Reinforced concrete bridges - Computational Analysis and Design of Bridge Structures - page 104

in which f t ′ is given by

= 1
2

f

′

k f

ρ (4.2g)

t e s yh

where:
ρ s is the ratio of the volume of transverse confining steel to the volume
of confined concrete core
f yh is the yield strength of transverse reinforcement
k e is the confinement coefficient

For circular hoops

2

1 − ( s 2 d )

′

s

k = (4.2h)

e

1 − ρ

cc

For circular spirals

1 − ( s 2 d )

′

s

k

= (4.2i)

e

1 − ρ

cc

where:
ρ cc is the ratio of the area of longitudinal reinforcement to the area of
core of the section
s ′ is the clear spacing between spirals of hoop bars
d s is the diameter of spiral

Due to its generality, the Mander et al. (1988b) model (Figure 4.2) has
enjoyed widespread use in design and research despite a few shortcomings.

4.2.2 Reinforcing steel
The stress-strain relation of reinforcing steel exhibits an initial linear
elastic portion, a yield plateau, a strain-hardening range in which the
stress again increases with strain, and finally a range in which the stress
drops off until fracture occurs. The length of the yield plateau and strain-
hardening regions decreases as the strength of the steel increases. For
monotonic loading, reinforced steel is represented as either an elastic-
perfectly plastic material or an elastic strain-hardening material. It can
also be represented using a trilinear stress-strain curve or a complete
stress-strain curve. Most often elastic-perfectly plastic representation is
selected (Darwin 1993).
In the analysis of moments and axial loads, two different models of the
stress-strain performance of the reinforcing steel may be adopted. For nominal