Civil Engineering Reference
In-Depth Information
or the criterion, that at yielding,
(
1
√
2
σ
Y
=
σ
1
− σ
2
)
2
+
(
σ
1
− σ
3
)
2
+
(
σ
2
− σ
3
)
2
,
(2.3)
where
σ
Y
is the yield stress from the uniaxial tensile test.
It can also be shown that the octahedral shear stress at yield is (Hill, 1989)
2
3
τ
Y
,
τ
hY
=
(2.4)
which when substituted into Equation 2.2 provides
σ
Y
√
3
τ
Y
=
,
(2.5)
where
τ
Y
is the yield stress in pure shear. Therefore, a theoretical relationship is
established between yield stress in shear and tension.
Example 2.1
Determine the allowable shear stress for use in design,
f
v
, if the allowable
axial tensile stress,
f
t
, is specified as 0.55
F
y
and 0.60
F
y
(
F
y
is the axial tensile
yield stress).
For
f
t
=
0.55
F
y
/
√
3
0.55
F
y
;
f
v
=
allowable shear stress
=
=
0.32
F
y
.
0.60
F
y
/
√
3
0.35
F
y
.
AREMA (2008) recommends the allowable shear stress for structural steel
to be 0.35
F
y
.
For
f
t
=
0.60
F
y
;
f
v
=
allowable shear stress
=
=
2.2.2 D
UCTILITY
Ductility is the ability of steel to withstand large strains after yielding and prior to frac-
ture. Ductility is necessary in railway bridges and many civil engineering structures
to provide advance warning of overstress conditions and potential failure. Ductility
also enables the redistribution of stresses when a member yields in redundant sys-
tems, in continuous members, and at locations of stress concentration (i.e., holes and
discontinuities). Adequate ductility also assists in the prevention of lamellar tearing
in thick elements.
∗
Ductility is measured by simple tensile tests and specified as a
minimum percentage elongation over a given gage length (usually 8 in.). Only ductile
steels are used in modern railway bridge fabrication.
2.2.3 F
RACTURE
R
ESISTANCE
Brittle fracture occurs as cleavage failure with little associated plastic deformation.
Once initiated, brittle fracture cracks can propagate at very high rates as elastic strain
∗
Such as the relatively thick flange plates typically required for railway loads on long-span girders.
