CONTINUOUS BEAM 165 



The reactions of the continuous beam in (a) may be replaced by 

 the reactions of the two simple beams loaded with the uniform load w 

 in (b), and the reactions and the load of the simple beam with the span 

 L : + L 2 and carrying a negative load r 2 ' in (c). The reactions in (a) 

 will then have the following values ; R i = r i r/ ; R 2 = r 2 -j- r 2 ; 

 R 3 = r 3 r,'. 



Now the upward curvature of the beam in (a) due to the load r 2 

 will be neutralized by the load above equal to r 2 ' which is transferred 

 to the reaction R 2 by flexure in the beam. The upward deflection of 



(-Load w per //>?. ft. 



K-- L, --* --- L --- -H 



the beam in (c) at any point will be the bending moment divided by E I 

 at the same point in (d) due to a bending moment polygon with a maxi- 

 mum moment M 2 = r X ^\ = ?V X L 2 ; and the downward deflection 

 of the beam in (b) at any point will be the bending moment divided 

 by E I Sit the same point in (d) due to the bending moment polygons 

 for a uniform load w covering the simple spans in (b). But the de- 

 flection of the beam in (a) is zero at the reaction R 2 , and therefore the 

 bending moment at the corresponding point in (d) is zero. 



