A stable design method for multi-cavity corrugated steel plate composite wall under complex loads

Abstract

The present invention discloses a stability design method of a multi - cavity corrugated steel plate composite wall under complex loads. First, the ultimate moment bearing capacities of the multi - cavity corrugated steel plate composite wall about the strong axis and the weak axis are obtained through calculation, which are calculated by formulas (4) and (5) respectively. Then, the corresponding stability coefficients are obtained according to the boundary conditions and load conditions. Finally, the above physical parameters are substituted into the N - M z -M y correlation formulas, and the relationships that the axial pressure N, the in - plane moment M z and the out - of - plane moment M y of the multi - cavity corrugated steel plate composite wall need to satisfy when ensuring stability can be obtained. The simply - supported on both sides in - plane compression - bending, simply - supported on three sides bi - axial compression - bending, and simply - supported on four sides bi - axial compression - bending satisfy formulas (1), (2), and (3) respectively: #imgabs0##imgabs1##imgabs2#

Description

Technical Field

[0001] The invention relates to a stability calculation method for a multi-cavity corrugated steel plate composite wall under complex loads, and belongs to the field of structural engineering technology. Technical Background

[0002] The multi-cavity corrugated steel plate composite wall is a new type of steel-concrete composite lateral force resisting structure. It is composed of rectangular steel tube concrete and corrugated steel plate concrete cavities arranged alternately. The corrugated steel plate has the advantages of large cross-sectional rigidity and small steel consumption, which can effectively restrain the internal concrete, thereby improving the ultimate bearing capacity of the wall. In actual engineering, the boundary conditions of the multi-cavity corrugated steel plate composite wall are very complex and will be subject to complex loads such as combined compression and bending. In order to ensure the safety of the structure, the calculation of its stability performance is crucial.

[0003] The stability design method of multi-cavity corrugated steel plate composite wall can only refer to other forms of composite wall. However, the structure of different forms of composite wall is different, and multi-cavity corrugated steel plate composite wall has obvious anisotropic stiffness, so the stability calculation method of other forms of composite wall is obviously not suitable for multi-cavity corrugated steel plate composite wall. Summary of the invention

[0004] In order to solve the above problems, the present invention proposes a stable design method for multi-cavity corrugated steel plate composite wall, which includes the formula for the correlation between axial pressure and bending moment, and the calculation formula for the moment bearing capacity of the section rotating around the strong axis and the weak axis. The applicable objects include two-side simply supported multi-cavity corrugated steel plate composite wall under in-plane compression and bending load, three-side simply supported multi-cavity corrugated steel plate composite wall under bidirectional compression and bending load, and four-side simply supported multi-cavity corrugated steel plate composite wall under bidirectional compression and bending load.

[0005] A stable design method for a multi-cavity corrugated steel plate composite wall under complex loads comprises the following steps:

[0006] The boundary conditions of the multi-cavity corrugated steel plate composite wall are two-side simple support, three-side simple support and four-side simple support, and the loads are the combined action of axial pressure and bending moment in the plane, and the combined action of axial pressure and bidirectional bending moment;

[0007] The correlation between axial pressure and bending moment is calculated and designed for the two-side simply supported multi-cavity corrugated steel plate composite wall under in-plane compression and bending load, the three-side simply supported multi-cavity corrugated steel plate composite wall under bidirectional compression and bending load, and the four-side simply supported multi-cavity corrugated steel plate composite wall under bidirectional compression and bending load. The ultimate bending moment bearing capacity around the strong axis and the weak axis is calculated and designed to obtain the multi-cavity corrugated steel plate composite wall with stability that meets the design requirements.

[0008] (1) Ultimate bearing capacity of multi-cavity corrugated steel plate composite wall under complex boundary conditions and complex loads

[0009] For a composite wall with multiple cavities of corrugated steel plates and simply supported on both sides under in-plane compression and bending loads, the out-of-plane stability must satisfy equation (1):

[0010]

[0011] For a three-side simply supported multi-cavity corrugated steel plate composite wall under bidirectional compression and bending load, the out-of-plane stability must satisfy equation (2):

[0012]

[0013] For a composite wall with four-sided simple support and multiple cavities of corrugated steel plates under bidirectional compression and bending loads, the out-of-plane stability must satisfy equation (3):

[0014]

[0015] The meanings of the parameters in formulas (1)-(3) are as follows:

[0016] N——Design value of axial pressure of multi-cavity corrugated steel plate composite wall;

[0017] M z ——Design value of in-plane bending moment of multi-cavity corrugated steel plate composite wall;

[0018] M y ——Design value of out-of-plane bending moment of multi-cavity corrugated steel plate composite wall;

[0019] α1——correction coefficient, take 0.45;

[0020] ——Out-of-plane stability coefficient of multi-cavity corrugated steel plate composite wall under axial compressive load under corresponding boundary conditions;

[0021] ——Out-of-plane stability coefficient of multi-cavity corrugated steel plate composite wall under pure bending load under corresponding boundary conditions;

[0022] M uz ——Sectional moment bearing capacity of multi-cavity corrugated steel plate composite wall rotating along the strong axis;

[0023] M uy ——Sectional bending moment bearing capacity of multi-cavity corrugated steel plate composite wall rotating along the weak axis.

[0024] N u,th ——Cross-sectional bearing capacity of multi-cavity corrugated steel plate composite wall;

[0025] (2) Ultimate moment bearing capacity of multi-cavity corrugated steel plate composite wall section around strong axis and weak axis

[0026] According to the principle of equal front and rear equivalent areas, the cross section of the multi-cavity corrugated steel plate composite wall is equivalent to a rectangular cross section of the same width, so the moment bearing capacity M around the strong axis is uz Calculate according to formula (4):

[0027]

[0028] Where B is the overall width of the composite wall; t' c is the equivalent steel plate width; d' c is the equivalent wall thickness; x is the height of the compression zone. The calculation formula for the above parameters is as follows:

[0029] B=(n w +1)b c +n w b w (5)

[0030]

[0031]

[0032]

[0033] Section moment bearing capacity M of multi-cavity corrugated steel plate composite wall rotating around weak axis uy Calculate according to formula (9):

[0034]

[0035] where d w,avg is the average cross-sectional thickness of the corrugated cavity, is the maximum cross-sectional thickness d w,max and minimum cross-sectional thickness d w,min The average value of d1 is the distance from the edge of the steel tube concrete column to the crest of the corrugated cavity; y0 is the height of the compression zone, which is calculated as follows:

[0036]

[0037] The meanings of the remaining parameters appearing in equations (4)-(10) are shown as follows:

[0038] f ck ——standard value of axial compressive strength of concrete;

[0039] f y ——yield strength of steel;

[0040] d c ——The thickness of the rectangular steel tube (i.e. the thickness of the composite wall);

[0041] b c ——the width of the steel pipe column;

[0042] t c ——Thickness of steel pipe column;

[0043] b w ——Wavelength of the waveform cavity;

[0044] t w ——Thickness of corrugated cavity plate;

[0045] n w ——Number of waveform cavities.

[0046] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0047] 1. Comprehensively solve the stability calculation problem of multi-cavity corrugated steel plate composite wall under complex loads.

[0048] 2. The stability calculation method of the multi-cavity corrugated steel plate composite wall under complex loads proposed in the present invention fills the gap in the relevant field, can accurately reflect the NM correlation of the composite wall under complex loads, improves the accuracy while ensuring the safety of the composite wall, supplements and standardizes the structural design process, and reduces the construction cost. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1a This is the front view of the multi-cavity corrugated steel plate composite wall;

[0050] Figure 1b This is a top view of a multi-cavity corrugated steel plate composite wall;

[0051] Figure 1c This is the left view of the multi-cavity corrugated steel plate composite wall;

[0052] Figure 1d This is the dimension drawing of corrugated steel plate;

[0053] Figure 2a Schematic diagram of the equivalent front section for calculating the moment bearing capacity about the strong axis. The dotted line represents the neutral axis.

[0054] Figure 2b Schematic diagram of the equivalent rear section for calculating the moment bearing capacity about the strong axis. The dotted line represents the neutral axis.

[0055] Figure 3 Schematic diagram of the cross section for calculating the moment bearing capacity around the weak axis;

[0056] Figure 4 NM is the load of the two-side simply supported multi-cavity corrugated composite wall under complex loads. z Related curves, the squares represent finite element examples, and the curves represent NM z Correlation curve. DETAILED DESCRIPTION

[0057] The technical solution of the present invention is further described below in conjunction with the accompanying drawings, which is specifically divided into five steps (1), (2), (3), (4), and (5):

[0058] (1) Determine the out-of-plane stability calculation formula of the multi-cavity corrugated steel plate composite wall based on boundary conditions and load conditions

[0059] For a composite wall with multiple cavities of corrugated steel plates and simply supported on both sides under in-plane compression and bending loads, the out-of-plane stability must satisfy equation (1):

[0060]

[0061] For a three-side simply supported multi-cavity corrugated steel plate composite wall under bidirectional compression and bending load, the out-of-plane stability must satisfy equation (2):

[0062]

[0063] For a composite wall with four-sided simple support and multiple cavities of corrugated steel plates under bidirectional compression and bending loads, the out-of-plane stability must satisfy equation (3):

[0064]

[0065] The meanings of the parameters in formula (1)-(2) are as follows:

[0066] N——Design value of axial pressure of multi-cavity corrugated steel plate composite wall;

[0067] M z ——Design value of in-plane bending moment of multi-cavity corrugated steel plate composite wall;

[0068] M y ——Design value of out-of-plane bending moment of multi-cavity corrugated steel plate composite wall;

[0069] α1——correction coefficient, take 0.45;

[0070] ——Out-of-plane stability coefficient of multi-cavity corrugated steel plate composite wall under axial compressive load under corresponding boundary conditions;

[0071] ——Out-of-plane stability coefficient of multi-cavity corrugated steel plate composite wall under pure bending load under corresponding boundary conditions;

[0072] M uz ——Sectional moment bearing capacity of multi-cavity corrugated steel plate composite wall rotating along the strong axis;

[0073] M uy ——Sectional bending moment bearing capacity of multi-cavity corrugated steel plate composite wall rotating along the weak axis.

[0074] N u,th——Cross-sectional bearing capacity of multi-cavity corrugated steel plate composite wall;

[0075] (2) Determine the ultimate moment bearing capacity of the multi-cavity corrugated steel plate composite wall section around the strong axis and weak axis

[0076] According to the principle of equal front and rear equivalent areas, the cross section of the multi-cavity corrugated steel plate composite wall is equivalent to a rectangular cross section of the same width, so the moment bearing capacity M around the strong axis is uz Calculate according to formula (4):

[0077]

[0078] Where B is the overall width of the composite wall; t' c is the equivalent steel plate width; d' c is the equivalent wall thickness; x is the height of the compression zone. The calculation formula for the above parameters is as follows:

[0079] B=(n w +1)b c +n w b w (5)

[0080]

[0081]

[0082]

[0083] Section moment bearing capacity M of multi-cavity corrugated steel plate composite wall rotating around weak axis uy Calculate according to formula (9):

[0084]

[0085] where d w,avg is the average cross-sectional thickness of the corrugated cavity, is the maximum cross-sectional thickness d w,max and minimum cross-sectional thickness d w,min The average value of d1 is the distance from the edge of the steel tube concrete column to the crest of the corrugated cavity; y0 is the height of the compression zone, which is calculated as follows:

[0086]

[0087] The meanings of the remaining parameters appearing in equations (4)-(10) are shown as follows:

[0088] f ck ——standard value of axial compressive strength of concrete;

[0089] f y ——yield strength of steel;

[0090] dc ——The thickness of the rectangular steel tube (i.e. the thickness of the composite wall);

[0091] b c ——the width of the steel pipe column;

[0092] t c ——Thickness of steel pipe column;

[0093] b w ——Wavelength of the waveform cavity;

[0094] t w ——Thickness of corrugated cavity plate;

[0095] n w ——Number of waveform cavities.

[0096] (3) Determine the regularized slenderness ratio based on boundary conditions and load conditions

[0097] Regularized slenderness ratio λ of multi-cavity corrugated steel plate composite wall n It can be calculated as follows:

[0098]

[0099] Where: The ultimate compressive bearing capacity of the cross section is N u,th Calculate according to formula (12):

[0100] N u,th =A c f ck +A s f y (12)

[0101] Among them A c is the area of ​​concrete, A s is the area of ​​the steel, calculated according to formula (13) and (14) respectively; f ck and f y They are the standard value of the axial compressive strength of concrete and the yield strength of steel respectively.

[0102] A c =2(n w +1)(d c -2t c )(b c -2t c )+n w b w (d w,avg -2t w ) (13)

[0103] A s =2(n w +1)[d c b c-(d c -2t c )(b c -2t c )] (14)

[0104] For a wall with two simply supported axial compression, the critical buckling load N cr The calculation formula is as follows:

[0105]

[0106] Where a is the effective length of the member; D x is the bending stiffness constant in the x direction;

[0107] D x =E s I s,y +E c I c,y (16)

[0108] Where E s and E c are the elastic moduli of steel and concrete respectively; I s,y is the moment of inertia of the steel part of the cross section about the y-axis; I c,y is the moment of inertia of the concrete portion of the cross section about the y-axis.

[0109]

[0110]

[0111] For a three-sided simply supported axial compression wall, the critical buckling load N cr The calculation formula is as follows:

[0112]

[0113] Where a and b are the height and width of the wall respectively; D xy is the free torsional stiffness constant. The calculation formula is as follows:

[0114]

[0115] Among them J s,col is the free torsional inertia moment of the steel in the concrete-filled steel tube column, J c,col is the free torsional inertia moment of the concrete in the steel tube concrete column; J s,cell is the free torsional inertia moment of the steel in the corrugated cavity, J c,cell is the free torsional inertia moment of concrete in the corrugated cavity; when calculating the free torsional inertia moment, the corrugated cavity takes the average cross section. The above parameters are calculated according to the following formulas:

[0116]

[0117]

[0118]

[0119]

[0120] For a three-sided simply supported pure bending wall, the critical buckling load N cr The calculation formula is as follows:

[0121]

[0122] For a wall with four sides simply supported under axial compression, the critical buckling load N cr The calculation formula is as follows:

[0123]

[0124] Where k is calculated according to the formula.

[0125]

[0126] Where α = a / b; D y is the bending stiffness constant in the y direction; H is calculated from D xy and D μ It consists of two parts. The calculation formula is as follows:

[0127]

[0128]

[0129] Where D μ,col and D μ,cell are the additional stiffness caused by the column and corrugated cavity in another direction, and the calculation formula is as follows:

[0130]

[0131]

[0132] μ in equations (30) and (31) s and μ c are the Poisson's ratios of steel and concrete respectively, and μ s =0.3, μ c =0.2.

[0133] For a four-sided simply supported pure bending wall, the critical buckling load N cr The calculation formula is as follows:

[0134]

[0135] Where k is calculated according to formula (33).

[0136]

[0137] Substituting the obtained section bearing capacity and critical buckling load into formula (11), the corresponding regularized slenderness ratio can be obtained.

[0138] (4) Determine the stability coefficient under axial compression and pure bending based on boundary conditions

[0139] Out-of-plane stability coefficient of composite wall with multi-cavity corrugated steel plates under axial compression load under simply supported conditions on both sides Calculate according to formula (34), and calculate according to formula (35) for simply supported walls on three sides and simply supported walls on four sides:

[0140]

[0141]

[0142] Out-of-plane stability coefficient of three-side and four-side simply supported multi-cavity corrugated steel plate composite walls under pure bending load All are calculated according to formula (36);

[0143]

[0144] where λ n is the normalized slenderness ratio of the multi-cavity corrugated steel plate composite wall.

[0145] (5) Determine NM y -M z Correlation

[0146] Get the stability factor and the ultimate moment bearing capacity M of the cross section around the strong axis and weak axis uz 、M uy Then, according to the corresponding boundary conditions and load conditions, substitute the corresponding formula to obtain NM y or NM y -M z Correlation relationship.

[0147] In order to illustrate the accuracy and effectiveness of this method in calculating the stability of multi-cavity corrugated steel plate composite walls under complex loads, a simple-supported multi-cavity corrugated steel plate composite wall under the combined action of compression and bending is taken as an example, and several actual component examples are taken for verification. z A comparison of the correlation curves is described below.

[0148] Figure 4 The curve in the figure represents the NM of the simply supported multi-cavity corrugated steel plate composite wall on both sides. zThe relevant curve can be calculated by formula (1). The square represents the finite element calculation result of the combined wall under the combined action of axial compression load and bending moment. When the calculation point is located on the inside of the curve, it means that the curve is dangerous; when the calculation point is located on the outside of the curve, it means that the curve is suitable for the stability calculation of the combined wall. It can be seen that the calculation points are all distributed on the outside of the curve, and the inner envelope of the curve and the calculation point is well matched, NM z The correlation curves enable safe and accurate prediction of the stability of combined walls.

[0149] In summary, the formula of the present invention can accurately reflect the correlation between the axial force and the bending moment of the multi-cavity corrugated steel plate composite wall under complex loads, filling the gap in the existing structural design technology.

Claims

1. A method for designing the stability of a multi-cavity corrugated steel plate composite wall under complex loads, characterized in that: include: The boundary conditions of the multi-cavity corrugated steel plate composite wall are two-side simple support, three-side simple support and four-side simple support, and the loads are the combined action of axial pressure and in-plane bending moment, and the combined action of axial pressure and bidirectional bending moment. Firstly, the calculation formula of the ultimate moment bearing capacity of the multi-cavity corrugated steel plate composite wall around the strong axis and the weak axis is given. Then, the compression-bending stability bearing capacity of the two-side simply supported multi-cavity corrugated steel plate composite wall under the action of in-plane compression-bending load, the three-side simply supported multi-cavity corrugated steel plate composite wall under the action of bidirectional compression-bending load, and the four-side simply supported multi-cavity corrugated steel plate composite wall under the action of bidirectional compression-bending load are calculated and designed. Then, the regularized slenderness ratio is determined in combination with the boundary conditions and load conditions, the stability coefficient under axial compression and pure bending is determined in combination with the boundary conditions, and finally NM is determined. y -M z The correlation relationship was obtained, and the multi-cavity corrugated steel plate composite wall whose stability met the design requirements was obtained; For the composite wall with two-sided simply supported multi-cavity corrugated steel plates under in-plane compression and bending load, the compression and bending stability bearing capacity calculation and design are carried out. To maintain out-of-plane stability, the following formula (1) must be satisfied: For the three-side simply supported multi-cavity corrugated steel plate composite wall under bidirectional compression and bending load, the bidirectional compression and bending stability bearing capacity calculation and design are carried out. To maintain the out-of-plane stability, formula (2) must be satisfied: For the four-side simply supported multi-cavity corrugated steel plate composite wall under bidirectional compression and bending load, the bidirectional compression and bending stability bearing capacity calculation and design are carried out. To maintain the out-of-plane stability, the formula (3) must be satisfied: The meanings of the parameters in formulas (1)-(3) are as follows: N——Design value of axial pressure of multi-cavity corrugated steel plate composite wall; M z ——Design value of in-plane bending moment of multi-cavity corrugated steel plate composite wall; M y ——Design value of out-of-plane bending moment of multi-cavity corrugated steel plate composite wall; α1——correction coefficient; ——Out-of-plane stability coefficient of multi-cavity corrugated steel plate composite wall under axial compressive load under corresponding boundary conditions; ——Out-of-plane stability coefficient of multi-cavity corrugated steel plate composite wall under pure bending load under corresponding boundary conditions; M uz ——Sectional moment bearing capacity of multi-cavity corrugated steel plate composite wall rotating along the strong axis; M uy ——Sectional moment bearing capacity of multi-cavity corrugated steel plate composite wall rotating along the weak axis; N u,th ——Cross-sectional bearing capacity of multi-cavity corrugated steel plate composite wall.

2. The stability design method of the multi-cavity corrugated steel plate composite wall under complex loads according to claim 1 is characterized in that: Calculation and design of ultimate moment bearing capacity around strong and weak axes, including: According to the principle of equal front and rear equivalent areas, the cross section of the multi-cavity corrugated steel plate composite wall is equivalent to a rectangular cross section of the same width, so the moment bearing capacity M around the strong axis is uz Calculate according to formula (4): Where B is the overall width of the composite wall; t' c is the equivalent steel plate width; d' c is the equivalent wall thickness; x is the height of the compression zone. The calculation formulas for the above parameters are as follows: B=(n w +1)b c +n w b w (5) Section moment bearing capacity M of multi-cavity corrugated steel plate composite wall rotating around weak axis uy Calculate according to formula (9): where d w,avg is the average cross-sectional thickness of the corrugated cavity, is the maximum cross-sectional thickness d w,max and minimum cross-sectional thickness d w,min The average value of d1 is the distance from the edge of the steel tube concrete column to the crest of the corrugated cavity; y0 is the height of the compression zone, which is calculated as follows: The meanings of the remaining parameters appearing in equations (4)-(10) are shown as follows: f ck ——standard value of axial compressive strength of concrete; f y ——yield strength of steel; d c ——Thickness of rectangular steel tube; b c ——the width of the steel pipe column; t c ——Thickness of steel pipe column; b w ——Wavelength of the waveform cavity; t w ——Thickness of corrugated cavity plate; n w ——Number of waveform cavities.

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