Structural Concrete - Hassoun

Summary 413
SUMMARY
Sections 11.1–11.3
1. The plastic centroid can be obtained by determining the location of the resultant force produced
by the steel and the concrete, assuming both are stressed in compression to f y and
0.85f ′ c, respectively.
2. On a load–moment interaction diagram the following cases of analysis are developed:
a. Axial compression, P 0
b. Maximum nominal axial load, P n,max = 0.8P 0 (for tied columns) and P n,max = 0.85P 0 (for
spiral columns)
c. Compression failure occurs when P n > P b or e < e b
d. Balanced condition, P b and M b
e. Tension failure occurs when P n < P b or e > e b
f. Pure flexure
Section 11.4
1. For compression-controlled sections, φ = 0.65, while for tension-controlled section, φ = 0.9.
2. For the transition region,
⎧
⎪0.65 + ( ε t − 0.002 ) ( )
250
for tied columns
φ = ⎨
3
⎪0.75 +(ε
⎩
t − 0.002)(50) for spiral columns
Section 11.5
For a balanced section,
Section 11.6
c b =
β 1 = 0.85
87d t
87 + f y
and a b = β 1 c b
for f ′ c ≤ 4ksi
P b = C c + C s − T = 0.85f ′ cab + A ′ s(f y − 0.85f ′ c)−A s f y
M b = P b e b = C c
(
d − a 2 − d′′ )
+ Td ′′ + C s (d − d ′ − d ′′ )
e b = M b
P b
The equations for the general analysis of rectangular sections under eccentric forces are
summarized.