Nonlinear Material Behavior of the Bridge Components - Finite Element Analysis and Design of Steel and Steel-Concrete Composite Bridges - page 54

Stress (MPa)

840

HPS 100W

700

HPS 70W

560

50W

420

36

280

140

Strain

0.04
Figure 2.3 Typical example engineering stress-strain curves for American bridge
structural steels.

0 0.08 0.12 0.16 0.20 0.24 0.28

Table 2.4 Nominal Strength of American ASTM A709 Steel Grades

HPS
50W

HPS
70W

Grade 36 50 50S 50W HPS 100W

Plate thickness
(mm)

t 102 t 102 N/A t 102 t 102 t 102 t 64 64 t

102

<

Shapes All All All All N/A N/A N/A N/A

f u (MPa) 400 448 448 483 483 586 758 689

f y (MPa) 248 345 345 345 345 483 689 620

using the von Mises yield criterion, which is commonly used to predict the
onset of yielding in steel subject to multiaxial states of stress as follows:

s

s x s y

2 + s y s z 2 + s z s x

2 +6 t xy 2 + t yz 2 + t zx 2

ð Þ

f y ¼ ð 2 : 1 Þ

2

For the state of pure shear in one direction, the normal stresses are equal
to zero; the shear yield stress ( f yv ) can be determined as follows:

1
3

f yv ¼ p f y 0 : 58 f y ð 2 : 2 Þ

The shear modulus ( G ) based on Young's modulus ( E ) and Poisson's
ratio ( n ) is given as

E s
21+ u ð

G¼

Þ ¼ 11, 200 ksi 77, 200 MPa

ð Þ ð 2 :

3 Þ