Introduction - Computational Analysis and Design of Bridge Structures - page 7

the best scheme is selected and cost estimates are conducted. The detailed
design stage is a process in which all the details of the bridge structure for
construction are finalized. Finally, the construction design stage is the pro-
cess in which the step-by-step procedures for the building of the bridge
are provided. Each of the earlier design stages must carefully consider the
requirements of the subsequent stages. For example, the bridge constructa-
bility must be considered during the detailed design stage; in addition, costs
and construction schedules as well as aesthetics must be considered during
the preliminary design stage. An existing bridge in the United States goes
through the inspection and load-rating cycles every two years.
Bridge structural analysis, the main subject of this topic, is essential for
all four stages. Different stages can adopt different modeling techniques,
varied from hand calculation to the approximate method and then to the
reined method. In this topic, constructability, especially constructability
of extra-long span bridges, is discussed and demonstrated. Various issues
such as deflection, strength of concrete and steel, and stability during critical
stages of construction are covered in Chapters 4 through 12, 14, 15, and 17.
In the United States, the load and resistance factor design (LRFD)
method is the latest advancement in transportation structures design prac-
tice (AASHTO 2013). The combination of the factored loads, termed limit
states in LRFD, cannot exceed the strength of the material multiplied by a
resistance factor less than unity (1.0). Several limit states are included for
service, strength, and extreme event considerations. The limit state concept
has been universally accepted by many different codes worldwide. A graphi-
cal representation of the LRFD process is shown in Figure 1.5a with load
( Q ) and resistance ( R ) and later evolved to Figure 1.5b in terms of ( R − Q ).
The reliability index β, which shares a similar idea with the safety factor
in allowable stress design method, was set at a target of β = 3.5 in the
LRFD code (AASHTO 2013). As can be seen in both figures, the factored
safety margin is small, but when the theoretical actual loads and nominal

Resistance ( R )

Load ( Q )

f ( R,Q )

γ RN φ RN

β σ

R = Q

R R R , Q

Q R

- -

( R − Q )

R − Q

Each variable is represented by mean
and standard deviation. (a) (b)

Figure 1.5 Concept of load and resistance factor design. (a) Probability of occurrence
based on R and Q . (b) Probability of occurrence based on ( R − Q ).