Elastic Equilibrium of Semi-Infinite Solid. 4.1 



any point in the loaded area. Comparing the above two ex- 

 pressions we have 





VzX 



Thus tlie direction of gravity becomes, in consequence of the 

 attraction of the loa(b inchned to the vertical at the angle Ç-'' which 

 will be determined bv 



ta„^. = ^L.i^^(4^) (91) 



while its tilting effect is expressed by 



tanc = ( ^^''^) (92) 



§33. In the present exam])le, in which a uniform material 

 loading is confined in the circle of radius «, we have, from the 

 formula (58), 



// /Î + 2« 



fe-''J,(lry,(l-a)df] 



Referring to tlie fcirmula^ (^>1)- (^^~) 'Ti^<1 (^J-t)i ^^'C' obtain 



taiic = - — . ^ . aa-[ e,co,-r,, ) (9d) 



tan/' = — — . — '— . aa?\—e^co^ — -f]A (94) 



-a'- g'' ^ 2 /«=o. 



The function h'^^co^ — ri^ has been discussed already and the 

 expression which is suitable for the calculation of its value at a 

 point not near to the edge of the circle has been established in 

 terms of q. Using the ^-series in §24 we shall have 



aa?l^^e,oj,-rj\ = 2-yjL . q'%l-\-'èq'-'iq'-9q' + 2^,f+ ). (95) 



It is equally interesting and important to find the value of 9 

 at the point near the edge of the loaded area. This will be 



