Nonlinear Material Behavior of the Bridge Components - Finite Element Analysis and Design of Steel and Steel-Concrete Composite Bridges - page 53

Stress

E st

f y

f p

0.2 %
offset
line

E s

e y

e st

Strain
Figure 2.2 Initial part of the stress-strain curve for steels with a yield plateau.

corresponding to the tensile strength f u . The slope of the stress-strain curve
constantly varies during strain hardening. The tangent slope of the curve at
the onset of strain hardening ( E st ) is often used for analysis of steel behavior at
high strain levels. Tensile coupon test results are usually presented by engi-
neering stress-strain curves where stress is calculated based on the unde-
formed cross-sectional area of the specimen. As the specimen is loaded,
the cross-sectional area is constantly being reduced, which is known as neck-
ing phenomena. The true stress at any given point can be calculated with
respect to the contracted area at that point in time. In nonlinear structural
analyses, true stress-strain curves should be used. Figure 2.3 shows typical
stress-strain curves for steels in the A709 [ 2.1 ] specification. Steels with
f y 70 ksi (483 MPa) show definite yield plateaus with similar ductility.
The HPS 100W steel does not have a clearly defined yield plateau and shows
slightly lower ductility compared to the lower-strength steels. The amount
of strain hardening decreases with increasing yield strength. The minimum
specified yield strength ( f y ) and tensile strength ( f u ) are shown in Table 2.4 for
steel grades included in the A709 specification. Plates with thickness up to
4 in. (101.6 mm) are available in all grades, except for 50S. Rolled shapes are
not available in the HPS grades. The shear yield stress ( f yv ) can be determined