CALCULATION OF REACTIONS 



103 



Graphic Calculation of Reactions. The graphic method for 

 calculating the reactions given in Fig. 56 and Fig. 57 may be proved 

 as follows: In Fig. 5/a the intersection of 2, W and the center line 

 of the bent is at A. Draw A-B and A-C, lay off 2 W so that it is 

 bisected by the point A, and draw 1-2 and 3-4. Then 1-2 equals V 

 and 34 equals V as shown in the following proof : 



Proof. To calculate V take moments of external forces about 

 C, and 



4 times area triangle A-^- 



3-4 XL 



But area triangle A-^-C is also equal to - and 



4 



3 ~ 4 X L 



which proves the construction. It may be proved in like manner that 



J-2 = V. 



FIG. 5/a. 



TRANSVERSE BENT WITH VENTILATOR. The calcu- 

 lation of the wind stresses in a transverse bent with a monitor venti- 

 lator is shown in Fig. 57b. The bents are spaced 32' o" centers and 



