BY R. W. H. HAWKEN. 99 
The problem, as it occurs in Engineering Practice, 
will now be stated. 
The design of a column depends mainly on the 
maximum stress at the extreme fibre; to get this it is 
necessary to take account of both direct compression and 
bending stress, thus :—Referring to Fig. 1 or Fig. 2,— 
if P be the load on the column 
A be area of cross section 
y be distance of extreme fibre from neutral axis 
f, be stress at extreme fibre due to bending only 
I. be moment of inertia of section and r radius of 
gyration where [=Ar? 
f be total stress at the extreme fibre at the point C 
on the column=f, +p 
n be maximum deflection 
P 
p be — 
A 
then 
Pxnxy pny 
ee eae eee eee ee (9) 
aac 1 
jeeye 
MOD he ep et i, SG tao wees eel ae (10) 
re 
so that if we know the quantity ‘n’ we can calculate f 
and from (10) we can express p in terms of f, thus :— 
72 
and thus say, for any material, what direct stresses can be 
applied to a column to cause a certain allowable stress f, 
according to the material used, at the extreme fibre. 
