RECTANGULAR BEAMS 65 



It should be remembered that the true maximum intensity of 

 shear will generally be from 10 to 15 per cent higher than the 

 value thus determined. 



The longitudinal tension in the concrete near the end of beam 

 modifies the distribution of the shear, increasing the shearing 

 stress somewhat at the neutral axis and decreasing it at the level 

 of the reinforcement. Equation (3), however, gives results 

 which are sufficiently accurate and are derived for beams having 

 the horizontal bars straight throughout. When any web rein- 

 forcement is used, the distribution and the amount of the shearing 

 stresses at the end of a simply supported beam are materially 

 different from the foregoing. The analysis of the stresses become 

 more complex and a determination of their value impracticable. 

 Even here, however, the above formula serves a useful purpose. 

 It is found that shear is the chief factor in the failure of a 

 beam by diagonal tension and either formula (3) or formula (4) 

 may be used in design if properly controlled by the results of 

 experiments. 



36. Inclined Tensile Stresses. To determine the approximate 

 amount and direction of the diagonal tensile stresses in the 

 concrete of reinforced concrete beams, the two equations given 

 in Art. 29 will apply. The equations there given are as follows: 



(1) 



(2) 



Although we properly neglected any tension which may exist 

 in the concrete, when making the "moment calculations" and 

 when deriving the formula for horizontal and vertical shear, 

 still when it comes to the consideration of diagonal tensile 

 stresses this tension must be taken into account. As already 

 explained, when the maximum fiber stresses in a beam at the 

 section of maximum bending moment have reached their allow- 

 able working values, the cracks near this section, across the 

 bottom of the beam, show that tension in the concrete no longer 

 exists. This is the reason why the concrete is not considered 

 to take any tension in the moment calculations. But it must be 

 understood that cracks due to the same cause do not exist near 

 the ends of the beam where the bending moment is small and 

 where the diagonal tension cracks are 'likely to occur. Also, 

 maximum vertical and maximum horizontal shear will be found 

 at the ends of a beam where the tension in the concrete exists, 



