Stability - Computational Analysis and Design of Bridge Structures - page 456

Figure 14.21 The first mode of buckling (out of plane) considering all loads accumulated
up to the current stage in initial stress stiffness matrix ( K σ ) and including
total accumulated initial stress stiffness (from stages 1 to 3) in K 0 .
Figure 14.21 shows the first mode of buckling considering all loads
accumulated up to stage 3 in the initial stress stiffness matrix ( K σ ) and
including total accumulated initial stress stiffness (from stages 1 to 3) in
K 0 . The buckling pattern is out of plane. The corresponding critical load
factor (λ) is 4.23, much lower than that when considering only live loads,
indicating that the critical load factors in bifurcated buckling analysis is
engineering meaningful only when the acting loads are clearly defined.
Also, the nature of acting loads is shown by the difference of Figure 14.21
from Figures 14.18 through 14.20.
Because most bridges are built in many stages, whenever the initial stress
stiffness is evaluated in any stage, the initial stress should be accumulated
from the first stage to the stage prior to (or upto) the current stage. Also, the
initial stress stiffness should be able to include the linear stiffness matrix (as
the so-called initial stress considered). Moreover, it has to be able to pick
a particular load case as the acting load case in buckling analysis. Further,
to be more practical, the analyzed extreme live loads should be able to be
saved as load cases. To simplify, (1) when computing K 0 of Equation 14.4,
stiffness due to accumulated initial stress should be able to be included,
(2) when computing K σ of Equation 14.4, the acting loads should be able to
be selected among many different dead and live load cases, and (3) analyzed
extreme live loads should be able to be treated as a regular load case, which
are very important and practical features when initial stress problems such
as buckling or stability are regarded.