Structural Concrete - Hassoun

366 Chapter 11 Members in Compression and Bending
Reinforced concrete tied column under construction. The two columns are separated by an expansion joint.
1.
where
P n − C c − C s + T = 0 (11.10)
C c = 0.85f c ′ ab
C s = A ′ s (f s ′ − 0.85f c ′ ′
) (If compression steel yields, then f s = f y .)
T = A s f s (If tension steel yields, then f s = f y .)
2. Taking moments about A s ,
(
P n e ′ − C c d − a )
− C
2 s (d − d ′ )=0 (11.11)
The quantity e ′ = e + d ′′ ,ande ′ = (e + d − h/2) for symmetrical reinforcement (d ′′ is the
distance from the plastic centroid to the centroid of the tension steel.)
P n = 1 [ (
C
e ′ c d − a )
]
+ C
2 s (d − d ′ )
(11.12)
Taking moments about C c ,
(
P n
[e ′ − d − a )] (
− T d − a ) ( ) a
− C
2
2 s
2 − d′ = 0 (11.13)
and
P n = T(d − a∕2)+C s(a∕2 − d ′ )
(e ′ + a∕2 − d)
(11.14)