106 REINFORCED CONCRETE CONSTRUCTION 

 and solving for x 2 (see Fig. 50) , we have 



x t = or <5|1- 



z \ 



wl 2 

 For any bending moment M = 



x,= OK 1(1-^1^ 



(the meaning of this formula will be clear after studying Art. 54). 



If it is desired to bend up a number of rods two or more at a 

 time, then x 2 should be determined for each bend. After this is 

 done, the remaining horizontal bars should be pecure against 

 slipping. 



For concentrated and unsymmetrical loading, the maximum 

 moments at various sections will need to be determined, in order 



FIG. 51. 



to ascertain the points where the horizontal bars may be bent up. 

 From these maximum moments obtain the required area of 

 horizontal rods at the different points (1, 2, 3, and 4, Fig. 51). 

 Plot a curve to scale, as shown. Thus, ab represents the area 

 required at the point a. On the center ordinate lay off the 

 required areas of the rods, and draw horizontals as shown. The 

 rods may be bent up where these horizontals cut the curve but 

 it would be better, however, to carry them a short distance 

 beyond the theoretical points. 



PROBLEMS 



(Working stresses recommended by the Joint Committee to be used 



throughout.) 



33. A simply supported beam of 12 ft. span (c. to c. of supports) and 18 in. 

 breadth is to carry a uniform load (live plus dead) of 6000 Ib. per foot 

 and rest upon concrete supports. Considering the reactions as uniformly 



