330 THE STONE AECH. [CHAP. XV. 



ellipse, the span 152 ft., the rise th as much, the depth of key 

 j^th the span. The crown settled only two inches upon re- 

 moval of centres." [ Woodbury : Theory of the Arch.'] 



In general, we must first assume the depth at key in view of 

 the strength of the material, the character of the workmanship, 

 the load, etc. Then the thrust being found, we find the mean 

 pressure per unit of area as above. If this mean pressure 

 exceeds ^-th the ultimate resisting power of the material, make 

 a new supposition, increase the thickness, find the thrust and 

 pressure anew, and so on, till the results are satisfactory. 



The ultimate resisting power of granite may be taken at 

 6,000 Ibs., brick 1,200, sandstone 4,000, limestone 5,000 Ibs. per 

 square inch. These values are, of course, very general, and sub- 

 ject to considerable variations, according to the kind and quality 

 of the stone. The strength of the material to be used must, for 

 any particular case, be determined by actual experiment. 



The weight of a cubic foot of stone may, in general, be as- 

 sumed at 160 Ibs., brick masonry at 125 Ibs. 



11. Iucreae of thickness due to change of form. 

 Having obtained a thickness which satisfies all the conditions, 

 we must, if the arch be very light, make some further provi- 

 sion for the change of form which is sure to take place after 

 the removal of the centres. By this change of form the pres- 

 sure line is altered, and the thickness may need to be increased. 

 In general, we need only to increase the depth from the key to 

 the springing. This increase need not exceed fifty per cent, at 

 the joint of rupture and weakest intermediate joint. [ Wood- 

 bury : Theory of the Arch^\ 



12. Thus, by a simple and rapid construction, we can deter- 

 mine, for any particular case, the thrust, joint of rupture, and 

 proper thickness of the abutments, without the use of tables or 

 the intricate formulae usually employed. There is no diificulty 

 in laying down on paper and verifying all the elements of the 

 most complex case. The method is entirely independent of 

 all particular assumptions, and is therefore especially valuable 

 when irregularities of outline or construction place the arch 

 almost beyond the reach of calculation. It is general, and may 

 be applied with equal ease to loaded and unloaded, full circle, 

 Begmental, or elliptical arches with any form of surcharge. 



