Elastic Investigation - Elastic Study Results
Elastic Investigation - Elastic Study Results |
|
| Of the two ground
motions considered, the larger magnitude motion at the farther
distance showed a much larger effect in the transverse direction.
The displacements laterally amplified by a factor of 3 though the motion was only twice as large in magnitude (Figure
1).
In the vertical direction, the end displacements were about the same even
though there was still a factor of 2 large accelerations (Figure 1).
|
 |
Figure 1 - Lateral vs. Vertical displacement of the deck at the P11 support. Two earthquakes shown. |
| Given the larger ground motion, it
is of interest to see how the different components effect the end
displacements.
The transverse peak displacement at the end of the span gets larger when considering the longitudinal motion in addition to the transverse and vertical motions. This suggests some minor coupling between longitudinal motion and transverse response. Another thing to note is that the vertical motion increases when the longitudinal and/or transverse accelerations are included in the analysis. This effect is further studied in the Nonlinear Model with the nonlinear geometric coupling of the deck and the tower through the cables.. If only the transverse ground motion is considered, then only transverse motion is seen at the top of the bridge. |
 |
Figure 2 - Effects of the different constituents of motion
|
| Given the second ground motion and
all its components (LTV), differences in models can be inspected.
As the transverse stiffness was increased, the transverse moment demands went up. Knowing that in the field that there was yielding, and that stiffness between the uncracked and the uncracked with wings values caused penetration of the yield surface, it can be conjectured that this is further evidence of the in-situ deck structural properties. Model G and LTU exhibited behavior that did not cross the elastic envelope (Figure 3).
|
 |
Figure 3 - PM interaction for strong bending of the deck
|
| From the damage,
it is hard to tell what has actually happened at the main span pylon
joint. But, from the observation of the weak axis bending
capacity verses its demand, we can say that the damage is not due to weak
axis plastic hinging. The D/C ratios are far too low. Thus,
between Figure 3 and Figure 4, it can be hypothesized that the primary mode of
failure is hinging about the strong axis.
However, strong axis plastic hinging is not all that has happened to the deck at the pylon face (see Damage). From the residual twist left in the section, there must have been torsion. Also, the crack along the length of the deck spine still requires consideration. |
 |
Figure 4 - PM interaction for weak bending of the deck
|
| There was virtually no difference
between the displacement of the top of the bridge in the transverse
direction weather of not the gap element was used or the vertical movement
was restrained.
In contrast, the longitudinal displacements of the top of the bridge were different depending of the model used. In the case were the vertical displacements were constrained at the ends, less displacement was observed in analysis. As the bridge tries to move in the longitudinal direction, the restraint of freedom for one side to come out of its support allows for more stiffness in this direction of motion. Thus, less movement is seen. |
 |
Figure 5 - Top of bridge longitudinal verses transverse displacement
|
| Going back to the differences
between the uncracked with and without wing deck properties, there is a
difference in the motion of the main tower.
Contrary to initial assumption, the lateral motion was increased when the wings were considered. In general, as you lower the predominant period of the structure, displacements should go down; in this case, they went up (Figure 6).
|
 |
Figure 6 - Top of bridge longitudinal verses transverse displacement |
| Consideration of the elastic
analysis also gives us basis for the assumption of the shearing
plane of concrete.
The assumption is that there was so much confining steel in the pylon, that when in bending, the cover concrete simple disassociated form the core for lack of cohesion. Figure 7 supports this in that there was not sufficient demand to even approach the yield surface of the material. The pylon remain uncracked with no spalling due to excess compression force.
|
 |
Figure 7 - Capacity orbit verses demand just on the deck on the main pylon |
|
|