Bending and Axial Loads - Unified Theory of Concrete Structures - page 112

φ

Figure 3.16 Bi-linear M- curves showing effect of compression steel

from 0 to 1% increases the ductility ratio from 6.2 to 10.8. It is clear that the compression

steel is indeed very effective in increasing the ductility of flexural beams.
In short, the effects of the tension and compression reinforcement on the ductility of concrete
structures are very profound. Such information is crucial in the design of reinforced concrete
structures to resist earthquake.

µ

3.3 Combined Bending and Axial Load
In Sections 3.1 and 3.2 we have studied the bending action of reinforced concrete members.
The bending analysis and design of such members have been based on the three fundamental
principles of parallel stress equilibrium, Bernoulli compatibility and uniaxial constitutive laws
of materials. In this section we will apply these same principles to reinforced concrete members
subjected to combined bending and axial load. To limit the scope of this presentation, however,
only the nonlinear theory dealing with mild steel reinforced concrete members at ultimate load
stage will be included. This section is, in fact, an extension of Section 3.2 to cover combined
bending and axial load.

3.3.1 Plastic Centroid and Eccentric Loading
A member subjected to axial compression, with or without bending, is called a column. A
concentric load on a column is defined as a load that produces a uniform stress in the column
section and induces no bending moment. In the case of a symmetrically reinforced rectangular
cross-section a concentric load is located at the geometric centroid of the concrete section.