APPENDIX.] THE BRACED AKOH. 395 



Comparing these results with those in our table above, Art. 

 19, for the same case not continuous at the crown, we see that 

 the strains in the upper flanges are much less, and are, more- 

 over, of opposite character ; while the strains in the lower 

 flanges are greatly increased, and nothing is gained. This re- 

 sult might also have been anticipated, since the effect of insert- 

 ing the flange H is to reduce the effective height from 29.5 to 

 19.5 ft., and, moreover, for total dead and live load, nearly the 

 whole weight comes directly upon the continuous lower rib, and 

 the upper aids but very little. 



23. Strains due to Temperature. We have, in addition, 

 strains due to change of temperature to be taken into account 

 in determining the total maximum strains. 



For the present case we have, from Art. 165, for the thrust 

 due to change of temperature, 



15 El Act 



~ 



8AA 2 



or, substituting in the place of -^ the square of the radius of 



A. 



gyration = ^, we have 



1 K in A />2 c + 

 H = 



Now g- is approximately the half depth of arch ; hence (p = 

 25 sq. ft. = 3600 sq. inches. Taking 5 tons to the square inch 

 as our unit strain, we may take the area of our flanges, as de- 

 termined from the above table of strains at about 25 square 

 inches. Hence A = 50. Taking E = 14,000 tons per sq. inch, 

 h* 19.5 2 54,756 sq. inches, and supposing the temperature 

 to vary 25 (Centigrade) on each side of the mean, we have, 

 assuming e at 0.000012, the thrust H = about 25 tons. 



It is easy to find either by moments or diagram, or both, the 

 strains due to this thrust. Since the temperature varies between 

 25 on both sides of the mean, this thrust can be both positive 

 and negative, and the corresponding strains have, therefore, 

 double sign. "We find, therefore, ' 



