Introduction - Computational Analysis and Design of Bridge Structures - page 8

-

1 = - 2

S 1 ≠ S 2

-

1 = -

S 2 S 1

2

Figure 1.6 Statistical comparison of various methods with exact value.

resistances are observed, the actual safety margin is actually much wider.
LRFD also accounts for the different probabilities of occurrence for loads
and resistances.
Due to the limitations and assumptions in an analysis, it is not sta-
tistically possible to get exact results by any analytical method. In the
AASHTO LRFD code, both the approximate method and the refined
method, which will be covered in more detail in Chapter 2, are accepted.
It is noted that the bias values, the dif fer ence bet ween the means of the
expected result and the exact value ( X 1 and X 2 in Figure 1.6), of the
approximate and refined methods, however, are both close to 1.0. The
coefficient of variation (CV), defined as the ratio of the standard devia-
tion σ to the mean μ, is lower with the use of the refined method (shown
as the solid line curve versus the approximate method shown as the
dotted line curve, respectively, in Figure 1.6). The lowest CV, which
means the closest to the exact results, of all methods results from the
field load test, which is 4, the least variation. But a field test is costly and
time consuming, so oftentimes it is conducted for a few cases and then
validated by numerical methods. In these situations, numerical meth-
ods are used to simulate all cases. Figure 1.7a shows the side view of a
simple-span steel girder bridge on the U.S. Interstate Highway System.
Figure 1.7b shows that accelerometers are deployed to detect the modal
frequencies (shown in Figure 1.7c) and their associated modes. The
results are then compared with the numerical results from the finite ele-
ment model as shown in Figure 1.8. This process is repeated several times
until modal results based on the test and numerical method are close.
This technique is called updating. Finite element model updating is the
process to ensure that the finite element analysis (FEA) model results bet-
ter reflect the measured data than the initial models.