132 REINFORCED CONCRETE CONSTRUCTION 



A special case, however, occurs with continuous beams of two 

 spans. Such beams should be designed for a positive bending 



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 moment of ^ in the middle of each span and a negative moment 



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 of - r over the center support. 



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The shear at each support of continuous beams with fixed ends 

 may be taken at one-half the span load. If the ends are simply 

 supported the shear in the end spans near the second support 

 will be approximately six-tenths of a span load. 



Many of the building laws in the United States, to provide for 

 the possibility of poor construction and other conditions, give 



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 the more conservative figure to be used throughout. It 



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must be understood that when -^ is used, it is absolutely neces- 

 sary that the beam be really continuous both in design and 

 construction. 



In applying the values for bending moment given above to the 

 various cases in all-concrete construction, the assumption is 

 made that the moment of inertia of the beam is constant through- 

 out its length. While this is not strictly true, extensive studies 

 of various cases in reinforced concrete show that a large change 

 in the moment of inertia makes a very small change in the bend- 

 ing moment, so that the relations are substantially correct. 



Some engineers consider that the use of more steel is necessary 

 between supports than the amount just sufficient to resist the 



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 bending moment ^-- They consider that by figuring for a 



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 moment of - ^ at the center of span, the stresses over the sup- 



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ports are relieved, and the design is more economical. It is 

 true that the negative bending moment over the support de- 

 creases with the increase of steel at the center of span, but it is 

 also true that the consequent decrease of steel over the supports 

 does not offset the increase in steel needed throughout the beam. 

 Mr. Sanford E. Thompson in an article published in the issue 

 of Engineering News of January 13, 1910, under the title 

 "Continuity in Reinforced Concrete Beams/' shows that a beam 



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designed for a moment '- in the middle of span requires 25 



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