CN114722510A - Deflection calculation method of rectangular thin plate and computer readable storage medium - Google Patents

Deflection calculation method of rectangular thin plate and computer readable storage medium Download PDF

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CN114722510A
CN114722510A CN202011525444.9A CN202011525444A CN114722510A CN 114722510 A CN114722510 A CN 114722510A CN 202011525444 A CN202011525444 A CN 202011525444A CN 114722510 A CN114722510 A CN 114722510A
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王新堂
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College of Science and Technology of Ningbo University
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Abstract

The method for calculating the deflection of the rectangular sheet is characterized in that the length of the rectangular sheet is a, the width of the rectangular sheet is L, the thickness of the rectangular sheet is t, L/20 is not less than t and not more than L/5, the elastic modulus of the rectangular sheet is E, the Poisson ratio of the rectangular sheet is mu, uniformly distributed vertical loads q are applied to the rectangular sheet under various boundary conditions, and the deflection delta of the rectangular sheet is calculated by adopting the following formula: i) under the condition of simply supporting four sides, the deflection delta of the rectangular thin plate is calculated by the formula
Figure DDA0002850655910000011
ii) under the conditions of simple three-edge support and fixed one-edge support, the deflection delta of the rectangular sheet is calculated by the formula
Figure DDA0002850655910000012
iii) under the condition of two-side simple support and two-side fixed support, the deflection delta of the rectangular sheet is calculated by the formula
Figure DDA0002850655910000013
The method for calculating the deflection of the rectangular thin plate in the elastic state enables the deflection of the rectangular thin plate to be calculated more simply.

Description

Deflection calculation method of rectangular thin plate and computer readable storage medium
Technical Field
The invention relates to the technical field of deflection calculation of structural engineering, in particular to a deflection calculation method of a rectangular thin plate in an elastic state, and specifically relates to a rigidity judgment method of an assembled composite floor slab by using a calculation method of the maximum vertical displacement of the rectangular elastic thin plate made of common three materials under three different boundary conditions.
Background
Sheeting is a common base element in building construction, and the flexibility of sheeting is an important aspect of the design of sheeting. Since the sheet is different from general rod units such as beams and columns, the calculation of the deflection of the sheet in an elastic state is very complicated according to the general sheet theory, and the calculation of the deflection of the sheet is also very complicated even under the simplest boundary conditions and the uniform load conditions. Therefore, there is a need for an improved method for calculating sheet deflection in the elastic state.
Disclosure of Invention
The invention provides a simpler method for calculating the deflection of the rectangular thin plate in an elastic state aiming at the technical current situation.
A further object of the present invention is to provide a computer-readable storage medium, which can calculate the deflection of a rectangular sheet.
The technical scheme adopted by the invention for solving the above-mentioned primary technical problems is as follows: the method for calculating the deflection of the rectangular thin plate in the elastic state is characterized in that the length of the rectangular thin plate is a, the width of the rectangular thin plate is L, the thickness of the rectangular thin plate is t, t is more than or equal to L/20 and less than or equal to L/5, the elastic modulus of the rectangular thin plate is E, the Poisson ratio of the rectangular thin plate is mu, uniformly distributed vertical loads q are applied to the rectangular thin plate under various boundary conditions, and the deflection delta of the rectangular thin plate is calculated by adopting the following formula:
i) under the condition of simply supporting four sides, the deflection delta of the rectangular thin plate is calculated by the formula
Figure BDA0002850655890000011
In the formula (1), the reaction mixture is,
Figure BDA0002850655890000012
or
Figure BDA0002850655890000021
ii) under the condition of simple three-side support and fixed one-side support, the deflection delta of the rectangular sheet is calculated by the formula
Figure BDA0002850655890000022
In the formula (3), the reaction mixture is,
Figure BDA0002850655890000023
or
Figure BDA0002850655890000024
iii) under the condition of two-side simple support and two-side fixed support, the deflection delta of the rectangular sheet is calculated by the formula
Figure BDA0002850655890000025
In the formula (5), the reaction mixture is,
Figure BDA0002850655890000026
or alternatively
Figure BDA0002850655890000027
Wherein eta is the correlation coefficient of the deflection of the thin plate and the deflection of a beam unit cut from the thin plate, and xi is 0.91/(1-u)2) (7)。
Taking a method for calculating the deflection delta of the rectangular thin plate under the condition of simply supporting four sides as an example, the method for calculating the deflection delta of the rectangular thin plate comprises the following steps,
step one, establishing a rectangular sheet calculation model: the length of the rectangular thin plate is a, the width of the rectangular thin plate is L, the thickness of the rectangular thin plate is t, t is more than or equal to L/20 and less than or equal to L/5, the elastic modulus of the material is E, the Poisson ratio is mu, and the uniformly distributed vertical load is q;
step two, establishing a beam unit calculation model under the condition of four-side simple support:cutting a beam unit with the width of B, the length of L and the thickness of t along the length direction of the rectangular thin plate, wherein the line load borne by the simply supported beam model is q0B q, the deflection delta of the simply supported beam according to the basic theory of the beam0Is calculated by the formula
Figure BDA0002850655890000028
In the formula (8), ξ is 0.91/(1-u)2) (7)；
Step three, introducing a correlation coefficient eta of the deflection of the thin plate and the deflection of the beam unit according to the correlation relationship of the deflection of the thin plate and the deflection of the beam unit intercepted from the thin plate, wherein the correlation coefficient eta comprises a comprehensive influence effect of a two-way effect and a boundary constraint effect of the thin plate on the deflection of the beam unit, and the deflection delta of the rectangular thin plate under the condition of simply supporting four sides is calculated as
Figure BDA0002850655890000031
Step four, determining a correlation coefficient eta introduced in a deflection delta calculation formula (1) of the rectangular sheet under the condition of simply supporting four sides:
taking a as 2m, 3m and 4m respectively according to the common geometric dimension of the rectangular thin plate, assuming that L/a is changed within the range of 0.4-1.2, taking L/a as 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1 and 1.2 respectively, and carrying out finite element numerical modeling analysis on the rectangular thin plate under the condition of four sides simple support to obtain corresponding deflection delta1；
② because delta-delta1(9) I.e. by
Figure BDA0002850655890000032
Simply support L/a and delta in four sides1Respectively carrying the data into an expression (10) to obtain a group of data corresponding to the correlation coefficient eta and the L/a;
carrying out numerical fitting on a group of data corresponding to the correlation coefficient eta and the L/a obtained in the step II to obtain a fitting curve, wherein the functional relation expression of the correlation coefficient eta and the L/a corresponding to the fitting curve is
Figure BDA0002850655890000033
Or alternatively
Figure BDA0002850655890000034
The method for calculating the deflection delta of the rectangular thin plate under the condition of three-side simple support and one-side fixed support and the method for calculating the deflection delta of the rectangular thin plate under the condition of two-side simple support and two-side fixed support are obtained by referring to the method for calculating the deflection delta of the rectangular thin plate under the condition of four-side simple support.
The technical scheme adopted by the invention for solving the further technical problems is as follows: a computer-readable storage medium, wherein a computer program is stored thereon, and when executed by a processor, the computer program performs the above calculation method to calculate the deflection of the rectangular sheet and output the calculation result.
Compared with the prior art, the invention has the advantages that: according to the correlation relationship between the deflection of the thin plate and the deflection of the beam unit intercepted from the thin plate, a correlation coefficient eta is introduced into a deflection calculation formula of the beam unit under three different boundary conditions, the correlation coefficient eta represents the comprehensive influence effect of the two-way effect and the boundary constraint effect of the thin plate on the deflection of the beam unit, so that a rectangular thin plate deflection calculation formula which is similar to the deflection calculation formula of the beam unit under the three different boundary conditions is obtained, the deflection calculation of rectangular thin plates made of different materials under an elastic state is solved, the deflection calculation formula of the rectangular thin plate is simpler and is more convenient to use in the actual use process, the deflection value calculated by the correlation coefficient eta through the deflection calculation formula is equal to the deflection value calculated by a finite element calculation method of the rectangular thin plate, and the deflection value calculated by the finite element calculation method is subjected to numerical fitting determination, the maximum error of the deflection calculation of the rectangular thin plate can be smaller than 3%, and the deflection calculation of the rectangular thin plate keeps higher accuracy.
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FIG. 1 is a schematic structural view of a rectangular thin plate in example 1 of the present invention;
FIG. 2 is a schematic structural view of a beam unit cut out from a rectangular thin plate in example 1 of the present invention;
fig. 3 is a beam element calculation model in embodiment 1 of the present invention;
FIG. 4 is a graph of the length-to-width ratio L/a of the rectangular thin plate and the correlation coefficient η in example 1 of the present invention;
FIG. 5 is a structure of a rectangular thin plate in example 2 of the present invention;
fig. 6 is a beam element calculation model in embodiment 2 of the present invention;
FIG. 7 is a graph of the length-to-width ratio L/a of a rectangular thin plate and the correlation coefficient η according to example 2 of the present invention;
FIG. 8 is a schematic structural view of a rectangular thin plate in example 3 of the present invention;
fig. 9 is a beam element calculation model in embodiment 3 of the present invention;
FIG. 10 is a graph of the length-to-width ratio L/a of the rectangular thin plate and the correlation coefficient η in example 3 of the present invention.
Detailed Description
The invention is described in further detail below with reference to the accompanying examples.
Example 1
The rectangular thin plate in the embodiment is a rectangular thin plate under the condition of four simply-supported sides, and the method for calculating the deflection delta of the rectangular thin plate comprises the following steps,
step one, establishing a rectangular sheet calculation model: as shown in FIG. 1, the rectangular thin plate in the embodiment has a length a, a width L, a thickness t, L/20 ≤ t ≤ L/5, a material elastic modulus E, a Poisson's ratio μ, and a uniformly distributed vertical load q;
step two, establishing a beam unit calculation model under the condition of four-side simple support: cutting a beam unit with the width of B, the length of L and the thickness of t (see figures 1-2) along the length direction of the rectangular thin plate, wherein the line load of the simply supported beam model is q0B · q (see fig. 3), the deflection Δ of the simply supported beam according to the basic theory of the beam0Is calculated by the formula
Figure BDA0002850655890000041
In the formula (8), ξ is 0.91/(1-u)2) (7)；
Step three, introducing a correlation coefficient eta of the deflection of the thin plate and the deflection of the simply supported beam according to the correlation relationship of the deflection of the thin plate and the deflection of the beam unit intercepted from the thin plate, wherein the correlation coefficient eta comprises a comprehensive influence effect of a two-way effect and a boundary constraint effect of the thin plate on the deflection of the simply supported beam, and the deflection delta of the rectangular thin plate under the condition of four sides simple support is calculated as
Figure BDA0002850655890000051
Step four, determining a correlation coefficient eta introduced in a deflection delta calculation formula (1) of the rectangular thin plate under the condition of simply supporting four sides:
taking a as 2m, 3m and 4m respectively according to the common geometric dimension of the rectangular thin plate, assuming that L/a is changed within the range of 0.4-1.2, taking L/a as 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1 and 1.2 respectively, and carrying out finite element numerical modeling analysis on the rectangular thin plate under the condition of four sides simple support to obtain corresponding deflection delta1(see FIG. 4);
② because delta-delta1(9) I.e. by
Figure BDA0002850655890000052
Simply support L/a and delta in four sides1Respectively carrying the data into an expression (10) to obtain a group of data corresponding to the correlation coefficient eta and the L/a;
carrying out numerical fitting on a group of data corresponding to the correlation coefficient eta and the L/a obtained in the step II to obtain a fitting curve (see figure 4), wherein the functional relation expression of the correlation coefficient eta and the L/a corresponding to the fitting curve is
Figure BDA0002850655890000053
Or
Figure BDA0002850655890000054
The checking process of the deflection calculation accuracy of the rectangular sheet in the embodiment is as follows:
the length a of the rectangular thin plate is 4m, the thickness t is 30mm, and the elastic modulus E is 2.7 × 107kN/m2The Poisson ratio is mu equal to 0.16, and the uniform load is q equal to 2kN/m2。
② substituting each data into the formula (7) and the formula (1) to obtain Δ ═ 0.458 η L4 (11)；
Thirdly, calculating the correlation coefficient eta according to the calculation formula (2a) of the correlation coefficient etaaAnd calculating the obtained correlation coefficient etaaSubstituting into formula (11) to obtain the deflection delta corresponding to different length-width ratios L/a of the rectangular thin plate under the action of uniform loada。
Fourthly, calculating the correlation coefficient eta according to the calculation formula (2b) of the correlation coefficient etabAnd calculating the obtained correlation coefficient etabSubstituting into formula (11) to obtain the deflection delta corresponding to different length-width ratios L/a of the rectangular thin plate under the action of uniform loadb。
Respectively making L/a equal to 0.4, 0.45, 0.55, 0.65, 0.75, 0.85, 0.95, 1.05 and 1.15; then, finite element model calculation is carried out corresponding to each group of geometric dimensions to obtain the deflection delta corresponding to different length-width ratios L/a of the rectangular thin plate under the action of uniformly distributed load1。
The results of the above calculations are shown in table 1.
TABLE 1 deflection calculation results of rectangular sheets under simply supported four sides
Figure BDA0002850655890000055
Figure BDA0002850655890000061
As shown in Table 1, at the same aspect ratio L/a, Δa、ΔbAnd delta1The relatively close relationship indicates that the deflection of the rectangular thin plate is calculated by using the calculation formula of the inventionWith extremely high accuracy, and the two fitting equations (3 fits and 2 fits into segments, respectively) are relatively close, with the computational accuracy of the 2 fits into segments being slightly higher than the 3 fits, but with a maximum error of only 1.69%.
Example 2
The rectangular thin plate in the embodiment is a rectangular thin plate with three simple sides and one fixed side, and the method for calculating the deflection delta of the rectangular thin plate comprises the following steps,
step one, establishing a rectangular sheet calculation model: as shown in fig. 5, the rectangular thin plate in this embodiment has a length a, a width L, a thickness t, L/20 ≤ t ≤ L/5, a material elastic modulus E, a poisson's ratio μ, and a uniformly distributed vertical load q;
step two, establishing a beam unit calculation model under the conditions of three-side simple support and one-side fixed support: cutting a beam unit with width B, length L and thickness t along the length direction of the rectangular thin plate, and according to the basic theory of the beam, as shown in FIG. 6, the deflection delta of the beam unit with three sides simply supported and one side fixedly supported0Is calculated by the formula
Figure BDA0002850655890000062
In the formula (12), ξ is 0.91/(1-u)2) (7)；
Introducing a correlation coefficient eta of the deflection of the thin plate and the deflection of the three-edge simply-supported and one-edge fixedly-supported beam unit according to the correlation relationship of the deflection of the thin plate and the deflection of the beam unit intercepted from the thin plate, wherein the correlation coefficient eta comprises the comprehensive influence effect of the two-way effect and the boundary constraint effect of the thin plate on the deflection of the three-edge simply-supported and one-edge fixedly-supported beam unit, and the deflection delta of the rectangular thin plate under the condition of three-edge simply-supported and one-edge fixedly-supported is calculated as
Figure BDA0002850655890000063
Step four, determining the correlation coefficient eta introduced in the deflection delta calculation formula (3) of the rectangular sheet under the condition of three-side simple support and one-side fixed support:
firstly, according to the common geometric dimension of the rectangular thin plate, a is taken as 2m, 3m and 4m respectively, and L/a is assumed to be changed within the range of 0.4-1.2Taking the L/a as 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1 and 1.2 respectively, and carrying out finite element numerical modeling analysis on the rectangular sheet under the conditions of three-side simple support and one-side fixed support to obtain the corresponding deflection delta1(see FIG. 7);
② because delta-delta1(9) I.e. by
Figure BDA0002850655890000071
The L/a and delta under the condition of three-side simple branch and one-side fixed branch1Respectively carrying into the formula (13) to obtain a group of data corresponding to the correlation coefficient eta and the L/a;
carrying out numerical fitting on a group of data corresponding to the correlation coefficient eta and the L/a obtained in the step II to obtain a fitting curve (see figure 7), wherein the functional relation expression of the correlation coefficient eta and the L/a corresponding to the fitting curve is
Figure BDA0002850655890000072
Or
Figure BDA0002850655890000073
The deflection calculation accuracy checking process of the rectangular sheet in the embodiment is as follows:
the length a of the rectangular thin plate is 4m, the thickness t is 15mm, and the elastic modulus E is 2.1 × 108kN/m2The Poisson ratio is mu equal to 0.3, and the uniform load is q equal to 2kN/m2。
② substituting each data into the formula (7) and the formula (3) to obtain Δ ═ 0.183 η L4 (14)；
Thirdly, calculating the correlation coefficient eta according to the calculation formula (4a) of the correlation coefficient etaaAnd calculating the obtained correlation coefficient etaaSubstituting into the formula (14), the deflection delta corresponding to different length-width ratios L/a of the rectangular thin plate under the action of uniform load is obtaineda。
Fourthly, calculating the correlation coefficient eta according to the calculation formula (4b) of the correlation coefficient etabAnd calculating the obtained correlation coefficient etabIn the alternative to the equation (14),obtaining the deflection delta corresponding to the different length-width ratios L/a of the rectangular thin plate under the action of uniformly distributed loadb。
Fifthly, respectively making L/a equal to 0.4, 0.45, 0.55, 0.65, 0.75, 0.85, 0.95, 1.05 and 1.15; then, carrying out finite element model calculation corresponding to each group of geometric dimensions to obtain the deflection delta corresponding to the different length-width ratios L/a of the rectangular thin plate under the action of uniform load distribution1。
The results of the above calculations are shown in table 2.
TABLE 2 results of the calculation of the deflection of rectangular sheets under the conditions of three-edge simple support and one-edge fixed support
Figure BDA0002850655890000074
Figure BDA0002850655890000081
As shown in Table 2, at the same aspect ratio L/a, Δa、ΔbAnd delta1The approximation indicates that the deflection of the rectangular sheet calculated by the calculation formula of the invention has extremely high precision, and the two fitting formulas (3 fitting and 2 fitting in a segment) are relatively close, wherein the calculation precision of the 2 fitting in the segment is slightly higher than that of the 3 fitting, but the maximum error is only 1.38%.
Example 3
The rectangular thin plate in the embodiment is a rectangular thin plate under the condition of two-side simple support and two-side fixed support, and the method for calculating the deflection delta of the rectangular thin plate comprises the following steps,
step one, establishing a rectangular sheet calculation model: as shown in fig. 8, the rectangular thin plate in this embodiment has a length a, a width L, a thickness t, L/20 ≤ t ≤ L/5, a material elastic modulus E, a poisson's ratio μ, and a uniformly distributed vertical load q;
step two, establishing a beam unit calculation model under the conditions of two-side simple support and two-side fixed support: cutting a beam unit having a width B, a length L and a thickness t along the length direction of the rectangular thin plateThe basic theory of the beam is that the deflection delta of the beam unit with two sides simply supported and two sides fixedly supported is shown in FIG. 90Is calculated by the formula
Figure BDA0002850655890000082
In the formula (15), ξ is 0.91/(1-u)2) (7)；
Introducing the relevant coefficient eta of the deflection of the thin plate and the deflection of the beam unit with two sides simply supported and fixedly supported according to the relevant relation of the deflection of the thin plate and the deflection of the beam unit intercepted from the middle of the thin plate, wherein the relevant coefficient eta comprises the comprehensive influence effect of the bidirectional effect and the boundary constraint effect of the thin plate on the deflection of the beam unit with two sides simply supported and fixedly supported, and the deflection delta of the rectangular thin plate under the condition of two sides simply supported and fixedly supported is calculated as follows
Figure BDA0002850655890000083
Step four, determining a correlation coefficient eta introduced in a deflection delta calculation formula (5) of the rectangular sheet under the conditions of two-side simple support and two-side fixed support:
taking a as 2m, 3m and 4m respectively according to the common geometric dimension of the rectangular sheet, assuming that L/a is changed within the range of 0.4-1.2, taking L/a as 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1 and 1.2 respectively, and carrying out finite element numerical modeling analysis on the rectangular sheet under the condition of two-side simple support and two-side fixed support to obtain corresponding deflection delta1(see FIG. 10);
② because delta-delta1(9) I.e. by
Figure BDA0002850655890000091
The L/a and delta under the condition of simply supporting two sides and fixedly supporting two sides1Respectively carrying the data into an expression (10) to obtain a group of data corresponding to the correlation coefficient eta and the L/a;
carrying out numerical fitting on a group of data corresponding to the correlation coefficient eta and the L/a obtained in the step II to obtain a fitting curve (see figure 10),
the functional relation expression of the correlation coefficient eta and the L/a corresponding to the fitting curve is
Figure BDA0002850655890000092
Or
Figure BDA0002850655890000093
The checking process of the deflection calculation accuracy of the rectangular sheet in the embodiment is as follows:
the length a of the rectangular thin plate is 4m, the thickness t is 20mm, and the elastic modulus E is 8 × 107kN/m2The Poisson ratio is mu equal to 0.28, and the uniform load is q equal to 2kN/m2。
② substituting each data into the formula (7) and the formula (5) to obtain Δ ═ 0.098 η L4 (17)；
Thirdly, calculating the correlation coefficient eta according to the calculation formula (6a) of the correlation coefficient etaaAnd calculating the obtained correlation coefficient etaaSubstituting into formula (17) to obtain the deflection delta corresponding to different length-width ratios L/a of the rectangular thin plate under the action of uniform loada。
Fourthly, calculating the correlation coefficient eta according to the calculation formula (6b) of the correlation coefficient etabAnd calculating the obtained correlation coefficient etabSubstituting into formula (17) to obtain the deflection delta corresponding to different length-width ratios L/a of the rectangular thin plate under the action of uniform loadb。
Respectively making L/a equal to 0.4, 0.45, 0.55, 0.65, 0.75, 0.85, 0.95, 1.05 and 1.15; then, carrying out finite element model calculation corresponding to each group of geometric dimensions to obtain the deflection delta corresponding to the different length-width ratios L/a of the rectangular thin plate under the action of uniform load distribution1。
The results of the above calculations are shown in table 3.
TABLE 3 deflection calculation results of rectangular sheets under the conditions of two-side simple support and two-side fixed support
Figure BDA0002850655890000094
Figure BDA0002850655890000101
As shown in Table 3, at the same aspect ratio L/a, Δa、ΔbAnd delta1The approximation indicates that the deflection of the rectangular thin plate calculated by the calculation formula of the invention has extremely high precision, and the two fitting formulas (3 fitting and 2 fitting by segmentation respectively) are approximate, and the maximum error is only 2.17%, which is obviously less than 5%.
The present embodiment also provides a computer-readable storage medium having stored thereon a computer program that, when executed by a processor, executes the above-described calculation method to calculate the deflection of the rectangular sheet and output the calculation result.

Claims (2)

1. The method for calculating the deflection of the rectangular thin plate is characterized in that the length of the rectangular thin plate is a, the width of the rectangular thin plate is L, the thickness of the rectangular thin plate is t, L/20 is equal to or more than t and equal to or less than L/5, the elastic modulus of the rectangular thin plate is E, the Poisson ratio of the rectangular thin plate is mu, uniformly distributed vertical loads q are applied to the rectangular thin plate under various boundary conditions, and the deflection delta of the rectangular thin plate is calculated by adopting the following formula:
i) under the condition of simply supporting four sides, the deflection delta of the rectangular thin plate is calculated by the formula
Figure FDA0002850655880000011
In the formula (1), the reaction mixture is,
Figure FDA0002850655880000012
or
Figure FDA0002850655880000013
ii) under the conditions of simple three-edge support and fixed one-edge support, the deflection delta of the rectangular sheet is calculated by the formula
Figure FDA0002850655880000014
In the formula (3), the reaction mixture is,
Figure FDA0002850655880000015
or
Figure FDA0002850655880000016
iii) under the condition of two-side simple support and two-side fixed support, the deflection delta of the rectangular sheet is calculated by the formula
Figure FDA0002850655880000017
In the formula (5), the reaction mixture is,
Figure FDA0002850655880000018
or
Figure FDA0002850655880000019
Wherein eta is the correlation coefficient of the deflection of the thin plate and the deflection of a beam unit cut from the thin plate, and xi is 0.91/(1-u)2) (7)。
2. A computer-readable storage medium, on which a computer program is stored which, when being executed by a processor, carries out the method of claim 1.
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Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20070059107A1 (en) * 2005-09-09 2007-03-15 Van Riper Edwin D Slab-on-ground foundation design method
CN105389432A (en) * 2015-11-09 2016-03-09 宋伟宁 Method for calculating load distribution intensity and maximum bending moment of rectangular two-way slab system
CN110569545A (en) * 2019-08-06 2019-12-13 湖北大成空间科技股份有限公司 Method for determining deflection and internal force of prefabricated combined type cavity floor
KR20200093307A (en) * 2019-01-28 2020-08-05 연세대학교 산학협력단 Slab Optimum Design Method and System having Floor Vibration Filtering of two-way slab

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20070059107A1 (en) * 2005-09-09 2007-03-15 Van Riper Edwin D Slab-on-ground foundation design method
CN105389432A (en) * 2015-11-09 2016-03-09 宋伟宁 Method for calculating load distribution intensity and maximum bending moment of rectangular two-way slab system
KR20200093307A (en) * 2019-01-28 2020-08-05 연세대학교 산학협력단 Slab Optimum Design Method and System having Floor Vibration Filtering of two-way slab
CN110569545A (en) * 2019-08-06 2019-12-13 湖北大成空间科技股份有限公司 Method for determining deflection and internal force of prefabricated combined type cavity floor

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
程选生;杜永峰;党育;: "热载下三边简支一边固支矩形薄板的解", 低温建筑技术, no. 04, 28 August 2007 (2007-08-28) *
金凌如等: "薄壁钢桁架-轻骨料混凝土组合楼板受力性能试验研究", 建筑结构学报, vol. 37, 31 May 2016 (2016-05-31) *

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