Section III., 1892. [ 23 ] Trans. Rot. Soc. Canada. 



II. — Upon the Flexure of Columns. 

 By Prof. H. T.'^BovEY, M.Inst.C.E., McGill University, Montreal. 



(Read June 1, 1892.) 



The ordinary moment equation is expressed iu the form 



and this is sufficieuUy accurate if the deviation of the axis of the strut 

 from the vertical is so small that j J( J may be disregarded without ; 

 sensible error. The more correct equation is 





p being the radius of curvature. 



Consider, e. g., a strut with both ends hinged. Then 



— à' y dy — sin d.dd 

 where a- E I = P', 



P' being the least thrust which will bend the strut laterally. Integrating, 



-|- = COS é' — cos 6'„ (1) 



fi„ being the value of 6 at end of strut. 



-r . ■ ^» , ■ ^ 



Jjet Bin,, = /<ana sin .-; = jn sin (/> 



Then ^ = 2/,2(l_sinV^) 



2/< 

 01- y-~^ «îos '^ (2) 



Let Y be the max. deviation of the axis of the strut from the vertical, i.e., the value of y 

 when H = or ff) = 0. Then 



Again, 



2w 2 



ds = pdO — ■ 



a v/ 1 — /4^ sin ^0 

 Hence, if / be the length of the strut. 



7T 



-.2" 



2 C'' . d(p 2 



