SLABS, CROSS-BEAMS, AND GIRDERS 163 



point should be chosen. It should be noticed, however, that 

 the column has some strengthening action at the support and it 

 will not be necessary to keep too closely to the allowable stress. 

 Another point to be noted in the design of a continuous beam 

 at the supports is the bond stress of the compressive reinforce- 

 ment. The general formula for horizontal shear at any point 

 of a beam (see Art. 29) is 



, VQ 

 vb=^- 



At the support, the quantities V and 7 are constant and the 

 horizontal shear per linear inch at any horizontal plane is seen 

 to be proportional to the statical moment of the effective area 



outside such plane about the neutral axis. At the neutral axis 



y 

 this shear per linear inch has been shown to be vb=^ } and the 



V 



resulting bond per square inch of the surface is ./ The shear 



per linear inch between the compression rods and the concrete 

 will, therefore, very closely equal 



F Q of equivalent compressive steel area 

 jd Total Q of compression area 



(By the term equivalent steel area is meant the area of the 

 steel multiplied by n and considered equivalent to concrete at 

 the same horizontal plane.) If this quantity be divided by 

 2o' } considering o' the circumference of a rod in compression, 

 then the result will be the bond per square inch of surface along 

 the compression rods. 



Now the total statical moment of the compression area about 

 the neutral axis equals the total moment of the tension area, 

 which is na(l k)d. The moment of the compressive steel is 

 equal to na' s (kd-d'). Hence, for bond stress of compressive 

 steel per square inch, 



V a' 8 (kd-d>) 

 ~ 



a s (l-k)d 



If now we let d c = diameter of compression rods, d t = diameter 

 of tension rods, and Io= total circumference of the tension rods, 

 then the above formula reduces to 



V d c (kd-d') 



dt(l-k)d 



This formula shows that the bond stress per square inch for the 

 tension and compression rods will be proportional to the product 



