An optimization method of concrete rotating shell structure combining function and cost

Abstract

The application relates to an optimization method of a concrete rotating shell structure combining function and cost, and relates to the fields of building structure design and engineering cost, and comprises the following steps: taking a curved surface microelement, obtaining a balance formula based on rotating shell film theory, and obtaining a normal direction load q from radial film internal force and ring film internal force n and radial line direction load, combining the structural characteristics and stress formula of a hyperboloid concrete shell body, combining the wind load borne by the concrete shell body, respectively performing load combination on the bearing capacity and normal use limit state, optimizing the wall thickness according to the load, and obtaining a target function of the total price F of the concrete shell body structure, and optimizing the special structure of the rotating shell; high-performance self-compacting concrete is adopted, and the concrete pouring problem of a concrete shell structure with complex shape, dense reinforcement and thin wall is effectively solved. On the basis of meeting the building function requirement, the same volume is saved, the cost is saved, and the engineering cost is reduced.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of architectural structure design and engineering cost, and particularly relates to an optimization method of a concrete rotating shell structure combining function and cost. BACKGROUND

[0002] With the development of the construction industry, higher and higher requirements are put forward for concrete materials and their construction technology. With the development of the construction industry, higher and higher requirements are put forward for architectural structure design and engineering cost. According to the functional requirements of the architectural structure, the concrete shell structure is widely used in special structure engineering, and in order to save materials and space, the thin-walled structure is used in the optimization design of the concrete shell structure. In the past shell structure design, only the strength design is focused on, and the optimization design is ignored, or only the shape optimization of the ordinary shell structure is proposed without giving an optimization method of the complex shell structure combining the architectural function and the cost. How to meet the architectural function conditions and minimize the engineering cost is a subject that we urgently need to study and solve. SUMMARY

[0003] The purpose of the present application is to overcome the shortcomings of the prior art, and to provide an optimization method of a concrete rotating shell structure combining function and cost based on the rotating shell thin film theory, which calculates the structure, studies the structure type, material selection, construction technology, and takes the total cost of the structure as the objective function. Under the premise of meeting the architectural function requirements, the structure surface area and cross-sectional volume are minimized under the same volume, so as to save materials and costs and reduce the engineering cost.

[0004] The present application is realized by the following technical solutions:

[0005] An optimization method of a concrete rotating shell structure combining function and cost, comprising the following steps:

[0006] S1, the first curvature radius r1 of a point A on the curved surface in the rotating shell is the curvature radius of the radial direction (the direction of the radial line), the second curvature radius r2 of the point A is the curvature radius of the ring direction (the direction of the tangent plane containing the parallel circle tangent, that is, the direction of the tangent plane containing the parallel circle tangent and perpendicular to the radial line rotating surface), since r1 and r2 are both the curvature radius of point A, and are both perpendicular to the tangent plane of the middle surface at point A, r1 and r2 are collinear and fall on the normal line of the middle surface at point A, so r1 and r2 are the radial principal curvature and the ring principal curvature of the middle surface at point A. The curvature radius of the parallel circle is r, and the angle between the normal line of the middle surface at point A (the line perpendicular to the radial line in the radial line rotating surface) and the rotating axis is The angle between the radial line surface at point A and the reference radial line surface is θ (that is, the angle of the radial line relative to the initial position rotation).

[0007] Take the curved surface micro-element ABCD, AB curve is located on a parallel circle, CD curve is located on another parallel circle, AD curve is located on a radial line, BC curve is located on another radial line, q n and respectively, the load in the normal direction and the radial direction, is the total vertical external load acting on the part above the parallel circle where the shell AB curve is located; due to rotational symmetry, it is known that the normal stress on AD curve and BC curve is equal;

[0008] Let and respectively represent the radial membrane internal force and the hoop membrane internal force of the shell, and the algebraic sum of each component is zero, so the equilibrium equation is obtained:

[0009]

[0010] The radial membrane internal force on the shell section is calculated as follows:

[0011]

[0012] The hoop membrane internal force on the shell section is calculated as follows:

[0013]

[0014] The radial membrane internal force and the hoop membrane internal force of the shell under the action of external load and structural self-weight are functions of the amplitude angle , and from the structure of the shell micro-element, we have:

[0015]

[0016] From formulas (1)-(4), the load q n in the normal direction and the load in the radial direction of the curved surface micro-element can be obtained.

[0017] S2, if the rotating shell is a single-leaf hyperboloid concrete shell, the single-leaf hyperboloid is generated by rotating a hyperbola around its principal axis, then its standard formula is:

[0018]

[0019] According to the calculation method in step S1, the equilibrium equation of the single-leaf hyperboloid rotating shell under the condition of axial symmetry is obtained as:

[0020]

[0021] Under the action of the self-weight load of the shell, assuming that the specific gravity of concrete is γ and the wall thickness is δ, which is a function of height, then the load is:

[0022]

[0023] Substitute equation (7) into equation (6) and get the value of N θ and N φ Internal force:

[0024]

[0025] Where q r is the normal load of any point, N φ and N θ represent the radial internal force and hoop internal force of the hyperbolic shell respectively, K is the curvature of the surface in the shell, and V is an auxiliary variable.

[0026] In addition to the structure self-weight, considering the wind load borne by the concrete shell, the load combination of the bearing capacity and the normal use limit state is taken, and the most unfavorable state is taken. According to the different internal force combination at different heights, the wall thickness of the hyperbolic concrete shell is designed according to the failure stress of the component, and the method for optimizing the design of the wall thickness change is:

[0027] Let δ and δ0 be the wall thickness and the thickness of the top of the shell respectively, where δ is a variable and δ0 is a constant. Then:

[0028]

[0029] Where mg is the gravity per unit volume, N is the normal stress, and Z is the height of the shell element. Due to the action of gravity, the normal stress N is in the direction of extruding the element.

[0030] The total amount of hoop steel and longitudinal steel and the amount of concrete used in the shell wall are related to the shape of the rotating shell, which is a nonlinear function of the amplitude angle , where represents the amplitude angle at the lower opening, and represents the amplitude angle at the upper opening. Let F be the total price of the structure. Combining equations (8)-(9), the objective function of the total price F of the structure is:

[0031]

[0032] Where β Z is the wind load adjustment coefficient, ρ 1和 ρ2 represent the relative density of concrete and steel respectively, σ is the longitudinal reinforcement ratio, C1 and C2 are the price coefficients of steel and concrete respectively; f y is the tensile strength design value of steel.

[0033] ​According to the specific constraint conditions of the concrete shell in the structural function, the optimization result of the total price F of the structure is obtained from the formula (10), and the final optimized structure of the concrete shell is obtained.

[0034] Further, the concrete is a non-vibrating self-compacting concrete, which comprises the following components in parts by weight: cement 250-300 parts, admixture one 70-110 parts, admixture two 60-80 parts, admixture three 20-30 parts, admixture four 10-20, sand 750-850 parts, stone 800-900 parts, water 150-200 parts, and additive 20-40 parts.

[0035] Further, the admixture one is fly ash, the admixture two is metallurgical slag powder, the admixture three can be silica fume, and the admixture four can be zeolite powder.

[0036] Further, the additive comprises 4-8 parts of polycarboxylic acid superplasticizer and 20-30 parts of viscosity modifying material of type TZ-IV. The selection of the concrete additive should meet the requirements of the current national standards “Concrete Additive Standard” (GB8076-2016) and “Concrete Additive Application Technical Standard” (GB50119-2013). The polycarboxylic acid superplasticizer can effectively reduce the water consumption of the concrete, so as to achieve low porosity, high density, and improve the durability of the concrete.

[0037] Further, the concrete comprises the following components in parts by weight: cement 283 parts, admixture one 84.9 parts, admixture two 66.1 parts, admixture three 23.6 parts, admixture four 14.2 parts, sand 826 parts, stone 886 parts, water 191 parts, and additive comprising 5.80 parts of polycarboxylic acid superplasticizer and 23.6 parts of viscosity modifying material of type TZ-IV.

[0038] Further, the cement is P.0 42.5 Portland cement.

[0039] Further, the stone is granite with a particle size of 5-16 mm, the content of needle-like particles is less than 10%, and the void ratio is less than 40%.

[0040] Further, the sand is medium sand with qualified gradation, and the clay content is less than 1%.

[0041] The increase of the amount of ultra-fine active admixture (total fine powder) in the above concrete ingredients can greatly improve the interface structure inside the concrete, further reduce the defects inside the concrete, enhance the crack resistance of the concrete, and improve the structural strength and durability of the concrete; the addition of metallurgical slag powder, admixture, polycarboxylic acid superplasticizer, and TZ-IV viscosity modifying material can increase the consistency of the concrete, so that the concrete does not separate and does not stratify under a large flowability.

[0042] Further, the maximum lateral pressure acting on the formwork during the concrete shell pouring process can be calculated according to the following formula, and the smaller value of F1 and F2 is taken:

[0043] ①

[0044] ② F2=1.15γ c h

[0045] Wherein: γ c — the gravity density of concrete, taken as 24.00 kN / m 3 ;

[0046] t0— the initial setting time of the newly poured concrete, taken as 200 / (T+15);

[0047] T— the temperature of the concrete into the mold, taken as Celsius;

[0048] V— the pouring speed of the concrete taken as 2.20 m / h;

[0049] h— the total height from the lateral pressure calculation position to the top surface of the newly poured concrete;

[0050] a1— the correction coefficient of the admixture, taken as 1.15;

[0051] a2— the correction coefficient of the concrete slump, taken as 1.10.

[0052] The present application is based on the rotating shell thin film theory, and takes the total construction cost as the objective function, optimizes the special structure of the rotating shell, so as to meet the process, safety, and applicable building function requirements. The structure calculation, structure size, material selection, and other comprehensive optimizations are carried out with the structure cost as the objective function. The advantages are that the optimization objective function considers multiple factors such as structure stress, structure size, and material, meets the building function requirements, achieves the minimum structure surface area and cross-sectional volume under the same volume, thereby saving materials and costs, and reducing the engineering cost, so it is more scientific and economic and reasonable. Through the raw material selection and mix proportion design of the non-vibrating concrete mixture, high-performance self-compacting concrete can be obtained, which meets the requirements of building structure stress and construction, and ensures the engineering quality. BRIEF DESCRIPTION OF DRAWINGS

[0053] Figure 1 It is the force diagram of the microelement of the curved surface of the rotating shell of the present application.

[0054] Figure 2 It is a structural schematic diagram of the single-leaf hyperboloid rotating shell of the present application. DETAILED DESCRIPTION

[0055] There are two theories for the stress analysis of thin shell: moment theory and non-moment theory. The moment theory, also known as bending theory, considers that the shell has a certain thickness and stiffness, so there are bending moment and bending stress in the shell in addition to tensile stress and compressive stress. The non-moment theory, also known as membrane theory, considers that the thickness of the shell is much smaller than the diameter, so the shell can only bear tensile stress and compressive stress, and cannot bear bending moment and bending stress, i.e. the bending moment is ignored in the internal force analysis.

[0056] The optimization method of the concrete rotating shell structure combining the functions and costs of the present application mainly bases on the membrane theory of the rotating shell. The bending moment and transverse shear force of the rotating shell structure sharply decay near the edge, and most of the structure is still in the stress state of the membrane theory. According to the functional requirements of the building, the rotating shell structure is designed and optimized in combination with the structure cost, and specifically includes the following steps:

[0057] S1, as Figure 1 , let the curvature radius of a point A on the curved surface in the radial direction (the direction of the radial line) be the first curvature radius r1 of the point, then r1=AG1, the curvature radius of the point A in the ring direction (the direction of the tangent plane containing the parallel circle tangent, i.e. the direction containing the parallel circle tangent and perpendicular to the radial line rotation surface) is the second curvature radius r2 of the point, then r2=AG2, and the center of the second curvature radius falls on the rotation axis OO'. Since AG1 and AG2 are both the curvature radius of point A, they are both perpendicular to the tangent plane of the middle surface at point A, so AG2G1 are collinear, and all fall on the normal line of the middle surface at point A, then r1 and r2 are the radial and ring main curvatures of the middle surface at point A. The curvature radius of the parallel circle is r, and the angle between the normal line of the middle surface at point A (the line perpendicular to the radial line in the radial line rotation surface) and the rotation axis is The angle between the radial line surface at point A and the reference radial line surface is θ (i.e. the angle of the radial line relative to the initial position rotation).

[0058] Take the curved surface microelement ABCD, the AB curve is located on a parallel circle, the CD curve is located on another parallel circle, the AD curve is located on a radial line, the BC curve is located on another radial line, q n and are the loads in the normal direction and the radial direction respectively, is the total vertical external load acting on the part above the parallel circle where the AB curve is located. Due to the rotational symmetry, it can be known that the normal stress on the AD curve and the BC curve is equal.

[0059] , and and respectively represent the radial membrane internal force and the ring membrane internal force of the shell, and the algebraic sum of each component is zero, so the balance equation is obtained:

[0060]

[0061] The radial membrane internal force on the shell section is calculated as follows:

[0062]

[0063] The hoop membrane internal force on the shell section is calculated as follows:

[0064]

[0065] The radial membrane internal force of the shell under the action of external load and structural self-weight is and the hoop membrane internal force is a function of the amplitude angle , and is obtained from the structure of the shell microelement in Figure 1

[0066] The load q in the normal direction of the curved surface microelement n and the load in the radial direction

[0067] are obtained from formulas (1)-(4)

[0068] S2, if the rotating shell is a single-leaf hyperboloid concrete shell, the single-leaf hyperboloid is generated by rotating a hyperbola around its principal axis, such as Figure 2 , then its standard formula is:

[0069]

[0070] According to the calculation method in step S1, the equilibrium equation of the hyperboloid rotating shell under the condition of axial symmetry is:

[0071]

[0072] Under the action of the self-weight load of the shell, assuming that the specific gravity of concrete is γ and the wall thickness is δ, which is a function of the height, then the load is:

[0073]

[0074] Substitute formula (7) into formula (6), and obtain N θ and N φ internal force values about from the standard formula (5) of the single-leaf hyperboloid:

[0075]

[0076] where q r is the normal load of any point, N φ and N θ represent the radial internal force and hoop internal force of the hyperboloid rotating shell, respectively, K is the curvature of the surface in the shell, and V is an auxiliary variable.

[0077] Taking a concrete hyperbolic cooling tower as an example, in addition to the structural self-weight, the wind load of such a high-rise structure is also considered, and the load combination of the bearing capacity and the normal use limit state is carried out, and the most unfavorable one is taken for design. The normal load and the ring load of the hyperbolic rotating shell change with the height, whether under the action of the self-weight or the horizontal wind load. It is obviously unreasonable to select the same wall thickness for design when the limit bearing capacity is different, which will waste materials and increase the cost. The wall thickness of the tower should be designed according to the different internal force combinations at different heights, and the wall thickness change should be optimized and designed according to the failure stress of the component. The specific design and optimization method in the application is as follows:

[0078] Let δ and δ0 be the tower wall thickness and the shell top thickness respectively, wherein δ is a variable, and δ0 is a constant. Then:

[0079]

[0080] Wherein mg is the gravity per unit volume, N is the normal stress, the normal stress N is in the direction of extruding the microelement due to the action of gravity, and Z is the height of the shell microelement.

[0081] The total amount of the ring steel and the longitudinal steel of the concrete tower wall and the amount of the concrete of the tower wall are related to the shape of the rotating shell, which is a nonlinear function of the amplitude angle , wherein represents the amplitude angle at the lower opening, and represents the amplitude angle at the upper opening. Let F be the total price of the structure. The objective function of the total price F of the structure is obtained by combining formulas (8)-(9):

[0082]

[0083] Wherein β Z is a wind load adjustment coefficient, ρ 1和 ρ2 respectively represent the relative density of concrete and steel, σ is the longitudinal steel reinforcement ratio, δ is the tower wall thickness, C1 and C2 are respectively the steel and concrete price coefficients; f y is the tensile strength design value of the steel.

[0084] The optimization result of the total price F of the structure is obtained according to the specific constraint conditions of the concrete shell in the structure function according to formula (10), and the final optimized structure of the concrete shell is obtained.

[0085] Since the internal force of the structure changes with the change of the load, the above method can be used to optimize the shape of the structure according to the function and stress characteristics of the structure, to scientifically calculate the internal force, and to further adjust the section size (such as wall thickness) and the use of materials (such as the strength grade of the steel and concrete) according to the target function (10) of the shell structure, the constraints of the water spraying area, the amplitude angle and the horizontal radius requirements at the upper opening, the amplitude angle requirements at the lower part connected with the foundation, the structure weight, the wind load, etc., so as to fully play the synergistic effect of the steel and concrete, and to adjust the proportion of the steel and concrete according to the market prices of the steel and concrete at that time, so as to achieve the purpose of reducing the engineering cost.

[0086] In engineering practical applications, no matter what kind of rotating shell, the optimization design has at least two variables of nonlinear programming problem, and the optimization design is carried out according to the constraint conditions such as building function and the total cost as the target function after adding the calculation parameters, and the optimization solution is obtained through the calculation program.

[0087] Since the concrete rotating shell structure is a thin-walled structure, we develop high-performance self-compacting concrete suitable for concrete rotating shell structure and taking into account the function and cost through experimental study on the performance of self-compacting concrete mixture, from the selection of concrete raw materials, mix proportion design and corresponding quality control technology (including the selection of admixtures and special aggregates) and other aspects. The concrete has good fluidity, segregation resistance, filling property and plasticity performance index, and can rely on the performance of the concrete itself to self-compacting under the action of gravity, effectively solving the problem of concrete pouring in structures with complex shape, dense reinforcement, thin wall and difficult vibration, effectively improving the concrete strength and durability, and ensuring the engineering quality. And the concrete can use a large amount of industrial waste as mineral admixture to reduce the engineering cost.

[0088] The above self-compacting concrete without vibration includes the following components by weight: cement 250-300 parts, admixture one 70-110 parts, admixture two 60-80 parts, admixture three 20-30 parts, admixture four 10-20 parts, sand 750-850 parts, stone 800-900 parts, water 150-200 parts, and admixture 20-40 parts.

[0089] The admixture one can be selected from Class II fly ash, the admixture two can be selected from metallurgical slag powder, the admixture three can be selected from silica fume, and the admixture four can be selected from ultra-fine active admixture zeolite powder. The stone is selected from granite with a particle size of 5-16 mm, the needle-like particle content is less than 10%, and the void ratio is less than 40%. The sand is selected from medium sand with qualified gradation, the clay content is less than 1%, and the water is tap water. The cement is P.0 42.5 Portland cement.

[0090] The selection of the concrete admixture should meet the requirements of the current national standard "Concrete Admixture Standard" (GB8076-2016) and "Concrete Admixture Application Technical Standard" (GB50119-2013). The polycarboxylate superplasticizer can effectively reduce the water consumption of concrete, thereby achieving low porosity, high density, and improving the durability of concrete. In this embodiment, the admixture is selected as polycarboxylate superplasticizer liquid 4-8 parts and viscosity modifying material of type TZ-IV 20-30 parts. The polycarboxylate superplasticizer liquid can prevent the loss of concrete slump, can make the water-reducing rate of concrete reach more than 30%, and a small amount of admixture can give the concrete high fluidity, can reduce the shrinkage of concrete, improve the workability of concrete, and meet the construction requirements of the thin-walled structure of the concrete rotating shell.

[0091] The viscosity modifying material is a composite material obtained by reaction of polyvinyl alcohol and other high molecular synthetic materials, inorganic materials and other additives, which can adjust the loose degree and wrapping property of the concrete in the self-compacting concrete, ensure the high fluidity, high cohesiveness and adhesiveness of the self-compacting concrete, and reduce the shrinkage and cracking of the concrete due to its certain expansion performance. At the same time, the TZ-IV viscosity modifying material can optimize the internal pore structure of the hardened concrete, improve the density of the concrete, and greatly improve the frost resistance and chloride ion penetration resistance of the concrete, thereby significantly improving the workability and durability of the self-compacting concrete, and the amount of admixture is low and the adaptability is wide.

[0092] Increasing the amount of ultra-fine active admixture (total fine powder) can greatly improve the internal interface structure of the concrete, further reduce the internal defects of the concrete, and improve the crack resistance and strength of the concrete. For reinforced concrete structures in open air and coastal areas, chloride ions are the main culprit for damaging reinforced concrete, which can accelerate the corrosion of steel bars and cause the destruction of concrete structures. The present case is an open-air reinforced concrete structure located in a coastal area, and the influence of sea wind chloride ions is large. The design increases the mineral admixture zeolite powder to increase the viscosity of the concrete and reduce the porosity, effectively improving the carbonation resistance and chloride ion penetration resistance of the concrete, and greatly improving the mechanical properties and durability of the reinforced concrete. The addition of metallurgical slag powder, admixture, polycarboxylate superplasticizer and viscosity modifying material can increase the consistency of the concrete, so that the concrete does not separate and stratify under the condition of high fluidity.

[0093] In this embodiment, the amount of each component is as follows: cement 283 parts, admixture one 84.9 parts, admixture two 66.1 parts, admixture three 23.6 parts, admixture four 14.2 parts, sand 826 parts, stone 886 parts, water 191 parts, polycarboxylate superplasticizer 5.80 parts, and viscosity modifying material of type TZ-IV 23.6 parts. The specific ratio and index are shown in Table 1.

[0094] Table 1C 30Mix proportion of self-compacting concrete

[0095]

[0096]

[0097] The non-vibrating high-performance self-compacting concrete of the present application can flow through the steel bars and pipes (embedded parts) to fill any gap in the formwork and self-compacting under the action of gravity to form a solid body according to the structural size of the building shell, the thickness and density of the steel bars and embedded parts.

[0098] In addition to meeting the current relevant national standards, the installation of the formwork of the self-compacting concrete component should also consider the flow and static pressure effect of the self-compacting concrete mixture on the side formwork. The maximum side pressure of the side formwork is tested and verified before construction. Since the maximum side pressure of the self-compacting concrete on the side formwork is greater than that of ordinary concrete, the maximum side pressure can be increased by 15% of the side pressure of ordinary concrete according to the test and practical verification. The bearing capacity, stiffness and stability of the formwork and supporting system are calculated in advance.

[0099] During the pouring process of the concrete shell, the pressure of the self-compacting concrete on the formwork is greater than that of ordinary concrete. The maximum side pressure of the concrete on the formwork can be calculated according to the following formula, and the smaller value of F1 and F2 is taken:

[0100] ①

[0101] ② F2=1.15γ c h

[0102] Where: γ c — the gravity density of concrete, taken as 24.00 kN / m 3 ;

[0103] t0— the initial setting time of the newly poured concrete, taken as 200 / (T+15);

[0104] T— the pouring temperature of the concrete, taken in Celsius;

[0105] V— the pouring speed of the concrete, taken as 2.20 m / h;

[0106] h— the total height from the side pressure calculation position to the top surface of the newly poured concrete;

[0107] a1— the correction coefficient of the admixture, taken as 1.15;

[0108] a2— the correction coefficient of the concrete slump, taken as 1.10.

[0109] Higher temperatures of concrete increase the water demand to maintain a given slump; reduce the setting and finishing time, increase the risk of plastic shrinkage; and reduce the final strength. The optimum concrete temperature should be between 10-15°C, and for mass concrete, the temperature should be even lower. In summer, the above temperatures are difficult to achieve without artificial cooling, and the temperature of the concrete should not exceed 30-35°C.

[0110] Controlling the temperature of each component can regulate the temperature of the concrete, and the contribution of each component is determined by its temperature, specific heat capacity and mass fraction, as shown in the following formula:

[0111]

[0112] The temperature of the concrete can be calculated.

[0113] Wa, Wc, Wwa, Ww are the mass of aggregate, cement, water contained in aggregate and water, respectively, in kg Ta, Tc, Tw are the temperatures of aggregate, cement and water.

[0114] Taking a hyperbolic cooling tower of a thermal power plant as an example, the water spraying area of the cooling tower is 3400m 2 , and the structure thereof is optimized according to the method of the present application:

[0115] 1. According to the cooling efficiency, water spraying area, heat dissipation and safety, applicability and other functional constraint conditions of the building function process professional circulating water system, in order to obtain the best heat dissipation effect, the cooling tower is designed in the form of single-leaf hyperbolic rotating shell.

[0116] 2. The cooling tower is a high-rise structure mainly bearing wind load, and the load is mainly wind load and structural self-weight, and it is particularly sensitive to wind load, so the load combination should be carried out for the bearing capacity and normal use limit state respectively, and the most unfavorable one is taken for design.

[0117] 3. According to the stress characteristics of the structure, the tower body is designed in the form of hyperbolic rotating shell structure, which can not only reduce the wind resistance, but also can ensure the stability and safety of the structure with the least material, improve the cooling efficiency, and the internal force calculation is carried out by applying the rotating shell membrane theory, the structure is optimized and calculated and analyzed, the wall thickness is selected according to buckling stability, the tower bottom inclination angle, tower top inclination angle, structure size and stress state are determined, the cross section of the high stress part is thickened and the steel bars are densified, the stress part is adjusted according to the structural reinforcement, the steel bars and concrete strength grade are reasonably selected, and the high strength steel bars with good cost performance are used, and other measures are used for optimization.

[0118] 4. The total cost of the structure of formula (10) in the application is taken as the objective function, and the parameters such as the wall thickness of the tower, the relative density of the concrete and the reinforcing steel, the reinforcing ratio of the reinforcing steel, the price coefficient of the reinforcing steel and the concrete, and the wind load adjustment coefficient are substituted into the function formula for comprehensive optimization. The building functions such as process, safety, and applicability are met, the structure section and volume are minimized under the same volume, the material and cost are saved, the engineering cost is reduced, and the structure is more scientific and economically reasonable.

[0119] 5. The final optimization result is that the concrete hyperboloid cooling tower is designed, the tower height is 85 meters, the maximum diameter at the bottom is 69.8 meters, the throat diameter is 37.9 meters, the top diameter is 42.3 meters, the maximum wall thickness of the shell is 650 mm, the minimum wall thickness is 180 mm, the concrete consumption of the tower body is 4238.6 m 3 , and the reinforcing steel consumption is 221.7 t. The ring plate foundation is adopted, and the structure adopts the C 30 self-compacting concrete.

[0120] 6. If the conventional design of the ordinary reinforced concrete structure is adopted, that is, the structure is calculated according to the linear load changing with the height, and the ordinary concrete is adopted for the structure concrete material, the calculation result is that the wall thickness of the shell at the bottom is 700 mm, the wall thickness at the top is 250 mm, the concrete consumption of the tower body is 5482.73 m 3 , the reinforcing steel consumption is 279.12 t. The ring plate foundation is adopted, and the structure adopts the ordinary concrete. 30

[0121] 7. Compared with the result obtained by the conventional design method (such as the structure is calculated according to the linear load changing with the height, and the ordinary concrete is adopted for the structure concrete material), the optimization design method of the application can save the structure cost by 13%-15% by comprehensively considering the construction process and other factors, the design is more scientific and economically reasonable, and good economic benefits can be obtained.

[0122] The above detailed description is specific to the feasible embodiments of the application, and the embodiments are not used to limit the patent scope of the application. Any equivalent implementation or change without departing from the application should be included in the patent scope of the application.​

Claims

1. A method for optimizing a concrete rotating shell structure that combines functionality and cost, characterized by, The method comprises the following steps: S1, the first radius of curvature of the point A is the radius of curvature of the point A in the radial direction of the curved surface in the rotating shell , the second radius of curvature of the point A is the radius of curvature of the point A in the circumferential direction , the radius of curvature of the parallel circle is , the angle between the normal of the median surface at the point A and the rotation axis is , the angle between the radial surface at the point A and the reference radial surface is ; Take a curved microelement ABCD, AB curve is located on a parallel circle, CD curve is located on another parallel circle, AD curve is located on a radial line, and BC curve is located on another radial line, and are the loads in the normal direction and the radial direction, respectively, is the total vertical external load acting on the part of the shell above the parallel circle where the AB curve is located; due to rotational symmetry, it can be known that the normal stresses on the AD curve and the BC curve are equal; With and denote the radial and hoop membrane internal forces of the shell, respectively, and the equilibrium equations are obtained by setting the algebraic sum of the components to zero: （1） The radial membrane internal force on the shell section is calculated according to the following formula: （2） The hoop membrane internal force on the shell section is calculated according to the following formula: （3） The radial membrane internal force of the shell under the action of external load and structural self-weight and the hoop membrane internal force are functions of the amplitude and can be obtained from the structure of the shell element. （4） The load of the curved surface micro-unit in the normal direction and the radial direction can be obtained from formulas (1)-(4) and formulas (5)-(8) ; S2, for a single-leaf hyperboloid, the standard formula is: （5） According to the calculation method in step S1, the equilibrium equation of the single-leaf hyperboloid rotating shell under the axial symmetry condition is obtained as follows: （6） wherein, and respectively represent the radial and circumferential internal forces of the double curved shell. Under the dead load of the shell, let the specific gravity of concrete be , and the wall thickness be , which is a function of height, then the load is: （7） wherein, N is the normal force at any point; Substitute equation (7) into equation (6) and use the standard equation (5) of a single hyperboloid to obtain the value of N θ and Internal forces:​ （8） wherein , is the curvature of the curved surface in the housing, is an auxiliary variable; In addition to the structural self-weight, the wind load borne by the concrete shell is considered, and the load combination of the bearing capacity and the normal use limit state is carried out, the most unfavorable state is taken, and the wall thickness of the hyperboloid concrete shell is designed according to the different internal force combinations at different heights and the failure stress of the component as the standard, and the method for optimizing the design of the wall thickness is as follows: Let and are the wall thickness and the shell top thickness, respectively, where, is a variable, is a constant, then: （9） wherein, G is the gravity force per unit volume, σ is the normal stress due to the gravity force, the direction is the direction of the extrusion of the microelement, h is the height of the microelement of the shell. The total amount of circumferential and longitudinal reinforcement in the concrete shell wall, as well as the amount of concrete used in the shell wall, are related to the shape of the rotating shell and are related to the angle. nonlinear functions, with Indicates the angle at the lower opening. Indicates the argument at the upper opening, let... Given the total structural cost, we can obtain the total structural cost by combining formulas (8) and (9). The objective function is: （10） wherein, is the wind load adjustment coefficient, 和 respectively represent the relative density of concrete and steel bar, is the longitudinal steel reinforcement ratio, and respectively are the steel and concrete price coefficients, is the tensile strength design value of steel bar; Based on formula (10) and the specific constraints of the concrete shell in terms of structural function, the total structural cost is obtained. The optimization results are obtained, and the final optimized structure of the concrete shell is thus obtained.

2. The method for optimizing a concrete rotating shell structure combining function and cost according to claim 1, characterized in that, The concrete shell adopts the non-vibrating high-performance self-compacting concrete, which comprises the following components in parts by weight: cement 250-300 parts, admixture one 70-110 parts, admixture two 60-80 parts, admixture three 20-30 parts, admixture four 10-20 parts, sand 750-850 parts, stone 800-900 parts, water 150-200 parts, and additive 20-40 parts.

3. The method for optimizing a concrete rotating shell structure combining function and cost according to claim 2, characterized in that, The admixture one is fly ash, the admixture two is metallurgical slag powder, the admixture three is silica fume, and the admixture four is zeolite powder.

4. The method for optimizing a concrete rotating shell structure combining function and cost according to claim 2, characterized in that, The additive comprises polycarboxylic acid superplasticizer 4-8 parts and viscosity modifying material of type TZ-IV 20-30 parts.

5. The method for optimizing a concrete rotating shell structure combining function and cost according to claim 2, characterized in that, The concrete comprises the following components in parts by weight: cement 283 parts, admixture one 84.9 parts, admixture two 66.1 parts, admixture three 23.6 parts, admixture four 14.2 parts, sand 826 parts, stone 886 parts, water 191 parts, and additive comprising polycarboxylic acid superplasticizer 5.80 parts and viscosity modifying material of type TZ-IV 23.6 parts.

6. The method for optimizing a concrete rotating shell structure in terms of function and cost according to claim 2, characterized in that, The cement is P.0 42.5 Portland cement.

7. The method of claim 2, wherein the method is characterized by: The stone is granite with a particle size of 5-16 mm, the content of needle-like particles is less than 10%, and the porosity is less than 40%.

8. The method of claim 2, wherein the concrete rotating shell structure is optimized in terms of function and cost, and the method further comprises: The sand is medium sand with qualified gradation, and the clay content is less than 1%. ​

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