CHAP. XIV.] 



THE BRACED ARCH. 

 TABLE, FOR VALUE OF y. 



265 



Instead of determining the curves enveloped by the reac- 

 tions, the expressions for which are in this case somewhat com- 

 plicated, it will be found preferable to find the distances GI c% 

 of the intersections </> and ty of the reactions [see Fig. 92] with 

 the verticals through the centres of gravity of the end cross- 

 sections. For small central angles a, we have 



15 (0 a?) 



15 (0 + x) 



[ 



[ 



where 0, A, A and a?, have the same signification as above. 



Since I divided by A equals the square of the radius of gyra- 

 tion = /, we have 



o z r 



+ See 



15(0 -x) 



2A 

 15 (0 + as) 



t K 45/01 

 a-5. fj. 



For braced arches when^ the material is nearly all in the 

 flanges, the material in the bracing being very small, we may 

 call the radius of gyration half the depth of the arch measured 

 upon the radius from centre to centre of flanges ; or represent- 

 ing thia depth by d, 



