CN103226076A - Method and apparatus for measuring early elastic modulus of cement-based materials - Google Patents

Abstract

The invention discloses a method for measuring an early elastic modulus of cement-based materials. The method comprises: filling and packaging mixed to-be-detected cement-based materials into a hollow straight pipe with uniform sections; horizontally putting the hollow straight pipe on two support points to form a combined free-beam composed of the to-be-detected cement-based materials and the hollow straight pipe, wherein the two support points are arranged at positions away from one end of the hollow straight pipe by 0.224l and 0.776l respectively, and l is a length of the hollow straight pipe; continuously monitoring a first natural frequency of the combined free-beam through a vibration sensor arranged at a midpoint of the combined free-beam; and finally calculating the elastic modulus of the cement-based materials at an age of t according to the first natural frequency. The invention further discloses an apparatus for measuring the early elastic modulus of the cement-based materials. The method and the apparatus can continuously monitor, without de-molding, processes that the early elastic modulus of the cement-based materials changes with the age under different maintenance temperatures after the cement-based materials are put into a mold, and are simple in structure and low in cost.

Description

Early stage elastic modulus measuring method of a kind of cement-based material and measurement mechanism

Technical field

The present invention relates to a kind of method of testing of cement-based material mechanical property, relate in particular to early stage elastic modulus measuring method of a kind of cement-based material and measurement mechanism.

Background technology

The related question synthesis of early stage cracking of xoncrete structure and complexity have contained the every aspect of the early stage calorifics of cement-based material, mechanics and deformation performance, and mineral admixture and additive are used the complicacy that has also increased its early stage performance greatly.Both at home and abroad the researcher has carried out great deal of experimental to the early stage macro property of concrete, attempts to illustrate concrete ftracture in early days mechanism, early stage performance variation law and technical parameter problems of value.Wherein early stage elastic modulus is one of hot issue of being concerned about of researchist with the development and change process in the length of time, but traditional pass through the method that the load deformation relationship is tried to achieve elastic modulus, at least to after test specimen is built form removal in a day, carry out, therefore be difficult to record the more early stage elastic modulus of cement-based material by traditional method.But early the length of time, elastic modulus was extremely important with contraction estimation, Crack Control etc. for its early stage stress for cement-based material, therefore how to make things convenient for, accurately measured units such as becoming design, construction, scientific research and be concerned about one of emphasis.

Summary of the invention

Technical matters to be solved by this invention is to overcome the deficiencies in the prior art, early stage elastic modulus measuring method of a kind of cement-based material and measurement mechanism are provided, can be implemented in from going into the commitment of mould to sclerosis, nondestructively the elastic modulus to cement-based material carries out continuous monitoring with development of age, thereby provides elastic modulus parameter accurately for the research of the early stage mechanics of cement-based material, deformation performance and Numerical Simulation Analysis.

The present invention specifically solves the problems of the technologies described above by the following technical solutions:

The early stage elastic modulus measuring method of a kind of cement-based material, the cement-based material to be measured that at first will mix and stir are full of and are packaged in prismatic hollow straight tube; Should lie in a horizontal plane on two fulcrums by hollow straight tube then, the combination free beam that formation is made up of cement-based material to be measured and hollow straight tube, two fulcrums are arranged at the hollow straight tube of distance wherein an end 0.224l place and 0.776l place respectively, and l is the length of described hollow straight tube; By being arranged at the vibration transducer of described combination free beam midpoint, continue to monitor first natural frequency of vibration of combination free beam; Calculate the elastic modulus of cement-based material to be measured when be t the length of time by following formula:

$E_c\left(t\right)=[\mathrm{EI}\left(t\right)-E_a{I}_a]\frac{64}{\mathrm{\π}{d}_i^4}$

In the formula, E _cThe elastic modulus of the cement-based material to be measured when (t) representing to be t the length of time; E _aI _aRigidity for described hollow straight tube; d _iBe described hollow straight tube internal diameter; The rigidity of combination free beam when EI (t) represents to be t the length of time obtains by finding the solution following equation:

$\mathrm{EI}\left(t\right)=0.0788\stackrel{\&OverBar;}{m}{l}^4{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="130401143535.png"\; state="\{\{state\}\}">f</figure-callout>}}^2$

Wherein,

Uniform quality for the combination free beam of unit length; L is the length of combination free beam; F is first natural frequency of vibration of combination free beam during t in the length of time, and t watered from cement-based material and counted after charging into hollow straight tube the length of time.

Further, this method also comprises by adjusting the early stage elastic modulus of described hollow straight tube temperature survey cement-based material to be measured under different curing.Thereby realize providing elastic modulus parameter accurately to early stage mechanics, deformation performance research and the Numerical Simulation Analysis of cement-based material under different curing.

The cement-based material to be measured that mixes and stirs for the ease of perfusion, but described hollow straight tube can be at one end or two ends the lid or the plug of folding and sealing are set; But also both ends open seals an end with the tube sealing cock body earlier, more hollow straight tube is filled the cement-based material to be measured that mixes and stirs after, utilize the tube sealing cock body that another openend is sealed.

A kind of early stage elastic modulus measurement mechanism of cement-based material that uses above-mentioned measuring method comprises:

Prismatic hollow straight tube is used to pour into cement-based material to be measured;

Two bearing edges are used to support described hollow straight tube, form the combination free beam of being made up of cement-based material to be measured and hollow straight tube;

Vibration measurement device comprises the vibration transducer that is arranged at described combination free beam midpoint, and the vibration signals collecting treating apparatus that is connected with vibration transducer.

Preferably, described measurement mechanism also comprises the temperature control equipment that is used to adjust described hollow straight tube temperature.

Preferably, the cross section of described hollow straight tube is circle or rectangle.The cross sectional dimensions of described hollow straight tube is less than 150mm, and length is 400-1000mm.The material of described hollow straight tube is plastics or or macromolecular material or alloy material.

Compared to existing technology, the present invention has following beneficial effect:

One, the present invention is the nondestructive test method, before test can advance to initial set the length of time.Because also not sclerosis fully before cement-based material condenses, be difficult to carry out load test and obtain elastic modulus by form removal, the inventive method does not need form removal, therefore can promptly can test behind the device installation in position, and mixture pouring and the whole process of device installation can be finished in 15 minutes.

Two, the present invention is a kind of monitoring method of active received signal, do not need artificial excitation, whole observation process is automatic and continuous, simultaneously can set curing temperature, the process that can be after the device installation promptly can the early stage elastic modulus of continuous monitoring different curing cement-based material changes with the length of time.

Three, apparatus of the present invention are simple in structure, and are with low cost, and measuring method is easy to implement.

Description of drawings

Fig. 1 is the structural representation of the early stage elastic modulus measurement mechanism of cement-based material of the present invention in the embodiment; Among the figure, 1 is hollow straight tube, and 2 is bearing edge, and 3 is vibration transducer, and 4 is data collecting instrument, and 5 is computing machine, and 6 is worktable, and 7 is the tube sealing cock body, and 8 is power supply, and 9 is power regulating switch;

Fig. 2 is the single order mode curve of free beam;

Fig. 3 is for water cement ratio is 0.35, curing temperature is 25.0 ℃ cement paste elastic modulus progress curve.

Embodiment

Below in conjunction with accompanying drawing technical scheme of the present invention is elaborated:

Thinking of the present invention is that cement-based material to be measured and hollow straight tube are formed the combination free beam, by being arranged at the vibration transducer of combination free beam midpoint, continue to monitor the natural frequency of vibration of combination free beam, try to achieve the elastic modulus in length of time morning of cement-based material to be measured then according to the mechanical characteristic of combination free beam.

The early stage elastic modulus measurement mechanism of cement-based material of the present invention as shown in Figure 1, comprises hollow straight tube 1, two bearing edges 2, vibration transducer 3 and the data collecting instruments 4 that are connected successively with vibration transducer 3, computing machine 5.Measurement mechanism of the present invention also comprises the temperature control equipment that is used to adjust described hollow straight tube 1 temperature, adopted a kind of easy hollow straight tube temperature control equipment in this embodiment: the tube wall of hollow straight tube 1 is wound with resistive heater outward, outer parcel one deck insulation material, resistive heater is connected with power supply 8 by power regulating switch 9, energized 8 backs can make the tube wall of hollow straight tube 1 be heated to predetermined curing temperature by regulating power switch 9.In this embodiment, the xsect of hollow straight tube 1 is circular, both ends open, and cross-sectional diameter is no more than 100mm, preferred plastics of material (for example polystyrene) or alloy material, length is 600-1000mm.Vibration transducer 3 can adopt sensors such as accelerometer or strainometer, and data collecting instrument 4 is with the adaptive data acquiring and recording equipment of sensor 3.

When carrying out the early stage elastic modulus of cement-based material, specifically in accordance with the following methods:

Step 1, regulate power switch 9, hollow straight tube 1 is heated to predetermined curing temperature according to the test needs;

Step 2, according to test objective according to match ratio mix cement mixture;

Step 3, with the end sealing of tube sealing cock body 7 with hollow straight tube 1, the mixture that stirs is poured in the hollow straight tube 1 the slight simultaneously concussion of pouring, bubble in the vent pipe;

Step 4, when cement mixture is about to fill, stop, leaving about 10mm and highly do not water cement mixture,, use tube sealing cock body 7 that cement mixture is enclosed in the hollow straight tube 1 hollow straight tube 1 another openend wiped clean;

Step 5, filling is had the hollow straight tube 1 of cement mixture to be placed horizontally to be fixed on two bearing edges 2 on the worktable 6, the position of two bearing edges 2 is respectively the hollow straight tube 1 of distance wherein an end 0.224l place and 0.776l place, l is the length of hollow straight tube 1, thereby forms the combination free girder construction of being made up of cement mixture and hollow straight tube 1;

Step 6, the sensor 3 of gathering vibration signal is installed, and is connected with data collecting instrument 4 in the midpoint of hollow straight tube 1;

Step 7, log-on data Acquisition Instrument 4, by the sensor 3 continuous collecting combination free beams vibration signal under the environmental interference around, and by data collecting instrument 4 recorded and stored;

The vibration signal of step 8,5 pairs of data Acquisition Instruments of computing machine, 4 records is handled the natural frequency of vibration that obtains the combination free beam through time domain and frequency domain transform, and according to the first calculation of natural vibration frequency combination free beam rigidity.Wherein, from vibration signal, extract the natural frequency of vibration and be existing mature technology, for example the DH5922 Dynamic Signal detecting and analysing system of the magnificent measuring technology in east, Jiangsu incorporated company etc.The rigidity of combination free beam can obtain by finding the solution following equation:

$\mathrm{EI}\left(t\right)=0.0788\stackrel{\&OverBar;}{m}{l}^4{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="130401143535.png"\; state="\{\{state\}\}">f</figure-callout>}}^2$

Wherein, Uniform quality for unit length combination free beam; L is the length of combination free beam; F is first natural frequency of vibration of the combination free beam when being t the length of time, and t watered from cement-based material and counted after charging into hollow straight tube the length of time;

Step 9, calculate cement mixture elastic modulus in different length of time by following formula:

$E_c\left(t\right)=[\mathrm{EI}\left(t\right)-E_a{I}_a]\frac{64}{\mathrm{\&pi;}{d}_i^4}$

In the formula, E _cThe elastic modulus of the cement-based material to be measured when (t) representing to be t the length of time; E _aI _aRigidity for hollow straight tube 1; d _iInternal diameter for hollow straight tube 1; The rigidity of combination free beam when EI (t) represents to be t the length of time;

Step 10, draw the early stage elastic modulus progress curve of cement-based material by result of calculation;

Step 11, the additive that adopts different match ratio, admixture variety classes and volume and the cement mixture of mineral admixture, repeating step 2～step 10 obtains different mixture ratio and admixture cement-based material elastic modulus progress curve under this curing temperature; By adjusting different curing temperatures, can obtain different mixture ratio and admixture cement-based material elastic modulus progress curve under the different curing.

In order to make the public further understand technical solution of the present invention, provide below technical solution of the present invention the theoretical derivation process:

The horizontal free vibration differential equation of beam is shown in (1):

$\mathrm{EI}\left(t\right)\frac{{\&PartialD;}^{4}y(x,t)}{\&PartialD;x^4}+\stackrel{\&OverBar;}{m}\frac{{\&PartialD;}^{2}y(x,t)}{\&PartialD;{\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="130401143535.png"\; state="\{\{state\}\}">t</figure-callout>}}^2}=0---\left(1\right)$

In the formula, EI (t) is a free beam rigidity, is the function of t in the length of time; Y (x t) is the amount of deflection of beam, be about beam length direction x and the length of time t function;

Be the free beam linear mass.

For the horizontal free vibration differential equation of beam that (1) formula is described, the vibration shape that taking into account system has and the time is irrelevant promptly adopts the separation of variable to find the solution, and the beam vibration function is decomposed into the product of spatial function Y (x) and function of time T (t).

So establish equation (1) separate for

y(x,t)=Y(x)T(t) （2）

In the formula, Y (x) is a model function of vibration, characterizes whole vibration of beam form; T (t) is the function of time, characterizes the vibration regularity of putting on the beam.Formula (2) substitution equation (1) is got

$\mathrm{EI}\left(t\right)\frac{{\&PartialD;}^4\left[y\left(x\right)T\left(t\right)\right]}{\&PartialD;x^4}+\stackrel{\&OverBar;}{m}\frac{{\&PartialD;}^2\left[Y\left(x\right)T\left(t\right)\right]}{\&PartialD;{\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="130401143535.png"\; state="\{\{state\}\}">t</figure-callout>}}^2}=0$

Variables separation gets

$\frac{1}{T\left(t\right)}\frac{d^{2}T\left(t\right)}{\mathrm{<figure-callout\; id="2"\; label="d\; t"\; filenames="130401143535.png"\; state="\{\{state\}\}">d</figure-callout>}{t}^{}{}^2}=-\frac{1}{Y\left(x\right)}\frac{\mathrm{EI}\left(t\right)}{\stackrel{\&OverBar;}{m}}\frac{d^{4}Y\left(x\right)}{d{x}^4}$

The following formula equal sign left side and t are irrelevant, and equal sign the right is irrelevant with x, and then the both sides of equation must equal same constant, establish this constant and are-ω ², order $a^2=\frac{\mathrm{EI}}{\stackrel{\&OverBar;}{m}},$ ${\mathrm{\&beta;}}^4=\frac{{\mathrm{\&omega;}}^2}{a^2}$

Then obtain two second order ordinary differential equations

$\frac{d^{2}T\left(t\right)}{\mathrm{<figure-callout\; id="2"\; label="d\; t"\; filenames="130401143535.png"\; state="\{\{state\}\}">d</figure-callout>}{t}^{}{}^2}+{\mathrm{\&omega;}}^{2}T=0---\left(3\right)$

$\frac{d^{4}Y\left(x\right)}{d{x}^4}-{\mathrm{\&beta;}}^{4}Y=0---\left(4\right)$

Formula (3), separating of (4) are respectively

Y(x)=C ₁cosβx+C ₂sinβx+C ₃coshβx+C ₄sinhβx （6）

The principal oscillation that gets beam is

Constant C in the formula ₁, C ₂, C ₃, C ₄And natural frequency ω is determined constant by boundary condition

Determine by starting condition.

For free beam, the two ends freedom, promptly moment of flexure and shearing equal zero, promptly

Promptly

Y″(0)=0，Y″′(0)=0

Y″(l)=0，Y″'(l)=0

The boundary condition substitution (6) at x=0 place is got

C ₂=C ₄，C ₁=C ₃

The boundary condition substitution (6) at x=l place is got

(sinhβl-sinβl)C ₁+(coshβl-cosβl)C ₂=0

(coshβl-cosβl)C ₁+(sinhβl+sinβl)C ₂=0

If following formula is set up and C ₁, C ₂Untrivialo solution is arranged, then have

$\left|\begin{array}{cc}\sinh \mathrm{\&beta;l}-\sin \mathrm{\&beta;l}& \cosh \mathrm{\&beta;l}-\cos \mathrm{\&beta;l}\\ \cosh \mathrm{\&beta;l}-\cos \mathrm{\&beta;l}& \sinh \mathrm{\&beta;l}+\sin \mathrm{\&beta;l}\end{array}\right|=0$

Find the solution this determinant, obtain frequency equation

coshβl cosβl=1

The root of separating the first order mode of winning is β l=1.506 π.

The single order inherent circular frequency that gets free beam thus is

$\mathrm{\&omega;}={\mathrm{\&beta;}}^{2}a={\left(\mathrm{\&beta;l}\right)}^2\sqrt{\frac{\mathrm{EI}}{\stackrel{\&OverBar;}{m}{\mathrm{<figure-callout\; id="4"\; label="l"\; filenames="130401143535.png,130401143541.png"\; state="\{\{state\}\}">l</figure-callout>}}^4}}=22.385\sqrt{\frac{\mathrm{EI}}{\stackrel{\&OverBar;}{m}{\mathrm{<figure-callout\; id="4"\; label="l"\; filenames="130401143535.png,130401143541.png"\; state="\{\{state\}\}">l</figure-callout>}}^4}}=\mathrm{\&xi;}\sqrt{\frac{\mathrm{EI}}{\stackrel{\&OverBar;}{m}{\mathrm{<figure-callout\; id="4"\; label="l"\; filenames="130401143535.png,130401143541.png"\; state="\{\{state\}\}">l</figure-callout>}}^4}}$

ξ in the formula=22.385 are called the first first order mode coefficient of free beam.

Order $r=\frac{C_1}{{\mathrm{<figure-callout\; id="2"\; label="C"\; filenames="130401143535.png"\; state="\{\{state\}\}">C</figure-callout>}}_2}=\frac{\sin \mathrm{\&beta;l}-\sinh \mathrm{\&beta;l}}{\cos \mathrm{\&beta;l}+\cosh \mathrm{\&beta;l}}$

Then corresponding principal mode is

Y(x)=C ₁[cosβx-coshβx+r(sinβx-sinhβx)]

The first order mode curve of winning, as shown in Figure 2.As seen from the figure, under this state, beam has two nodes, make Y (x)=0 can get two node locations respectively at 0.224l and 0.776l place from test specimen one side end face, therefore, two edges of a knife that support free beam are located at 0.224l and 0.776l place respectively, first natural frequency of vibration that can more accurate mensuration combination beam.

According to following formula, get the computing formula of elastic modulus:

$\mathrm{EI}\left(t\right)=\frac{\stackrel{\&OverBar;}{m}{\mathrm{<figure-callout\; id="4"\; label="l"\; filenames="130401143535.png,130401143541.png"\; state="\{\{state\}\}">l</figure-callout>}}^4}{{\mathrm{\&xi;}}^2}{\mathrm{\&omega;}}^2$

ξ=22.385 and ω=2 π f substitutions are got

$\mathrm{EI}\left(t\right)=0.0788\stackrel{\&OverBar;}{m}{l}^4{f}^2---\left(8\right)$

Again

$\mathrm{EI}\left(t\right)=E_a{I}_a+E_c{I}_c\left(t\right)=E_a{I}_a+E_c\left(t\right)\frac{\mathrm{\&pi;}{\mathrm{<figure-callout\; id="4"\; label="d\; i"\; filenames="130401143535.png,130401143541.png"\; state="\{\{state\}\}">d</figure-callout>}}_i^{}}{64}---\left(9\right)$

In the formula, E _aI _aBe hollow straight tube rigidity; E _cI _cRigidity when (t) being t the length of time for cement-based material to be measured; E _cElastic modulus when (t) being t the length of time for water material; d _iInternal diameter for hollow straight tube.

Elastic modulus when therefore, cement-based material is t the length of time is:

$E_c\left(t\right)=[\mathrm{EI}\left(t\right)-E_a{I}_a]\frac{64}{\mathrm{\&pi;}{d}_i^4}---\left(10\right)$

Fig. 3 has shown that the water cement ratio that utilizes the inventive method to obtain is 0.35, curing temperature is 25.0 ℃ cement paste elastic modulus progress curve.

Claims (9)

1. the early stage elastic modulus measuring method of cement-based material is characterized in that, the cement-based material to be measured that at first will mix and stir is full of and is packaged in prismatic hollow straight tube; Should lie in a horizontal plane on two fulcrums by hollow straight tube then, form the combination free beam of being made up of cement-based material to be measured and hollow straight tube, two fulcrums are arranged at a wherein end 0.224 of the hollow straight tube of distance respectively lPlace and 0.776 lThe place, lLength for described hollow straight tube; By being arranged at the vibration transducer of described combination free beam midpoint, continue to monitor first natural frequency of vibration of combination free beam; Calculating cement-based material to be measured by following formula in the length of time is tThe time elastic modulus:

In the formula,

Expression is the length of time

The time the elastic modulus of cement-based material to be measured; Rigidity for described hollow straight tube;

Be described hollow straight tube internal diameter;

Expression is the length of time The time combination free beam rigidity, obtain by finding the solution following equation:

Wherein,

Uniform quality for the combination free beam of unit length; Length for the combination free beam;

Be the length of time tThe time combination free beam first natural frequency of vibration, the length of time tWater from cement-based material and to count after charging into hollow straight tube.

2. the early stage elastic modulus measuring method of cement-based material according to claim 1 is characterized in that this method also comprises by adjusting described hollow straight tube temperature, measures the early stage elastic modulus of cement-based material to be measured under different curing.

3. the early stage elastic modulus measuring method of cement-based material according to claim 1 is characterized in that the cross section of described hollow straight tube is circle or rectangle.

4. the early stage elastic modulus measuring method of cement-based material according to claim 1 is characterized in that first natural frequency of vibration of described combination free beam is carried out time and frequency domain analysis by the vibration signal that vibration transducer is gathered and obtained.

5. the early stage elastic modulus measurement mechanism of cement-based material that uses the described measuring method of claim 1 is characterized in that, comprising:

Prismatic hollow straight tube is used to pour into cement-based material to be measured;

Two bearing edges are used to support described hollow straight tube, form the combination free beam of being made up of cement-based material to be measured and hollow straight tube;

Vibration measurement device comprises the vibration transducer that is arranged at described combination free beam midpoint, and the vibration signals collecting treating apparatus that is connected with vibration transducer.

6. as the early stage elastic modulus measurement mechanism of cement-based material as described in the claim 5, it is characterized in that, also comprise the temperature control equipment that is used to adjust described hollow straight tube temperature.

7. as the early stage elastic modulus measurement mechanism of cement-based material as described in the claim 5, it is characterized in that the cross section of described hollow straight tube is circular.

8. as the early stage elastic modulus measurement mechanism of cement-based material as described in the claim 5, it is characterized in that the cross sectional dimensions of described hollow straight tube is less than 150mm, length is 400-1000mm.

9. as the early stage elastic modulus measurement mechanism of cement-based material as described in the claim 5, it is characterized in that the material of described hollow straight tube is plastics or macromolecular material or alloy material.

Images