Structural Concrete - Hassoun

11.17 Parme Load Contour Method 405
A
B
8 no. 10 bars
C
D
Figure 11.29 Example 11.19: Biaxial load, Bresler method: P n
= 421.5 K.
Solution
1. Determine the uniaxial load capacity P nx about the x-axis when e y = 12 in. In this case, b = 16 in.,
h = 24 in., d = 21.5 in., d ′ = 2.5 in., and A s = A ′ s = 3.81 in.2 . The solution will be performed
using statics following the steps of Examples 11.2 and 11.4 for balanced and compression-control
conditions.
a. For the balanced condition,
c b =
(
87
87 + f y
)
d =
( ) 87
21.5 = 12.72 in.
147
a b = 0.80(12.72) =10.18 in. (β 1 = 0.8when f c ′ = 5ksi)
C c = 0.85f c ′ ab = 692.3 K
( )
′ c − d
f s = 87 ′
= 69.9ksi
c
Then f s ′ C s = A ′ s (f y − 0.85f c ′)=212.4K T = A s f y = 228.6 K
P 0x = C c + C s − T = 676.1 K
φP bx = 0.65P bx = 439.5K (φ = 0.65 for ε t = 0.002)
b. For e y = 12 in. < d = 21.5 in., assume compression failure and follow the steps of Example
11.4togeta = 10.65 in. and c = a/0.8 = 13.31 in. > c b = 12.72 in. Thus, compression controls.
Check
( )
f s ′ c − d = 87 ′
= 70 ksi > f
c
y