1 68 DEFLECTION OF BEAMS 



3 4 ii 



R 2 = R 3 = -w L w L wL 



2 10 10 



Continuous Beam of n Spans. To calculate the reactions for a 

 continuous beam of n spans, equal or unequal, loaded with any system 

 or systems of loads proceed as follows : 



Calculate the bending moment due to the external load, or loads, 

 or system of loads in each span considered as a simple beam. Take 

 a simple beam having a total length equal to the length of the con- 

 tinuous beam, and load it with the bending moment polygons found 

 as above. Also load the beam with the bending moment polygons due 

 to the reactions. The reactions being unknown, the bending moments 

 at the reactions will be unknown. Now calculate the bending moment 

 in the simple beam at points corresponding to each reaction and place 

 the result equal to zero, for the reason that the deflection at the sup- 

 ports is zero. 



For a continuous beam of n spans there will be n + i equations 

 which is equal to the number of unknown reactions. Solving these 

 equations the unknown moments will be found, and the reactions may 

 be calculated algebraically. 



Transverse Bent. The problem of the calculation of the point 

 of contra-flexure in the columns of a transverse bent the algebraic 



solution of which is given in Chapter XI will now be solved by the 

 use of moment areas. The nomenclature in Fig. 8 is the same as in 



