Art. 113. 



COLUMN FORMULAS. 



189 



tion (51) will give some idea concerning this contingency, but 

 with elastic supports, the column's end will turn under a much 

 less load than when the supports are rigid. 



113. Column Formulas. By a column formula is usually 

 meant an equation which gives the average working stress by 

 which the total stress in a column, concentrically loaded, must 

 be divided in order to obtain its area. Finding the required area 

 of a column's cross section is, therefore, a very simple matter, 

 since all specifications give one or more column formulas. It is 

 not as simple, however, as finding the required area of a tension 

 member, because the shortest method of solving the formula, is 

 by trial. 



It is assumed that care has been taken to have the column 

 straight and the load concentric, but practically it is impossible 

 to know, in any particular case, how great the variations from 

 ideal conditions are. 



If the condition of the column approaches very closely to 

 the ideal, as explained in Article 111, then equations (54), (57), 

 (58), (59) and (55) are applicable, and are used for the prac- 

 tical column by many engineers, particularly in continental 

 Europe. Equation (57), which applies to a column with pivoted 

 ends, was published by Euler in 1759, and is called Eider's For- 

 mula. The question arises, does the practical column approach 

 the ideal closely enough so that its strength will be but slightly 

 below that given by Euler 's Formula? It is only by experiments 

 that the effect of variations from the ideal column can be deter- 

 mined. With experiments on practical columns, a good test of 

 Euler 's Formula cannot be made because the end conditions are 

 uncertain, as is apparent from a careful reading of Article 112. 

 Then, too, Euler 's Formula is not applicable beyond the elastic 

 limit, but in a steel column the stress at failure does not exceed 

 this limit much. 



Most engineers in this country base their column formulas 

 upon experiments, and put them in terms of the maximum al- 

 lowed unit stress. These experiments eliminate, to a certain ex- 

 tent, the uncertainties as to end conditions, and show rather wide 

 variations from the mean, as would be expected, particularly 

 when multiple flexure occurs. It is highly desirable to have more 

 experiments in order to reduce the discrepancies between various 

 column formulas now in use. 



Equation (52) might be used as a column formula if a sat- 



