386 NOTE TO CHAP. XIV. [APPENDIX. 



NOTE TO CHAPTER XIY. 



THE BRACED ARCH. 



19. The subject of braced arches is an important, one, and 

 is treated in no work with the fulness and completeness it 

 deserves. The methods and formulae of Chapter XIV. will, 

 we believe, render the determination of the strains in this class 

 of structure easy, and we propose in the following to illustrate 

 their use, so far as may be necessary to render their application 

 clear. 



In PI. 4, Fig. X., we have represented a braced circular 

 arch with parallel flanges. Span of centre line = 175 ft. ; 

 radius, 201.4 ft. ; rise, 20 ft. In practice, the panels would be 

 taken of equal length ; for convenience of calculation, however, 

 we suppose the panel length to vary so that the horizontal pro- 

 jection is constant, and equal to 25 ft. Depth of arch, 10 ft. 

 Hence, span of lower flange = 170.6 ft. ; rise, 19.5 ft. ; radius, 

 196.4 ft. Span of upper flange, 179.34 ft. ; rise, 20.5 ft. ; radius, 

 206.4 ft. 



Since the flanges are, in practice, broken lines, and not true 

 curves, the depth or lever arm for upper flanges is 9.43 ft., for 

 lower flanges, 10.4 ft. 



The determination of the other dimensions required is then 

 easy, and a simple question of trigonometry. 



Thus we have for the half central angle a = 25 45', and for 

 the distances of the apices from the chord of the centre line : 



For 1... -4.5 3.... 4.7 5.... 11.3 7.... 14.6 ft. 

 " 2.... 10.8 4.... 18.5 6.... 23.4 8.... 25 " 



"We suppose the load at each apex 10 tons, and shall consider 

 ls. Arch hinged at crown or apex 8, and at the ends of 



the lower flange the flanges H and A being removed. 



2c?. Arch hinged at apex 8, and at the ends of the centre 



line the flanges A and E butting against a skew back or pivoted 



plate, and the flange H only being removed. 



3d. Arch continuous at crown the flange H being retained, 



and hinged at ends of .ower flanges. 



