23 



In this case the deflection h of the column in no way- 

 depends upon the eccentricity of the loading. The further 

 the line of stress is from the axis of the column the greater 

 will be the bending moment M upon the holding supports at 

 the ends, but, provided these remain firm, the deflection of 

 the column is in no way affected. 



The table supplied to enable computations to be made 

 of the deflection in Case 1 will also serve for the same purpose 

 for Case 3. 



In modern formulae for the computation of the load on 

 long columns, especially when there is eccentricity of loading, 

 the deflection of the column under load is made the basis of 

 the formula used. In many of these the assumptions made 

 as to the deflection of the column are far from correct accord- 

 ing to the foregoing calculations. The object of the writer is 

 to make some contribution towards that more exact knowledge 

 necessary for progress in engineering design. 



Table giving maximum of deflections of Pin-jointed Columns 

 under axial load or deflectio?is of Columns with ends 

 fixed under any load the line of action of which is 'parallel 

 to the axis: — 



l I 



Values of — for pin-jointed columns or — 



h 



2a 4a 



Corresponding values of — . 



for columns with fixed ends. 



1 



1-57080 







1-57092 



•0111 



1-57127 



•0222 



1-57187 



•0333 



1-57271 



•0444 



1-57379 



•0554 



1-57511 



•0664 



1-57668 



•0773 



1-57849 



•0882 



1-58054 



-0900 



1-58284 



•1097 



1-58539 



•1204 



1-58820 



•1310 



1-59125 



•1414 



1-59457 



•1517 



1-59814 



•1619 



1-60198 



•1721 



In this table I = length of column. 



h = maximum deflection. 



EI 



a 2 = where P is the load in compression. 



