Curved concrete bridges - Computational Analysis and Design of Bridge Structures - page 173

equivalent transverse load, which can result in significant tension on the
inside of the curve and compression on the outside edge (Fu and Tang 2001).
The magnitudes of such effects depend on the radius of curvature, span con-
figuration, cross-sectional geometry, and load patterns among other param-
eters. The global structural analysis is required to capture such effects.
In the early development by Hsu (1994), a set of equations is given for
solving single-cell torsion. A reinforced concrete prismatic member is sub-
jected to an external torque T as shown in Figure 6.2a. The external torque
is resisted by an internal torque formed by the circulatory shear flow q along
the periphery of the cross section. The shear flow q occupies a zone, called
the shear flow zone, which has a thickness denoted t d . This thickness t d , or
an equivalent thickness for a uniform shear stress, is a variable determined
from the equilibrium and compatibility conditions. It is not the same as the
given wall thickness h of a hollow member. Element A in the shear flow zone
(Figure 6.2a) is subjected to a shear stress τ lt = q / t d as shown in Figure 6.2b.
In bridge engineering, many reinforced concrete bridges consist of mul-
ticell boxes. Therefore, a set of simultaneous equations to analyze struc-
tural torsion for multicell boxes is needed (Fu and Yang 1996; Fu and Tang
2001). In this chapter, equations for single- and multicell box are listed.

6.1.2.1 Equations for multiple cells
Assume a structural section has N cells (Figure 6.3). According to restraint
condition θ = θ 1 = θ 2 = . . . = θ N , a set of simultaneous equations for cell i
can be obtained.

T

h

t

A

τ lt = q / t d

q

l

t d

τ lt

A

(a) (b)

Figure 6.2 Hollow box subjected to torsion. (a) Shear flow in an element. (b) Shear
stress on element A.