Structural Concrete - Hassoun

11.17 Parme Load Contour Method 407
c. Take moments about A s using Eq. 11.11:
3. Determine the theoretical axial load P n0
:
P n0
= 0.85f ′ c A g + A st (f y − 0.85f ′ c )
d ′′ = 5.5in. e ′ = 13.5in.
P ny = 1 [ (
C
e ′ c d − a )
]
+ C
2 s (d − d ′ )
= 683.8 K
= 0.85(5)(16 × 24)+10.16(60 − 0.85 × 5) =2198.4K φP n0 = 0.65P n0 = 1429 K
4. Using the Bresler equation (Eq. 11.31), multiply by 100:
100
= 100
P u 476.2 + 100
444.5 − 100
1429 = 0.365
P u = 274 K and P n = P u
0.65 = 421.5 K
Notes
1. Approximate equations or the ACI charts may be used to calculate P nx and P ny . However, since
the Bresler equation is an approximate solution, it is preferable to use accurate procedures,
as was done in this example, to calculate P nx and P ny . Many approximations in the solution
will produce inaccurate results. Computer programs based on statics are available and may
be used with proper checking of the output.
2. In Example 11.19, the areas of the corner bars were used twice, once to calculate P nx and
once to calculate P ny . The results obtained are consistent with similar solutions. A conservative
solution is to use half of the corner bars in each direction, giving A s = A ′ s = 2(1.27) =
2.54 in. 2 , which will reduce the values of P nx and P ny .
Example 11.20
Determine the nominal design load, P n , for the column section of the previous example using the Parme
load contour method; see Fig. 11.30.
Solution
1. Assume β = 0.65. The uniaxial load capacities in the direction of x and y axes were calculated in
Example 11.19:
P ux = 476.2 K P uy = 444.5 K P nx = 732.6K P ny = 683.8K
2. The moment capacity of the section about the x-axis is
M 0x = P nx e y = 732.6 × 12
The moment capacity of the section about the y-axis is
M 0y = P ny e x = 683.8 × 8K⋅ in
3. Let the nominal load capacity be P n . The nominal design moment on the section about the x-axis
is
M nx = P n e y = P n × 12 K ⋅ in.
and that about the y-axis is
M ny = P n e x = 8P n