Reinforced concrete structure design method, electronic device, and medium

Abstract

The application provides a reinforced concrete structure design method, an electronic device and a medium. The method comprises the following steps: calculating the axial force ultimate bearing capacity and the bending moment ultimate bearing capacity of a characteristic point according to basic parameters of a current reinforced concrete structure, and establishing a functional relationship between the axial force ultimate bearing capacity and the bending moment ultimate bearing capacity of a characteristic curve; constructing a limit bearing capacity envelope; if the internal force calculation values of all sections of the current reinforced concrete structure are located in the limit bearing capacity envelope, the bearing capacity of the current reinforced concrete structure meets the requirements, otherwise, the basic parameters of the current reinforced concrete structure are adjusted until the internal force calculation values of all sections of the reinforced concrete structure are located in the limit bearing capacity envelope. The application can simultaneously perform the reinforcement calculation and the bearing capacity review of multiple sections based on the structure bearing capacity envelope, and improves the design efficiency and quality of the reinforced concrete structure.

Description

Technical Field

[0001] This invention belongs to the field of reinforced concrete structure design technology, and in particular relates to a reinforced concrete structure design method, electronic equipment and medium. Background Technology

[0002] Reinforced concrete structures are widely used in hydropower stations due to their excellent load-bearing capacity and durability, especially in critical structures such as water-retaining structures, spillway structures, and water conveyance structures. Their design mainly includes calculations of internal forces and reinforcement details for each section. Internal force calculations are typically performed using structural mechanics methods or the finite element method, while reinforcement calculations are based on structural load-bearing capacity formulas. In practical design, two typical scenarios exist: one is reinforcement design, where a reinforcement scheme needs to be designed for a new concrete member. First, based on the internal force calculation results, the internal force combinations of multiple sections of the member are obtained. Then, reinforcement calculations are performed for each of these sections, and finally, the reinforcement results of each section are combined to obtain the final reinforcement parameters of the member. The second is load-bearing capacity verification, where the load-bearing capacity of an existing reinforced concrete member needs to be re-verified when its stress conditions change. Based on the internal force calculation results of the member, the internal force combinations of multiple sections of the member are obtained. Then, reinforcement calculations are performed for each of these sections, and finally, the reinforcement results of each section are compared with the original reinforcement parameters of the member to achieve load-bearing capacity verification. However, traditional design methods have significant shortcomings in both scenarios: on the one hand, the design process involves a lot of repetitive work, requiring the analysis of internal forces in each section and the calculation of reinforcement, which is cumbersome and inefficient; on the other hand, the design process has low visualization, and users have a low perception of the margin of structural design. Summary of the Invention

[0003] The purpose of this invention is to address the shortcomings of existing technologies by providing a method, electronic device, and medium for designing reinforced concrete structures, which can perform reinforcement calculations and load-bearing capacity verification for multiple sections, thereby improving the efficiency and quality of reinforced concrete structure design.

[0004] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0005] A method for designing reinforced concrete structures includes the following steps:

[0006] S1. Based on the basic parameters of reinforced concrete structures and the formula for the bearing capacity of the normal section of reinforced concrete structures, the axial force ultimate bearing capacity and bending moment ultimate bearing capacity of characteristic points are calculated, and the functional relationship between the axial force ultimate bearing capacity and bending moment ultimate bearing capacity of the characteristic curve is established.

[0007] S2. Based on the functional relationship between the axial force ultimate bearing capacity and the bending moment ultimate bearing capacity of the characteristic points, and the axial force ultimate bearing capacity and the bending moment ultimate bearing capacity of the characteristic curve, construct the ultimate bearing capacity envelope.

[0008] S3. If the calculated internal force values ​​of all sections of the reinforced concrete structure are within the envelope of the ultimate bearing capacity, then the bearing capacity of the reinforced concrete structure meets the requirements. Otherwise, adjust the basic parameters of the reinforced concrete structure and repeat steps S1-S2 until the calculated internal force values ​​of all sections of the reinforced concrete structure are within the envelope of the ultimate bearing capacity.

[0009] The internal force calculation values ​​include axial force calculation values ​​and bending moment calculation values;

[0010] The characteristic points include at least the axial compression point, the boundary point between large and small eccentric compression, the yield point of the compressed steel under large eccentric compression, the pure bending point, the boundary point between large and small eccentric tension, and the axial tension point.

[0011] The characteristic curves include the small eccentric compression curve, the large eccentric compression curve, the large eccentric tension curve, and the small eccentric tension curve.

[0012] This invention constructs a load-bearing capacity envelope for all stress types within a structure and compares it with the internal force combinations of multiple sections in current reinforced concrete structures. This enables the calculation of reinforcement and verification of load-bearing capacity for multiple sections of reinforced concrete structures. Compared to existing methods that can only design structures for a single section, this invention, based on the structural load-bearing capacity envelope, can simultaneously perform reinforcement calculations and verification of load-bearing capacity for multiple sections, improving the efficiency and quality of reinforced concrete structure design.

[0013] Furthermore, the basic parameters include the width of the reinforced concrete structure, the height of the reinforced concrete structure, the design strength of the steel reinforcement, the elastic modulus of the steel reinforcement, the compressive strength of the concrete, the ultimate compressive strain of the concrete, and the reinforcement area.

[0014] Further, in S3, the reinforcement area of ​​the reinforced concrete structure is adjusted, and steps S1-S2 are repeated until the calculated internal force values ​​of all sections of the reinforced concrete structure are within the bearing capacity envelope.

[0015] Furthermore, based on the basic parameters of the reinforced concrete structure, a finite element model of the reinforced concrete structure is constructed. The reinforced concrete structure is divided into multiple sections by meshing, and the reinforced concrete structure is simulated and analyzed to obtain the calculated internal force values ​​of each section of the reinforced concrete structure.

[0016] The expression for calculating internal forces is as follows:

[0017]

[0018] Where, N iM is the calculated value of the axial force at the i-th section. i Let σ be the calculated bending moment value for the i-th section. i,j h is the normal stress value at the j-th stress point in the i-th section. i,j y is the distance between the j-th stress point and the (j+1)-th stress point in the i-th section. i,j Let n be the distance from the center of the j-th stress point and the (j+1)-th stress point in the i-th section to the center of the i-th section, n be the number of stress points in the i-th section, and m be the number of reinforced concrete sections.

[0019] Furthermore, the functional relationship between the axial force ultimate bearing capacity and the bending moment ultimate bearing capacity of the small eccentric compression curve is shown below:

[0020]

[0021] When x > h, take x = h

[0022] Where, N u M is the ultimate bearing capacity of axial force. u Let x be the ultimate bending moment bearing capacity, x be the height of the compression zone, and f be the ultimate bending moment bearing capacity. c ρ is the compressive strength of concrete, b is the width of the reinforced concrete structure, h is the height of the reinforced concrete structure, and f is the concrete compressive strength. y ′ represents the design strength value of the compression reinforcement, f y A′ is the design value of the tensile strength of the reinforcing steel. S A is the area of ​​the compression reinforcement. s Let ξ be the area of ​​the tensile reinforcement, 'a' be the distance from the resultant point of the longitudinal tensile reinforcement to the tension edge, 'a' be the distance from the resultant point of the longitudinal compressive reinforcement to the compression edge, and 'h0' be the effective height of the reinforced concrete structure, where h0 = ha. b This refers to the relative height of the pressure zone.

[0023] Furthermore, the axial force ultimate bearing capacity and bending moment ultimate bearing capacity at the boundary between large and small eccentric compression are obtained by the following formulas:

[0024] N u =f c bξ b h0+f y 'A' S -f y A s

[0025]

[0026] Where, N u M is the ultimate bearing capacity of axial force. u For the ultimate bending moment bearing capacity, f cρ is the compressive strength of concrete, b is the width of the reinforced concrete structure, h is the height of the reinforced concrete structure, and f is the concrete compressive strength. y ′ represents the design strength value of the compression reinforcement, f y A′ is the design value of the tensile strength of the reinforcing steel. S A is the area of ​​the compression reinforcement. s ξ represents the area of ​​the tensile reinforcement. b h0 is the height of the relative limit compression zone, h0 is the effective height of the reinforced concrete structure, h0 = ha, a is the distance from the resultant point of the longitudinal tensile reinforcement to the tension edge, and a′ is the distance from the resultant point of the longitudinal compressive reinforcement to the compression edge.

[0027] Furthermore, when the compressed steel reinforcement is in the yield state, the functional relationship between the axial force ultimate bearing capacity and the bending moment ultimate bearing capacity of the large eccentric compression curve is as follows:

[0028]

[0029]

[0030] When the compressed steel reinforcement is not in the yielding state, the functional relationship between the axial force ultimate bearing capacity and the bending moment ultimate bearing capacity of the large eccentric compression curve is as follows:

[0031] M u =N u e0

[0032]

[0033] Where, N u M is the ultimate bearing capacity of axial force. u For the ultimate bending moment bearing capacity, f c ρ is the compressive strength of concrete, b is the width of the reinforced concrete structure, h is the height of the reinforced concrete structure, x is the height of the compression zone, and f is the compressive strength of concrete. y ′ represents the design strength value of the compression reinforcement, f y A′ is the design value of the tensile strength of the reinforcing steel. S A is the area of ​​the compression reinforcement. s ξ represents the area of ​​the tensile reinforcement. b h0 is the height of the relative limit compression zone, h0 is the effective height of the reinforced concrete structure, h0 = ha, a is the distance from the resultant point of the longitudinal tensile reinforcement to the tension edge, a′ is the distance from the resultant point of the longitudinal compressive reinforcement to the compression edge, e is the distance from the point of application of the axial compressive force to the tensile reinforcement, e0 is the eccentricity of the axial compressive force relative to the centroid of the section, and e′ is the distance from the point of application of the axial compressive force to the compressive reinforcement.

[0034] Furthermore, the axial force ultimate bearing capacity and bending moment ultimate bearing capacity of the compressive steel reinforcement at the yield point under large eccentric compression are obtained by the following formula:

[0035] N u =2f c ba′+f y 'A' S -f y A s

[0036]

[0037] Where, N u M is the ultimate bearing capacity of axial force. u For the ultimate bending moment bearing capacity, f c ρ is the compressive strength of concrete, b is the width of the reinforced concrete structure, h is the height of the reinforced concrete structure, and f is the concrete compressive strength. y ′ represents the design strength value of the compression reinforcement, f y A′ is the design value of the tensile strength of the reinforcing steel. S A is the area of ​​the compression reinforcement. s denoted as , where is the area of ​​the tensile reinforcement, 'a' is the distance from the resultant point of the longitudinal tensile reinforcement to the tensile edge, and 'a′' is the distance from the resultant point of the longitudinal compressive reinforcement to the compressive edge.

[0038] Furthermore, when the compressed steel reinforcement is in the yield state, the ultimate moment bearing capacity at the pure bending point is obtained by the following formula:

[0039]

[0040] When the compressed steel reinforcement is not in a yield state, the ultimate bearing capacity of the bending moment at the pure bending point is obtained by the following formula:

[0041] M u =f y A s (h0-a)

[0042] Among them, M u Let f be the ultimate bending moment bearing capacity, ξ be the relative height of the compression zone, and f be the ultimate bending moment bearing capacity. c ρ is the compressive strength of concrete, b is the width of the reinforced concrete structure, h is the height of the reinforced concrete structure, x is the height of the compression zone, and f is the compressive strength of concrete. y ′ represents the design strength value of the compression reinforcement, f y A′ is the design value of the tensile strength of the reinforcing steel. S A is the area of ​​the compression reinforcement. s ξ represents the area of ​​the tensile reinforcement. bh0 is the height of the relative limit compression zone, h0 is the effective height of the reinforced concrete structure, h0 = ha, a is the distance from the resultant point of the longitudinal tensile reinforcement to the tension edge, and a′ is the distance from the resultant point of the longitudinal compressive reinforcement to the compression edge.

[0043] Furthermore, when the compressed steel reinforcement is in the yield state, the functional relationship between the axial force ultimate bearing capacity and the bending moment ultimate bearing capacity of the large eccentric tension curve is as follows:

[0044]

[0045] When the compressed steel reinforcement is not in the yielding state, the functional relationship between the axial force ultimate bearing capacity and the bending moment ultimate bearing capacity of the eccentric tension curve is as follows:

[0046] M u =N u e0

[0047]

[0048] Where, N u M is the ultimate bearing capacity of axial force. u For the ultimate bending moment bearing capacity, f c ρ is the compressive strength of concrete, b is the width of the reinforced concrete structure, h is the height of the reinforced concrete structure, x is the height of the compression zone, and f is the compressive strength of concrete. y ′ represents the design strength value of the compression reinforcement, f y A′ is the design value of the tensile strength of the reinforcing steel. S A is the area of ​​the compression reinforcement. s ξ represents the area of ​​the tensile reinforcement. b h0 is the height of the relative limit compression zone, h0 is the effective height of the reinforced concrete structure, h0 = ha, a is the distance from the resultant point of the longitudinal tensile reinforcement to the tension edge, a′ is the distance from the resultant point of the longitudinal compressive reinforcement to the compression edge, e is the distance from the point of application of the axial compressive force to the tensile reinforcement, e0 is the eccentricity of the axial compressive force relative to the centroid of the section, and e′ is the distance from the point of application of the axial compressive force to the compressive reinforcement.

[0049] Furthermore, the ultimate bearing capacity of the axial force and the ultimate bearing capacity of the bending moment at the axial compression point are obtained by the following formulas:

[0050] N u =f c bh+f y 'A' S +f y A s

[0051] M u =0

[0052] Where, Nu M is the ultimate bearing capacity of axial force. u For the ultimate bending moment bearing capacity, f c ρ is the compressive strength of concrete, b is the width of the reinforced concrete structure, h is the height of the reinforced concrete structure, and f is the concrete compressive strength. y ′ represents the design strength value of the compression reinforcement, f y A′ is the design value of the tensile strength of the reinforcing steel. S A is the area of ​​the compression reinforcement. s This represents the area of ​​the tensile reinforcement.

[0053] Furthermore, the axial force ultimate bearing capacity and bending moment ultimate bearing capacity at the tension boundary between large and small eccentricities are obtained by the following formulas:

[0054] N u =f y A s

[0055]

[0056] Where, N u M is the ultimate bearing capacity of axial force. u For the ultimate bending moment bearing capacity, f y A represents the design value of the tensile strength of the reinforcing steel. s denoted as , where h is the area of ​​the tensile reinforcement, h is the height of the reinforced concrete structure, and a is the distance from the resultant point of the longitudinal tensile reinforcement to the tensile edge.

[0057] Furthermore, the ultimate bearing capacity of the axial force and the ultimate bearing capacity of the bending moment at the axial tension point are obtained by the following formulas:

[0058] N u =f y 'A' S +f y A s

[0059] M u =0

[0060] Where, N u M is the ultimate bearing capacity of axial force. u For the ultimate bending moment bearing capacity, f y ′ represents the design strength value of the compression reinforcement, f y A′ is the design value of the tensile strength of the reinforcing steel. S A is the area of ​​the compression reinforcement. s This represents the area of ​​the tensile reinforcement.

[0061] Based on the same inventive concept, the present invention also provides an electronic device, comprising:

[0062] One or more processors;

[0063] A memory having stored one or more programs that, when executed by one or more processors, cause the one or more processors to implement the steps of a reinforced concrete structure design method.

[0064] Based on the same inventive concept, the present invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of a reinforced concrete structure design method.

[0065] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0066] This invention constructs a load-bearing capacity envelope for all stress types within a structure and compares it with the internal force combinations of multiple sections in current reinforced concrete structures. This enables the calculation of reinforcement and verification of load-bearing capacity for multiple sections of reinforced concrete structures. Compared to existing methods that can only design structures for a single section, this invention, based on the structural load-bearing capacity envelope, can simultaneously perform reinforcement calculations and verification of load-bearing capacity for multiple sections, improving the efficiency and quality of reinforced concrete structure design. Attached Figure Description

[0067] Figure 1 This is a schematic diagram of the finite element method mesh model of the lining structure according to an embodiment of the present invention;

[0068] Figure 2 This is a schematic diagram of the lining normal stress results according to an embodiment of the present invention;

[0069] Figure 3 This is a cross-sectional diagram of a reinforced concrete member according to an embodiment of the present invention;

[0070] Figure 4 This is a schematic diagram of the Nu-Mu correlation curve in an embodiment of the present invention;

[0071] Figure 5 This is a calculation diagram of the compressive bearing capacity of the rectangular cross-section eccentrically compressed member according to an embodiment of the present invention;

[0072] Figure 6 This is a calculation diagram of the compressive bearing capacity of the rectangular cross-section eccentric tension member according to an embodiment of the present invention;

[0073] Figure 7 This is a schematic diagram of the normal section bearing capacity calculation program according to an embodiment of the present invention;

[0074] Figure 8 This is a schematic diagram illustrating that the load-bearing capacity verification of this embodiment of the invention does not meet the requirements.

[0075] Figure 9 This is a schematic diagram illustrating the load-bearing capacity verification of an embodiment of the present invention;

[0076] Figure 10 This is a schematic diagram of reinforcement calculation according to an embodiment of the present invention. Detailed Implementation

[0077] The present invention will be described in detail below with reference to embodiments. It should be noted that, unless otherwise specified, the embodiments and features in the embodiments of the present invention can be combined with each other. For ease of description, the words "upper," "lower," "left," and "right" appearing below only indicate that they are consistent with the upper, lower, left, and right directions of the drawings themselves, and do not limit the structure.

[0078] Example 1

[0079] This embodiment proposes a method for multi-section reinforcement calculation and bearing capacity verification. This method automatically acquires the bearing capacity curve of a reinforced concrete structure and compares it with the internal force combinations of multiple sections of the structure, thus achieving automatic reinforcement calculation and bearing capacity verification for multiple sections. This method not only improves design efficiency but also significantly enhances design quality, making the design process more intuitive and efficient.

[0080] This method, through in-depth analysis of the formulas for calculating the bearing capacity of reinforced concrete structures, derives formulas for the bearing capacity of members under axial compression, small eccentric compression, large eccentric compression, pure bending, large eccentric tension, small eccentric tension, and axial tension. By establishing a functional relationship between bending moment and axial force, a scatter plot of bending moment and axial force with sufficient accuracy is generated. Based on these scatter plots, an envelope diagram of bending moment and axial force under known structural design parameters is generated. This envelope diagram is then displayed alongside the design values ​​of internal forces in the structural section on the same chart, allowing for a direct assessment of whether the section's bearing capacity meets design requirements.

[0081] This method, centered on visual programming technology, automatically calculates and obtains the structural bearing capacity curve, effectively solving the problems of tedious and inefficient calculations in the design of multi-section structures. It easily obtains the relationship between the bearing capacity of a section and the internal forces acting on it, and intuitively performs automatic reinforcement calculations and bearing capacity verification for multiple sections, achieving automation and visualization of the entire design process and greatly improving design efficiency and quality.

[0082] The reinforced concrete structure design method of this embodiment includes the following steps:

[0083] Step 1: The internal forces of the lining structure are calculated using the linear elastic finite element method to obtain the internal force results of multiple sections of the lining structure.

[0084] Step 1.1: Establish the finite element model. Taking a rectangular lining cross-section as an example, the finite element method mesh model is determined by geometric parameters (lining width, lining height, lining thickness) and mesh parameters (number of radial meshes, number of circumferential meshes, calculation range), such as... Figure 1 As shown.

[0085] Step 1.2: Determine the calculation parameters. The loads such as internal water pressure, external water pressure, and surrounding rock pressure are included in the form of surface forces on the inner and outer surfaces of the lining, and the self-weight load of the lining is included in the form of volume forces. Elastic modulus and Poisson's ratio parameters are assigned to the lining unit and the surrounding rock unit.

[0086] Step 1.3: Determine boundary conditions. Apply normal constraints to all sides of the surrounding rock element except the top.

[0087] Step 1.4: Obtaining Stress Results. Using the finite element method, considering the parameters and boundaries of steps 1.1, 1.2, and 1.3, a finite element model is established. The finite element program is run to obtain the normal stress results of the lining section, as shown below. Figure 2 As shown.

[0088] Step 1.5: Obtain internal force results. Based on the stress results from Step 1.4, extract the normal stress and shear stress for each section, and integrate the normal stress and shear stress respectively to obtain the calculated axial force N for each section. i and the calculated value of bending moment M i ,in:

[0089]

[0090] Where, N i M is the calculated value of the axial force at the i-th section. i Let σ be the calculated bending moment value for the i-th section. i,j h is the normal stress value at the j-th stress point in the i-th section. i,j y is the distance between the j-th stress point and the (j+1)-th stress point in the i-th section. i,j Let n be the distance from the center of the j-th stress point and the (j+1)-th stress point in the i-th section to the center of the i-th section, n be the number of stress points in the i-th section, and m be the number of reinforced concrete sections.

[0091] The internal force results for each section can form a set of calculated internal force values:

[0092] R={{N1, M1}, {N2, M2}, ..., {N2, M2}}.

[0093] Step 2: Having obtained the calculated internal force set R for all sections of the lining structure from Step 1, these calculated internal force values ​​can be plotted in a coordinate system with bending moment on the horizontal axis and axial force on the vertical axis, forming a set of calculated load points. To visually represent the relationship between the calculated load point set and the structural bearing capacity, the envelope method is introduced. This involves plotting all load points under the ultimate bearing capacity condition in a coordinate system with bending moment on the horizontal axis and axial force on the vertical axis, and connecting them to form a closed curve, thus forming the bearing capacity envelope. If the envelope encloses all elements in set R, the bearing capacity meets the requirements; otherwise, the bearing capacity does not meet the requirements.

[0094] As can be seen from the above analysis, this envelope is composed of load points under all ultimate bearing capacity conditions of this section. In order to accurately obtain this bearing capacity envelope, the characteristics of the envelope will be analyzed next.

[0095] Step 2.1: As Figure 3 As shown, based on the different stress characteristics of the structure, the structure can be divided into axially compressed sections, eccentrically compressed sections, pure bending sections, eccentrically tensioned sections, and axially tensioned sections.

[0096] Based on the stress σ of the tensile or compressive reinforcement on the side with smaller stress. s Whether or not yielding has been achieved, the eccentrically compressed section is divided into a small eccentrically compressed section (when not yielding) and a large eccentrically compressed section (when yielding); according to whether the axial force point is located on the outside or inside of the tensile reinforcement, the eccentrically tensioned member is divided into a large eccentrically tensioned member (when on the outside) and a small eccentrically tensioned member (when on the inside).

[0097] Step 2.2: To construct an envelope matching the cross-section type in Step 2.1, analysis shows that the Nu-Mu envelope should consist of the following parts: (1) Characteristic points: axial compression point, large and small eccentric compression boundary point, pure bending point, large and small eccentric tension boundary point, and axial tension point; (2) Characteristic curves: small eccentric compression curve, large eccentric compression curve, large eccentric tension curve, and small eccentric tension curve. Therefore, the schematic diagram of the Nu-Mu envelope can be obtained as follows: Figure 4 As shown, the Nu-Mu envelope consists of the axial compression point A, the boundary point between large and small eccentric compression B, the large eccentric compression point C (when the compression is at the boundary between the yield and non-yield of the steel reinforcement), the pure bending point D, the boundary point between large and small eccentric tension E, the axial tension point F, and the small eccentric compression curve AB, the large eccentric compression curve BC (when the compressed steel reinforcement is in the yield state), the large eccentric compression curve CD (when the compressed steel reinforcement is not in the yield state), the large eccentric tension curve DE, and the small eccentric tension curve EF.

[0098] To obtain the accurate Nu-Mu envelope of a given component, it is necessary to perform piecewise analysis by combining the calculation formula of the positive section bearing capacity of reinforced concrete structure and its related assumptions, so as to obtain the Nu and Mu values ​​of each characteristic point and the curve equation of each characteristic curve. Finally, Nu-Mu related curves are plotted based on the analysis results.

[0099] Step 3: Derive the solution methods for points A, B, C, D, E, F, and curves AB, BC, CD, DE, EF, obtaining the relevant formulas for the Nu-Mu envelope. Among them, formulas 3-9 and 24-26 are the basic formulas for the bearing capacity of the normal section of reinforced concrete structures.

[0100] Step 3.1: Derive the calculation formula for the axial compression point A. The ultimate bearing capacity of the cross section is a combination of the compressive bearing capacity of the concrete and the longitudinal reinforcement. The calculation formulas for the bearing capacity of the axial compression point A are shown in Equations 1 and 2.

[0101] N u =f c bh+f y 'A' S +f y A s (Equation 1)

[0102] M u =0 (Equation 2)

[0103] Where, N u The ultimate bearing capacity of axial force is N and M. u For the ultimate bending moment bearing capacity, N·mm, f c The compressive strength of concrete, N / mm² 2 b is the width of the reinforced concrete structure (mm), h is the height of the reinforced concrete structure (mm), f y ′ represents the design strength of the compressed steel reinforcement, in N / mm². 2 f y This represents the design strength of the tensile reinforcement, in N / mm². 2 A′ S The area of ​​the compression steel reinforcement is in mm. 2 A s The area of ​​the tensile reinforcement is in mm. 2 .

[0104] Step 3.2: Derive the calculation formula for eccentric compression. For a general eccentrically compressed member, the calculation diagram of the compressive bearing capacity of the normal section is as follows: Figure 5 As shown, the basic formula for the bearing capacity of the normal section of an eccentrically compressed member is as follows:

[0105] N u =f c bx+f y 'A' S-σ s A s (Equation 3)

[0106]

[0107] When x > h, take x = h (Equation 9)

[0108] Where, N u σ is the ultimate bearing capacity of axial force. s Tensile stress in the reinforcing steel bar, N / mm 2 e is the distance from the point of application of the axial compressive force to the tensile reinforcement, in mm; e0 is the eccentricity of the axial compressive force relative to the centroid of the section (reinforced concrete structure), in mm; a is the distance from the resultant force point of the longitudinal tensile reinforcement to the tension edge, in mm; a′ is the distance from the resultant force point of the longitudinal compressive reinforcement to the compression edge, in mm; x is the height of the compression zone, in mm; h0 is the effective height of the reinforced concrete structure, h0 = ha, in mm; ξ is the relative height of the compression zone. ξ b E represents the relative height of the boundary pressure zone. s The elastic modulus of the steel reinforcement is expressed in N / mm². 2 .

[0109] Step 3.2.1: Derive the calculation formula for the small eccentric compression curve AB. At this point, the height of the compression zone is greater than the limit compression zone height, the reinforcement in the compression zone is in yielding condition, and the stress in the tension zone reinforcement is less than the yield stress. Based on the plane section assumption, the relationship between the height of the compression zone and the stress in the tension zone reinforcement needs to be established, i.e., Equation 7. From Equations 3, 7, 8, and 9, the expression for the compression zone height x with respect to the axial force is obtained as shown in Equation 10. From Equations 4, 5, 6, and 10, the expression for the bending moment with respect to the compression zone height x is obtained as shown in Equation 11, thus establishing the M value of the small eccentric compression curve AB. u ~x~N u The functional relationship between them.

[0110]

[0111] Step 3.2.2: Derive the calculation formula for the boundary point B between large and small eccentric compression. At this point, the height of the compression zone is equal to the height of the boundary compression zone. Both the compression zone and tension zone reinforcement are in a yield state. The normal section bearing capacity of the dividing point B of the large and small eccentric compression can be directly obtained from equations 3, 4, 5, 6, 7, and 8.

[0112] N u =f c bx+f y 'A' S -f y A s =f c bξ b h0+fy 'A' S -f y A s (Equation 12)

[0113]

[0114] Step 3.2.3: Derive the calculation formula for large eccentric compression. At this point, the height of the compression zone is less than the height of the limit compression zone. If the reinforcement in the tension zone is in yielding, it is necessary to distinguish whether the reinforcement in the compression zone is in yielding and discuss the cases separately.

[0115] Step 3.2.3.1: Derive the calculation formula for the large eccentric compression (compression reinforcement in yield state) curve BC. For the large eccentric compression curve BC, x > 2a′, and the compression zone reinforcement is in the yield state. The expression for the compression zone height x with respect to the axial force can be obtained from equations 3, 7, 8, and 9, as shown in equation 14. The expression for the bending moment with respect to the compression zone height x can be obtained from equations 4, 5, 6, and 14, as shown in equation 15. Thus, the M of the large eccentric compression (compression reinforcement in yield state) curve BC is established. u ~x~N u The functional relationship between them.

[0116]

[0117] Step 3.2.3.2: Derive the calculation formula for point C under large eccentric compression (when the compression is at the boundary between the yield and non-yield of the steel reinforcement). For the yield boundary point C of the steel reinforcement under large eccentric compression, x = 2a′, the tension zone steel reinforcement is in yield, and the compression zone steel reinforcement is just in yield. The normal section bearing capacity at this point can be directly obtained from equations 3 to 8.

[0118] N u =f c bx+f y 'A' S -f y A s =2f c ba′+f y 'A' S -f y A s (Equation 16)

[0119]

[0120] Step 3.2.3.3: Derive the calculation formula for the large eccentric compression curve CD (compression reinforcement not in yield state). For the large eccentric compression curve CD, x < 2a′, the stress in the compression zone reinforcement is less than the allowable stress of the reinforcement, and it is not in yield state. However, assuming that the resultant point of the concrete compressive stress coincides with the point of application of the compression reinforcement, the distance e′ from the point of application of the axial pressure to the point of application of the compression zone reinforcement is calculated using the moment balance formula with the moment center as the point of application of the resultant point of the compression zone reinforcement as the moment center. The expression for the axial force is shown in Equation 18. Furthermore, the expression for the bending moment with respect to e′ is shown in Equation 20, thus establishing the M of the large eccentric compression curve CD. u ~e′~N u The functional relationship between them.

[0121]

[0122] M u =h(e0)=N u e0 (Equation 20)

[0123] Where e′ is the distance from the point of application of axial pressure to the compressed steel bar, in mm.

[0124] Step 3.3: Derive the formula for calculating the pure bending point D.

[0125] Step 3.3.1: When x≥2a′, the reinforcement in the compression zone is in a yield state. M can be calculated from equations 3, 4, 5, and 6. u .

[0126]

[0127] Step 3.3.2: When x < 2a′, the stress in the compression zone reinforcement is less than the allowable stress of the reinforcement, and it is not in a yielding state. However, assuming that the resultant point of the concrete compressive stress coincides with the point of application of the compressive stress in the compression reinforcement, M is calculated using the moment balance formula with the resultant point of the compression zone reinforcement as the moment center. u .

[0128] M u =f y A s (h0-a) (Formula 23)

[0129] Step 3.4: Derive the calculation formula for eccentric tension. Based on the equilibrium conditions of force and moment, the basic calculation formula for the tensile bearing capacity of a rectangular cross-section eccentrically tensioned member can be derived.

[0130]

[0131]

[0132] Where, σ s ′ represents the tensile stress in the compressed steel reinforcement, N / mm2 .

[0133] like Figure 6 As shown, based on whether the point of application of the axial force is located on the outside or inside of the tensile reinforcement, eccentric tension members are divided into large eccentric tension members (when on the outside) and small eccentric tension members (when on the inside).

[0134] Step 3.4.1: Derive the calculation formula for the DE curve under large eccentric tension.

[0135] Step 3.4.1.1: When x ≥ 2a′, the reinforcement in the compression zone is in a yield state. M can be established using equations 24 and 25. u ~x~N u The functional relationship between them.

[0136]

[0137] Step 3.4.1.2: When x < 2a′, the stress in the compression zone reinforcement is less than the allowable stress of the reinforcement, and it is not in a yielding state. However, assuming that the resultant point of the concrete compressive stress coincides with the point of application of the compressive stress in the compression reinforcement, M is calculated using the moment balance formula with the resultant point of the compression zone reinforcement as the moment center. u Thus establishing M u ~e′~N u The functional relationship between them.

[0138]

[0139] M u =h(e0)=N u e0 (Equation 31)

[0140] Step 3.4.2: Derive the formula for calculating the tension boundary point E of major and minor eccentricity. According to the definition of major and minor eccentricity, at the boundary point, At this point, the axial force acts on the position of the tensioned reinforcement, resulting in the following formula.

[0141] N u =f y A s (Equation 32)

[0142]

[0143] Step 3.4.3: Derive the formula for calculating the EF curve under small eccentric tension. For members under small eccentric tension, all reinforcement reaches the design value. According to the formula for calculating reinforcement under small eccentric tension, M can be obtained. u With N u The relationship between them is linear, so we only need to find the bearing capacity of the axially tensioned member and connect it with the dividing point of the large and small eccentric tensions.

[0144] Step 3.5: Derive the formula for calculating the axial tension point F. For an axially tensioned section, the following formula is easily obtained.

[0145] N u =f y 'A' S +f y A s (Equation 34)

[0146] M u =0 (Equation 35)

[0147] Step 3.6: Through steps 3.1 to 3.5, we can obtain: (1) the M of the axial compression point A, the boundary point between large and small eccentric compression B, the yield point of the compressed steel bar under large eccentric compression C, the pure bending point D, the boundary point between large and small eccentric tension E, and the axial tension point F. u and N u The expression can be used to solve for M at each point when parameters such as structural width, structural height, concrete compressive strength, design value of steel reinforcement strength, and steel reinforcement elastic modulus are known. u and N u (2) The curves with small eccentric compression (AB), large eccentric compression (when the compressed steel yields) (BC), large eccentric compression (when the compressed steel does not yield) (CD), large eccentric tension (DE), and small eccentric tension (EF) are M. u With N u The functional relationship between them.

[0148] As can be seen from the conclusions in (1) and (2), the above methods can completely describe the M-shaped envelope of the load-bearing capacity of a structure (component) under specific design parameters. u With N u The functional relationship between them. To display the carrying capacity envelope in the coordinate system, firstly based on M... u With N u The functional relationship between them can form an M with sufficient accuracy. u With N u The scattered points between the points are then connected to form a closed curve, which forms the bearing capacity envelope when the design parameters such as structural width, structural height, concrete compressive strength, steel reinforcement strength design value, and steel reinforcement elastic modulus are known.

[0149] Step 4: Simultaneously plot the calculated internal force set R of all sections of the lining structure in Step 1 with the ultimate bearing capacity envelope in Step 3 on a coordinate system for comparison. If all points are within the envelope, the bearing capacity of the structure's normal section meets the requirements. If there are points outside the envelope, increase the reinforcement area by a certain increment to meet the bearing capacity requirements.

[0150] Step 5: Further utilize programming technology, following the ideas in Steps 1 to 4, to write the above results into calculation code, obtain the load-bearing capacity curve of the structure through program calculation, and automatically judge whether the load-bearing capacity of the structure's normal section meets the requirements.

[0151] In the calculation of reinforcement in reinforced concrete structures, traditional design methods suffer from numerous drawbacks, including repetitive work, cumbersome procedures, low efficiency, low visualization, and limited user awareness of structural design margins. This embodiment first analyzes the calculation principles and proposes N... u and M u The envelope diagram calculation method, combined with visual programming technology, enables the automatic acquisition of the relationship between the structural bearing capacity and the internal forces on the cross-section structure. It can intuitively perform automatic reinforcement calculation and bearing capacity verification for multiple cross-sections, realizing the automation and visualization of the entire design process, and greatly improving design efficiency and quality.

[0152] Example 2

[0153] Taking the underground cavern lining structure of a hydropower station as an example, this paper provides a detailed explanation of the multi-section reinforcement calculation and bearing capacity verification method based on visual programming technology.

[0154] Step (1): The internal forces of each typical section of the lining structure are obtained by using the finite element method. The combination table of internal forces of some sections is shown in Table 1.

[0155] Table 1 Combination of Internal Forces in Lining Structure Sections

[0156]

[0157]

[0158] Step (2): Based on the aforementioned Nu-Mu envelope formulas, C# language was used for programming design, and a calculation program supporting multi-section reinforcement calculation and bearing capacity verification was developed based on visual programming technology. The program results are as follows: Figure 7 As shown, the program consists of two parameter input interfaces (section design parameters and section reinforcement parameters), three operation buttons (import data, perform reinforcement calculation, and verify bearing capacity), and a curve display interface. The section design parameters include: section width, section height, reinforcement design strength, reinforcement elastic modulus, concrete compressive strength, and concrete ultimate compressive strain. The section reinforcement parameters include: inner reinforcement area, outer reinforcement area, distance from inner reinforcement to edge, and distance from outer reinforcement to edge.

[0159] Step (3): Click the "Import Data" button on the program interface to import the data shown in Table 1 into the program in batches. If you want to perform a bearing capacity verification, set the section design parameters and reinforcement parameters according to the requirements, and click the "Bearing Capacity Verification" button to perform the bearing capacity verification calculation. If the bearing capacity does not meet the requirements, a pop-up window will appear. Figure 8 The prompt box shown reads, "Bearing capacity does not meet requirements. Please reset the rebar area or click on the reinforcement calculation to configure the rebar." If the bearing capacity meets the requirements, a pop-up window will appear as follows: Figure 9 The prompt box shown indicates "Bearing capacity meets requirements." To perform reinforcement calculations, set the section design parameters and reinforcement parameters (excluding reinforcement area) according to your needs. The program will automatically increase the reinforcement ratio gradually from 0, simultaneously calculate the Nu-Mu envelope, and determine whether the target internal force combination is within the envelope. The reinforcement area corresponding to the target internal force combination exactly within the envelope is the desired result. Figure 10 As shown.

[0160] Example 3

[0161] This embodiment provides an electronic device, including:

[0162] One or more processors;

[0163] A memory that stores one or more programs, which, when executed by one or more processors, cause the one or more processors to implement the steps of a reinforced concrete structure design method.

[0164] In some implementations, the memory may be high-speed random access memory (RAM), and may also include non-volatile memory, such as at least one disk storage device.

[0165] In other implementations, the processor can be any type of general-purpose processor, such as a central processing unit (CPU) or a digital signal processor (DSP), and there is no limitation here.

[0166] This embodiment provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of a reinforced concrete structure design method.

[0167] The above embodiments should be understood as being used only to illustrate the present invention more clearly, and not to limit the scope of the present invention. After reading the present invention, any modifications of the present invention in various equivalent forms by those skilled in the art fall within the scope defined by the appended claims.

Claims

1. A method of designing a reinforced concrete structure, characterized by, The method comprises the following steps: S1, according to the basic parameters of the reinforced concrete structure, combining the basic formula of the bearing capacity of the normal section of the reinforced concrete structure, the ultimate bearing capacity of the axial force and the ultimate bearing capacity of the bending moment of the characteristic point are calculated to establish the functional relationship between the ultimate bearing capacity of the axial force and the ultimate bearing capacity of the bending moment of the characteristic curve; S2, according to the ultimate bearing capacity of the axial force and the ultimate bearing capacity of the bending moment of the characteristic point, the functional relationship between the ultimate bearing capacity of the axial force and the ultimate bearing capacity of the bending moment of the characteristic curve, the ultimate bearing capacity envelope is constructed; S3, if the internal force calculation value of all sections of the reinforced concrete structure is located in the ultimate bearing capacity envelope, the bearing capacity of the reinforced concrete structure meets the requirements, otherwise, the basic parameters of the reinforced concrete structure are adjusted, and steps S1-S2 are repeated until the internal force calculation value of all sections of the reinforced concrete structure is located in the ultimate bearing capacity envelope; Wherein, the internal force calculation value includes the axial force calculation value and the bending moment calculation value; The characteristic point at least includes the axial compression point, the large and small eccentric compression dividing point, the large eccentric compression when the compression reinforcement yield dividing point, the pure bending point, the large and small eccentric tension dividing point, the axial tension point; The characteristic curve includes the small eccentric compression curve, the large eccentric compression curve, the large eccentric tension curve, and the small eccentric tension curve; Wherein, according to the basic parameters of the reinforced concrete structure, the finite element model of the reinforced concrete structure is constructed, the reinforced concrete structure is divided into multiple sections by mesh, and the simulation analysis of the reinforced concrete structure is carried out to obtain the internal force calculation value of each section of the reinforced concrete structure; The expression of the internal force calculation value is as follows: in, For the first Calculated axial force values ​​for each cross section For the first Calculated bending moment values ​​for each section. For the first The first section Normal stress value at each stress point For the first The first section The stress point and the first The distance between stress points For the first The first section The stress point and the first From the center of the stress point to the first The distance between the centers of each cross section For the first Number of stress points in a cross section This refers to the number of cross sections in the reinforced concrete structure.

2. The reinforced concrete structure design method according to claim 1, characterized by, The basic parameters include the width of the reinforced concrete structure, the height of the reinforced concrete structure, the steel design strength, the steel elastic modulus, the concrete compressive strength, the concrete ultimate compressive strain, and the reinforcement area.

3. The reinforced concrete structure design method according to claim 1, characterized by, The functional relationship between the ultimate bearing capacity of the axial force and the ultimate bearing capacity of the bending moment of the small eccentric compression curve is as follows: + ； wherein, is the axial force ultimate bearing capacity, is the bending moment ultimate bearing capacity, is the compression zone height, is the concrete compressive strength is the width of the reinforced concrete structure, is the height of the reinforced concrete structure, is the compressive reinforcement strength design value, is the tensile reinforcement strength design value, is the compressive reinforcement area, is the tensile reinforcement area, is the distance from the longitudinal tensile reinforcement force point to the tensile edge, is the distance from the longitudinal compressive reinforcement force point to the compressive edge, is the effective height of the reinforced concrete structure, , Hr is the relative limit of the height of the compression zone.

4. The reinforced concrete structure design method according to claim 1, characterized by, The ultimate bearing capacity of the axial force and the ultimate bearing capacity of the bending moment of the large and small eccentric compression dividing point are obtained by the following formula: wherein, is the axial force ultimate capacity, is the bending moment ultimate capacity, is the concrete compressive strength is the width of the reinforced concrete structure, is the height of the reinforced concrete structure, is the compressive reinforcement strength design value, is the tensile reinforcement strength design value, is the compressive reinforcement area, is the tensile reinforcement area, is the relative limit compressive zone height, is the effective height of the reinforced concrete structure, , is the distance from the longitudinal tensile reinforcement force point to the tensile edge, is the distance from the longitudinal compressive reinforcement force point to the compressive edge.

5. The reinforced concrete structure design method according to claim 1, characterized by, When the compression reinforcement is in the yield state, the functional relationship between the ultimate bearing capacity of the axial force and the ultimate bearing capacity of the bending moment of the large eccentric compression curve is as follows: When the compression reinforcement is not in the yield state, the functional relationship between the ultimate bearing capacity of the axial force and the ultimate bearing capacity of the bending moment of the large eccentric compression curve is as follows: wherein, is the axial force ultimate capacity, is the bending moment ultimate capacity, is the concrete compressive strength is the width of the reinforced concrete structure, is the height of the reinforced concrete structure, is the compressive zone height, is the compressive reinforcement strength design value, is the tensile reinforcement strength design value, is the compressive reinforcement area, is the tensile reinforcement area, is the relative limit compressive zone height, is the effective height of the reinforced concrete structure, , is the distance from the longitudinal tensile reinforcement force point to the tensile edge, is the distance from the longitudinal compressive reinforcement force point to the compressive edge, is the distance from the axial pressure action point to the tensile reinforcement, is the eccentricity of the axial pressure to the center of gravity of the section, is the distance from the axial pressure action point to the compressive reinforcement.

6. The reinforced concrete structure design method according to claim 1, characterized by, The ultimate bearing capacity of the axial force and the ultimate bearing capacity of the bending moment of the large eccentric compression when the compression reinforcement yield dividing point are obtained by the following formula: wherein, is the axial force ultimate bearing capacity, is the bending moment ultimate bearing capacity, is the concrete compressive strength is the width of the reinforced concrete structure, is the height of the reinforced concrete structure, is the compressive reinforcement strength design value, is the tensile reinforcement strength design value, is the compressive reinforcement area, is the tensile reinforcement area, is the distance from the longitudinal tensile reinforcement force point to the tensile edge, is the distance from the longitudinal compressive reinforcement force point to the compressive edge.

7. The reinforced concrete structure design method according to claim 1, characterized by, When the compression reinforcement is in the yield state, the ultimate bearing capacity of the bending moment of the pure bending point is obtained by the following formula: ， When the compression reinforcement is not in the yield state, the ultimate bearing capacity of the bending moment of the pure bending point is obtained by the following formula: wherein, Mcris the ultimate bending capacity, hcris the relative compressive zone height, fcis the compressive strength of concrete b is the width of the reinforced concrete structure, h is the height of the reinforced concrete structure, hcis the compressive zone height, fycis the design value of compressive reinforcement strength, fyctis the design value of tensile reinforcement strength, Asis the area of compressive reinforcement, Atis the area of tensile reinforcement, hcris the relative limit compressive zone height, h is the effective height of the reinforced concrete structure, , is the distance from the force point of longitudinal tensile reinforcement to the tensile edge, is the distance from the force point of longitudinal compressive reinforcement to the compressive edge.

8. The reinforced concrete structure design method according to claim 1, characterized by, When the compression reinforcement is in the yield state, the functional relationship between the ultimate bearing capacity of the axial force and the ultimate bearing capacity of the bending moment of the large eccentric tension curve is as follows: When the compression reinforcement is not in the yield state, the functional relationship between the ultimate bearing capacity of the axial force and the ultimate bearing capacity of the bending moment of the large eccentric tension curve is as follows: wherein, is the axial force ultimate capacity, is the bending moment ultimate capacity, is the concrete compressive strength is the width of the reinforced concrete structure, is the height of the reinforced concrete structure, is the compressive zone height, is the compressive reinforcement strength design value, is the tensile reinforcement strength design value, is the compressive reinforcement area, is the tensile reinforcement area, is the relative limit compressive zone height, is the effective height of the reinforced concrete structure, , is the distance from the longitudinal tensile reinforcement force point to the tensile edge, is the distance from the longitudinal compressive reinforcement force point to the compressive edge, is the distance from the axial pressure action point to the tensile reinforcement, is the eccentricity of the axial pressure to the center of gravity of the section, is the distance from the axial pressure action point to the compressive reinforcement.

9. The reinforced concrete structure design method according to claim 1, characterized by, The ultimate bearing capacity of the axial force and the ultimate bearing capacity of the bending moment of the axial compression point are obtained by the following formula: The axial force ultimate load-carrying capacity and the bending moment ultimate load-carrying capacity of the size eccentric tension dividing point are obtained by the following formula: = The axial force ultimate load-carrying capacity and the bending moment ultimate load-carrying capacity of the axial tension point are obtained by the following formula: wherein, is the axial force ultimate bearing capacity, is the bending moment ultimate bearing capacity, is the concrete compressive strength, is the compressive reinforcement strength design value, is the tensile reinforcement strength design value, is the compressive reinforcement area, is the tensile reinforcement area, is the width of the reinforced concrete structure, is the height of the reinforced concrete structure, is the distance from the longitudinal tensile reinforcement force point to the tensile edge.

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