Design of a column - Reinforced Concrete with FRP Bars: Mechanics and Design - page 333

r = (0.3)(20 in.) = 6.0 in.: radius of gyration of the column
kl u /r = 27.0

From Table 9.2 it can be concluded that the maximum value of the
(kl u /r) max is associated with the case of single curvature; therefore:

(kl u /r) max = 29−12(11.4/113.7) = 27.8

kl u /r = 27< (kl u /r) max

Hence slenderness effects may be disregarded.
P-M diagram: The interaction diagram was built following the proce-
dure discussed in Chapter 5. The assumed parameters and the geometry of
a generic rectangular section are displayed in Figure 9.4.
For the analysis, it is assumed that the cross-section reinforcement is
applied at i different levels (varying from 0 to Nf f - 1) of depth df(i), f (i), and the
spacing of the side reinforcement, sf, f , is constant.
The interaction diagram is constructed by locating the critical points
listed next.
Condition 1: pure compression (c = +∞). The strain and stress distribu-
tions corresponding to point 1 are shown in Figure 9.5. Because the entire
cross section is in compression, the contribution of the FRP reinforcement
is neglected and reflected with an equivalent area of concrete.
The combined nominal axial and moment capacities, P n and M nx , are

P = 0.85 f ′ bh

n c

(9.3)

M nx = 0

Condition 2: neutral axis intersecting the bottom fiber (c = h). The strain
and stress distributions for this condition are shown in Figure 9.6. The
concrete stress distribution, σ c (x), is approximated by the stress block. The

b

y

c c

d f (i)

i th

s f C g

x

h

Figure 9.4 Generic rectangular cross section.