124 REINFORCED CONCRETE CONSTRUCTION 



accurate to give nearly equal spacing to the inclined . rods closer spacing, 

 however, being favored toward the support. The four rods will be bent up 

 two at a time. To investigate for diagonal tension, the line AB, Fig. 60, 

 should be divided into four equal spaces and the position of two of the rods 

 determined by a line projected up at an inclination of 45 degrees with the 

 horizontal, and beginning at about the point marked 1. The place to bend 

 up the other two rods should be determined by a parallel line passing prac- 

 tically through the point 3. The points to bend up the rods between the 

 right support and the adjacent concentrated load, to provide for diagonal 

 tension, is determined in a similar manner to the above. 



An investigation must now be made to see whether the tensile stresses in 

 the bottom of the beam will permit the bending of the rods as required for 

 diagonal tension. Fig. 61 shows the bending moment curve plotted to 

 scale, and the points where the rods may be bent up are determined by the 

 method described in Art. 45. It is clear that the rods cannot be bent up as 

 desired to provide tho oughly for diagonal tension. The points where the 

 rods are actually bent up are about 2 in. beyond the theoretical points as 

 determined by moment. * 



The area ABNM, Fig. 60, represents the amount of diagonal tension to 

 be taken by inclined rods. We have just found, however, that the rods 

 cannot be bent up at just the proper points to take all of this. If each 

 bent-up rod is assumed to take diagonal tension to the amount of one-half 

 its tensile value on each side of itself, then the area bBNc remains unprovided 

 for. Stirrups will be provided to take diagonal tension between the point 

 t, where the line be produced meets the neutral line, and the adjacent load. 

 Only two stirrups are required, but it would seem advisable in a design of this 

 kind to also place stirrups at the positions indicated by the dotted lines. 

 The spacing of the stirrups is determined by the formula 



2V 



and the student should be familiar with the method of procedure. The 

 length of embedment of the inclined rods should be 50 diameters, or 

 37 1/2 in. 



In the above problem the web reinforcement could be designed to take 

 considerably less than 2/3 the diagonal tension with safety. The bent-up 

 rods would not change but the number of stirrups theoretically required 

 might be reduced. In a problem of this kind is found the maximum 

 deviation from the assumption of Art. 41 pertaining to the coefficient 2/3 

 in the formulas for the design of web reinforcement due, of course, to the 

 trapezoidal shape of the shear diagram. 



51. Deflection of Beams. Very little has been accomplished 

 with respect to the determination of formulas for the deflection 

 of reinforced concrete beams. The difficulty which has been 

 experienced has been due to the fact that the beam action is 

 complicated as far as it pertains to deflection. During the early 

 loading, the concrete assists the steel in taking tension and the 



