Simplified Design for Columns - Simplified Design of Reinforced Concrete Buildings - page 156

(3) Point 5:

For columns with 2 or 3 layers of reinforcement:

h

Compression Face

d n

Layer n, A sn

d i

d 1

h

Layer i, A si

Layer 1, A s1

Tension Face

1.5" (typ.)

Figure 5-5 Notation for Eqs. (5-1) and (5-2)

Table 5-2 Constants for Points 2-4

Point No. C 1 C 2 C 3

2 2.89 1.00 0.85

3 2.14 1.35 0.63

4 1.70 1.69 0.50

φ M n = 4A s1 d 1

For columns with 4 or 5 layers of reinforcement:

M n = 4(A s1 + A s2 )(d 1 - s φ

2 )

where s = center to center spacing of the bars

In both equations, φ = 0.90; also, A s1 and A s2 are in. 2 , d 1 and s are in in., and φ M n is in ft-kips.

M n approximately 3% larger than the
exact values (at most). The equations for Point 5 will produce conservative values of

The simplified equations for Points 2-4 will produce values of φ P n and φ

M n for the majority of
cases. For columns subjected to small axial loads and large bending moments, a more precise investigation into
the adequacy of the section should be made because of the approximate shape of the simplified interaction
diagram in the tension-controlled region. However, for typical building columns, load combinations of this type
are rarely encountered.

φ