REENFORCED CONCRETE 



163 



form of stirrups, or -loops (Fig. 110). It can be shown that the 

 maximum shear in a beam is inclined at an angle of 45 to the axis 

 of the beam.* Therefore to be effective, vertical stirrups cannot be 

 spaced farther apart than the depth of the beam. In actual prac- 

 tice it is customary to make the distance apart about one half this 



amount, or - , where h denotes the depth of the beam. 

 ft 



Since the maximum shear is inclined at an angle of 45 to the 

 vertical, the effective area of the stirrups is V5 times their cross- 

 sectional area ; but since the maximum shear is also approximately 

 equal to V2 times the average shear,t it is usual simply to design 

 the stirrups to carry the average shear. 



Column 



Column. 



Transverse Section 

 Through Beams and Slab 



FIG. 110 



For instance, suppose that the maximum shear on any cross sec- 

 tion of a beam has an average value of 100 lb./in. 2 , which, as shown 

 by the results of tests, is about the maximum limit for good work. 

 Then, assuming that the concrete carries 30 lb./in. 2 of this shear, 

 the vertical stirrups must be designed to carry the .remainder, or 

 70 lb./in. 2 Therefore if the beam is of breadth b and depth A, the 

 total shear to be carried by the stirrups is 70 bh, and consequently for 

 a working stress of 15,000 lb./in. 2 in the steel, the required area is 



70 bh _ 004m 

 s ~ 15,000 



or .47 per cent of the total area of the cross section. Since the 

 stirrups are usually in the form of a double loop, the required 



* Slocum and Hancock, Strength of Materials, revised edition, article 28, p. 25, Ginn 

 and Company. t Ibid., article 55, pp. 59 and 60. 



