Civil Engineering Reference
In-Depth Information
F
U3
Steel 3 = Q&T HSLA
F
Y3
F
U2
F
Y2
Steel 2 = HSLA steel
F
U1
Steel 1 = Carbon steel
F
Y1
Stress (s)
Strain ( )
0.002
FIGURE 2.1
Idealized tensile stress-strain behavior of typical bridge structural steels.
exhibited by stress-strain curves are the elastic modulus (linear slope of the initial
portion of the curve up to yield stress), the existence of yielding, and plastic behavior,
with some unrestricted flow and strain hardening, until the ultimate stress is attained.
Yield stress in tension can be measured by simple tensile tests (ASTM, 2000).Yield
stress in compression is generally assumed to be equal to that in tension.
∗
Yield stress
in shear may be established from theoretical considerations of the yield criteria. Var-
ious yield criteria have been proposed, but most are in conflict with experimental
evidencethatyieldstressisnotinfluencedbyhydrostatic(oroctahedralnormal)stress.
Two theories, the Tresca and von Mises yield criteria, meet the necessary requirement
of being pressure independent. The von Mises criterion is most suitable for ductile
materials with similar compression and tensile strength, and also accounts for the
influence of intermediate principal stress (Chen and Han, 1988; Chatterjee, 1991). It
has also been shown by experiment that the von Mises criterion best represents the
yield behavior of most metals (Chakrabarty, 2006).
The von Mises yield criterion is based on the octahedral shear stress,
τ
h
, attaining
a critical value,
τ
hY
, at yielding. The octahedral shear stress,
τ
h
, in terms of principal
stresses,
σ
1
,
σ
2
,
σ
3
is
3
(
σ
1
− σ
2
)
2
1
τ
h
=
+
(
σ
1
− σ
3
)
2
+
(
σ
2
− σ
3
)
2
.
(2.1)
Yielding in uniaxial tension will occur when
σ
1
= σ
Y
and
σ
2
= σ
3
=
0. Substitution
of these values into Equation 2.1 provides
√
2
3
σ
Y
τ
hY
=
(2.2)
∗
It is actually about 5% higher that the tensile yield stress.
