CN102323976A - Shrinkage creep and prestress loss computation method of concrete bridge - Google Patents

Abstract

The invention provides a shrinkage creep and prestress loss computation method of a concrete bridge. According to the invention, the shrinkage creep and prestress loss computation method of the concrete bridge, in which the time variation and the uncertainty are simultaneously considered, is obtained by analyzing the time variation of concrete through utilizing an age-adjusted effective modulus method (AEMM) and analyzing the uncertainty of the concrete through utilizing an accurate and rapidly-sampled Latin hypercube sampling (LHS) method; a prestress loss computation formula in which the time variation and the uncertainty of shrinkage creep and the interaction between the shrinkage creep and reinforcement stress relaxation are simultaneously considered is deduced according to a prestressed reinforcing steel and concrete stress balance equation and deformation coordination conditions and on the basis of the AEEM method and the LHS method; and a prestress loss computation method of the concrete bridge, in which the shrinkage creep and the stress relaxation are considered, is formed. In the structural internal force value field interval computed according to the shrinkage creep and prestress loss computation method disclosed by the invention, the unfavorable stress state of the bridge structure can be considered from multiple aspects in the designing process, so that the reliability of structure computation result is higher and the structure safety is better.

Description

Concrete-bridge shrinkage and creep and loss of prestress computing method

Technical field

The present invention relates to transportation bridges and culverts engineering field, particularly relate to a kind of consideration time variation and probabilistic concrete-bridge shrinkage and creep and loss of prestress computing method.

Background technology

Special advantages such as Prestressed Concrete Bridges is strong with its span ability, operating technique is ripe, driving is comfortable, construction costs is low, maintenance is simple have wide future in engineering applications in the science of bridge building field.According to incompletely statistics, worldwide in the bridge construction beam, concrete-bridge shared ratio in all bridge types is maximum: wherein the concrete-bridge of the Europe and the U.S. accounts for more than 70% of institute's bridge construction beam; China's ratio is bigger, and concrete-bridge accounts for more than 90%.Continuous maturation along with concrete-bridge design, operating technique; The continuous progress of high-performance high-strength concrete material; Concrete-bridge by freely supported structure, for a short time stride the footpath continuous structure, develop into large span continuous structure gradually, and the footpath of striding of different bridge types is also constantly being refreshed.

In the Prestressed Concrete Bridges develop rapidly, the long-span bridge girder construction that it builds up has also engendered disease in various degree.Stride footpath prestressed concrete continuous beam bridge greatly and mainly adopt the box structure form; After the operation several years; Disease has in various degree all appearred in the footpath Continuous Box Girder Bridge of striding greatly more than 70%; Its middle girder span centre downwarp and case beam 1/4L left and right sides web cracking are particularly outstanding, become restriction and stride the gordian technique difficult problem that the footpath concrete-bridge further develops greatly.As, the South Sea, the Guangdong Jinsha bridge that built up in 1994 is for striding the footpath prestressed concrete continuous rigid-framed bridge greatly, and the span centre downwarp reaches 22cm after 6 years, and a large amount of diagonal cracks appear in the case web; The Huangshi Yangtze Bridge that nineteen ninety-five builds up is the large span prestressed concrete continuous rigid-framed bridge, and the span centre downwarp has reached 70cm at present, and a large amount of cracks also appear in the case beam.Many crossover beams are through after the consolidation process, and span centre downwarp and case web cracking still can not obtain fine control, and bridge structure safe receives serious threat, has caused harmful effect socially, has brought the tremendous economic loss to country.

Find after these disease problems of Chinese scholars analysis that the main cause that causes box-beam structure span centre downwarp and web cracking disease to occur has: 1. concrete shrinkage and creep is big.High-strength concrete shrinkage and creep mechanism understanding is insufficient, the various shrinkage and creep computing method of present bridge structure, and the span centre downwarp value that calculates differs and reaches more than 30%, and there are notable difference in Theoretical Calculation and bridge actual forced status.2. it is big to stride the long-term loss of prestress of concrete bridge girder construction greatly.The lax loss of prestress that causes of concrete shrinkage and creep and reinforcement stresses accounts for more than 30% in total losses; It is the major influence factors of the long-term loss of prestress of concrete-bridge; The effective prestress of decision bridge structure; But relevant at present loss of prestress computing method result of calculation difference is bigger, is one of principal element that influences downwarp of bridge structure span centre and web cracking disease.

To above problem, the main method of concrete-bridge control span centre downwarp at present and web cracking disease has: 1. increase beam body camber, change the arrangement of presstressed reinforcing steel.2. superstructure partly adopts steel case beam or part to adopt the steel web to improve the web shear resistance.3. the bridge structure of existing span centre downwarp and case beam cracking is reinforced.These technology have been slowed down span centre downwarp and case beam cracking disease to a certain extent; But these technology all are not the solutions that proposes to main disease reason such as concrete-bridge shrinkage and creep and loss of prestress; Thereby for fundamentally solving the disease problem of concrete-bridge, further improving shrinkage and creep, loss of prestress analysis theories and computing method is the problems that press for solution at present.

Summary of the invention

Technical matters to be solved by this invention is: a kind of concrete-bridge shrinkage and creep and loss of prestress computing method are provided; Utilize by the effective modulus method of adjustment in the length of time and consider its time variation; Utilize the Latin hypercube sampling to consider its uncertainty, reach and consider time variation and probabilistic purpose when two kinds of methods are calculated simultaneously.This method when design can multiple consideration bridge structure unfavorable stress, fraction is higher as a result, safety of structure is better to make Structure Calculation.

The technical scheme that the present invention adopted is: concrete-bridge shrinkage and creep and loss of prestress computing method comprise:

Concrete-bridge shrinkage and creep computing method are the statistical estimation results that obtain uncertain parameters according to Latin hypercube sampling stochastic finite element method; The set that obtains the concrete shrinkage strain and the coefficient of creeping according to the statistical estimation result is interval; Obtain concrete-bridge shrinkage and creep computing formula according to concrete shrinkage and creep strain-stress relation, the effective modulus function of pressing adjustment in the length of time, set interval and superposition principle then; Form a kind of consideration time variation and probabilistic concrete-bridge shrinkage and creep analytical approach, and in finite element analysis software, realize these shrinkage and creep computing method.

Concrete-bridge loss of prestress computing method are the statistical estimation results that obtain uncertain parameters according to Latin hypercube sampling stochastic finite element method; In conjunction with the concrete shrinkage and creep strain-stress relation, by effective modulus function and the presstressed reinforcing steel strain-stress relation adjusted the length of time; The loss of prestress set that obtain the concrete shrinkage strain, the combined actions such as coefficient and reinforcement stresses are lax of creeping causes is interval; According to the interval loss of prestress computing formula that obtains concrete-bridge of set, form the concrete-bridge loss of prestress computing method of considering shrinkage and creep and stress relaxation.

Described computing method, in the concrete-bridge shrinkage and creep computing method, statistical estimation result, the contraction strain of uncertain parameters and the set interval of the coefficient of creeping obtain according to following method:

A) introduce uncertain parameters

The uncertainty, the concrete cube compressive strength f that represent nominal creep coefficient, nominal contraction coefficient respectively _Cm, envionmental humidity RH and prestress load influential factors;

B) obtaining each uncertain parameters is the fiducial interval of 1-α based on the fiducial limit of standard value:

In the formula (1), α value 0.05, σ is a standard deviation, n is a sample number, z _α/2Be normal distribution fiducial limit value,

For

The fiducial interval lower bound, For The fiducial interval upper bound, i value 1,2 ... 5;

C) according to the fiducial interval of uncertain parameters

; The n five equilibrium is carried out in the interval; Obtain n+1 frontier point and n sub-interval, according to formula (1) each uncertain parameters

of actual bridge is taken a sample then; The creep uncertain parameters

of coefficient, nominal contraction coefficient of name is randomly drawed a sample in each sub-range through the Latin hypercube sampling, then to all sample random alignment statistical estimations;

D) contain design specifications according to highway reinforced concrete and prestressed concrete bridge, the result of the statistical estimation of integrating step C obtains contraction strain and creeps the coefficient sets interval:

In the formula (2), ε _Cs0Be concrete name contraction coefficient, ε _Cs(t, t _s) be t for shrinking beginning length of time _s, to calculate the length of time be the contraction strain of t, β _s(t-t _s) for shrinking the coefficient of development in time, β _RHBe the contraction coefficient relevant with mean annual humidity,

Be the contraction coefficient relevant with concrete crushing strength, and:

β _ScFor according to the fixed coefficient of cement kind, φ ₀Be the concrete name coefficient of creeping, φ (t, t ₀) for load age be t ₀, to calculate the length of time be the coefficient of creeping of t, β _c(t-t ₀) be the coefficient that develops in time after loading, φ _RHBe the coefficient relevant of creeping with mean annual humidity,

Be the coefficient relevant of creeping with concrete crushing strength, and:

β (t ₀) be the function of development in time of creeping, and:

$\mathrm{\&beta;}\left(t_0\right)=\frac{1}{0.1+{{\mathrm{<figure-callout\; id="0"\; label="t"\; filenames="HDA0000070849440000021.png,HDA0000070849440000022.png"\; state="\{\{state\}\}">t</figure-callout>}}_0}^{0.2}}---\left(2c\right)$

Described computing method, the method that obtains concrete-bridge shrinkage and creep computing formula is:

A) be t to load age ₀And stress continually varying xoncrete structure, the concrete shrinkage and creep strain-stress relation of any time t is expressed as:

${\mathrm{\&epsiv;}}_c\left(t\right)=\frac{{\mathrm{\&sigma;}}_c\left(t_0\right)}{E\left(t_0\right)}[1+\mathrm{\&phi;}(t,t_0)]+\frac{{\mathrm{\&sigma;}}_c\left(t\right)-{\mathrm{\&sigma;}}_c\left(t_0\right)}{E(t,t_0)}+{\mathrm{\&epsiv;}}_{\mathrm{cs}}(t,t_s)---\left(3\right)$

In the formula (2), ε _cConcrete strain value when (t) being any time t, σ _c(t0), σ _c(t) be respectively t ₀, the concrete stress during t, E (t ₀) be that concrete is at t ₀Elastic modulus constantly, E (t, t ₀) be the effective modulus of concrete by adjustment in the length of time, promptly load age is t ₀, calculate the modulus of elasticity of concrete when being t the length of time;

B) the effective modulus function E (t, the t that adjust by the length of time ₀) be expressed as:

$E(t,t_0)=\frac{E\left(t_0\right)}{1+\mathrm{\&chi;}(t,t_0)\mathrm{\&phi;}(t,t_0)}---\left(4\right)$

$\mathrm{\&chi;}(t,t_0)=\frac{1}{1-R(t,t_0)}-\frac{1}{\mathrm{\&phi;}(t,t_0)}---\left(5\right)$

$R(t,t_0)=\frac{{\mathrm{\&sigma;}}_c\left(t\right)}{{\mathrm{\&sigma;}}_c\left(t_0\right)}---\left(6\right)$

In the formula: χ (t, t ₀) be that concrete load age is t ₀, calculate the aging coefficient when being t the length of time, R (t, t ₀) for the concrete load age be t ₀, calculate the coefficient of relaxation when being t the length of time;

C), combine superposition principle to obtain any time to be by the axle power N and the moment M of concrete-bridge shrinkage and creep generation according to (1)～(6) formulas:

$N=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\left(\underset{j=1}{\overset{i-1}{\mathrm{\&Sigma;}}}\mathrm{\&eta;}(t_i,t_j)\mathrm{\&Delta;N}\left(t_j\right)\right)+\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\left(E(t_i,t_{i-1})A_c{\mathrm{\&Delta;\&epsiv;}}_{\mathrm{cs}}(t_i,t_{i-1})\right)---\left(7\right)$

$M=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\left(\underset{j=1}{\overset{i-1}{\mathrm{\&Sigma;}}}\mathrm{\&eta;}(t_i,t_j)\mathrm{\&Delta;M}\left(t_j\right)\right)+\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\left(E(t_i,t_{i-1})I_c\mathrm{\&Delta;}{\mathrm{\&psi;}}_{\mathrm{cs}}(t_i,t_{i-1})\right)---\left(8\right)$

$\mathrm{\&eta;}(t_i,t_{i-1})=\frac{E(t_i,t_{i-1})}{E\left(t_j\right)}(\mathrm{\&phi;}(t_i,t_j)-\mathrm{\&phi;}(t_{i-1},t_j))---\left(9\right)$

In formula (7)～(9), Δ ε _Cs(t _i, t _I-1) be t _I-1To t _iConcrete shrinkage strain increment constantly, Δ ψ _Cs(t _i, t _I-1) be t _I-1To t _iThe curvature increment that concrete shrinkage constantly causes, Δ N (t _j), Δ M (t _j) be respectively t _iTo t _jAxle power and moment of flexure increment constantly, E (t _i, t _I-1) be t _I-1To t _iEffective modulus constantly by adjustment in the length of time, E (t _j) be t _jConcrete elastic modulus of the moment, φ (t _i, t _j) be t _jTo t _iConcrete creep coefficient constantly, I _cBe the bending resistance moment of inertia of concrete section, A _cBe the area of section of xoncrete structure, η (t _i, t _j) be intermediate parameters.

Described computing method, utilization APDL language makes concrete-bridge shrinkage and creep computing method accomplished in finite element analysis software:

In the ANSYS program is calculated pre-processing module, embed modulus of elasticity of concrete with adjustment in the length of time the time with changing function, promptly the effective modulus by adjustment in the length of time carries out the time variation analysis.In post-processing module; Utilize the APDL language; The uncertain statistical study flow process of establishment PDS module; Give stochastic variable distribution function type, utilization Latin hypercube sampling is carried out the shrinkage and creep uncertainty analysis through stochastic variable parametric statistics analytical parameters fiducial interval to concrete-bridge.Idiographic flow is seen Fig. 1.

Described computing method; In the concrete-bridge loss of prestress computing method; Obtain the statistical estimation result of uncertain parameters, and the method in the loss of prestress set interval that causes of concrete shrinkage strain, interaction such as coefficient and reinforcement stresses are lax of creeping is:

A) introduce uncertain parameters λ ₁, λ ₂, λ ₃, λ ₄, λ ₅Represent creep 28 days cubic compressive strength f of coefficient of uncertainty, concrete of coefficient, contraction strain of concrete-bridge respectively _Cm, probabilistic influence that envionmental humidity RH and reinforcement stresses are lax;

B) obtain each uncertain parameters λ _iFiducial limit based on standard value is the fiducial interval of 1-α:

$({\stackrel{\&OverBar;}{\mathrm{\&lambda;}}}_i-\frac{\mathrm{\&sigma;}}{\sqrt{n}}{z}_{\mathrm{\&alpha;}/2},{\stackrel{\&OverBar;}{\mathrm{\&lambda;}}}_i+\frac{\mathrm{\&sigma;}}{\sqrt{n}}{z}_{\mathrm{\&alpha;}/2})=[\underset{\&OverBar;}{\mathrm{\&lambda;}},\stackrel{\&OverBar;}{\mathrm{\&lambda;}}]---\left(10\right)$

In the formula (10), α value 0.05, σ is a standard deviation, n is a sample number, z _α/2Be normal distribution fiducial limit value, λBe λ _iThe fiducial interval lower bound,

Be λ _iThe fiducial interval upper bound, i value 1,2 ... 5;

C) according to uncertain parameters λ _iFiducial interval, the n five equilibrium is carried out in the interval, obtain n+1 frontier point and n sub-interval, then according to formula (10) each uncertain parameters λ to actual bridge _iTake a sample; Uncertain parameters λ to the coefficient of creeping, contraction strain ₁, λ ₂, randomly draw a sample in each sub-range through the Latin hypercube sampling, then to all sample random alignment statistical estimations;

D) according to formula (3), concrete caused because of shrinkage and creep when (4) obtained any time t strain-stress relation:

${\mathrm{\&epsiv;}}_c\left(t\right)=\frac{{\mathrm{\&sigma;}}_c\left(t_0\right)}{E\left(t_0\right)}[1+\mathrm{\&phi;}(t,t_0)]+\frac{[{\mathrm{\&sigma;}}_c\left(t\right)-{\mathrm{\&sigma;}}_c\left(t_0\right)][1+\mathrm{\&chi;}(t,t_0)\mathrm{\&phi;}(t,t_0)]}{E\left(t_0\right)}+{\mathrm{\&epsiv;}}_{\mathrm{cs}}(t,t_0)---\left(11\right)$

E) stress relaxation of considering presstressed reinforcing steel is lost, and the strain-stress relation that obtains any time deformed bar is:

${\mathrm{\&epsiv;}}_p\left(t\right)=\frac{{\mathrm{\&sigma;}}_p\left(t\right)-{\stackrel{\&OverBar;}{\mathrm{\&sigma;}}}_p\left(t\right)}{E_p}---\left(12\right)$

${\stackrel{\&OverBar;}{\mathrm{\&sigma;}}}_p\left(t\right)={\mathrm{\&sigma;}}_p\left(t_0\right)[\frac{{\mathrm{\&sigma;}}_p\left(t_0\right)}{f_{\mathrm{pk}}}-0.55]\frac{\log (t-t_0)}{45}---\left(13\right)$

In formula (12), (13), ε _p(t) be the strain value of deformed bar, E _pBe the elastic modulus of deformed bar, σ _p(t ₀), σ _p(t) be respectively deformed bar at t ₀, t stress value constantly,

Be the lax loss of prestress that causes of reinforcement stresses, f _PkBe the deformed bar strength standard value;

F) contain design specifications according to highway reinforced concrete and prestressed concrete bridge, the result of the statistical estimation of integrating step C, and formula (13) obtain contraction strain and creep the coefficient sets interval:

$\left\{\begin{array}{c}{\mathrm{\&epsiv;}}_{\mathrm{cs}}(t,t_s)={\mathrm{\&lambda;}}_2{\mathrm{\&epsiv;}}_{\mathrm{<figure-callout\; id="0"\; label="cs"\; filenames="HDA0000070849440000021.png,HDA0000070849440000022.png"\; state="\{\{state\}\}">cs</figure-callout>}0}\&CenterDot;{\mathrm{\&beta;}}_s(t-t_s)\\ {\mathrm{\&epsiv;}}_{\mathrm{<figure-callout\; id="0"\; label="cs"\; filenames="HDA0000070849440000021.png,HDA0000070849440000022.png"\; state="\{\{state\}\}">cs</figure-callout>}0}={\mathrm{\&epsiv;}}_s\left({\mathrm{\&lambda;}}_3{f}_{\mathrm{cm}}\right)\&CenterDot;{\mathrm{\&lambda;}}_4{\mathrm{\&beta;}}_{\mathrm{RH}}\\ \mathrm{\&phi;}(t,t_0)={\mathrm{\&lambda;}}_1{\mathrm{\&phi;}}_0\&CenterDot;{\mathrm{\&beta;}}_c(t-t_0)\\ {\mathrm{\&phi;}}_0={\mathrm{\&lambda;}}_4{\mathrm{\&phi;}}_{\mathrm{RH}}\&CenterDot;\mathrm{\&beta;}\left({\mathrm{\&lambda;}}_3{f}_{\mathrm{cm}}\right)\&CenterDot;\mathrm{\&beta;}\left(t_0\right)\\ {\stackrel{\&OverBar;}{\mathrm{\&sigma;}}}_p\left(t\right)={\mathrm{\&lambda;}}_5{\mathrm{\&sigma;}}_p\left(t_0\right)[\frac{{\mathrm{\&sigma;}}_p\left(t_0\right)}{f_{\mathrm{pk}}}-0.55]\frac{\lg (t-t_0)}{45}\end{array}\right.{\mathrm{\&lambda;}}_i\&Element;[\underset{\&OverBar;}{\mathrm{\&lambda;}},\stackrel{\&OverBar;}{\mathrm{\&lambda;}}]---\left(14\right)$

Described computing method, the method that obtains the loss of prestress computing formula is:

A) the concrete stress balance equation is:

σ _c(t)＝-μρσ _p(t) (15)

ρ＝1+e _op ²/r _c ² (16)

r _c ²＝I _c/A _c (17)

μ＝A _p/A _c (18)

In formula (15)～(18), σ _c(t), σ _p(t) be respectively concrete and deformed bar at t STRESS VARIATION value constantly, A _p, A _cBe respectively presstressed reinforcing steel and concrete section area, e _OpBe the distance of deformed bar center of gravity to the concrete section center of gravity, I _cBe the concrete section moment of inertia;

B), can get according to deformed bar and concrete deformation cooperation condition in the same level height of presstressed reinforcing steel:

ε _c(t)-ε _c(t ₀)＝ε _p(t)-ε _p(t ₀) (19)

In the formula (19), ε _c(t) be concrete strain value, ε _p(t) be the strain value of deformed bar;

C), obtain considering concrete shrinkage and creep time variation and the reinforcement stresses interactional loss of prestress σ that relaxes according to formula (11)～(19) _Ps(t) computing formula is:

${\mathrm{\&sigma;}}_{\mathrm{ps}}\left(t\right)=\frac{{\mathrm{\&epsiv;}}_{\mathrm{cs}}(t,t_0)+\frac{{\mathrm{\&sigma;}}_c\left(t_0\right)\mathrm{\&phi;}(t,t_0)}{E\left(t_0\right)}+\frac{{\stackrel{\&OverBar;}{\mathrm{\&sigma;}}}_p\left(t\right)}{E_p}}{\frac{1}{E_p}+\frac{\mathrm{\&mu;\&rho;}}{E\left(t_0\right)}[1+\mathrm{\&chi;}(t,t_0)\mathrm{\&phi;}(t,t_0)]}---\left(20\right)$

The present invention compared with prior art has following major advantage:

Conventional shrinkage and creep and loss of prestress computing method, the long-term internal force of the bridge structure of acquisition is a determinacy value.And concrete-bridge shrinkage and creep and loss of prestress computing method that the present invention proposes; Consider its time variation and uncertainty simultaneously; The long-term internal force of bridge structure that obtains is that codomain is interval; Compare with conventional computing method, the codomain interval when design can multiple consideration bridge structure unfavorable stress, fraction is higher as a result, safety of structure is better to make Structure Calculation.

Description of drawings

Fig. 1 is for considering time variation and probabilistic shrinkage and creep analysis process.

Fig. 2 is a concrete simply supported beam creep test model, among the figure: 1 expression distribution beam; 2 is the creep test beam; 3 are the strain measuring point; 4 is the amount of deflection measuring point.

Fig. 3 is a beams of concrete shrinkage test illustraton of model, and among the figure: 5 is clock gauge; 6 are the shrinkage test beam.

Fig. 4 is the index variation curve map of creeping.

Fig. 5 is the contraction strain change curve.

Fig. 6 is the loss of prestress illustraton of model, and among the figure: 7 is φ 8 reinforcing bars; 8 is φ 6 reinforcing bars; 9 is φ s15.2 reinforcing bar; 10 is φ 8 reinforcing bars.

Fig. 7 is test beam loss of prestress comparative analysis figure.

Embodiment

Concrete shrinkage and creep has time variation and uncertainty simultaneously; And problems such as a specific character are all only considered wherein at present relevant research; The present invention is through proposing concrete-bridge shrinkage and creep and loss of prestress computing method; Simultaneously it considers time variation and uncertainty, and it is interval to obtain bridge structure internal force codomain, to solve the technical barrier that concrete-bridge shrinkage and creep, loss of prestress calculating and structure actual working state do not conform to.

Utilization of the present invention is analyzed concrete time variation by the effective modulus method (AEMM method) of adjustment in the length of time; Utilization Latin hypercube sampling stochastic finite element method accurate, sampling fast (LHS method) is analyzed concrete uncertainty, obtains to consider simultaneously time variation and probabilistic concrete-bridge shrinkage and creep analytical approach; According to presstressed reinforcing steel and concrete stress balance equation and distortion cooperation condition; Based on AEMM method and LHS method; Derive consider simultaneously the shrinkage and creep time variation with uncertain and with the interactional loss of prestress computing formula of relaxation of steel, form the concrete-bridge loss of prestress computing method of considering shrinkage and creep and stress relaxation.Its concrete steps are following:

(1) consider time variation and probabilistic concrete-bridge shrinkage and creep analytical approach, comprise following three steps:

1. set up the effective modulus function of considering time variation by adjustment in the length of time

$E(t,t_0)=\frac{E\left(t_0\right)}{1+\mathrm{\&chi;}(t,t_0)\mathrm{\&phi;}(t,t_0)}$

In the formula, E (t, t ₀) be the effective modulus of concrete by adjustment in the length of time, promptly load age is t ₀, calculate the modulus of elasticity of concrete (MPa) when being t the length of time; E (t ₀) be that concrete is at t ₀Elastic modulus constantly; φ (t, t ₀) be load age t ₀, calculate the concrete creep coefficient when being t the length of time; χ (t, t ₀) be concrete aging coefficient,

R (t, t ₀) for the concrete load age be t ₀, calculate the coefficient of relaxation when being t the length of time,

2. make up and consider probabilistic Latin hypercube sampling STOCHASTIC FINITE ELEMENT fiducial interval

Consider the uncertainty that concrete-bridge is crept, shunk, introduce uncertain parameters respectively

Come to represent respectively name creep uncertainty, the concrete cube compressive strength f of coefficient, nominal contraction coefficient _Cm, influential factors such as envionmental humidity RH and prestress load.

Each uncertain parameters is based on a fiducial interval that fiducial limit is 1-α of standard value:

Order:

In the formula, σ is a standard deviation; N is a sample number; z _α/2Be normal distribution fiducial limit value.

According to uncertain parameters

fiducial interval; The n five equilibrium is carried out in the interval; Obtain n+1 frontier point and n sub-interval; To the contraction strain and the coefficient of creeping; Randomly draw a sample in each sub-range through the Latin hypercube sampling, then to all sample random alignment statistical estimations.

3. set up and consider time variation and probabilistic concrete-bridge shrinkage and creep analytical approach

According to above-mentioned effective modulus function and statistical estimation result, obtain contraction strain and the coefficient sets interval of creeping is by length of time adjustment:

In the formula, ε _Cs0Be concrete name contraction coefficient; φ ₀Be the concrete name coefficient of creeping.

Concrete-bridge shrinkage and creep according to superposition principle and following formula calculating is uncertain interval, and with the effective modulus replacement modulus of elasticity of concrete E (τ) that adjusts by the length of time, then any time can be expressed as by the internal force that the concrete-bridge shrinkage and creep produces:

$N=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\left(\underset{j=1}{\overset{i-1}{\mathrm{\&Sigma;}}}\mathrm{\&eta;}(t_i,t_j)\mathrm{\&Delta;N}\left(t_j\right)\right)+\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\left(E(t_i,t_{i-1})A_c{\mathrm{\&Delta;\&epsiv;}}_{\mathrm{cs}}(t_i,t_{i-1})\right)$

$M=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\left(\underset{j=1}{\overset{i-1}{\mathrm{\&Sigma;}}}\mathrm{\&eta;}(t_i,t_j)\mathrm{\&Delta;M}\left(t_j\right)\right)+\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\left(E(t_i,t_{i-1})I_c\mathrm{\&Delta;}{\mathrm{\&psi;}}_{\mathrm{cs}}(t_i,t_{i-1})\right)$

$\mathrm{\&eta;}(t_i,t_{i-1})=\frac{E(t_i,t_{i-1})}{E\left(t_j\right)}(\mathrm{\&phi;}(t_i,t_j)-\mathrm{\&phi;}(t_{i-1},t_j))$

In the formula, Δ ε _Cs(t _i, t _I-1) be t _I-1To t _iConcrete shrinkage strain increment constantly, Δ ψ _Cs(t _i, t _I-1) be t _I-1To t _iThe curvature increment that concrete shrinkage constantly causes, Δ N (t _j), Δ M (t _j) be respectively t _iTo t _jAxle power and moment of flexure increment constantly, E (t _i, t _I-1) be t _I-1To t _iEffective modulus constantly by adjustment in the length of time, E (t _j) be t _jConcrete elastic modulus of the moment, φ (t _i, t _j) be t _jTo t _iConcrete creep coefficient constantly, I _cBe the bending resistance moment of inertia of concrete section, A _cBe the area of section of xoncrete structure, η (t _i, t _j) be intermediate parameters.

If do not consider the influence of concrete shrinkage in calculating, the rear section of then removing a power N and moment M two formulas gets final product.

(2) the concrete-bridge loss of prestress computing method of consideration shrinkage and creep and stress relaxation

Concrete-bridge shrinkage and creep, the uncertainty that stress of prestressed steel is lax mainly show the lax aspects such as uncertainty that cause loss of prestress of the coefficient of creeping, contraction strain and reinforcement stresses.Influence parameter according to each, adopt λ respectively ₁, λ ₂Represent the creep coefficient of uncertainty of coefficient, contraction strain of concrete-bridge, adopt λ ₃, λ ₄, λ ₅Consider the uncertainty influence that concrete crushing strength, envionmental humidity RH and reinforcement stresses are lax respectively.

Each uncertain parameters is that the fiducial interval of 1-α is based on the fiducial limit of standard value:

$({\stackrel{\&OverBar;}{\mathrm{\&lambda;}}}_i-\frac{\mathrm{\&sigma;}}{\sqrt{n}}{z}_{\mathrm{\&alpha;}/2},{\stackrel{\&OverBar;}{\mathrm{\&lambda;}}}_i+\frac{\mathrm{\&sigma;}}{\sqrt{n}}{z}_{\mathrm{\&alpha;}/2})=[\underset{\&OverBar;}{\mathrm{\&lambda;}},\stackrel{\&OverBar;}{\mathrm{\&lambda;}}]$

According to uncertain parameters λ _iFiducial interval is carried out the n five equilibrium with the interval, obtains n+1 frontier point and n sub-interval, to the contraction strain and the coefficient of creeping, randomly draws a sample in each sub-range through the Latin hypercube sampling, then to all sample random alignment statistical estimations.

Contain design specifications according to the fiducial interval of each uncertain parameters and highway reinforced concrete and prestressed concrete bridge, obtain contraction strain, the set of creep coefficient and the lax analysis results such as loss of prestress that cause of reinforcement stresses is interval:

$\left\{\begin{array}{c}{\mathrm{\&epsiv;}}_{\mathrm{cs}}(t,t_s)={\mathrm{\&lambda;}}_2{\mathrm{\&epsiv;}}_{\mathrm{<figure-callout\; id="0"\; label="cs"\; filenames="HDA0000070849440000021.png,HDA0000070849440000022.png"\; state="\{\{state\}\}">cs</figure-callout>}0}\&CenterDot;{\mathrm{\&beta;}}_s(t-t_s)\\ {\mathrm{\&epsiv;}}_{\mathrm{<figure-callout\; id="0"\; label="cs"\; filenames="HDA0000070849440000021.png,HDA0000070849440000022.png"\; state="\{\{state\}\}">cs</figure-callout>}0}={\mathrm{\&epsiv;}}_s\left({\mathrm{\&lambda;}}_3{f}_{\mathrm{cm}}\right)\&CenterDot;{\mathrm{\&lambda;}}_4{\mathrm{\&beta;}}_{\mathrm{RH}}\\ \mathrm{\&phi;}(t,t_0)={\mathrm{\&lambda;}}_1{\mathrm{\&phi;}}_0\&CenterDot;{\mathrm{\&beta;}}_c(t-t_0)\\ {\mathrm{\&phi;}}_0={\mathrm{\&lambda;}}_4{\mathrm{\&phi;}}_{\mathrm{RH}}\&CenterDot;\mathrm{\&beta;}\left({\mathrm{\&lambda;}}_3{f}_{\mathrm{cm}}\right)\&CenterDot;\mathrm{\&beta;}\left(t_0\right)\\ {\stackrel{\&OverBar;}{\mathrm{\&sigma;}}}_p\left(t\right)={\mathrm{\&lambda;}}_5{\mathrm{\&sigma;}}_p\left(t_0\right)[\frac{{\mathrm{\&sigma;}}_p\left(t_0\right)}{f_{\mathrm{pk}}}-0.55]\frac{\lg (t-t_0)}{45}\end{array}\right.{\mathrm{\&lambda;}}_i\&Element;[\underset{\&OverBar;}{\mathrm{\&lambda;}},\stackrel{\&OverBar;}{\mathrm{\&lambda;}}]$

Consider that the lax interactional loss of prestress computing formula of concrete shrinkage and creep time variation and reinforcement stresses is:

${\mathrm{\&sigma;}}_{\mathrm{ps}}\left(t\right)=\frac{{\mathrm{\&epsiv;}}_{\mathrm{cs}}(t,t_0)+\frac{{\mathrm{\&sigma;}}_c\left(t_0\right)\mathrm{\&phi;}(t,t_0)}{E\left(t_0\right)}+\frac{{\stackrel{\&OverBar;}{\mathrm{\&sigma;}}}_p\left(t\right)}{E_p}}{\frac{1}{E_p}+\frac{\mathrm{\&mu;\&rho;}}{E\left(t_0\right)}[1+\mathrm{\&chi;}(t,t_0)\mathrm{\&phi;}(t,t_0)]}$

Below in conjunction with accompanying drawing and instance the present invention is explained further details.

Embodiment 1, considers time variation and probabilistic concrete-bridge shrinkage and creep analytical approach:

(1) sets up the effective modulus function of considering time variation by adjustment in the length of time

To load age is t ₀And stress continually varying xoncrete structure, its concrete shrinkage and creep strain-stress relation can be expressed as:

${\mathrm{\&epsiv;}}_c\left(t\right)={\mathrm{\&sigma;}}_c\left(t_0\right)[\frac{1}{E\left(t_0\right)}+C(t,t_0)]+{\&Integral;}_{t_0}^t[\frac{1}{E\left(\mathrm{\&tau;}\right)}+C(t,\mathrm{\&tau;})]\mathrm{d\&sigma;}\left(\mathrm{\&tau;}\right)+{\mathrm{\&epsiv;}}_{\mathrm{cs}}(t,t_s)$

In the formula, t ₀, τ, t represent load age respectively, the age of concrete (d) when a certain length of time after loading and calculating are crept; E (t ₀), E (τ) is that concrete is at t ₀, τ elastic modulus (MPa) constantly; σ _c(t ₀) be to load t constantly ₀The time concrete initial stress (MPa); (t τ) is the concrete creep degree to C; ε _Cs(t, t _s) be t for shrinking beginning length of time _s, calculate the concrete shrinkage strain value when being t the length of time.

And the relation of the creep degree and the coefficient of creeping is:

$C(t,t_0)=\frac{\mathrm{\&phi;}(t,t_0)}{E\left(t_0\right)}$

In the formula, φ (t, t ₀) be load age t ₀, calculate the concrete creep coefficient when being t the length of time.

Can get following formula integral part utilization mean value theorem:

${\mathrm{\&epsiv;}}_c\left(t\right)=\frac{{\mathrm{\&sigma;}}_c\left(t_0\right)}{E\left(t_0\right)}[1+\mathrm{\&phi;}(t,t_0)]+\frac{{\mathrm{\&sigma;}}_c\left(t\right)-{\mathrm{\&sigma;}}_c\left(t_0\right)}{E(t,t_0)}+{\mathrm{\&epsiv;}}_{\mathrm{cs}}(t,t_s)$

In the formula, E (t, t ₀) be the effective modulus of concrete by adjustment in the length of time, promptly load age is t ₀, calculate the modulus of elasticity of concrete when being t the length of time; σ _c(t) be t concrete stress constantly.

The effective modulus function of adjustment can be expressed as by the length of time:

$E\left({t,t}_0\right)=\frac{E\left(t_0\right)}{1+\mathrm{\&chi;}(t,t_0)\mathrm{\&phi;}(t,t_0)}$

In the formula, χ (t, t ₀) be concrete aging coefficient,

R (t, t ₀) for the concrete load age be t ₀, calculate the coefficient of relaxation when being t the length of time,

(2) make up the uncertainty of considering that probabilistic Latin hypercube sampling STOCHASTIC FINITE ELEMENT fiducial interval concrete-bridge is crept, shunk, mainly show the uncertain aspect of its influence factor, therefore introduce uncertain parameters

The uncertainty, the concrete cube compressive strength f that represent nominal creep coefficient, nominal contraction coefficient respectively _Cm, major influence factors such as envionmental humidity RH and prestress load effect.

Suppose the equal accord with normal distribution of each uncertain parameters and separate, get sampling number N=15, corresponding deterministic parsing parameter value is obtained according to the probability distribution of each Uncertain Stochastic variable in the sampling back.

Then the stochastic variable vector of concrete-bridge shrinkage and creep uncertain parameters is:

i＝1，2，Λ，5

Because

is separate; And 5 uncertain parameters are Normal Distribution function characteristic all, then:

In the formula, μ is an average of deferring to the stochastic variable of normal distribution;

Unbiased estimator for μ; σ ²Be variance of a random variable, σ is a standard deviation, following various σ same meaning; N is a sample number.

And

In the formula, z _α/2Be normal distribution fiducial limit value.

So just obtain each uncertain parameters standardized normal distribution α quantile, and based on the fiducial interval that fiducial limit is 1-α of standard value μ:

Order:

According to standard deviation sigma and sampling sample number n, obtain z _α/2, the average of each uncertain parameters of substitution and standard deviation can be tried to achieve the uncertain parameters fiducial interval of various confidence levels.

According to uncertain parameters fiducial interval; The n five equilibrium is carried out in the interval; Obtain n+1 frontier point and n sub-interval; To the contraction strain and the coefficient of creeping; Randomly draw a sample in each sub-range through the Latin hypercube sampling, then to all sample random alignment statistical estimations.

(3) set up consideration time variation and probabilistic concrete-bridge shrinkage and creep analytical approach

According to above-mentioned effective modulus function and statistical estimation result, obtain contraction strain and the coefficient sets interval of creeping is by length of time adjustment:

In the formula, ε _Cs0Be concrete name contraction coefficient; φ ₀Be the concrete name coefficient of creeping.

According to superposition principle, and the concrete-bridge shrinkage and creep that following formula calculates is uncertain interval, and with the effective modulus replacement modulus of elasticity of concrete E (τ) by adjustment in the length of time, then any time by the internal force that the concrete-bridge shrinkage and creep produces is:

$N=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\left(\underset{j=1}{\overset{i-1}{\mathrm{\&Sigma;}}}\mathrm{\&eta;}(t_i,t_j)\mathrm{\&Delta;N}\left(t_j\right)\right)+\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\left(E(t_i,t_{i-1})A_c{\mathrm{\&Delta;\&epsiv;}}_{\mathrm{cs}}(t_i,t_{i-1})\right)$

$M=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\left(\underset{j=1}{\overset{i-1}{\mathrm{\&Sigma;}}}\mathrm{\&eta;}(t_i,t_j)\mathrm{\&Delta;M}\left(t_j\right)\right)+\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\left(E(t_i,t_{i-1})I_c\mathrm{\&Delta;}{\mathrm{\&psi;}}_{\mathrm{cs}}(t_i,t_{i-1})\right)$

$\mathrm{\&eta;}(t_i,t_{i-1})=\frac{E(t_i,t_{i-1})}{E\left(t_j\right)}(\mathrm{\&phi;}(t_i,t_j)-\mathrm{\&phi;}(t_{i-1},t_j))$

In the formula: Δ ε _Cs(t _i, t _I-1) be the contraction strain increment; Δ ψ _Cs(t _i, t _I-1) for shrinking the curvature increment that causes, Δ N (t _j), Δ M (t _j) be t _iTo t _jAxle power and moment of flexure increment constantly; E (t _i, t _I-1) for pressing the effective modulus of adjustment in the length of time; E (t _j) be t _jConcrete elastic modulus of the moment.

If do not consider the influence of concrete shrinkage in calculating, the rear section of then removing a power N and moment M two formulas gets final product.

Embodiment 2, consider the application of time variation and probabilistic concrete-bridge shrinkage and creep analytical approach:

Be the consideration time variation that checking proposes and the correctness of probabilistic concrete-bridge shrinkage and creep analytical approach, through the ANSYS software programming computational analysis flow process, see Fig. 1, and use this method that the concrete test model is carried out the shrinkage and creep effect analysis.

This computational analysis flow process detailed process is: ANSYS software comprises pre-processing module and post-processing module.(PREP7) sets up the effective modulus function by adjustment in the length of time in pre-processing module, gets into then to find the solution module (SOLU) this effective modulus is carried out the time variation analysis, through the GET order result of calculation extracted.Got into post-processing module thereupon.Utilize APDL language establishment PDS (ANSYS Parametric Design Language) module; Analyze parametric confidence interval through uncertain variable, distribution function, LHS matrix of variables etc.; Get into circulation according to stacking method then; In conjunction with effective modulus function and LHS STOCHASTIC FINITE ELEMENT calculating internal force and displacement by adjustment in the length of time; And turn back to parametric confidence interval through circular file (file.loop) and uncertain Analysis of Sensitivity in Variables, proceed cyclic process and obtain until solving result.

The creep test model: adopt the PSC free beam of straight line arrangement of reinforcement, post-stretching, beam length 355cm, sectional dimension is 40cm * 40cm, and is as shown in Figure 2.Lower edge all applies compressive pre-stress on the test beam, and deformed bar adopts φ 15.20 steel hinge lines, and longitudinal reinforcement adopts φ 12 screw-thread steels, and stirrup adopts φ 8 round steel, and the beam body adopts the C50 concrete.The creep test model adopts straight line arrangement of reinforcement and the construction of full framing method, the beam body concrete pour into a mould the intensity that finishes reach design load 85% after carry out prestressed stretch-draw.Test beam adopts 2 load modes of span centre, and the load loading position is respectively L/4 and 3L/4 cross section, and load is 6.0kN.

The shrinkage test model: concrete shrinkage test test specimen sectional dimension is 15cm * 15cm, the long 250cm of test specimen.The concrete shrinkage test specimen is as shown in Figure 3.For reflecting environment temperature, humidity situation better, concrete shrinkage test test specimen disposal pouring is accomplished, and does not all carry out other processing.Test specimen inside is buried vibrating string extensometer test strain underground along the test specimen length direction.

The result of calculation of creeping is as shown in Figure 4, and contraction result of calculation is as shown in Figure 5.Result of calculation shows, adopts concrete-bridge shrinkage and creep analytical approach of the present invention, and the coefficient of creeping that calculates, values of shrinkage strain is consistent with the trial value variation tendency and coincide good.Coefficient, contraction strain determinacy calculated value and the trial value difference of wherein creeping is very little, and the coefficient maximum difference of creeping is merely 0.06, and the contraction strain maximum difference is merely 52u ε, and trial value all is positioned at the middle part of 95% fiducial limit scope.This shows, consider time variation and probabilistic concrete-bridge shrinkage and creep analytical approach, when calculating the shrinkage and creep effect of concrete bridge girder construction, result of calculation rationally, reliably.

Embodiment 3, consider the concrete-bridge loss of prestress computing method of shrinkage and creep and stress relaxation:

(1) considers the loss of prestress computing formula that time variation and reinforcement stresses are lax

When the concrete load age by t ₀When being changed to t, because the lax time variation of concrete-bridge shrinkage and creep and reinforcement stresses, the tension of concrete compressive stress and presstressed reinforcing steel all can reduce in time on the arbitrary section, and changing value is equal, satisfies cross section internal force balance condition:

σ _c(t)＝-μρσ _p(t)

ρ＝1+e _op ²/r _c ²

r _c ²＝I _c/A _c

μ＝A _p/A _c

In the formula, σ _c(t), σ _p(t) be that concrete and deformed bar are at t stress value constantly; A _p, A _cBe respectively presstressed reinforcing steel and concrete section area; e _OpBe the distance of deformed bar center of gravity to the concrete section center of gravity; I _cBe the concrete section moment of inertia.

In the same level height of presstressed reinforcing steel, can get according to presstressed reinforcing steel and concrete deformation cooperation condition:

ε _c(t)-ε _c(t ₀)＝ε _p(t)-ε _p(t ₀)

In the formula, ε _c(t), ε _c(t ₀) be that concrete is at t and t ₀Strain value constantly; ε _p(t), ε _p(t ₀) deformed bar is at t and t ₀Strain value constantly.

To load age is t ₀And stress continually varying concrete-bridge, through effective modulus method by adjustment in the length of time, when considering the time variation of xoncrete structure shrinkage and creep, the concrete strain-stress relation of any time t:

${\mathrm{\&epsiv;}}_c\left(t\right)=\frac{{\mathrm{\&sigma;}}_c\left(t_0\right)}{E\left(t_0\right)}[1+\mathrm{\&phi;}(t,t_0)]+\frac{[{\mathrm{\&sigma;}}_c\left(t\right)-{\mathrm{\&sigma;}}_c\left(t_0\right)][1+\mathrm{\&chi;}(t,t_0)\mathrm{\&phi;}(t,t_0)]}{E\left(t_0\right)}+{\mathrm{\&epsiv;}}_{\mathrm{cs}}(t,t_0)$

In the formula, χ (t, t ₀) be the concrete aging coefficient.Simplify when calculating χ (t, t ₀) span be generally 0.5～1.0.

Consider the stress relaxation loss of presstressed reinforcing steel, the strain-stress relation that obtains any time deformed bar is:

${\mathrm{\&epsiv;}}_p\left(t\right)=\frac{{\mathrm{\&sigma;}}_p\left(t\right)-{\stackrel{\&OverBar;}{\mathrm{\&sigma;}}}_p\left(t\right)}{E_p}$

${\stackrel{\&OverBar;}{\mathrm{\&sigma;}}}_p\left(t\right)={\mathrm{\&sigma;}}_p\left(t_0\right)[\frac{{\mathrm{\&sigma;}}_p\left(t_0\right)}{f_{\mathrm{pk}}}-0.55]\frac{\lg (t-t_0)}{45}$

In the formula,

Be the lax loss of prestress that causes of reinforcement stresses; f _PkBe the deformed bar strength standard value.

Obtain according to above-mentioned formula arrangement, consider that the lax interactional loss of prestress computing formula of concrete shrinkage and creep time variation and reinforcement stresses is:

${\mathrm{\&sigma;}}_{\mathrm{ps}}\left(t\right)=\frac{{\mathrm{\&epsiv;}}_{\mathrm{cs}}(t,t_0)+\frac{{\mathrm{\&sigma;}}_c\left(t_0\right)\mathrm{\&phi;}(t,t_0)}{E\left(t_0\right)}+\frac{{\stackrel{\&OverBar;}{\mathrm{\&sigma;}}}_p\left(t\right)}{E_p}}{\frac{1}{E_p}+\frac{\mathrm{\&mu;\&rho;}}{E\left(t_0\right)}[1+\mathrm{\&chi;}(t,t_0)\mathrm{\&phi;}(t,t_0)]}$

(2) consider the lax interactional loss of prestress computing method of time variation, uncertainty and reinforcement stresses thereof

Concrete-bridge shrinkage and creep, the uncertainty that stress of prestressed steel is lax mainly show the lax aspects such as uncertainty that cause loss of prestress of the coefficient of creeping, contraction strain and reinforcement stresses.Influence parameter according to each, adopt λ respectively ₁, λ ₂Represent the creep coefficient of uncertainty of coefficient, contraction strain of concrete-bridge, adopt λ ₃, λ ₄, λ ₅Consider the uncertainty influence that concrete crushing strength, envionmental humidity RH and reinforcement stresses are lax respectively.

Then uncertain parameters is that the fiducial interval of 1-α is based on the fiducial limit of standard value:

$({\stackrel{\&OverBar;}{\mathrm{\&lambda;}}}_i-\frac{\mathrm{\&sigma;}}{\sqrt{n}}{z}_{\mathrm{\&alpha;}/2},{\stackrel{\&OverBar;}{\mathrm{\&lambda;}}}_i+\frac{\mathrm{\&sigma;}}{\sqrt{n}}{z}_{\mathrm{\&alpha;}/2})=[\underset{\&OverBar;}{\mathrm{\&lambda;}},\stackrel{\&OverBar;}{\mathrm{\&lambda;}}]$

According to uncertain parameters λ _iFiducial interval is carried out the n five equilibrium with the interval, obtains n+1 frontier point and n sub-interval, to the contraction strain and the coefficient of creeping, randomly draws a sample in each sub-range through the Latin hypercube sampling, then to all sample random alignment statistical estimations.

Contain design specifications according to the fiducial interval of each uncertain parameters and highway reinforced concrete and prestressed concrete bridge, find the solution and obtain contraction strain, the coefficient of creeping, and the set of the lax loss of prestress that causes of reinforcement stresses etc. interval:

$\left\{\begin{array}{c}{\mathrm{\&epsiv;}}_{\mathrm{cs}}(t,t_s)={\mathrm{\&lambda;}}_2{\mathrm{\&epsiv;}}_{\mathrm{<figure-callout\; id="0"\; label="cs"\; filenames="HDA0000070849440000021.png,HDA0000070849440000022.png"\; state="\{\{state\}\}">cs</figure-callout>}0}\&CenterDot;{\mathrm{\&beta;}}_s(t-t_s)\\ {\mathrm{\&epsiv;}}_{\mathrm{<figure-callout\; id="0"\; label="cs"\; filenames="HDA0000070849440000021.png,HDA0000070849440000022.png"\; state="\{\{state\}\}">cs</figure-callout>}0}={\mathrm{\&epsiv;}}_s\left({\mathrm{\&lambda;}}_3{f}_{\mathrm{cm}}\right)\&CenterDot;{\mathrm{\&lambda;}}_4{\mathrm{\&beta;}}_{\mathrm{RH}}\\ \mathrm{\&phi;}(t,t_0)={\mathrm{\&lambda;}}_1{\mathrm{\&phi;}}_0\&CenterDot;{\mathrm{\&beta;}}_c(t-t_0)\\ {\mathrm{\&phi;}}_0={\mathrm{\&lambda;}}_4{\mathrm{\&phi;}}_{\mathrm{RH}}\&CenterDot;\mathrm{\&beta;}\left({\mathrm{\&lambda;}}_3{f}_{\mathrm{cm}}\right)\&CenterDot;\mathrm{\&beta;}\left(t_0\right)\\ {\stackrel{\&OverBar;}{\mathrm{\&sigma;}}}_p\left(t\right)={\mathrm{\&lambda;}}_5{\mathrm{\&sigma;}}_p\left(t_0\right)[\frac{{\mathrm{\&sigma;}}_p\left(t_0\right)}{f_{\mathrm{pk}}}-0.55]\frac{\lg (t-t_0)}{45}\end{array}\right.{\mathrm{\&lambda;}}_i\&Element;[\underset{\&OverBar;}{\mathrm{\&lambda;}},\stackrel{\&OverBar;}{\mathrm{\&lambda;}}]$

Obtain contraction strain, the coefficient of creeping, the lax codomain that causes stress loss of reinforcement stresses according to following formula; In the loss of prestress computing formula in substitution (1) bar, can obtain to consider the concrete shrinkage and creep time variation with uncertain and with the lax interactional loss of prestress calculated value of reinforcement stresses.

Embodiment 4, consider the concrete-bridge loss of prestress Application of calculating method of shrinkage and creep and stress relaxation:

For verifying the correctness of the loss of prestress computing method that propose, use this method that the normal concrete test model is carried out long-term loss of prestress value and calculate.

Test model: the loss of prestress test model is 1 normal concrete prestress test free beam, and test model is 100 * 200mm, adopts φ ^s15.2 prestress wire, post-tensioned construction.The test of steel chord type pressure transducer is adopted in its loss of prestress, and concrete strain adopts the clock gauge monitoring.Test duration is to measure 1 time 1st month every day, plays jede Woche measurement 2 times on the 2nd month, and jede Woche is measured 1 time after half a year, and test duration is more than 1 year.Test model is as shown in Figure 6.

Loss of prestress result of calculation is as shown in Figure 7; The loss of prestress method of loss of prestress test monitoring data and proposition is calculated really qualitative value and is coincide good; The long-term loss of prestress codomain that adopts this method to calculate is interval, when carrying out the prestressed reinforced concrete construction design, guarantees that loss of prestress codomain interval value all satisfies code requirement; Make the long-term loss of prestress prediction of structure have bigger fraction, make the long-term stress performance of structure safer, reliable.

Claims (6)

1. concrete-bridge shrinkage and creep and loss of prestress computing method is characterized in that:

Concrete-bridge shrinkage and creep computing method are the statistical estimation results that obtain uncertain parameters according to Latin hypercube sampling stochastic finite element method; The set that obtains the concrete shrinkage strain and the coefficient of creeping according to the statistical estimation result is interval; Obtain concrete-bridge shrinkage and creep computing formula according to concrete shrinkage and creep strain-stress relation, the effective modulus function of pressing adjustment in the length of time, set interval and superposition principle then; Form a kind of consideration time variation and probabilistic concrete-bridge shrinkage and creep analytical approach, and in finite element analysis software, realize these shrinkage and creep computing method;

Concrete-bridge loss of prestress computing method are the statistical estimation results that obtain uncertain parameters according to Latin hypercube sampling stochastic finite element method; In conjunction with the concrete shrinkage and creep strain-stress relation, by effective modulus function and the stress of prestressed steel-strain stress relation adjusted the length of time; The loss of prestress set that obtain the concrete shrinkage strain, the lax combined action of creep coefficient and reinforcement stresses causes is interval; According to the interval loss of prestress computing formula that obtains concrete-bridge of set, form the concrete-bridge loss of prestress computing method of considering shrinkage and creep and stress relaxation.

2. computing method according to claim 1 is characterized in that, in the computing method of concrete-bridge shrinkage and creep, statistical estimation result, the contraction strain of uncertain parameters and the set interval of the coefficient of creeping obtain according to following method:

A) introduce uncertain parameters

The uncertainty, the concrete cube compressive strength f that represent nominal creep coefficient, nominal contraction coefficient respectively _Cm, envionmental humidity RH and prestress load influential factors;

B) obtaining each uncertain parameters

is the fiducial interval of 1-α based on the fiducial limit of standard value:

In the formula (1), α value 0.05, σ is a standard deviation, n is a sample number, z _α/2Be normal distribution fiducial limit value,

For The fiducial interval lower bound,

For

The fiducial interval upper bound, i value 1,2 ... 5;

C) according to the fiducial interval of uncertain parameters

; The n five equilibrium is carried out in the interval; Obtain n+1 frontier point and n sub-interval, according to formula (1) each uncertain parameters

of actual bridge is taken a sample then; The creep uncertain parameters

of coefficient, nominal contraction coefficient of name is randomly drawed a sample in each sub-range through the Latin hypercube sampling, then to all sample random alignment statistical estimations;

D) contain design specifications according to highway reinforced concrete and prestressed concrete bridge, the result of the statistical estimation of integrating step C obtains contraction strain and creeps the coefficient sets interval:

In the formula (2), ε _Cs0Be concrete name contraction coefficient, ε _Cs(t, t _s) be t for shrinking beginning length of time _s, to calculate the length of time be the contraction strain of t, β _s(t-t _s) for shrinking the coefficient of development in time, β _RHBe the contraction coefficient relevant with mean annual humidity,

Be the contraction coefficient relevant with concrete crushing strength, and:

β _ScFor according to the fixed coefficient of cement kind, φ ₀Be the concrete name coefficient of creeping, φ (t, t ₀) for load age be t ₀, to calculate the length of time be the coefficient of creeping of t, β _c(t-t ₀) be the coefficient that develops in time after loading, φ _RHBe the coefficient relevant of creeping with mean annual humidity,

Be the coefficient relevant of creeping with concrete crushing strength, and:

β (t ₀) be the function of development in time of creeping, and:

$\mathrm{\&beta;}\left(t_0\right)=\frac{1}{0.1+{t_0}^{0.2}}---\left(2c\right).$

3. computing method according to claim 2 is characterized in that, the method that obtains concrete-bridge shrinkage and creep computing formula is:

A) be t to load age ₀And stress continually varying xoncrete structure, the concrete shrinkage and creep strain-stress relation of any time t is expressed as:

${\mathrm{\&epsiv;}}_c\left(t\right)=\frac{{\mathrm{\&sigma;}}_c\left(t_0\right)}{E\left(t_0\right)}[1+\mathrm{\&phi;}(t,t_0)]+\frac{{\mathrm{\&sigma;}}_c\left(t\right)-{\mathrm{\&sigma;}}_c\left(t_0\right)}{E(t,t_0)}+{\mathrm{\&epsiv;}}_{\mathrm{cs}}(t,t_s)---\left(3\right)$

In the formula (2), ε _cConcrete strain value when (t) being any time t, σ _c(t ₀), σ _c(t) be respectively t ₀, the concrete stress during t, E (t ₀) be that concrete is at t ₀Elastic modulus constantly, E (t, t ₀) be the effective modulus of concrete by adjustment in the length of time, promptly load age is t ₀, calculate the modulus of elasticity of concrete when being t the length of time;

B) the effective modulus function E (t, the t that adjust by the length of time ₀) be expressed as:

$E(t,t_0)=\frac{E\left(t_0\right)}{1+\mathrm{\&chi;}(t,t_0)\mathrm{\&phi;}(t,t_0)}---\left(4\right)$

$\mathrm{\&chi;}(t,t_0)=\frac{1}{1-R(t,t_0)}-\frac{1}{\mathrm{\&phi;}(t,t_0)}---\left(5\right)$

$R(t,t_0)=\frac{{\mathrm{\&sigma;}}_c\left(t\right)}{{\mathrm{\&sigma;}}_c\left(t_0\right)}---\left(6\right)$

In the formula: χ (t, t ₀) be that concrete load age is t ₀, calculate the aging coefficient when being t the length of time, R (t, t ₀) for the concrete load age be t ₀, calculate the coefficient of relaxation when being t the length of time;

C), combine superposition principle to obtain any time to be by the axle power N and the moment M of concrete-bridge shrinkage and creep generation according to (1)～(6) formulas:

$N=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\left(\underset{j=1}{\overset{i-1}{\mathrm{\&Sigma;}}}\mathrm{\&eta;}(t_i,t_j)\mathrm{\&Delta;N}\left(t_j\right)\right)+\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\left(E(t_i,t_{i-1})A_c{\mathrm{\&Delta;\&epsiv;}}_{\mathrm{cs}}(t_i,t_{i-1})\right)---\left(7\right)$

$M=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\left(\underset{j=1}{\overset{i-1}{\mathrm{\&Sigma;}}}\mathrm{\&eta;}(t_i,t_j)\mathrm{\&Delta;M}\left(t_j\right)\right)+\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\left(E(t_i,t_{i-1})I_c\mathrm{\&Delta;}{\mathrm{\&psi;}}_{\mathrm{cs}}(t_i,t_{i-1})\right)---\left(8\right)$

$\mathrm{\&eta;}(t_i,t_{i-1})=\frac{E(t_i,t_{i-1})}{E\left(t_j\right)}(\mathrm{\&phi;}(t_i,t_j)-\mathrm{\&phi;}(t_{i-1},t_j))---\left(9\right)$

In formula (7)～(9), Δ ε _Cs(t _i, t _I-1) be t _I-1To t _iConcrete shrinkage strain increment constantly, Δ ψ _Cs(t _i, t _I-1) be t _I-1To t _iThe curvature increment that concrete shrinkage constantly causes, Δ N (t _j), Δ M (t _j) be respectively t _iTo t _jAxle power and moment of flexure increment constantly, E (t _i, t _I-1) be t _I-1To t _iEffective modulus constantly by adjustment in the length of time, E (t _j) be t _jConcrete elastic modulus of the moment, φ (t _i, t _j) be t _jTo t _iConcrete creep coefficient constantly, I _cBe the bending resistance moment of inertia of concrete section, A _cBe the area of section of xoncrete structure, η (t _i, t _j) be intermediate parameters.

4. computing method according to claim 3; It is characterized in that: the computing method that realize this shrinkage and creep in the finite element analysis software are handled through the APDL language; Its treatment step comprises: with changing function, promptly the effective modulus by adjustment in the length of time is carried out the time variation analysis when at first the embedding modulus of elasticity of concrete was adjusted with the length of time in ANSYS program calculating pre-processing module; Calculate in the post-processing module in the ANSYS program then; Utilize APDL language establishment PDS module to realize uncertain statistical study flow process; Give stochastic variable distribution function type; Through stochastic variable parametric statistics methods analyst parametric confidence interval, concrete-bridge is carried out the shrinkage and creep uncertainty analysis.

5. computing method according to claim 1; It is characterized in that: in the concrete-bridge loss of prestress computing method; Obtain the statistical estimation result of uncertain parameters, and the interval method of loss of prestress set that concrete shrinkage strain, creep coefficient and the interaction of reinforcement stresses relaxation phase cause is:

A) introduce uncertain parameters λ ₁, λ ₂, λ ₃, λ ₄, λ ₅Represent creep 28 days cubic compressive strength f of coefficient of uncertainty, concrete of coefficient, contraction strain of concrete-bridge respectively _Cm, probabilistic influence that envionmental humidity RH and reinforcement stresses are lax;

B) obtain each uncertain parameters λ _iFiducial limit based on standard value is the fiducial interval of 1-α:

$({\stackrel{\&OverBar;}{\mathrm{\&lambda;}}}_i-\frac{\mathrm{\&sigma;}}{\sqrt{n}}{z}_{\mathrm{\&alpha;}/2},{\stackrel{\&OverBar;}{\mathrm{\&lambda;}}}_i+\frac{\mathrm{\&sigma;}}{\sqrt{n}}{z}_{\mathrm{\&alpha;}/2})=[\underset{\&OverBar;}{\mathrm{\&lambda;}},\stackrel{\&OverBar;}{\mathrm{\&lambda;}}]---\left(10\right)$

In the formula (10), α value 0.05, σ is a standard deviation, n is a sample number, z _α/2Be normal distribution fiducial limit value, λBe λ _iThe fiducial interval lower bound,

Be λ _iThe fiducial interval upper bound, i value 1,2 ... 5;

C) according to uncertain parameters λ _iFiducial interval, the n five equilibrium is carried out in the interval, obtain n+1 frontier point and n sub-interval, then according to formula (10) each uncertain parameters λ to actual bridge _iTake a sample; Uncertain parameters λ to the coefficient of creeping, contraction strain ₁, λ ₂, randomly draw a sample in each sub-range through the Latin hypercube sampling, then to all sample random alignment statistical estimations;

D) according to formula (3), concrete caused because of shrinkage and creep when (4) obtained any time t strain-stress relation:

${\mathrm{\&epsiv;}}_c\left(t\right)=\frac{{\mathrm{\&sigma;}}_c\left(t_0\right)}{E\left(t_0\right)}[1+\mathrm{\&phi;}(t,t_0)]+\frac{[{\mathrm{\&sigma;}}_c\left(t\right)-{\mathrm{\&sigma;}}_c\left(t_0\right)][1+\mathrm{\&chi;}(t,t_0)\mathrm{\&phi;}(t,t_0)]}{E\left(t_0\right)}+{\mathrm{\&epsiv;}}_{\mathrm{cs}}(t,t_0)---\left(11\right)$

E) stress relaxation of considering presstressed reinforcing steel is lost, and the strain-stress relation that obtains any time deformed bar is:

${\mathrm{\&epsiv;}}_p\left(t\right)=\frac{{\mathrm{\&sigma;}}_p\left(t\right)-{\stackrel{\&OverBar;}{\mathrm{\&sigma;}}}_p\left(t\right)}{E_p}---\left(12\right)$

${\stackrel{\&OverBar;}{\mathrm{\&sigma;}}}_p\left(t\right)={\mathrm{\&sigma;}}_p\left(t_0\right)[\frac{{\mathrm{\&sigma;}}_p\left(t_0\right)}{f_{\mathrm{pk}}}-0.55]\frac{\log (t-t_0)}{45}---\left(13\right)$

In formula (12), (13), ε _p(t) be the strain value of deformed bar, E _pBe the elastic modulus of deformed bar, σ _p(t ₀), σ _p(t) be respectively deformed bar at t ₀, t stress value constantly,

Be the lax loss of prestress that causes of reinforcement stresses, f _PkBe the deformed bar strength standard value;

F) contain design specifications according to highway reinforced concrete and prestressed concrete bridge, the result of the statistical estimation of integrating step C, and formula (13) obtain contraction strain and creep the coefficient sets interval:

$\left\{\begin{array}{c}{\mathrm{\&epsiv;}}_{\mathrm{cs}}(t,t_s)={\mathrm{\&lambda;}}_2{\mathrm{\&epsiv;}}_{\mathrm{cs}0}\&CenterDot;{\mathrm{\&beta;}}_s(t-t_s)\\ {\mathrm{\&epsiv;}}_{\mathrm{cs}0}={\mathrm{\&epsiv;}}_s\left({\mathrm{\&lambda;}}_3{f}_{\mathrm{cm}}\right)\&CenterDot;{\mathrm{\&lambda;}}_4{\mathrm{\&beta;}}_{\mathrm{RH}}\\ \mathrm{\&phi;}(t,t_0)={\mathrm{\&lambda;}}_1{\mathrm{\&phi;}}_0\&CenterDot;{\mathrm{\&beta;}}_c(t-t_0)\\ {\mathrm{\&phi;}}_0={\mathrm{\&lambda;}}_4{\mathrm{\&phi;}}_{\mathrm{RH}}\&CenterDot;\mathrm{\&beta;}\left({\mathrm{\&lambda;}}_3{f}_{\mathrm{cm}}\right)\&CenterDot;\mathrm{\&beta;}\left(t_0\right)\\ {\stackrel{\&OverBar;}{\mathrm{\&sigma;}}}_p\left(t\right)={\mathrm{\&lambda;}}_5{\mathrm{\&sigma;}}_p\left(t_0\right)[\frac{{\mathrm{\&sigma;}}_p\left(t_0\right)}{f_{\mathrm{pk}}}-0.55]\frac{\lg (t-t_0)}{45}\end{array}\right.{\mathrm{\&lambda;}}_i\&Element;[\underset{\&OverBar;}{\mathrm{\&lambda;}},\stackrel{\&OverBar;}{\mathrm{\&lambda;}}]---\left(14\right).$

6. computing method according to claim 5 is characterized in that, the method that obtains the loss of prestress computing formula is:

A) the concrete stress balance equation is:

σ _c(t)＝-μρσ _p(t) (15)

ρ＝1+e _op ²/r _c ² (16)

r _c ²＝I _c/A _c (17)

μ＝A _p/A _c (18)

In formula (15)～(18), σ _c(t), σ _p(t) be respectively concrete and deformed bar at t STRESS VARIATION value constantly, A _p, A _cBe respectively presstressed reinforcing steel and concrete section area, e _OpBe the distance of deformed bar center of gravity to the concrete section center of gravity, I _cBe the concrete section moment of inertia;

B), can get according to deformed bar and concrete deformation cooperation condition in the same level height of presstressed reinforcing steel:

ε _c(t)-ε _c(t ₀)＝ε _p(t)-ε _p(t ₀) (19)

In the formula (19), ε _c(t) be concrete strain value, ε _p(t) be the strain value of deformed bar;

C), obtain considering concrete shrinkage and creep time variation and the reinforcement stresses interactional loss of prestress σ that relaxes according to formula (11)～(19) _Ps(t) computing formula is:

${\mathrm{\&sigma;}}_{\mathrm{ps}}\left(t\right)=\frac{{\mathrm{\&epsiv;}}_{\mathrm{cs}}(t,t_0)+\frac{{\mathrm{\&sigma;}}_c\left(t_0\right)\mathrm{\&phi;}(t,t_0)}{E\left(t_0\right)}+\frac{{\stackrel{\&OverBar;}{\mathrm{\&sigma;}}}_p\left(t\right)}{E_p}}{\frac{1}{E_p}+\frac{\mathrm{\&mu;\&rho;}}{E\left(t_0\right)}[1+\mathrm{\&chi;}(t,t_0)\mathrm{\&phi;}(t,t_0)]}---\left(20\right).$

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