load. 



Arrange it thus, M = - 



o 



Eliminating fractions, SM = WL 



U7 



Dividing, W = f 



LJ 



The student can see that after obtaining the bending moment 

 for the concentrated load the bending moment had only to be 

 equated to that for a uniformly distributed load. If he does a 

 little thinking he will see that if the concentrated load is off center 

 very far the bending moment is greater than it is at the center of 

 the span, yet the equation of the uniformly distributed load was 

 made on the basis of the maximum moment being at the center of 

 the span. 



The method of equivalent uniformly distributed loads is in 

 common use in many designing offices, but only because it saves 

 a little time and because beams come in stock sizes. It always 

 gives a trifle larger beam than is necessary, so it is a safe method 

 to use. When the greatest possible economy is desired, or the 

 i size selected is on the border line between a heavy and a 

 li^ht beam, the exact method should be used to obtain the size, 

 as thereby considerable saving may be effected. The exact method 

 should be used also when a built-up girder is to be designed. 



The uniform load has been found. Divide it by the concentrated 

 load and get a factor we will call m. Then divide the span by the 



