CHAP. XVI.] THE INVERTED ARCH. 339 



The maximum moment itself is 

 A 2 A 2 (1 - 



2 Z 2 m=(5/5-in Z 2 m=0.18034 Z 2 m. 



2 ?tt (1 - F) 1 + 



For a simple girder uniformly loaded, the maximum moment 

 is %p 1?. The maximum moment is then reduced from \ tc 

 0.18, or to about |<l, or is faths the maximum moment for a 

 simple girder of same span and load.* 



If we represent the dead load by^, then, since the stiffening 

 truss sustains only the moving load, we have 



0.18 m Z 2 _ 36 m . j m (0.6 If 

 i (p -\- m) 1? p + m % (p + m) &' 



That is, the maximum moment in the stiffening truss is tht 

 same as for a simple girder of^ths the span, loaded only with 

 the moving load. 



19. Summary, The reaction at the end abutment and the 

 chain reaction at each apex having been found, as above, for 

 any given load, we might have found the strains in every 

 piece by the method of Arts. 8-13. This would, however, in 

 this case have proved long and tedious. The construction of 

 the curve of maximum moments and shear is preferable. 



We can therefore readily determine the strains in such a 

 combination as that represented in Fig. 111. We have already, 

 Arts. 90-94, given practical and simple methods for the deter- 

 mination of the strains in braced arches of the usual forms of 

 construction. 



It will be observed that it is by no means necessary that the 

 arrangement of bracing and flanges should be the same as that 

 shown in Figs. 90 and 94. 



Thus we may treat the arch represented in Fig. 5 (c) accord- 

 ing to Art. 158. as hinged at both abutments and crown, or, 

 making the lower flange continuous at the crown, we may find 

 the resultant pressures at the abutments by Art. 159, and then 

 follow these pressures through precisely as shown in the Fig. 



The combination of Fig. Ill being of considerable impor- 

 tance, as the more usual form of construction of suspension 

 bridges, and not falling under our classification of " braced 

 arches," we have considered it desirable to discuss it somewhat 



* Rankine gives -/j-ths for a girder whose ends are fixed, the greatest mo 

 ment occurring for a load over ^ds the span. 



