Members subjected to combined axial load and bending moment - Reinforced Concrete with FRP Bars: Mechanics and Design - page 164

5.6 BENDING MOMENT AND AXIAL FORCE

Based on the existing knowledge, the design of concrete columns with rectan-
gular or circular cross sections using FRP longitudinal bars and ties appears
doable and a design methodology is presented as follows. As the basis of this
methodology, the following considerations and assumptions are made:

• The strength of a GFRP RC cross section under combined flexure and
axial load can be calculated by satisfying strain compatibility.
• GFRP longitudinal reinforcement is considered effective only in ten-
sion. The maximum design tensile strain of longitudinal bars must be
less than 0.01 to limit lateral deflections.
• The area of the FRP reinforcement subject to compression is replaced
with an equivalent area of concrete as if the FRP bars in compression
were not present in the cross section.
• A modified and unified formulation of the strength-reduction factor
for the interaction diagram is derived using comparative target reli-
ability indices to meet appropriate safety requirements.
• Based on ACI 440.1R-06, the contributions of concrete, V c , and ties,
V f , to the total shear strength, V n , are reformulated to accommodate
the case of column cross sections.

The combined nominal moment and axial force ( M n , P n ) are multiplied by
the appropriate strength-reduction factor, ϕ, to obtain the design strength
(ϕ M n , ϕ P n ) of the cross section. The design strength must be equal to or
greater than the factored ultimate moment and axial load:

(ϕ M n , ϕ P n ) ≥ ( M u , P u ) (5.20)

The factored pair of ultimate moment and axial load ( M u , P u ) denotes the
effects of the various combinations of loads to which a structure is subjected.
Similarly to steel RC columns, an “interaction diagram” can be gener-
ated by plotting the nominal axial force strength, P n , against the corre-
sponding nominal moment strength, M n . This diagram defines the strength
of a cross section at different eccentricities of the load, which must encom-
pass all the points associated with ( M u , P u ). With such assumptions, typical
design interaction diagrams, (ϕ M n , ϕ P n ), may be formulated as shown in the
following section.

5.6.1 Interaction diagram for rectangular
cross section
This section summarizes a procedure to build the interaction diagram of
a rectangular cross section in a way that is similar to what is typically