164 



DEFLECTION OF BEAMS 



duced, they will intersect at 2 on a line through the center of gravity 

 of the moment-area polygon, and the strings 1-2 and 2-3 will be 

 tangents to the elastic curve at the supports R 1 and R 2} respectively. 

 This gives an easy method of constructing the tangents to the elastic 

 curve without constructing the curve. It is also seen that the tan- 



FIG. 5. 



gents to the elastic curve depend only on the amount of the moment 

 area and position of its center of gravity, and are independent of the 

 arrangement of the moment areas. 



Continuous Beams. A beam which in an unstrained condition 

 rests on more than two supports is a continuous beam. For a straight 

 beam the supports must all be on the same level. Beams of one span 

 with one end fixed and the other end supported, or with both ends 

 fixed, may also be considered as continuous beams. 



In Fig. 6a the continuous beam in (a) with spans L t and L 2 carries 

 a uniform load w per lineal foot. It is required to calculate the re- 

 actions R l} R 2 , and R z . 



