306 CALCULATIONS OF MOMENTS AND SHEARS. Art. 155. 



=^0 Gi[a 



unusual because a load at 6 will increase the moment about 5', 

 while others to the left of the section decrease it. 







a 3 + 

 ~~L 



Substituting this value of ^ in the moment equation, we 

 have then when M<>' is a maximum. 



tt 



dx L La 



Equation (92) is the criterion for a maximum moment at any 

 point of the top chord. To satisfy this equation, a load will, in 

 general, have to stand at 6 so that a part of it may be considered 

 with GI and the remainder with G> Having determined the max- 

 imum moment at 5' the stress in 5-7 is easily obtained. 



155. Calculation of Moments and Shears by Wheel Loads. 



It is evident from the preceding discussions that, in the calcula- 

 tions involved in getting maximum stresses in girders and trusses, 

 it is necessary often to know the distance of any wheel from any 

 other wheel, the center of gravity of any number of wheels, the 

 left reaction, and the sum of the loads for any number of loads, 

 and the sum of the moments, about any wheel of a number of 

 preceding wheels. In order to save time and avoid mistakes as 

 much as possible, tables are made and carefully checked, showing 

 the total distances of each wheel from the first wheel, the total 

 weight at any wheel, of all the preceding wheels, and the sum of 

 the moments at any wheel of all the preceding wheels. 



Such a set of tables, which has been found of convenient 

 arrangement, is given below (pages 307-310). The tables are 

 made up for one rail of Cooper's E40 loading. 



A diagram might be made showing the position of the center 

 of gravity for any possible combination of loads. This would 

 reduce the number of forces on a span to two or three for the 

 determination of moments, shears and reactions. With a table, 

 however, these are determined by dealing with the individual 

 wheel loads. 



Another method of determining the moment at any point 

 of a truss or the shear in any panel, is to calculate the panel 

 concentrations, from the proper position of the loads and from 

 these, the resulting moments and shears. This may be done 



