RECTANGULAR BEAMS 73 



y 

 bars is -7-3 divided by the sum in inches of the circumference of 



the bars at the given vertical cross-section. // u = uuit bond 

 stress* and lo the total circumference of all bars in a beam at the 

 given section, then 



V 



u= v ., 

 Io]d 



The above formula shows that the bond stress is a simple 

 function of the shear and varies with the shear. Thus, shear 

 diagrams may be used to represent the variation of bond stress 

 along a beam. In most cases, plain horizontal rods are sufficient 

 but, under unusual circumstances, deformed bars are employed to 

 obtain a mechanical bond in addition to the strength resulting 

 from adhesion of concrete to steel. When using the above 

 formula, the average value of j=7/8 may be taken. 



If we consider simply supported beams, experiments show 

 that when stirrups are used the beam is stiffened and the bond 

 stress along the horizontal rods near the end of beam is somewhat 

 reduced. A reason for this may be shown in the fact that, after 

 the concrete begins to crack from diagonal tension (Fig. 38) , 

 the stirrups aid in carrying part of the tensile stress which results 

 from the bending moment then existing at the line of the diagonal 

 crack; the stress in the horizontal rods at the end of beam is thus 

 reduced and likewise the liability of failure through bond. A 

 greater reduction of the bond stress has been found to exist when 

 the web reinforcement is provided by means of bent rods. The 

 reduction becomes considerable when about one-half of all the rods 

 are bent up provided, however, that a sufficient number of rods 

 be thus employed. Results seem to indicate that no reduction 

 should be considered in design unless the number of rods bent be 

 greater than two and that the bends be made at at least two points 

 at each end of beam. Tests show that for conditions especially 

 favorable, an average of 50 per cent more bond stress may safely 

 be allowed on the horizontal rods at the end of beam than would 

 be considered safe by the above formula. No allowance should 

 be made when only stirrups are employed for the web reinforce- 

 ment. The bond stress in continuous beams will receive atten- 

 tion in Art. 63. 



The bond strength of vertical (or inclined) stirrups may be 

 insufficient to develop the required strength of the stirrups with 

 respect to tension. This possibility must also be investigated in 



