GIRDERS AND TRUSSES 125 



The theory of coefficients is as follows: Assuming the truss 

 to be symmetrically loaded with uniform loading on each panel, 

 half the load on the middle panel alternately pulls and pushes 

 (or pushes and pulls) on all the web members until the end of the 

 truss is reached. Each panel load, as its point of application is 

 reached, is added and the end web member carries half the entire 

 load on the truss. Thus the load on the web members increases 

 from the center to the ends and the load on a chord increases from 

 the ends to the center. The end half panel load is carried by the 

 abutment. It creates no stress in the truss. 



For irregular and unsymmetrical loading find the reactions as 

 for a simple beam similarly loaded with concentrated loads, and 

 the panel joint where the maximum moment occurs is the point 

 of zero shear. From this point the loads run up and down the 

 web members to the ends, instead of from the center panel, as in 

 the case of uniform and symmetrical loading. For unsymmetri- 

 cally loaded trusses the weight per panel is used instead of the 

 proportion of weight (coefficient). 



A truss being merely a skeleton beam, a study of the manner 

 in which the loads go to the abutments shows that the weight 

 on each panel is really the shear on the panel. It is thus feasible 

 and practical to consider the truss as a beam and from the re- 

 action at either end subtract in succession the loads on the panel 

 joints until the point of zero shear is reached. In Fig. 80 is 

 shown a truss with the shear diagram. The shear on gh = 

 25,000 Ibs. ; on ef = 15,000 Ibs. ; on cd = 5000 Ibs., the panel load 

 being 10,000 Ibs. concentrated at the joints. The skeleton truss 

 lies on the center lines of the members, the panel length being 

 10 ft. and the height 10 ft. The length of a diagonal - 14.14 ft., 



, 14.14 x 25,000 

 so the compression in gh - - =^ 35,950 Ibs. The 



, 14.14 x 15,000 01 _ 

 compression in ef - - ^ 21,750 Ibs. The com- 



14.14 x 5000 

 pression in dc - - r^r - - 7190 Ibs. 



With the load considered as applied on the upper chord the 

 tension in gf - 15,000 Ibs.; the tension in ec - 5000 Ibs.; and 

 the tension in bd - 0. With the load considered as applied on 

 the lower chord the tension in gf - 25,000 Ibs. ; the tension in ec 

 - 15,000 Ibs.; and the tension in bd - 5000 Ibs. 



