As discussed in chapter 4, it was believed that with more data and a better magnet an equation to estimate the remaining cross-sectional area of a strand could be developed.
However, due to many variables, such as magnetic permeability and metallurgy, an equation was not obtained during the time frame of this thesis. Nevertheless, another, more empirical approach for estimating the remaining viable cross-sectional area was developed.
This approach was developed during and after experiments with corroded prestressing strands. Corroded strands of a ẵ” diameter from a box-beam bridge were tested with a 114" and 11516" concrete block gaps. Only ẵ” diameter strand was tested
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because it was all that was available in a pre-corroded condition. Two samples were tested and readings were recorded every 4 inches along their length at the right pole.
Wires in sample 2 were removed to create regions of increased cross-sectional area loss.
The test set-up for these experiments can be seen in figure 5-8. Observations of the strands along their length were recorded as follows:
Figure 5-8: Test set-up for corroded strand.
1) Sample 1
i) From 4"-12" 6 wires were visibly present.
ii) At 16" 6 wires were visibly present with separation between the wires (see figure 5-9).
iii) At 20" 5 wires were visibly present.
iv) At 24" 4-5 wires were visibly present.
v) From 28"-32" 4wires were visibly present
vi) At 36" there is a transition from 4 to 3 wires being visibly present vii) At 40" 2 wires were visibly present.
42 2) Sample 2
i) At 4" 4 wires were visibly present.
ii) From 8"-16" 5 wires were visibly present.
iii) At 20" 3 wires were visibly present.
iv) At 24" 2 wires were visibly present.
v) From 32"-36" 1 wire was visibly present.
Figure 5-9: Separation of wires in corroded strand.
In addition to the observations previously listed, the strands were severely corroded as can be seen in figures 5-8 and 5-9. The results from these experiments can be seen in table 5-5.
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Table 5-5: Results from corroded strand experiments (measured in Gauss).
Sample 1 Sample 2 Sample 1 Sample 2
1670 1540 1430 1390
1690 1570 1440 1400
1670 1590 1430 1400
1620 1540 1420 1400
1590 1510 1410 1380
1550 1500 1410 1360
1590 1490 1410 1350
1530 1490 1390 1340
1520 1450 1390 1320
1470 1360
Distance Along
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1 1/4" Concrete Gap 1 15/16" Concrete Gap
20 24 28 32 36
Longitudinal Axis (in.) 4
8 12 16
The first instinct when estimating the remaining viable cross-sectional area was to measure the diameter of the strand at the points of interest with calipers. This, however, was impractical because the strands had expanded during the corrosion process, and in the field, the strand will be embedded in concrete, thus, making it impossible to measure the diameter with calipers.
To overcome these issues, a healthy (non-corroded) strand was dissected and separated into its seven individual wires. From previous results, a healthy ẵ” diameter strand produced a 1505 Gauss (G) reading at a 11516" concrete gap. Again, first instinct was to assume that this would be distributed evenly over the 7 wires (215 G per wire), however, when one wire was placed on the magnet at a 11516" concrete gap, a reading of 1350 G, nearly 90 percent of the total, was observed. As each wire was added to the magnet, an increase of 20-25 Gauss was observed for each wire added. In addition, it was observed that wires were not always attracted to each other, but in most instances repelled one another. This is believed to be due to how the magnetic domains in each
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wire align themselves in the field. The orientation of one wire to another produces a give and take affect that results in a net magnetization of 1505 G when they are all together.
With the data and observations from the experiments, an approach to estimate the remaining viable cross-sectional area was proposed.
The proposed approach used the known readings of a healthy strand and that of one wire taken from a healthy strand at a given gap. An example of calculations to determine the remaining viable cross-sectional area of a strand can be seen in figure 5-10.
The example was calculated in MathCAD.
Figure 5-10: Example calculation of estimating remaining cross-sectional area.
Bstrand 1505G:= Magnetization for a healthy 1/2" strand at a 1 15/16" gap
Bwire 1350G:= Magnetization for a healthy wire taken from a 1/2" strand at a 1 15/16" gap
B:= Bstrand Bwire- =155 G
Mper.wire B
6 =25.833 G
:= Net magnetization per wire for the 6 remaining wires
Mcorroded 1390G:= Magnetization at a point on a corroded strand As 0.153in:= 2 Area of steel in 1/2" diameter strand
Awire As
7 =0.022 in 2
:= Area per wire in a 1/2" strand
wire (Mcorroded Bwire- )
Mper.wire + 1=2.548
:= Estimate of total viable wire left
The +1 wire accounts for the wire that was not used to determine the net magnetization per wire
Acorroded:= wire Awire =0.056 in 2 Estimate of remaining viable cross-sectional area of corroded strand.
%lost 100 As Acorroded-
As 100
- =36.406
:= Percent cross-sectional area loss due to corrosion
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In this example, the observed reading of 1390 G was taken from sample 1 at 36” along its length where it was observed that 3 to 4 wires were present. If 3 to 4 healthy wires were present there would be a cross-sectional area of 0.066 in2 to 0.087428 in2. The estimate of 0.056 in2 is reasonable as the strand is severely corroded. Estimates of the remaining area for samples 1 and 2 can be seen in table 5-6.
Table 5-6: Estimates of remaining cross-sectional areas of samples 1 and 2 at a 𝟏𝟏𝟓𝟏𝟔" concrete gap.
Sample 1 Sample 2 0.089544 0.055701 0.098005 0.064161 0.089544 0.064161 0.081083 0.064161 0.072622 0.04724 0.072622 0.030318 0.072622 0.021857 0.055701 0.013396 0.055701 0.003526 0.030318
Distance Along
16 20 24 28 32 36 40
Remaing Area (in2) Longitudinal Axis (in.)
4 8 12
For this approach to be used the gap as well as the magnetization of a healthy strand and wire at that gap would need to be known.
The purposed estimating technique does contain shortfalls, such as validation, range restrictions, and contradicting estimates. Although the estimates provided are reasonable when compared to the visual evidence of the strand, there is still no validation of the actual amount of remaining steel. To rectify this, rust could be removed from the lab specimens and the area calculated, but investigation into the healthy diameter and
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area of a ẵ” nominal strand has hindered this attempt. The area of steel listed with a ẵ”
strand is 0.153in2 which when distributed over seven wires yields 0.021857in2 per wire.
This in turn yields a calculated diameter of 0.1668in., which does not match the measured diameter of 0.130in. The area of 0.153in2 may be nominalized and be the reason for this discrepancy. Neither the ASTM nor other publications have an explanation of how the area is calculated or give an approximate diameter size for the wires that are to be used in the strand. Investigation into this issue will need to be continued so this or any other estimation approach can be properly calibrated.
Another shortcoming of this approach may be attributed to inadequate field strength. As previously mentioned, the magnetization of one wire is 1350G, which is within the range of the estimating approach, but once the magnetization drops below approximately 1320G the estimate increases from the expected. One explanation of this discrepancy is due to the field strength of the magnet being used.
The field strength of the magnet alone on the right pole is 1460G. At 11516"
concrete gap a ẵ” diameter strand has a magnetization of 1505G. From other specimens tested at smaller gaps, it is known that the magnetization of a ẵ” diameter specimen is capable of being higher. As with the first magnet at this distance, there is less magnetization. In short, the magnetic capacity of the strand is not being filled. However, at this same distance (11516") the wire’s capacity may be filled or at least have a higher a higher degree of saturation to area than the strand. This cause’s a few problems when trying to estimate the area. The estimation is more or less based on a linear approach, but the data show that the magnetization although nearly linear, is curved. Nevertheless, it
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appears that this causes the estimates to err on the side of caution, i.e. there is more area remaining than estimated.
The other problem is that there could be two estimates for a magnetization of 1460G; 0in2 or 0.115in2 for this region. Since the magnetization curve of a strand or any other ferromagnetic material is non-linear (see figure 5-11), there will be errors when estimating the area. Nonetheless, these errors could be minimized by optimizing the electromagnet design for size of specimens and gap being tested for. In other words, if the field strength were increased to ensure the specimens being magnetized would be at or near complete saturation, the error in estimating would be reduced as the data would become more linearized. Until such an electromagnet becomes available, the estimating approach proposed here gives reasonable, conservative estimates and, with more testing and scrutinization, could become an effective estimating tool.
Figure 5-11: Magnetization curve for iron (http://info.ee.surrey.ac.uk/Workshop/advice/coils/mu/BH_iron.png)
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Chapter 6
Conclusion