The prestress loss is one of the main factors affecting the safety of prestressed concrete structure. While the detecting signals like sound and light are difficult to spread in steel strands, there is no effective method for prestress detection of the bonded prestressed steel strands in existing structures yet. In this paper, taking into consideration that the electromagnetic oscillation characteristic can make the signal propagate effectively on the bonded prestressed steel strands, a nondestructive prestress detection method based on the electromagnetic effect to detect oscillation frequency is proposed. In a detection circuit, the steel strands are simulated as an inductance component, in which an induced electromagnetic signal passes through the steel strands to form resonance. And then, a frequency meter is used to detect the oscillation frequency of the resonant circuit. The oscillation frequency is supposed to have relationship with the prestress loading on the steel strands. A section of steel strands with a length of 1.2 m is adopted to test the correlation of stress and oscillation frequency. Both the theoretical and experimental results show that the resonant frequency of the circuit decreases with the increase of the stress of the strand and is linear in a certain range.
Prestressed concrete structures are widely used in civil engineering and hydraulic engineering because of their advantages of reducing deformation, improving bearing capacity and cracking resistance. However, the stress relaxation of prestressing tendons, the occurrence of cracks and shrinkage of concrete, and the deformation of anchorages result in loss of prestress. This will decrease the service life of the structures. Therefore, it is important to detect the health status of the prestressed structure at regular intervals.
The expression of the new analytical model [
The vibrating wire strain gauge (VWSG) [
In practical engineering, the length of the prestressed steel strand is up to tens of meters, while the length of the strand used in the test is only 1.2 m. The reason for this is that the purpose of the experiment is to verify the relationship between the stress and magnetism characteristic in Section
The aim of this study is to measure the stress of existing prestressed structures. Accordingly, an electromagnetic oscillation (EMO) method is proposed. To verify the effectiveness of this method, a series of stress tests by electromagnetic oscillation loading on two ends of the steel strand are implemented in laboratory. The form of the steel strand is similar to the inductance in an LC oscillation circuit. Meanwhile, an EMO circuit is created. It is based on the magnetoelastic effect to measure the electromagnetic oscillation frequency and calculate the stress of prestressed structures. The theory which is deduced in Section
As shown in Figure
Circuit schematic.
Vector model.
And the vector diagram can be written as
And it can be drawn from circuit diagram 1 that
Under parallel resonance situation, there is no pure resistance in the circuit, and
For conductors, the conductor generates a magnetic field inside and around it when the current passes through it. The magnetic lines of force are concentric closed rings, and the direction is determined by the right-hand rule. As the current changes, the flux changes. Assuming
As shown in Figure
Magnetic field of concentric.
Assume
The inductance of the steel strand is the result of the interaction between the internal flux linkage and the external flux linkage. For the inductance generated by the internal flux linkage, the skin effect is ignored here, and assuming that the current is evenly distributed inside the steel strand, then the current per unit area is equal and can be simply expressed as
Substituting
For magnetic wires, the magnetic permeability is
It can be assumed that the strand is uniform in thickness, for the strand thickness is
This part of the magnetic flux is not around the whole strand but rather part of its cross-sectional area
The internal magnetic chain inside the entire steel strand can be obtained by integrating
The inductance produced by the internal flux chain of (
For the inductance generated by the external magnetic flux, as shown in Figure
Concentric magnetic field of the external magnetic flux linkage.
Since this part of the magnetic flux surrounds the entire current, the magnetic chain is numerically equal to the magnetic flux. The differential
The external magnetic chain between
The inductance between the two external points of the wire can be written as
Thus, the total inductance can be expressed as
Since the strand is ferromagnetic, the magnetic permeability is
According to the simplified constitutive relation of the linear elastic material, the stress value of linear elastic material can be expressed as
It can be assumed that if
For the magnetic field strength
As the length changes of the steel strand stretching process are much larger than the cross-sectional area changes, the current size
The magnetic induction intensity
For the magnetization
Under the effect of stress, when a small length change occurs, the cross-section radius
Combining (
Then combining (
Substituting
The results are shown in Figure
Relationship diagram between frequency and stress.
According to the working principle of the
The steel strand used in the test is a common 1 × 7 strand structure whose parameters are shown in Table
Parameters of the steel strand.
Structure of steel strand | Nominal diameter ofsteel strand, |
Nominal area of steel strand, |
Ultimate tensile strength, |
Maximum tension, |
Nonproportional extension force, |
Maximum elongation, |
Stress relaxation rate after 1000 h, |
---|---|---|---|---|---|---|---|
No less than | No less than | No less than | No less than | No more than | |||
1 × 7 | 15.2 | 139 | 1720 | 241 | 217 | 3.5 | 4.5 |
An
Circuit principle diagram.
During the experiments, the steel strand is preloaded to 2 kN, and the final load is set to 8 kN. Such small stress is chosen based on the following reasons: (1) we hope the deformation of the steel strand can be limited in elastic range to test multiple equal cycles; (2) due to the clip limitation of loading, much larger tension may cause relative slippage between the test machine and the strand.
Before the test, the universal testing machine was used to clamp the ends of the insulated steel strand. The wire, which was leaded from both ends of the steel strand, is oriented perpendicular to the surface of the paper. The jaw clamps the 2/3 position of the end of the insulated steel strand to confirm that the steel strand and wire are not directly contacted with the universal testing machine, and the joints were twined by insulating tape. And the structure of the experimental system is shown in Figure
The experiment structure diagram.
The test procedure is as follows. Firstly, turning on the power supply of the oscillation circuit, the universal testing machine is used to preload the steel strand to 2 kN. After three times of loading, it is confirmed that the applied load and the deformation of the steel strand tend to be stable. Finally, the loading rate of 10 mm/min is loaded to 8 kN. In this period, the frequency meter collects the frequency data once per second, and the collected data are transmitted to the mobile device via bluetooth, and a total of 1 set of test data is collected during the loading process. After the data collection, the tension is unloaded to zero, and the change trend of the frequency is observed during unloading. At the end of a trial, the stress-strain data and corresponding curves are derived from the software which is used in the test. In this way, the same steel strand specimen is loaded 6 times, and a total of 6 sets of data are collected during these processes.
Under the same experimental conditions, the 6 loading tests have been completed. The effective data and the calculated data are shown in Table
The experimental data.
Median strain (10−4) | Median stress (MPa) | Measurement times | Repeatability error | Standard deviation | Median frequency (kHz) | |||||
---|---|---|---|---|---|---|---|---|---|---|
Loading 1 |
Loading 2 |
Loading 3 |
Loading 4 |
Loading 5 |
Loading 6 | |||||
0.7379 | 14.3885 | 74.3009 | 74.2940 | 74.2838 | 74.2754 | 74.2748 | 74.2677 | 0.0170% | 0.01266 | 74.28277 |
1.0146 | 19.7842 | 74.3018 | 74.2926 | 74.2838 | 74.2751 | 74.2746 | 74.2669 | 0.0174% | 0.01294 | 74.28247 |
1.2987 | 25.3237 | 74.3018 | 74.2911 | 74.2828 | 74.2750 | 74.2740 | 74.2656 | 0.0176% | 0.01309 | 74.28172 |
1.6012 | 31.2230 | 74.3010 | 74.2900 | 74.2817 | 74.2748 | 74.2733 | 74.2647 | 0.0175% | 0.01300 | 74.28092 |
1.9111 | 37.2662 | 74.2995 | 74.2889 | 74.2809 | 74.2747 | 74.2720 | 74.2639 | 0.0172% | 0.01274 | 74.27998 |
2.162 | 42.1583 | 74.2995 | 74.2883 | 74.2804 | 74.2742 | 74.2720 | 74.2632 | 0.0173% | 0.01287 | 74.27960 |
2.4682 | 46.6906 | 74.2984 | 74.2881 | 74.2807 | 74.2736 | 74.2712 | 74.2625 | 0.0173% | 0.01284 | 74.27908 |
2.7449 | 50.9353 | 74.2972 | 74.2875 | 74.2809 | 74.2734 | 74.2705 | 74.2619 | 0.0171% | 0.01266 | 74.27857 |
3.0142 | 54.1727 | 74.2951 | 74.2869 | 74.2809 | 74.2738 | 74.2696 | 74.2619 | 0.0162% | 0.01206 | 74.27803 |
3.2835 | 57.5540 | 74.2951 | 74.2855 | 74.2804 | 74.2745 | 74.2687 | 74.2617 | 0.0161% | 0.01198 | 74.27765 |
In the experiment, the steel strand is in the linear elastic stage. So, the stress of the steel strand increases with the increase of the applied load of the universal testing machine. And the increase of stress will lead to the increase of strain. In general, the load, stress, and strain of the steel strand increase with time.
As shown in Figure
Relationship diagram between median frequency and median stress.
Relationship diagram between stress and strain.
The following conclusions can be drawn from the analysis: As can be seen from Loading 1, 2, 5, and 6, the oscillation frequency decreases with the increase of time, while the stress increases with the increase of time. It can be concluded that the oscillation frequency decreases with the increase of stress and has a linear relationship within a certain range. This is consistent with the theoretical derivation of the second part of the article. As shown in Loading 3 and 4 of Table Figure It can be concluded from the analysis of the relationship between the median frequency and time in Figure The relationships shown in Figure
It is a challenging problem to detect the prestressing force of the structural steel strand in service concrete. The deformation of concrete, the relaxation of the prestressed steel strand, the corrosion of the steel strand, and the creep of concrete will cause the loss of prestress. However, the prestress loss has not been solved well, so it is important to detect the prestressed concrete structure effectively. The traditional method for detecting the prestressing force of the steel strand in the existing structure is complex, and the equipment that is used to obtain the prestressing force is expensive and inconvenient to carry. The vibration frequency of the oscillating circuit is used to detect the loss of prestress in the steel strand, which avoids the damage to the structure caused by the prestress detection and provides a timely and accurate method for detecting prestress.
The idea of the whole system is to connect the steel strand to the oscillating circuit, and the steel strand is equivalent to inductance in the circuit. The vibration frequency of the circuit is obtained by vibration, and the prestressing force in the steel strand can be obtained by calculation. A series of experimental data show that there is a certain relationship between the prestress of the steel strand and the frequency of oscillation. The inverse proportion relationship between the stress and frequency is obtained by data analysis, which is consistent with the theoretical derivation of this paper. It is proved that the method of detecting the prestressing force in the steel strand by the oscillation frequency of the circuit is practicable. It is also verified the previous conjecture that there is a certain relationship between the electromagnetic force and the strand force.
Adopting the EMO circuit, the experiments have been greatly improved in measuring accuracy and range. The measuring force of the steel strand is closer to the actual situation. The frequency meter used in the experiment is in the range of 20–200 kHz, whose measuring range is larger than the original one. And the measurement accuracy is 0.001 kHz.
Compared with the traditional method, it is more convenient and feasible to measure the prestressing force of the steel strand by the oscillating circuit, and it can reflect the force of the steel strand without any damage to prestressed structures.
Nevertheless, in the process of the steel strand, the experiment has failed to solve the rotation and frequency drift well. These are the problems that we have to deal with in the next step.
The authors declare that there are no conflicts of interest regarding the publication of this paper.
This work is jointly supported by the National Key Research and Development Program of China (2017YFC0806007), the Science and Technology Construction Project of Ministry of Transport of China (2015319814020), the Technology Innovation Project of Chongqing Social and People’s Livelihood (CSTC2016SHMSZX30026), the Program for Innovation Team Building at Institutions of Higher Education in Chongqing (CXTDG201602013), the Urumqi Science and Technology Plan (Y161320008), the Scientific and Technological Research Program of Chongqing Municipal Education Commission (KJ1400321 and KJ1605202), the National Science Fund for Distinguished Young Scholars (51425801), and the National Natural Science Foundation of China (11372366 and 51508059).