212 Struts and Tie-Rods with Lateral and Xon-A.vial Loads, 



from this, and its base-line when considered as a bending 

 moment diagram obtained exactly as before. 



Effect of Non-Alignment of Supports. — It is a well known 

 fact that in a continuous beam with lateral loads only a 

 small amount of settlement or movement in any support may 

 make a considerable modification in the magnitudes of the 

 bending moments existing in the girder. It does not always 

 follow that a movement in any one support will have large 

 effects, but it is necessary to investigate the matter closely. 

 The importance of this cannot well be overstated when 

 designing continuous beams with end loads, since if the 

 moments caused by the deflexion of the beam are sufficiently 

 great to be taken into account, it is extremely likely that 

 a comparatively slight movement in any support will be 

 commensurate with the natural deflexion of the beam, and 

 hence its effect in altering the moments due to the end load 

 is considerable. 



Referring again to a continuous beam with lateral loading 

 only and assuming that a certain pier is out of line by an 

 amount S, it is necessary first to find the characteristic points 

 on the supposition that the piers are in alignment. ^ 



Set off to the scale of moments, distances equal to 2EIy-~ 



$ . . . l 



and 2EI ^—^ above or below the original characteristic points 



according as the moment over the support is increased or 

 decreased by the non-alignment of the pier. The points thus 

 determined are the new characteristic points for the pier c. 

 Since if any one support has settled by an amount 8, it 

 follows that in the case of a bridge of equal spans the 

 supports to the right and left of the sunken pier will be left 



with a superelevation of - above the chord line, so that it 



is necessary in addition to alter the characteristic points for 



Fig. 6. 



->- 



onrxTYxyy^orrrrrpcxTYxrxTXXxro 





these piers by an amount proportional to - , after which the 

 base-line may be drawn exactly as before. 



