100 THE STRUT PROBLEM. 
The difficulty is that from the assumptions of central 
loading, n is indeterminate, and various devices have been 
adopted to make practical use of (11): the best known 
is that of Professor Rankine, who, following the analogy* 
]2 
-of beam deflection, said n for a constant {=c— where ¢ is 
7 
-constant for the material, and thus obtained the familiar 
Rankine-Gordon formula 
this is still extensively used, it has been modified empiric- 
1X2 
ally to the ‘ parabolic formula ’ p=t{ of -) }. . (12a) 
r 
} l 
-and to the ‘straight line formula ‘=f 1x) » af (26) 
r 
‘these latter are easy of application, and, over limited ranges 
for f and k chosen with judgment are suitable for ordinary 
-design. T 
*The analogy of beam and strut is not nearly complete and may be 
-deceptive. In a beam the deflection varies directly as the load, whereas 
in a column the rate of change of deflection increases with the load, for 
this reason breaking test results for apparent central loading which may 
.and do conform to Rankine’s formula, do not give a true indication of what 
will happen under loads used in practice. The curves appended show 
this; f/p is not constant for the same column, in fact the curves have 
been drawn to deduce the varying amount ; in a beam the various curves 
would be straight lines parallel to the axis. For these reasons any table 
~of breaking strengths of columns can only be a very rough indication of 
how the column is stressed under working conditions. For columns 
with a definite eccentricity of loading these remarks apply with equal 
‘force. Plate VI illustrates these remarks; both when results are being 
determined in terms of |/r and of (1/r)?. 
f 
{That is if the fact is kept in mind that the ratio — varies with f 
see Plate VI.) p 
