50 Figure 3.2 – Left: The northern reinforcement wall formed flat against the face of the north-facing columns. 71 Figure 3.11 – Flexibility percentage difference indicator results for baseline to R1. reinforcement wall along y = 4) comparison considering modes 6 and 7.
INTRODUCTION
- Motivation
- Background and Significance
- SHE™ Program Overview
- Damage/Reinforcement Detection
- SAP2000®
The mass of the structure is self-explanatory in that it may not be direct. Gutschmidt and Cornwell developed an indicator that does this [19]. The proportional flexibility matrix is the mode shape matrix multiplied by its transpose, with these two terms divided by the corresponding natural frequency squared.
BASELINE STEEL STRUCTURE
Structure and Geometry
The heat of curing caused one of the bottoms of the bucket to warp, so wooden strips were used to level it. These brackets had two holes in each arm, so that each joint of the structure had four different connection points.
Instrumentation
The origin of the coordinate system was chosen as the southwest column with a positive x-direction extending to the east, a positive y-direction extending to the north, and a positive z-direction. The record length of the time history for each measurement was 1.1 seconds at a sampling rate of 10240 per second.
Modal Processing
Most peaks produced mode shapes that were coupled, so sometimes it was best to look for a peak on the smoothed graph to obtain a clearer mode shape. It was not labeled as a pure form of torsional mode, even though all floors exhibit torsion, but rather a form of "squeeze mode".
SAP2000® Baseline Model
The first floor north/south face beams bend out of phase and the east/west beams bend out of phase (first order). The north/south first floor beams are bent in phase (order 1) and the east/west face beams are bent in phase (order 2). 17 67.43 The second and third floor beams of the north/south face bend in phase (order 1) and the beams of the east/west face bend out of phase (order 2).
The computer mode shape that matched experimental mode shape 5 was the first mode that occurred at 6,730 Hz. However, these modes did not occur at the same frequencies as those of experimental mode 5 and computer mode 1. Computer mode 3 occurring at 8.257 Hz is very similar to experimental mode 7 occurring at 10.156 Hz.
Another computational mode shape that was similar to an experimental mode shape was mode 4 occurring at 18.276 Hz.
Conclusions
As expected, the exact frequencies between computer model and experimental results did not match; however, the sequence in which the computer mode shapes occurred was similar to the sequence forming the experimental mode shapes, specifically up to 20 Hz. Although the model did not match the experimental results, it contextualized the experimental data by producing trend behaviors such as mode ordering or common mode shapes.
REINFORCING WALL STRUCTURE
Construction
Machine bolts with a nominal diameter of 0.25 inches were used to secure the wall on the north face of the structure. A washer was used on the outer and inner face of the wall through which the bolt passed. The wall was fixed to the structure in five different places of each of the two columns of the north face.
This resulted in a total of thirteen connections of the reinforcement wall to the facade of the structure. The wall was then moved into place by bringing it through the top of the structure and into the closed structure. This was done so that the wall could be connected to the front of the columns as well as to the beams.
The locations of the connections were very similar to the connections of the reinforcement wall on the north side.
Predicted Effect
However, the overall predicted effect of the reinforcing wall goes back to the fundamental concept of natural frequency, which is equal to the square root of the stiffness divided by the mass. The reinforcing wall could increase the stiffness of the structure so much that the mass of the reinforcing wall is negligible, in which case the frequency response of the structure would shift upward (increase) or vice versa. However, the added mass of the reinforcement wall could result in a greater total increase in mass relative to the total increase in stiffness, in which case the frequency response of the structure would shift downward (decrease).
The double bracing wall configuration of the structure was constructed so that the structure could resist more movements in the planar x and y directions. Again, this may result in less coupled torsional motion due to the stiffness of the timber and ties, or it may result in more coupled motion due to the again asymmetric configuration of the reinforcing walls. The total increase in mass can dominate the total increase in stiffness so that the frequency content is shifted downward.
Mode Comparison
For the R1 case, it is quite clear that a reinforcement wall was added on the north side of the structure where y = 4 in Figure 3.6. In the R2 configuration, an additional reinforcement wall was added to the west side of the structure at x. When the second reinforcing wall is added, a torsional movement occurs again with the sway more stabilized.
When the first reinforcing wall is added, the torsion is more stabilized by being more symmetrical. The eastward sway is reduced with the addition of the first retaining wall; however, the torsion is still prominent. The torsion is reduced and more organized and the slight sway is reduced with the addition of each reinforcing wall.
Following the trend of the other mode sets, the mode shapes become less erratic with the addition of each reinforcing wall.
Reinforcement Detection
At 94.492 Hz, higher-order column bending and support translation occur in the seventh-mode baseline configuration. While the underlying mode is highly correlated, the similarities in mode shapes in this set are best seen in the YZ view, where each column bends in the same way. No single indicator could consistently detect and locate changes in structure in all cases.
A "maybe" was assigned in Table 3.5 because the wall at y = 4 was reliably located, but the indicated change in the origin column would confuse an inspector. The flexibility percentage difference indicator was mostly erratic and inconsistent, showing little structural change, for the R1 to R2 comparison, earning mostly "No" labels in these categories. The normal modal flexibility indicator was inconsistent across all comparisons, showing change in the incorrect columns and random threshold color scatter.
The Strain Energy indicator showed damage in the wrong columns and was mostly similar in all of them.
Conclusions
In some cases, such as COMAC, the reinforcement detection plots showed more variation with the additional data. However, in some cases, such as Modal Curvature Distribution and Flexibility Percentage Difference, one or more outlier data nodes can distort the entire graph, causing that specific node or nodes to appear as the only changed part of the tree. Overall, the gain detection results were no better than when only the 16-column base data nodes were considered.
While some of the indices proved more effective than others, none were able to practically detect and localize the change for an inspector of this structure. The percentage difference indicator worked best; The indicator showed a good distribution of the color threshold where the gain was set for all cases. For the baseline comparison with R1, it was able to detect and localize damage for three out of five mode group comparisons.
It was less reliable for a baseline comparison with the R2, but showed good color dispersion where it is.
CONCLUSION
Summary
However, the added effective mass of the reinforcement may be greater than the added stiffness. By visual inspection, the mode shapes showed the effectiveness of the reinforcement in reducing movements such as bending and lateral movement. The nine damage/reinforcement detection indices included in SHE™ were used in observing the effectiveness of the reinforcing walls.
COMAC, COMAC on Curvature, and Curvature Division showed very little change in the structure when the reinforcement was added. In the case where the baseline structure and the single reinforcing wall structure were considered, it indicated damage and location for three of the five mode set comparisons. When comparing the baseline structure with the double reinforcement wall structure, the flexibility percentage indicator showed a good threshold color distribution where the reinforcement was located.
The results could be misinterpreted due to noise in the data, the result of greater excitation and/or a large increase in effective mass when the gain was added.
Lessons Learned
An example of environmental data collected from a structural configuration with minimal added or reduced mass should be investigated. The many plots generated by SHE™, such as FRFs, mode shapes and damage detection/reinforcement plots, make it more user and inspector friendly. For the mode matching process between structural configurations to be efficient, a balance of data nodes for a specific structure must be found.
Adding reinforcement does not always cause an increase in the natural frequencies of a structure. The overall increase in the effective mass of the structure may be greater than the overall increase in stiffness, especially in a structure of this smaller size. It's important to be aware of the expected damage/boost effects when determining matching mod forms, otherwise the similarities can easily be overlooked.
The location and amount of excitation can affect experimental mode shapes and damage/strengthening detection results.
Future Work
Rubber washers are designed to reduce the stiffness of each steel structure joint. This reduced the stiffness of the overall structure from the baseline; no structural members were changed and the joints were not tightened back to their original torque. By reducing the global stiffness of the structure relative to the minimum change in mass, the overall frequency response of the structure should decrease.
The mode shapes of the more flexible structure should be aligned in the same order as the baselines, taking into account that no lateral bracing has been added and that the boundary conditions remain. This means that oscillation mode shapes should be visible at lower frequencies, followed by slight torsion, column bending and localized beam bending. For the three configurations of rubber washers, the tests and analyzes were carried out in the same way as for the basic structure.
With the base mode shapes available, the rubber washer configurations were coordinated with each other and with the base line. Alternatively, the strut could move slightly inward, causing the entire structure to brace, reducing flexibility. Statistical Confidence Limits for Damage Indicators in Structural Health Monitoring,” Proceedings of the International Conference on Modal Analysis, 2001.
