102 REINFORCED CONCRETE CONSTRUCTION 



parts and dotted arcs of circles are drawn with centers at A. 1 

 The reason for projecting the neutral axis AD upon a plane 

 making 45 degrees with the horizontal may need some explana- 

 tion. Our formula for the required total area of steel in each 

 bend is 



_2 0.77s 

 a ~3 f.jd 



Hence the sum of the stresses in the inclined bars at each bend 

 is given by the following formula 



, _2 0.77s 

 as J*-3 ~jT 



2 7(atD) 2 7(at#), 

 But any ordmate as BC = = -- ^ Also. xy = -- -- r^ ^ 



3 ]d 3 ]d 



and Bx = Q.7s. Then, the 



2 7(at No. 1 bars)0.7s 

 area BC yx = =- r, 



o yd 



(the bars being practically half way between x and B), and 

 represents the sum of the stresses in the No. 1 bars. Similarly, 

 the area xyy'x' represents the sum of the stresses in the No. 2 bars. 



In practice the line AC need not.be drawn. For example, no 

 matter what angle the line AC makes with the line AB } the 

 points 1, 2, 3, and 4 will be the same; the points 1, 2, and 3 will 

 remain practically half way between B and x } x and z', and x f 

 and z", respectively, while A4 will remain as 2/3 Ax ". 



The bond strength in these inclined bars must now be in- 

 vestigated. This strength should be provided in the upper 

 portion of the beam. As with vertical stirrups, we shall arbitra- 

 rily assume that no stress is transmitted from the steel to the 

 concrete below a point which is 0.6 d below the upper surface of 

 the beam. 



We will assume that the stress in an inclined bar is its working 

 stress. This gives the maximum condition. Using the notation 

 of the preceding article and V for length, 



l'ou = a s f s 

 and for round or square bars, 



or 



I' = ~ diameters. 

 4u 



i From Taylor and Thompson's "Concrete, Plain and Reinforced," 2nd edition, page 475. 

 Copyright, 1905, 1909, by Frederick W. Taylor. 



