Page 254 - Handbook of Civil Engineering Calculations, Second Edition

REINFORCED CONCRETE 2.39

FIGURE 23. Interaction diagram.

and the latter on an uncracked section. The subscript b as used by the ACI Code in the
present instance does not refer to balanced design. However, its use illustrates the analogy
with ultimate-strength analysis.) Let F denote the point representing M o .
For simplicity, the interaction diagram is assumed to be linear between E and F. The
interaction equation for a cracked section may therefore be expressed in any of the fol-
lowing forms:

M M o
P
M M o (M b M o ) P P b (45a)
P b
M b M o
P b M o
P (45b)
M o M b P b M/P
The ACI Code gives the following approximations: For spiral columns:

(46a)
M o 0.12A st f y D s
where D s diameter of circle through center of longitudinal reinforcement. For symmet-
ric tied columns:
M o 0.40A s f y (d d
) (46b)
For unsymmetric tied columns:

M o 0.40A s f y jd (46c)