A method for calculating the reinforcement of the three-dimensional finite element static and dynamic analysis of a hydropower station powerhouse

Abstract

The present invention discloses a method for calculating the reinforcement of a three-dimensional finite element static and dynamic analysis of a hydropower station powerhouse, which comprises the following steps: S1. Establish an overall three-dimensional finite element model of the powerhouse to obtain the internal forces and stresses of each point of the structure under the static and dynamic combination; S2. Select the cross-sections of the key parts and each point of the structure where the stress is greater than the preset stress threshold to extract the internal forces, and the internal forces include axial force and bending moment; S3. Carry out the reinforcement design for the bent frame structure: consider the second-order effect of the bent frame column to amplify the bending moment, adopt the envelope diagram method for reinforcement design according to the axial force and the second-order bending moment, conduct a two-way bending check on the reinforcement design, and adjust the reinforcement design according to the check result; S4: Carry out the reinforcement design for the non-bent frame structure: adopt the envelope diagram method for the reinforcement design of the non-bent frame structure according to the axial force and the bending moment.

Description

Technical Field

[0001] The present invention belongs to the field of water conservancy and hydropower project construction, and particularly relates to a method for calculating the reinforcement of a three-dimensional finite element static and dynamic analysis of a hydropower station powerhouse. Background Art

[0002] As the main building structure for hydropower generation, a hydropower station powerhouse is usually vertically divided into an upper structure and a lower structure with the generator floor as the boundary. The upper structure consists of walls, slabs, beams, columns, etc., similar to a single-story power station structure; the lower structure consists of a large-volume concrete structure that houses the hydro-generator, and the stiffness and mass of the upper structure are significantly lower than those of the lower structure. The western region is an area with intensive construction of water conservancy projects in China. This region is rich in water energy resources and is also located in an area with frequent earthquakes. During the construction of water conservancy projects, the seismic safety of hydropower station powerhouses cannot be ignored. Through the investigation of past hydropower project disasters, it is found that the seismic damage of large-volume concrete structures in hydropower projects is less, while the seismic damage of auxiliary buildings mainly composed of bent column structures is more serious. The stiffness of the bent column structure is small, and the second-order effect becomes an important factor affecting its seismic performance, especially obvious under medium and large earthquakes. How to reasonably consider the reinforcement of bent columns in hydropower projects is a current research hotspot. Summary of the Invention

[0003] Aiming at the above deficiencies in the prior art, a method for calculating the reinforcement of a three-dimensional finite element static and dynamic analysis of a hydropower station powerhouse provided by the present invention solves the problems of insufficient accuracy and efficiency in the static and dynamic reinforcement design of existing hydraulic structures.

[0004] In order to achieve the above invention object, the technical solution adopted by the present invention is: a method for calculating the reinforcement of a three-dimensional finite element static and dynamic analysis of a hydropower station powerhouse, including the following steps:

[0005] S1. Establish an overall three-dimensional finite element model of the powerhouse to obtain the internal forces and stresses of each point of the structure under the combined static and dynamic conditions;

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

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

[0008] S4: Carry out reinforcement design for the non-bent structure: use the envelope diagram method for reinforcement design of the non-bent structure according to the axial force and the bending moment.

[0009] Furthermore: The specific content of S1 is as follows:

[0010] S11. Establish a three-dimensional finite element model of the entire factory building, including the upper bent structure, the lower mass concrete structure, and the foundation;

[0011] S12. According to the three-dimensional finite element model of the entire factory building, use the finite element method to calculate by the mode superposition response spectrum method under seismic conditions;

[0012] S13. Use the CQC or SRSS method to combine the internal forces and stresses of each point of the structure obtained from different modes, and use the SRSS method to combine the internal forces and stresses of each point of the structure obtained from earthquakes in different directions to obtain the internal forces and stresses of each point of the structure under seismic conditions;

[0013] S14. According to the most unfavorable principle, perform static-dynamic combination on the internal forces and stresses of each point of the structure under seismic conditions to obtain the internal forces and stresses of each point of the structure under static-dynamic combination.

[0014] Furthermore: In S2, the methods for extracting the axial force and bending moment of any cross-section include the nodal force method and the path integral method.

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

[0016] S31. Judge 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 amplified considering the second-order effect at the column ends of the bent column;

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

[0018] S33. Judge whether the ratio of the second-order bending moment to the first-order bending moment is less than 1.4. If so, carry out the reinforcement design according to the second-order bending moment and enter S34;

[0019] If not, re-design the column size, modify the column length size and width size, and return to S31;

[0020] S34. Conduct a two-way bending check on the current reinforcement amount and judge whether the check result meets the two-way bending requirements;

[0021] If so, carry out the reinforcement design according to the current reinforcement amount. If not, increase the steel usage until the two-way bending requirements are met, and carry out the reinforcement design according to the reinforcement amount with increased steel usage.

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

[0023] For the bent columns of the sway frame structure, if the following formula is satisfied, the second-order effect is ignored;

[0024]

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

[0026] For the bent columns of a non-sway frame structure, if the following formula is satisfied, the second-order effect is ignored;

[0027]

[0028] Wherein, M 1 / M 2 is the ratio of the smaller end moment to the larger end moment.

[0029] Furthermore: In the S31, the method for calculating the second-order moment after considering the amplification of the second-order effect at the column ends of the bent columns is specifically as follows:

[0030] For the bent columns of a sway frame structure, the expression for calculating the second-order moment after considering the amplification of the second-order effect at the column ends of the bent columns is specifically the following formula:

[0031]

[0032] Wherein, M 1 ' is the second-order moment corresponding to one end of the column end of the sway frame structure, M' 2 is the second-order moment corresponding to the other end of the column end of the sway frame structure, M 1ns is the first column end moment caused by the gravity load, M 2ns is the second column end moment caused by the gravity load, δ s is the first moment amplification factor, and its expression is specifically:

[0033]

[0034] Wherein, ΣP u is the sum of all vertical loads on the same floor, ΣP c is the sum of all critical loads on the same floor, and its expression is specifically:

[0035]

[0036] Wherein, E c is the elastic modulus of concrete, and I g is the moment of inertia of the cross-section;

[0037] For the bent columns of a non-sway frame structure, the expression for calculating the second-order moment after considering the amplification of the second-order effect at the column ends of the bent columns is specifically the following formula:

[0038] M c =δ ns M 2

[0039] In the formula, M c is the second-order moment corresponding to the column end of the non-sway frame structure, and δ ns is the second moment amplification factor, and its expression is specifically:

[0040]

[0041] Furthermore: The specific content of S32 is:

[0042] Judge whether the relationship formula between the unsupported length and the radius of gyration is satisfied. The relationship formula between the unsupported length and the radius of gyration is specifically:

[0043]

[0044] If so, the moment does not need to be further amplified along the column length. If not, the moment needs to be further amplified along the column length. The amplified moment M 4 has the following specific expression:

[0045] M 4 = δ ns M 3

[0046] In the formula, M 3 is the first-order moment along the column body.

[0047] Furthermore: In S34, the method for performing the two-way bending check is specifically:

[0048] Judge whether the moment on the envelope diagram of the current reinforcement ratio satisfies the two-way bending formula. If so, the check result meets the two-way bending requirements. If not, the check result does not meet the two-way bending requirements. Among them, the two-way bending formula is specifically the following formula:

[0049]

[0050] In the formula, M ux , M uy are the moments of the cross-section. is the axial force P uy of the cross-section when M u is 0, and the moment on the envelope diagram at the corresponding position. is the axial force P ux of the cross-section when M u is 0, and the moment on the envelope diagram at the corresponding position. K is the check coefficient, which takes 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] Furthermore: S4 includes the following sub-steps:

[0052] S41. Preset the amount of reinforcement;

[0053] S42. Based on the set reinforcement quantity, calculate the critical bearing capacity that the cross-section can provide according to the cross-section concrete and reinforcement quantity of the non-frame 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 reinforcement quantity meets the requirements, and the reinforcement design is completed. If not, increase the current reinforcement quantity and return to S42.

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

[0056] Among them, the coordinates of the first boundary point are (0, P uc ), and the expression of the first coordinate value P uc is specifically:

[0057] P uc = 0.8 * P 0

[0058] P 0 = φ uc * [0.85 * f c ′ * ( A g - A s - A s ′) + f y * ( A s + A s ′)]

[0059] In the formula, P 0 is the intermediate coordinate value, f c ′ is the specific compressive strength of the concrete, A g is the total cross-sectional area of the concrete, A s is the tension reinforcement area, A s ′ is the longitudinal non-prestressed compression reinforcement area, f y is the concrete yield strength, φ uc is the first strength reduction coefficient;

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

[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), and the third coordinate value Put The expression is specifically as follows:

[0063]

[0064] 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, and β 1 is the coefficient of the ratio of the height of the equivalent rectangular compressive stress diagram block to the height from the compressed edge of the cross-section to the neutral axis, ε c is the maximum strain of the compressed fiber at the outermost edge of the concrete, and φ ub is the second strength reduction coefficient, d′ is the cover thickness of the steel bar in the compressed zone, and d″ is the cover thickness of the steel bar in the tension zone;

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

[0066]

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

[0068]

[0069] The expression of the fifth coordinate value M u is specifically as follows:

[0070]

[0071] The coordinates of the fifth boundary point are (M 5 , P uc ), and the expression of the sixth coordinate value M 5 is specifically as follows:

[0072]

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

[0074] (1) The present invention provides a method for calculating the reinforcement of a three-dimensional finite element static and dynamic analysis of a hydropower station powerhouse, comprehensively considering the reinforcement design requirements in the states of pure tension, pure compression, flexure-tension, flexure-compression, and pure flexure of the cross-section, and providing a highly accurate and efficient solution for the static and dynamic reinforcement design of existing hydraulic structures. In addition, for the second-order effect problem of a 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 most of the calculation methods are equivalent linear methods. Under the action of large dynamic loads such as earthquakes, the structure will undergo elastoplastic 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 a bent column structure considering the second-order effect and bidirectional bending, incorporates a multi-degree-of-freedom system structure with nonlinearity, and improves the reinforcement design of the bent structure. BRIEF DESCRIPTION OF THE DRAWINGS

[0076] Figure 1 It is a flowchart of a method for calculating the reinforcement of a three-dimensional finite element static and dynamic analysis of a hydropower station powerhouse according to the present invention.

[0077] Figure 2 It is a schematic diagram of different methods.

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

[0079] Figure 4 It is a logarithmic table diagram of the effective length coefficient of a non-sway frame.

[0080] Figure 5 It is a logarithmic table diagram of the effective length coefficient of a sway frame.

[0081] Figure 6 It is a schematic diagram of the positions of each point.

[0082] Figure 7 It is a schematic diagram of double reinforcement of axial tension and bending.

[0083] Figure 8 It is a diagram of the combined action of bending and axial force. DETAILED DESCRIPTION OF THE INVENTION

[0084] The following describes the specific embodiments of the present invention to facilitate those skilled in the art of the present technology to understand the present invention. However, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those of ordinary skill in the art of the present technology, as long as various changes are within the spirit and scope of the present invention defined and determined by the appended claims, these changes are obvious, and all inventions and creations using the concept of the present invention are within the scope of protection.

[0085] As Figure 1As shown, in an embodiment of the present invention, a method for calculating the reinforcement of a three-dimensional finite element static and dynamic analysis of a hydropower station powerhouse includes the following steps:

[0086] S1. Establish an overall three-dimensional finite element model of the powerhouse to obtain the internal forces and stresses of each point of the structure under the static and dynamic combination;

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

[0088] S3. Carry out the reinforcement design for the bent frame structure: consider the second-order effect of the bent frame column to amplify the bending moment, and use the envelope diagram method for reinforcement design according to the axial force and the second-order bending moment, conduct a two-way bending check on the reinforcement design, and adjust the reinforcement design according to the check result;

[0089] S4: Carry out the reinforcement design for the non-bent frame structure: use the envelope diagram method for reinforcement design of the non-bent frame structure according to the axial force and the bending moment.

[0090] The specific content of S1 is as follows:

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

[0092] S12. According to the overall three-dimensional finite element model of the powerhouse, use the finite element method to calculate by the mode superposition response spectrum method under the seismic condition; in this embodiment, when carrying out the mode superposition response spectrum method calculation, the order of the mode combination is selected according to the modal participation mass not less than 90% of the total mass of the structure;

[0093] S13. Use the CQC or SRSS method to combine the internal forces and stresses of each point of the structure obtained from different modes, and use the SRSS method to combine the internal forces and stresses of each point of the structure obtained from earthquakes in different directions to obtain the internal forces and stresses of each point of the structure under the seismic condition;

[0094] S14. Carry out the static and dynamic combination of the internal forces and stresses of each point of the structure under the seismic condition according to the most unfavorable principle to obtain the internal forces and stresses of each point of the structure under the static and dynamic combination.

[0095] In S2, the methods for extracting the axial force and bending moment of any cross-section include the nodal force method and the path integral method.

[0096] For a ground workshop, its superstructure has low stiffness, large span and high height. Under the action of earthquake, the superstructure often has significant responses due to the "whiplash effect". Therefore, when calculating the reinforcement of the unit section of the workshop, it is necessary to focus on selecting the variable-section positions and positions with relatively large stresses in the superstructure for reinforcement design; for the lower large-volume concrete structure, stress concentration may occur at the overlapping parts of the air duct with the floor and beam system, the contact parts of the steel spiral case with the concrete, and the parts with excessive concentrated loads, and all need to be checked for reinforcement design as key parts. As a general-purpose finite element program, the solid elements of Ansys cannot directly extract internal forces. Therefore, to obtain the axial force and bending moment of a certain section, this embodiment adopts two methods:

[0097] (1) Node force method. When selecting the red dot area as the control section to extract internal forces, it can be obtained by extracting the node forces in the area. First, take the control section as the boundary, divide the structure into upper and lower unit sets, use the command CMSEL to intersect to obtain the internal forces of the interface nodes, use the command SPOINT to specify the center point position for obtaining internal forces, and finally use the *GET command to extract the result of FSUM, that is, the sum of the unit node forces in the red area for the specified point. This method is applicable to the case where the mesh is relatively regular and the axial force direction is the same as the overall coordinate system. The extracted result has high accuracy, is independent of the number of elements, whether it is connected, whether it contains the model boundary, etc., and has high calculation efficiency.

[0098] (2) Path integral method. When there are no nodes at some sections of concern, the path integral method can be used. As Figure 2 shown, the integral path can be set at any position, map the stress to the path, and integrate the normal stress to obtain the axial force, and integrate the distance between the stress and the center to obtain the bending moment. The path can be any curve; the coordinate axis and the axial force direction can be at any angle.

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

[0100] S31. Judge whether the second-order effect of the bending moment of the bent column is ignored. If so, take the extracted bending moment as the first-order bending moment. If not, calculate the second-order bending moment after considering the second-order effect amplification at the column end of the bent column;

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

[0102] S33. Judge whether the ratio of the second-order bending moment to the first-order bending moment is less than 1.4. If so, carry out the reinforcement design according to the second-order bending moment and enter S34;

[0103] If not, re-design the column size, modify the column length size and width size, and return to S31;

[0104] S34. Perform a two-way bending check on the current reinforcement amount, and determine whether the check result meets the two-way bending requirements;

[0105] If so, perform the reinforcement design according to the current reinforcement amount. If not, increase the amount of steel until the two-way bending requirements are met, and perform the reinforcement design according to the reinforcement amount with the increased steel amount.

[0106] In the above S31, the method for determining whether the second-order effect of the moment of the bent column is ignored is specifically as follows:

[0107] For the bent column of the sway frame structure, if the following formula is satisfied, the second-order effect is ignored;

[0108]

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

[0110] The effective length coefficient k reflects the column end restraint condition and depends on the relative stiffness ψ A and ψ B , and the expression of the relative stiffness ψ is:

[0111]

[0112] The relative stiffness ψ A and ψ B of the column and the beam at the top and bottom connections obtained through the above calculation, and the relative stiffness schematic diagram is as Figure 3 shown. By checking the Figures 4 - 5 logarithmic table of the effective length coefficient, the effective length coefficient can be determined. Figure 4 is the logarithmic table for the non-sway frame structure, Figure 5 and is the logarithmic table for the sway frame structure.

[0113] For the bent column of the non-sway frame structure, if the following formula is satisfied, the second-order effect is ignored;

[0114]

[0115] In the formula, M 1 / M 2 is the ratio of the smaller end moment to the larger end moment.

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

[0117] For the bent column of the sway frame structure, the expression for calculating the second-order moment after considering the second-order effect amplification at the column end of the bent column is specifically the following formula:

[0118]

[0119] Wherein, M 1 ' is the secondary moment corresponding to one end of the column end of the sway frame structure, and M' 2 is the secondary moment corresponding to the other end of the column end of the sway frame structure, and M 1ns is the first column end moment caused by the gravity load, and M 2ns is the second column end moment caused by the gravity load, and δ s is the first moment amplification factor, and its expression is specifically:

[0120]

[0121] Wherein, ΣP u is the sum of all vertical loads in the same story, and ΣP c is the sum of all critical loads in the same story, and its expression is specifically:

[0122]

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

[0124] For the bent columns of the non-sway frame structure, the expression for calculating the secondary moment after considering the amplification of the secondary effect at the column ends of the bent columns is specifically the following formula:

[0125] M c = δ ns M 2

[0126] Wherein, M c is the secondary moment corresponding to the column end of the non-sway frame structure, and δ ns is the second moment amplification factor, and its expression is specifically:

[0127]

[0128] The specific content of S32 is:

[0129] Judge whether the relationship between the unsupported length and the radius of gyration is satisfied. The relationship between the unsupported length and the radius of gyration is specifically:

[0130]

[0131] If so, the bending moment does not need to be further amplified along the column length; if not, the bending moment along the column length needs to be further amplified, and the amplified bending moment M 4 is specifically expressed as:

[0132] M 4 = δ ns M 3

[0133] In the formula, M 3 is the first-order bending moment along the column body direction.

[0134] In S34, the method for performing the two-way bending check is specifically as follows:

[0135] Judge whether the bending moment on the envelope diagram of the current reinforcement ratio meets the two-way bending formula. If so, the check result meets the two-way bending requirements; if not, the check result does not meet the two-way bending requirements. Among them, the two-way bending formula is specifically the following formula:

[0136]

[0137] In the formula, M ux , M uy are the bending moments of the section, is the bending moment on the envelope diagram at the corresponding position when M uy is 0 and the axial force P u of the section, is the bending moment on the envelope diagram at the corresponding position when M ux is 0 and the axial force P u of the section. K is the check coefficient, taking 1.5 when the section is a rectangular section and taking 1.75 when the section is a circular or square section. The positions of each point are as Figure 6 shown.

[0138] S4 includes the following sub-steps:

[0139] S41. Preset the amount of reinforcement;

[0140] S42. Based on the set amount of reinforcement, calculate the critical bearing capacity that the section can provide according to the section concrete and the amount of reinforcement of the non-frame structure, and determine the boundary of the envelope diagram;

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

[0142] In this embodiment, the preset amount of reinforcement takes into account the influence of the control section under the combined action of axial tension and bending moment, so as to Figure 7Taking the rectangular cross-section as an example, when the control cross-section is in the states of pure compression, pure tension, pure bending, tension-bending, and compression-bending, the five-point envelope diagrams that can be provided by the concrete and steel bars are as Figure 8 shown.

[0143] In the above-mentioned S42, the boundaries of the envelope diagram include the first to fifth boundary points;

[0144] Among them, the coordinates of the first boundary point are (0, P uc ), and the expression of the first coordinate value P uc is specifically:

[0145] P uc = 0.8 * P 0

[0146] P 0 = φ uc * [0.85 * f c ′ * (A g - A s - A s ′) + f y * (A s + A s ′)]

[0147] In the formula, P 0 is the intermediate coordinate value, f c ′ is the specific compressive strength of the concrete, A g is the total area of the concrete cross-section, A s is the area of the tensile reinforcement, A s ′ is the area of the longitudinal non-prestressed compression reinforcement, f y is the yield strength of the concrete, φ uc is the first strength reduction coefficient. For the pure compression state, the first strength reduction coefficient takes the value of 0.65;

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

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

[0150] For the pure tension state, the first strength reduction coefficient takes the value of 0.9;

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

[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, and β 1 is the coefficient of the ratio of the height of the equivalent rectangular compressive stress diagram block to the height from the compressed edge of the cross-section to the neutral axis, ε c is the maximum strain of the compressed fiber at the outermost edge of the concrete, and φ ub is the second strength reduction coefficient. For the pure bending state, the value of the second strength reduction coefficient is 0.9. d′ is the cover thickness of the compressed area steel bar, and d″ is the cover thickness of the tension area steel bar;

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

[0155]

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

[0157]

[0158] In the formula, φ ua is the third strength reduction coefficient. For the balanced state, the value of the third strength reduction coefficient is 0.65, and c t is the distance from the maximum strain fiber to the neutral axis, and its specific expression is:

[0159]

[0160] For the balanced state, when the tension steel bar in the cross-section reaches the strain corresponding to the concrete yield strength f y , if the compressed concrete just reaches its assumed ultimate strain of 0.003, there is a balanced strain condition in the cross-section. According to the principle of similar triangles, the strain distribution relationship is:

[0161] Then there is a balanced strain condition 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] P u and M uIt can be obtained according to the following formula:

[0166]

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

[0168] The expression of the fifth coordinate value M u is specifically as follows:

[0169]

[0170] The coordinates of the fifth boundary point are (M 5 , P uc ). The expression of the sixth coordinate value M 5 is specifically as follows:

[0171]

[0172] For a single-reinforcement section member, generally only tensile steel bars are arranged in the tensile zone. If 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 a double-reinforcement section member, tensile and compressive steel bars need to be arranged simultaneously. If n steel bars with a diameter of D 1 are arranged in the single-width range of the tensile zone, then As = n * π * D 1 2 / 4; if m steel bars with a diameter of D 2 are arranged in the single-width range of the compression zone, then When A s = A s ′, it is bilaterally symmetric reinforcement. When A s ≠ A s ′, it is bilaterally asymmetric reinforcement.

[0174] The beneficial effects of the present invention are as follows: The present invention provides a method for calculating the reinforcement of the three-dimensional finite element static and dynamic analysis of a hydropower station powerhouse, comprehensively considering the reinforcement design requirements in the states of pure tension, pure compression, bending tension, bending compression, and pure bending of the section, and providing a highly accurate and efficient solution for the static and dynamic reinforcement design of existing hydraulic structures. In addition, for the second-order effect problem of a 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 most of the calculation methods are equivalent linear methods. Under the action of large dynamic loads such as earthquakes, the structure will undergo elastoplastic 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 system of the present invention systematically summarizes the complete reinforcement process for bent columns considering second-order effects and bi-directional bending, takes into account the non-linear multi-degree-of-freedom system structure, and improves the reinforcement design of bent structures.

[0176] In the description of the present invention, it should be understood that the orientation or positional relationship indicated by terms such as "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 of the present invention. In addition, the terms "first", "second", "third" are only used for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly specifying the quantity of technical features. Therefore, the features defined by "first", "second", "third" may explicitly or implicitly include one or more of such 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; 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.

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 1 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.

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 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 M′1 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:

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: 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.

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: 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.

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: 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.

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: 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 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; 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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