Straight and curved steel I-girder bridges - Computational Analysis and Design of Bridge Structures - page 197

M y

P

M x

T

Total
normal
stress

Warping
normal
stress

M y x
I y

P
A

M x y
I x

= σ = + + +

Figure 7.3 Illustration of the general I-girder normal stresses, which can occur in a
curved or skewed I-shaped girder.

restraint to girders. The total torsional resistance is the sum of nonrestrained
torsion (pure torsion) and restrained torsion (warping), as expressed in
Equation 7.1.

T GJ = θ ′ − EC w θ ′′′ (7.1)

where:
G is the shear modulus of elasticity of steel
J is the torsional constant of cross section and can be approximated
using Equation 7.2 for rolled and built-up I shapes
E is the modulus of elasticity of steel
C w is the warping constant of cross section and can be approximated as
I y h 2 /4 for rolled and built-up I shapes
I y is the lateral moment of inertia about y -axis
h is the distance between centerlines of top and bottom flanges
θ is the rotation angle of cross section along the girder axis

For the calculation of section properties, including C w , refer to AISC,
Design Guide 9: Torsional Analysis of Structural Steel Members (2003).