Buckling of Deep Beams. 



205 



Now it is worth while to note that the correction to the 

 buckling load due to putting the load at height q above 

 the centre of the end instead of at that centre is 



4-012x1-025 



q EC _ 4-012 x 1-025 x 4 y-p 



I I 2 ~ 7T 2 7 



= 1-666 1 R, 



(99) 



thus showing once again the intimate connexion between 

 the strut problem and the buckling beam problem. 



Fig. 14. 



Mr 



Case 11. — Beam under a total load W distributed as a 

 uniform load w per unit length, the load at x being situated, 

 before the beam is strained, at (#, p, q). The beam is fixed 

 iit one end and free at the other as in the last case. 



We have now to extend equation (71a) to the case where 

 the distributed load is not on the central line. 



Dealing with the element in fig. 9 we find that the load 

 wdx, when the beam is twisted, has a torque wdx(qr+p) 

 about the tangent at D'. Then, instead of (71 a), we get 



GW^ + rfT.+ iwte(5T+p)=0, . . . (100) 

 and instead of (71) 



dT {i dh. 



which, when M = 3 as in the present case, is equivalent to 



K »S=-&-(^)- • • • ( ]o2 ) 



