Approximate and refined analysis methods - Computational Analysis and Design of Bridge Structures - page 31

(a) (b)

(c) (d)

Figure 2.13 (a-d) 2D grillage meshes.

2.4.2 Orthotropic plate method
The orthotropic deck bridge is a special kind of deck, which can be solved
by the orthotropic plate theory. The general differential equation given for
the orthotropic plate can be found in any topic discussing plate bending
theory and is listed in Equation 2.4.

4

w
x

w
x y

4 4

w
y

δ
δ

δ
δ δ

δ
δ

( + + ) + ( , ) = p x y (2.4)

D D D D

x xy yx y

4 2 4

2

where:
w is the deflection of the plate at any point ( x , y )
D x , D y , D xy , and D yx are stiffness of the longitudinal flexure, the
transverse flexure, longitudinal torsion, and transverse torsion,
respectively
p ( x , y ) is the loading intensity of any point

A simplified analysis is made by assuming:

• For decks with closed ribs: D y ≅ 0
• For decks with open ribs: D y ≅ 0, D xy ≅ D yx ≅ 0

Based on Hambly (1991), the moment and flexure relationships are shown
in Equation 2.5a and principle stresses are shown in Equation 2.5b.