Laterally loaded Struts and Tie-rods. 715 
series bears to the first term. The errors involved in calcu- 
lating f c the maximum intensity of stress due to the axial and 
lateral forces combined will be less than these amounts, the 
error depending on the amount of the lateral compared with 
the axial load, and the shape of cross section. Similarly the 
error in calculating ft will be greater than .the above 
amounts. 
Prof. Perry's approximation mentioned above consists in 
substituting — cos l -j' TT f° r ^(t — ^ 2 ) in (1), which is equi- 
valent to substituting a smaller but not a uniformly dis- 
tributed load j-wl for the actual lateral load wl. This gives 
#0 = 8 /p 6 _p) and M 0=8^ 2 - p e Jp > 
the deflexion being rather below the true value for all values 
of P. The most serious error arising from this approxi- 
mation is that in calculating the bending stress for high 
ratios of-^ assuming the limits of elasticity not to be exceeded. 
p "« 
For p- =0*9 the error is 3 J per cent, on the deflexion and 
somewhat less on the bending stress ; that on the maximum 
tensile stress ft is proportionally more than that on the bending 
stress. 
Case II. 
Uniform straight strut with central lateral load W and ends 
freely hinged. 
The equation in this case is 
^ EI' y " 2EI^2 x p • • • • W 
and the conditions being as before, 
w^ /EI. I /p~ m .... 
^=2PVp tan 2VEl~lP' • • (10) 
and at the centre 
- M p=TA/? tan !V£ • • • • M 
M and y being evidently infinite for P= =P e . 
