Dynamic/earthquake analysis - Computational Analysis and Design of Bridge Structures - page 519

where f is the fundamental frequency of the pedestrian bridge where it can
be manually calculated by assuming a single-DOF (SDOF) system or found
from the computer model (shown in detail in the next section), K is a con-
figuration factor varied from 0.6 to 1.0, and ψ is the dynamic response fac-
tor depending on the span length l and decay of vibration δ based on bridge
composition.
The serviceability of a pedestrian bridge is important for obvious reasons.
In design, the overriding factors for serviceability are the structure's dynamic
characteristics—stiffness and its ability to avoid resonance.

17.2.3 Bridge earthquake analysis
AASHTO guide specifications in LRFD (2012), differing from the early
practices, is adopting displacement-based design procedures instead of the
traditional force-based “ R -factor” method. It is widely recognized that
the traditional force-based design (FBD) approach cannot provide the appro-
priate means for implementing concepts of performance-based design.
Performance levels as shown in Table 17.2 are described in terms of dis-
placements where damage is in closer correlation with displacements rather
than forces. As a consequence, new design approaches, based on displace-
ments, have been recently implemented. The former force approach was
based on generating design-level earthquake demands by reducing ultimate
elastic response spectra forces by a reduction factor ( R -factor). The reduc-
tion factor was selected based on structure geometry, anticipated ductility,
and acceptable risk. The newly adopted displacement approach is based on
comparing the elastic displacement demand to the inelastic displacement
capacity of the primary structural components while ensuring a minimum
level of inelastic capacity at all potential plastic hinge locations.
Based on their requirements, four seismic design categories (SDCs) are
established in AASHTO guide specifications (2012): SDC A (for simple-span
bridges), B, C, and D. Three global seismic design strategies are allowed:
type 1—ductile substructure/elastic superstructure, type 2—elastic sub-
structure/ductile (steel) superstructure, and type 3—elastic superstructure/
elastic substructure/fusing mechanism (seismic isolation or energy dissipa-
tion) in between.
Based on Equation 17.1, differential equation governing the response of
a structure to horizontal earthquake ground motion ü g ( t ) is converted to

  

mu cu ku + + = − mlu

g ( )

(17.9)

where:
u is the vector of N lateral floor displacements relative to the ground
m , c , and k are the mass, classical damping, and lateral stiff matrices of
the system; each element of the influence vector l is equal to unity