230 



CRITERION FOR MAXIMUM MOMENT. Art. 144. 



Substituting in the last equation for R^ and differentiating 

 we have for a maximum, 



(82) 



or 







This then is the condition for maximum moment at point 6. 

 With nothing but concentrated loads on the span, it will, in gen- 

 eral, be impossible to satisfy this condition unless there is a load 

 at 7 or 5, part of which may b3 counted with G 2 and part with G 3 



or GV When all of the load at 7 is counted with G 2 , 



and when all of it is counted with 3 , 



provided 



a L 



this particular position gives a maximum moment at 6. It 

 is evident that so long as equation (82) holds true, a change in x, 

 that is, a movement of the loads, so that one will come at 7, will 

 not change the moment 3/ 6 . This will not be true if the movement 

 causes any loads to pass 1, 5, 7, or 15, in which case G, G or G 2 

 may change. G will change if there is any uniform load on the 

 span, but in any case, the change in the moment M 6 will be slight 

 as it will be due to a small movement. Hence we may always 

 test by equation (82) with a load at 7 or 5, unless the uniform 

 load reaches 7 or 5. With the type of loads usually specified, the 

 uniform load would not reach 7 or 5. 



Equation (82) is used, therefore, to find what loads of those 

 on the span (with one at 7 or 5) will give a maximum moment at 

 6. Since several different loadings may each give a maximum, 

 the moments must be calculated to see which is the greatest of 

 these. With a little practice, it will not be necessary to test every 

 possible loading by equation (82). 



When c=y^2> as in a Warren truss, equation ($2) becomes 



G G^XG, 



L a 



When c=p or when alternate web members are vertical (as 

 in a Pratt truss) equation (82) becomes 



a 



n 



(84) 



