CN103530459A - Giant combined member shrinkage and creep calculation method with humidity distribution taken into consideration - Google Patents

Abstract

The invention relates to a giant combined member shrinkage and creep calculation method with humidity distribution taken into consideration. The method includes the steps of firstly, obtaining humidity distribution data, changing along with the age, of the cross section of a member according to the humidity of the environment where the member is located and the age condition of the member; secondly, conducting fiber unit division on the member according to the material composition, creep parameters and stress features of the cross section, and calculating the area of each fiber unit, the centroid coordinate of each fiber unit and the humidity change condition in the centroid position of each fiber unit; thirdly, calculating the elastic strain of each fiber unit; fourthly, calculating initial stress of each fiber unit, and calculating the inelastic shrinkage and creep strain of all the fiber units with different types of humidity distribution according to a shrinkage and creep module; fifthly, calculating virtual stress of each fiber unit, obtaining virtual internal force according to the virtual stress integral, and obtaining a strain value of the whole member according to the virtual internal force. Compared with the prior art, the method has the advantages of being simple and clear in calculation process, accurate in result and the like.

Description

Consider the huge combined member shrinkage and creep computing method of moisture distribution

Technical field

The present invention relates to a kind of building shrinkage and creep computing method, especially relate to a kind of huge combined member shrinkage and creep computing method of considering moisture distribution.

Background technology

Because mixed structure can carry out textural association by Steel concrete effectively, overall economic efficiency, take precautions against natural calamities, the very superior feature of performance such as wind resistance, antidetonation and anti-destruction continuously, Mixed Architecture is used widely in high-rise building.

Huge post in mega-frame and the huge vertical members such as shear wall in Core Walls Structure are due to the larger vertical force of carrying, and sectional dimension is huge, and in order to meet better bearing capacity and axial compression ratio requirement, huge vertical member generally adopts shaped steel and concrete combined component.

Huge combined member is also subject to non-load action except being subject to load action, mainly comprises that concrete shrinkage and creep, structure temperature change, ground relative settlement.The leading construction of the otherness of the otherness of vertical load, member section stress performance, the time variation of effect of non load and high-rise building, can cause the vertical deformation difference between member.An outstanding feature of mixed structure is that Core Walls Structure adopts concrete material, and outside framework adopts steel or the higher section form of steel ratio.Concrete material has the characteristic of shrinkage and creep, and this will cause the further vertical deformation difference of structure.Due to cumulative effect, along with the height of high-rise building constantly increases, the vertical deformation difference that effect of non load causes such as shrink, creep and also can constantly increase, and reach maximum at top layer.Vertical deformation difference all has adverse effect to the structural elements of high-rise building and non-structural element.

Vertical deformation difference can cause the non-structural elements such as curtain wall, partition wall, dynamo-electric pipeline and elevator impaired, causes the problem of permanance and architectural appearance aspect; Vertical differential deformation will affect the levelness of building roof, in the horizontal member (as semi-girder truss) of the huge post of contact and Core Walls Structure, cause additional internal force, thereby the Internal Force Redistribution that causes vertical member, when serious, can cause structure partial to lose efficacy or be unwell to continuing to use, cause larger economic loss.

In the current structural design about huge combined member, there is following problem: the one, the impact of the moisture distribution of not considering member section during design on shrinkage and creep inelastic strain, makes to predict the outcome inaccurate; The 2nd, the Prediction Model of Concrete Shrinkage and Creep of selecting falls behind, and predicted value is inaccurate; The 3rd, in the process of vertical deformation, do not consider the effect of eccentric load, the moment of flexure that eccentric load produces can make vertical member distortion inhomogeneous equally, the impact that horizontal member is produced to parasitic moment.

Along with the widespread use of high-rise building, because the performance of huge combined member is better than normal concrete member, huge combined member is applied more and more extensive in Super High Mixed Architecture.Yet related experiment shows, will be bigger than normal if predict by the method for predicting the vertical deformation of normal concrete member that huge combined member obtains deformation values.Owing to burying shaped steel in huge combined member, hindered in concrete humidity to external diffusion, make the moisture distribution in huge combined member be different from normal concrete member, thereby make the long-term vertical deformation of huge combined member also be different from normal concrete member.Yet in the design of the current huge combined member in reality, inreal consideration shaped steel is for the inhibition of humidity in concrete.All concrete shrinkage and creep computation models are not all considered the impact that DIFFERENT WET Degree distributions shrinks, creeps and calculate at present.The humidity that is all the whole member section of hypothesis as the model of the contraction of being advised in ACI, CEB-FIP and B3 model, the calculating of creeping is all uniform.Experiment shows, with CEB-FIP model, calculate respectively the vertical deformation of huge combined member and normal concrete member, compare with actual result, the calculated value of normal concrete member and actual result are coincide better, but the calculated value of huge combined member and actual result differ more, consider that result of calculation and the actual value of different humidity distribution corrected Calculation model is afterwards comparatively approaching.

The huge combined members such as the huge post in Super High structure and Core Walls Structure normally consist of the interior combined Steel concrete burying.Combination shaped steel generally all contains closed region, makes its inner concrete in air-tight state.Because the combination shaped steel in huge combined member has hindered in concrete humidity to external diffusion, make the moisture distribution in huge combined member be different from normal concrete member, thereby make the long-term vertical deformation of huge combined member also be different from normal concrete member.Yet, in the design of the current huge combined member in reality, inreal consideration shaped steel, for the inhibition of humidity in concrete, therefore calculates the vertical deformation of the huge combined member of estimation that meeting is too high with the shrinkage and creep computation model that calculates normal concrete post.

Therefore,, while calculating the vertical deformation of huge combined member, be necessary to consider the impact that the different humidity in cross section distributes.

Summary of the invention

Object of the present invention is exactly to provide in order to overcome the defect of above-mentioned prior art existence the huge combined member shrinkage and creep computing method that a kind of computation process is simple and clear, result is considered moisture distribution accurately, is applicable to the huge combined member consisting of the interior combined Steel concrete burying.

Object of the present invention can be achieved through the following technical solutions:

Huge combined member shrinkage and creep computing method for moisture distribution, comprise the following steps:

(1), according to the residing ambient humidity of member and member condition in the length of time, obtain the moisture distribution data that member section changed with the length of time;

(2) according to the material composition in cross section, the parameter of creeping and loading characteristic, member is carried out to fiber element division, calculate the humidity situation of change at area, centre of form coordinate and the fiber element centre of form place of each fiber element;

(3) calculate the elastic strain of each fiber element;

(4) according to the elastic modulus of the elastic strain of member and material, calculate the primary stress of each fiber element, according to shrinkage and creep model, calculate the non-resilient shrinkage and creep strain of the fiber element of each different humidity distribution;

(5) according to the shrinkage and creep strain of every fiber element, calculate its virtual stress, then draw virtual internal force according to virtual stress integration, by virtual internal force, draw the strain value of member integrated.

The moisture distribution data that described member section changed with the length of time are specially:

$\frac{\&PartialD;\mathrm{\&theta;}}{\&PartialD;t}=D\left(\mathrm{\&theta;}\right)(\frac{{\&PartialD;}^2\mathrm{\&theta;}}{{\&PartialD;x}^2}+\frac{{\&PartialD;}^2\mathrm{\&theta;}}{{\&PartialD;\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="HDA0000394148440000032.png"\; state="\{\{state\}\}">y</figure-callout>}}^2}+\frac{{\&PartialD;}^2\mathrm{\&theta;}}{{\&PartialD;z}^2})+{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_z+{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_c$

${\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_z=\frac{{\&PartialD;\mathrm{\&theta;}}_z}{\&PartialD;t},{\mathrm{\&theta;}}_z=-\frac{w_{\mathrm{<figure-callout\; id="0"\; label="z\; w\; s"\; filenames="DEST\_PATH\_HDA0000411634340000051.png,HDA0000394148440000041.png"\; state="\{\{state\}\}">z</figure-callout>}}}{w_s},{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_c=\frac{{\&PartialD;\mathrm{\&theta;}}_c}{\&PartialD;t},{\mathrm{\&theta;}}_c=-\frac{w_{\mathrm{<figure-callout\; id="0"\; label="c\; w\; s"\; filenames="DEST\_PATH\_HDA0000411634340000051.png,HDA0000394148440000041.png"\; state="\{\{state\}\}">c</figure-callout>}}}{w_s}$

In formula, θ is concrete humidity, θ=w/w _s0, w is the water cut in concrete, w _s0for concrete initial water content, t is the age of concrete, and D (θ) is humidity coefficient of diffusion,

for concrete humidity is from reduced rate, θ _zfor concrete humidity is from reducing time-history curves, w _zrepresent that concrete humidity is from reducing amount,

for concrete humidity self-propagation rate, θ _cfor concrete humidity self-propagation time-history curves, w _zrepresent concrete humidity self-propagation amount.

The described rule that member is carried out to fiber element division is:

(1) according to different moisture distribution, divide different fiber elements;

(2) concrete in cross section is divided into different fiber elements from steel;

(3) for different stress forms, the simplification degree that fiber is divided is different: for axis compression member, by the different demarcation fiber of moisture distribution difference and material; For eccentric compression member, meeting under the prerequisite of axis compression member fiber division principle, eccentric compression member is divided fiber element according to the position of eccentric force effect: if eccentricity pressure acts on the axis of symmetry in cross section, same material is identical perpendicular to the axial stress of symmetry, and fiber element is evenly divided along this axis of symmetry direction; If eccentricity pressure acts on the optional position in cross section, according to the shape facility in cross section, cross section is divided into a plurality of fiber elements along different directions.

Described step 3), in, the elastic strain of calculating each fiber element is specially:

The fiber strain ε (x, y) that on each fiber element cross section, the centre of form (x, y) is located can use the elastic strain ε of cross section position of form center ₀with the curvature around cross section centre of form axle

be expressed as:

On cross section, all stress σ (x, y) caused cross section internal force and moments of flexure by fibrous bundle are tried to achieve by integration:

Wherein, N is cross section internal force, M _y, M _xbe respectively on cross section around y axle and moment of flexure around the effect of x axle, K _sfor section rigidity matrix, the area that A is fiber element:

$\begin{array}{c}{K}_s=\left[\begin{array}{ccc}\&Integral;E(x,y)\mathrm{dA}& \&Integral;E(x,y)\mathrm{xdA}& \&Integral;E(x,y)\mathrm{ydA}\\ \&Integral;E(x,y)\mathrm{xdA}& \&Integral;E(x,y)x^2\mathrm{dA}& \&Integral;E(x,y)\mathrm{xydA}\\ \&Integral;E(x,y)\mathrm{ydA}& \&Integral;E(x,y)\mathrm{xydA}& \&Integral;E(x,y)y^2\mathrm{dA}\end{array}\right]\\ =\left[\begin{array}{ccc}\mathrm{\&Sigma;}{E}_i{A}_i& \mathrm{\&Sigma;}{E}_i{A}_i{x}_i& \mathrm{\&Sigma;}{E}_i{A}_i{y}_i\\ \mathrm{\&Sigma;}{E}_i{A}_i{x}_i& \mathrm{\&Sigma;}{E}_i{x_i}^2& \mathrm{\&Sigma;}{E}_i{A}_i{y}_i\\ \mathrm{\&Sigma;}{E}_i{A}_i{y}_i& \mathrm{\&Sigma;}{E}_i{A}_i{x}_i{y}_i& \mathrm{\&Sigma;}{E}_i{A}_i{y_i}^2\end{array}\right];i=1,\&CenterDot;\&CenterDot;\&CenterDot;,n\end{array}$

By matrix inversion, can obtain cross section flexibility matrix

then according to the suffered power in fiber element cross section, try to achieve the elastic strain ε in fiber element cross section ₀:

According to the elastic strain ε in fiber element cross section ₀can calculate the primary stress of fiber element: σ with the elastic modulus E of material ₀=E ε ₀.

Described step 4) the shrinkage and creep model in is B3 model.

Described step 4) concrete steps of calculating non-resilient shrinkage and creep strain in are:

Suppose fiber element axial compression, load age is t ' time, the strain stress (t) under normal effect of stress:

ε(t)＝J(t，t′)σ+ε _sh(t)

Wherein, σ is axial stress, ε _sh(t) be contraction strain, J (t, t ') is for creeping function;

Time dependent contraction strain limit of utilization is shunk to be multiplied by and is considered that the related coefficient of relative humidity, time effect and size effect represents:

ε _sh(t)＝-ε _sh∞k _hS(t)

ε wherein _{sh ∞}for limit contraction strain, k _hfor humidity effect coefficient, S (t) is for shrinking time dependent function; The formula of function J (t, t ') of creeping is:

$J(t,t^{\&prime;})=\frac{1}{E\left(t^{\&prime;}\right)}+C_0(t,t^{\&prime;})+C_d(t,t^{\&prime;},t_0)$

Wherein

for transient elastic strain compliance function, E (t ') is load age concrete elastic modulus of t ' time, C ₀(t, t ') is basic crrep compliance function, C _d(t, t ', t ₀) be dry crrep compliance function, t represents the age of concrete, t ₀for curing age.

Described step 5), in, the calculation procedure of the strain value of member integrated is specially:

(1) calculate the virtual stress value of fiber:

(2) by virtual stress integration, draw the fictitious force on member section

$\left\{\begin{array}{c}\tilde{N}\\ {\tilde{M}}_y\\ {\tilde{M}}_x\end{array}\right\}=\left\{\begin{array}{c}\text{\&Integral;}\widetilde{\mathrm{\&sigma;}}(x,y)\mathrm{dA}\\ \text{\&Integral;}\widetilde{\mathrm{\&sigma;}}(x,y)\mathrm{xdA}\\ \text{\&Integral;}\widetilde{\mathrm{\&sigma;}}(x,y)\mathrm{ydA}\end{array}\right\}=\left\{\begin{array}{c}\mathrm{\&Sigma;}{\widetilde{\mathrm{\&sigma;}}}_i{A}_i\\ \mathrm{\&Sigma;}{\widetilde{\mathrm{\&sigma;}}}_i{A}_i{x}_i\\ \mathrm{\&Sigma;}{\widetilde{\mathrm{\&sigma;}}}_i{A}_i{y}_i\end{array}\right\}$

(3) according to fictitious force, calculate the strain value of fibre section:

Compared with prior art, the present invention has the following advantages:

1,, in the design of existing huge combined member, inreal consideration shaped steel, for the inhibition of humidity in concrete, therefore calculates the vertical deformation of the huge combined member of estimation that meeting is too high with the shrinkage and creep computation model that calculates normal concrete post.For above-mentioned situation, adopt the shrinkage and creep computing method of the correction fiber model of consideration moisture distribution proposed by the invention can calculate exactly the shrinkage and creep value of the huge combined member of arbitrary section form;

2, the present invention has derived and has considered the shrinkage and creep computing method of the huge combined member of moisture distribution on the basis of considering member section moisture distribution, concrete shrinkage and creep B3 forecast model and fiber model analytical approach, and be applied in the middle of the vertical deformation difference calculating of Super High structure, this analytical approach has the operability of engineering application, better meets engineering construction development need;

3, the B3 model that in the present invention, shrinkage and creep model adopts Bazant to propose, this B3 model formation definite conception, physical significance are clear, matching check through test figure in Northwestern Univ USA's shrinkage and creep database, and compare with ACI model and CEB-FIP (1990) model, prove that its precision of prediction is the highest.

Accompanying drawing explanation

Fig. 1 is computing method process flow diagram of the present invention;

Fig. 2 is infinitesimal hexahedron schematic diagram of the present invention;

Fig. 3 is that fiber of the present invention is divided schematic diagram;

Wherein, figure (3a) is axis compression member schematic diagram; Figure (3b) is single shaft eccentric compression member schematic diagram; Figure (3c) is optional position eccentric compression member schematic diagram;

Fig. 4 is the huge post schematic diagram of exemplary position bottom certain super-high building structure adopting in embodiment;

Fig. 5 is the schematic cross-section at 1 place in Fig. 4;

Fig. 6 is the moisture distribution schematic diagram of the member section at 2 places in Fig. 5;

Fig. 7 is the member strain that obtains after example of the present invention 1 is implemented rule schematic diagram over time;

Wherein, figure (7a) members contract strain comparison diagram; Figure (7b) is member creep strain comparison diagram; Figure (7c) is member overall strain comparison diagram.

Embodiment

Below in conjunction with the drawings and specific embodiments, the present invention is described in detail.The present embodiment be take technical solution of the present invention and is implemented as prerequisite, provided detailed embodiment and concrete operating process, but protection scope of the present invention is not limited to following embodiment.

As shown in Figure 1, a kind of huge combined member shrinkage and creep computing method of considering moisture distribution, comprise the following steps:

(1), according to the residing ambient humidity of member and member condition in the length of time, obtain the moisture distribution data that member section changed with the length of time;

(2) according to the material composition in cross section, the parameter of creeping and loading characteristic, member is carried out to fiber element division, calculate the humidity situation of change at area, centre of form coordinate and the fiber element centre of form place of each fiber element;

(3) calculate the elastic strain of each fiber element;

(4) according to the elastic modulus of the elastic strain of member and material, calculate the primary stress of each fiber element, according to shrinkage and creep model, calculate the non-resilient shrinkage and creep strain of the fiber element of each different humidity distribution;

(5) according to the shrinkage and creep strainometer of every fiber element, calculate its virtual stress, then draw virtual internal force according to virtual stress integration, by virtual internal force, draw the strain value of member integrated.

1, the moisture distribution that member section changed with the length of time

Because reinforcing bar is not obvious to the inhibition of humidity, in analyzing, do not consider the inhibition of reinforcing bar to humidity diffusion in concrete remittance herein.

(1) establish a certain infinitesimal hexahedron length in concrete and be respectively dx, dy, dz, as shown in Figure 2., within the Δ t time, what from the left interface of infinitesimal hexahedron, flow into can evaporated water be q _xdydz Δ t, what from the right interface of infinitesimal hexahedron, flow out can evaporated water be q _x+dxdydz Δ t, so the current variable quantity that x direction of principal axis causes is

Q _x＝(q _x+dx-q _x)dydzΔt (1)

According to FICK diffusion law, thinking can evaporated water q _xbe directly proportional to concrete water cut gradient, and can evaporation water direction of the traffic contrary with water cut gradient direction, that is:

$q_x=-D_x\left(w\right)\frac{\&PartialD;w}{\&PartialD;x}{q}_x---\left(2\right)$

D in formula _x(w) represent the humidity coefficient of diffusion of concrete x direction, w is the water cut in concrete.

Bring (2) formula into (1) Shi Ke get:

$Q_x=\frac{\&PartialD;}{\&PartialD;x}\left(D_x\left(w\right)\frac{\&PartialD;w}{\&PartialD;x}\right)\mathrm{dxdydz\&Delta;t}---\left(3\right)$

The change of moisture content amount that in like manner can obtain y, z direction is respectively:

$Q_y=\frac{\&PartialD;}{\&PartialD;y}\left(D_y\left(w\right)\frac{\&PartialD;w}{\&PartialD;y}\right)\mathrm{dxdydz\&Delta;t}---\left(4\right)$

$Q_z=\frac{\&PartialD;}{\&PartialD;z}\left(D_z\left(w\right)\frac{\&PartialD;w}{\&PartialD;z}\right)\mathrm{dxdydz\&Delta;t}---\left(5\right)$

According to Soret effect, because can causing moisture diffusion in concrete, the impact of thermograde flows.Therefore, in time Δ t, by thermograde, caused in infinitesimal hexahedron can evaporation water variable quantity be:

$Q_T=K_T\frac{\&PartialD;T}{\&PartialD;t}\mathrm{dxdydz\&Delta;t}---\left(6\right)$

K in formula _tfor experimental constant, T is concrete temperature.

Because inside concrete hydration also can cause the consumption of its internal moisture, i.e. concrete self-desiccation effect.Within the Δ t time, micro unit internal consumption can evaporation water content be:

$Q_h=-\frac{{\&PartialD;w}_z}{\&PartialD;t}\mathrm{dxdydz\&Delta;t}---\left(7\right)$

Can evaporation water and can produce in concrete carbonization course of reaction,, within the Δ t time, due to carburizing reagent, what in concrete infinitesimal, produce can evaporation water be:

$Q_c=\frac{{\&PartialD;w}_c}{\&PartialD;t}\mathrm{dxdydz\&Delta;t}---\left(8\right)$

Within the Δ t time, in infinitesimal hexahedron, total change of moisture content amount is:

$Q_w=\frac{\&PartialD;w}{\&PartialD;t}\mathrm{dxdydz\&Delta;t}---\left(9\right)$

According to formula (3)～(9), by the hexahedral law of conservation of mass of infinitesimal, can be obtained:

Q _w＝Q _x+Q _y+Q _z+Q _T+Q _h+Q _c (10)

According to the people's such as Basha research, show, at normal temperatures, the humidity that the humidity diffusion ratio that thermograde causes causes because of moist gradient spreads wants slow three orders of magnitude, therefore, and Q _tcan ignore.

If under supposition starting condition, the humidity coefficient of diffusion of concrete all directions is identical,

D _x(w)=D _y(w)=D _z(w)=D (w), and to establish concrete initial water content be w _s0, concrete humidity θ=w/w _s0, bringing formula (3)～(9) into formula (10) rear arrangement can obtain:

$\frac{\&PartialD;\mathrm{\&theta;}}{\&PartialD;t}=D\left(\mathrm{\&theta;}\right)(\frac{{\&PartialD;}^2\mathrm{\&theta;}}{{\&PartialD;x}^2}+\frac{{\&PartialD;}^2\mathrm{\&theta;}}{{\&PartialD;\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="HDA0000394148440000032.png"\; state="\{\{state\}\}">y</figure-callout>}}^2}+\frac{{\&PartialD;}^2\mathrm{\&theta;}}{{\&PartialD;z}^2})+{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_z+{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_c---\left(11\right)$

${\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_z=\frac{{\&PartialD;\mathrm{\&theta;}}_z}{\&PartialD;t},{\mathrm{\&theta;}}_z=-\frac{w_{\mathrm{<figure-callout\; id="0"\; label="z\; w\; s"\; filenames="DEST\_PATH\_HDA0000411634340000051.png,HDA0000394148440000041.png"\; state="\{\{state\}\}">z</figure-callout>}}}{w_s},{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_c=\frac{{\&PartialD;\mathrm{\&theta;}}_c}{\&PartialD;t},{\mathrm{\&theta;}}_c=-\frac{w_c}{w_{s0}}---\left(12\right)$

In formula, θ is concrete humidity, θ=w/w _s0, w is the water cut in concrete, w _s0for concrete initial water content, t is the age of concrete, and D (θ) is humidity coefficient of diffusion,

for concrete humidity is from reduced rate, θ _zfor concrete humidity is from reducing time-history curves, w _zrepresent that concrete humidity is from reducing amount, for concrete humidity self-propagation rate, θ _cfor concrete humidity self-propagation time-history curves, w _zrepresent concrete humidity self-propagation amount.

Formula (11) is concrete final governing equation.

(2) moisture field starting condition: suppose that xoncrete structure is saturated in initial time inside herein

w(x，y，z，0)＝1 (13)

(3) moisture field boundary condition:

The first kind: concrete surface moisture is known

w(t)＝θ _w(t) (14)

Equations of The Second Kind: the humidity variable quantity on concrete and extraneous surface in contact is known function

$-D\left(w\right)\frac{\&PartialD;\mathrm{\&theta;}}{\&PartialD;t}{=t}_w\left(t\right)---\left(15\right)$

The 3rd class: supposition is directly proportional to ambient humidity difference through moisture flow and the concrete surface humidity of concrete surface:

$-D\left(w\right)\frac{\&PartialD;\mathrm{\&theta;}}{\&PartialD;n}={\mathrm{\&beta;}}_{\mathrm{\&theta;}}\left({\mathrm{\&theta;}-\mathrm{\&theta;}}_h\right)---\left(16\right)$

β wherein _θrepresent humidity exchange coefficient, θ _hrepresent ambient humidity.

The 4th class: when concrete contacts with solid, if contact is good, humidity and humidity variable quantity are continuous

${\mathrm{\&theta;}}_1={\mathrm{\&theta;}}_2,{\mathrm{<figure-callout\; id="1"\; label="D"\; filenames="DEST\_PATH\_HDA0000411634340000051.png,HDA0000394148440000021.png"\; state="\{\{state\}\}">D</figure-callout>}}_1\frac{{\&PartialD;\mathrm{\&theta;}}_1}{\&PartialD;n}={\mathrm{<figure-callout\; id="1"\; label="D"\; filenames="DEST\_PATH\_HDA0000411634340000051.png,HDA0000394148440000021.png"\; state="\{\{state\}\}">D</figure-callout>}}_1\frac{{\&PartialD;\mathrm{\&theta;}}_2}{\&PartialD;n}---\left(17\right)$

θ wherein ₁represent first kind solid surface humidity, D ₁the humidity exchange coefficient that represents first kind solid, θ ₂represent Equations of The Second Kind solid surface humidity, D ₂the humidity exchange coefficient that represents Equations of The Second Kind solid.

2, fiber element is divided

According to the composition difference of moisture distribution difference, material in cross section and the fiber that loading characteristic carries out cross section, divide, general division rule is:

(1) concrete humidity at cross section zones of different place is different, and the calculating parameter of shrinkage and creep is different, need to divide different fiber elements according to different moisture distribution.

(2) because elastic modulus and the shrinkage and creep parameter of material are different, the concrete in cross section must be divided into different fibers from steel.Steel are divided into reinforcing bar and reinforcing bar, because reinforcing bar in cross section is more, distribute more random, and the principle that reinforcing bar can be equated with the centre of form according to area is reduced to the belt-like zone of rectangle or annular, facilitates overall calculation.

(3), for different stress forms, the simplification degree that fiber is divided is different.Axis compression member can be only by the different demarcation fiber of moisture distribution difference and material, as shown in figure (3a), for example can be according to steel, be exposed to airborne concrete and sealed concrete is divided into three fiber elements by whole cross section.Meeting under the prerequisite of axis compression member fiber division principle, eccentric compression member can be divided fiber element according to the position of eccentric force effect: as shown in figure (3b), if eccentricity pressure acts on the axis of symmetry in cross section, same material is identical perpendicular to the axial stress of symmetry, fiber element evenly can be divided along this axis of symmetry direction; As shown in figure (3c), if eccentricity pressure acts on the optional position in cross section, should cross section be divided into a plurality of fiber elements along different directions according to the shape facility in cross section, fiber element quantity is more, calculates the shrinkage and creep value simulating more accurate.In division, complete behind fibre section, should calculate area and the centre of form coordinate figure of each fiber element.

3, the elastic strain of calculating each fiber element is specially:

Under the effect of constant external force, structural elements can produce initial elastic strain, first according to fibrosis model and plane cross-section assumption, calculates the initial elasticity strain of member, and circular is as follows:

The fiber strain ε (x, y) that on each fiber element cross section, the centre of form (x, y) is located can use the elastic strain ε of cross section position of form center ₀with the curvature around cross section centre of form axle

be expressed as:

On cross section, all stress σ (x, y) caused cross section internal force and moments of flexure by fibrous bundle are tried to achieve by integration:

Wherein, N is cross section internal force, M _y, M _xbe respectively on cross section around y axle and moment of flexure around the effect of x axle, K _sfor section rigidity matrix, the area that A is fiber element:

$\begin{array}{c}{K}_s=\left[\begin{array}{ccc}\&Integral;E(x,y)\mathrm{dA}& \&Integral;E(x,y)\mathrm{xdA}& \&Integral;E(x,y)\mathrm{ydA}\\ \&Integral;E(x,y)\mathrm{xdA}& \&Integral;E(x,y)x^2\mathrm{dA}& \&Integral;E(x,y)\mathrm{xydA}\\ \&Integral;E(x,y)\mathrm{ydA}& \&Integral;E(x,y)\mathrm{xydA}& \&Integral;E(x,y){\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="HDA0000394148440000032.png"\; state="\{\{state\}\}">y</figure-callout>}}^2\mathrm{dA}\end{array}\right]\\ =\left[\begin{array}{ccc}\mathrm{\&Sigma;}{E}_i{A}_i& \mathrm{\&Sigma;}{E}_i{A}_i{x}_i& \mathrm{\&Sigma;}{E}_i{A}_i{y}_i\\ \mathrm{\&Sigma;}{E}_i{A}_i{x}_i& \mathrm{\&Sigma;}{E}_i{x_i}^2& \mathrm{\&Sigma;}{E}_i{A}_i{y}_i\\ \mathrm{\&Sigma;}{E}_i{A}_i{y}_i& \mathrm{\&Sigma;}{E}_i{A}_i{x}_i{y}_i& \mathrm{\&Sigma;}{E}_i{A}_i{y_i}^2\end{array}\right];i=1,\&CenterDot;\&CenterDot;\&CenterDot;,n\end{array}---\left(20\right)$

By matrix inversion, can obtain cross section flexibility matrix

then according to the suffered power in fiber element cross section, try to achieve the elastic strain ε in fiber element cross section ₀:

According to the elastic strain ε in fiber element cross section ₀can calculate the primary stress of fiber element: σ with the elastic modulus E of material ₀=E ε ₀.

4, calculate the shrinkage and creep value of fiber element

Suppose that fiber element is all axial compression, like this according to primary stress, just can calculate according to the formula of shrinkage and creep model the shrinkage and creep strain of fiber element.

The B3 model that shrinkage and creep model adopts Bazant to propose.B3 model formation definite conception, physical significance are clear.Through the matching check of test figure in Northwestern Univ USA's shrinkage and creep database, and compare with ACI model and CEB-FIP (1990) model, prove that its precision of prediction is the highest.Circular is as follows: B3 model is divided into elastic strain, creep strain, contraction strain by concrete strain, and creep strain comprises basic creep strain and dry creep strain.Load age is t ' time, the strain stress (t) under normal effect of stress:

ε(t)＝J(t，t′)σ+ε _sh(t) (23)

σ is axial stress, and ε (t) is strain (σ and ε to draw for just), ε _sh(t) be contraction strain (when volume reduces, being negative).

Time dependent contraction strain can limit of utilization be shunk to be multiplied by and is considered that the related coefficient of relative humidity, time effect and size effect represents:

ε _sh(t，t0)＝-ε _sh∞k _hS(t) (24)

ε _{sh ∞}for limit contraction strain, k _hfor humidity effect coefficient, S (t) is for shrinking time dependent function.

The generation of shrinking is mainly the distortion that moisture evaporation, hydrated cementitious and carbonization drying shrinkage cause, wherein hydrated cementitious and carbonization drying shrinkage can be ignored, the main drawdown deformation of paying close attention to due to moisture evaporation generation.Contraction strain is subject to concrete humidity effect larger, considers and does not consider that the contraction strain of moisture distribution differs larger.

For the distortion being caused by load, comprise elastic deformation, basic time deformation and dry time deformation, can represent with the function J that creeps (t, t '):

$J(t,t^{\&prime;})=\frac{1}{E\left(t^{\&prime;}\right)}+C_0(t,t^{\&prime;})+C_d(t,t^{\&prime;},t_0)---\left(25\right)$

for transient elastic strain compliance function, wherein E (t ') is load age concrete elastic modulus of t ' time, C ₀(t, t ') is basic crrep compliance function, C _d(t, t ', t ₀) be dry crrep compliance function.T represents the age of concrete, t ' expression concrete load age, t ₀for curing age.

Substantially creep be member under constant wet environment, construction material inside does not have moisture motion change, member itself is due to inner cement gelinite Plastic Flow, the creeping of the inner and mortar microfracture development generation of aggregate; Dry evaporation of creeping mainly due to moisture causes, and shrinks similarly, and difference is that it has considered the impact of institute's load application.Substantially creeping can be with reference to the literature content of Bazant with the specific formula for calculation of dry compliance function of creeping.By above analysis, can be found out, concrete relative humidity not only affects shrinkage value, and also has impact to a certain degree to creeping, and therefore, for the division in different humidity region in cross section, is absolutely necessary.

5, calculate the strain value of member integrated

By B3 model, calculate (comprising elastic strain and shrinkage and creep strain) after the overall strain value of each fiber element, according to the reverse strain value of deriving the global sections in cross section of the integration method of fiber model, circular is as follows:

(1) according to fiber overall strain value, calculate the virtual stress value of fiber:

represent the centre of form coordinate data of fiber element.Because comprise the strain being produced by shrinkage and creep in ε (x, y), so

necessary being not, but the virtual stress of supposing for calculated population strain.

(2) by virtual stress integration, draw the fictitious force on member section

$\left\{\begin{array}{c}\tilde{N}\\ {\tilde{M}}_y\\ {\tilde{M}}_x\end{array}\right\}=\left\{\begin{array}{c}\text{\&Integral;}\widetilde{\mathrm{\&sigma;}}(x,y)\mathrm{dA}\\ \text{\&Integral;}\widetilde{\mathrm{\&sigma;}}(x,y)\mathrm{xdA}\\ \text{\&Integral;}\widetilde{\mathrm{\&sigma;}}(x,y)\mathrm{ydA}\end{array}\right\}=\left\{\begin{array}{c}\mathrm{\&Sigma;}{\widetilde{\mathrm{\&sigma;}}}_i{A}_i\\ \mathrm{\&Sigma;}{\widetilde{\mathrm{\&sigma;}}}_i{A}_i{x}_i\\ \mathrm{\&Sigma;}{\widetilde{\mathrm{\&sigma;}}}_i{A}_i{y}_i\end{array}\right\}---\left(26\right)$

(3) according to fictitious force, calculate the strain value of fibre section:

Wherein

for cross section flexibility matrix, concrete visible (21).

With concrete member shown in Fig. 3, above-mentioned shrinkage and creep computing method are described.

1. assumed condition

Choose the huge post of exemplary position of certain super-high building structure bottom, as shown in Figure 4, carry out the shrinkage and creep of huge member under axle pressure effect calculate according to method of the present invention, for simplifying computation process, this example basic assumption condition is as follows:

(1) suppose the suffered axle pressure P=100MN of huge post, and temporal evolution not.

(2) consider that work progress successively loads the impact on shrinkage and creep, the load age of supposing member is 1 year, and member has been built after 1 year and started to load.

(3) member section form as shown in Figure 5, supposes that the outside concrete relative humidity of member is 60%, and inner sealed concrete humidity is 90%.

(4) sectional dimension of members is 5m * 3m; Reinforcing bar size: 2200 * 850 * 40 * 40 (mm); Reinforcing bar level interval: 1650mm; Steel plate vertical spacing: 1400mm; The area of reinforcement: 0.42m ².By take upper section information, can draw: steel area (reinforcing bar+area of reinforcement) is 1.14m ², inner sealed concrete area is 4.38m ², outside concrete area is 9.48m ².Humidity diffusion coefficient D=0.000001m ²/ h, the humidity coefficient of diffusion of shaped steel is 0, and the humidity exchange coefficient of concrete and air is 0.001m/h, and during concrete initial set, relative humidity is 90%, and surrounding environment relative humidity is 60%.

2. computing method

(1) member section moisture distribution simulation.According to the residing environmental baseline of member, by above-mentioned humidity analogy method, can be obtained, the moisture distribution of member section is as shown in Figure 6.

(1) divide fiber element.The in the situation that of axial compression, different according to the moisture distribution difference in cross section and material type, fiber element is divided as shown in figure (3a).

(2) calculate the elastic strain value of fiber element.Because member section is only subject to axle pressure and member section and moisture distribution symmetrical, as long as choose Unit 1/4th, calculate (unit 1-9).The elastic strain value of fiber element is:

${\mathrm{\&epsiv;}}_0=\frac{\mathrm{<figure-callout\; id="4"\; label="P"\; filenames="HDA0000394148440000021.png,HDA0000394148440000033.png"\; state="\{\{state\}\}">P</figure-callout>}}{4\underset{i=1}{\overset{8}{\mathrm{\&Sigma;}}}{E}_c{A}_{\mathrm{ci}}+E_s{A}_s}$

E wherein _c, A _cifor concrete elastic modulus and area, the modulus of elasticity of concrete here need be considered its time variation energy; E _s, A _selastic modulus and area for steel.

(3) calculate the shrinkage and creep value of fiber element.Because steel do not produce shrinkage and creep, so its shrinkage and creep value is 0.The shrinkage and creep value of calculating respectively each fiber element of considering moisture distribution according to B3 model, is respectively ε _shi, ε _cei.

(4) calculate the whole strain value in cross section.First calculate the overall strain value of each fiber element:

ε _i＝ε ₀+ε _shi+ε _cri

ε ₉＝ε ₀

Then calculate the virtual stress of each fiber element:

${\widetilde{\mathrm{\&sigma;}}}_i=E_c{\mathrm{\&epsiv;}}_i$

Next calculate the fictitious force in cross section:

$\tilde{N}=4\underset{i=1}{\overset{8}{\mathrm{\&Sigma;}}}{\widetilde{\mathrm{\&sigma;}}}_i{A}_i+{\widetilde{\mathrm{\&sigma;}}}_9{\mathrm{<figure-callout\; id="9"\; label="A"\; filenames="HDA0000394148440000021.png"\; state="\{\{state\}\}">A</figure-callout>}}_9$

A wherein _iarea of section for each fiber element.

Finally obtain the strain value of cross section integral body:

$\mathrm{\&epsiv;}=\frac{\tilde{N}}{4\underset{i=1}{\overset{8}{\mathrm{\&Sigma;}}}{E}_c{A}_{\mathrm{ci}}+E_s{A}_s}$

3. result of calculation

Calculate according to the method described above the shrinkage and creep value of huge hybrid component under axle pressure effect as shown in figure (7a)～figure (7c) and table 1-table 3.

Table 1 is considered the correction fiber model of humidity and the value of creeping of B3 model

Table 2 is considered the correction fiber model of humidity and the shrinkage value of B3 model

Table 3 is considered the correction fiber model of humidity and the overall strain value of B3 model

ε in table _c, ε _s, ε be respectively consider member section different humidity distribute resulting cross-sectional constriction, creep and overall strain value.ε ' _c, ε ' _s, ε ' is respectively and do not consider the resulting cross-sectional constriction of moisture distribution, creeps and overall strain value.

By Fig. 7 and Biao 1-3, can be found out, the contraction strain of huge combined member is subject to humidity effect larger, and still, along with the growth of the age of concrete, in concrete, moisture diffusion is tending towards even.The difference of the contraction strain that therefore, two kinds of methods calculate also can constantly reduce along with the increase in the length of time.Creep strain is subject to humidity effect less, and therefore, consideration different humidity is distributed in does not consider that the result obtaining is more or less the same.Owing to having considered the inhibition of shaped steel to humidity diffusion, vertical deformation that the fiber model algorithm based on B3 model is calculated is less than the B3 model of inhibition of not considering shaped steel.As can be seen here, vertical compression deformation impact is very important on member to consider the different moisture distribution of member section.

Claims (7)

1. huge combined member shrinkage and creep computing method of considering moisture distribution, is characterized in that, comprise the following steps:

(1), according to the residing ambient humidity of member and member condition in the length of time, obtain the moisture distribution data that member section changed with the length of time;

(2) according to the material composition in cross section, the parameter of creeping and loading characteristic, member is carried out to fiber element division, calculate the humidity situation of change at area, centre of form coordinate and the fiber element centre of form place of each fiber element;

(3) calculate the elastic strain of each fiber element;

(4) according to the elastic modulus of the elastic strain of member and material, calculate the primary stress of each fiber element, according to shrinkage and creep model, calculate the non-resilient shrinkage and creep strain of the fiber element of each different humidity distribution;

(5) according to the shrinkage and creep strain of every fiber element, calculate its virtual stress, then draw virtual internal force according to virtual stress integration, by virtual internal force, draw the strain value of member integrated.

2. a kind of huge combined member shrinkage and creep computing method of considering moisture distribution according to claim 1, is characterized in that, the moisture distribution data that described member section changed with the length of time are specially:

$\frac{\&PartialD;\mathrm{\&theta;}}{\&PartialD;t}=D\left(\mathrm{\&theta;}\right)(\frac{{\&PartialD;}^2\mathrm{\&theta;}}{{\&PartialD;x}^2}+\frac{{\&PartialD;}^2\mathrm{\&theta;}}{{\&PartialD;y}^2}+\frac{{\&PartialD;}^2\mathrm{\&theta;}}{{\&PartialD;z}^2})+{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_z+{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_c$

${\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_z=\frac{{\&PartialD;\mathrm{\&theta;}}_z}{\&PartialD;t},{\mathrm{\&theta;}}_z=-\frac{w_z}{w_{s0}},{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_c=\frac{{\&PartialD;\mathrm{\&theta;}}_c}{\&PartialD;t},{\mathrm{\&theta;}}_c=-\frac{w_c}{w_{s0}}$

In formula, θ is concrete humidity, θ=w/w _s0, w is the water cut in concrete, w _s0for concrete initial water content, t is the age of concrete, and D (θ) is humidity coefficient of diffusion, θ _zfor concrete humidity is from reduced rate, θ _zfor concrete humidity is from reducing time-history curves, w _zrepresent that concrete humidity is from reducing amount, θ _cfor concrete humidity self-propagation rate, θ _cfor concrete humidity self-propagation time-history curves, w _zrepresent concrete humidity self-propagation amount.

3. a kind of huge combined member shrinkage and creep computing method of considering moisture distribution according to claim 1, is characterized in that, the described rule that member is carried out to fiber element division is:

(1) according to different moisture distribution, divide different fiber elements;

(2) concrete in cross section is divided into different fiber elements from steel;

(3) for different stress forms, the simplification degree that fiber is divided is different: for axis compression member, by the different demarcation fiber of moisture distribution difference and material; For eccentric compression member, meeting under the prerequisite of axis compression member fiber division principle, eccentric compression member is divided fiber element according to the position of eccentric force effect: if eccentricity pressure acts on the axis of symmetry in cross section, same material is identical perpendicular to the axial stress of symmetry, and fiber element is evenly divided along this axis of symmetry direction; If eccentricity pressure acts on the optional position in cross section, according to the shape facility in cross section, cross section is divided into a plurality of fiber elements along different directions.

4. a kind of huge combined member shrinkage and creep computing method of considering moisture distribution according to claim 1, is characterized in that described step 3) in, the elastic strain of calculating each fiber element is specially:

The fiber strain ε (x, y) that on each fiber element cross section, the centre of form (x, y) is located can use the elastic strain ε of cross section position of form center ₀with the curvature around cross section centre of form axle

be expressed as:

On cross section, all stress σ (x, y) caused cross section internal force and moments of flexure by fibrous bundle are tried to achieve by integration:

Wherein, N is cross section internal force, M _y, M _xbe respectively on cross section around y axle and moment of flexure around the effect of x axle, K _sfor section rigidity matrix, the area that A is fiber element:

$\begin{array}{c}{K}_s=\left[\begin{array}{ccc}\&Integral;E(x,y)\mathrm{dA}& \&Integral;E(x,y)\mathrm{xdA}& \&Integral;E(x,y)\mathrm{ydA}\\ \&Integral;E(x,y)\mathrm{xdA}& \&Integral;E(x,y)x^2\mathrm{dA}& \&Integral;E(x,y)\mathrm{xydA}\\ \&Integral;E(x,y)\mathrm{ydA}& \&Integral;E(x,y)\mathrm{xydA}& \&Integral;E(x,y)y^2\mathrm{dA}\end{array}\right]\\ =\left[\begin{array}{ccc}\mathrm{\&Sigma;}{E}_i{A}_i& \mathrm{\&Sigma;}{E}_i{A}_i{x}_i& \mathrm{\&Sigma;}{E}_i{A}_i{y}_i\\ \mathrm{\&Sigma;}{E}_i{A}_i{x}_i& \mathrm{\&Sigma;}{E}_i{x_i}^2& \mathrm{\&Sigma;}{E}_i{A}_i{y}_i\\ \mathrm{\&Sigma;}{E}_i{A}_i{y}_i& \mathrm{\&Sigma;}{E}_i{A}_i{x}_i{y}_i& \mathrm{\&Sigma;}{E}_i{A}_i{y_i}^2\end{array}\right];i=1,\&CenterDot;\&CenterDot;\&CenterDot;,n\end{array}$

By matrix inversion, can obtain cross section flexibility matrix

then according to the suffered power in fiber element cross section, try to achieve the elastic strain ε in fiber element cross section ₀:

According to the elastic strain ε in fiber element cross section ₀can calculate the primary stress of fiber element: σ with the elastic modulus E of material ₀=E ε ₀.

5. a kind of huge combined member shrinkage and creep computing method of considering moisture distribution according to claim 1, is characterized in that described step 4) in shrinkage and creep model be B3 model.

6. a kind of huge combined member shrinkage and creep computing method of considering moisture distribution according to claim 1, is characterized in that described step 4) in calculate non-resilient shrinkage and creep strain concrete steps be:

Suppose fiber element axial compression, load age is t ' time, the strain stress (t) under normal effect of stress:

ε(t)＝J(t，t′)σ+ε _sh(t)

Wherein, σ is axial stress, ε _sh(t) be contraction strain, J (t, t ') is for creeping function;

Time dependent contraction strain limit of utilization is shunk to be multiplied by and is considered that the related coefficient of relative humidity, time effect and size effect represents:

ε _sh(t)＝-ε _sh∞k _hS(t)

ε wherein _{sh ∞}for limit contraction strain, k _hfor humidity effect coefficient, S (t) is for shrinking time dependent function; The formula of function J (t, t ') of creeping is:

$J(t,t^{\&prime;})=\frac{1}{E\left(t^{\&prime;}\right)}+C_0(t,t^{\&prime;})+C_d(t,t^{\&prime;},t_0)$

Wherein for transient elastic strain compliance function, E (t ') is load age concrete elastic modulus of t ' time, C ₀(t, t ') is basic crrep compliance function, C _d(t, t ', t ₀) be dry crrep compliance function, t represents the age of concrete, t ₀for curing age.

7. a kind of huge combined member shrinkage and creep computing method of considering moisture distribution according to claim 6, is characterized in that described step 5) in, the calculation procedure of the strain value of member integrated is specially:

(1) calculate the virtual stress value of fiber:

(2) by virtual stress integration, draw the fictitious force on member section

$\left\{\begin{array}{c}\tilde{N}\\ {\tilde{M}}_y\\ {\tilde{M}}_x\end{array}\right\}=\left\{\begin{array}{c}\text{\&Integral;}\widetilde{\mathrm{\&sigma;}}(x,y)\mathrm{dA}\\ \text{\&Integral;}\widetilde{\mathrm{\&sigma;}}(x,y)\mathrm{xdA}\\ \text{\&Integral;}\widetilde{\mathrm{\&sigma;}}(x,y)\mathrm{ydA}\end{array}\right\}=\left\{\begin{array}{c}\mathrm{\&Sigma;}{\widetilde{\mathrm{\&sigma;}}}_i{A}_i\\ \mathrm{\&Sigma;}{\widetilde{\mathrm{\&sigma;}}}_i{A}_i{x}_i\\ \mathrm{\&Sigma;}{\widetilde{\mathrm{\&sigma;}}}_i{A}_i{y}_i\end{array}\right\}$

(3) according to fictitious force, calculate the strain value of fibre section:

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