CHAP. XIV.1 THE BBACED ABGH. 



PART III. 



APPLICATION OF THE GRAPHICAL METHOD TO THE ARcb 



CHAPTER XIV. 



THE BRACED ABCH. 



147. Different kinds of Braced Arches. Just as in gird- 

 ers, \te may distinguish between the solid beam, or " plate gird 1 

 er," axd the open work, or framed girder ; so, regarding the arch 

 as a b*nt beam, we may distinguish the braced arch and the 

 solid anh, or arch proper. "The strains in the various pieces 

 couiposiig the braced arch may be easily found by the method 

 of Arts. -15, or by calculation by the method of moments of 

 Art. 14 fo* any loading, if only aU the outer forces acting 

 upon the ar\h are known : that is, so soon as, in addition to the 

 load, we kno^r also the reactions at the abutments, or the hori- 

 zontal thrust md vertical reactions at the points of support, and 

 the moments, tf any, which exist at these points. 



We may distnguish three classes of braced arches : viz., 1st. 

 Arch hinged at both crown and springing ; 2d. Arch hinged 

 at spring line oriy continuous at crown ; 3d. Arch continu 

 ous at crown and faced at abutments. 



15. Arch hliigtd at both Crown and Abutments. This 

 form of construction [PI. 23, Fig. 90], owing to the hinges at 

 crown and abutment, affords for live load but little of the 

 advantage of a true a-ch. It is, in fact, an arch only in form, 

 but in principle is mor nearly analogous to a simple triangular 

 truss of two rafters, these rafters being curved and braced ; the 

 thrust being taken by tie abutments, instead of resisted by a 

 tie line A B. 



The case presents no esoecial difficulty, and may be easily 

 calculated or diagramed, jrovided that not more than two 

 pieces, the strains in which are unknown, meet at any apeK. 

 Thus, in PI. 23, Fig. 90, the kjsultant at the abutment due tc 

 any weight P being known, it ttay be directly resolved into tii^ 



