Members subjected to combined axial load and bending moment - Reinforced Concrete with FRP Bars: Mechanics and Design - page 154

research carried out at Lehigh University and the University of Illinois in
the early 1930s (see reference 10). The maximum compressive stress that
the concrete can develop at a strain beyond the yield point of the reinforc-
ing steel, f y , is taken equal to 85% of the compressive strength of a 6 by
12 in. (152 by 308 mm) concrete cylinder. The nominal capacity of an axi-
ally loaded steel RC column, P o , is defined as the sum of the forces carried
by the concrete, P c , and the steel, P s , as given by the following equation:

PPP =+= 0.85 f ′⋅ (-) AA fA + ⋅

(5.1) o c s c g s y s

where A g is the gross cross-sectional area of the column, A s is the area
of the longitudinal steel reinforcement, and f ′ c is the nominal compressive
strength of the concrete. ACI 318-11 also requires that the vertical spacing
of ties not exceed 16 longitudinal bar diameters (to prevent bar buckling),
48 tie diameters (to ensure sufficient tie area to restrain the lateral displace-
ment of the longitudinal bars), or the least lateral dimension of the column
(to develop the maximum strength of the concrete core).

COMMENTARY

Experimental studies performed between the late 1950s and early 1960s
(referenced in De Luca, Matta, and Nanni [10]) showed that steel ties pro-
vide transverse constraint to the concrete core, allowing the column to
fail in a more gradual manner than without ties. It was also found that ties
offered sufficient restraint against buckling of the longitudinal bars up to
compressive failure of the concrete, with negligible influence on the ulti-
mate load.
Few experimental studies have attempted to characterize the influence
of the size of reinforced concrete columns on their structural behavior;
however, the current ACI design specifications for RC columns neglect any
size effect on the nominal axial strength. Bazant and Kwon [21] tested a
total of 26 scaled RC columns of different sizes under eccentric axial load.
The existence of a size effect on the ultimate capacity was observed and it
was consistent with the fracture mechanics-based mathematical formula-
tion derived by Bazant [22]. Sener, Barr, and Abusiaf [23] tested a total of
27 square RC columns with different scales and slenderness ratios under
concentric axial load. The largest cross section had dimensions of 7.9 × 7.9
in. (200 × 200 mm) and reinforcement ratio of 4.91%. It was found that a
reduction in strength occurred at increasing size and slenderness, which was
in good agreement with Bazant's size-effect law. Nemecek and Bittnar [24]