Civil Engineering Reference
In-Depth Information
7.2.6.1.3.1.3 Inelastic Buckling under Pure Shear
In order to account
for residual stresses (which, however, are generally not great in girder webs) and
geometric eccentricities (such as out-of-flatness, which is typical in girder webs),
Equation 7.61 is reduced to
2.12
E
F
y
h
t
w
≤
(7.62)
2.12
t
w
E
/
F
y
, transverse web stiffeners
for design purposes. Therefore, when
h
≥
are required.
7.2.6.1.3.1.4 Combined Bending and Shear
7.2.6.1.3.1.4.1 Strength Criteria
The web plate is subjected to a combination
of shear forces and bending moment depending on location in the span. Since shear
stress is greatest at the neutral axis where normal flexural stresses are zero and normal
bending stress is greatest at the flange where shear stresses are less than average, it is
generally sufficient to design for shear and flexural allowable stresses independently.
Also, in ordinary steel railway girder design, the bending moment carried by the web
plate is relatively small (see Equation 7.36a). However, the design engineer may need
to review shear and flexure interaction in situations when
• Flexural stress is at a maximum allowable value and shear stress is greater
than 55% of allowable shear stress or
• Shear stress is at a maximum allowable value and bending stress exceeds
70% of allowable flexural stress.
This interaction criterion is plotted in
Figure 7.13.
An interaction equation can be
developed, using a factor of safety (FS) of 1.82, as
0.75
F
y
≤
1.05
f
v
F
y
f
b
≤
−
0.55
F
y
,
(7.63)
where
f
v
is the shear stress in the web;
F
v
=
0.35
F
y
is the allowable web shear stress;
f
b
is the flexural stress in the web and is equal to
M
w
/S
w
, where
M
w
is the moment
carried by the web plate (see Equation 7.35) and
S
w
is the web plate section modulus;
F
b
=
0.55
F
y
is the allowable web flexural stress.
7.2.6.1.3.1.4.2 Stability Criteria
Shear and flexural buckling may have to be
considered together when
f
v
/
exceeds 0.40
∗
(Timoshenko and Gere, 1961). For a
τ
∗
When
f
v
/
τ
<
0.4 the critical bending stress is negligibly affected by the presence of shear stresses.
