COLUMNS AND STRUTS 103 



in which A and B are undetermined constants.* For x = or l> 

 y = ; whence 



B = and A = 



For x = I, -f- = ; whence 



- 



From the last condition, 



This equation is of the form u = tan w, and from this it is found by 

 trial that 



Consequently, 



20 El 2 

 P = - = p approximately. 



This equation is of the same form as formula (50) of the preceding 

 article, the difference between the numerical constants in the two 

 formulas being due to the approximate nature of the solution given 

 in Article 83. 



85. Modification of Euler's formula. It has been found by ex- 

 periment that Euler's formula applies correctly only to very long 

 columns, and that for short columns or those of medium length it 

 gives a value of P considerably too large. 



: y short columns or blocks fail solely by crushing, the tendency 

 to buckle in such cases being practically zero. Therefore, if p denotes 

 the crushing strength of the material and F the area of a cross 

 section, the breaking load for a very short column is P 



tlculu*, p. 440. 



t As Euler's formula is based upon the assumption that the column is of sufficient 

 to buckle sideways, it is evident a priori that it cannot be applied to very short 

 columns in which this tendency is practically zero. Thus, in formula (48), as I ap- 

 proaches zero P approaches infinity, which of course is inadmissible. 



