Three-dimensional finite element static and dynamic analysis reinforcement calculation method for hydropower house

Abstract

The invention discloses a three-dimensional finite element static and dynamic analysis reinforcement calculation method for a hydropower station plant, which comprises the following steps of: S1, establishing an integral three-dimensional finite element model of the plant, and obtaining internal force and stress of each point of a structure under a static and dynamic combination; s2, selecting the key part and the section of each point of the structure with the stress greater than a preset stress threshold value to perform internal force extraction, wherein the internal force comprises axial force and bending moment; s3, reinforcement design is conducted on the framed bent structure, specifically, the bending moment is amplified by considering the second-order effect of a framed bent column, reinforcement design is conducted through an envelope diagram method according to the axial force and the second-order bending moment, bidirectional bending checking is conducted on reinforcement design, and the reinforcement design is adjusted according to the checking result; and S4, reinforcement design is conducted on the non-framed bent structure, specifically, reinforcement design is conducted on the non-framed bent structure through an envelope diagram method according to the axial force and the bending moment.

Description

Technical Field

[0001] The invention belongs to the field of water conservancy and hydropower engineering construction, and specifically relates to a three-dimensional finite element static and dynamic analysis reinforcement calculation method for a hydropower station plant building. Background Art

[0002] As the main building structure for hydropower generation, the powerhouse of a hydropower station is usually divided vertically into an upper structure and a lower structure with the generator bottom plate as the boundary. The upper structure is composed of walls, plates, beams, columns, etc., which is similar to the structure of a single-layer power station; the lower structure is composed of a large concrete structure that accommodates the turbine generator, and the stiffness and mass of the upper structure are significantly lower than those of the lower structure. The western region is a region with intensive water conservancy project construction in my country. The region is rich in hydropower resources and is also located in an earthquake-prone area. The seismic safety of hydropower station buildings cannot be ignored during the construction of water conservancy projects. Through the investigation of previous hydropower project disasters, it was found that there was less earthquake damage to large concrete structures in hydropower station projects, and the auxiliary buildings mainly composed of bent column structures had more severe earthquake damage. The bent column structure has a small stiffness, and the second-order effect becomes an important factor affecting its seismic performance, especially under medium and large earthquakes. How to reasonably consider the reinforcement of bent columns in hydropower station projects is a hot topic of research at present. Summary of the invention

[0003] In view of the above-mentioned deficiencies in the prior art, the present invention provides a three-dimensional finite element static and dynamic analysis reinforcement calculation method for a hydropower plant building, which solves the problem of insufficient accuracy and efficiency in the static and dynamic reinforcement design of existing hydraulic structures.

[0004] In order to achieve the above-mentioned invention object, the technical solution adopted by the present invention is: a three-dimensional finite element static and dynamic analysis reinforcement calculation method for a hydropower plant building, comprising the following steps:

[0005] S1. Establish a three-dimensional finite element model of the entire plant to obtain the internal forces and stresses of each point of the structure under static and dynamic combinations;

[0006] S2. Select the cross-sections of key parts and points of the structure where the stress is greater than the preset stress threshold to extract the internal forces, which include axial force and bending moment;

[0007] S3. Design reinforcement for bent structure: consider the second-order effect of bent column to amplify the bending moment, use envelope diagram method to design reinforcement according to axial force and second-order bending moment, perform bidirectional bending check on reinforcement design, and adjust reinforcement design according to the check result;

[0008] S4: Reinforcement design for non-bent structures: Reinforcement design for non-bent structures is performed using the envelope diagram method based on axial force and bending moment.

[0009] Further: S1 specifically includes:

[0010] S11. Establish the overall three-dimensional finite element model of the plant, including the upper frame structure, the lower mass concrete structure and the foundation;

[0011] S12. Based on the overall three-dimensional finite element model of the plant, the finite element method is used to perform vibration mode decomposition response spectrum calculation under earthquake conditions;

[0012] S13. Combining the internal forces and stresses of each point of the structure obtained from different vibration modes by using CQC or SRSS method, and combining the internal forces and stresses of each point of the structure obtained from earthquakes in different directions by using SRSS method, to obtain the internal forces and stresses of each point of the structure under earthquake conditions;

[0013] S14. According to the most unfavorable principle, the internal forces and stresses of each point of the structure under the earthquake condition are statically and dynamically combined to obtain the internal forces and stresses of each point of the structure under the static and dynamic combination.

[0014] Further: In S2, the method for extracting the axial force and bending moment of any cross section includes a node force method and a path integral method.

[0015] Further: S3 includes the following sub-steps:

[0016] S31. Determine whether the bending moment of the bent column ignores the second-order effect. If so, take the extracted bending moment as the first-order bending moment. If not, calculate the second-order bending moment of the bent column end after considering the amplified second-order effect.

[0017] S32, determining whether the bending moment of the bent column needs to be further amplified along the length direction of the column;

[0018] S33, judging whether the ratio of the second-order bending moment to the first-order bending moment is less than 1.4, if so, performing reinforcement design according to the second-order bending moment, and entering S34;

[0019] If not, redesign the size of the column, modify the length and width of the column, and return to S31;

[0020] S34, performing bidirectional bending check on the current reinforcement amount, and determining whether the check result meets the bidirectional bending requirement;

[0021] If yes, then the reinforcement design is carried out according to the current reinforcement amount. If no, then the amount of steel bars is increased until the two-way bending requirements are met, and the reinforcement design is carried out according to the reinforcement amount of the increased steel bars.

[0022] Further: In said S31, the method for judging whether the bending moment of the bent column ignores the second-order effect is specifically as follows:

[0023] For bent columns of frame structures with lateral displacement, the second-order effect can be ignored if the following equation is satisfied:

[0024]

[0025] Where k is the effective length coefficient, l u is the unsupported length, r is the radius of gyration;

[0026] For bent columns of frame structures without side shift, the second-order effect can be ignored if the following equation is satisfied:

[0027]

[0028] Where M1 / M2 is the ratio of the bending moment at the smaller end to the bending moment at the larger end.

[0029] Further: In the above S31, the method for calculating the second-order bending moment at the bent column end after considering the amplified second-order effect is specifically as follows:

[0030] For bent columns of frame structures with lateral displacement, the expression for calculating the second-order bending moment at the bent column end after considering the amplified second-order effect is as follows:

[0031]

[0032] Where M1' is the second-order bending moment corresponding to one end of the column end of the frame structure with lateral displacement, M'2 is the second-order bending moment corresponding to the other end of the column end of the frame structure with lateral displacement, and M 1ns is the bending moment at the first column end caused by gravity load, M 2ns is the bending moment at the second column end caused by gravity load, δ s is the first bending moment magnification factor, and its specific expression is:

[0033]

[0034] Where, ΣP u is the sum of all vertical loads in the same layer, ΣP c is the sum of all critical loads in the same layer, and its specific expression is:

[0035]

[0036] In the formula, E c is the elastic modulus of concrete, I g is the section moment of inertia;

[0037] For the bent columns of the frame structure without side shift, the expression for calculating the second-order bending moment at the bent column end after considering the amplified second-order effect is as follows:

[0038] M c =δ ns M2

[0039] Where M c is the second-order bending moment corresponding to the column end of the frame structure without side displacement, δ nsis the second bending moment magnification factor, and its specific expression is:

[0040]

[0041] Further: the S32 is specifically:

[0042] Determine whether the relationship between the unsupported length and the gyration radius is satisfied, wherein the relationship between the unsupported length and the gyration radius is specifically:

[0043]

[0044] If yes, the bending moment does not need to be further amplified along the length of the column. If no, the bending moment needs to be further amplified along the length of the column. The expression of the amplified bending moment M4 is:

[0045] M4=δ ns M3

[0046] Where M3 is the first-order bending moment along the column shaft.

[0047] Further: In said S34, the method for performing bidirectional bending verification is specifically as follows:

[0048] Determine whether the bending moment on the envelope diagram of the current reinforcement quantity satisfies the bidirectional bending formula. If so, the verification result satisfies the bidirectional bending requirements. If not, the verification result does not meet the bidirectional bending requirements. The bidirectional bending formula is specifically as follows:

[0049]

[0050] Where M ux ,、M uy is the bending moment of the cross section, For M uy When it is 0, the axial force P of the section u The bending moment on the envelope diagram of the corresponding position, For M ux When it is 0, the axial force P of the section u The bending moment on the envelope diagram at the corresponding position, K is the verification coefficient, which is 1.5 when the cross section is a rectangular cross section and 1.75 when the cross section is a circular or square cross section.

[0051] Further: S4 includes the following sub-steps:

[0052] S41. Preset the number of reinforcements;

[0053] S42, based on the set number of reinforcements, calculate the critical bearing capacity that the cross section can provide according to the cross-sectional concrete and the number of reinforcements of the non-bent structure, and determine the boundary of the envelope diagram;

[0054] S43, determine whether the axial force and bending moment fall within the envelope diagram. If so, the current number of reinforcements meets the requirements and the reinforcement design is completed. If not, increase the current number of reinforcements and return to S42.

[0055] Further: in said S42, the boundary of the envelope diagram includes first to fifth boundary points;

[0056] The coordinates of the first boundary point are (0, P uc ), the first coordinate value P uc The specific expression is:

[0057] P uc =0.8*P0

[0058] P0=φ uc *[0.85*f c ′* ( A g -A s -A s ′)+f y * ( A s +A s ′)]

[0059] Where P0 is the intermediate coordinate value, f c ' is the specific compressive strength of concrete, A g is the total area of ​​the concrete cross section, A s is the tensile reinforcement area, A s ′ is the longitudinal non-prestressed compression reinforcement area, f y is the yield strength of concrete, φ uc is the first strength reduction factor;

[0060] The coordinates of the second boundary point are (0, P ut ), the second coordinate value P ut The specific expression is:

[0061] P ut =0.8*φ ut *f y *(A s +A s ′)

[0062] The coordinates of the third boundary point are (M ub , 0), the third coordinate value P ut The specific expression is:

[0063]

[0064] In the formula, E sis the elastic modulus of the steel bar, b is the length dimension, h is the width dimension, c is the distance from the maximum strain fiber to the neutral axis, β1 is the coefficient of the ratio of the height of the equivalent rectangular compressive stress block to the height from the compression side of the section to the neutral axis, ε c is the maximum strain of the compressive fiber at the outermost edge of the concrete, φ ub is the second strength reduction factor, d′ is the thickness of the protective layer of the steel bars in the compression zone, and d″ is the thickness of the protective layer of the steel bars in the tension zone;

[0065] The coordinates of the fourth boundary point are (M u , P u ), the fourth coordinate value P u The specific expression is:

[0066]

[0067] In the formula, φ ua is the third strength reduction factor, c t is the distance from the maximum strain fiber to the neutral axis, and its specific expression is:

[0068]

[0069] The fifth coordinate value M u The specific expression is:

[0070]

[0071] The coordinates of the fifth boundary point are (M5, P uc ), the expression of the sixth coordinate value M5 is specifically:

[0072]

[0073] The beneficial effects of the present invention are:

[0074] (1) The present invention provides a three-dimensional finite element static and dynamic analysis reinforcement calculation method for a hydropower plant building, which comprehensively considers the reinforcement design requirements when the cross section is in pure tension, pure compression, bending tension, bending compression and pure bending, and provides a high-precision and high-efficiency solution for the static and dynamic reinforcement design of existing hydraulic structures. In addition, for the second-order effect problem of the multi-degree-of-freedom system structure, due to the complexity of the structural system, theoretical research is mostly based on the assumption that the structure is in a linear elastic state, and the calculation methods are mostly equivalent linear methods. Under the action of large dynamic loads such as earthquakes, the structure will undergo elastic-plastic deformation, and the analysis method based on the assumption that the structure is in a linear elastic working state is no longer applicable.

[0075] (2) The present invention systematically summarizes the complete reinforcement process of the frame-column structure considering the second-order effect and bidirectional bending, takes into account the nonlinear multi-degree-of-freedom system structure, and improves the reinforcement design of the frame structure. BRIEF DESCRIPTION OF THE DRAWINGS

[0076] Figure 1 The present invention is a flow chart of a method for calculating reinforcement arrangement of a hydropower plant building using three-dimensional finite element static and dynamic analysis.

[0077] Figure 2 Schematic diagram of different methods.

[0078] Figure 3 It is a schematic diagram of relative stiffness.

[0079] Figure 4 This is a logarithmic table of the effective length coefficient of the frame with no side shift.

[0080] Figure 5 This is a logarithmic table of the effective length coefficient of the frame with side shift.

[0081] Figure 6 Schematic diagram of the location of each point.

[0082] Figure 7 Schematic diagram of dual reinforcement of axial tension and bending.

[0083] Figure 8 This is the combined action diagram of bending and axial force. DETAILED DESCRIPTION

[0084] The specific implementation modes of the present invention are described below so that those skilled in the art can understand the present invention. However, it should be clear that the present invention is not limited to the scope of the specific implementation modes. For those of ordinary skill in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the attached claims, these changes are obvious, and all inventions and creations utilizing the concept of the present invention are protected.

[0085] like Figure 1 As shown, in one embodiment of the present invention, a three-dimensional finite element static and dynamic analysis reinforcement calculation method for a hydropower plant building includes the following steps:

[0086] S1. Establish a three-dimensional finite element model of the entire plant to obtain the internal forces and stresses of each point of the structure under static and dynamic combinations;

[0087] S2. Select the cross-sections of key parts and points of the structure where the stress is greater than the preset stress threshold to extract the internal forces, which include axial force and bending moment;

[0088] S3. Design reinforcement for bent structure: consider the second-order effect of bent column to amplify the bending moment, use envelope diagram method to design reinforcement according to axial force and second-order bending moment, perform bidirectional bending check on reinforcement design, and adjust reinforcement design according to the check result;

[0089] S4: Reinforcement design for non-bent structures: Reinforcement design for non-bent structures is performed using the envelope diagram method based on axial force and bending moment.

[0090] The S1 is specifically:

[0091] S11. Establish the overall three-dimensional finite element model of the plant, including the upper frame structure, the lower mass concrete structure and the foundation;

[0092] S12. Based on the overall three-dimensional finite element model of the plant, the finite element method is used to perform modal decomposition response spectrum calculation under earthquake conditions; in this embodiment, when performing modal decomposition response spectrum calculation, the order of modal combination is selected according to the modal participation mass being not less than 90% of the total mass of the structure;

[0093] S13. Combining the internal forces and stresses of each point of the structure obtained from different vibration modes by using CQC or SRSS method, and combining the internal forces and stresses of each point of the structure obtained from earthquakes in different directions by using SRSS method, to obtain the internal forces and stresses of each point of the structure under earthquake conditions;

[0094] S14. According to the most unfavorable principle, the internal forces and stresses of each point of the structure under the earthquake condition are statically and dynamically combined to obtain the internal forces and stresses of each point of the structure under the static and dynamic combination.

[0095] In S2, the method for extracting the axial force and bending moment of any cross section includes a node force method and a path integral method.

[0096] For ground plants, the upper structure has low rigidity, large span and high height. Under earthquake action, the upper structure often responds significantly due to the "whip effect". Therefore, when calculating the reinforcement of the plant unit section, it is necessary to focus on the variable cross-section positions and the positions with relatively large stresses in the upper structure for reinforcement design; for the lower large-volume concrete structure, the parts where the wind hood overlaps with the floor slab and the beam system, the parts where the steel volute contacts the concrete, and the parts subject to excessive concentrated loads are all likely to produce stress concentration phenomena, and all need to be checked for reinforcement design as key parts. As a general finite element program, Ansys's solid unit cannot directly extract internal forces. Therefore, to obtain the axial force and bending moment of a certain section, this embodiment adopts two approaches:

[0097] (1) Nodal force method: When the red dot area is selected as the controlling section to extract the internal force, the nodal force in the area can be obtained. First, the structure is divided into two upper and lower unit sets with the controlling section as the boundary. The internal force of the interface node is obtained by intersecting with the command CMSEL. The center point position of the internal force is specified with the command SPOINT. Finally, the result of FSUM can be extracted with the command *GET, which is the sum of the nodal force of the unit in the red area to the specified point. This method is suitable for situations where the mesh is relatively regular and the axial force direction is the same as the overall coordinate system. The extracted results are highly accurate and have nothing to do with the number of units, whether they are connected, whether they contain model boundaries, etc., and the calculation efficiency is high.

[0098] (2) Path integral method: When there are no nodes at certain cross sections of interest, the path integral method can be used. Figure 2 As shown in the figure, an integral path can be set at any position, and the stress can be mapped to the path. The axial force can be obtained by integrating the normal stress, and the bending moment can be obtained by integrating the distance between the stress and the center. The path can be an arbitrary curve; the coordinate axis and the axial force direction can be at any angle.

[0099] The S3 comprises the following sub-steps:

[0100] S31. Determine whether the bending moment of the bent column ignores the second-order effect. If so, take the extracted bending moment as the first-order bending moment. If not, calculate the second-order bending moment of the bent column end after considering the amplified second-order effect.

[0101] S32, determining whether the bending moment of the bent column needs to be further amplified along the length direction of the column;

[0102] S33, judging whether the ratio of the second-order bending moment to the first-order bending moment is less than 1.4, if so, performing reinforcement design according to the second-order bending moment, and entering S34;

[0103] If not, redesign the size of the column, modify the length and width of the column, and return to S31;

[0104] S34, performing bidirectional bending check on the current reinforcement amount, and determining whether the check result meets the bidirectional bending requirement;

[0105] If yes, then the reinforcement design is carried out according to the current reinforcement amount. If no, then the amount of steel bars is increased until the two-way bending requirements are met, and the reinforcement design is carried out according to the reinforcement amount of the increased steel bars.

[0106] In S31, the method for judging whether the bending moment of the bent column ignores the second-order effect is specifically as follows:

[0107] For bent columns of frame structures with lateral displacement, the second-order effect can be ignored if the following equation is satisfied:

[0108]

[0109] Where k is the effective length coefficient, l u is the unsupported length, r is the radius of gyration, in this embodiment r = 0.3h;

[0110] The effective length factor k reflects the column end restraint condition and depends on the relative stiffness of the column and beam at the top and bottom connections ψ A and ψ B , the expression of relative stiffness ψ is:

[0111]

[0112] The relative stiffness of the column and beam at the top and bottom connections obtained by the above calculation is ψ A and ψ B , the relative stiffness diagram is as follows Figure 3 As shown, by checking Figures 4-5 The effective length coefficient logarithmic table can be used to determine the effective length coefficient. Figure 4 is a logarithmic table of frame structures without side shift, Figure 5 Logarithmic table for frame structure with lateral displacement.

[0113] For bent columns of frame structures without side shift, the second-order effect can be ignored if the following equation is satisfied:

[0114]

[0115] Where M1 / M2 is the ratio of the bending moment at the smaller end to the bending moment at the larger end.

[0116] In S31, the method for calculating the second-order bending moment at the bent column end after considering the amplified second-order effect is specifically as follows:

[0117] For bent columns of frame structures with lateral displacement, the expression for calculating the second-order bending moment at the bent column end after considering the amplified second-order effect is as follows:

[0118]

[0119] Where M1' is the second-order bending moment corresponding to one end of the column end of the frame structure with lateral displacement, M'2 is the second-order bending moment corresponding to the other end of the column end of the frame structure with lateral displacement, and M 1ns is the bending moment at the first column end caused by gravity load, M 2ns is the bending moment at the second column end caused by gravity load, δ s is the first bending moment magnification factor, and its specific expression is:

[0120]

[0121] Where, ΣP u is the sum of all vertical loads in the same layer, ΣP cis the sum of all critical loads in the same layer, and its specific expression is:

[0122]

[0123] In the formula, E c is the elastic modulus of concrete, I g is the section inertia moment. The above formula comprehensively considers the ability of concrete columns to resist lateral displacement after the stiffness variability caused by concrete cracking, mutation and nonlinearity of stress-strain curve.

[0124] For the bent columns of the frame structure without side shift, the expression for calculating the second-order bending moment at the bent column end after considering the amplified second-order effect is as follows:

[0125] M c =δ ns M2

[0126] Where M c is the second-order bending moment corresponding to the column end of the frame structure without side displacement, δ ns is the second bending moment magnification factor, and its specific expression is:

[0127]

[0128] The S32 is specifically:

[0129] Determine whether the relationship between the unsupported length and the gyration radius is satisfied, wherein the relationship between the unsupported length and the gyration radius is specifically:

[0130]

[0131] If yes, the bending moment does not need to be further amplified along the length of the column. If no, the bending moment needs to be further amplified along the length of the column. The expression of the amplified bending moment M4 is:

[0132] M4=δ ns M3

[0133] Where M3 is the first-order bending moment along the column shaft.

[0134] In S34, the method for performing bidirectional bending verification is specifically as follows:

[0135] Determine whether the bending moment on the envelope diagram of the current reinforcement quantity satisfies the bidirectional bending formula. If so, the verification result satisfies the bidirectional bending requirements. If not, the verification result does not meet the bidirectional bending requirements. The bidirectional bending formula is specifically as follows:

[0136]

[0137] Where M ux ,、Muy is the bending moment of the cross section, For M uy When it is 0, the axial force P of the section u The bending moment on the envelope diagram of the corresponding position, For M ux When it is 0, the axial force P of the section u The bending moment on the envelope diagram at the corresponding position, K is the calibration coefficient, when the cross section is a rectangular cross section, it is 1.5, when the cross section is a circular or square cross section, it is 1.75, the position of each point is as follows Figure 6 shown.

[0138] The S4 comprises the following sub-steps:

[0139] S41. Preset the number of reinforcements;

[0140] S42, based on the set number of reinforcements, calculate the critical bearing capacity that the cross section can provide according to the cross-sectional concrete and the number of reinforcements of the non-bent structure, and determine the boundary of the envelope diagram;

[0141] S43, determine whether the axial force and bending moment fall within the envelope diagram. If so, the current number of reinforcements meets the requirements and the reinforcement design is completed. If not, increase the current number of reinforcements and return to S42.

[0142] In this embodiment, the number of reinforcements is pre-set to take into account the combined effects of axial tension and bending moment on the controlling section. Figure 7 Taking the rectangular section as an example, when the controlling section is in pure compression, pure tension, pure bending, tension-bending and compression-bending states, the five-point envelope diagram that concrete and steel bars can provide is as follows: Figure 8 shown.

[0143] In the above S42, the boundary of the envelope diagram includes first to fifth boundary points;

[0144] The coordinates of the first boundary point are (0, P uc ), the first coordinate value P uc The specific expression is:

[0145] P uc =0.8*P0

[0146] P0=φ uc *[0.85*f c ′*(A g -A s -A s ′)+f y *(A s +A s ′)]

[0147] Where P0 is the intermediate coordinate value, f c' is the specific compressive strength of concrete, A g is the total area of ​​the concrete cross section, A s is the tensile reinforcement area, A s ′ is the longitudinal non-prestressed compression reinforcement area, f y is the yield strength of concrete, φ uc is the first strength reduction coefficient. For pure pressure state, the first strength reduction coefficient is 0.65;

[0148] The coordinates of the second boundary point are (0, P ut ), the second coordinate value P ut The specific expression is:

[0149] P ut =0.8*φ ut *f y *(A s +A s ′)

[0150] For the pure tension state, the first strength reduction factor is 0.9;

[0151] The coordinates of the third boundary point are (M ub , 0), the third coordinate value P ut The specific expression is:

[0152]

[0153] In the formula, E s is the elastic modulus of the steel bar, b is the length dimension, h is the width dimension, c is the distance from the maximum strain fiber to the neutral axis, β1 is the coefficient of the ratio of the height of the equivalent rectangular compressive stress block to the height from the compression side of the section to the neutral axis, ε c is the maximum strain of the compressive fiber at the outermost edge of the concrete, φ ub is the second strength reduction factor. For pure bending state, the second strength reduction factor is 0.9. d′ is the thickness of the protective layer of the steel bars in the compression zone, and d″ is the thickness of the protective layer of the steel bars in the tension zone.

[0154] The distance c from the maximum strain fiber to the neutral axis can be calculated by the following formula;

[0155]

[0156] The coordinates of the fourth boundary point are (M u , P u ), the fourth coordinate value P u The specific expression is:

[0157]

[0158] In the formula, φ uais the third strength reduction factor. For the equilibrium state, the third strength reduction factor is 0.65. t is the distance from the maximum strain fiber to the neutral axis, and its specific expression is:

[0159]

[0160] For the equilibrium state, when the tensile reinforcement in the section reaches the yield strength of the concrete, y When the corresponding strain is reached, if the compressed concrete just reaches its assumed ultimate strain of 0.003, then there is an equilibrium strain condition in the section. According to the principle of similar triangles, the strain distribution relationship is:

[0161] Then there is a balanced strain state in the cross section. According to the principle of similar triangles, the strain distribution relationship is:

[0162]

[0163] According to the above formula, the distance c from the maximum strain fiber to the neutral axis can be solved t .

[0164]

[0165] The equilibrium state P u and M u It can be obtained according to the following formula:

[0166]

[0167] In the formula, ε y is the steel bar yield strain, ε c is the concrete strain at the edge of the compression zone.

[0168] The fifth coordinate value M u The specific expression is:

[0169]

[0170] The coordinates of the fifth boundary point are (M5, P uc ), the expression of the sixth coordinate value M5 is specifically:

[0171]

[0172] For single-reinforced cross-section members, the stress-bearing steel bars are generally only arranged in the tension zone, and n steel bars with a diameter of D are arranged in the single width range, then As = n*π*D 2 / 4,A s ′=0.

[0173] For double-reinforced cross-section members, it is necessary to configure stress-bearing steel bars in both the tension zone and the compression zone, and configure n steel bars with a diameter of D1 in the single width range of the tension zone, then As = n*π*D1 2 / 4; m steel bars with a diameter of D2 are arranged in the single width range of the compression zone, then When A s =A s ′ is bilateral symmetrical reinforcement. s ≠A s ′ is asymmetric reinforcement on both sides.

[0174] The beneficial effects of the present invention are as follows: the present invention provides a three-dimensional finite element static and dynamic analysis reinforcement calculation method for a hydropower station building, which comprehensively considers the reinforcement design requirements when the cross section is in pure tension, pure compression, bending tension, bending compression and pure bending, and provides a high-precision and high-efficiency solution for the static and dynamic reinforcement design of existing hydraulic structures. In addition, for the second-order effect problem of the multi-degree-of-freedom system structure, due to the complexity of the structural system, theoretical research is mostly based on the assumption that the structure is in a linear elastic state, and the calculation methods are mostly equivalent linear methods. Under the action of large dynamic loads such as earthquakes, the structure will undergo elastic-plastic deformation, and the analysis method based on the assumption that the structure is in a linear elastic working state is no longer applicable.

[0175] The present invention systematically summarizes the complete reinforcement process of the bent-column structure considering the second-order effect and bidirectional bending, takes the nonlinear multi-degree-of-freedom system structure into account, and improves the reinforcement design of the bent structure.

[0176] In the description of the present invention, it is necessary to understand that the orientation or positional relationship indicated by the terms "center", "thickness", "upper", "lower", "horizontal", "top", "bottom", "inner", "outer", "radial", etc. is based on the orientation or positional relationship shown in the drawings, and is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the present invention. In addition, the terms "first", "second", and "third" are used only for descriptive purposes, and cannot be understood as indicating or implying the relative importance or the number of implicitly specified technical features. Therefore, the features defined by "first", "second", and "third" may explicitly or implicitly include one or more of the features.

Claims

1. A three-dimensional finite element static and dynamic analysis reinforcement calculation method for a hydropower plant building, characterized in that: The following steps are involved: S1. Establish a three-dimensional finite element model of the entire plant to obtain the internal forces and stresses of each point of the structure under static and dynamic combinations; S2. Select the cross-sections of key parts and points of the structure where the stress is greater than the preset stress threshold to extract the internal forces, which include axial force and bending moment; S3. Design reinforcement for bent structure: consider the second-order effect of bent column to amplify the bending moment, use envelope diagram method to design reinforcement according to axial force and second-order bending moment, perform bidirectional bending check on reinforcement design, and adjust reinforcement design according to the check result; S4: Reinforcement design for non-bent structures: Reinforcement design for non-bent structures is performed using the envelope diagram method based on axial force and bending moment.

2. The three-dimensional finite element static and dynamic analysis reinforcement calculation method for a hydropower plant building according to claim 1 is characterized in that: The S1 is specifically: S11. Establish the overall three-dimensional finite element model of the plant, including the upper frame structure, the lower mass concrete structure and the foundation; S12. Based on the overall three-dimensional finite element model of the plant, the finite element method is used to perform vibration mode decomposition response spectrum calculation under earthquake conditions; S13. Combining the internal forces and stresses of each point of the structure obtained from different vibration modes by using CQC or SRSS method, and combining the internal forces and stresses of each point of the structure obtained from earthquakes in different directions by using SRSS method, to obtain the internal forces and stresses of each point of the structure under earthquake conditions; S14. According to the most unfavorable principle, the internal forces and stresses of each point of the structure under the earthquake condition are statically and dynamically combined to obtain the internal forces and stresses of each point of the structure under the static and dynamic combination.

3. The three-dimensional finite element static and dynamic analysis reinforcement calculation method for a hydropower plant building according to claim 1 is characterized in that: In S2, the method for extracting the axial force and bending moment of any cross section includes a node force method and a path integral method.

4. The three-dimensional finite element static and dynamic analysis reinforcement calculation method for a hydropower plant building according to claim 3 is characterized in that: The S3 comprises the following sub-steps: S31. Determine whether the bending moment of the bent column ignores the second-order effect. If so, take the extracted bending moment as the first-order bending moment. If not, calculate the second-order bending moment of the bent column end after considering the amplified second-order effect. S32, determining whether the bending moment of the bent column needs to be further amplified along the length direction of the column; S33, judging whether the ratio of the second-order bending moment to the first-order bending moment is less than 1.4, if so, performing reinforcement design according to the second-order bending moment, and entering S34; If not, redesign the size of the column, modify the length and width of the column, and return to S31; S34, performing bidirectional bending check on the current reinforcement amount, and determining whether the check result meets the bidirectional bending requirement; If yes, then the reinforcement design is carried out according to the current reinforcement amount. If no, then the amount of steel bars is increased until the two-way bending requirements are met, and the reinforcement design is carried out according to the reinforcement amount of the increased steel bars.

5. The method for calculating reinforcement arrangement of a hydropower plant building by three-dimensional finite element static and dynamic analysis according to claim 4 is characterized in that: In S31, the method for judging whether the bending moment of the bent column ignores the second-order effect is specifically as follows: For bent columns of frame structures with lateral displacement, the second-order effect can be ignored if the following equation is satisfied: Where k is the effective length coefficient, l u is the unsupported length, r is the radius of gyration; For bent columns of frame structures without side shift, the second-order effect can be ignored if the following equation is satisfied: Where M1 / M2 is the ratio of the bending moment at the smaller end to the bending moment at the larger end.

6. The method for calculating reinforcement arrangement of a hydropower plant building by three-dimensional finite element static and dynamic analysis according to claim 5 is characterized in that: In S31, the method for calculating the second-order bending moment at the bent column end after considering the amplified second-order effect is specifically as follows: For bent columns of frame structures with lateral displacement, the expression for calculating the second-order bending moment at the bent column end after considering the amplified second-order effect is as follows: Where M1' is the second-order bending moment corresponding to one end of the column end of the frame structure with lateral displacement, M'2 is the second-order bending moment corresponding to the other end of the column end of the frame structure with lateral displacement, and M 1ns is the bending moment at the first column end caused by gravity load, M 2ns is the bending moment at the second column end caused by gravity load, δ s is the first bending moment magnification factor, and its specific expression is: Where, ΣP u is the sum of all vertical loads in the same layer, ΣP c is the sum of all critical loads in the same layer, and its specific expression is: In the formula, E c is the elastic modulus of concrete, I g is the section moment of inertia; For the bent columns of the frame structure without side shift, the expression for calculating the second-order bending moment at the bent column end after considering the amplified second-order effect is as follows: M c =δ ns M2 Where M c is the second-order bending moment corresponding to the column end of the frame structure without side displacement, δ ns is the second bending moment magnification factor, and its specific expression is:

7. The method for calculating reinforcement arrangement of a hydropower plant building by three-dimensional finite element static and dynamic analysis according to claim 6 is characterized in that: The S32 is specifically: Determine whether the relationship between the unsupported length and the gyration radius is satisfied, wherein the relationship between the unsupported length and the gyration radius is specifically: If yes, the bending moment does not need to be further amplified along the length of the column. If no, the bending moment needs to be further amplified along the length of the column. The expression of the amplified bending moment M4 is: M4=δ ns M3 Where M3 is the first-order bending moment along the column shaft.

8. The method for calculating reinforcement arrangement of a hydropower plant building by three-dimensional finite element static and dynamic analysis according to claim 7 is characterized in that: In S34, the method for performing bidirectional bending verification is specifically as follows: Determine whether the bending moment on the envelope diagram of the current reinforcement quantity satisfies the bidirectional bending formula. If so, the verification result satisfies the bidirectional bending requirements. If not, the verification result does not meet the bidirectional bending requirements. The bidirectional bending formula is specifically as follows: Where M ux ,,M uy is the bending moment of the cross section, For M uy When it is 0, the axial force P of the section u The bending moment on the envelope diagram of the corresponding position, For M ux When it is 0, the axial force P of the section u The bending moment on the envelope diagram at the corresponding position, K is the verification coefficient, which is 1.5 when the cross section is a rectangular cross section and 1.75 when the cross section is a circular or square cross section.

9. The method for calculating reinforcement arrangement of a hydropower plant building by three-dimensional finite element static and dynamic analysis according to claim 8 is characterized in that: The S4 comprises the following sub-steps: S41. Preset the number of reinforcements; S42, based on the set number of reinforcements, calculate the critical bearing capacity that the cross section can provide according to the cross-sectional concrete and the number of reinforcements of the non-bent structure, and determine the boundary of the envelope diagram; S43, determine whether the axial force and bending moment fall within the envelope diagram. If so, the current number of reinforcements meets the requirements and the reinforcement design is completed. If not, increase the current number of reinforcements and return to S42.

10. The method for calculating reinforcement arrangement of a hydropower plant building by three-dimensional finite element static and dynamic analysis according to claim 9 is characterized in that: In the above S42, the boundary of the envelope diagram includes first to fifth boundary points; The coordinates of the first boundary point are (0, P uc ), the first coordinate value P uc The specific expression is: P uc =0.8*P0 P0=φ uc *[0.85*f c '*(AND g -AND s -AND s ′)+f y *(AND s +A s ′)] Where P0 is the middle coordinate value, f c ' is the specific compressive strength of concrete, A g is the total area of ​​the concrete cross section, A s is the tensile reinforcement area, A s ′ is the longitudinal non-prestressed compression reinforcement area, f y is the yield strength of concrete, φ uc is the first strength reduction factor; The coordinates of the second boundary point are (0, P ut ), the second coordinate value P ut The specific expression is: P ut =0.8*φ ut *f y *(A s +A s ′) The coordinates of the third boundary point are (M ub , 0), the third coordinate value P ut The specific expression is: In the formula, E s is the elastic modulus of the steel bar, b is the length dimension, h is the width dimension, c is the distance from the maximum strain fiber to the neutral axis, β1 is the coefficient of the ratio of the height of the equivalent rectangular compressive stress block to the height from the compression side of the section to the neutral axis, ε c is the maximum strain of the compressive fiber at the outermost edge of the concrete, φ ub is the second strength reduction factor, d′ is the thickness of the protective layer of the steel bars in the compression zone, and d″ is the thickness of the protective layer of the steel bars in the tension zone; The coordinates of the fourth boundary point are (M u , P u ), the fourth coordinate value P u The specific expression is: In the formula, φ ua is the third strength reduction factor, c t is the distance from the maximum strain fiber to the neutral axis, and its specific expression is: The fifth coordinate value M u The specific expression is: The coordinates of the fifth boundary point are (M5, P uc ), the expression of the sixth coordinate value M5 is specifically:

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