STRENGTH OF MATERIALS 



Since for any point I the fraction ^ is proportional to J ib (the 

 denominator being constant), the elastic curve is called the influence 

 line for reactions. 



For a number of concentrated loads J\, P 2 , - -, P n the same method 

 applies, 72 2 in this case being given by the equation 

 .7" . 71. J- 



or, more briefly, 



^ = -T 



To determine the reactions for a beam continuous over four sup- 

 ports and bearing a single concentrated load P at any point /, suppose 

 the two middle supports removed. Then if a unit load is placed at B 



73) and the elastic 

 curve draun, the ordinate 

 1.. this curve at any jM.int 

 / i- the influence number 

 J Similarly, by ]!. 

 4 a unit load at C and con- 

 structing the correspond i n g 

 elastic curve, the influence 

 number J ic is obtained. Now the reaction 7?, must be of such amount 

 as to counteract the deflections at B due to a load P at / and a load 

 fi s at (7. Therefore 



Hi 



FIG. 73 



Similarly the reaction B a must be of such amount as to counteract the 

 deflections at C due to a load P at / and a load R^ at B. Therefore 



By Maxwell's theorem, J bi = J^ and J ci =J ic . Making these substi 

 tutions and solving the above equations simultaneously for /?, and R 9 



_ p 



