CN101988858B - Method of measuring reinforced concrete creep stress by using engineering safety monitoring rebar stressometer - Google Patents

Abstract

The invention discloses a method of computing reinforced concrete creep stress which obtains constraint factors reflecting the actual constraint status of a reinforced concrete structure according to the rebar stress actually measured by a rebar stressometer and further finding the relationship between the reinforced concrete creep stress and the rebar stress. Compared with the method of obtaining the concrete stress through complicated mathematic changes by using buried complicated strainometer and non-stressometer in the prior art, the invention has the advantages of higher accuracy and economy. The invention provides powerful reference for reflecting the status of the internal force of the composite material reinforced concrete and evaluating the safety of the reinforced concrete structure.

Description

Method according to reinforcement stresses instrumentation dimension reinforced concrete Creep Stress

Technical field

The invention provides in a kind of reinforced concrete structure according to the method for reinforcement stresses instrumentation dimension reinforced concrete Creep Stress, be applicable to reinforced concrete structure receive external force load, temperature load, autogenous volumetric deformation, creep and the drying shrinkage load under the measurement of Creep Stress.

Background technology

Reinforced concrete structure is a common structural form in the civil engineering works such as water conservancy, water power, traffic and industrial civil building; This structure is composited by reinforcing bar and two kinds of materials of concrete; Can give full play to the resistance to tension and the concrete anti-pressure ability of reinforcing bar, have advantages of high bearing capacity.Owing to be composited by reinforcing bar and concrete; The stress that reinforced concrete structure produces except receiving the external load effect; The difference of reinforcing bar and concrete calorifics and mechanical property also can cause it to produce stress, and externally environmental factor changes when greatly perhaps both performance differences are obvious, its numerical value even the stress that causes above external load; Cause concrete not bear external load and also can produce the crack, influence the security and the permanance of structure.

Stress trajectory is an effective means of understanding the reinforced concrete structure stress state; The method of this stress of observation is that the reinforcement stresses meter is set on reinforcing bar in the prior art; In concrete, bury concrete stress meter and strainometer underground; Through observing reinforcing bar and concrete stress change respectively, hold reinforcing bar and concrete stress state.The reinforcement stresses meter is buried underground simply, cost is low, but concrete stress meter and strainometer are not only buried complicacy underground, and must be unstressed meter cooperate, and change through complex mathematical and can obtain concrete stress, so, have cost height, shortcoming that precision is low.Therefore, can be only observed result through the reinforcement stresses meter directly to calculate concrete stress be that engineering technical personnel hope a problem solving.

Prior art addresses the above problem with the single influence factor angle that influences reinforced concrete structure stress from the simplification restrained condition of structure often; But facts have proved; The concrete calculated stress and the measured stress that draw like this differ bigger; Certain difficulty is caused to safety assessment in some position even the opposite phenomenon of sign occurs.Therefore, single from this respect consider can not the complete reaction structure virtual condition.

Summary of the invention

The objective of the invention is to improve deficiency of the prior art; Provide a kind of physical constraint state to start with from structure, multiple influence factor individualism such as consider external load, temperature load, autogenous volumetric deformation simultaneously and creep and when existing simultaneously by the method for reinforcement stresses instrumentation dimension reinforced concrete Creep Stress.

The objective of the invention is to realize like this:

At first consider single influence factor effect, under single influence factor, divide free state, restrained condition and the research of part restrained condition fully; On above-mentioned research basis, consider time factor again, the relation under the different affecting factors of research consideration process between reinforcement stresses and the concrete creep stress; Further research is considered the concrete creep influence down, the relation between reinforcement stresses and the concrete creep stress; Research is at last set up and to be met relational expression actual, reinforcement stresses and concrete stress when multiple factor exists simultaneously.If modulus of elasticity of concrete is E _c, concrete section is long-pending to be A _cThe reinforcing bar elastic modulus is E _s, reinforcing steel area is A _s, the suffered external constraint coefficient of structure is f, the reinforced concrete cross section is as shown in Figure 1.

One external loads

Under the outer load P effect, structural strain is ε, coordinates according to balance equation and strain, then

σ _c＝E _c·ε (1)

σ _s＝E _s·ε (2)

E _c·ε·A _c+E _s·ε·A _s＝P (3)

$\mathrm{\ϵ}=\frac{P}{E_c\·A_c+E_s\·A_s}---\left(4\right)$

So: ${\mathrm{\σ}}_c=\frac{P\·E_c}{E_c\·A_c+E_s\·A_s}=\mathrm{\ϵ}\·E_c---\left(5\right)$

${\mathrm{\σ}}_s=\frac{P\·E_s}{E_c\·A_c+E_s\·A_s}=\mathrm{\ϵ}\·E_s---\left(6\right)$

At reinforcement stresses σ _sUnder the known case, can get by formula (6):

Substitution formula (5) can get concrete stress.

Wherein: σ _cBe concrete stress;

σ _sBe the actual measurement reinforcement stresses;

ε is a reinforced concrete strain;

E _cBe modulus of elasticity of concrete;

E _sBe the reinforcing bar elastic modulus;

A _cFor concrete section amasss;

A _sBe reinforcing steel area;

P is the suffered external loads of structure.

Two temperature loads

(1) Free Transform

If thermal expansion coefficient of concrete is α _c, the reinforcing bar thermalexpansioncoefficient _sActual measurement reinforced concrete temperature variation is Δ T ℃, considers that reinforcing bar is identical with concrete deformation all not stress, then:

Concrete Free Transform: ε _c=α _cΔ T (7)

The Free Transform of reinforcing bar: ε _s=α _sΔ T (8)

Modified difference is: (α _s-α _c) Δ T (9)

If the additional deformation that concrete and reinforcing bar retrain each other is ε _Gc, then:

ε _gc(E _c·A _c+E _s·A _s)＝E _s·(α _s-α _c)·ΔT·A _s (11)

${\mathrm{\ϵ}}_{\mathrm{gc}}=\frac{E_s\·({\mathrm{\α}}_s-{\mathrm{\α}}_c)\·\mathrm{\ΔT}\·A_s}{E_c\·A_c+E_s\·A_s}---\left(12\right)$

${\mathrm{\Δ\σ}}_c=E_c\·{\mathrm{\ϵ}}_{\mathrm{gc}}=\frac{E_c\·E_s\·({\mathrm{\α}}_s-{\mathrm{\α}}_c)\·\mathrm{\ΔT}\·A_s}{E_c\·A_c+E_s\·A_s}---\left(13\right)$

$\mathrm{\Δ}{\mathrm{\σ}}_s=E_s[{\mathrm{\ϵ}}_{\mathrm{gc}}-({\mathrm{\α}}_s-{\mathrm{\α}}_c)\·\mathrm{\ΔT}]={\mathrm{\σ}}_c\·(-\frac{A_c}{A_s})=-\mathrm{\Δ}{\mathrm{\σ}}_c/{\mathrm{\λ}}_s---\left(14\right)$

Wherein: λ _sThe ratio of reinforcement for reinforced concrete;

Δ σ _sBe actual measurement reinforcement stresses increment;

Δ σ _cBe the concrete creep stress increment;

(2) full constraint

By ε _c=0 ε _s=0

σ _c＝E _c(ε _c-α _cΔT)，σ _s＝E _s(ε _s-α _sΔT)

Obtain: σ _c=-α _cΔ TE _cσ _s=-α _sΔ TE _s

(3) constraint factor is f

Draw concrete overall strain when free by formula (7)～(14):

$\mathrm{\ϵ}={\mathrm{\ϵ}}_{\mathrm{gc}}+{\mathrm{\α}}_c\·\mathrm{\ΔT}=\frac{({\mathrm{\α}}_s-{\mathrm{\α}}_c)\·\mathrm{\ΔT}\·E_s\·A_s}{E_c\·A_c+E_s\·A_s}+{\mathrm{\α}}_c\·\mathrm{\ΔT}---\left(15\right)$

When constraint factor is f:

${\mathrm{\ϵ}}_f=(1-f)\·\mathrm{\ϵ}=(1-f)\·(\frac{({\mathrm{\α}}_s-{\mathrm{\α}}_c)\·\mathrm{\ΔT}\·E_s\·A_s}{E_c\·A_c+E_s\·A_s}+{\mathrm{\α}}_c\·\mathrm{\ΔT})$

$\mathrm{\Δ}{\mathrm{\σ}}_c=E_c\·({\mathrm{\ϵ}}_f-{\mathrm{\α}}_c\·\mathrm{\ΔT})=((1-f)\·(\frac{({\mathrm{\α}}_s-{\mathrm{\α}}_c)\·\mathrm{\ΔT}\·E_s\·A_s}{E_c\·A_c+E_s\·A_s}+{\mathrm{\α}}_c\·\mathrm{\ΔT})-{\mathrm{\α}}_c\·\mathrm{\ΔT})\·E_c$

$=(1-f)\·\left(\frac{({\mathrm{\α}}_s-{\mathrm{\α}}_c)\·\mathrm{\ΔT}\·E_c\·E_s\·A_s}{E_c\·A_c+E_s\·A_s}\right)-f\·{\mathrm{\α}}_c\·\mathrm{\ΔT}\·E_c---\left(16\right)$

$\mathrm{\Δ}{\mathrm{\σ}}_s=-(1-f)\·\left(\frac{({\mathrm{\α}}_s-{\mathrm{\α}}_c)\·\mathrm{\ΔT}\·E_c\·E_s\·A_c}{E_c\·A_c+E_s\·A_s}\right)-f\·{\mathrm{\α}}_s\·\mathrm{\ΔT}\·E_s---\left(17\right)$

In the engineering reality, Δ σ _sCan record, it is following to obtain constraint factor f according to formula (17):

$f=\frac{(E_c\·A_c+E_s\·A_s)\·\mathrm{\Δ}{\mathrm{\σ}}_s+({\mathrm{\α}}_s-{\mathrm{\α}}_c)\·\mathrm{\ΔT}\·E_c\·E_s\·A_c}{-{\mathrm{\α}}_c\·\mathrm{\ΔT}\·E_c\·E_s\·A_c-{\mathrm{\α}}_s\·\mathrm{\ΔT}\·E_s\·E_s\·A_s}---\left(18\right)$

Can get concrete stress increment Delta σ to f substitution (16) formula _c

Three autogenous volumetric deformations or drying shrinkage

(1) free fully

Suppose that reinforced concrete structure does not have constraint, can Free Transform, concrete autogenous volumetric deformation is ε ₀, the stressed F of concrete _c, reinforcing steel bar bear F _s

Self-equilibrating equation according to the cross section: F _c+ F _s=0 (19)

And F _c=σ _cA _cF _s=σ _sA _s

If retraining the reinforcing bar additional strain that causes each other is ε _s, then:

σ _c＝ε _c·E _c σ _s＝ε _s·E _s

According to deformation compatibility condition: ε _c=ε _s-ε ₀(20)

Various getting: E more than the associating _c(ε _s--ε ₀) A _c+ E _sε _sA _s=0 (21)

${\mathrm{\ϵ}}_s=\frac{E_c\·{\mathrm{\ϵ}}_0\·A_c}{E_c\·A_c+E_s\·A_s}=\frac{E_c\·{\mathrm{\ϵ}}_0}{E_c+\frac{E_s\·A_s}{A_c}}$

If

Be the ratio of reinforcement, ${\mathrm{\ϵ}}_s=\frac{E_c\·{\mathrm{\ϵ}}_0}{E_c+E_s\·{\mathrm{\λ}}_s}---\left(22\right)$

So ${\mathrm{\σ}}_s={\mathrm{\ϵ}}_s\·E_s=\frac{E_c\·E_s\·{\mathrm{\ϵ}}_0}{E_c+E_s\·{\mathrm{\λ}}_s}---\left(23\right)$

${\mathrm{\σ}}_c=-{\mathrm{\σ}}_s\·\frac{A_s}{A_c}=-{\mathrm{\σ}}_s\·{\mathrm{\λ}}_s---\left(24\right)$

Retrain the concrete strain that causes each other:

(2) full constraint

By ε _c=0 ε _s=0

Get σ _c=E _c(ε _c-ε ₀The ε of)=- ₀E _cσ _s=ε _sE _s=0

(3) constraint factor is f

Concrete overall strain when free:

$\mathrm{\ϵ}={\mathrm{\ϵ}}_c+{\mathrm{\ϵ}}_0=\frac{-E_s\·{\mathrm{\ϵ}}_0\·A_s}{E_c\·A_c+E_s\·A_s}+{\mathrm{\ϵ}}_0---\left(25\right)$

When constraint factor is f:

${\mathrm{\ϵ}}_f=(1-f)\·\mathrm{\ϵ}=(1-f)\·(\frac{-E_s\·{\mathrm{\ϵ}}_0\·A_s}{E_c\·A_c+E_s\·A_s}+{\mathrm{\ϵ}}_0)$

${\mathrm{\σ}}_c=E_c\·({\mathrm{\ϵ}}_f-{\mathrm{\ϵ}}_0)=E_c\·((1-f)\·(\frac{-E_s\·{\mathrm{\ϵ}}_0\·A_s}{E_c\·A_c+E_s\·A_s}+{\mathrm{\ϵ}}_0)-{\mathrm{\ϵ}}_0)$

$=(1-f)\·\frac{-E_s\·E_c\·{\mathrm{\ϵ}}_0\·A_s}{E_c\·A_c+E_s\·A_s}-f\·{\mathrm{\ϵ}}_0\·E_c---\left(26\right)$

${\mathrm{\σ}}_s=E_s\·({\mathrm{\ϵ}}_f-0)=E_s\·(1-f)\·(\frac{-E_s\·{\mathrm{\ϵ}}_0\·A_s}{E_c\·A_c+E_s\·A_s}+{\mathrm{\ϵ}}_0)$

$=(1-f)\·\frac{E_s\·E_c\·{\mathrm{\ϵ}}_0\·A_c}{E_c\·A_c+E_s\·A_s}---\left(27\right)$

In the engineering reality, σ _sCan record, it is following to obtain constraint factor f according to formula (27):

$f=\frac{E_c\·E_s\·A_c\·{\mathrm{\ϵ}}_0-(E_c\·A_c+E_s\·A_s)\·{\mathrm{\σ}}_s}{E_c\·E_s\·A_c\·{\mathrm{\ϵ}}_0}---\left(28\right)$

Can get σ to f substitution (26) formula _c

When autogenous volumetric deformation is increment Delta ε ₀The time, with the ε in the formula (26) (28) ₀, σ _sAnd σ _cChange Δ ε into ₀, Δ σ _sWith Δ σ _cCan obtain the stress increment that incremental deformation causes.Autogenous volumetric deformation can obtain according to the measuring and calculating of concrete test related specifications, perhaps can obtain through autogenous volumetric deformation measuring apparatus.

Stress when four account temperature, autogenous volumetric deformation and loading procedure

Generally speaking, temperature, autogenous volumetric deformation, load all are processes, are the integrated value of 0～t each factor stress in the period at t stress value constantly, that is:

${\mathrm{\σ}}_s\left(t\right)=\underset{0}{\overset{t}{\∫}}d{\mathrm{\σ}}_s---\left(29\right)$

Can limit of integration 0～t be divided into the summation of N part:

${\mathrm{\σ}}_s\left(t\right)\underset{i=1}{\overset{N}{\mathrm{\Σ}}}\mathrm{\Δ}{\mathrm{\σ}}_{\mathrm{si}}\left(\mathrm{\τ}\right)\mathrm{N\Δ\τ}=t---\left(30\right)$

${\mathrm{\σ}}_c\left(t\right)=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\Δ\σ}}_{\mathrm{ci}}\left(\mathrm{\τ}\right)$

Δσ _si(τ)＝Δσ _si ^T(τ)+Δσ _si ^z(τ)

Δσ _ci(τ)＝Δσ _ci ^T(τ)+Δσ _ci ^z(τ)

$\mathrm{\Δ}{{\mathrm{\σ}}_{\mathrm{ci}}}^T\left(\mathrm{\τ}\right)=(1-f\left(\mathrm{\τ}\right))\·\left(\frac{({\mathrm{\α}}_s-{\mathrm{\α}}_c)\·\mathrm{\ΔT}\left(\mathrm{\τ}\right)\·E_c\left(\mathrm{\τ}\right)\·E_s\·A_s}{E_c\left(\mathrm{\τ}\right)\·A_c+E_s\·A_s}\right)-f\left(\mathrm{\τ}\right)\·{\mathrm{\α}}_c\·\mathrm{\ΔT}\left(\mathrm{\τ}\right)\·E_c\left(\mathrm{\τ}\right)---\left(31\right)$

$\mathrm{\Δ}{{\mathrm{\σ}}_{\mathrm{si}}}^T\left(\mathrm{\τ}\right)=-(1-f\left(\mathrm{\τ}\right))\·\left(\frac{({\mathrm{\α}}_s-{\mathrm{\α}}_c)\·\mathrm{\ΔT}\left(\mathrm{\τ}\right)\·E_c\left(\mathrm{\τ}\right)\·E_s\·A_c}{E_c\left(\mathrm{\τ}\right)\·A_c+E_s\·A_s}\right)-f\left(\mathrm{\τ}\right)\·{\mathrm{\α}}_s\·\mathrm{\ΔT}\left(\mathrm{\τ}\right)\·E_s\left(\mathrm{\τ}\right)---\left(32\right)$

${{\mathrm{\Δ\σ}}_{\mathrm{ci}}}^z\left(\mathrm{\τ}\right)=(1-f\left(\mathrm{\τ}\right))\·\frac{-E_s\·E_c\left(\mathrm{\τ}\right)\·\mathrm{\Δ}{\mathrm{\ϵ}}_0\left(\mathrm{\τ}\right)\·A_s}{E_c\left(\mathrm{\τ}\right)\·A_c+E_s\·A_s}-f\left(\mathrm{\τ}\right)\·\mathrm{\Δ}{\mathrm{\ϵ}}_0\left(\mathrm{\τ}\right)\·E_c\left(\mathrm{\τ}\right)---\left(33\right)$

${{\mathrm{\Δ\σ}}_{\mathrm{si}}}^z\left(\mathrm{\τ}\right)=(1-f\left(\mathrm{\τ}\right))\·\frac{E_s\·E_c\left(\mathrm{\τ}\right)\·\mathrm{\Δ}{\mathrm{\ϵ}}_0\left(\mathrm{\τ}\right)\·A_c}{E_c\left(\mathrm{\τ}\right)\·A_c+E_s\·A_s}---\left(34\right)$

In the formula: E _c(τ) be the elastic modulus of length of time during τ, τ=n Δ τ; F (τ) is the constraint factor of length of time during τ.

Δ σ _Ci ^T(τ), Δ σ _Ci ^z(τ), Δ σ _Si ^T(τ), Δ σ _Si ^zThe stress increment that (τ) causes for the temperature in the i period and autogenous volumetric deformation;

Δ T (τ) and Δ ε ₀(τ) be interior temperature variation and autogenous volumetric deformation of i period, the stress increment that external load causes is considered more rationally effectively as reinforcement stresses.

Five influences of creeping

Creeping is a concrete critical nature; Concrete stress is lax under the effects of creep; Stress reallocation between concrete and the reinforcing bar; Allocation scheme is relevant with load form, the stress that is produced by temperature variation, strain variation and under effects of creep, reallocate different by the stress that external load produces.

(1) coefficient of relaxation

The calculating that creeping influences adopts explicit solution to derive, and concrete creep degree is expressed with following formula:

$C(t,\mathrm{\&tau;})=(A_1+A_2{\mathrm{\&tau;}}^{-{\mathrm{\&alpha;}}_1})(1-e^{-k_1(t-\mathrm{\&tau;})})+({\mathrm{<figure-callout\; id="1"\; label="B"\; filenames="HSA00000109844500041.png,HSA00000109844500051.png"\; state="\{\{state\}\}">B</figure-callout>}}_1+{\mathrm{<figure-callout\; id="2"\; label="B"\; filenames="HSA00000109844500013.png,HSA00000109844500041.png"\; state="\{\{state\}\}">B</figure-callout>}}_2{\mathrm{\&tau;}}^{-{\mathrm{\&alpha;}}_2})(1-e^{-k_2(t-\mathrm{\&tau;})})+D{e}^{-k_{3}t}(1-e^{-k_3(t-\mathrm{\&tau;})})---\left(35\right)$

In the formula: t is that concrete is from the time that is poured into calculation time;

Age of concrete when τ is loading;

K1, k2, k3 is the rate parameter of creeping, and obtains according to material test, immeasurable firm number;

α 1, α 2, A1, A2, B1, B2, D are the creep degree parameter, obtain according to material test,

If φ (t, τ)=E (τ) C (t, τ), then coefficient of relaxation is to be the exponential formula at the end with e:

$K(t,\mathrm{\&tau;})=e^{-a\&CenterDot;\mathrm{\&phi;}{(t,\mathrm{\&tau;})}^b}---\left(36\right)$

In the formula: a, the desirable a=0.72 of b～0.80, b=0.85

Then at τ in the length of time ₀The stress Δ σ (τ that loading causes ₀) can use computes to t stress constantly

Δσ(t，τ ₀)＝Δσ(τ ₀)·K(t，τ ₀)(37)

In the formula, Δ σ (t, τ ₀) be at τ in the length of time ₀The stress process reallocation back that loading causes is at t stress constantly.

(2) temperature stress

Temperature stress during Free Transform

Being located at τ moment temperature variation is Δ T (τ), causes that concrete and reinforcement stresses are respectively:

$\mathrm{\&Delta;}{{\mathrm{\&sigma;}}_s}^T\left(\mathrm{\&tau;}\right)=-\frac{({\mathrm{\&alpha;}}_s-{\mathrm{\&alpha;}}_c)\&CenterDot;\mathrm{\&Delta;T}\left(\mathrm{\&tau;}\right)\&CenterDot;E_c\left(\mathrm{\&tau;}\right)\&CenterDot;E_s\&CenterDot;A_c}{E_c\left(\mathrm{\&tau;}\right)\&CenterDot;A_c+E_s\&CenterDot;A_s}$

$\mathrm{\&Delta;}{{\mathrm{\&sigma;}}_c}^T\left(\mathrm{\&tau;}\right)=\frac{({\mathrm{\&alpha;}}_s-{\mathrm{\&alpha;}}_c)\&CenterDot;\mathrm{\&Delta;T}\left(\mathrm{\&tau;}\right)\&CenterDot;E_c\left(\mathrm{\&tau;}\right)\&CenterDot;E_s\&CenterDot;A_s}{E_c\left(\mathrm{\&tau;}\right)\&CenterDot;A_c+E_s\&CenterDot;A_s}$

During to t, concrete is because lax becoming:

Δσ _c ^T(t，τ)＝Δσ _c ^T(τ)·K(t，τ) (38)

Can get by equilibrium condition $\mathrm{\&Delta;}{{\mathrm{\&sigma;}}_s}^T(t,\mathrm{\&tau;})=\mathrm{\&Delta;}{{\mathrm{\&sigma;}}_c}^T\left(\mathrm{\&tau;}\right)\&CenterDot;(-\frac{A_c}{A_s})---\left(39\right)$

When constraint factor is f (τ)

During to t, concrete is because lax becoming:

$\mathrm{\&Delta;}{{\mathrm{\&sigma;}}_c}^T(t,\mathrm{\&tau;})=\mathrm{\&Delta;}{{\mathrm{\&sigma;}}_c}^T\left(\mathrm{\&tau;}\right)\&CenterDot;K(t,\mathrm{\&tau;})$

$=[(1-f\left(\mathrm{\&tau;}\right))\&CenterDot;\left(\frac{({\mathrm{\&alpha;}}_s-{\mathrm{\&alpha;}}_c)\&CenterDot;\mathrm{\&Delta;T}\left(\mathrm{\&tau;}\right)\&CenterDot;E_c\left(\mathrm{\&tau;}\right)\&CenterDot;E_s\&CenterDot;A_s}{E_c\left(\mathrm{\&tau;}\right)\&CenterDot;A_c+E_s\&CenterDot;A_s}\right)-f\left(\mathrm{\&tau;}\right)\&CenterDot;{\mathrm{\&alpha;}}_c\&CenterDot;\mathrm{\&Delta;T}\left(\mathrm{\&tau;}\right)\&CenterDot;E_c\left(\mathrm{\&tau;}\right)]\&CenterDot;K(t,\mathrm{\&tau;})---\left(40\right)$

Reinforcement stresses becomes:

$\mathrm{\&Delta;}{{\mathrm{\&sigma;}}_s}^T(t,\mathrm{\&tau;})=-(1-f\left(\mathrm{\&tau;}\right))\&CenterDot;\left(\frac{({\mathrm{\&alpha;}}_s-{\mathrm{\&alpha;}}_c)\&CenterDot;\mathrm{\&Delta;T}\left(\mathrm{\&tau;}\right)\&CenterDot;E_c\left(\mathrm{\&tau;}\right)\&CenterDot;E_s\&CenterDot;A_c}{E_c\left(\mathrm{\&tau;}\right)\&CenterDot;A_c+E_s\&CenterDot;A_s}\right)\&CenterDot;K(t,\mathrm{\&tau;})-f\left(\mathrm{\&tau;}\right)\&CenterDot;{\mathrm{\&alpha;}}_s\&CenterDot;\mathrm{\&Delta;T}\left(\mathrm{\&tau;}\right)\&CenterDot;E_s---\left(41\right)$

(3) during load action because the concrete stress transfer of creeping and causing

Apply external load Δ p the length of time at T, concrete that causes and reinforcement stresses are respectively Δ σ _c ^p(τ) with Δ σ _s ^p(τ), satisfy:

A _sΔ σ _s ^p(τ)+A _cΔ σ _c ^p(τ)=Δ p, then

Constantly concrete stress is lax and reduce to t, and then reinforcement stresses increases,

So satisfy equilibrium condition and ratio stress relation, that is:

$\mathrm{\&Delta;}{{\mathrm{\&sigma;}}_c}^p(t,\mathrm{\&tau;})=\frac{E_c\left(\mathrm{\&tau;}\right)}{E_s}\&CenterDot;K(t,\mathrm{\&tau;})\&CenterDot;\mathrm{\&Delta;}{{\mathrm{\&sigma;}}_s}^p(t,\mathrm{\&tau;})---\left(42\right)$

(4) total stress when account temperature, autogenous volumetric deformation and stress relaxation simultaneously

${\mathrm{\&sigma;}}_c\left(t\right)=\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}\mathrm{\&Delta;}{{\mathrm{\&sigma;}}_{\mathrm{ci}}}^T(t,\mathrm{\&tau;})+\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}\mathrm{\&Delta;}{{\mathrm{\&sigma;}}_{\mathrm{ci}}}^Z(t,\mathrm{\&tau;})---\left(43\right)$

${\mathrm{\&sigma;}}_s\left(t\right)=\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}\mathrm{\&Delta;}{{\mathrm{\&sigma;}}_{\mathrm{si}}}^T(t,\mathrm{\&tau;})+\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}\mathrm{\&Delta;}{{\mathrm{\&sigma;}}_{\mathrm{si}}}^Z(t,\mathrm{\&tau;})---\left(44\right)$

That is: ${\mathrm{\&sigma;}}_c\left(t\right)=\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}\mathrm{\&Delta;}{{\mathrm{\&sigma;}}_{\mathrm{Ci}}}^T\left(\mathrm{\&tau;}\right)\&CenterDot;K(t,\mathrm{\&tau;})+\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}\mathrm{\&Delta;}{{\mathrm{\&sigma;}}_{\mathrm{Ci}}}^Z\left(\mathrm{\&tau;}\right)\&CenterDot;K(t,\mathrm{\&tau;})$

${\mathrm{\&sigma;}}_s\left(t\right)=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\mathrm{\&Delta;}{{\mathrm{\&sigma;}}_{\mathrm{si}}}^T\left(\mathrm{\&tau;}\right)\&CenterDot;K(t,\mathrm{\&tau;})+\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\mathrm{\&Delta;}{{\mathrm{\&sigma;}}_{\mathrm{si}}}^Z\left(\mathrm{\&tau;}\right)\&CenterDot;K(t,\mathrm{\&tau;})$

Wherein, Δ σ _Ci ^T(τ), Δ σ _Ci ^Z(τ) see formula (31), (33);

Δ σ _Si ^T(τ), Δ σ _Si ^Z(τ) see formula (32), (34);

(t τ) sees formula (36) to K.

The relation of six reinforcement stresseses and concrete stress

Target of the present invention is according to reinforcement stresses instrumentation amount concrete creep stress, supposes to have drawn a part reinforcement stresses process: σ with the reinforcement stresses meter _s(t), how to ask σ according to as above deriving _c(t)

Wherein known:

E ₀Be concrete final elastic modulus

$C(t,\mathrm{\&tau;})=(A_1+A_2{\mathrm{\&tau;}}^{-{\mathrm{\&alpha;}}_1})(1-e^{-k_1(t-\mathrm{\&tau;})})+({\mathrm{<figure-callout\; id="1"\; label="B"\; filenames="HSA00000109844500041.png,HSA00000109844500051.png"\; state="\{\{state\}\}">B</figure-callout>}}_1+{\mathrm{<figure-callout\; id="2"\; label="B"\; filenames="HSA00000109844500013.png,HSA00000109844500041.png"\; state="\{\{state\}\}">B</figure-callout>}}_2{\mathrm{\&tau;}}^{-{\mathrm{\&alpha;}}_2})(1-e^{-k_2(t-\mathrm{\&tau;})})+D{e}^{-k_{3}t}(1-e^{-k_3(t-\mathrm{\&tau;})})$

Observed temperature changes T (τ), actual measurement autogenous volumetric deformation ε _z(τ), concrete and reinforcing bar thermal expansivity are α _cAnd α _s, ask σ _c(t)

If the structural constraint coefficient is f, the reinforcement stresses that temperature variation causes is σ _s ^T(t), the reinforcement stresses that causes of autogenous volumetric deformation is σ _s ^Z(t),

Then:

σ _s(t)＝σ _s ^T(t)+σ _s ^Z(t) (45)

${{\mathrm{\&sigma;}}_s}^T\left(t\right)=-(1-f)\&CenterDot;\left(\frac{({\mathrm{\&alpha;}}_s-{\mathrm{\&alpha;}}_c)\&CenterDot;\mathrm{\&Delta;T}\&CenterDot;E_c\&CenterDot;E_s\&CenterDot;A_c}{E_c\&CenterDot;A_c+E_s\&CenterDot;A_s}\right)-f\&CenterDot;{\mathrm{\&alpha;}}_s\&CenterDot;\mathrm{\&Delta;T}\&CenterDot;E_s---\left(46\right)$

${{\mathrm{\&sigma;}}_s}^Z\left(t\right)=(1-f)\&CenterDot;\frac{E_s\&CenterDot;E_c\&CenterDot;{\mathrm{\&epsiv;}}_0\&CenterDot;A_c}{E_c\&CenterDot;A_c+E_s\&CenterDot;A_s}---\left(47\right)$

Bring formula (46), (47) into (45), merge and to put in order:

$f=\frac{[{\mathrm{\&epsiv;}}_0-({\mathrm{\&alpha;}}_s-{\mathrm{\&alpha;}}_c)\&CenterDot;\mathrm{\&Delta;T}]\&CenterDot;E_c\&CenterDot;E_s\&CenterDot;A_c-(E_c\&CenterDot;A_c+E_s\&CenterDot;A_s)\&CenterDot;{\mathrm{\&sigma;}}_s\left(t\right)}{({\mathrm{\&alpha;}}_c\&CenterDot;\mathrm{\&Delta;T}+{\mathrm{\&epsiv;}}_0)\&CenterDot;E_c\&CenterDot;E_s\&CenterDot;A_c+{\mathrm{\&alpha;}}_s\&CenterDot;\mathrm{\&Delta;T}\&CenterDot;E_s\&CenterDot;E_s\&CenterDot;A_s}---\left(48\right)$

Constraint factor f (16) and (26) formula of bringing into is got:

$\mathrm{\&Delta;}{{\mathrm{\&sigma;}}_{\mathrm{ci}}}^T\left(\mathrm{\&tau;}\right)=(1-f)\&CenterDot;\left(\frac{({\mathrm{\&alpha;}}_s-{\mathrm{\&alpha;}}_c)\&CenterDot;\mathrm{\&Delta;T}\left(\mathrm{\&tau;}\right)\&CenterDot;E_c\left(\mathrm{\&tau;}\right)\&CenterDot;E_s\&CenterDot;A_s}{E_c\left(\mathrm{\&tau;}\right)\&CenterDot;A_c+E_s\&CenterDot;A_s}\right)-f\&CenterDot;{\mathrm{\&alpha;}}_c\&CenterDot;\mathrm{\&Delta;T}\left(\mathrm{\&tau;}\right)\&CenterDot;E_c\left(\mathrm{\&tau;}\right)---\left(49\right)$

${{\mathrm{\&Delta;\&sigma;}}_{\mathrm{ci}}}^z\left(\mathrm{\&tau;}\right)=(1-f)\&CenterDot;\frac{-E_s\&CenterDot;E_c\left(\mathrm{\&tau;}\right)\&CenterDot;\mathrm{\&Delta;}{\mathrm{\&epsiv;}}_0\left(\mathrm{\&tau;}\right)\&CenterDot;A_s}{E_c\left(\mathrm{\&tau;}\right)\&CenterDot;A_c+E_s\&CenterDot;A_s}-f\&CenterDot;\mathrm{\&Delta;}{\mathrm{\&epsiv;}}_0\left(\mathrm{\&tau;}\right)\&CenterDot;E_c\left(\mathrm{\&tau;}\right)---\left(50\right)$

Consider concrete creeping

${\mathrm{\&sigma;}}_c^T\left(t\right)=\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}\mathrm{\&Delta;}{{\mathrm{\&sigma;}}_{\mathrm{ci}}}^T\left(\mathrm{\&tau;}\right)\&CenterDot;K(t,\mathrm{\&tau;})---\left(51\right)$

${\mathrm{\&sigma;}}_c^Z\left(t\right)=\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}\mathrm{\&Delta;}{{\mathrm{\&sigma;}}_{\mathrm{ci}}}^Z\left(\mathrm{\&tau;}\right)\&CenterDot;K(t,\mathrm{\&tau;})---\left(52\right)$

Can release concrete stress is: σ _c(t)=σ _c ^T(t)+σ _c ^Z(t) (53)

Therefore in the engineering reality, the influence of external force load mainly is to be born by reinforcing bar, considers the influence of external force load in the reinforcement stresses and goes, and revealing its influence to concrete stress with the form body of reinforcement stresses is fully reasonably; In general, the reinforced concrete structure under the free fully and complete restrained condition is seldom, and the overwhelming majority is to be under the part restrained condition, and therefore, constraint factor just becomes the key of being inquired into concrete creep stress by the reinforcement stresses meter.The present invention carries it into described formula and calculates said constraint factor, and then calculate the Creep Stress of reinforced concrete through said formula through the reinforcement stresses of the reinforcing bar that is provided with in the reinforcing bar meter actual measurement concrete.Very approaching under the Creep Stress of the reinforced concrete that this method draws and the kindred circumstances through the result of calculation of using ripe emulated computation method.But this method is very simple.

Description of drawings

Below in conjunction with accompanying drawing the present invention is described further.

Fig. 1 is the simple synoptic diagram of reinforced concrete structure xsect;

Fig. 2 reinforced concrete simple-supported beam model one

Fig. 3 reinforced concrete simple-supported beam model two

Fig. 4 load and the different elevations of the different cross section place concrete stress graph of creeping and causing

Fig. 5 external load, temperature and the different elevations of the different cross section place concrete stress graph of creeping and causing

Fig. 6 Reinforced Concrete Model three

The different elevations of the different cross section that Fig. 7 temperature variation causes place concrete stress

Fig. 8 Reinforced Concrete Model four

The different elevations of the different cross section that Fig. 9 autogenous volumetric deformation causes place concrete stress

Figure 10 test specimen instrument layout figure

Figure 11 simulation calculation grid

Figure 121 # specimen test and simulation calculation stress path line

Figure 132 # specimen test and simulation calculation stress path line

Figure 143 # specimen test and simulation calculation stress path line

Figure 154 # specimen test and simulation calculation stress path line

Figure 16 is the sharp hinge of its seawater of Pu just---the Hongdong of overflowing

Figure 17 is the sharp hinge of its seawater of Pu just---the Hongdong section overflows

Figure 18 Simulation Calculation

Figure 19 reinforcing bar distributes

Figure 20 reinforcement stresses correlation curve

Figure 21 concrete stress correlation curve

Embodiment

For the actual measurement reinforcement stresses of front foundation and the relational expression between the concrete creep stress; In order to verify its correctness, rationality and validity; The present invention influences parameter and different angles are verified from different: set up a large amount of models and carried out finite element simulation and calculate checking; Made the reinforced concrete test block checking that makes an experiment, carried out actual engineering verification in conjunction with the measured data of actual engineering.

Application examples 1

Get a free beam, length * wide * height=3.0m * 0.5m * 0.5m, two ends receive evenly load, and model is seen shown in Figure 2, the single steel bar area A _s=0.0021m ², the reinforcing bar elastic modulus E _s=2.06 * 10 ⁵MPa, modulus of elasticity of concrete E _c=3.65 * 10 ⁴MPa.The research outer load is made reinforcing bar and the concrete stress Changing Pattern of time spent, verifies the rationality of formula (5), (6), and finite element simulation calculates and adopts saptis finite element software series, down together.Concrete under the different ratios of reinforcement and load action and reinforcement stresses see the following form 1 with table 2.

${\mathrm{\&sigma;}}_c=\frac{P\&CenterDot;E_c}{E_c\&CenterDot;A_c+E_s\&CenterDot;A_s}=\mathrm{\&epsiv;}\&CenterDot;E_c---\left(5\right)$

${\mathrm{\&sigma;}}_s=\frac{P\&CenterDot;E_s}{E_c\&CenterDot;A_c+E_s\&CenterDot;A_s}=\mathrm{\&epsiv;}\&CenterDot;E_s---\left(6\right)$

At reinforcement stresses σ _sUnder the known case, can get by formula (6):

Substitution formula (5) can get concrete stress.

Wherein: σ _cBe concrete stress, σ _sBe reinforcement stresses, E _cBe modulus of elasticity of concrete, E _sBe reinforcing bar elastic modulus, A _cLong-pending for concrete section, ε is a reinforced concrete strain, A _sBe reinforcing steel area, P is an external loads.

Reinforcing bar and concrete stress (unit: MPa) when table 1 ratio of reinforcement 3.4%, different load

Annotate: the ratio of reinforcement is meant the ratio of the area of reinforcement and concrete area, i.e. A _s/ A _c, down together.

Reinforcing bar and concrete stress (unit: MPa) when table 2 ratio of reinforcement 0.84%, different load

Can find out according to top result of calculation; Formula calculates reinforcement stresses and finite element simulation calculating reinforcement stresses is very approaching; The concrete creep stress error that draws according to both is also very little; Therefore, it is rationally effective that formula calculates concrete creep stress, and the reinforcement stresses that finite element simulation calculates can be used as a kind of effective way of inquiring into concrete creep stress.

Application examples 2

Get another free beam, length * wide * height=10.0m * 2.0m * 2.0m, span centre receives vertical load, and model is seen shown in Figure 3, the same example of the characterisitic parameter of reinforcing bar.Can find out that by application examples 1 under the condition of not surveying reinforcement stresses, finite element simulation calculates reinforcement stresses and also can be used as the method for inquiring into concrete creep stress.The calculated value and the simulation calculation value of formula (5), (6) are seen shown in the table 3.

${\mathrm{\&sigma;}}_c=\frac{P\&CenterDot;E_c}{E_c\&CenterDot;A_c+E_s\&CenterDot;A_s}---\left(5\right)$

${\mathrm{\&sigma;}}_s=\frac{P\&CenterDot;E_s}{E_c\&CenterDot;A_c+E_s\&CenterDot;A_s}---\left(6\right)$

Wherein: σ _cBe concrete stress, σ _sBe reinforcement stresses, E _cBe modulus of elasticity of concrete, E _sBe reinforcing bar elastic modulus, A _cFor concrete section amasss, A _sBe reinforcing steel area, P is an external loads.

Table 3 is apart from the reinforcing bar and the concrete stress (unit: MPa) at differing heights place, beam bottom

Annotate: x is the distance apart from beam end, and z is the distance apart from the beam bottom.

Can find out from last table result of calculation; Near the constraint of structure and load; Formula calculating concrete creep stress and simulation calculation concrete stress error are very little, and reinforcement stresses and the concrete creep stress of deriving thus can reflect the stress state and the mechanical characteristic of free beam well.

Application examples 3

Change model two into the two ends evenly load, consider the rationality of formula (42) when concrete creep influences under the effect of checking external load.The concrete creep process is shown in the following formula:

$C(t,\mathrm{\&tau;})=(2.5\&times;{10}^{-8}+\frac{2.0\&times;{10}^{-6}}{\mathrm{\&tau;}})(1-e^{-0.3(t-\mathrm{\&tau;})})+(7.0\&times;{10}^{-8}+\frac{5.0\&times;{10}^{-7}}{\mathrm{\&tau;}})(1-e^{-0.005(t-\mathrm{\&tau;})})$

φ (t, τ)=EC (t, τ), coefficient of relaxation then:

$K(t,\mathrm{\&tau;})=e^{-a\&CenterDot;\mathrm{\&phi;}{(t,\mathrm{\&tau;})}^b}$

In the formula: a, b get a=0.78, b=0.80, and load age is 10d.

$\mathrm{\&Delta;}{{\mathrm{\&sigma;}}_c}^p(t,\mathrm{\&tau;})=\frac{E_c\left(\mathrm{\&tau;}\right)}{E_s}\&CenterDot;K(t,\mathrm{\&tau;})\&CenterDot;\mathrm{\&Delta;}{{\mathrm{\&sigma;}}_s}^p(t,\mathrm{\&tau;})---\left(42\right)$

The reinforcement stresses that the reinforcement stresses of this model calculates with finite element simulation is as known conditions.Table 4 is seen in should creep power and the contrast of simulation calculation stress of concrete when deriving on the different cross section apart from different length of time of concrete bottom differing heights according to reinforcement stresses and formula (42), and load is seen Fig. 4 with the different elevations of the different cross section place concrete stress graph that causes of creeping.Result of calculation shows that because the existence of creeping, As time goes on stress relaxation constantly takes place concrete, and stress transfer and heavily distribution take place.The concrete creep stress that concrete creep stress that formula calculates and FEM calculation go out is very approaching, can reflect the stress state and the mechanical characteristic of this structure well.

Application examples 4

Account temperature changes on the basis of model two, considers simultaneously to creep to its influence, and according to formula (40)～(41), external load and temperature variation occur in 10d in the length of time, and the concrete creep process adopts following formula:

$C(t,\mathrm{\&tau;})=(2.5\&times;{10}^{-8}+\frac{2.0\&times;{10}^{-6}}{\mathrm{\&tau;}})(1-e^{-0.3(t-\mathrm{\&tau;})})+(7.0\&times;{10}^{-8}+\frac{5.0\&times;{10}^{-7}}{\mathrm{\&tau;}})(1-e^{-0.005(t-\mathrm{\&tau;})})$

φ (t, τ)=EC (t, τ), coefficient of relaxation then:

$K(t,\mathrm{\&tau;})=e^{-a\&CenterDot;\mathrm{\&phi;}{(t,\mathrm{\&tau;})}^b}$

In the formula: a, b are fitting coefficient, get a=0.72, b=0.85, and load age is 10d.

$\mathrm{\&Delta;}{{\mathrm{\&sigma;}}_s}^T(t,\mathrm{\&tau;})=-(1-f\left(\mathrm{\&tau;}\right))\&CenterDot;\left(\frac{({\mathrm{\&alpha;}}_s-{\mathrm{\&alpha;}}_c)\&CenterDot;\mathrm{\&Delta;T}\left(\mathrm{\&tau;}\right)\&CenterDot;E_c\left(\mathrm{\&tau;}\right)\&CenterDot;E_s\&CenterDot;A_c}{E_c\left(\mathrm{\&tau;}\right)\&CenterDot;A_c+E_s\&CenterDot;A_s}\right)\&CenterDot;K(t,\mathrm{\&tau;})-f\left(\mathrm{\&tau;}\right)\&CenterDot;{\mathrm{\&alpha;}}_s\&CenterDot;\mathrm{\&Delta;T}\left(\mathrm{\&tau;}\right)\&CenterDot;E_s---\left(41\right)$

According to reinforcement stresses increment (41) formula, can draw constraint factor f (τ), substitution (40) formula promptly obtains the concrete creep stress increment:

$\mathrm{\&Delta;}{{\mathrm{\&sigma;}}_c}^T(t,\mathrm{\&tau;})=\mathrm{\&Delta;}{{\mathrm{\&sigma;}}_c}^T\left(\mathrm{\&tau;}\right)\&CenterDot;K(t,\mathrm{\&tau;})$

$=[(1-f\left(\mathrm{\&tau;}\right))\&CenterDot;\left(\frac{({\mathrm{\&alpha;}}_s-{\mathrm{\&alpha;}}_c)\&CenterDot;\mathrm{\&Delta;T}\left(\mathrm{\&tau;}\right)\&CenterDot;E_c\left(\mathrm{\&tau;}\right)\&CenterDot;E_s\&CenterDot;A_s}{E_c\left(\mathrm{\&tau;}\right)\&CenterDot;A_c+E_s\&CenterDot;A_s}\right)-f\left(\mathrm{\&tau;}\right)\&CenterDot;{\mathrm{\&alpha;}}_c\&CenterDot;\mathrm{\&Delta;T}\left(\mathrm{\&tau;}\right)\&CenterDot;E_c\left(\mathrm{\&tau;}\right)]\&CenterDot;K(t,\mathrm{\&tau;})---\left(40\right)$

Concrete stress when the reinforcement stresses that calculates according to finite element simulation is derived apart from different length of time of concrete bottom differing heights contrasts with simulation calculation stress sees table 5, and load is seen Fig. 5 with the different elevations of the different cross section place concrete stress graph that causes of creeping.Because the existence of creeping, stress transfer takes place along with the time and heavily distributes in concrete.The concrete creep stress error that concrete creep stress that formula calculates and FEM calculation go out is very little, so formula calculates the stress state and the mechanical characteristic of reflect structure well.

Application examples 5

Adopt the model one of not considering external load to participate in calculating, thermal expansion coefficient of concrete is α _c=8 * 10 ^-6, the reinforcing bar thermal expansivity is α _s=12 * 10 ^-6, according to formula (13)～(14), consider that the reinforced concrete structure temperature variation is 30 ℃, 20 ℃, 10 ℃ ,-10 ℃ ,-20 ℃ and-30 ℃ of six kinds of operating modes, result of calculation is seen table 6 and table 7.

${\mathrm{\&Delta;\&sigma;}}_c=E_c\&CenterDot;{\mathrm{\&epsiv;}}_{\mathrm{gc}}=\frac{E_c\&CenterDot;E_s\&CenterDot;({\mathrm{\&alpha;}}_s-{\mathrm{\&alpha;}}_c)\&CenterDot;\mathrm{\&Delta;T}\&CenterDot;A_s}{E_c\&CenterDot;A_c+E_s\&CenterDot;A_s}---\left(13\right)$

$\mathrm{\&Delta;}{\mathrm{\&sigma;}}_s=E_s[{\mathrm{\&epsiv;}}_{\mathrm{gc}}-({\mathrm{\&alpha;}}_s-{\mathrm{\&alpha;}}_c)\&CenterDot;\mathrm{\&Delta;T}]={\mathrm{\&sigma;}}_c\&CenterDot;(-\frac{A_c}{A_s})=-\mathrm{\&Delta;}{\mathrm{\&sigma;}}_c/{\mathrm{\&lambda;}}_s---\left(14\right)$

In the formula: E _cBe modulus of elasticity of concrete, E _sBe reinforcing bar elastic modulus, A _cFor concrete section amasss, A _sBe reinforcing steel area, ε _GcBe the additional deformation that retrains each other, λ _sBe the ratio of reinforcement of reinforced concrete, Δ σ _sBe the reinforcement stresses increment, Δ σ _cBe the concrete creep stress increment;

Reinforcing bar and concrete stress (unit: MPa) when table 6 ratio of reinforcement 3.4%, different alternating temperature

Reinforcing bar and concrete stress (unit: MPa) when table 7 ratio of reinforcement 0.84%, different alternating temperature

Can find out that according to top result of calculation under the autogenous volumetric deformation influence, formula calculates reinforcement stresses and finite element simulation calculating reinforcement stresses is very approaching, the concrete creep stress error that draws according to reinforcement stresses is very little.Therefore, it is rationally effective that formula calculates concrete creep stress, and when considering autogenous volumetric deformation, the reinforcement stresses that finite element simulation calculates can be used as the effective way of inquiring into concrete creep stress.

Application examples 6

Adopt the model one of not considering external load to participate in calculating, consider that the reinforced concrete structure temperature variation is 10 ℃, research temperature variation causes under different constraint factors concrete and reinforcement stresses Changing Pattern calculate and adopt formula (16)～(18).According to the research of front, the reinforcement stresses that finite element simulation calculates can be used as known reinforcement stresses.Concrete creep stress according to reinforcement stresses draws is seen table 8 and table 9, can find out from this table, and derivation of equation concrete creep stress and simulation calculation concrete creep stress coincide fine, and this formula can be used as the strong foundation of inquiring into concrete creep stress.

${\mathrm{\&Delta;\&sigma;}}_c=(1-f)\&CenterDot;\left(\frac{({\mathrm{\&alpha;}}_s-{\mathrm{\&alpha;}}_c)\&CenterDot;\mathrm{\&Delta;T}\&CenterDot;E_c\&CenterDot;E_s\&CenterDot;A_s}{E_c\&CenterDot;A_c+E_s\&CenterDot;A_s}\right)-f\&CenterDot;{\mathrm{\&alpha;}}_c\&CenterDot;\mathrm{\&Delta;T}\&CenterDot;E_c---\left(16\right)$

$\mathrm{\&Delta;}{\mathrm{\&sigma;}}_s=-(1-f)\&CenterDot;\left(\frac{({\mathrm{\&alpha;}}_s-{\mathrm{\&alpha;}}_c)\&CenterDot;\mathrm{\&Delta;T}\&CenterDot;E_c\&CenterDot;E_s\&CenterDot;A_c}{E_c\&CenterDot;A_c+E_s\&CenterDot;A_s}\right)-f\&CenterDot;{\mathrm{\&alpha;}}_s\&CenterDot;\mathrm{\&Delta;T}\&CenterDot;E_s---\left(17\right)$

$f=\frac{(E_c\&CenterDot;A_c+E_s\&CenterDot;A_s)\&CenterDot;\mathrm{\&Delta;}{\mathrm{\&sigma;}}_s+({\mathrm{\&alpha;}}_s-{\mathrm{\&alpha;}}_c)\&CenterDot;\mathrm{\&Delta;T}\&CenterDot;E_c\&CenterDot;E_s\&CenterDot;A_c}{-{\mathrm{\&alpha;}}_c\&CenterDot;\mathrm{\&Delta;T}\&CenterDot;E_c\&CenterDot;E_s\&CenterDot;A_c-{\mathrm{\&alpha;}}_s\&CenterDot;\mathrm{\&Delta;T}\&CenterDot;E_s\&CenterDot;E_s\&CenterDot;A_s}---\left(18\right)$

Know that the reinforcement stresses increment just can inquire into the constraint factor of structure, and then draw the reinforced concrete Creep Stress; Know the constraint factor of structure, also can inquire into reinforcement stresses increment and reinforced concrete Creep Stress increment.

In the formula, modulus of elasticity of concrete is E _c, concrete section is long-pending to be A _c, the reinforcing bar elastic modulus is E _s, reinforcing steel area is A _s, thermal expansion coefficient of concrete is α _c, the reinforcing bar thermal expansivity is α _s, concrete creep stress Δ σ _c, reinforcement stresses Δ σ _s, temperature variation is Δ T ℃;

Reinforcing bar and concrete stress (unit: MPa) during table 8 ratio of reinforcement 3.4%

Reinforcing bar and coagulation upper stress (unit: MPa) during table 9 ratio of reinforcement 0.84%

Application examples 7

Consider that the reinforced concrete structure temperature changes continuously, suppose that change procedure is: being 0 ℃ during 0d, is 30 ℃ during 30d, and medium temperature changes by linear interpolation, calculates and adopts formula (31), the variation of stress of concrete and reinforcing bar during the research temperature variation.Calculating and adopting the model one of considering external load, constraint factor f is zero.Reinforcement stresses adopts finite element simulation to calculate reinforcement stresses.Reinforcing bar and concrete stress are seen table 10 and table 11 during the difference ratio of reinforcement.

$\mathrm{\&Delta;}{{\mathrm{\&sigma;}}_{\mathrm{ci}}}^T\left(\mathrm{\&tau;}\right)=(1-f\left(\mathrm{\&tau;}\right))\&CenterDot;\left(\frac{({\mathrm{\&alpha;}}_s-{\mathrm{\&alpha;}}_c)\&CenterDot;\mathrm{\&Delta;T}\left(\mathrm{\&tau;}\right)\&CenterDot;E_c\left(\mathrm{\&tau;}\right)\&CenterDot;E_s\&CenterDot;A_s}{E_c\left(\mathrm{\&tau;}\right)\&CenterDot;A_c+E_s\&CenterDot;A_s}\right)-f\left(\mathrm{\&tau;}\right)\&CenterDot;{\mathrm{\&alpha;}}_c\&CenterDot;\mathrm{\&Delta;T}\left(\mathrm{\&tau;}\right)\&CenterDot;E_c\left(\mathrm{\&tau;}\right)---\left(31\right)$

According to the continuous Changing Pattern of the temperature of above-mentioned hypothesis, can get: Δ T (τ)=a Δ t, a=1 here, Δ t is the period.The restrained condition of this model can know that constraint factor is zero, and modulus of elasticity of concrete is constant, and therefore (31) formula can be changed to:

$\mathrm{\&Delta;}{\mathrm{\&sigma;}}_c\left(\mathrm{\&tau;}\right)=\frac{E_c\left(\mathrm{\&tau;}\right)\&CenterDot;E_s\&CenterDot;({\mathrm{\&alpha;}}_s-{\mathrm{\&alpha;}}_c)\&CenterDot;\mathrm{\&Delta;T}\left(\mathrm{\&tau;}\right)\&CenterDot;A_s}{E_c\left(\mathrm{\&tau;}\right)\&CenterDot;A_c+E_s\&CenterDot;A_s}=\frac{E_c\&CenterDot;E_s\&CenterDot;({\mathrm{\&alpha;}}_s-{\mathrm{\&alpha;}}_c)\&CenterDot;\mathrm{\&Delta;t}\&CenterDot;A_s}{E_c\&CenterDot;A_c+E_s\&CenterDot;A_s}$

${\mathrm{\&sigma;}}_c\left(t\right)=\underset{0}{\overset{t}{\&Integral;}}\frac{E_c\&CenterDot;E_s\&CenterDot;({\mathrm{\&alpha;}}_s-{\mathrm{\&alpha;}}_c)\&CenterDot;A_s}{E_c\&CenterDot;A_c+E_s\&CenterDot;A_s}d\mathrm{\&tau;}=\frac{E_c\&CenterDot;E_s\&CenterDot;({\mathrm{\&alpha;}}_s-{\mathrm{\&alpha;}}_c)\&CenterDot;A_s\&CenterDot;t}{E_c\&CenterDot;A_c+E_s\&CenterDot;A_s}$

${\mathrm{\&sigma;}}_s\left(t\right)={\mathrm{\&sigma;}}_c\&CenterDot;(-\frac{A_c}{A_s})=-{\mathrm{\&sigma;}}_c\left(t\right)/{\mathrm{\&lambda;}}_s$

In the formula, t is the length of time, d.

Reinforcing bar and concrete stress (unit: MPa) during the continuous alternating temperature of table 10 ratio of reinforcement 3.4%

Reinforcing bar and concrete stress (unit: MPa) during the continuous alternating temperature of table 11 ratio of reinforcement 0.84%

Application examples 8

Adopt new finite element simulation computation model, promptly the concrete test block of a 10m * 5m * 5m on the ground is seen Fig. 6.Modulus of elasticity of concrete is with changing the length of time; Get

reinforcing bar and arrange 10 row at thickness direction; Spacing 0.5m; 9 layers of short transverses, spacing 0.5m, reinforcing bar elastic modulus are with changing the length of time; Other parameters are provided with reference model one, calculate and adopt formula (18), (31) and (32).Reinforcement stresses adopts the finite element simulation calculated stress as known reinforcement stresses, according to the cross dimensions A=5 * 5=25m of concrete sample ², the single steel bar area A _s=0.0021m ², A _c=25-0.0021 * 90=24.811m ²

$f=\frac{(E_c\&CenterDot;A_c+E_s\&CenterDot;A_s)\&CenterDot;\mathrm{\&Delta;}{\mathrm{\&sigma;}}_s+({\mathrm{\&alpha;}}_s-{\mathrm{\&alpha;}}_c)\&CenterDot;\mathrm{\&Delta;T}\&CenterDot;E_c\&CenterDot;E_s\&CenterDot;A_c}{-{\mathrm{\&alpha;}}_c\&CenterDot;\mathrm{\&Delta;T}\&CenterDot;E_c\&CenterDot;E_s\&CenterDot;A_c-{\mathrm{\&alpha;}}_s\&CenterDot;\mathrm{\&Delta;T}\&CenterDot;E_s\&CenterDot;E_s\&CenterDot;A_s}---\left(18\right)$

When considering time factor, formula (18) becomes:

$f\left(\mathrm{\&tau;}\right)=\frac{(E_c\left(\mathrm{\&tau;}\right)\&CenterDot;A_c+E_s\&CenterDot;A_s)\&CenterDot;\mathrm{\&Delta;}{\mathrm{\&sigma;}}_s\left(\mathrm{\&tau;}\right)+({\mathrm{\&alpha;}}_s-{\mathrm{\&alpha;}}_c)\&CenterDot;\mathrm{\&Delta;T}\left(\mathrm{\&tau;}\right)\&CenterDot;E_c\left(\mathrm{\&tau;}\right)\&CenterDot;E_s\&CenterDot;A_c}{-{\mathrm{\&alpha;}}_c\&CenterDot;\mathrm{\&Delta;T}\left(\mathrm{\&tau;}\right)\&CenterDot;E_c\left(\mathrm{\&tau;}\right)\&CenterDot;E_s\&CenterDot;A_c-{\mathrm{\&alpha;}}_s\&CenterDot;\mathrm{\&Delta;T}\left(\mathrm{\&tau;}\right)\&CenterDot;E_s\&CenterDot;E_s\&CenterDot;A_s}$

Obtaining constraint factor f behind formula (32) the substitution following formula,, promptly obtain considering the reinforced concrete Creep Stress of time factor f substitution formula (31) again.

$\mathrm{\&Delta;}{{\mathrm{\&sigma;}}_{\mathrm{ci}}}^T\left(\mathrm{\&tau;}\right)=(1-f\left(\mathrm{\&tau;}\right))\&CenterDot;\left(\frac{({\mathrm{\&alpha;}}_s-{\mathrm{\&alpha;}}_c)\&CenterDot;\mathrm{\&Delta;T}\left(\mathrm{\&tau;}\right)\&CenterDot;E_c\left(\mathrm{\&tau;}\right)\&CenterDot;E_s\&CenterDot;A_s}{E_c\left(\mathrm{\&tau;}\right)\&CenterDot;A_c+E_s\&CenterDot;A_s}\right)-f\left(\mathrm{\&tau;}\right)\&CenterDot;{\mathrm{\&alpha;}}_c\&CenterDot;\mathrm{\&Delta;T}\left(\mathrm{\&tau;}\right)\&CenterDot;E_c\left(\mathrm{\&tau;}\right)---\left(31\right)$

Temperature changing process is seen table 12; Reinforcement stresses during apart from different length of time of concrete bottom differing heights and concrete stress of deriving thus and simulation calculation stress contrast sees that the different cross section difference elevations place concrete stress comparison diagram that table 13, temperature variation cause sees Fig. 7.Can find out from result of calculation, identical fine with the concrete creep stress that finite element simulation calculates according to the reinforcement stresses in the different length of times by the concrete creep stress that formula draws.

Table 12 temperature changing process

The length of time/d	0.0	2.0	3.0	6.0	7.0	13.0	14.0	27.0	28.0	29.0
											Temperature course/℃	20.0	20.0	15.0	15.0	10.0	10.0	5.0	5.0	0.0	0.0

[0271]?

Application examples 9

Calculate and adopt the model one of not considering external load; Calculating parameter E _s=2.06 * 10 ⁵MPa, E _c=3.65 * 10 ⁴MPa supposes concrete autogenous volumetric deformation is calculated for 6 kinds of operating modes such as-150 μ ε ,-100 μ ε ,-50 μ ε, 50 μ ε, 100 μ ε, 150 μ ε.Ratio of reinforcement λ _sGet 3.4%, calculate and adopt formula (23), (24).Cross dimensions A=0.5 * 0.5=0.25m according to concrete sample ², the single steel bar area A _s=0.0021m ², get A _c=0.25-0.0021 * 4=0.2416m ², the variation of stress of concrete and reinforcing bar during the research autogenous volumetric deformation, autogenous volumetric deformation can also obtain according to the associative operation standard according to autogenous volumetric deformation measuring apparatus in the actual engineering.Reinforcement stresses adopts finite element simulation to calculate reinforcement stresses, inquires into concrete creep stress with this, and result of calculation is seen table 14 and table 15.

${\mathrm{\&sigma;}}_s={\mathrm{\&epsiv;}}_s\&CenterDot;E_s=\frac{E_c\&CenterDot;E_s\&CenterDot;{\mathrm{\&epsiv;}}_0}{E_c+E_s\&CenterDot;{\mathrm{\&lambda;}}_s}---\left(23\right)$

${\mathrm{\&sigma;}}_c=-{\mathrm{\&sigma;}}_s\&CenterDot;\frac{A_s}{A_c}=-{\mathrm{\&sigma;}}_s\&CenterDot;{\mathrm{\&lambda;}}_s---\left(24\right)$

In the formula: E _cBe modulus of elasticity of concrete, E _sBe reinforcing bar elastic modulus, A _cFor concrete section amasss, A _sBe reinforcing steel area, ε ₀Be concrete autogenous volumetric deformation, λ _sBe the ratio of reinforcement of reinforced concrete, σ _sBe reinforcement stresses increment, σ _cBe concrete creep stress;

Reinforcing bar and concrete stress (unit: MPa) when table 14 ratio of reinforcement 3.4%, different autogenous volumetric deformation

Reinforcing bar and concrete stress (unit: MPa) when table 15 ratio of reinforcement 0.84%, different autogenous volumetric deformation

Application examples 10

Consider that the xoncrete structure autogenous volume changes continuously; Suppose that structure autogenous volumetric deformation process is: being 0 μ ε during 0d, is-150 μ ε during 30d, and middle period autogenous volumetric deformation is by linear interpolation; Simulation calculation adopts model one; Calculate and adopt formula (33), reinforcement stresses to adopt finite element simulation to calculate reinforcement stresses, the autogenous volumetric deformation in the actual engineering can obtain according to the associative operation standard according to concrete test or autogenous volumetric deformation measuring apparatus.Result of calculation is seen table 16 and table 17.

${{\mathrm{\&Delta;\&sigma;}}_{\mathrm{ci}}}^z\left(\mathrm{\&tau;}\right)=(1-f\left(\mathrm{\&tau;}\right))\&CenterDot;\frac{-E_s\&CenterDot;E_c\left(\mathrm{\&tau;}\right)\&CenterDot;\mathrm{\&Delta;}{\mathrm{\&epsiv;}}_0\left(\mathrm{\&tau;}\right)\&CenterDot;A_s}{E_c\left(\mathrm{\&tau;}\right)\&CenterDot;A_c+E_s\&CenterDot;A_s}-f\left(\mathrm{\&tau;}\right)\&CenterDot;\mathrm{\&Delta;}{\mathrm{\&epsiv;}}_0\left(\mathrm{\&tau;}\right)\&CenterDot;E_c\left(\mathrm{\&tau;}\right)---\left(33\right)$

According to the continuous Changing Pattern of above-mentioned autogenous volume, can get: Δ ε (τ)=-a Δ t, a=5 * 10 here ^-6, Δ t is the period.Can know that in conjunction with the restrained condition of this model constraint factor is zero, modulus of elasticity of concrete is constant, and therefore (33) formula can be changed to

$\mathrm{\&Delta;}{{\mathrm{\&sigma;}}_c}^z\left(\mathrm{\&tau;}\right)=\frac{-E_c\&CenterDot;E_s\&CenterDot;\mathrm{\&Delta;\&epsiv;}\left(\mathrm{\&tau;}\right)\&CenterDot;A_s}{E_c\&CenterDot;A_c+E_s\&CenterDot;A_s}=\frac{5\&CenterDot;E_c\&CenterDot;E_s\&CenterDot;\mathrm{\&Delta;t}\&CenterDot;A_s}{E_c\&CenterDot;A_c+E_s\&CenterDot;A_s}\&times;{10}^{-6}$

${{\mathrm{\&sigma;}}_c}^z\left(t\right)=\underset{0}{\overset{\mathrm{<figure-callout\; id="5"\; label="t"\; filenames="HSA00000109844500032.png,HSA00000109844500041.png"\; state="\{\{state\}\}">t</figure-callout>}}{\&Integral;}}\frac{5\&CenterDot;E_c\&CenterDot;E_s\&CenterDot;A_s}{E_c\&CenterDot;A_c+E_s\&CenterDot;A_s}\&times;{10}^{-6}d\mathrm{\&tau;}=\frac{5\&CenterDot;E_c\&CenterDot;E_s\&CenterDot;A_s\&CenterDot;t}{E_c\&CenterDot;A_c+E_s\&CenterDot;A_s}\&times;{10}^{-6}$

${{\mathrm{\&sigma;}}_s}^z\left(t\right)={\mathrm{\&sigma;}}_c\&CenterDot;(-\frac{A_c}{A_s})=-{\mathrm{\&sigma;}}_c\left(t\right)/{\mathrm{\&lambda;}}_s$

In the formula, t is the length of time, d.

Reinforcing bar and concrete stress (unit: MPa) when table 16 ratio of reinforcement 3.4% autogenous volume changes continuously

Reinforcing bar and concrete stress (unit: MPa) when table 17 ratio of reinforcement 0.84% autogenous volume changes continuously

Calculate and can find out through top lots of emulation, it is consistent with the simulation calculation reinforcement stresses that formula calculates reinforcement stresses, therefore can inquire into reinforcing bar surrounding concrete stress according to reinforcement stresses.

Application examples 11

Adopt new finite element model; It is the concrete test block of a 10m * 1m * 5m on the ground; Modulus of elasticity of concrete is got

reinforcing bar and is arranged 2 row, spacing 0.5m at thickness direction with changing the length of time; 9 layers of short transverses; Spacing 0.5m, reinforcing bar elastic modulus do not change with the length of time, and other parameters and operating mode are provided with reference to last example.Cross dimensions A=1 * 5=5m according to concrete sample ², the single steel bar area A _s=0.0021m ², get A _c=5-0.0021 * 18=4.9622m ²Computation model is seen Fig. 8, and the autogenous volumetric deformation process is seen table 18, calculates and adopts formula (26) and (28).The reinforcement stresses that reinforcement stresses employing finite element simulation calculates is as known stress.Autogenous volumetric deformation in the actual engineering can obtain according to the associative operation standard according to concrete test and autogenous volumetric deformation measuring apparatus.Reinforcement stresses during apart from different length of time of concrete bottom differing heights and concrete stress of deriving thus and simulation calculation stress contrast sees that the different cross section difference elevations place concrete stress comparison diagram that table 19, autogenous volumetric deformation cause sees Fig. 9.

${\mathrm{\&sigma;}}_c=E_c\&CenterDot;({\mathrm{\&epsiv;}}_f-{\mathrm{\&epsiv;}}_0)=E_c\&CenterDot;((1-f)\&CenterDot;(\frac{-E_s\&CenterDot;{\mathrm{\&epsiv;}}_0\&CenterDot;A_s}{E_c\&CenterDot;A_c+E_s\&CenterDot;A_s}+{\mathrm{\&epsiv;}}_0)-{\mathrm{\&epsiv;}}_0)$

$=(1-f)\&CenterDot;\frac{-E_s\&CenterDot;E_c\&CenterDot;{\mathrm{\&epsiv;}}_0\&CenterDot;A_s}{E_c\&CenterDot;A_c+E_s\&CenterDot;A_s}-f\&CenterDot;{\mathrm{\&epsiv;}}_0\&CenterDot;E_c---\left(26\right)$

$f=\frac{E_c\&CenterDot;E_s\&CenterDot;A_c\&CenterDot;{\mathrm{\&epsiv;}}_0-(E_c\&CenterDot;A_c+E_s\&CenterDot;A_s)\&CenterDot;{\mathrm{\&sigma;}}_s}{E_c\&CenterDot;E_s\&CenterDot;A_c\&CenterDot;{\mathrm{\&epsiv;}}_0}---\left(28\right)$

Can get σ to f substitution (26) formula _c

When autogenous volumetric deformation is increment Delta ε ₀The time, with the ε in the formula (26) (28) ₀, σ _sAnd σ _cChange Δ ε into ₀, Δ σ _sWith Δ σ _cCan obtain the stress increment that incremental deformation causes.

When considering time course constantly, become at formula (26) (28)

${\mathrm{\&sigma;}}_c\left(\mathrm{\&tau;}\right)=E_c\left(\mathrm{\&tau;}\right)\&CenterDot;((1-f\left(\mathrm{\&tau;}\right))\&CenterDot;(\frac{-E_s\&CenterDot;{\mathrm{\&epsiv;}}_0\left(\mathrm{\&tau;}\right)\&CenterDot;A_s}{E_c\left(\mathrm{\&tau;}\right)\&CenterDot;A_c+E_s\&CenterDot;A_s}+{\mathrm{\&epsiv;}}_0\left(\mathrm{\&tau;}\right))-{\mathrm{\&epsiv;}}_0\left(\mathrm{\&tau;}\right))$

$=(1-f\left(\mathrm{\&tau;}\right))\&CenterDot;\frac{-E_s\&CenterDot;E_c\left(\mathrm{\&tau;}\right)\&CenterDot;{\mathrm{\&epsiv;}}_0\left(\mathrm{\&tau;}\right)\&CenterDot;A_s}{E_c\left(\mathrm{\&tau;}\right)\&CenterDot;A_c+E_s\&CenterDot;A_s}-f\left(\mathrm{\&tau;}\right)\&CenterDot;{\mathrm{\&epsiv;}}_0\left(\mathrm{\&tau;}\right)\&CenterDot;E_c\left(\mathrm{\&tau;}\right)$

$f\left(\mathrm{\&tau;}\right)=\frac{E_c\left(\mathrm{\&tau;}\right)\&CenterDot;E_s\&CenterDot;A_c\&CenterDot;{\mathrm{\&epsiv;}}_0\left(\mathrm{\&tau;}\right)-(E_c\left(\mathrm{\&tau;}\right)\&CenterDot;A_c+E_s\&CenterDot;A_s)\&CenterDot;{\mathrm{\&sigma;}}_s\left(\mathrm{\&tau;}\right)}{E_c\left(\mathrm{\&tau;}\right)\&CenterDot;E_s\&CenterDot;A_c\&CenterDot;{\mathrm{\&epsiv;}}_0\left(\mathrm{\&tau;}\right)}$

Table 18 autogenous volumetric deformation process

The length of time/d	0.00	2.00	2.50	6.00	6.50	12.00	13.50	27.00	27.50	28.50
											Autogenous volumetric deformation/μ ε	0.00	0.00	-3.20	-3.20	-9.15	-9.15	-25.65	-25.65	-55.35	-55.35

[0308]?

Application examples 12

For the correctness of existence, above-mentioned theory analysis and the formula of verifying extra-stress, understand situation such as the extra-stress rule of development, numerical values recited, influence factor, carried out shop experiment.Shop experiment is carried out in certain actual power station on-site concrete testing laboratory.Differential resistance type reinforcement stresses meter and concrete strain gauge test are adopted in test.

Testing tool: differential resistance type reinforcement stresses meter: KL-18;

Differential resistance type strainometer: DI-10;

Readout instrument: SQ-5 digital electric bridge;

Instrument layout: each test specimen is arranged 1 reinforcement stresses meter, 1 strainometer, and the embedding manner of reinforcement stresses meter and strainometer is according to corresponding standard operation.Like Figure 10 is test specimen instrument layout figure;

Die trial: adopt the thick multi-plywood of 15mm of engineering site molding to manufacture die trial size 25 * 25 * 100cm, upper opening 25 * 100cm;

Sample dimensions: 25 * 25 * 100cm;

Bar diameter: φ 18;

Test specimen quantity: 4;

Concrete mix: adopt power station diversion tunnel plug concrete mix;

Concrete mixing: in the laboratory, adopt pony mixer to mix system;

Vibrate: testing laboratory's shaking table;

The test specimen maintenance: maintenance is 14 days in fog room, natural curing then.

Test: the observation in per 8 hours 1 time test specimen is built after of reinforcement stresses meter, observe 1 every day after 3 days, and observation on the 2nd is 1 time after 1 month, observes 1 first quarter moon stop to observe.

Reinforcement stresses adopts the actual measurement reinforcement stresses, utilizes formula (12)～(14) and saptis simulation calculation program that the test concrete block is calculated, and compares with test figure.Calculating parameter is got test parameters, and the simulation calculation grid is seen Figure 11, and test and result of calculation are seen Figure 12～15.

${\mathrm{\&Delta;\&sigma;}}_c=E_c\&CenterDot;{\mathrm{\&epsiv;}}_{\mathrm{gc}}=\frac{E_c\&CenterDot;E_s\&CenterDot;({\mathrm{\&alpha;}}_s-{\mathrm{\&alpha;}}_c)\&CenterDot;\mathrm{\&Delta;T}\&CenterDot;A_s}{E_c\&CenterDot;A_c+E_s\&CenterDot;A_s}---\left(13\right)$

$\mathrm{\&Delta;}{\mathrm{\&sigma;}}_s=E_s[{\mathrm{\&epsiv;}}_{\mathrm{gc}}-({\mathrm{\&alpha;}}_s-{\mathrm{\&alpha;}}_c)\&CenterDot;\mathrm{\&Delta;T}]={\mathrm{\&sigma;}}_c\&CenterDot;(-\frac{A_c}{A_s})=-\mathrm{\&Delta;}{\mathrm{\&sigma;}}_c/{\mathrm{\&lambda;}}_s---\left(14\right)$

This test findings shows, at such one concrete sample that does not receive under external force, the complete free state, because the difference of thermal expansivity causes inner reinforcing bar and concrete to produce bigger stress, has verified the existence of extra-stress; Simultaneously with the temperature variation different regularity of change; Reinforcing bar shows as to compressive stress and changes when promptly heating up; Show as during cooling to tension and change; Concrete stress is just in time opposite, adds the simulation calculation result, formula result of calculation is similar with test findings, has also disclosed the development and change rule of extra-stress.

Because the existence of extra-stress will be to the stressed generation material impact of structural entity.

Application examples 13

It is domestic that certain water-control project is positioned at Gongliu County, Ili Prefecture, Xinjiang, is the maximum tributary in the Yilihe River--maximum controlled engineering in the planning of master stream ,-Tekes river.The hinge dam site is positioned at little gill lattice Lang He and about 300m place, mouthful downstream is converged in master stream, Tekes river, and the 41km apart from county town, Gongliu County is apart from Yining City 139km.

This engineering is the first-class engineering of big (1) type, and barrage, flood releasing structure and power tunnel water inlet are 1 grade of buildings, and generating diversion tunnel and power station factory building are 2 grades of buildings, and temporary buildings such as diversion tunnel, downstream cofferdam are 4 grades of buildingss.Figure 16 is seen in the Hongdong distribution of overflowing, and certain section is seen Figure 17.

Get certain typical section and calculate, formula adopts (48)～(50), and compares analysis with measured data.The concrete thermodynamic parameter adopts actual engineering concrete thermal parameters; Arrangement of reinforcement form and actual engineering are in full accord, and parameter is with reference to reinforcing bar thermodynamic parameter of the same type; The embedding manner of reinforcement stresses meter is according to corresponding standard operation.Simulation Calculation is seen Figure 18～Figure 19.After actual engineering is built, reinforcement stresses meter observation in per 2 hours 1 time, observation in per 4,8 hours was once observed 1 time after 1 month in per 1 day after 1 day, and per 1 week observation is 1 time after 1 year, observes stopping observation after 4 years.Calculating is adopted the actual measurement reinforcement stresses with reinforcement stresses, and result of calculation and measured data are seen Figure 20～Figure 21.

$f=\frac{[{\mathrm{\&epsiv;}}_0-({\mathrm{\&alpha;}}_s-{\mathrm{\&alpha;}}_c)\&CenterDot;\mathrm{\&Delta;T}]\&CenterDot;E_c\&CenterDot;E_s\&CenterDot;A_c-(E_c\&CenterDot;A_c+E_s\&CenterDot;A_s)\&CenterDot;{\mathrm{\&sigma;}}_s\left(t\right)}{({\mathrm{\&alpha;}}_c\&CenterDot;\mathrm{\&Delta;T}+{\mathrm{\&epsiv;}}_0)\&CenterDot;E_c\&CenterDot;E_s\&CenterDot;A_c+{\mathrm{\&alpha;}}_s\&CenterDot;\mathrm{\&Delta;T}\&CenterDot;E_s\&CenterDot;E_s\&CenterDot;A_s}---\left(48\right)$

When considering time course, formula (48) becomes

$f\left(\mathrm{\&tau;}\right)=\frac{[{\mathrm{\&epsiv;}}_0\left(\mathrm{\&tau;}\right)-({\mathrm{\&alpha;}}_s-{\mathrm{\&alpha;}}_c)\&CenterDot;\mathrm{\&Delta;T}\left(\mathrm{\&tau;}\right)]\&CenterDot;E_c\left(\mathrm{\&tau;}\right)\&CenterDot;E_s\&CenterDot;A_c-(E_c\left(\mathrm{\&tau;}\right)\&CenterDot;A_c+E_s\&CenterDot;A_s)\&CenterDot;{\mathrm{\&sigma;}}_s\left(\mathrm{\&tau;}\right)}{({\mathrm{\&alpha;}}_c\&CenterDot;\mathrm{\&Delta;T}\left(\mathrm{\&tau;}\right)+{\mathrm{\&epsiv;}}_0\left(\mathrm{\&tau;}\right))\&CenterDot;E_c\left(\mathrm{\&tau;}\right)\&CenterDot;E_s\&CenterDot;A_c+{\mathrm{\&alpha;}}_s\&CenterDot;\mathrm{\&Delta;T}\left(\mathrm{\&tau;}\right)\&CenterDot;E_s\&CenterDot;E_s\&CenterDot;A_s}$

Constraint factor f (τ) (16) and (26) formula of bringing into is got:

$\mathrm{\&Delta;}{{\mathrm{\&sigma;}}_{\mathrm{ci}}}^T\left(\mathrm{\&tau;}\right)=(1-f)\&CenterDot;\left(\frac{({\mathrm{\&alpha;}}_s-{\mathrm{\&alpha;}}_c)\&CenterDot;\mathrm{\&Delta;T}\left(\mathrm{\&tau;}\right)\&CenterDot;E_c\left(\mathrm{\&tau;}\right)\&CenterDot;E_s\&CenterDot;A_s}{E_c\left(\mathrm{\&tau;}\right)\&CenterDot;A_c+E_s\&CenterDot;A_s}\right)-f\&CenterDot;{\mathrm{\&alpha;}}_c\&CenterDot;\mathrm{\&Delta;T}\left(\mathrm{\&tau;}\right)\&CenterDot;E_c\left(\mathrm{\&tau;}\right)---\left(49\right)$

${{\mathrm{\&Delta;\&sigma;}}_{\mathrm{ci}}}^z\left(\mathrm{\&tau;}\right)=(1-f)\&CenterDot;\frac{-E_s\&CenterDot;E_c\left(\mathrm{\&tau;}\right)\&CenterDot;\mathrm{\&Delta;}{\mathrm{\&epsiv;}}_0\left(\mathrm{\&tau;}\right)\&CenterDot;A_s}{E_c\left(\mathrm{\&tau;}\right)\&CenterDot;A_c+E_s\&CenterDot;A_s}-f\&CenterDot;\mathrm{\&Delta;}{\mathrm{\&epsiv;}}_0\left(\mathrm{\&tau;}\right)\&CenterDot;E_c\left(\mathrm{\&tau;}\right)---\left(50\right)$

Claims (1)

1. 2.1, a kind of method according to reinforcement stresses instrumentation dimension reinforced concrete Creep Stress, it is characterized in that: structure bearing temperature load, consider structure physical constraint state:

   (1), confirms the physical constraint coefficient of structure according to the actual measurement reinforcement stresses of reinforcement stresses meter

   Modulus of elasticity of concrete is

   

   Concrete section is long-pending for

   

   The reinforcing bar elastic modulus is

   

   Reinforcing steel area is

   

   Thermal expansion coefficient of concrete is

   The reinforcing bar thermal expansivity is

   

   The actual measurement reinforcement stresses increment is

   

   and

   Observed temperature is changed to

   

   ℃

   Draw the physical constraint coefficient of structure according to above-mentioned parameter:

   

   （18）

   (2) confirm reinforced concrete Creep Stress increment according to constraint factor

   

   （16）。

   2, a kind of method according to reinforcement stresses instrumentation dimension reinforced concrete Creep Stress, it is characterized in that: structure is born autogenous volumetric deformation, considers structure physical constraint state:

   (1), confirms the physical constraint coefficient of structure according to the actual measurement reinforcement stresses of reinforcement stresses meter

   Modulus of elasticity of concrete is

   

   Concrete section is long-pending for

   

   The reinforcing bar elastic modulus is

   

   Reinforcing steel area is

   

   Thermal expansion coefficient of concrete is

   

   The reinforcing bar thermal expansivity is

   

   The actual measurement reinforcement stresses

   

   and

   The actual measurement concrete autogenous volumetric deformation is

   

   Draw the physical constraint coefficient of structure according to above-mentioned parameter:

   

   （28）

   (2) confirm the reinforced concrete Creep Stress according to constraint factor

   （26）

   When cubic deformation is increment

   

   , with in the formula (28) (26),

   

   and

   

   changes

   

   into,

   

   with

   

   can obtain the stress increment that incremental deformation causes.

   3, a kind of method according to reinforcement stresses instrumentation dimension reinforced concrete Creep Stress is characterized in that: structure bearing temperature load, autogenous volumetric deformation and loading procedure, consider structure physical constraint state:

   (1), confirms the physical constraint coefficient of structure according to the actual measurement reinforcement stresses of reinforcement stresses meter

   Modulus of elasticity of concrete is

   

   Concrete section is long-pending for

   

   The reinforcing bar elastic modulus is

   

   Reinforcing steel area is

   

   Thermal expansion coefficient of concrete is

   

   The reinforcing bar thermal expansivity is

   

   The age of concrete;

   

   The actual measurement concrete temperature is changed to

   

   The actual measurement autogenous volumetric deformation is

   

   Temperature variation causes, and the reinforcement stresses increment is

   

   Autogenous volume change cause the reinforcement stresses increment is

   

   Temperature variation causes, and the concrete stress increment is

   Autogenous volume changes the concrete stress increment

   

   that causes

   The actual measurement reinforcement stresses increment

   

   and

   Concrete stress increment

   

   Concrete creep stress;

   

   Time, t,

   The five equilibrium number of 0 ~ t, N

   Draw the physical constraint coefficient of structure according to above-mentioned parameter:

   

   (2) confirm the reinforced concrete Creep Stress according to constraint factor

   

   ?（31）

   

   （33）

   

   

   

   。

   4, a kind of method by reinforcement stresses instrumentation dimension reinforced concrete Creep Stress is characterized in that: structure bearing temperature load, and the influence of considering to creep, according to the physical constraint state of structure:

   (1), confirms the physical constraint coefficient of structure according to the actual measurement reinforcement stresses of reinforcement stresses meter

   Modulus of elasticity of concrete is

   

   Concrete section is long-pending for

   

   The reinforcing bar elastic modulus is

   Reinforcing steel area is

   

   Thermal expansion coefficient of concrete is

   

   The reinforcing bar thermal expansivity is

   

   Actual measurement reinforcement stresses increment

   

   The actual measurement concrete temperature is changed to

   

   The concrete coefficient of relaxation is

   

   

   ; The age of concrete and

   t, the time,

   

   （41）

   (2) confirm the reinforced concrete Creep Stress

   According to reinforcement stresses increment (41) formula; Can draw constraint factor

   

   ; Substitution (40) formula promptly obtains the concrete creep stress increment:

   

   

   ?（40）。

   5, a kind of method by reinforcement stresses instrumentation dimension reinforced concrete Creep Stress, it is characterized in that: structure is born the external force load, considers the influence of creeping:

   Modulus of elasticity of concrete is

   

   Concrete section is long-pending for

   

   The reinforcing bar elastic modulus is

   Reinforcing steel area is

   

   External load

   ; The age of concrete

   Actual measurement reinforcement stresses increment

   

   The actual measurement concrete temperature is changed to

   

   The concrete coefficient of relaxation is

   

   The concrete stress increment that the external force load causes

   

   τ applies the reinforcement stresses increment

   

   that external load causes at t constantly the length of time

   Apply external load Δ p the length of time at τ; Concrete that causes and reinforcement stresses increment are respectively

   

   and

   

   ; Satisfy:

   

   , then

   

   ; Constantly concrete stress is lax and reduce to t; Then reinforcement stresses increases

   So satisfy equilibrium condition and ratio stress relation, that is:

   

   (42)。

   6, a kind of by reinforcement stresses instrumentation dimension reinforced concrete Creep Stress, it is characterized in that: account temperature, autogenous volume and creep when influencing:

   (1), confirms the physical constraint coefficient of structure according to the actual measurement reinforcement stresses of reinforcement stresses meter

   Modulus of elasticity of concrete is

   

   Concrete section is long-pending for

   

   The reinforcing bar elastic modulus is

   Reinforcing steel area is

   

   Thermal expansion coefficient of concrete is

   

   The reinforcing bar thermal expansivity is

   

   Actual measurement reinforcement stresses increment

   

   ; The age of concrete

   N, the five equilibrium number of 0 ~ t

   The actual measurement concrete temperature is changed to

   The concrete coefficient of relaxation is

   

   and

   The actual measurement autogenous volumetric deformation is

   

   , draws the physical constraint coefficient of structure according to these parameters:

   

   (2) confirm reinforced concrete Creep Stress according to constraint factor

   

   （31）

   

   （33）

   

   。

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