Laterally leaded Struts and Tie-rods. 713 
Case I. 
Uniform straight strut with uniformly distributed load w 
per unit length, and ends freely hinged. 
EI 8=-Ki-* 2 )-^< • • ■ « 
dhj , P to (P A 
The conditions being y = for «= - and -r~ = for #=0, 
the solution is * ^ tV 
26' 2 ?#Z 2 wEIa, Z /T - /~F \ 
and at the origin 
and the bending moment with sign reversed is 
M = P i/o + ^=^(l-se4< V /| [ ), . . (5) 
° r M =^ 
mVf.- 1 ) (6 > 
where P e is Euler's limiting value of P for the ideal strut, in 
7T 2 EI 
this case — ^— , which value makes M and y infinite. 
. P 
The actual working value of p- will rarely reach as much 
as \ when there is no lateral load, and with a lateral load 
J- may be taken as an extreme value. As the resistance to 
bending under end thrust alone in a plane perpendicular to 
that of the lateral loads will often be less than that to bending 
P 
under end thrust in the plane of the lateral loads, p- will 
often be much less than -J-, as for example in a rectangular 
section the depth of which is considerably greater than the- 
breadth. 
