Civil Engineering Reference
In-Depth Information
parameters needed from the stress-strain curve are the measured initial
Young's modulus (
E
o
), the measured proportional limit stress (
s
p
), the mea-
sured static yield stress (
s
y
) that is commonly taken as the 0.1% or 0.2% proof
stress (
s
0.1
or
s
0.2
) for materials having a rounded stress-strain curve with no
distinct yield plateau, the measured ultimate tensile strength (
s
u
), and the
measured elongation after fracture (
e
f
). It should be noted that structural steel
members used in bridges undergo large inelastic strains. Therefore, the engi-
neering stress-strain curves must be converted to true stress-logarithmic plas-
tic true strain curves. The true stress (
s
true
) and plastic true strain (
e
true
s
true
¼s
1+
e
ð
Þ
ð
5
:
1
Þ
e
pl
true
¼
ln 1 +
e
ð
Þs
true
=
E
o
ð
5
:
2
Þ
where
E
o
is the initial Young's modulus
s
and
e
are the measured nominal
(engineering) stress and strain values, respectively.
The initial part of the stress-strain curve from origin to the proportional limit
stress can be represented based on linear elastic model as given in ABAQUS
[1.29]. The linear elastic model can define isotropic, orthotropic, or aniso-
tropic material behavior and is valid for small elastic strains (normally less
than 5%). Depending on the number of symmetry planes for the elastic
properties, a material can be classified as either isotropic (an infinite number
of symmetry planes passing through every point) or anisotropic (no symme-
try planes). Some materials have a restricted number of symmetry planes
passing through every point; for example, orthotropic materials have two
orthogonal symmetry planes for the elastic properties. The number of inde-
pendent components of the elasticity tensor depends on such symmetry
properties. The simplest form of linear elasticity is the isotropic case. The
elastic properties are completely defined by giving the Young's modulus
(
E
o
) and the Poisson's ratio (
u
). The shear modulus (
G
) can be expressed
in terms of
E
o
. Values of Poisson's ratio approaching 0.5 result in nearly
incompressible behavior.
The nonlinear part of the curve passed the proportional limit stress can be
represented based on classical plasticity model as given in ABAQUS [1.29].
The model allows the input of a nonlinear curve by giving tabular values of
stresses and strains. When performing an elastic-plastic analysis at finite
strains, it is assumed that the plastic strains dominate the deformation and
that the elastic strains are small. It is justified because structural steels used
in bridges have a well-defined yield stress.
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