180 COLUMNS ECCENTRICALLY LOADED. Art. 110. 



Extracting the square root and transforming 



~p~ dy 



~EI dx== l/2eiyy 2 () 



Integrating again, the equation of the elastic line is: 



ET- ei 



when x-Q, y=0 hence C'=Q 



~P 



\m 



& 



=vers l e ' ' . (48) 



when x=--l, i'=y m ax and (48) becomes 



/r = c +r =rcrs ( (6) 



where ^^i^ (49) 



From (b) 



/)/71"C Ml I S*S\& H I 



=e(secOlY) (50) 



cos 



Equation (50) determines the maximum eccentricity which 

 is e-\-y max -, having this the eccentricity at any section may be 

 found, it being e+?/ ma x ?/, 2/ being obtained from equation (48). 

 Stresses are found as in a block. The maximum stress will occur 

 in the extreme fibre at the base on the compression or concave 

 side. 



(51) 



P == S * = *'"** 



^ U^ 1 IJ^'X^/)/ ( 52 ) 



Equations (48), (49), (50), (51), and (52) give complete 

 information with regard to stresses in and deflections of origi- 

 nally straight and homogeneous columns within the 'clastic limit. 

 If the average unit stress allowable is found from equation (52) 

 the area of a column's cross section is determined as simply as 

 that of a tension member. This equation is, however, so difficult 

 of application that it is not used in practice; it may be used as 

 an occasional check upon results obtained by the usual methods. 

 P 

 -j- appears on both sides of the equation (see equation (49) ) 



while Vi and / also depend upon the section which is to be found. 



