Structural Concrete - Hassoun

3.9 Singly Reinforced Rectangular Section in Bending 105
Table 3.3
Values of ρ t
and R u
for Sections in Transition
Region with ε t
= 0.004, f y
= 60 ksi, and One
RowofBars(φ = 0.817)
f ′ c (ksi) ρ b
ρ t
(limit) R u
(psi)
3 0.0214 0.0155 617
4 0.0285 0.0206 822
5 0.0335 0.0243 980
6 0.0377 0.0273 1116
Example 3.1
For the section shown in Fig. 3.13, calculate
a. The balanced steel reinforcement
b. The maximum reinforcement area allowed by the ACI Code for a tension-controlled section and
in the transition region
c. The position of the neutral axis and the depth of the equivalent compressive stress block for the
tension-controlled section in b.
Given: f ′ c = 4ksiandf y = 60 ksi. 8.13
9.56
ksi
4.06
Figure 3.13 Example 3.1.
Solution
f
a. ′ ( )
c 87
ρ b = 0.85β 1
f y 87 + f y
Because f c ′ = 4000 psi, β 1 = 0.85:
( )( )
ρ b =(0.85) 2 4 87
= 0.0285
60 87 + 60