Art. 157. 



GRAPHICAL METHODS. 



313 



These three fractions are the slopes of the lines EK, EM, 

 and EF, and since the slope of EF is greater than that of EM, 

 and less than that of EK, wheel 11 at I) will give a maximum 

 moment. 



Therefore, when a thread stretched between the points where 

 verticals from the ends of the span cut the "load line/' intersects 

 the "step" over the load at the point tvhere a maximum moment 

 is wanted, this position will cfive one of the maximum moments 

 ai the point. 



Having found the proper position of the load, the moment 

 at D may be found graphically by placing a diagram of the truss 

 on an equilibrium polygon for the typical loading, which must 

 be drawn to the proper scale. After drawing the closing line 

 the moment may be scaled off. 1 



To find the position of the loads for maximum shear in a panel 



C 1 C 1 



we have from equation (89) - = , G being the total load on the 



A. LJ p 



span,, and G 2 the load in the panel in which the maximum shear is 

 wanted. In Fig. 209 lay off A'C' equal to one panel length, regard- 

 less of position for a maximum. Now if lines be drawn through 1, 



C 1 

 2', 3', etc., from A', their slopes will equal . Now if we make 



A'B'=AB, B'T V B'T 2J B'T S , etc., will represent the total load 

 which may be on the span in order that equation (89) may 

 be satisfied, when wheels 1, 2, 3, &c, respectively, are at the right 

 hand end of the panel in question. Projecting points T lf T 2 , T 3 , 

 &c on to the load line, we see that load 4 must be at B, the right 

 hand end of the bridge, when load 1 is at the right hand end of 

 the panel in question. That is, wheel 1 must be at the right hand 

 end of all panels w r hich it passes in going from B towards A, for 

 maximum shears in those panels, until wheel 4 reaches B, or 

 wheel 1 is said to govern for this distance. Likewise wheel 2 gov- 

 erns at all panel points which it passes when the load moves from 

 wheel 4 at B to wheel 10 at B, and wheel 3 governs at all points 

 which it passes when the load moves from wheel 10 at B to wheel 

 16 at B. The distances that the wheels move while they govern, 

 are called their respective "fields of shear/ 1 and it will be found 

 that these fields overlap by distances equal to the distances be- 

 tween the successive wheels. 



1 A convenient form of equilibrium polygon and a description of this 

 method may be found by looking up the reference given on page 312. 



