Civil Engineering Reference
In-Depth Information
1) and uses Equations
7.20 and 7.24 as the basis for steel beam and girder flexural design because the actual
moment gradient along the unbraced length of a beam or girder is difficult to assess
for moving train live loads.
AREMA (2008) conservatively neglects this effect (
C
b
=
7.2.3 S
HEARING OF
B
EAMS AND
G
IRDERS
Shear stresses will exist due to the change in bending stresses at adjacent sections
(Figure 7.4).
Equilibrium of moments and neglecting infinitesimals of higher order
leads to
d
M
−
V
d
x
=
0,
(7.27)
d
M
d
x
=
V
=
shear force.
(7.28)
Referring to Figure 7.5
M
I
x
MQ
I
x
F
=−
y
d
A
=−
.
(7.29)
shaded
area
The change in force,
F
, acting normal to the shaded area in
Figure 7.5
i
s the shear
flow,
q
,or
d
F
d
x
=−
(
d
M
/d
x)Q
I
x
VQ
I
x
q
=
=−
(7.30)
w
(
x
)
V
M
+ d
M
M
V
+ d
V
FIGURE 7.4
Shearing of a beam.
