Handbook of Civil Engineering Calculations

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 0.
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-
3wing forms:

/ P \ ( M-M 0 \

M = M 0 + — (M 6 -M 0 ) P = Pb(M J (45fl)

\^b I \ Mb ~ Mo I

P~ M

0 -M^MlP ^

The ACI Code gives the following approximations: For spiral columns:

M 0 = MUJyD, (46«)

where Ds = diameter of circle through center of longitudinal reinforcement. For symmet-
ric tied columns:

M 0 = QMA 8 fy(d - d') (466)

For unsymmetric tied columns:

M 0 = OAOAsfyjd (46c)

For symmetric spiral columns: