Reinforced concrete bridges - Computational Analysis and Design of Bridge Structures - page 102

The stress-strain relationships corresponding to unconfined concrete,
confined concrete, and longitudinal steel reinforcement are discussed in the
Sections 4.2.1 through 4.2.3.

4.2.1 unconfined and confined concrete
Numerous stress-strain relationships for unconfined and confined concrete
were developed. The two most popular ones based on their usage are listed
here. Kent and Park (1971) proposed a stress-strain equation for both
unconfined and confined concrete, in which Hognestad's (1951) equation
was generalized to describe the postpeak stress-strain behavior in a more
complete manner. In this model, the ascending branch is represented by
modifying the Hognestad second-degree parabola by replacing 0.85 f c ʹ with
f c ′ and strain at peak stress for unconfined concrete ε co with 0.002. Kent
and Park modified their model again in 1982 as shown in Figure 4.1.

2

2 ε

−

ε
ε

c c

f f

′

= (4.1)

c c

ε

co co

Mander et al. (1988a) first tested circular, rectangular, and square full-
scale columns at seismic strain rates to investigate the influence of different
transverse reinforcement arrangements on the confinement effectiveness
and overall performance. Mander et al. (1988b) went on to model their
experimental results. It was observed that if the peak strain and stress
coordinates (ε cc , f c ′ ) could be found, then the performance over the entire
stress-strain range was consistent, regardless of the arrangement of the

f c

(0.002 K , Kf c ′ )

Confined concrete

f c ′

Unconfined concrete

ε c

0.002

Figure 4.1 Stress-strain behavior of compressed concrete confined by rectangular steel hoops.
(Data from Kent, D.C. and Park, R., J Struct Div ., 97(ST7), 1969-1990, 1971.)