CN101587046A - Method for evaluating eccentric straight-line prestressed concrete beam bridge bearing ability based on dynamic measurement process - Google Patents

Abstract

The invention provides a method for evaluating eccentric straight-line prestressed concrete beam bridge bearing ability based on dynamic measurement process, which includes the steps of: executing forced vibration test for beam bridge structure and acquiring single point vibration movement respond of the structure; establishing structure finite element numeric analysis model for analyzing effect of prestress level to dynamic characteristics of structure; recognizing effective prestress of structure from measured structural power respond variation amount using a method based on sensitivity; calculating anti-crack bearing capacity during test for prestressed concrete beam bridge according to measured effective prestress value. Compared with conventional nondestructive detection method, the method provided by the invention has the advantages of simple and shortcut test process, strict and integral evaluating theory, high precision of test result or the like, and can be conveniently applied to test and evaluation for prestressed concrete beam bridge.

Description

Method for evaluating eccentric straight-line prestressed concrete beam bridge bearing ability based on dynamic measurement of pile

Technical field

The invention belongs to the vibration monitoring of engineering structure field, relate to the vibration-testing and the assessment of prestressed concrete beam bridge, assess this major issue at eccentric straight-line prestressed reinforced-concrete beam bridge bearing capacity, propose to assess the beam bridge bearing capacity by the method for vibration-testing and effective prestress identification.

Background technology

Prestressed concrete beam bridge is the bridge type that the most extensively adopts on the highway.Research is very important at the appraisal procedure of the fast evaluation method of this kind bridge, particularly bearing capacity.At present, the most widely used bridge appraisal procedure remains method based on visual inspection in the practice.Such method is effective really when there is local significant deficiency in bridge.But but be difficult to the integral status of full-bridge is assessed.Other method comprises some nondestructiving detecting means, supersonic sounding technology for example, acoustic emission or the like.These methods all are faced with the problem identical with the naked eyes detection method: promptly can't make assessment to the bridge structure integral status.

In order to address this problem, proposed structural appraisal method, responded by the forced vibration or the random vibration of gathering structure, and structural response is analyzed based on the structural dynamic test, obtain every physical parameter of structure, and then the situation of evaluation structure and ability.Doebling etc. ^[1]With Farrar etc. ^[2]Summed up development based on the appraisal procedure of structural dynamic test.According to their summary, also has bibliographical information at the correlative study of prestressed concrete beam bridge.For prestressed concrete beam bridge, the size of bridge prestress value is to estimate the important parameter of this bridge cracking resistance load.Yet the prestress value of beam bridge began reducing from that time that prestressed stretch-draw is finished always.Therefore, the assessment of the existing prestress value of beam bridge is very important for the assessment of bridge situation and ability.Lu and Law ^[3]A kind of method for testing vibration of eccentric straight-line prestressed reinforced-concrete beam bridge prestress value identification has been proposed.In the middle of their research, presstressed reinforcing steel is assumed to be and is positioned at the beam section centre of form, without acceptance of persons.This hypothesis is not inconsistent with the actual conditions of most of prestressed concrete beams.

[1]DOEBLING?S.W.，FARRAR?C.R.，and?PRIME，M.B.，“A?Summary?Review?of?Vibration-based?DamageIdentification?Methods.”，Shock?and?Vibration?Dig.，30(2)，91-105，1998.

[2]FARRAR?C.R.，DOEBLING?S.W.and?DUFFEY?T.A..，“Vibration-based?Damage?Detection.”SD2000，Struct.Dyn.Forum，April?11-17，1999.

[3]LU?Z.R.，LAW?S.S.，“Identification?of?Prestress?Force?from?Measured?Structural?Responses”，MechanicalSystems?and?Signal?Processing?20，2006.

Summary of the invention

The objective of the invention is at the deficiencies in the prior art, a kind of method for evaluating eccentric straight-line prestressed concrete beam bridge bearing ability based on dynamic measurement of pile is proposed, identify the effective prestress of prestress reinforced-concrete beam by the test and the dynamic response signal of the single measuring point of analytical structure, effectively measure the cracking resistance load-bearing capacity of prestressed concrete beam bridge.

For reaching above purpose, solution of the present invention is:

A kind of method for evaluating eccentric straight-line prestressed concrete beam bridge bearing ability based on dynamic measurement of pile identifies the effective prestress of structure and based on the cracking resistance bearing capacity of this evaluation structure from prestressed concrete beam bridge forced vibration response.Further, it may further comprise the steps:

1) the single-point vibratory response that beam bridge structure is carried out the forced vibration test and obtains structure;

2) set up the structure finite element numerical analysis model and analyze of the influence of prestress level structural dynamic characteristic;

3) adopt the effective prestress that from the structural dynamic response variable quantity that measures, identifies structure based on the optimization method of susceptibility;

Cracking resistance load-bearing capacity when 4) calculating the prestressed concrete beam bridge test according to the effective prestress value that measures.

According to structural shape and support situation, estimate the perpendicular curved vibration shape in the first five rank of structure before the vibration-testing, determine exciting mode, exciting point and the pick-up point of forced vibration test in view of the above, obtain pumping signal and structure vibration signals synchronously.

According to the equation of motion under the given external load effect, determine eccentric straight-line prestressed reinforced-concrete beam bridge because the construction geometry stiffness matrix that eccentric straight-line prestressed effect causes passes through the influence of finite element numerical analysis model analysis prestress level to structural dynamic characteristic based on this.

Based on the susceptibility matrix of finite element model derivation structural response, and adopt optimization method from the structural dynamic response variable quantity that measures, to identify the effective prestress of structure to prestress value.

Dead load remains unchanged, determine the structure effective prestress with to the relation of the cracking resistance bearing capacity of mobile load with evaluation structure cracking resistance bearing capacity.

Be subjected to the configuration forces vibratory response of eccentric straight-line prestressed effect

For the concrete beam bridge that is subjected to the eccentric prestress effect (as Fig. 1), its equation of motion under given external load effect is as follows:

$\left[M\right]\left\{\stackrel{\·\·}{x}\right\}+\left[C\right]\left\{\stackrel{\·}{x}\right\}+\left[K\right]\left\{x\right\}=\left[D\right]\left\{F\right\}---\left(1\right)$

In this equation, M is a mass matrix, and C is a damping matrix, and K is a stiffness matrix, D be power converting vector x, Then be respectively displacement structure, speed, acceleration responsive).Suppose that beam is the bernoulli beam.Full beam is divided into N unit altogether.Its stiffness matrix can be expressed as:

$K=\stackrel{\‾}{K}-K_G+K_B=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}({\stackrel{\‾}{k}}^i-k_G^i+k_B^i)---\left(2\right)$

Wherein, K, K _GAnd K _BBe the integral rigidity matrix, be respectively the elastic stiffness battle array, the geometric stiffness battle array that is caused by prestress axial force T and the geometric stiffness battle array that is caused by prestress eccentric bending moment B=T * e, e is the prestress eccentric throw; k ⁱ, k _G ⁱAnd k _B ⁱGeometric stiffness battle array that is respectively the elastic stiffness battle array of unit, causes by axial force and the geometric stiffness battle array that causes by eccentric bending moment.The geometric stiffness battle array that has adopted following unitary elasticity Stiffness Matrix among the present invention and caused by axle power,

${\stackrel{\‾}{k}}^i=\frac{2\mathrm{EI}}{l^3}\left(\begin{array}{cccc}6& 3l& -6& 3l\\ 3l& 2l^2& -3l& l^2\\ -6& -3l& 6& -3l\\ 3l& l^2& -3l& 2l^2\end{array}\right)---\left(3a\right)$ $k_G^i=\frac{T}{30l}\left(\begin{array}{cccc}36& 3l& -36& 3l\\ 3l& 4l^2& -3l& -l^2\\ -36& -3l& 36& -3l\\ 3l& -l^2& -3l& 4l^2\end{array}\right)---\left(3b\right)$

Wherein, EI is the beam element bending stiffness, and l is a beam element length.The geometric stiffness battle array k that the unit is caused by moment of flexure B _B ⁱCan push away by following formula:

$k_B^i={\∫}_0^l\frac{\mathrm{EA}}{2}{\left({\stackrel{\·}{v}}_B^i\right)}^2{\left[N^{\′}\right]}^T\left[N^{\′}\right]\mathrm{dx}---\left(4\right)$

Wherein EA is a beam axial push-pull rigidity, v _B ⁱBe element deformation, N ' is the unit shape function.If it is as follows by the geometric stiffness battle array that moment of flexure causes that employing Hermetian trinomial, is tried to achieve the unit as shape function:

$k_B^i=\frac{\mathrm{EA}}{2}{\left(\frac{v_B^{i1}-v_B^{i2}}{l}\right)}^2\·\frac{1}{30l}\left(\begin{array}{cccc}36& 3l& -36& 3l\\ 3l& 4l^2& -3l& -l^2\\ -36& -3l& 36& -3l\\ 3l& -l^2& -3l& 4l^2\end{array}\right)---\left(5\right)$

Wherein, v _B ^I1And v _B ^I2Being respectively is the node distortion at two ends, unit.For the free beam that is subjected to the eccentric prestress effect, structure can be tried to achieve by following equation by the distortion that the simple bending square causes:

$v_B\left(x\right)=-\frac{{\mathrm{Bx}}^2}{2\mathrm{EI}}+\frac{{\mathrm{BL}}_{\mathrm{Beam}}x}{2\mathrm{EI}}---\left(6\right)$

L is the beam entire length in the formula.

Prestress identification based on susceptibility

Equation (1) equal sign both sides can obtain the following differential equation (8) to prestress value F differentiate,

$\left[M\right]\left\{\frac{\∂\stackrel{\·\·}{x}}{\∂T}\right\}+\left[C\right]\left\{\frac{\∂\stackrel{\·}{x}}{\∂T}\right\}+\left[K\right]\left\{\frac{\∂x}{\∂T}\right\}=-\frac{\∂\left[K\right]}{\∂T}\left\{x\right\}-a_2\frac{\∂\left[K\right]}{\∂T}\left\{\stackrel{\·}{x}\right\}---\left(8\right)$

In equation (8), unknown quantity is the susceptibility of structural response for prestress value.The right of equation is the binomial of structural response.This part can be calculated by equation (1).After obtaining the susceptibility matrix S of structural response to prestress value, can be according to equation (9) in the hope of the change amount Δ T of prestress value,

{ΔR}＝[S]{ΔT} (9)

Because the R-F relation is non-linear.In order to obtain a convergent structure, need carry out the numerical value iteration.The convergence threshold values expression formula of iteration can be made as:

|ΔT _i+1/T _i|≤r (10)

Wherein r is the threshold values of termination of iterations.

The cracking resistance load assessment

The cracking resistance load is one of important indicator in the prestressed concrete beam bridge assessment.By the response identification prestress value under the configuration forces vibration is a kind of method of effective such bridge capacity of assessment.

For the bridge of active service, its load comprises two types of mobile load and dead loads.When calculating prestressed girder cross section normal stress, three types load need be considered: mobile load, dead load and prestress.Suppose that all presstressed reinforcing steels all are arranged in the bottom of beam, the normal stress value at the bottom of the prestressed concrete beam beam can be expressed as follows:

$\mathrm{\σ}=\frac{N_y}{A_i}+\frac{N_y{e}_y}{W_i}-\frac{M_{\mathrm{di}}}{W_i}-\frac{M_{\mathrm{ds}}+M_l}{W_p}---\left(11\right)$

Wherein, N _y, N _lBe respectively the initial prestress and the prestressed loss value of this beam.e _yIt is prestressed eccentricity value; A _iAnd A _pInitial and permanent area of section for beam.W _iAnd W _pInitial and permanent cross sectional moment of inertia for beam; M _Di, M _DsAnd M _lBe respectively by the initial dead load of structure the moment of flexure value that the second stage of dead load and mobile load cause.Consider that prestress value can be thereupon the passing of time and lose, the normal stress σ of beam can change.If the loss of prestress value is N _l, the normal stress at the bottom of the beam can be expressed as,

$\mathrm{\σ}=(\frac{N_y}{A_i}+\frac{N_y{e}_y}{W_i}-\frac{M_{\mathrm{di}}}{W_i}-\frac{M_{\mathrm{ds}}+M_l}{W_p})-(\frac{N_l}{A_p}+\frac{N_{l}e}{W_p})---\left(12\right)$

When beam be subjected to tension to surpass the tensile strength of beam the time, the crack will produce.For fear of the generation in crack, the σ that calculates must be greater than concrete intensity level σ _Cs(tension is for negative).Along with the loss of prestress value, the cracking resistance bearing capacity of structure will continue to reduce.Suppose that dead load remains unchanged, structure will be determined by following equation the cracking resistance bearing capacity of mobile load,

$M_l\≤[\frac{N_y}{A_i}+\frac{N_{y}e}{W_i}-\frac{M_{\mathrm{di}}}{W_i}-N_l\×(\frac{1}{A_p}+\frac{e}{W_p})+{\mathrm{\σ}}_{\mathrm{cs}}]\×W_p-M_{\mathrm{ds}}---\left(13\right)$

Owing to adopted such scheme, the present invention to have following characteristics: based on wavelet analysis solved systemicly that structure random environment exciting field of living in flexible bridge structure dynamic test and the mode identification can not be surveyed, the main mode of structure is in key issues such as low-frequency range dense distribution, the noisy amount of structural environment vibration-testing signal are big.It implements fast and simplely can not cause damage to structure simultaneously, can conveniently be used in quick test and the assessment of labour prestressed concrete beam bridge under uninterrupted traffic stream situation; Simultaneously the inventive method is based on strict theoretical, the recognition accuracy height, and convergence is good.

Description of drawings

Fig. 1 is the process flow diagram that the present invention is based on the eccentric straight-line prestressed reinforced-concrete beam bridge of forced vibration testing evaluation cracking resistance bearing capacity.

Fig. 2 is for implementing certain prestressed concrete simply supported slab beam bridge size in the example.

Fig. 3 is external excitation signal, acceleration responsive signal and susceptibility time-histories under the simple harmonic quantity excitation.

Embodiment

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

As shown in Figure 2, this bridge main span is striden and directly is 25m.Girder section is long-pending to be 0.91m ², moment of inertia is 0.1747m ⁴Have four presstressed reinforcing steels at the bottom of the beam.Eccentric throw is 0.45m.Initial prestressed stretch-draw value is 3.23 * 10 ⁶N.Concrete implementation step is:

1) the single-point vibratory response that bridge structure is carried out the forced vibration test and obtained structure: adopt the FEM finite element simulation to simulate the forced vibration test of this bridge structure under the simple harmonic quantity excitation in this example, measuring structure supports 10m place exciting, the structural response when supporting 7.5m place's pick-up (as Fig. 2) apart from the right side in distance beam-ends left side.The excitation of structure and acceleration responsive time-histories are seen Fig. 3.

2) set up the structure finite element numerical analysis model, computation structure response is to the susceptibility of loss of prestress, calculate structure susceptibility time-histories see Fig. 3.

3) adopt the effective prestress that identifies structure based on the optimization method of susceptibility from the structural dynamic response variable quantity that measures, common mode has been intended two-stage loss of prestress value in this example.Setting prestressed loss value in the operating mode 1 is 0.3MN, and setting prestressed loss value in operating mode 2 is 0.6MN.According to simulation gained signal, the prestress loss value obtains through iterative computation.Recognition result is as shown in table 1, and recognition result and desired value are accurately coincide.In addition, adopt recognition methods of the present invention, calculated convergence rate is all very fast, has verified the high efficiency of this method.

Table 1: loss of prestress and cracking resistance bearing capacity loss recognition result

Cracking resistance load-bearing capacity when 4) calculating the prestressed concrete beam bridge test according to the effective prestress value that measures, bearing capacity loss recognition result sees Table 1.

The above-mentioned description to embodiment is can understand and apply the invention for ease of those skilled in the art.The person skilled in the art obviously can easily make various modifications to these embodiment, and needn't pass through performing creative labour being applied in the General Principle of this explanation among other embodiment.Therefore, the invention is not restricted to the embodiment here, those skilled in the art should be within protection scope of the present invention for improvement and modification that the present invention makes according to announcement of the present invention.

Claims (6)

1, a kind of method for evaluating eccentric straight-line prestressed concrete beam bridge bearing ability based on dynamic measurement of pile is characterized in that: identify the effective prestress of structure and based on the cracking resistance bearing capacity of this evaluation structure from prestressed concrete beam bridge forced vibration response.

2, the method for evaluating eccentric straight-line prestressed concrete beam bridge bearing ability based on dynamic measurement of pile as claimed in claim 1, it is characterized in that: it may further comprise the steps:

1) the single-point vibratory response that beam bridge structure is carried out the forced vibration test and obtains structure;

2) set up the structure finite element numerical analysis model and analyze of the influence of prestress level structural dynamic characteristic;

3) adopt the effective prestress that from the structural dynamic response variable quantity that measures, identifies structure based on the optimization method of susceptibility;

Cracking resistance load-bearing capacity when 4) calculating the prestressed concrete beam bridge test according to the effective prestress value that measures.

3, the method for evaluating eccentric straight-line prestressed concrete beam bridge bearing ability based on dynamic measurement of pile as claimed in claim 2, it is characterized in that: vibration-testing is preceding according to structural shape and support situation, estimate the perpendicular curved vibration shape in the first five rank of structure, determine exciting mode, exciting point and the pick-up point of forced vibration test in view of the above, obtain pumping signal and structure vibration signals synchronously.

4, the method for evaluating eccentric straight-line prestressed concrete beam bridge bearing ability based on dynamic measurement of pile as claimed in claim 2, it is characterized in that: according to the equation of motion under the given external load effect, determine eccentric straight-line prestressed reinforced-concrete beam bridge because the construction geometry stiffness matrix that eccentric straight-line prestressed effect causes passes through the influence of finite element numerical analysis model analysis prestress level to structural dynamic characteristic based on this.

5, the method for evaluating eccentric straight-line prestressed concrete beam bridge bearing ability based on dynamic measurement of pile as claimed in claim 2, it is characterized in that:, and adopt optimization method from the structural dynamic response variable quantity that measures, to identify the effective prestress of structure based on the susceptibility matrix of finite element model derivation structural response to prestress value.

6, the method for evaluating eccentric straight-line prestressed concrete beam bridge bearing ability based on dynamic measurement of pile as claimed in claim 2, it is characterized in that: dead load remains unchanged, determine the structure effective prestress with to the relation of the cracking resistance bearing capacity of mobile load with evaluation structure cracking resistance bearing capacity.

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