Straight and curved steel box girder bridges - Computational Analysis and Design of Bridge Structures - page 239

4 A

b t

2

J =

∑

)

(8.4)

(

where:
A is the enclosed area of the box section
b is the width of the individual plate element in the box
t is the thickness of the plate element in the box

For the approximation of the torsional constant of a multicell box, the
intermediate webs can be ignored as shear stress flows over these webs are
negligible due to countereffects from two adjacent cells. Therefore, Equation
8.4 is still applicable as if the intermediate webs were removed. When
calculating torsional constant using Equation 8.4, open-section segments
such as cantilevered flanges can be ignored as resistance to torsion from
these segments is not comparable to that from closed cells, or simply sum
the torsional constant of these open segments (Equation 7.2) and that of
closed cells (Equation 8.4) as the total of the entire section.
For analysis purposes, top lateral bracing, as shown in Figure 8.2, may
be transformed to an equivalent thickness of plate t eq by

=

E
G

2 A

b

d 2

t (cos α sin ) α (8.5)

eq

where:
E is the steel modulus of elasticity
G is the steel shearing modulus of elasticity
A d is the area of the lateral-bracing diagonal
b is the clear box width between top flanges
α is the angle of lateral-bracing diagonal with respect to transverse
direction

Kollbrunner and Basler (1966) provide a more complete list of equivalent
thickness for quasibox girder as shown in Table 8.1.
To properly close the section and minimize warping stresses, the cross-
sectional area of the lateral-bracing diagonal A d should be at least 0.03 b .
The internal stresses produced by St. Venant torsion in a closed section
are shearing stresses around the perimeter, as shown in Figure 8.6, and
defined by

T
At

τ = (8.6)

2