716 Prof. A. Morley on 
Using the expansion 
n\T W M i , ^ P ^ ^ /PV , 17tt 6 /P\3 -^ 
Wl.Wf f 7T 2 P 17tt 2 /P\ 2 . 1 
- M o=X + 4^- P 1 1+ IOP/r68o(pJ + - &c -}^ • (13) 
which very clearly shows the relation of the calculation by 
the method (b) to the true bending moment. For — = i 
the error is under 4 per cent. *« 5 
Case III. 
Uniform straight strut with uniformly distributed load w 
per unit length and ends fixed in the direction of the axis 
of x. 
The equation is 
d 2 y , P w /I 2 A , M, 
di* + wry=-mkzV*m,- • ■ ( u > 
where Mi is the bending moment at the ends. The con- 
ditions being ~ = for x = 0, y = for #=~, and ^ =0 for 
I dx * 2' dx 
x= - the solution 
- h { *- h Vf - h/Jfc V£*-» V0 
gives 
^, T d 2 y wEI W /El / P~ / /P" 
EI J = T" - IV P COSec VeI 2 C ° S V EI * X ' ^ 
The points of inflexion are at a distance from the centre 
given by 
/EI 1 ( /EI 2 . / /P] 
which varies from — 7= when P = to - when P = P = — — 
2\/3 4 e / 2 
Euler's limiting value for the ideal strut fixed at both ends. 
