Structural Concrete - Hassoun

384 Chapter 11 Members in Compression and Bending
A
B
C
Figure 11.15
Example 11.9: Properties of circular segments.
The stresses in the compression steel have been reduced to take into account the concrete
displaced by the steel bars.
6. The balanced force is P b = C c + ΣC s − ΣT (φ = 0.75).
For a balanced section,
P b = 265.6 +(102.2 + 34.8)−(120 + 52.8) =230 K
ε t = 0.002 and φ = 0.65
φP b = 149.5 K
7. Take moments about the plastic centroid (axis A–A through the center of the section) for all forces:
M b = P b e b = C c × 4.16 + C s1 × 5.1 + C s2 × 2.1 + T 1 × 5.1 + T 2 × 2.1
= 2422.1K⋅ in. = 201.9 K⋅ ft
φM b = 131.2K⋅ ft
e b = 2422.1
230
= 10.5in.
11.11.2 Strength of Circular Columns for Compression Failure
A circular column section under eccentric load can be analyzed in similar steps as the balanced
section. This is achieved by assuming a value for c > c b or a > a b and calculating the forces in
concrete and steel at different locations to determine P n1 P n1 = C c + ΣC s − ΣT. Also,M n can be
calculated by taking moments about the plastic centroid (center of the section) and determining