RECTANGULAR BEAMS 



67 



tension. It will, therefore, increase toward the end of the beam. 

 At points nearer the neutral plane, the horizontal tensile stresses 

 become less and the inclined tension approaches the value of the 

 shearing stress, while its inclination approaches 45 degrees. 

 The student through all this discussion should keep in mind 

 that these diagonal tensile stresses can only occur where the 

 concrete still takes its proportion of the tensile stress. Fig. 32 

 is an attempt to represent roughly the general direction of the 

 inclined tensile stresses in a uniformly loaded beam with hori- 

 zontal reinforcement. 



From equation (1) it is evident that the intensity of the diagonal 

 tensile stress at any point depends upon the shear and horizontal 

 tension in the concrete. The percentage of reinforcement is 

 also a factor to be considered, since a large percentage reduces the 



Diagonal -tension -'' 

 cracks likely to occur 



'--Very little tension in 

 the concrete here (if any) 

 on account of concrete 

 cracking across the 

 tension face 



FIG. 32. 



horizontal deformation and consequently the tension in the 

 concrete, and tends to strengthen the beam as regards failure in 

 diagonal tension. Remembering that for a given percentage of 

 reinforcement, the horizontal tension in the concrete depends 

 entirely upon the bending moment, we may say that the strength 

 of a beam as regards diagonal tension failure depends upon the 

 relation between shear and bending moment and upon the 

 amount of reinforcement; shear, however, is the chief factor. 

 From the preceding considerations the student should now see 

 clearly that the character of the loading influences the strength 

 of a beam as regards diagonal tension, the amount of reinforce- 

 ment remaining the same. For example, Fig. 33 represents the 

 variation in moment and shear in a beam with a concentrated 

 load at the center; Fig. 34 represents the variation of these 

 functions in a beam loaded at the third points; while Fig. 35 

 shows similar curves for a uniformly loaded beam. In the first 



