A method for calculating and tensioning circumferential prestressed steel reinforcement in a circular water tank

Abstract

This invention discloses a method for calculating and tensioning circumferential prestressed steel reinforcement in a circular water tank. A three-dimensional finite element mesh model of a high-water-level, large-volume circular water tank-foundation system is constructed. Based on load conditions, boundary conditions of the foundation perimeter, and the three-dimensional finite element mesh model of the high-water-level, large-volume circular water tank-foundation system, the radial and circumferential stresses of the target water tank are calculated. Based on the radial and circumferential stresses of the target water tank and the finite element mesh model, the circumferential axial force and circumferential bending moment at different elevations of the finite element mesh model are calculated. The normal stress of the concrete at the edge of the target water tank is calculated based on the circumferential axial force and circumferential bending moment, and then the required amount of prestressed steel reinforcement for each section is calculated based on the concrete normal stress. Advantages: By establishing a three-dimensional finite element model of the high-level water tank-foundation system, and based on the internal force calculation results, a method for steel reinforcement and tensioning is provided with good accuracy, and the prestressed steel tensioning method facilitates rapid construction.

Description

Technical Field

[0001] This invention relates to a method for calculating and tensioning circumferential prestressed steel reinforcement in a circular water tank, belonging to the field of circular water tank structural design and construction technology. Background Technology

[0002] For large-volume circular water tank structures at high water levels in water diversion projects, the circumferential tensile force on the tank walls is significant under high internal water pressure, making vertical crack control a major challenge. For the portion of the tank structure below ground level, groundwater and surrounding rock resistance can offset some of the internal water pressure, allowing for reinforced concrete lining. However, for the portion above ground, the internal water pressure is entirely borne by the tank walls, and circumferential crack resistance may be insufficient, necessitating the use of prestressed concrete to control wall cracks. Currently, however, there are no readily available prestressed reinforcement methods or tensioning techniques for ultra-large-volume circular water tank structures with an above-ground height exceeding 30 meters. Summary of the Invention

[0003] The technical problem to be solved by the present invention is to overcome the defects of the prior art and provide a method for calculating and tensioning the circumferential prestressed steel reinforcement of a circular water tank.

[0004] To solve the above-mentioned technical problems, the present invention provides a method for calculating the circumferential prestressed steel reinforcement of a circular water tank, comprising:

[0005] The design information of the target water tank is obtained, including geometric information and the outward extension of the foundation range along the radial direction of the water tank. A three-dimensional finite element mesh model of the high-water-level large-volume circular water tank-foundation system is established based on the geometric information and the outward extension dimension information of the foundation range along the radial direction of the water tank.

[0006] The radial and circumferential stresses of the target water tank are calculated based on the predetermined load conditions, the boundary conditions of the foundation, and the three-dimensional finite element mesh model of the high-water-level large-volume circular water tank-foundation system. The load conditions include the self-weight of the target water tank, the design water level, and the air temperature at the location of the target water tank.

[0007] Based on the radial stress and circumferential stress of the target water tank and the three-dimensional finite element mesh model of the high-water-level large-volume circular water tank-foundation system, the circumferential axial force and circumferential bending moment at different elevations of the three-dimensional finite element mesh model of the high-water-level large-volume circular water tank-foundation system are calculated.

[0008] The normal stress of the concrete at the edge of the target pool is calculated based on the circumferential axial force and circumferential bending moment. Then, the amount of prestressed steel reinforcement required for each section is calculated based on the normal stress of the concrete.

[0009] Furthermore, after calculating the amount of prestressed steel reinforcement required for each section, the difference in reinforcement amount at each elevation is calculated, and the larger reinforcement amount is taken as the final reinforcement amount for elevations with a difference of less than 10%.

[0010] Furthermore, the geometric information includes: pool height, pool wall thickness, inlet pipe location and size, outlet pipe location and size, and the pool height includes the height above the pool floor and the height below the pool floor.

[0011] Furthermore, the extended range is more than twice the height H of the portion above the water tank floor.

[0012] Furthermore, based on the predetermined load conditions, the boundary conditions of the foundation perimeter, and the three-dimensional finite element mesh model of the high-water-level large-volume circular water tank-foundation system, the radial stress σ of the target water tank in cylindrical coordinate system (r, θ, z) is calculated using the finite element method. r and circumferential stress σ θ r, θ, z represent the radial, circumferential, and vertical coordinates of the cylindrical coordinate system, respectively.

[0013] Furthermore, the calculation of the circumferential axial force and circumferential bending moment at different elevations of the three-dimensional finite element mesh model of the high-water-level large-volume circular water tank-foundation system based on the radial and circumferential stresses of the target water tank and the three-dimensional finite element mesh model of the high-water-level large-volume circular water tank-foundation system includes:

[0014] In the three-dimensional finite element mesh model of the high-water-level large-volume circular water tank-foundation system, the portion of the water tank above ground level is divided into several elevation segments along the elevation direction. Several cross-sections are taken along the circumferential direction of each elevation segment. Based on the radial stress and circumferential stress integration, the circumferential axial force N at each cross-section at each elevation is obtained. ci Circumferential bending moment M ci ;

[0015] The maximum value of the circumferential axial force and circumferential bending moment at each elevation is taken as the circumferential axial force F at that elevation. N And circumferential bending moment M.

[0016] Furthermore, the calculation formulas for the circumferential axial force and circumferential bending moment of each cross-section are as follows:

[0017] N ci =∫σ ri d·h e

[0018] M ci =∫σ θi (r-r0)d·h e

[0019] In the formula, Nci M is the circumferential axial force at this cross section. ci h is the circumferential bending moment of this section. e The unit height at this elevation is the height corresponding to the unit mesh of the constructed three-dimensional finite element mesh model of the high-water-level large-volume circular water tank-foundation system, where r0 is the radius at the centroid of the cross-section, and σ is the unit height. ri The radial stress of this section is σ. θi This represents the circumferential stress at this cross section.

[0020] Furthermore, the formula for calculating the amount of prestressed steel reinforcement is as follows:

[0021]

[0022] In the formula, A p The amount of prestressed steel reinforcement is given, A0 is the converted cross-sectional area, and f is the amount of prestressed steel reinforcement. yp For the effective prestress of the prestressed steel bars, σ ck This represents the normal stress in the concrete at the edge of the pool.

[0023] The formula for calculating the converted cross-sectional area is as follows:

[0024] A0 = A c +α E A s +α E A′ s

[0025] In the formula, A c Let A be the cross-sectional area of ​​the concrete. c =bh, where b is the wall thickness of the pool and h is the unit height; α E A is the ratio of the elastic modulus of ordinary steel reinforcement to the elastic modulus of concrete. s The amount of reinforcement calculated for the inner side of the pool wall when using ordinary steel reinforcement; A′ s The amount of reinforcement required for the outer side of the pool wall when using ordinary steel reinforcement.

[0026] The normal stress in the concrete at the edge of the pool includes the normal stress σ in the concrete at the inner edge of the pool. ck1 The normal stress σ of the concrete at the outer edge of the pool ck2 ;

[0027] The normal stress σ in the concrete at the inner edge of the pool ck1 The calculation formula is:

[0028]

[0029] The normal stress σ in the concrete at the outer edge of the pool ck2 The calculation formula is:

[0030]

[0031] In the formula, w is the bending section modulus, for a rectangular section.

[0032] Furthermore, the process of confirming the method of dividing the elevation along the elevation direction into several elevation segments includes:

[0033] Method 1: Each Divide it into one section, where H is the height of the part above the ground level of the pool.

[0034] Method 2: Each section is 3-5 meters long;

[0035] The larger of method one and method two is taken as the final partitioning method.

[0036] A method for tensioning circumferential prestressed steel bars in a circular water tank.

[0037] A prestressed tendon embedding pipe is pre-embedded in the middle of the pool wall. The amount of prestressed tendon required for each section is calculated using the aforementioned calculation method for circumferential prestressed steel bars in a circular pool. Prestressed steel bars are then placed in the prestressed tendon embedding pipe. A buttress column is set at every 90° angle along the circumference on the outside of the pool wall for tensioning and anchoring the prestressed steel bars.

[0038] Each section of the water tank is tensioned in two stages for each ring of prestressed steel bars, with the central angle of each stage of prestressed steel bars being 180°. Both ends are tensioned simultaneously during the tensioning process.

[0039] The buttress columns are tensioned and anchored every 3 to 5 rings of prestressed steel bars along the elevation direction of the pool.

[0040] The beneficial effects achieved by this invention are as follows:

[0041] This invention overcomes the lack of existing methods for the circumferential prestressed steel reinforcement and tensioning of large-volume circular water tanks with an above-ground portion exceeding 30m in water diversion projects. By establishing a three-dimensional finite element model of the high-level water tank-foundation system and based on internal force calculations, this invention provides a method for the circumferential prestressed steel reinforcement and tensioning of large-volume circular water tanks with high water levels. The reinforcement method provided by this technology has good accuracy, and the prestressed steel tensioning method facilitates rapid construction. Attached Figure Description

[0042] Figure 1 This is a schematic diagram of the process of the present invention;

[0043] Figure 2 Schematic diagram of a large-volume circular water tank at high water level and its foundation system;

[0044] Figure 3A schematic diagram showing the division of the area above ground level of the pool along the elevation direction;

[0045] Figure 4 A schematic diagram of the cross-section taken for each circumferential segment;

[0046] Figure 5 This is a schematic diagram showing the arrangement of the buttress columns on the outer side of the pool wall.

[0047] In the diagram, 1-pool wall, 2-first buttress, 3-second buttress, 4-third buttress, and 5-fourth buttress. Detailed Implementation

[0048] The present invention will be further described below with reference to the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and should not be used to limit the scope of protection of the present invention.

[0049] Example 1,

[0050] like Figure 1 The diagram shows a flowchart of a method for calculating the circumferential prestressed steel reinforcement of a circular water tank, including the following steps:

[0051] Step 1.1) as Figure 2 As shown, the geometric information of the water tank was collected, including the height of the water tank (divided into the height above ground and the height below ground), the thickness of the water tank wall, the location and size of the inlet pipe, and the location and size of the outlet pipe. The foundation extends radially along the water tank. A three-dimensional finite element mesh model of the high-water-level, large-volume circular water tank-foundation system was established using finite element software. The height of the water tank above ground is 30.5m, the height of the water tank below ground is 54.9m, and the extension of the foundation is approximately 4 times the height H of the water tank above ground.

[0052] Step 1.2) Apply the following load conditions: the self-weight of the water tank (which can be determined according to the actual size of the water tank), the water pressure inside the tank (the water depth inside the tank is 79.5m), the groundwater pressure, the wind load, the temperature effect, and the boundary conditions (normal constraints) of the foundation. Calculate the stress of the water tank using the three-dimensional finite element method.

[0053] Step 1.3) Divide the portion of the pool above ground level into 8 segments along the elevation direction, such as... Figure 3 As shown, each segment represents a unit height, and the values ​​in the figure represent the elevation of the centroid of each unit. Several cross-sections are then taken along the circumferential direction of each segment, such as... Figure 4 As shown in the figure, the values ​​represent the deflection angle of the line connecting the cross section and the center of the circle relative to the x-axis. The radial stress σ in cylindrical coordinates (r, θ, z) is calculated based on this. r Circumferential stress σ θ Integrating, we obtain the circumferential axial force N at each of the eight cross sections at each elevation. ci Circumferential bending moment M ci .

[0054] N ci =∫σ ri d·h e

[0055] M ci =∫σ θi (r-r0)d·h e

[0056] In the formula, h e Let r0 be the height of the element at this elevation, and r0 be the radius at the centroid of the cross-section. Take the circumferential axial force N in all selected cross-sections at this elevation. ci Circumferential bending moment M ci The maximum value is taken as the circumferential axial force F at that elevation. N The circumferential bending moment M, the circumferential axial force and circumferential bending moment at each elevation of the upper water tank are shown in Table 1.

[0057] Table 1. Circumferential Axial Force and Circumferential Bending Moment at Various Elevations of the Upper Water Tank

[0058] 47.48 -275.94 167.31 43.42 338.47 190.19 39.35 688.83 196.65 35.28 1161.47 198.07 31.22 1727.77 202.77 27.15 2416.86 200.73 23.08 2432.33 176.06 19.02 816.45 212.77

[0059] Step 1.4) The circumferential axial force F obtained from finite element calculation N Given the circumferential bending moment M, and assuming the normal stress in the concrete is linearly distributed along the thickness of the cylinder wall, the normal stress σ in the concrete on the inner and outer sides of the pool wall edge is calculated. ck As shown in Table 2, the required amount of prestressed steel reinforcement A for each section is then calculated using the following formula. p As shown in Table 2

[0060]

[0061] In the formula, A0 is the converted cross-sectional area, as shown in Table 2; f yp The effective prestress of the prestressed steel bars is given by a standard strength of f. ptk For a steel strand with a strength of 1860 MPa, the effective prestress after considering prestress loss is f. yp =0.65f ptk =1209MPa.

[0062] The converted cross-sectional area A0 is calculated using the following formula.

[0063] A0 = A c +α E A s +α E A′ s

[0064] In the formula, A c Let A be the cross-sectional area of ​​the concrete. c=bh, where b is the wall thickness of the pool and g is the unit height; α E This is the ratio of the elastic modulus of ordinary steel reinforcement to the elastic modulus of concrete. The elastic modulus is determined according to the concrete grade and steel reinforcement type, referring to the "Code for Design of Hydraulic Concrete Structures" (SL 191-2008); A s A′ represents the amount of reinforcement on the inner side of the pool wall calculated according to the "Code for Design of Hydraulic Concrete Structures" (SL 191-2008). s The amount of reinforcement on the outside of the pool wall is calculated when configuring ordinary steel bars according to the "Code for Design of Hydraulic Concrete Structures" (SL 191-2008).

[0065] The normal stress in the concrete at the edge of the pool includes the normal stress σ in the concrete at the inner edge of the pool. ck1 The normal stress σ of the concrete at the outer edge of the pool ck2 ;

[0066] The normal stress σ in the concrete at the inner edge of the pool ck1 The calculation formula is:

[0067]

[0068] The normal stress σ in the concrete at the outer edge of the pool ck2 The calculation formula is:

[0069]

[0070] In the formula, w is the bending section modulus, for a rectangular section.

[0071] Table 2. Concrete normal stress and prestressed steel reinforcement at different elevations on the inner and outer sides of the pool wall edge.

[0072]

[0073] Step 1.5) If the reinforcement amount at elevations of 27.15m and 23.08m differs by no more than 10%, combine the reinforcement amounts at elevations of 27.15m and 23.08m, and both should be 2846mm². 2 / m reinforcement.

[0074] Example 2: A method for tensioning circumferential prestressed steel bars in a circular water tank, comprising:

[0075] Step 1.6) Embed the prestressed tendon pipes in the middle of pool wall 1. Configure the prestressed steel bars according to the reinforcement amount calculated in Step 1.5). The prestressed steel bars are placed in the middle of the pool wall. Set four buttress columns at a 90° angle on the outside of pool wall 1. Figure 5As shown, the first buttress column 2, the second buttress column 3, the third buttress column 4, and the fourth buttress column 5 are used for tensioning and anchoring of prestressed steel bars.

[0076] Step 1.7) Each section of the pool is tensioned in two stages for each ring of prestressed steel bars. The central angle of each prestressed steel bar is 180°. Both ends are tensioned simultaneously during tensioning.

[0077] Step 1.8) Buttress columns with altered tensioning and anchoring every 4 rings of prestressed steel bars along the height of the pool.

[0078] The circumferential prestressed steel reinforcement and tensioning method of this invention can be applied to the prestressed reinforcement design and construction of large-volume circular water tank structures at high water levels in water conservancy projects. This invention provides a method for calculating the amount of prestressed steel reinforcement by obtaining internal force values ​​from a three-dimensional finite element simulation of the high-level water tank-foundation system, and provides a prestressed steel tensioning method based on the calculated reinforcement amount. The reinforcement method provided by this technology has good accuracy, and the prestressed steel tensioning method facilitates rapid construction.

[0079] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0080] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0081] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1The function specified in one or more boxes.

[0082] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0083] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for calculating the circumferential prestressed steel reinforcement of a circular water tank, characterized in that, include: The design information of the target water tank is obtained, including geometric information and the outward extension of the foundation range along the radial direction of the water tank. A three-dimensional finite element mesh model of the high-water-level large-volume circular water tank-foundation system is established based on the geometric information and the outward extension dimension information of the foundation range along the radial direction of the water tank. The radial and circumferential stresses of the target water tank are calculated based on the predetermined load conditions, the boundary conditions of the foundation, and the three-dimensional finite element mesh model of the high-water-level large-volume circular water tank-foundation system. The load conditions include the self-weight of the target water tank, the design water level, and the air temperature at the location of the target water tank. Based on the radial and circumferential stresses of the target water tank and the three-dimensional finite element mesh model of the high-water-level large-volume circular water tank-foundation system, the circumferential axial force and circumferential bending moment at different elevations of the three-dimensional finite element mesh model of the high-water-level large-volume circular water tank-foundation system are calculated, including: In the three-dimensional finite element mesh model of the high-water-level large-volume circular water tank-foundation system, the portion of the water tank above ground level is divided into several elevation segments along the elevation direction. Several cross-sections are taken along the circumferential direction of each elevation segment. Based on the radial stress and circumferential stress integrals, the circumferential axial force at each cross-section at each elevation is obtained. Circumferential bending moment ; The maximum value of the circumferential axial force and circumferential bending moment at each elevation is taken as the circumferential axial force at that elevation. and circumferential bending moment ; The formulas for calculating the circumferential axial force and circumferential bending moment at each cross-section are as follows: ； ； In the formula, The circumferential axial force at this cross section. The circumferential bending moment of this section is... This refers to the element height at this elevation, where the element height corresponds to the height of the element mesh in the constructed three-dimensional finite element mesh model of the high-water-level large-volume circular water tank-foundation system. The radius at the centroid of the cross section is... The radial stress of this section is... The circumferential stress of this section is... These are the radial coordinates in the cylindrical coordinate system. Based on the circumferential axial force at the aforementioned elevation and circumferential bending moment The normal stress of the concrete at the edge of the target pool is calculated, and then the amount of prestressed steel reinforcement required for each section is calculated based on the normal stress of the concrete. The formula for calculating the amount of prestressed steel reinforcement is as follows: ； In the formula, This refers to the amount of prestressed steel reinforcement. To convert the cross-sectional area, The effective prestress of the prestressed steel bars, The normal stress of the concrete at the edge of the pool; The formula for calculating the converted cross-sectional area is as follows: ； In the formula, The cross-sectional area of ​​the concrete. , Because the pool walls are thick, Unit height; This is the ratio of the elastic modulus of ordinary steel reinforcement to the elastic modulus of concrete. The amount of reinforcement required for the inner side of the pool wall when using ordinary steel reinforcement; The amount of reinforcement required for the outer side of the pool wall when using ordinary steel reinforcement; The normal stress in the concrete at the edge of the pool includes the normal stress in the concrete at the inner edge of the pool. and the normal stress of the concrete at the outer edge of the pool ; The normal stress of the concrete at the inner edge of the pool The calculation formula is: ； The normal stress of the concrete at the outer edge of the pool The calculation formula is: ； In the formula, For a rectangular section, the bending section modulus is... .

2. The method for calculating the circumferential prestressed steel reinforcement of a circular water tank according to claim 1, characterized in that, After calculating the amount of prestressed steel reinforcement required for each section, the difference in reinforcement amount at each elevation is calculated, and the larger reinforcement amount is taken as the final reinforcement amount for elevations with a difference of less than 10%.

3. The method for calculating the circumferential prestressed steel reinforcement of a circular water tank according to claim 1, characterized in that, The geometric information includes: pool height, pool wall thickness, inlet pipe location and size, outlet pipe location and size, and the pool height includes the height above the pool floor and the height below the pool floor.

4. The method for calculating the circumferential prestressed steel reinforcement of a circular water tank according to claim 1, characterized in that, The extended range is more than twice the height H of the portion above the water tank floor.

5. The method for calculating the circumferential prestressed steel reinforcement of a circular water tank according to claim 1, characterized in that, Based on the predetermined load conditions, the boundary conditions of the foundation, and the three-dimensional finite element mesh model of the high-water-level large-volume circular water tank-foundation system, cylindrical coordinates were calculated using the finite element method. Radial stress of the target water tank and circumferential stress , These represent the radial coordinates, circumferential coordinates, and vertical coordinates of the cylindrical coordinate system, respectively.

6. The method for calculating the circumferential prestressed steel reinforcement of a circular water tank according to claim 1, characterized in that, The process of confirming the method of dividing the elevation along the elevation direction into several elevation segments includes: Method 1: Each Divide it into one section, where H is the height of the part above the ground of the pool; Method 2: Each section is 3-5 meters long; The larger of method one and method two is taken as the final partitioning method.

7. A method for tensioning circumferential prestressed steel bars in a circular water tank, characterized in that, A prestressed tendon embedding pipe is pre-embedded in the middle of the pool wall. The required amount of prestressed steel reinforcement for each section is calculated using the circumferential prestressed steel reinforcement calculation method for circular pools as described in any one of claims 1-6. Prestressed steel reinforcement is then installed in the prestressed tendon embedding pipe, with reinforcement added along the circumferential direction on the outer side of the pool wall. A buttress column is set at the corner for tensioning and anchoring of prestressed steel bars; The prestressed steel bars in each section of the water tank are tensioned in two stages, with the central angle of each stage of prestressed steel bars being [missing information]. Tensioning is performed simultaneously at both ends; The buttress columns are tensioned and anchored every 3 to 5 rings of prestressed steel bars along the elevation direction of the pool.

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