160 STEEL RAILWAY BRIDGES. CHAP. IV. 



loading for a span equal to two panel lengths. It is necessary to calculate the maximum end 

 shears and the shears at intermediate points by wheel concentrations, or to use equivalent uni- 

 form loads calculated for wheel concentrations. The calculated values of the moment, M, 

 shear, S, and floorbeam reaction, R, for Class E 60 are given in Table III. The equivalent 

 uniform load method has been advocated very strongly by Mr. J. A. L. Waddell who has de- 

 scribed its use in detail in his " De Pontibus." Live load stresses as calculated by the method 

 of equivalent uniform loads are too small for the chords and webs between the ends of the truss 

 and the quarter points, and are too large between the quarter points. The stresses obtained 

 for the counters are too large. The live load stresses calculated by the method of equivalent 

 uniform loads are sufficiently accurate for all practical purposes. Even though the equivalent 

 uniform load method is simple to apply and gives results which are sufficiently accurate, it is now 

 seldom used. 



Uniform Load and One or Two Excess Loads. A uniform load is used and to provide for 

 the wheel concentrations one or two excess loads are assumed to run on top of the uniform load. 

 This method is now rarely used. In a paper entitled "Rolling Loads on Bridges," published in 

 Bulletin No. 161, Am. Ry. Eng. Assoc., November 1913, Mr. J. E. Greiner, Consulting Engineer, 

 found that thirty-eight of the thirty-nine most important railroads in the country used a system 

 of wheel concentrations, and one road used a uniform load with a single excess load; the method 

 of equivalent uniform loads was not used. 



MAXIMUM STRESSES. The conditions of live loading for maximum stresses in beams 

 and trusses are as follows. 



Uniform Live Load on Beam or Girder. For bending moment the span should be fully 

 loaded. For shear the longer segment of the span should be loaded. 



Equal Joint Loads. For bending moment (chord stresses) the bridge should be fully loaded. 

 For shear (web stresses in trusses with parallel chords) the longer segment. of the truss should be 

 loaded for maximum stress, and the shorter segment of the truss should be loaded for maximum 

 counter stress (minimum stress). 



Point of Maximum Bending Moment in a Beam. The maximum bending moment in a 

 beam loaded with moving loads will come under a heavy load when this load is as far from one 

 end of the beam as the center of gravity of all the moving loads then on the beam is from the other 

 end of the beam. 



Wheel Loads, Bridge with Parallel Chords. The maximum bending moment at any joint 

 in the loaded chord will occur when the average load on the left of the section is equal to the 

 average load on the entire span. 



The maximum bending moment at any joint in the unloaded chord of a symmetrical Warren 

 truss will occur when the average load on the entire span is equal to the average load on the left 

 of the section, one-half of the load on the panel under the joint being considered as part of the 

 load on the left of the section. 



The maximum shear in any panel of a truss will occur when the average load on the panel is 

 equal to the average load on the entire bridge. 



Wheel Loads, Bridge with Inclined Chords. The criterion for maximum bending moment 

 in a bridge with vertical posts is the same as for bridges with parallel chords. 



For web members the criterion is that 



P/L = P,(i + ale)ll (I) 



where P = total load on the bridge; 



P 2 = load on the panel in question; 

 L = span of bridge; 

 / = panel length; 



a = distance from left, abutment to left end of panel in question; 



e distance from left abutment to intersection of top chord section of the panel produced 

 and the lower chord. (The intersection is to the left and outside of the span.) 



