Structural Concrete - Hassoun

362 Chapter 11 Members in Compression and Bending
For tied sections
φ = 0.65 +(ε t − 0.002)
( ) 250
3
[
1
or φ = 0.65 + 0.25 − 5 ]
c∕d t 3
(11.2)
c. When P u = 0, the case of pure flexure, then φ = 0.90 for tension-controlled sections and
varies between 0.90 and 0.65 (or 0.75) in the transition region.
11.5 BALANCED CONDITION: RECTANGULAR SECTIONS
A balanced condition occurs in a column section when a load is applied on the section and produces,
at nominal strength, a strain of 0.003 in the compressive fibers of concrete and a strain ε y = f y /E s in
the tension steel bars simultaneously. This is a special case where the neutral axis can be determined
from the strain diagram with known extreme values. When the applied eccentric load is greater than
P b , compression controls; if it is smaller than P b , tension controls in the section.
Columns supporting 52-story building, Minneapolis, Minnesota. (Colums are 96 × 64 in. with
round ends.).
The analysis of a balanced column section can be explained in steps (Fig. 11.5):
1. Let c equal the distance from the extreme compressive fibers to the neutral axis. From the
strain diagram,
c b (balanced)
d t
=
0.003
0.003 + f y ∕E s
(where E s = 29,000 ksi) (11.3)