RECTANGULAR BEAMS 101 



so the tension in the horizontal rods decreases gradually toward 

 the end of beam as it should. 



At the bend in a horizontal rod, the stress is transferred 

 gradually to the concrete as compression, and, if the bend is too 

 abrupt, the unit stress in the concrete in this vicinity may be- 

 come excessive. Theory tends to indicate that a radius of bend 

 equal to 12 diameters is satisfactory. Cracks following the line 

 of the rod are seldom seen in tests of beams having even sharper 

 bends in the reinforcement. 



The distance from the support to the point where web rein- 

 forcement is not needed is determined in the same manner as for 

 vertical stirrups. The bent rods, if of the same diameter, 

 should be so arranged that each rod will take an equal part of the 

 diagonal tension that is, if they can be bent in this way and 

 still provide satisfactorily for the horizontal tension. If the 

 rods cannot be bent at the desired points, vertical stirrups 

 must be used to provide for the diagonal tension either toward 

 the center, or toward the end of the beam. 



First of all, we shall assume that the rods can be bent up con- 

 veniently to provide for all the diagonal tension. Consider 

 uniform loading. The maximum shear V should be calculated 

 at the support, point D, Fig. 48. One-third of V will be taken 

 by the concrete and two-thirds by the bent bars. Point A should 

 also be determined namely, the point where the web reinforce- 

 ment is not needed. From this point to the left support, the 

 shear to be taken by the bent bars increases from zero to its 

 maximum value of 2/3 V at the support, and may be represented 

 by the triangle ABC. To construct this triangle draw a line 

 AB from point A at 45 degrees with the horizontal, and from 

 point D draw a line DB perpendicular to the line AB. Then, 

 consider the maximum shear per inch length of beam to be 



213V 

 represented by BC; in other words, BC=2/3vb = - Now, 



suppose we intend to bend two rods at a time and to bend in all 

 8 rods, all of the same diameter. Then each of them will take an 

 equal part of the diagonal tension. Divide the area of the tri- 

 angle into four equal parts, find centers of gravity of each part, 

 and from these centers of gravity draw lines to represent the 

 location of points to bend up the bars in the beam. The method 

 of division of the triangle into an equal number of parts is clearly 

 shown in the drawing, where the line AB is divided into equal 



