50 PRACTICAL STRUCTURAL DESIGN 



requires that the supports be immovable. The slightest settle- 

 ment causes increased stress and sometimes a reversal of stress. 

 As it is merely a matter of properly designed connections, con- 

 tinuous girders and beams are sometimes used in steel structures. 

 They are not common, however. 



The maximum stresses are invariably over the supports, and 

 lack of realization of this fact has caused distress to some de- 

 signers. The principle of continuous beams finds application in 

 reinforced concrete work. Owing to the monolithic character of 

 reinforced concrete there is no other proper way for designing in 

 this material. To assume that the bending moment on a span 



WL 

 = -= does not make it so, and designers who assumed that the 



o 



greater stiffness thus secured would permit the use of a smaller 

 moment over supports suffered in reputation thereby. 



By methods involving the use of higher mathematics it can be 

 proved that the sum of the moment in the middle of the span and 



WL 

 the moment at one support = -5 In the study of restrained 



o 



beams this has been shown, for, disregarding the signs, 



WL WL __ 3WL _ WL, 

 12 " 24 24 8 ' 



The smaller moment, however, is in the span and the larger 



WL 

 moment is over the support. To assume M = does not make 



LB 



WL 

 the moment over the support = -^j- based on the following reason- 



WL WL 3TFL 2WL WL 

 ing; j^r : ~24 24~ = ~24~' moment over the 



WL 



support is -775-' or nearly this amount, no matter what assumption 

 iz 



may be made for the bending coefficient in the middle of the 

 span. 

 When the moment of inertia of the beam, or slab, is constant, 



the tension over the support is that due to a moment = > 



24 



WL 

 if the span is designed for M = + r=- However, if the amount of 



1.Z 



steel is reduced so the resisting moment will be barely sufficient 



