NOTE TO CHAP. XTV. [APPENDIX. 



The strains in the present case are, we see, much greater 

 than for any of the others. Unless the maximum of stiffness 

 is essential, it would appear, then, undesirable to fix the arch at 

 the endsybr an arch of the above dimensions. 



87. Temperature Strains. The strains due to tempera- 

 ture are also very great. Thus, from Art. 165, we have 



H = 



4 A A 2 + 45 I' 



and for the distance of the point of action of this thrust, below 

 the crown of the centre line, 



_ (A o? + 6 I) A 

 * - ~ ~3"A~^ ' 



or since - = ^ 2 = 25 ft., 



_ 

 ~ 



_ h (a* 



For A = 60 square in., a = 87.5 ft., A = 20 ft. = 240 in., 

 g = 60 in. = 5 ft, e = 0.000012, E = 14,000 tons, t = 30, 

 we have 



H = 125 tons and e. = 6.7 ft. 



Hence we have the strains 



A = 228, C = 29.0, E = q= 30.0, G = 118.5, 

 B = 112.5, D = =F 13.0, F = q= 65.0, H = 137.5, 



1 2 = T 96.0, 3 4 = =F 67.0, 5 6 = q= 29.5, 

 23= 51.0, 45= 39.5, 6 7 = 25.0, 78 : 2 ' 5 ' 

 Therefore the total strains are 



C = + 169.5 D = + 154.4 



E _ F _ +175.8 G ._ + 227.7 _ + 241.1 



46.0 F_ G_ H- 



131.1 o, + 66.60, + 89.5 .. + 52.9 

 150 2d =_ T6.0 S4= - 89.0 -- 53.9 



_ 7 _+ 39.1 ^ s _+ 24.4 



-_ 46.6 7 ~_ 45.1 78 -- 24.0 



With the above we close our discussion of the braced arch. 

 Our design has been to illustrate the application of the for- 

 mulee and methods of Chapter XIV., and to show that by their 

 aid such a structure can be calculated with ease and certainty. 



