Straight and curved steel box girder bridges - Computational Analysis and Design of Bridge Structures - page 238

8.1.2.1 Mixed torsion
In curved box girder bridges, a vertical load may cause the girder twisted
about its longitudinal axis because of the bridge curvature. Uniform tor-
sion occurs if the rate of change of the twist angle is constant along the
girder and longitudinal warping displacement is not restrained and main-
taining a constant. St. Venant analyzed this problem and found that the
St. Venant shear stresses occur in the cross section (Figure 8.6). If there is
a variation of torque or if warping is prevented or altered along the girder,
longitudinal torsional warping stresses develop.
In general, both St. Venant torsion and the warping torsion are developed
when thin-walled members are twisted. Box girders are usually dominated
by St. Venant torsion because the closed cross section has a high torsional
stiffness. Box girders have large St. Venant stiffness, which may be 100-1000
times larger than that of a comparable I-section. The longitudinal normal
stresses resulting from the restrained warping in closed box sections are
usually negligible (Kollbrunner and Basler 1969).
St. Venant stiffness of the box section is a function of the shear modu-
lus of the steel ( G ) and the torsional constant J (or K t ), which is related
to the cross-sectional geometry. In curved box girder bridges, St. Venant
torsion provides most of the resistance that is given by

T GJ d
dz

θ

= (8.3)

where:
T is the torque on the cross section of the member
θ is the twist angle of the cross section
z is the longitudinal axis of the member

For box sections, as shear stress flows are formed in closed cells, equivalent
torsional constant for open sections as shown in Chapter 7 is no longer
applicable. The torsional constant J in Equation 8.3 for a single-cell box
girder is given by

T

τ

Figure 8.6 St. Venant torsion in a closed section.