Structural Concrete - Hassoun

402 Chapter 11 Members in Compression and Bending
4. Check minimum load capacity of the column from Eq. 10.7:
φP nmx = 0.85φ(0.85f c ′ (A g − A st )+f y A st ) (ACI Eq. 10.1)
= 0.85(0.75)(0.85)(4)(200.96 − 10.16)+(60)(10.16)
= 1023.2 K> 200 K, the section is adequate
11.16 SQUARE AND RECTANGULAR COLUMNS UNDER BIAXIAL BENDING
11.16.1 Bresler Reciprocal Method
Square or rectangular columns with unequal bending moments about their major axes will require
a different amount of reinforcement in each direction. An approximate method of analysis of such
sections was developed by Boris Bresler and is called the Bresler reciprocal method [9, 12]. According
to this method, the load capacity of the column under biaxial bending can be determined by
using the following expression:
1
= 1 + 1 − 1
(11.31)
P u P ux P uy P u0
or
where
1
= 1 + 1 − 1
(11.32)
P n P nx P ny P n0
P u = factored load under biaxial bending
P ux = factored uniaxial load when the load acts at eccentricity e y and e x = 0
P uy = factored uniaxial load when the load acts at an eccentricity e x and e y = 0
P u0
= factored axial load when e x = e y = 0
P n = P u
P
φ nx = P ux
P
φ ny = P uy
P
φ
n0
= P u 0
φ
The uniaxial load strengths P nx , P ny ,andP n0
can be calculated according to the equations and
method given earlier in this chapter. After that, they are substituted into Eq. 11.32 to calculate P n .
The Bresler equation is valid for all cases when P n is equal to or greater than 0.10P n0
. When P n
is less than 0.10P n0
, the axial force may be neglected and the section can be designed as a member
subjected to pure biaxial bending according to the following equations:
or
where
M ux
M x
M ux = P u e y = design moment about x-axis
M uy = P u e x = design moment about the y-axis
M x and M y = uniaxial moment strengths about the x and y axes
+ M uy
M y
≤ 1.0 (11.33)
M nx
M 0x
+ M ny
M 0y
≤ 1.0 (11.34)
M nx = M ux
M
φ ny = M uy
M
φ 0x = M x
M
φ 0y = M y
φ
The Bresler equation is not recommended when the section is subjected to axial tension loads.