404 NOTE TO CHAP. XIV. [APPENDIX. 



to an article in the Trans, of the Am. Soc. of Civil Eng. for 

 May, 1875, which, although written with precisely the opposite 

 intention, seems to prove so clearly the superiority for long 

 spans of the arch without hinges, that it is unnecessary to give 

 a comparison here. We have only to take the results and prop- 

 erly interpret them. 



Thus, while ostensibly investigating the strains in the centre 

 arch of the St. Louis bridge an arch which is continuous at 

 crown and fixed at the end the formula given in Art. 27 of 



the Supplement to Chap. XIY. is used, viz., H =^-7-. That 



2i fi 



is, the arch is considered as having hinges at both crown and 

 ends. 



Then, supposing the arch to be affected by temperature, the 

 above formula is applied to an arch hinged at crown in lower 

 chord and at ends in upper chord, of the same dimensions as 

 the St. Louis bridge. It is hardly necessary to point out here 

 that if the arch is really thus hinged, or can be supposed thus 

 hinged, there can be no temperature strains. If, however, it is 

 not hinged, then the above formula does not apply. The one 



2 



assumption contradicts the other. The formula H =^-7- can 



2i /t 



be applied to no arch which is strained by temperature. Such 

 a treatment would seem justified in view of the statement of 

 Capt. Eads, that for the greatest rise of temperature above the 

 mean, the lower arcji does all the duty at crown, and the upper 

 at the ends. If this were accurately so, then the results of the 

 article referred to would give the true strains. All that Capt. 

 Eads evidently intended to imply was, that a rise of tempera- 

 ture relieved the upper chord at crown of a great part of its 

 compression and increased that of the lower. It does not by 

 any means follow that the upper chord is entirely relieved, 

 under which supposition only can the lower chord be supposed 

 hinged. On the contrary, for an equal fall of temperature 

 below the mean, the lower chord is relieved and extra strain 

 brought in the upper chord at crown. If the adjustment were 

 just such that the previous compression in the lower chord 

 should be exactly neutralized, then the arch might be consid- 

 ered as hinged at the upper flange and lower ends, and thus 

 we should increase the rise of the arch by the depth, which 

 would decrease greatly the strains obtained. The one supposi- 



