236 STRESSES IN SIMPLE TRUSSES. Art. 127. 



For a partial live load, there must necessarily be some partial 

 panel loads ; for, if the head of the uniform live load is at a panel 

 point, the live load at that point is }P, an( i if it extends into the 

 panel, the panel load ahead will be less than y 2 P and the one be- 

 hind, less than P. It is an easy matter to let the head of the load 

 extend into the panel a distance x, write an equation for the 

 shear or moment whose maximum is desired, in terms of x, and 

 then to find the derivative of the shear or moment with respect to 

 X] placing this equal to zero, the value of x which will give the 

 desired maximum is found. 1 This, however, is a useless re- 

 finement, as the actual loads are not uniform and the true 

 stresses may vary greatly from those found by the use of the 

 uniform live load. It is always assumed (and this assumption 

 is on the safe side) that the live load is added a full panel load 

 at a time. The partial panel load ahead is neglected. We have 

 then to deal with full panel loads only, for both dead load and 

 live load. The dead load, of course, always acts as a full- load 

 over the entire bridge, but when the live load is considered, it 

 will be necessary to deal with partial loads as well as with full 

 load. 



It is sometimes convenient to calculate the stresses in a 

 truss for unit panel loads. The stresses for any other panel 

 load may then be gotten by proportion on the slide rule. In the 

 same way trusses may be gotten for a similar truss of different 

 dimensions, if all the angles between members are the same. 

 This is apparent, if it is remembered that, for any particular 

 loading, the stress diagrams made for different panel loads will 

 be similar figures. 



In trusses with parallel thords, it is more convenient to 

 write the stresses first, for the unit panel loads, in terms of func- 

 tions of the angle of inclination of the diagonal members with 

 the vertical, because these may be written by inspection and errors 

 arc less liable to occur. Thus if the stress in n diagonal mem- 

 ber is 4JP sec 6, 4J is called the coefficient of stress for this 

 particular member, while P sec is the same for all diagonals. 



The algebraic methods of getting stresses are usually pre- 

 ferred, particularly for trusses with parallel chords. If a stress 

 is determined by considering some joint, that joint should be 

 chosen at which the determination is the simplest. When the 



1 See Johnson's Modern Framed Structures, Ninth Edition, Part I, Art. 82. 



