with Lateral and Non- Axial Loads. 



209 



Let ko, fig. 4 5 represent any one span of a continuous 

 beam loaded in any manner, and kfo be the bending moment 

 diagram for the span taken as if it were discontinuous. Find 



Fiff. 4, 



~-~^°i 



the area and position of the centre of gravity of kfo, Let 

 the former be represented by A and the distance of the 

 latter from the right-hand support be taken as x. Then 

 we shall have 



OOi = 0L, 



where is the angle of slope of the beam at the left-hand 

 support and OOi is the distance by which the right 

 hand support lies beneath the tangent to the left-hand 

 support. 



Now (OOi)BIs= Moment of area of bending moment 

 din gram about o. 



.'. (00,)EI ~ Av-^(ajc)^ -(co)™ 



= 0LEI. 



This can be written 



L L 2 



2 ( aJc ) .oW 

 3 6"' 



Now at a point P one third of the span from k, erect a 

 perpendicular PR and make Pit equal in length to - ^\ 

 We have then 



U L 3 6 j ' 



Phil. Mag. S. G. Vol. 27. No. 157. Jan. 1914. P 



