Dynamic/earthquake analysis - Computational Analysis and Design of Bridge Structures - page 529

Spine model

Beam elements

(b)

Lumped
parameter

Plate or
shell elements

Grillage

(a)

(c)

Finite element

(d)

Figure 17.11 (a-d) Types of analytical models.

assumes linear relationship between stiffness and strength, effective sec-
tion properties should be determined for seismic analysis of reinforced con-
crete structures with the consideration of concrete crack and steel yielding.
One important note of the bridge modeling is that to catch all the essential
modes, a minimum of three elements per flexible column and four elements
per span should be used in the linear elastic model (AASHTO 2012).
The superstructure is idealized using equivalent linear elastic beam-column
elements. For either spine or grillage model of concrete structures, the effective
bending stiffness and thus the moment of inertia I eff can be taken as

M

y

E I

eff = ϕ

(17.18)

c

y

And the shear stiffness parameter ( GA ) eff for pier walls in the strong direc-
tion may be determined as

I
I

eff

( GA ) = G A

(17.19)

eff c cw

g

And the effective torsional moment of inertia J eff is determined by

J = 0 2 . J g (17.20)

eff

where:
M y is the moment capacity
φ y is the curvature of section at first yield of the reinforcing steel
E c is the modulus of elasticity
G c is the shear modulus of concrete
I g is the gross moment of inertia about the weak axis
A cw is the cross-sectional area of pier walls
J g is the gross torsional moment of inertia of the reinforced concrete
section