Bond, Development Lengths, and Splices - Design of Reinforced Concrete - page 203

7.8 CRITICAL SECTIONS FOR DEVELOPMENT LENGTH

Before the development length expressions can be applied in detail, it is necessary to under-
stand clearly the critical points for tensile and compressive stresses in the bars along the beam.
First, it is obvious that the bars will be stressed to their maximum values at those
points where maximum moments occur. Thus those points must be no closer in either di-
rection to the bar ends than the

d values computed.
There are, however, other critical points for development lengths. As an illustration, a
critical situation occurs whenever there is a tension bar whose neighboring bars have just
been cut off or bent over to the other face of the beam. Theoretically, if the moment is re-
duced by a third, one-third of the bars are cut off or bent and the remaining bars would be
stressed to their yield points. The full development lengths would be required for those bars.
This could bring up another matter in deciding the development length required for
the remaining bars. The Code (12.10.3) requires that bars that are cut off or bent be ex-
tended a distance beyond their theoretical flexure cutoff points by d or 12 bar diameters,
whichever is greater. In addition, the point where the other bars are bent or cut off must
also be at least a distance

d from their points of maximum stress (ACI 12.10.4). Thus
these two items might very well cause the remaining bars to have a stress less than f y , thus
permitting their development lengths to be reduced somewhat. A conservative approach is
normally used, however, in which the remaining bars are assumed to be stressed to f y .

7.9 EFFECT OF COMBINED SHEAR AND MOMENT

ON DEVELOPMENT LENGTHS
The ACI Code does not specifically consider the fact that shear affects the flexural tensile
stress in the reinforcing. The Code (12.10.3) does require bars to be extended a distance
beyond their theoretical cutoff points by a distance no less than the effective depth of the
member d or 12 bar diameters, whichever is larger. The Commentary (R12.10.3) states
that this extension is required to account for the fact that the locations of maximum mo-
ments may shift due to changes in loading, support settlement, and other factors. It can be
shown that a diagonal tension crack in a beam without stirrups can shift the location of the
computed tensile stress a distance approximately equal to d toward the point of zero mo-
ment. When stirrups are present, the effect is still there but is somewhat less severe.
The combined effect of shear and bending acting simultaneously on a beam may pro-
duce premature failure due to overstress in the flexural reinforcing. Professor Charles
Erdei 3-5 has done a great deal of work on this topic. His work demonstrates that web rein-
forcing participates in resisting bending moment. He shows that the presence of inclined
cracks increases the force in the tensile reinforcing at all points in the shear span except in
the region of maximum moment. The result is just as though we have a shifted moment

3 Erdei, C. K., 1961, “Shearing Resistance of Beams by the Load-Factor Method,” Concrete and Constructional
Engineering , 56(9), pp. 318-319.
4 Erdei, C. K., 1962, “Design of Reinforced Concrete for Combined Bending and Shear by Ultimate Lead
Theory,” Journal of the Reinforced Concrete Association , 1(1).
5 Erdei, C. K., 1963, “Ultimate Resistance of Reinforced Concrete Beams Subjected to Shear and Bending,”
European Concrete Committees Symposium on Shear , Wiesbaden, West Germany, pp. 102-114.