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

Abstract

The invention discloses a method for precisely testing external prestressing tendon tensioning force. A related test model is designed by the inventor, the boundary condition of an external prestressing tendon is simplified into a damper and a spring support, the prestressing tendon is further simplified into a simply supported stretching rope with an equivalent calculating length L0, a mass block is added to the middle of the prestressing tendon, the vibration balance equations of the stretching rope generated before and after the mass block is added to the middle of the prestressing tendon are optimized and built, the recognition algorithm of the equivalent calculating length L0 of the prestressing tendon is formed at last, and therefore the testing method is built. The testing of the method is convenient, testing cost is low, and only two vibration frequency tests need to be carried out on the prestressing tendon before and after the mass block is added. Testing precision is high, and the problem of the precise testing on the external prestressing tendon tensioning force can be solved well. The method is applied to the field of external prestressing strengthened bridge testing and can achieve the convenient and high-precision testing on the external prestressing tendon tensioning force, and therefore reliable essential data are provided for the detection and monitoring of the bridges of the kind.

Description

External prestressing steels stretching force method for accurate testing

Technical field

The invention belongs to bridge machinery, monitoring technique field, particularly relate to a kind of external prestressing steels stretching force method for accurate testing.

Background technology

External prestressing technique is a kind of conventional beam bridge reinforcement means.The size of external prestressing steels stretching force is an important indicator of such bridge External prestressed consolidation effect, in the reinforcing examination of such bridge, check and evaluation, all needs the stretching force size of test body External prestressed.But, in existing technological means, unless when constructing setting pressure sensor, adopt additive method to be difficult to the size of Accurate Measurement external prestressing steels stretching force.Frequency method be utilize stretching force size and stretching rope vibration frequency between deterministic dependence, carry out analytical calculation Suo Li size by the vibration frequency of stretching rope.External prestressing steels belongs to a kind of stretching rope, and frequency method therefore can be adopted to carry out the test of external prestressing steels stretching force.But, because external prestressing steels is normally contacted with bridge beam body by a lot of steering blocks, distance between steering block is very little (often in vitro presstressed reinforcing steel diameter 500 times within) usually, cause the computational length of external prestressing steels very little, the factors such as the contact stiffness of steering block and presstressed reinforcing steel, the anchoring rigidity of presstressed reinforcing steel, presstressed reinforcing steel vibration damper all can produce considerable influence to the test frequency of presstressed reinforcing steel, and these impacts are unknown.Therefore, adopt nominal frequencies method to be difficult to the stretching force of Accurate Measurement external prestressing steels, its measuring accuracy cannot engineering demands.How accurately to test the stretching force of external prestressing steels, be unsolved engineering roadblock always.Therefore, in external prestressing strengthening bridge being carried out an acceptance inspection or detects, be badly in need of a kind of can the method for Accurate Measurement external prestressing steels stretching force.

Summary of the invention

The technical problem to be solved in the present invention is to provide a kind of easy to operate, external prestressing steels stretching force method for accurate testing that precision is higher, to realize accurately testing external prestressing steels stretching force.

For solving the problems of the technologies described above, the present invention is by the following technical solutions: external prestressing steels stretching force method for accurate testing, first in spacing be L two steering gears between external prestressing steels on vibro-pickup is installed, vibro-pickup is connected vibration testing instrument, and test obtains 1 rank angle of throw frequencies omega of external prestressing steels ₁; Then the L/2 place, centre position of presstressed reinforcing steel in vitro, installs additional mass, obtains the external prestressing steels 1 rank angle of throw frequencies omega after additional mass with method test ₁'; Finally in conjunction with external prestressing steels rigidity EI, density of material ρ and sectional area A, and the mass weight M of actual measurement, adopt formulae discovery to go out the stretch-draw force value T of external prestressing steels ₀, formula is

$T_0=\frac{16M^4{\mathrm{\ω}}_1^2-{[{\left(\frac{{\mathrm{\ω}}_1}{{\mathrm{\ω}}_1^{\′}}\right)}^2-1]}^4{\mathrm{\π}}^4{\mathrm{EI}\left(\mathrm{\ρA}\right)}^3}{4{[{\left(\frac{{\mathrm{\ω}}_1}{{\mathrm{\ω}}_1^{\′}}\right)}^2-1]}^2{\mathrm{\π}}^2{M}^2\mathrm{\ρA}}\·$

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

Additional mass is 0.2 ~ 2 times of unit length presstressed reinforcing steel quality.

Additional mass is magnetic iron block, the magnetic iron block of varying number can be selected to be adsorbed on external prestressing steels, jointly form additional mass.

For the problem that existing frequency method test external prestressing steels stretching force precision is not high, inventor has devised dependence test model, by the boundary condition of external prestressing steels is reduced to a damping and spring-loaded, and further presstressed reinforcing steel is reduced to there is Equivalent Calculation length L ₀freely-supported stretching rope, additional mass in the middle of the presstressed reinforcing steel, optimizes the vibration balancing equation establishing drag-line before and after additional mass in the middle part of presstressed reinforcing steel, finally forms the Equivalent Calculation length L of presstressed reinforcing steel ₀recognizer, thereby establish external prestressing steels stretching force method for accurate testing.This method convenient test, testing cost is low, only needs the two-time vibration frequency test carrying out before and after additional mass to presstressed reinforcing steel; And measuring accuracy is high, the difficult problem that external prestressing steels stretching force is accurately tested can be solved well.Apply the present invention to external prestressing strengthening bridge machinery field, stretching force that is convenient, high precision measurement external prestressing steels can be realized, thus for such bridge detection, monitoring reliable basic data is provided.

Accompanying drawing explanation

Fig. 1 is external prestressing steels frequency test schematic diagram before additional mass.

Fig. 2 is external prestressing steels frequency test schematic diagram after additional mass.

Fig. 3 is that before additional mass, external prestressing steels simplifies calculating diagram.

Fig. 4 is that after additional mass, external prestressing steels simplifies calculating diagram.

Fig. 5 is additional mass profile and scheme of installation.

In figure: 1 steering gear, 2 presstressed reinforcing steels, 3 bridge beam body, 4 vibration frequency testers, 5 vibro-pickups, 6 masses (magnetic iron block), 7 damping spring systems, 8 springs.

Embodiment

Method of testing principle

External prestressing steels stretching force method for accurate testing of the present invention operates according to the following steps:

1. in two spacing be L steering gear between external prestressing steels on vibration testing instrument is installed, test obtains 1 rank angle of throw frequencies omega of presstressed reinforcing steel ₁, as shown in Figure 1.

2. at the L/2 place, centre position of presstressed reinforcing steel, an additional quality is the mass (as magnetic iron block) of M, adopts the method same with step 1, utilizes vibration testing instrument, and test obtains the presstressed reinforcing steel 1 rank angle of throw frequencies omega after additional mass ₁'; In order to obviously ω can be being measured ₁' with ω ₁difference while reduce additional mass on the impact of presstressed reinforcing steel 1 first order mode, require that the mass M of additional mass is between 0.2 ~ 2 times of unit length presstressed reinforcing steel quality;

3. as accompanying drawing 3, accompanying drawing 4 pairs of presstressed reinforcing steels simplify, set up the vibration balancing equation of presstressed reinforcing steel respectively, utilize in step 1 and step 2 the presstressed reinforcing steel 1 rank natural angular frequency ω before and after the additional mass testing and obtain ₁and ω ₁the effective calculating length L of ' identification presstressed reinforcing steel ₀, reasoning process is as follows:

As shown in Figure 3, for steering gear spacing be L, stretching force is T ₀external prestressing steels, its bendind rigidity is EI, and presstressed reinforcing steel density of material is ρ, and sectional area is A.Because steering gear has certain support stiffness to presstressed reinforcing steel, the boundary condition of external prestressing steels can be reduced to a damping and spring-loaded, after having constructed, damping size C and regidity of spring bearing K determines, but its size is unknown, therefore directly setting up vibration equation, is be difficult to draw that the presstressed reinforcing steel frequencies omega determined and stretching force are T ₀determination relation, meanwhile, because damping size and regidity of spring bearing are unknown, also directly cannot calculate stretching force by presstressed reinforcing steel frequencies omega is T ₀.Now, lateral position additional damping and spring-loaded can be equivalent to the impact on presstressed reinforcing steel computational length, when vibration analysis, presstressed reinforcing steel can be reduced to and there is Equivalent Calculation length L ₀freely-supported stretching rope, as shown in Figure 3.

When now drag-line does slight lateral vibration, its water vibration displacement is y (x, t), considers the impact of drag-line bending stiffness EI, can be formed the vibration balancing equation of drag-line by equilibrium of forces equation and moment of flexure balance equation:

$\mathrm{EI}\frac{{\∂}^{4}y(x,t)}{\∂x^4}+\mathrm{\ρA}\frac{{\∂}^{2}y(x,t)}{\∂t^2}-T_0\frac{{\∂}^{2}y(x,t)}{\∂x^2}=0---\left(1\right)$

Adopt Galerkin's Procedure to solve formula (1), obtain the natural frequency of drag-line:

${\mathrm{\ω}}_n=\sqrt{\frac{\mathrm{EI}}{\mathrm{\ρA}}{\left(\frac{\mathrm{n\π}}{L_0}\right)}^4+\frac{T_0}{\mathrm{\ρA}}{\left(\frac{\mathrm{n\π}}{L_0}\right)}^2}(n=\mathrm{1,2,3},\·\·\·)---\left(2\right)$

Observe above formula, presstressed reinforcing steel rigidity EI, density of material ρ and sectional area A are known, presstressed reinforcing steel vibration frequency ω _ncan be tested by vibration instrumentation and draw, therefore, only need the effective calculating length L determining presstressed reinforcing steel ₀, just can by actual measurement vibration frequency ω _nanalysis draws pre-stress rib stretching force T ₀.

In order to determine the effective calculating length L of presstressed reinforcing steel ₀, artificial apart from presstressed reinforcing steel left end L _mthe additional quality in place is the mass of M, as shown in Figure 4.Then presstressed reinforcing steel can be reduced to calculating diagram as shown in Figure 4, wherein $L_m^{\′}=L_m-\frac{L-L_0}{2}\·$

Now the vibration balancing equation of presstressed reinforcing steel becomes:

$\mathrm{EI}\frac{{\∂}^{4}y(x,t)}{\∂x^4}+[\mathrm{\ρA}+\mathrm{M\δ}(x-L_m^{\′})]\frac{{\∂}^{2}y(x,t)}{\∂t^2}-T_0\frac{{\∂}^{2}y(x,t)}{\∂x^2}=0---\left(3\right)$

In formula, $\mathrm{\δ}(x-L_m^{\′})=\left\{\begin{array}{cc}1& x=L_m^{\′}\\ 0& x\≠L_m^{\′}\end{array}\right.\·$

Same employing Galerkin's Procedure solves vibration balancing equation, supposes that additional mass is little on the impact of the vibration shape of presstressed reinforcing steel in solution procedure, can obtain the natural frequency of presstressed reinforcing steel after additional mass:

${\mathrm{\ω}}_n^{\′}=\frac{1}{\sqrt{1+\frac{2M}{\mathrm{\ρA}{L}_0}{\sin }^2\frac{\mathrm{n\π}{L}_m^{\′}}{L_0}}}\sqrt{\frac{\mathrm{EI}}{\mathrm{\ρA}}{\left(\frac{\mathrm{n\π}}{L_0}\right)}^4+\frac{T_0}{\mathrm{\ρA}}{\left(\frac{\mathrm{n\π}}{L_0}\right)}^2}(n=\mathrm{1,2,3},\·\·\·)---\left(4\right)$

Composite type (2) and formula (4), the fundamental frequency getting presstressed reinforcing steel is analyzed, and can draw

${\left(\frac{{\mathrm{\ω}}_1}{{\mathrm{\ω}}_1^{\′}}\right)}^2=1+\frac{2M}{\mathrm{\ρA}{L}_0}{\sin }^2\frac{\mathrm{\π}{L}_m^{\′}}{L_0}=1+\frac{2M}{\mathrm{\ρA}{L}_0}{\sin }^2\frac{\mathrm{\π}(2L_m-L+L_0)}{2L_0}---\left(5\right)$

Presstressed reinforcing steel 1 rank natural frequency ω before and after additional mass ₁and ω ₁' can be drawn by actual measurement, mass mass M and installation site L _mbe the determined value can surveyed and draw.Therefore, utilize the presstressed reinforcing steel 1 rank natural frequency before and after additional mass, the effective length L of presstressed reinforcing steel can be calculated by formula (5) ₀.If mass is installed on presstressed reinforcing steel centre position, namely substitution formula (5), can obtain

${\left(\frac{{\mathrm{\ω}}_1}{{\mathrm{\ω}}_1^{\′}}\right)}^2=1+\frac{2M}{\mathrm{\ρA}{L}_0}---\left(6\right)$

Above formula can be write as

$L_0=\frac{2M}{[{\left(\frac{{\mathrm{\ω}}_1}{{\mathrm{\ω}}_1^{\′}}\right)}^2-1]\mathrm{\ρA}}---\left(7\right)$

4. by effective length L ₀in substitution formula (2), calculate pre-stress rib stretching force T ₀, principle as shown in the formula.

$T_0=\mathrm{\ρA}{\left(\frac{{\mathrm{\ω}}_1{L}_0}{\mathrm{\π}}\right)}^2-\mathrm{EI}{\left(\frac{\mathrm{\π}}{L_0}\right)}^2=\frac{16M^4{\mathrm{\ω}}_1^2-{[{\left(\frac{{\mathrm{\ω}}_1}{{\mathrm{\ω}}_1^{\′}}\right)}^2-1]}^4{\mathrm{\π}}^4{\mathrm{EI}\left(\mathrm{\ρA}\right)}^3}{4{[{\left(\frac{{\mathrm{\ω}}_1}{{\mathrm{\ω}}_1^{\′}}\right)}^2-1]}^2{\mathrm{\π}}^2{M}^2\mathrm{\ρA}}---\left(8\right)$

Utilize above formula (8), the presstressed reinforcing steel 1 rank natural frequency ω before and after the additional mass that obtains will be tested in step 1 and step 2 ₁and ω ₁', just can calculate pre-stress rib stretching force T ₀exact value.

The present invention is further illustrated below in conjunction with embodiment and accompanying drawing.

Embodiment 1

As accompanying drawing 1, in spacing be L two steering gears between external prestressing steels on vibro-pickup is installed, vibro-pickup is connected vibration testing instrument, and test obtains 1 rank angle of throw frequencies omega of external prestressing steels ₁; As accompanying drawing 2, the L/2 place, centre position of presstressed reinforcing steel in vitro, install additional mass (magnetic iron block), installation method, as accompanying drawing 5, utilizes vibration testing instrument, and test obtains the external prestressing steels 1 rank angle of throw frequencies omega after additional mass ₁'; In conjunction with external prestressing steels rigidity EI, density of material ρ and sectional area A that design drawing provides, and the mass weight M of actual measurement, adopt formula (8) to calculate the stretch-draw force value T of external prestressing steels ₀.

$T_0=\frac{{16M}^4{\mathrm{\ω}}_1^2-{[{\left(\frac{{\mathrm{\ω}}_1}{{\mathrm{\ω}}_1^{\′}}\right)}^2-1]}^4{\mathrm{\π}}^4\mathrm{EI}{\left(\mathrm{\ρA}\right)}^3}{4{[{\left(\frac{{\mathrm{\ω}}_1}{{\mathrm{\ω}}_1^{\′}}\right)}^2-1]}^2{\mathrm{\π}}^2{M}^2\mathrm{\ρA}}$

Test result is in table 1

Table 1 embodiment 1 test result

Claims (3)

1. an external prestressing steels stretching force method for accurate testing, it is characterized in that: first in spacing be L two steering gears between external prestressing steels on vibro-pickup is installed, vibro-pickup is connected vibration testing instrument, and test obtains 1 rank angle of throw frequencies omega of external prestressing steels ₁; Then the L/2 place, centre position of presstressed reinforcing steel in vitro, installs additional mass, with method test obtain the external prestressing steels 1 rank angle of throw frequencies omega after additional mass ' ₁; Finally in conjunction with external prestressing steels rigidity EI, density of material ρ and sectional area A, and the mass weight M of actual measurement, adopt formulae discovery to go out the stretch-draw force value T of external prestressing steels ₀, formula is

Described L is less than or equal to the external prestressing steels diameter of 500 times.

2. external prestressing steels stretching force method for accurate testing according to claim 1, is characterized in that: described additional mass is 0.2 ~ 2 times of unit length presstressed reinforcing steel quality.

3. external prestressing steels stretching force method for accurate testing according to claim 2, is characterized in that: described additional mass is magnetic iron block.