2'J2 



LIMITING SPANS. 



Art. 1 Hi. 



the center of gravity of the total load is on the other side of the 

 center (101). In this case the load near the 'center becomes the 

 point about which the maximum moment is desired, and various 

 positions must be tested by equation (84) which becomes 



G _ G, 



L " = % L x 



If the center of gravity of the total load is not easily located 

 (x being therefore unknown) we must calculate the location of 

 the center of gravity and determine if it is possible to have the 

 assumed loading on the span and still satisfy equation (85). 

 Then if P be the load near the center, placed ye from the center, 

 the loading will give a maximum moment at P if 



/~*1 I D /"* f^ fl 



Cr, -f- r (jr . (jri IT f<(\\ 



r^r > i and ^L^TTe < ~L'" 



The nearest wheel to the center of gravity does not always govern. 

 146. Limits of Span for which a Particular Series of 

 Wheel Loads will give a Maximum Moment. It is evident 

 that for a girder of less than about 80 ft. span, the maximum 

 moment will occur when the drivers of one engine are near the 

 middle of the span, and the smaller loads come on at both ends 

 as the span increases, until both tenders are also on. If a certain 

 number of wheels, say 5, give a maximum moment in a given 

 span length, and 6 in another span length, there must be an in- 

 termediate length for which both give the same moment. In Fig. 

 202 for a maximum moment under wheel 4, the center of the span 

 is 0.57 ft. to the left of the wheel, and in Fig. 203 it is 0.235 ft. to 

 the right. In each case we can find E^ and I/ ma x in terms of L. 



Fig. 203- 



Putting the maximum moments equal to each other and solving 

 for L we get the maximum span on which the loading of Fig. 202 

 governs, and minimum span on which that of Fig. 203 governs. 

 Of course we must test by equation (86) in order to make sure 



