Structural Concrete - Hassoun

11.13 Design of Columns under Eccentric Loading 393
Figure 11.19 Values of K c
versus ρ g
(%).
Linear interpolation can be used. For example, K c = 0.1685 for ρ g = 6% and f ′ c = 4ksi.The
steps in designing a column section can be summarized as follows:
1. Assume an initial size of the column section bh.
2. Calculate K c = P u /(φbh 2 ).
3. Determine ρ g from Table 11.2 for the given f ′ c.
4. Determine A s = A ′ s = ρ g bh∕2 and choose bars and ties.
5. Determine φP n of the final section by statics (accurate solution). The value of φP n should be
greater than or equal to P u . If not, adjust bh or ρ g .
Alternatively, if a specific steel ratio is desired, say ρ g = 6%, then proceed as follows:
1. Assume ρ g as required and then calculate e = M u /P u .
2. Based on the given f ′ c and ρ g , determine K c from Table 11.2.
3. Calculate bh 2 = P u /φK c ; then choose b and h. Repeat steps 4 and 5. It should be checked that
ρ g is less than or equal to 8% and greater than or equal to 1%. Also, check that c calculated
by statics is greater than c b = 87d t /(87 + f y ) for compression failure to control.
Example 11.13
Determine the tension and compression reinforcement for a 16 × 24-in. rectangular tied column to
support P u = 780 K and M u = 390 K ⋅ ft. Use f c ′ = 4ksiandf y = 60 ksi.