RECTANGULAR BEAMS 93 



reinforcement, apply to the maximum unit shear at any point 



y 

 of a vertical section, which we have previously found to be =-TV 



This maximum extends from the horizontal steel up to the 

 neutral axis. The stress in the stirrups will consequently be 

 the greatest along a plane located between the neutral plane and 

 the horizontal rods. 



Assuming that the distance between centers of compression 



and tension (jd) is approximately 7/8d, it is clear that stirrups are 



y 

 required with horizontal bars, only when 7-7 is greater than 7/8(40) 



y 



= 35 Ib. per square inch. Also, 7-7 should not be greater than 



7/8(120) =105 Ib. per square inch with the most effective web 



y 

 reinforcement, j-j has been previously denoted by v , and we 



shall represent it in this manner hereafter. 



The manner of providing for diagonal tension in beams cannot 

 be impressed too strongly upon the student. First of all, notice 

 the most unfavorable part of the given beam as regards diagonal 

 tensile stresses. This will be at points of excessive shear com- 

 bined with considerable bending moment. Also, be careful to 

 extend sufficient horizontal steel to the ends of the beam to 

 provide for bending with low unit stresses in the steel. A great 

 many times it will be impracticable to provide as much reinforce- 

 ment as desired by means of bent-up rods, and some vertical 

 stirrups will be needed. In small beams, vertical stirrups only 

 are often employed throughout, but in large beams under heavy 

 shearing stresses, both should be used. In detail, stirrups may 

 be made in various forms, as indicated in Fig. 45. Special 

 attention is called to the many excellent features of the continu- 

 ous stirrup. Woven wire bent around the rods is a satisfactory 

 and very effective reinforcement. The Joint Committee recom- 

 mends that the longitudinal spacing of stirrups or bent rods 

 should not exceed three-fourths the depth of the beam. 



42. Vertical Stirrups. We have seen that the required area of 

 cross-secti9n of a vertical stirrup may be determined by the 

 formula 



2 7s 



~3 f a jd 



