CN115659107B - Method and system for calculating compressive strength of light ceramsite concrete - Google Patents
Method and system for calculating compressive strength of light ceramsite concrete Download PDFInfo
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Abstract
The invention provides a method and a system for calculating the compressive strength of light ceramsite concrete, wherein the method comprises the steps of setting the mixing proportion of the light ceramsite concrete; respectively attaching strain gauges to the front and the rear of the light ceramsite concrete test block, applying a load to the strain gauges, and recording the strain of the light ceramsite concrete test block in the loading process; fitting to obtain a correlation equation of the change of the elasticity modulus of the lightweight ceramsite concrete test block along with the loading time; constructing a strain energy density expression of an online elastic stage, and normalizing the strain energy density of the light ceramsite concrete test block under the action of unit uniform load; the method comprises the steps of drawing a change curve of normalized strain energy density along with the change of applied load, predicting the damage load of the lightweight ceramsite concrete test block, calculating the compressive strength of the lightweight ceramsite concrete test block based on the damage load, effectively improving the traditional analysis method and the finite element analysis method, and solving the problem of lack of research on the mechanical properties of the lightweight ceramsite concrete.
Description
Technical Field
The invention belongs to the technical field of light ceramsite concrete, and particularly relates to a method and a system for calculating the compressive strength of light ceramsite concrete.
Background
In the previous research, no systematic research is specially carried out on the mechanical properties of the light ceramsite concrete, and the corresponding numerical values are basically given according to the mechanical properties of common concrete in the analysis of the ceramsite concrete. However, compared with the traditional common concrete, the light ceramsite concrete has different stress conditions, so that the traditional method cannot predict the breaking load of the light ceramsite concrete and achieve the purpose of calculating the compressive strength of the light ceramsite concrete.
Disclosure of Invention
Aiming at the defects in the prior art, the method and the system for calculating the compressive strength of the lightweight ceramsite concrete solve the problem of lack of research on the mechanical property of the lightweight ceramsite concrete, and can effectively achieve the purposes of predicting the breaking load of the lightweight ceramsite concrete and calculating the compressive strength of the lightweight ceramsite concrete.
In order to achieve the above purpose, the invention adopts the technical scheme that:
the scheme provides a method for calculating the compressive strength of light ceramsite concrete, which comprises the following steps:
s1, setting the mixing proportion of light ceramsite concrete;
s2, respectively attaching strain gauges to the front and the rear of the light ceramsite concrete test block with the set mixing ratio, applying a load to the light ceramsite concrete test block, and recording the strain of the light ceramsite concrete test block in the loading process;
s3, fitting the applied load and the recorded strain data to obtain a correlation equation of the change of the elastic modulus of the lightweight ceramsite concrete test block along with the loading time;
s4, constructing a strain energy density expression of the on-line elastic stage based on the correlation equation, and normalizing the strain energy density of the lightweight ceramsite concrete test block under the action of uniformly distributed unit load to obtain normalized strain energy density;
s5, drawing a change curve of the normalized strain energy density along with the change of the applied load, predicting the damage load of the light ceramsite concrete test block, calculating the compressive strength of the light ceramsite concrete test block based on the damage load, and finishing the calculation of the compressive strength of the light ceramsite concrete.
The beneficial effects of the invention are: according to the method, the destruction load of the light ceramsite concrete test block is predicted by providing the normalized strain energy density method, the compressive strength of the light ceramsite concrete is calculated by applying the normalized strain energy density method, and compared with the method that the compressive strength of the test block cannot be directly calculated by directly using a traditional method, the method for predicting the destruction load of the light ceramsite concrete test block and calculating the compressive strength of the light ceramsite concrete by applying the normalized strain energy density method can be used for effectively perfecting the traditional analysis method and a finite element analysis method, and solving the problem that the research on the mechanical property of the light ceramsite concrete is lacked.
Further, fitting the applied load and the recorded strain data to obtain a correlation equation of the change of the elastic modulus of the lightweight ceramsite concrete test block along with the loading time, which specifically comprises the following steps:
calculating the correlation of the actually measured stress-strain of the test by using the Pearson correlation coefficient;
based on the correlation, fitting the applied load and the recorded strain data to obtain a stress-strain equation of the lightweight ceramsite concrete test block;
and obtaining a correlation equation of the change of the elastic modulus of the lightweight ceramsite concrete test block along with the loading time according to the stress-strain equation of the lightweight ceramsite concrete test block.
Still further, the expression of the correlation is as follows:
wherein the content of the first and second substances,
indicating the stress response measured in the testThe overall pearson correlation coefficient between the variations,
representing the overall covariance between experimentally measured stress strains,
、
、
both represent the overall average of strain and stress,
shows the compressive strength of the lightweight ceramsite concrete test block,
the strain value of the lightweight ceramsite concrete test block in the vertical direction is measured for eliminating errors,
the strain value of the lightweight ceramsite concrete test block in the vertical direction, which is measured by the front side strain gauge,
representing the strain value of the lightweight ceramsite concrete test block measured by the rear side strain gauge in the vertical direction;
the expression of the stress-strain equation is as follows:
wherein the content of the first and second substances,
、
、
both represent the coefficients of a fitted equation,
the compressive strain of the compressed light ceramsite concrete is expressed;
the related equation of the change of the elasticity modulus of the light ceramsite concrete test block along with the loading time is as follows:
wherein the content of the first and second substances,
the elastic modulus of the lightweight ceramsite concrete test block is shown.
Still further, the strain energy density expression is as follows:
wherein the content of the first and second substances,
which represents the density of the strain energy,
the compressive strain of the compressed light ceramsite concrete is shown.
The beneficial effects of the above further scheme are: and obtaining a stress-strain equation of the light ceramsite concrete by fitting the stress-strain value of the light ceramsite concrete, obtaining an elastic modulus change equation, and finally obtaining an expression of the strain energy density.
Still further, the expression of the normalized strain energy density is as follows:
wherein the content of the first and second substances,
the normalized strain energy density value is expressed,
the maximum value of the strain energy density under the action of unit uniform load is shown, and max represents the maximum operation.
The beneficial effects of the further scheme are as follows: and normalizing the strain energy density, and drawing a load-normalized strain energy density value curve to more intuitively express the state change of the light ceramsite concrete test block along with the change of the applied load so as to obtain the damage load of the light ceramsite concrete.
Still further, the expression of the compressive strength of the lightweight ceramsite concrete test block is as follows:
wherein the content of the first and second substances,
showing the cross-sectional area of the lightweight ceramsite concrete test block after compression deformation,
shows the cross-sectional area of the lightweight ceramsite concrete test block,
the strain value of the lightweight ceramsite concrete test block measured by the front side strain gauge in the horizontal direction is shown,
shows the lightweight ceramsite concrete test measured by a rear strain gageThe strain value of the block in the horizontal direction,
shows the compressive strength of the lightweight ceramsite concrete test block,
representing the predicted failure load.
Based on the calculation method, the invention also provides a calculation system for the compressive strength of the light ceramsite concrete, which comprises the following steps:
the first processing module is used for setting the mixing proportion of the light ceramsite concrete;
the second processing module is used for respectively attaching strain gauges to the front and the rear of the light ceramsite concrete test block with the set mixing ratio, applying load to the light ceramsite concrete test block and recording the strain of the light ceramsite concrete test block in the loading process;
the third processing module is used for fitting the applied load and the recorded strain data to obtain a correlation equation of the change of the elastic modulus of the light ceramsite concrete test block along with the loading time;
the fourth processing module is used for constructing a strain energy density expression of the online elastic stage based on the correlation equation, and normalizing the strain energy density of the lightweight ceramsite concrete test block under the action of uniformly distributed unit load to obtain normalized strain energy density;
and the fifth processing module is used for drawing a change curve of the normalized strain energy density along with the change of the applied load, predicting the damage load of the light ceramsite concrete test block, calculating the compressive strength of the light ceramsite concrete test block based on the damage load, and finishing the calculation of the compressive strength of the light ceramsite concrete.
The invention has the beneficial effects that: the invention applies the normalized strain energy density method to obtain the breaking load of the lightweight ceramsite concrete and calculate the compressive strength of the lightweight ceramsite concrete, can effectively improve the traditional analysis method and the finite element analysis method, and solves the problem of lack of research on the mechanical properties of the lightweight ceramsite concrete.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
FIG. 2 is a diagram illustrating a least square fitting method in this embodiment.
FIG. 3 is a graph showing the variation of the strain energy density with the applied load in this example.
Fig. 4 is a schematic diagram of the system structure of the present invention.
Detailed Description
The following description of the embodiments of the present invention is provided to facilitate the understanding of the present invention by those skilled in the art, but it should be understood that the present invention is not limited to the scope of the embodiments, and it will be apparent to those skilled in the art that various changes may be made without departing from the spirit and scope of the invention as defined and defined in the appended claims, and all matters produced by the invention using the inventive concept are protected.
Example 1
As shown in figure 1, the invention provides a method for calculating the compressive strength of light ceramsite concrete, which comprises the following steps:
s1, setting the mixing proportion of light ceramsite concrete;
in this embodiment, the mix proportion of the lightweight ceramsite concrete is designed according to the relevant specifications.
S2, respectively attaching strain gauges to the front and the back of the light ceramsite concrete test block with the set mixing proportion, applying a load to the light ceramsite concrete test block, and recording the strain of the light ceramsite concrete test block in the loading process;
s3, fitting the applied load and the recorded strain data to obtain a correlation equation of the change of the elastic modulus of the lightweight ceramsite concrete test block along with the loading time, which specifically comprises the following steps:
and (3) calculating the correlation of the stress strain actually measured in the test by using a Pearson correlation coefficient:
wherein, the first and the second end of the pipe are connected with each other,
representing the overall pearson correlation coefficient between experimentally measured stress strains,
represents the overall covariance between experimentally measured stress strains,
、
、
both represent the overall average of strain and stress,
shows the compressive strength of the lightweight ceramsite concrete test block,
the strain value of the lightweight ceramsite concrete test block in the vertical direction is measured for eliminating errors,
the strain value of the lightweight ceramsite concrete test block measured by the front side strain gauge in the vertical direction is shown,
representing the strain value of the lightweight ceramsite concrete test block measured by the rear side strain gauge in the vertical direction;
based on the correlation, fitting is carried out on the applied load and the recorded strain data to obtain a stress-strain equation of the lightweight ceramsite concrete test block:
wherein the content of the first and second substances,
、
、
both represent the coefficients of a fitted equation,
the compressive strain of the compressed light ceramsite concrete is expressed;
according to the stress-strain equation of the lightweight ceramsite concrete test block, obtaining a correlation equation of the change of the elastic modulus of the lightweight ceramsite concrete test block along with the loading time:
wherein the content of the first and second substances,
the elasticity modulus of the lightweight ceramsite concrete test block is shown;
s4, constructing a strain energy density expression of the on-line elastic stage based on the correlation equation, and normalizing the strain energy density of the lightweight ceramsite concrete test block under the action of uniformly distributed unit load to obtain normalized strain energy density;
the strain energy density expression is as follows:
wherein, the first and the second end of the pipe are connected with each other,
which represents the density of the strain energy,
the compressive strain of the compressed light ceramsite concrete is expressed;
the expression of the normalized strain energy density is as follows:
wherein the content of the first and second substances,
the normalized values of the strain energy density are expressed,
the maximum value of the strain energy density under the action of unit uniform load is expressed, and max represents the maximum operation;
s5, drawing a change curve of the normalized strain energy density along with the change of the applied load, predicting the damage load of the light ceramsite concrete test block, calculating the compressive strength of the light ceramsite concrete test block based on the damage load, and finishing the calculation of the compressive strength of the light ceramsite concrete;
wherein, the first and the second end of the pipe are connected with each other,
showing the cross-sectional area of the lightweight ceramsite concrete test block after compression deformation,
showing the cross-sectional area of the lightweight ceramsite concrete test block,
the strain value of the lightweight ceramsite concrete test block in the horizontal direction, which is measured by the front side strain gauge,
the strain value of the lightweight ceramsite concrete test block in the horizontal direction, which is measured by the rear side strain gauge,
shows the compressive strength of the lightweight ceramsite concrete test block,
representing the predicted failure load.
The present invention is further described below.
A1, designing the mixing proportion of the light ceramsite concrete according to relevant specifications, wherein the design is shown in Table 1, and the design is shown in Table 1.
TABLE 1
A2, respectively attaching strain gauges to the front and the back of the light ceramsite concrete test block with the set mixing proportion, applying a load to the light ceramsite concrete test block, and recording the strain of the light ceramsite concrete test block in the loading process.
A3, fitting the load applied in the experiment and the measured strain data to obtain a correlation equation of the change of the elastic modulus of the test block along with the load time, as shown in FIG. 2, wherein the actually measured data in FIG. 2 is scattered points obtained by performing a stress-strain test on the lightweight ceramsite concrete test block according to the mixing ratio in the table 1; the fitting curve is a stress-strain curve which is subjected to least square fitting according to the test numerical value; in the graph, the abscissa is a strain value, the ordinate is a stress value, the unit is MPa, and a stress-strain equation is obtained according to a fitting result:
the equation for the change in elastic modulus with strain is:
a4, constructing a strain energy density calculation formula of the online elastic stage based on the correlation equation, wherein the strain energy density calculation formula comprises the following steps:
normalizing the strain energy density of the light ceramsite concrete test block under the action of unit uniformly distributed load to obtain:
in this embodiment, the variation value of the normalized strain energy density value along with the applied load is shown in fig. 3, the unit of the load is kN, the normalized strain energy density value continuously increases and reaches the maximum value along with the increase of the load, and when the normalized strain energy density value reaches 1, the lightweight ceramsite concrete reaches the maximum bearing capacity of the test block.
And A5, drawing a change curve of the normalized strain energy density along with the change of the applied load, predicting the damage load of the light ceramsite concrete test block, calculating the compressive strength of the light ceramsite concrete test block based on the damage load, and finishing the calculation of the compressive strength of the light ceramsite concrete.
Through the design, the problem of lack of research on the mechanical properties of the lightweight ceramsite concrete is solved.
Example 2
As shown in fig. 4, the present invention provides a system for calculating the compressive strength of lightweight ceramsite concrete, comprising:
the first processing module is used for setting the mixing proportion of the light ceramsite concrete;
the second processing module is used for respectively attaching strain gauges to the front and the back of the light ceramsite concrete test block with the set mixing proportion, applying load to the light ceramsite concrete test block and recording the strain of the light ceramsite concrete test block in the loading process;
the third processing module is used for fitting the applied load and the recorded strain data to obtain a correlation equation of the change of the elastic modulus of the lightweight ceramsite concrete test block along with the loading time;
the fourth processing module is used for constructing a strain energy density expression of the online elastic stage based on the correlation equation, and normalizing the strain energy density of the lightweight ceramsite concrete test block under the action of uniformly distributed unit load to obtain normalized strain energy density;
and the fifth processing module is used for drawing a change curve of the normalized strain energy density along with the change of the applied load, predicting the damage load of the light ceramsite concrete test block, calculating the compressive strength of the light ceramsite concrete test block based on the damage load, and finishing the calculation of the compressive strength of the light ceramsite concrete.
The system for calculating the compressive strength of lightweight ceramsite concrete provided in the embodiment shown in fig. 4 can implement the technical solution shown in the above method embodiment, and the implementation principle and the beneficial effects are similar, and are not described herein again.
In the embodiment of the invention, the functional units can be divided according to the calculation method of the compressive strength of the lightweight ceramsite concrete, for example, each function can be divided into the functional units, and two or more functions can be integrated into one processing unit. The integrated unit may be implemented in the form of hardware, or may be implemented in the form of a software functional unit. It should be noted that the division of the cells in the present invention is schematic, and is only a logical division, and there may be another division manner in actual implementation.
In the embodiment of the invention, the system for calculating the compressive strength of the light ceramsite concrete comprises a hardware structure and/or a software module corresponding to each function in order to realize the principle and the beneficial effects of the method for calculating the compressive strength of the light ceramsite concrete. Those of skill in the art will readily appreciate that the various illustrative elements and algorithm steps described in connection with the embodiments disclosed herein may be implemented as hardware and/or combinations of hardware and computer software, where a function is performed in a hardware or computer software-driven manner, and that the function described may be implemented in any suitable manner for each particular application depending upon the particular application and design constraints imposed on the technology, but such implementation is not to be considered as beyond the scope of the present application.
In the embodiment, the invention provides a normalized strain energy density method and calculates the compressive strength of the light ceramsite concrete by applying the normalized strain energy density method, perfects the traditional analysis method and the finite element analysis method, and solves the problem of lack of research on the mechanical properties of the light ceramsite concrete.
Therefore, the invention establishes a calculation method for predicting the damage of the light ceramsite concrete, and applies a normalized strain energy density method to analyze the working behavior of the light ceramsite concrete, thereby achieving the purposes of predicting the damage load of the light ceramsite concrete and calculating the compressive strength of the light ceramsite concrete; in addition, the stress performance and the seismic performance of the composite material are researched by applying a normalized strain energy density method, and a new solution can be found for the problem of a complex engineering structure.
Claims (7)
1. A method for calculating the compressive strength of light ceramsite concrete is characterized by comprising the following steps of:
s1, setting the mixing proportion of light ceramsite concrete;
s2, respectively attaching strain gauges to the front and the back of the light ceramsite concrete test block with the set mixing proportion, applying a load to the light ceramsite concrete test block, and recording the strain of the light ceramsite concrete test block in the loading process;
s3, fitting the applied load and the recorded strain data to obtain a correlation equation of the change of the elastic modulus of the lightweight ceramsite concrete test block along with the loading time;
s4, constructing a strain energy density expression of the on-line elastic stage based on the correlation equation, and normalizing the strain energy density of the lightweight ceramsite concrete test block under the action of uniformly distributed unit load to obtain normalized strain energy density;
s5, drawing a change curve of the normalized strain energy density along with the change of the applied load, predicting the damage load of the light ceramsite concrete test block, calculating the compressive strength of the light ceramsite concrete test block based on the damage load, and completing the calculation of the compressive strength of the light ceramsite concrete.
2. The method for calculating the compressive strength of the lightweight ceramsite concrete according to claim 1, wherein the applied load and the recorded strain data are fitted to obtain a correlation equation of the change of the elastic modulus of the lightweight ceramsite concrete test block along with the loading time, which specifically comprises:
calculating the correlation of the actually measured stress and strain of the test by using the Pearson correlation coefficient;
based on the correlation, fitting the applied load and the recorded strain data to obtain a stress-strain equation of the lightweight ceramsite concrete test block;
and obtaining a correlation equation of the elasticity modulus of the light ceramsite concrete test block along with the change of the loading time according to the stress-strain equation of the light ceramsite concrete test block.
3. The method for calculating the compressive strength of lightweight ceramsite concrete according to claim 2, wherein the expression of the correlation is as follows:
wherein, the first and the second end of the pipe are connected with each other,
representing the overall pearson correlation coefficient between experimentally measured stress strains,
representing the experimentally measured stress-strainThe overall covariance of the two (c) cells,
、
、
both represent the overall average of strain and stress,
shows the compressive strength of the lightweight ceramsite concrete test block,
the strain value of the lightweight ceramsite concrete test block in the vertical direction is measured for eliminating errors,
the strain value of the lightweight ceramsite concrete test block measured by the front side strain gauge in the vertical direction is shown,
representing the strain value of the lightweight ceramsite concrete test block measured by the rear side strain gauge in the vertical direction;
the expression of the stress-strain equation is as follows:
wherein the content of the first and second substances,
、
、
both represent the coefficients of a fitted equation,
the compressive strain of the compressed light ceramsite concrete is expressed;
the related equation of the change of the elastic modulus of the lightweight ceramsite concrete test block along with the loading time is as follows:
wherein the content of the first and second substances,
the elastic modulus of the lightweight ceramsite concrete test block is shown.
4. The method for calculating the compressive strength of lightweight ceramsite concrete according to claim 3, wherein the strain energy density expression is as follows:
wherein the content of the first and second substances,
which represents the density of the strain energy,
the compressive strain of the compressed light ceramsite concrete is shown.
5. The method for calculating the compressive strength of lightweight ceramsite concrete according to claim 4, wherein the normalized strain energy density is expressed as follows:
wherein the content of the first and second substances,
the normalized strain energy density value is expressed,
the maximum value of the strain energy density under the action of unit uniform load is shown, and max represents the maximization operation.
6. The method for calculating the compressive strength of the lightweight ceramsite concrete according to claim 5, wherein the compressive strength of the lightweight ceramsite concrete test block is expressed as follows:
wherein the content of the first and second substances,
showing the cross-sectional area of the lightweight ceramsite concrete test block after compression deformation,
shows the cross-sectional area of the lightweight ceramsite concrete test block,
the strain value of the lightweight ceramsite concrete test block measured by the front side strain gauge in the horizontal direction is shown,
the strain value of the lightweight ceramsite concrete test block measured by the rear side strain gauge in the horizontal direction is shown,
shows the compressive strength of the lightweight ceramsite concrete test block,
representing the predicted failure load.
7. A system for calculating the compressive strength of light ceramsite concrete is characterized by comprising:
the first processing module is used for setting the mixing proportion of the light ceramsite concrete;
the second processing module is used for respectively attaching strain gauges to the front and the rear of the light ceramsite concrete test block with the set mixing ratio, applying load to the light ceramsite concrete test block and recording the strain of the light ceramsite concrete test block in the loading process;
the third processing module is used for fitting the applied load and the recorded strain data to obtain a correlation equation of the change of the elastic modulus of the lightweight ceramsite concrete test block along with the loading time;
the fourth processing module is used for constructing a strain energy density expression of the online elastic stage based on the correlation equation, and normalizing the strain energy density of the lightweight ceramsite concrete test block under the action of uniformly distributed unit load to obtain normalized strain energy density;
and the fifth processing module is used for drawing a change curve of the normalized strain energy density along with the change of the applied load, predicting the damage load of the light ceramsite concrete test block, calculating the compressive strength of the light ceramsite concrete test block based on the damage load, and finishing the calculation of the compressive strength of the light ceramsite concrete.
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