1 66 DEFLECTION OF BEAMS 



From the above discussion it follows that to calculate the reactions 

 of the continuous beam in (a) by moment areas, take a simple beam 

 with a span equal to L + L 2 , and load it with the bending moment 

 polygons for beams (b) and (c) as in (d) ; the bending moment in 

 beam (d) at the points corresponding to the reactions will be equal to 

 zero, and the reactions of beam (a) can be calculated by statics when 

 the M 2 is obtained. 



Continuous Beam Concentrated Loads. In (a) Fig. 6, a con- 

 tinuous beam of two equal spans of length L, is loaded with two 

 equal loads P, at the centers of the spans. Calculate the bending 



PL PL 



^ "^'i " ~,M ^ 



FIG. 6. 



moments and load a simple beam with a span equal to 2 L, with the 

 bending-moment diagrams due to P in each span, and with the nega- 

 tive bending-moment diagram due to the reaction R 2 . Then to find 

 M 2 , the bending moment at 2, take moments of forces to the left of 

 2, and 



M 2 L 2 P L 3 



+ 



To calculate R^ take moments in (a) about 2, and 



PL 







2 



