CN103557980B - Method for precisely testing external prestressing tendon tensioning force - Google Patents

Abstract

The invention discloses an accurate test method for the tensile force of external prestressed tendons. The inventor has designed a related test model, by simplifying the boundary conditions of external prestressed tendons to a damping and spring support, and further simplifying the prestressed tendons to have For simply supported tension cables with an equivalent calculated length L ₀ , a mass block is added in the middle of the prestressed tendon, and the vibration balance equation of the cable before and after the mass block is added in the middle of the prestressed tendon is optimized, and finally the equivalent calculated length of the prestressed tendon is formed The recognition algorithm of L ₀ , thus established the testing method of the present invention. This method is convenient for testing and low in testing cost. It only needs to test the vibration frequency twice before and after adding mass blocks to the prestressed tendons; and the test accuracy is high, which can well solve the problem of accurate testing of the tensile force of prestressed tendons in vitro. Applying the invention to the field of detection of external prestressed reinforced bridges can realize convenient and high-precision testing of the tensile force of external prestressed tendons, thereby providing reliable basic data for the detection and monitoring of such bridges.

Description

Precise test method for tensile force of prestressed tendon in vitro

technical field

The invention belongs to the technical field of bridge detection and monitoring, and in particular relates to an accurate test method for the tensile force of external prestressed tendons.

Background technique

External prestressing technique is a commonly used reinforcement method for girder bridges. The tensile force of external prestressed tendons is an important indicator of the effect of external prestressed reinforcement of this type of bridge. In the reinforcement acceptance, inspection and evaluation of this type of bridge, it is necessary to test the tensile force of external prestressed tendons. However, in the existing technical means, unless a pressure sensor is installed during construction, it is difficult to accurately measure the tensile force of the external prestressed tendons by other methods. The frequency method uses the deterministic relationship between the tension force and the vibration frequency of the tension cable to analyze and calculate the cable force through the vibration frequency of the tension cable. The external prestressed tendon is a kind of tension cable, so the frequency method can be used to test the tensile force of the external prestressed tendon. However, since the external prestressed tendons are usually in contact with the bridge girder through many turning blocks, the distance between the turning blocks is usually small (often within 500 times the diameter of the external prestressed tendons), resulting in the calculation of the external prestressed tendons The length is small, the contact stiffness between the steering block and the prestressed tendon, the anchorage stiffness of the prestressed tendon, the shock absorber of the prestressed tendon and other factors will have a great impact on the test frequency of the prestressed tendon, and these effects are unknown. Therefore, it is difficult to accurately measure the tensile force of external prestressed tendons with the conventional frequency method, and its test accuracy cannot meet the engineering requirements. How to accurately test the tensile force of external prestressed tendons has always been an unsolved engineering problem. Therefore, in the acceptance or testing of externally prestressed bridges, there is an urgent need for a method that can accurately measure the tensile force of externally prestressed tendons.

Contents of the invention

The technical problem to be solved by the present invention is to provide an accurate test method for the tensile force of external prestressed tendons with convenient operation and high precision, so as to realize accurate testing of the tensile force of external prestressed tendons.

In order to solve the above-mentioned technical problems, the present invention adopts the following technical proposals: an accurate test method for the tensile force of external prestressed tendons, at first install a vibration pick-up on the external prestressed tendons between the two steering gears with a spacing of L, and connect the vibration pick-ups to vibrate Test the instrument to obtain the first-order vibration angular frequency ω ₁ of the external prestressed tendon; then install an additional mass block at the middle position L/2 of the external prestressed tendon, and test the external prestressed tendon after the additional mass block is obtained by the same method The first-order vibration angular frequency ω ₁ ′; finally, combined with the stiffness EI of the external prestressed tendons, the material density ρ and the cross-sectional area A, and the measured weight M of the mass block, the tension value T ₀ of the external prestressed tendons is calculated using the formula, the formula for

${\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 16</span>}{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; 4</span>}}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{<span\; class="notranslate">\; [</span>{<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ]</span>}^{\mathrm{<span\; class="notranslate">\; 4</span>}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}^{\mathrm{<span\; class="notranslate">\; 4</span>}}{\mathrm{<span\; class="notranslate">\; EI</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&rho;A</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 3</span>}}}{\mathrm{<span\; class="notranslate">\; 4</span>}{<span\; class="notranslate">\; [</span>{<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ]</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; \&rho;A</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>$

L is less than or equal to 500 times the external prestressing tendon diameter.

The additional quality block is 0.2 to 2 times the mass of prestressed tendons per unit length.

The additional mass block is a magnetic iron block, and different numbers of magnetic iron blocks can be selected to be adsorbed on the external prestressed tendons to form the additional mass block together.

Aiming at the low accuracy of the existing frequency method for testing the tensile force of external prestressed tendons, the inventor designed a related test model, by simplifying the boundary conditions of external prestressed tendons into a damping and spring support, and further combining the prestressed tendons Simplify it into a simply supported tension cable with an equivalent calculated length L ₀ , add a mass block in the middle of the prestressed tendon, optimize and establish the vibration balance equation of the cable before and after the attached mass block in the middle of the prestressed tendon, and finally form the equivalent of the prestressed tendon The identification algorithm of the effective calculation length L ₀ is established, and the accurate test method for the tensile force of prestressed tendons in vitro is established. This method is convenient for testing and low in testing cost. It only needs to test the vibration frequency twice before and after adding mass blocks to the prestressed tendons; and the test accuracy is high, which can well solve the problem of accurate testing of the tensile force of prestressed tendons in vitro. Applying the invention to the field of detection of external prestressed reinforced bridges can realize convenient and high-precision testing of the tensile force of external prestressed tendons, thereby providing reliable basic data for the detection and monitoring of such bridges.

Description of drawings

Figure 1 is a schematic diagram of the frequency test of the external prestressed tendon of the additional mass precursor.

Fig. 2 is a schematic diagram of frequency test of prestressed tendons in vitro after mass block is added.

Fig. 3 is a simplified calculation diagram of the external prestressed tendon of the front of the additional mass block.

Fig. 4 is a simplified calculation diagram of external prestressed tendons after adding mass blocks.

Figure 5 is a schematic diagram of the appearance and installation of the additional mass block.

In the figure: 1 steering gear, 2 prestressed tendon, 3 bridge girder body, 4 vibration frequency tester, 5 vibration picker, 6 mass block (magnetic iron block), 7 damping spring system, 8 spring.

Detailed ways

Principle of test method

The precise test method of the external prestressed tendon tensile force of the present invention operates according to the following steps:

1. Install a vibration testing instrument on the external prestressed tendons between two steering gears with a spacing of L, and obtain the first-order vibration angular frequency ω ₁ of the prestressed tendons by testing, as shown in Figure 1.

2. At the middle position L/2 of the prestressed tendon, add a mass block with a mass of M (such as a magnetic iron block), and use the same method as step 1 to test the prestressed mass after the additional mass block is obtained by using a vibration tester. The first-order vibration angular frequency of the stress tendon ω ₁ ′; in order to reduce the influence of the additional mass block on the first-order mode shape of the prestressed tendon while clearly measuring the difference between ω ₁ ′ and ω ₁ , the mass M of the additional mass block is required Between 0.2 and 2 times the mass of prestressed tendons per unit length;

3. Simplify the prestressed tendons as shown in attached drawings 3 and 4, respectively establish the vibration balance equations of the prestressed tendons, and use the first-order natural angular frequencies of the prestressed tendons before and after the additional mass tested in steps 1 and 2 ω ₁ and ω ₁ ′ identify the effective calculation length L ₀ of the prestressed tendon, and the reasoning process is as follows:

As shown in Figure 3, for an external prestressed tendon with a diverter spacing of L and a tension of _T0 , its bending stiffness is EI, the material density of the prestressed tendon is ρ, and the cross-sectional area is A. Since the steering gear has a certain support stiffness for the prestressed tendons, the boundary conditions of the external prestressed tendons can be simplified as a damping and spring support. After the construction is completed, the damping size C and the spring support stiffness K are determined, but their size is Therefore, it is difficult to obtain a definite relationship between the prestressed tendon frequency ω and the tension force T ₀ by directly establishing the vibration equation. At the same time, because the damping size and spring support stiffness are unknown, it is also impossible to directly determine the prestressed tendon frequency ω The tensile force is calculated as T ₀ . At this time, the additional damping and spring support at the lateral position can be equivalent to the influence on the calculated length of the prestressed tendon, and in the vibration analysis, the prestressed tendon can be simplified as a simply supported tension cable with an equivalent calculated length L ₀ , as shown in Figure 3.

At this time, when the cable vibrates slightly laterally, its water vibration displacement is y(x, t). Considering the influence of the bending stiffness EI of the cable, the vibration balance equation of the cable can be formed from the force balance equation and the bending moment balance equation:

$\mathrm{<span\; class="notranslate">\; EI</span>}\frac{{<span\; class="notranslate">\; \&PartialD;</span>}^{\mathrm{<span\; class="notranslate">\; 4</span>}}\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}{<span\; class="notranslate">\; \&PartialD;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 4</span>}}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&rho;A</span>}\frac{{<span\; class="notranslate">\; \&PartialD;</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}{<span\; class="notranslate">\; \&PartialD;</span>{\mathrm{<span\; class="notranslate">\; t</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\frac{{<span\; class="notranslate">\; \&PartialD;</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}{<span\; class="notranslate">\; \&PartialD;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

Formula (1) is solved by the Galerkin method to obtain the natural frequency of the cable:

${\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; =</span>\sqrt{\frac{\mathrm{<span\; class="notranslate">\; EI</span>}}{\mathrm{<span\; class="notranslate">\; \&rho;A</span>}}{<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; n\&pi;</span>}}{{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{\mathrm{<span\; class="notranslate">\; \&rho;A</span>}}{<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; n\&pi;</span>}}{{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1,2,3</span>}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

Observing the above formula, the stiffness EI of the prestressed tendon, the material density ρ and the cross-sectional area A are known, and the vibration frequency ω _n of the prestressed tendon can be obtained by testing the vibration instrument. Therefore, it is only necessary to determine the effective calculation length of the prestressed tendon L ₀ , the tension T ₀ of the prestressed tendons can be obtained from the analysis of the measured vibration frequency ω _n .

In order to determine the effective calculated length L ₀ of the prestressed tendons, a mass block with mass M is artificially added at a distance L _m from the left end of the prestressed tendons, as shown in Figure 4. Then the prestressed tendon can be simplified as the calculation diagram shown in accompanying drawing 4, wherein $L_m^{\&prime;}=L_m-\frac{L-L_0}{2}\&Center\; Dot;$

At this time, the vibration balance equation of the prestressed tendon becomes:

$\mathrm{<span\; class="notranslate">\; EI</span>}\frac{{<span\; class="notranslate">\; \&PartialD;</span>}^{\mathrm{<span\; class="notranslate">\; 4</span>}}\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}{<span\; class="notranslate">\; \&PartialD;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 4</span>}}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; \&rho;A</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; M\&delta;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>\frac{{<span\; class="notranslate">\; \&PartialD;</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}{<span\; class="notranslate">\; \&PartialD;</span>{\mathrm{<span\; class="notranslate">\; t</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\frac{{<span\; class="notranslate">\; \&PartialD;</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}{<span\; class="notranslate">\; \&PartialD;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

In the formula, $\mathrm{\&delta;}(x-L_m^{\&prime;})=\left\{\begin{array}{cc}1& x=L_m^{\&prime;}\\ 0& x\&NotEqual;L_m^{\&prime;}\end{array}\right.\&CenterDot;$

The Galerkin method is also used to solve the vibration balance equation. In the process of solving, it is assumed that the additional mass block has little effect on the mode shape of the prestressed tendon, and the natural frequency of the prestressed tendon after the additional mass block can be obtained:

${\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\sqrt{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; \&rho;A</span>}{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{\mathrm{<span\; class="notranslate">\; sin</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\frac{\mathrm{<span\; class="notranslate">\; n\&pi;</span>}{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}{{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}}}\sqrt{\frac{\mathrm{<span\; class="notranslate">\; EI</span>}}{\mathrm{<span\; class="notranslate">\; \&rho;A</span>}}{<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; n\&pi;</span>}}{{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{\mathrm{<span\; class="notranslate">\; \&rho;A</span>}}{<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; n\&pi;</span>}}{{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1,2,3</span>}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

Combining formula (2) and formula (4), taking the first-order frequency of prestressed tendons for analysis, it can be concluded that

${<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; \&rho;A</span>}{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{\mathrm{<span\; class="notranslate">\; sin</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\frac{\mathrm{<span\; class="notranslate">\; \&pi;</span>}{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}{{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; \&rho;A</span>}{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{\mathrm{<span\; class="notranslate">\; sin</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\frac{\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

The first-order natural frequencies ω ₁ and ω ₁ ′ of the prestressed tendons before and after the additional mass can be obtained from actual measurements, and the mass M of the mass and the installation position L _m are definite values that can be obtained from actual measurements. Therefore, using the first-order natural frequency of the prestressed tendon before and after the additional mass, the effective length L ₀ of the prestressed tendon can be calculated by formula (5). If the mass block is installed in the middle of the prestressed tendons, that is Substituting into formula (5), we can get

${<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; \&rho;A</span>}{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$

The above formula can be written as

${\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; m</span>}}{<span\; class="notranslate">\; [</span>{<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ]</span>\mathrm{<span\; class="notranslate">\; \&rho;A</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$

4. Substitute the effective length L ₀ into the formula (2), and calculate the tension T ₀ of the prestressed tendon. The principle is as follows.

${\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&rho;A</span>}{<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; EI</span>}{<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 16</span>}{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; 4</span>}}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{<span\; class="notranslate">\; [</span>{<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ]</span>}^{\mathrm{<span\; class="notranslate">\; 4</span>}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}^{\mathrm{<span\; class="notranslate">\; 4</span>}}{\mathrm{<span\; class="notranslate">\; EI</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&rho;A</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 3</span>}}}{\mathrm{<span\; class="notranslate">\; 4</span>}{<span\; class="notranslate">\; [</span>{<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ]</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; \&rho;A</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 8</span>}<span\; class="notranslate">\; )</span>$

Using the above formula (8), the precise value of the tension T ₀ of the prestressed tendon can be calculated by comparing the first-order natural frequencies ω ₁ and ω ₁ ′ of the prestressed tendon before and after the additional mass measured in Step 1 and Step 2 .

Below in conjunction with embodiment and accompanying drawing, further illustrate the present invention.

Example 1

As accompanying drawing 1, on the external prestressed tendon between the two diverters with spacing L, vibration pickup is installed on the external prestressed tendon, the vibration pickup is connected to the vibration tester, and the first-order vibration angular frequency ω ₁ of the external prestressed tendon is obtained by testing; Attached Figure 2, at the middle position L/2 of the external prestressed tendon, install an additional mass block (magnetic iron block), the installation method is shown in Figure 5, use a vibration tester to test the external prestressed tendon after the additional mass block is obtained The first-order vibration angular frequency ω ₁ ′; combined with the external prestressed tendon stiffness EI, material density ρ and cross-sectional area A provided by the design drawings, and the measured mass weight M, the tension of the external prestressed tendon is calculated using formula (8). Pull force value T ₀ .

${\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; 16</span>}\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; 4</span>}}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{<span\; class="notranslate">\; [</span>{<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ]</span>}^{\mathrm{<span\; class="notranslate">\; 4</span>}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}^{\mathrm{<span\; class="notranslate">\; 4</span>}}\mathrm{<span\; class="notranslate">\; EI</span>}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&rho;A</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 3</span>}}}{\mathrm{<span\; class="notranslate">\; 4</span>}{<span\; class="notranslate">\; [</span>{<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ]</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; \&rho;A</span>}}$

The test results are shown in Table 1

Table 1 embodiment 1 test result

Claims (3)

1. a kind of test method for the tension force of external prestressed tendons is characterized in that: at first, on the external prestressed tendons between the two diverters at spacing, vibration pick-ups are installed, the vibration pick-ups are connected to the vibration tester, and the test results in The first-order vibration angular frequency ω ₁ of the external prestressed tendon; then, at the middle position L/2 of the external prestressed tendon, an additional mass block is installed, and the first-order vibration angular frequency of the external prestressed tendon after the additional mass block is obtained by the same method ω′ ₁ ; Finally, combined with the stiffness EI of the external prestressed tendon, the material density ρ and the cross-sectional area A, and the measured weight M of the mass block, the tensile force value T ₀ of the external prestressed tendon is calculated by the formula, the formula is Said L is less than or equal to 500 times the diameter of the external prestressing tendons. 2. The method for accurately testing the tensile force of external prestressed tendons according to claim 1, characterized in that: the additional mass is 0.2 to 2 times the mass of the prestressed tendons per unit length. 3. The method for accurately testing the tensile force of external prestressed tendons according to claim 2, characterized in that: the additional mass is a magnetic iron block.