Laterally loaded Struts and Tie-rods. 719 
Prof. Perry's approximation gives 
wl 2 3 ,, wl 2 P e 
For P = this underestimates the deflexion by 1\ percent, 
but gives the correct bending moment ; for other values of P 
it overestimates the value of the bending moment by a pro- 
portion which increases as P is increased ; e. g., if P = P e the 
p 
error is 2'Q per cent., and if -p =9, a very possible value in a 
1 e 
tie-rod of circular section, the error is over 12 per cent. If 
I is increased indefinitely M according to this approximation 
■. .. . L 7r 2 wtil . , , P wEI . .... 
approaches the limit -~ — p- instead ot —. p-, as in (24), a 
limit of error of 23 per cent, on the bending moment. But 
in cases where I is great the stress arising from the bending 
moment is usually unimportant compared with the axial 
tension, w being small. 
The intensity of bending stress 
The maximum intensity of tensile stress is 
and the maximum intensity of compressive stress is 
which when negative gives the minimum intensity of tensile 
stress. 
The pullp per unit area of cross section which with given 
load and dimensions makes/, a minimum may be found from" 
(28), and the value of p which makes/, zero may be found 
from (29). 
Case Y1.1 
Uniform straight tie-roi with central load W and ends 
freely hinged. 
The equation is 
dV_JP W (I \ < 
dx 2 EI'^ - 2EU2~V ^ U; 
