340 THE INVERTED ARCH [CHAP. XIV. 



fully. A better form of construction is that shown in Fig. 

 106, which is perfectly rigid, and the strains in which are 

 easily found by Art 158 or 159, according as we hinge it in 

 the centre or not. 



Reviewing now the preceding, we see that the graphical 

 method, as here developed, furnishes us with a simple, accurate 

 and practical solution of nearly every class of structure occur- 

 ring in the practice of the engineer or builder. In our first 

 chapter, we have a method by the resolution of forces applica- 

 ble to any framed structure, however irregular or unsymmetri- 

 cal, provided only there are no moments at the ends to be 

 determined. 



In Art. 125 we have explained fully the application of the 

 method for this case also, when these moments are known, and 

 in Chaps. YIIL to XIV. inclusive we have given practical con- 

 structions for the determination of these moments for all the 

 important classes of structures in which this condition occurs, 

 such as the continuous girder, braced arches, etc. 



When the structure is not framed, or composed of pieces the 

 strains in which can be definitely determined, we have the 

 method of moments of Chap. V., which, as we have seen, may 

 be extended so as to completely solve the difficult case of the 

 continuous girder, and which may, of course, be applied to 

 framed structures also, as illustrated in Fig. Ill (Art. 187) in 

 the case just discussed. Thus we have two distinct graphical 

 methods by which our results may be checked. The first 

 method includes a great variety of the most important and 

 usual structures, such as bridge girders, roof trusses, cranes, 

 etc., and in view of its ease and accuracy will undoubtedly be 

 found of great service by the engineer and architect. The 

 second method has important mechanical applications, as no- 

 ticed in Art. 41 ; and aside from these, and its application to 

 structures having end moments, such as the continuous girder, 

 etc., furnishes us with ready determinations of the centre of 

 gravity of areas (Chap. III.), the moment of inertia of areas 

 (Chap. VI.), and also gives us a very complete solution of the 

 stone arch (Chap. XV.). 



"We have also the analogous methods of calculation, viz.. 



