Structural Concrete - Hassoun

398 Chapter 11 Members in Compression and Bending
PC
Figure 11.23 Uniaxial bending with load P n
along the y-axis with eccentricity e y
.
Figure 11.24 Uniaxial bending with load P n
along the x-axis, with eccentricity e x
.
acting along the x-axis (Fig. 11.24) with an eccentricity e x , causing a combination of an axial load
P n and a moment M ny = P n e x .
If the load P n is acting anywhere such that its distance from the x-axis is e y and its distance
from the y-axis is e x , then the column section will be subjected to a combination of forces: An
axial load P n a moment about the x-axis = M nx = P n e y and a moment about the y-axis = M ny =
P n e x (Fig. 11.25). The column section in this case is said to be subjected to biaxial bending. The
analysis and design of columns under this combination of forces is not simple when the principles
of statics are used. The neutral axis is at an angle with respect to both axes, and lengthy calculations
are needed to determine the location of the neutral axis, strains, concrete compression area,
and internal forces and their point of application. Therefore, it was necessary to develop practical
solutions to estimate the strength of columns under axial load and biaxial bending. The formulas
developed relate the response of the column in biaxial bending to its uniaxial strength about each
major axis.
The biaxial bending strength of an axially loaded column can be represented by a
three-dimensional interaction curve, as shown in Fig. 11.26. The surface is formed by a series
of uniaxial interaction curves drawn radially from the P n axis. The curve M 0x represents the