66 REINFORCED CONCRETE CONSTRUCTION 



but in the preceding equations for shear we have neglected the 

 tension existing in the concrete, because the effect of such tension 

 on the distribution of the shear is very small and need not be 

 taken into account. When it comes to the matter of diagonal 

 tensile stresses, however, the tension in the concrete must be 

 considered. 



As already explained, it is impossible at any point to determine 

 how much tension still remains in tne concrete and, because of 

 this, our formulas for direction and magnitude of the diagonal 

 tensile stresses cannot be used to give us accurate results nor 

 can they be used in design. By means of them, however, we 

 can arrive at some important conclusions. 



Suppose, for example, at some point between the middle and 

 end of a beam, the stress in the steel is 3000 lb., due to a smaller 

 bending moment than the maximum. Consider E c = 2,000,000 

 and E s = 30,000,000. The steel and concrete at the bottom 'of 

 the beam will have the same deformation due to plane sections 

 remaining plane. We know, also, by definition that 



tensile stress in concrete f 8 

 Deformation^ = = ~ 



&C &8 



f IF 



or tensile stress in concrete = - * -- = 200 lb. per square inch. 



& 8 



This is about the ultimate tensile strength of a good concrete 

 and so between this point and the end of the beam, tensile stress 

 will exist in the concrete, even along the bottom of the beam. 

 Between this point and the center, tension will also exist in the 

 concrete but the lower limit of the stress will gradually approach 

 the neutral plane until the amount is approximately zero near the 

 section of maximum moment. The resulting diagonal tension 

 at the point of the beam referred to above, assuming a reasonable 

 shearing stress in the lower part of the beam, say 80 lb. per 

 square inch, will be by equation (1) 



t = 1/2(200) + Vl / 4 (200) 2 + 80 2 = 228 lb. per square inch. 



and it will have a direction inclined about 19 1/4 degrees from 

 the horizontal. This stress may exceed the ultimate strength of 

 the concrete and the result will be an inclined crack. 



The above discussion shows us that the maximum tensile 

 stresses become considerably inclined immediately above the 

 line of the steel. From equation (2) it is plain that this inclina- 

 tion is greater, the greater the shear, and the less the horizontal 



