Simplified Design for Columns - Simplified Design of Reinforced Concrete Buildings - page 173

(3) COLUMN SIZE AND REINFORCEMENT

With P u = 487 kips, try a 16 16 in. column with 1% reinforcement (see Fig. 5-2). Check for fire resistance:

From Table 10-2, for a fire resistance rating of 2 hours, minimum column dimension = 10 in. < 16 in. O.K.

×

Determine if the columns are slender.

22. In lieu of determining an “exact” value,
estimate k to be 1.2 (a value of k less than 1.2 is usually not realistic for columns in a sway frame.

As noted above, a column in a sway frame is slender if k˜ u /r ≥

For a 1st story column:

( ) − 8.5

1.2 15 ⎣ × 12 ⎦

k u

r

= = 43 > 22

()

0.3 16

For the 2nd through 5th story columns:

( ) − 8.5

1.2 12 × 12

k u

r

⎣ ⎦

= = 34 > 22

()

0.3 16

Therefore, slenderness must be considered for the entire column stack. To neglect slenderness effects, the size
of the column h would have to be:

( ) − 8.5

1.2 15 ⎣ × 12 ⎦

< 22 → h > 31.2in.

0.3h

Obviously, this column would not be practical for a building of the size considered. Reference 5.4 or 5.5 can
be used to determine the required reinforcement for the 16 × 16 in. column, including slenderness effects.

Figure 5.15 shows the results from spColumn for an interior 1st story column, including slenderness effects.
Thirty five percent of the gross moment of inertia of the slab column strip and seventy percent of the gross
moment of inertia of the column section were used to account for the cracked cross section.* It was assumed
that the column was fixed at the foundation; appropriate modifications can be made if this assumption is not
true, based on the actual footing size and soil conditions. Points 2, 4, 6, 8 and 10 correspond to the
load combinations given in ACI Eq. (9-1), (9-2), (9-3), (9-4) and (9-6) respectively. As can be seen from the
figure, 8-No.9 bars are required at the 1st floor. The amount of reinforcement can decrease at higher
elevations in the column stack.

Check for fire resistance: From Table 10-6, for a fire resistance rating of 4 hours or less, the required cover to
the main longitudinal reinforcement = 1.5 in. < provided cover = 1.875 in. O.K.

* The moments of inertia of the flexural and compression members are required in order to compute the effective length factor k of
the column. ACI R10.10 recommends using a value of 0.35 Ig for flexural members (to account for the effect of cracking and rein-
forcement on relative stiffness) and 0.70Ig for compression members when computing the relative stiffness at each end of the com-
pression member, where Ig is the gross moment of inertia of the section.