52 PRACTICAL STRUCTURAL DESIGN 



Assuming spans equal in length and loaded uniformly, the 

 coefficients to use in figuring the reactions on the supports are 

 given in Fig. 47. These coefficients give the total reaction due to 

 the load from the middle of one span to the middle of the adjacent 



span, one full panel 

 length. The moments 

 on each side of the 

 support differ, as 

 shown in Fig. 46, so 

 the shear at the edge 

 of the supports is pro- 

 portional to the mo- 

 Fig. 47 Coefficients for Reactions for Beams ment coefficients in 

 under Uniform Load over Several Equal Spans ^ ne spans Usuallv 

 and Freely Supported at the Ends. R = Cwl. 



however, it is safe to 



use half the reaction for the shear on each side of a support. The 

 three figures are all based on the assumption that the ends of the 

 beams are freely supported. 



Spans are not always equal in length for continuous beams 

 and the beams are not always uniformly loaded. A complete 

 discussion of such conditions is best treated graphically and will 

 be taken up in another chapter. 



When spans are unequal the reactions for continuous beams 

 must be computed for each span separately. The total reaction 

 on any intermediate support is equal to the sum of the reactions 

 for the adjacent spans. 



Let MI = moment at left end of span. 

 Mz = moment at right end of span. 

 Ri = reaction at left end. 

 R 2 = reaction at right end. 

 w = load per lineal foot. 



I = span. When the moment is in foot pounds the span 

 is in feet. 



R l x I - M 2 = -Mi + ~, 



by taking moments about Rz from which 



wl Mi - M 2 

 Ri = ~2 ; and 



wl M z MI 



