CHAP. XH.] METHODS COMBINED. 179 



find the reactions and follow them through by the method of 

 Art. 114. 



From the above reactions we can, however, easily determine 

 the distance of the inflection point. This will, of course, be 

 found only in the loaded span, at a distance from the middle 

 support. 



~- 



We can find the values of x corresponding to different values 

 of a, and thus plot the curve for the inflection points. Thus, 

 for 



a = a = l a = l a = l a = l 



This curve being drawn for any particular case, we can 

 easily find the position of the inflection point for any given 

 value of 0, and hence the reactions, and then find the strains in 

 the various pieces. 



Thus, in PI. 21, Fig. 82, the curve B e d being drawn, we 

 can at once find the inflection point * for any position a of 

 the weight P. We have simply to make B b = a and draw T) e. 

 1} e is the distance of the point of inflection from B. We can 

 now, as explained above, draw any line as P *', and then P C 

 and A A. The ordinates to the broken line A A P C from A C, 

 to the scale of distance, multiplied by the pole distance H to 

 scale of force, will give the moments at any point. Moreover, 

 H E is the shear at B. E a is the reaction at B, H a the re- 

 action at A, and H P the reaction at C. The reactions at B 

 and C are, of course, positive or upwards, that at A negative 

 or downwards. Hence E # H # 4- H P = P, as should be. 



The value of x for the inflection vertical is by Art. 112 



i a I 



x== f- \~7 > 



(i a) I ^ a 



or, substituting the value of i above, 



a I (2 I a) 



Since, therefore, in this case the value of x is no simpler than 

 that for i given above, it will be preferable to plot the first 

 curve directly as represented in Fig. 82. 



119. Approximate Construction. In practice it will be 



