EXTERNAL FORCES 37 



The maximum moment will occur twice on the span as the load 

 moves along, the moments being equal and distant one-fourth a 

 from the middle of the span. The maximum shear is at one end 

 when one of the wheels is 



directly over the edge of the j* " a '2^ 



support. j (fo i ('J . 



In Fig. 31 is illustrated the --fc- 

 case of two unequal loads at L 



fixed distance apart, moving 



Fig. 31 Two Unequal Rolling Loads 

 across a span. The maximum at Fixed Distance Apart 



moment is under the heavier 



load. The maximum end shear is under the heavier load when it 



is over the edge of the support. 



Let to = weight of lighter wheel load (A). 

 W - total load = A + B. 

 a = distance center to center of wheels. 

 y = distance from heavier wheel to mid-span. 

 Mmax = maximum bending moment under heavier load. 



wa 



In Fig. 32 is shown a graphical method for ascertaining the 

 bending moment when a load occupies a definite length on the 

 beam. The triangle is first drawn as though the entire weight 

 was concentrated at the center of gravity of the load. Drop ver- 

 tical lines from the ends of the load to intersect the triangle. 

 Connect the points of intersection by a straight line. Use this 

 line as the base of a parabola, which is then constructed as shown. 

 This method is also used if one end of the load rests on one 

 abutment. 



Overhanging Beams 



When beams overhang one or two supports the methods for 

 obtaining reactions, bending moments, and shears are no different 

 from those used for cantilever beams and beams resting freely 

 on two supports. The three examples following are from Greene's 

 "Structural Mechanics" ($d ed.). 



