APPENDIX.] THE BKACED ARCH. 



In short, the difficulty is but little if any greater than for a 

 simple girder, only for a long span and many panels the work 

 becomes tedious and wearisome. 



In such a case, perhaps the method of moments will be found 

 preferable to diagrams. Thus, for any condition of loading, we 

 can easily find the strains at certain given intervals or portions 

 of the span, as -^th, y^ths, etc. These strains being plotted to 

 scale along the span, we have a curve from which we can 

 readily determine the strain at other points. 



The strains in the flange's being thus known, we can readily 

 determine the transverse force, or force at right angles to the 

 rib, at any point. This force causes strain in the diagonals, and 

 has simply to be multiplied by the secant of the angle made 

 with it by any diagonal. 



As to the effects of temperature, the remarks of Art. 166 do 

 not seem to be substantiated by our results. It would seem 

 that, according to the received formulae, the strains due to tem- 

 perature are very great, and that by far the best form of con- 

 struction for short spans is that in which the arch is hinged at 

 both abutments and crown. 



28. Advantage of Arch with fixed Ends for long Spans. 

 We cannot conclude from our results above anything as to the 

 comparative advantages or disadvantages of the arch with fixed 

 ends. Different proportions will give altogether different re- 

 sults. "We can only say that for small spans the arch with 

 three hinges is undoubtedly the best construction. The ad- 

 vantages of continuity will be apparent only for long spans 

 where the point of inflexion is distant from the ends by a 

 greater proportion of the span. We have already seen the 

 same to be true of the continuous girder. If we were to judge 

 from comparisons of short spans only, we should be inclined 

 to discredit any great advantage for continuity. If, however, 

 we take longer spans, so as to bring the points of inflection well 

 out, we find a marked saving.* 



We had intended to give here a comparison of the strains in 

 a hinged arch with those in the central span of the St. Louis 

 bridge, as given in the Report of Capt. Eads to the Illinois and 

 St. Louis Bridge Co. for May, 1868. 



As this goes to press, however, our attention has been called 



* Art 17 of thia Appendix 



