718 Prof. A. Morley mi 
the points of inflexion which are at x= + v. The coefficients 
P 7 4 
of powers of-p are nearly unity, and with any assigned ratio 
P . 
p- the error is easily estimated and with usual working ratios 
will be very small. 
Case V. . 
Uniform straight tie-rod with uniformly distributed load w 
per unit length and ends freely hinged. 
This is the same as case I. with the sign of P reversed. The 
solution of the equation is 
■^/l-sech^Jcosliy^), (22) 
w id 2 _ wEI/. 
2P^ + «P 
and at the origin 
and at the origin the bending moment with sign reversed, 
8 
P^/o= ! f I (l-sech^^/^ ; or ^?^i_ S ech|^/g), (24) 
where P = . 
And expanding (24), 
2 
or 
°~~8~ 384 EI 
The errors involved in the use of the jnethod (b) are here 
P 
about the same as in case I. when-p is small, a condition 
e 
which would not be fulfilled in a tie-bar carrying a reasonable 
pull unless I is small or the lateral load is great. For tie-bars 
of considerable length (say I greater than 20 d for circular 
p 
sections) p- is generally greater than unity, and method (b) 
is no longer of any use when the lateral load is only the 
weight of the bar; but, on the other hand, the bending 
stresses are then small compared with the tension resulting 
from the axial pull P. 
