Civil Engineering Reference
In-Depth Information
Table 8.1
Equivalent thickness of the top bracing for the quasiclosed box
Type no.
Type of lateral bracing
Equivalent thinness
(
t
eq
)
1
λ
E
G
2λ
b
d
3
/
A
d
+ 2λ
3
/(3
A
f
)
2
b
d
A
d
S
d
=
qd
A
f
2
λ
E
G
2λ
b
2
d
3
/
A
d
+ 4
b
3
/
A
υ
+ λ
3
/(6
A
f
)
2
b
d
S
d
=
qd
A
d
A
f
A
v
3
λ
E
G
2λ
b
d
3
/(2
A
d
) + λ
3
/(6
A
f
)
qd
2
d
2
b
A
d
A
v
S
d
=
A
f
4
λ
E
G
2λ
b
qd
2
d
3
/
A
d
+ 8
d
3
/
A
υ
+ λ
3
/(6
A
f
)
2
b
d
A
d
A
v
S
d
=
where:
τ is the St. Venant shear stress in any plate
T
is the internal torque
A
is the enclosed area within the box girder
t
is the thickness of the plate
8.1.2.2 Torsional distortion
Torsional load causes the cross section to deform through bending of the
walls (Figure 8.4c). Normal stresses as shown in Figure 8.7 result from
warping torsion restraint and from distortion of the cross section. If the
box girder has no cross frames or diaphragms, the distortion is restrained
only by the transverse stiffness of the plate elements. In an open box girder
cross section, due to the lack of distortional stiffness, the torsional distortion
can be prevented through the use of internal cross frames (Figure 8.8) con-
necting top and bottom flanges. Figure
8.9 illustrates the general box girder
normal stresses, which can occur in a curved or skewed box-shaped girder.
Closed box sections, on the other hand, are extremely efficient at carrying
torsion by means of St. Venant torsional shear flow because the shear flow
around the circumference of the box has relatively large force couple dis-
tances (Figure 8.10). For this reason, a box-shaped girder can carry relatively
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