Abstract: With the development of the needs of industry and society, the number of water supply projects is increasing and the number of water pumping stations built is also increasing. However, the cost of water pumping stations is high (for example, the cost of a circulating cooling water pumping station in Ezhou Power Plant in Hubei Province is 5,000 More than million). According to relevant literature, the optimal design of pumping station can reduce the project cost by 5% ~ 25% (see Zhu Bofang, Li Bianmei and Zhang Weicheng, "Principles and Applications of Structural Design Optimization"). Visible, to explore the optimal design of the pump house, with significant economic significance.
Keywords: Reinforced concrete rectangular caisson structure water pump room optimization design
General pump room where the environment is more complex, construction, the use of construction methods and the corresponding structure of a variety of forms. The author chooses the most commonly used reinforced concrete rectangular caisson structure which is the most used in the riverside and seawater pumping station for the optimization design analysis and the optimization design formula and the optimization procedure.
First, optimize the design ideas
The goal of optimal design is to make the designed structure to be the lowest cost under the condition of satisfying safe use. Such structure is the optimal structure.
For reinforced concrete caisson structures, if the strength of each material designed is fully utilized, the entire structure is optimal.
Based on the above ideas, we can combine the method of freezing internal force with the method of 0.618 to optimize the design of caisson structure. First of all, we will conduct an internal force analysis of the proposed structural solution, and then freeze the internal force to optimize each component with the 0.618 method to obtain a new solution. Then, perform internal force reanalysis and repeat the above steps until the result of two calculations Close enough.
Second, the optimal design of structural components
Reinforced concrete caisson structure pump room is a combination of plate structure, frame structure and well-beam structure. The stress conditions are many, the calculation diagram also by location, conditions and different. However, according to the classification of reinforced concrete components can be divided into pure bending plate, bias plate, bending beam, biasing column four kinds of components, the following four elements on the optimal design derived.
1. Optimum design of pure curved plate components
Pure curved plate optimization can be divided by the unit board width to analyze.
(1) objective function
Take the objective function for the unit width, unit length of the material and the template cost and. Variables related to the objective function are plate thickness, steel area, and template area.
(2) Constraints
The strength constraints on bending resistance should be considered: ①maximum positive bending strength, ② maximum negative bending strength at both ends of slats, ③ maximum shear strength, ④ minimum and maximum reinforcement ratio, and ⑤ minimum thickness requirement.
(3) Optimization methods and steps
The optimization of slats is to find the minimum value of the objective function satisfying all of the above constraints. Can be understood as: When the cost of making the smallest, the amount of material should be the most provincial. Considering the constraints, under the condition of certain internal force, the area of ​​reinforcement can be calculated corresponding to each plate thickness value X, so the objective function is a one-dimensional search problem, and the 0.618 method can be used to find the optimal solution of X X ?, the steps are as follows:
â‘ find the upper and lower X as a one-dimensional search interval:
The upper limit of X: take the minimum bending moment and bending moment into the constraints â‘ , â‘¡, and then use the minimum reinforcement rate of the upper limit of X.
Lower limit of X: Similar to the above, take the plate end bending moment and minimum bending moment into constraint conditions â‘ , â‘¡, and then use the maximum reinforcement ratio of the lower limit of X.
② With the 0.618 method in the Xl, Xu? Range search, and find the minimum objective function corresponding X? And the corresponding reinforcement is the optimal solution. In the optimization calculation, for each given value of X, we can obtain the corresponding amount of reinforcement by the constraint ①~ ③, and then check the four quantities by the constraint ④, ⑤, and satisfy the required value. Then take the value of the amount of reinforcement into the constraints ①seeking objective function.
Calculation, bending moment, shear force are given as known conditions, which is calculated according to the pre-calculated good diagram.
2. Optimization Design of Bias Plate Components
The optimization of the bias plate member adopts the same 1m wide slab to analyze. The optimization method is basically the same as that of the pure bending plate, except that in the constraint condition, the axial force needs to be included.
(1) objective function
Take the objective function of the unit length of the slab of material and template cost and.
(2) Constraints
â‘ maximum bending compression strength.
a) Large eccentricity (ie ξ≤ξb).
b) Small eccentricity (ie when ξ≥ξb).
â‘¡ maximum shear strength.
â‘¢ minimum reinforcement ratio, the maximum reinforcement ratio.
â‘£ minimum plate thickness.
The optimization process of bias slats is the same as that of pure slats. Similarly, we can calculate the amount of reinforcement according to the constraint conditions (1) and (2) such that each value corresponding to the cross-section height X can be used to calculate the amount of reinforcement Determine the minimum amount of reinforcement that meets all the criteria to substitute for the objective function.
It is actually a one-dimensional search problem with only one design variable X.
(3) find the upper and lower X
Bias pressure of the X, the lower limit of the law and the pure bending slab is different, should be divided into large eccentric and small eccentric two cases of calculation.
â‘ big eccentric situation.
At this point X upper and lower limits Xu, Xl, respectively, that the constraint condition â‘ corresponds to the minimum and maximum reinforcement ratio of the situation.
â‘¡ small eccentric situation.
Also take constraints â‘ corresponding to the minimum and maximum reinforcement ratio of the situation, Xu, Xl were solved.
Compared with the constraint â‘£, whichever is greater is Xl.
3. Optimum Design of Rectangular Section Beam
Analogous to the above:
(1) objective function
To beam body material and template cost as the objective function.
(2) Constraints
â‘ maximum positive bending strength.
â‘¡ maximum negative bending strength of both ends of the beam.
â‘¢ maximum shear stress intensity.
â‘£ minimum, maximum reinforcement rate.
⑤ structural requirements minimum cross-sectional area of ​​steel.
â‘¥ beam minimum cross-sectional height requirements.
(3) Optimization methods and steps
Optimization methods and steps are basically the same as above.
4. Optimization design of rectangular cross-section column, the optimization method is basically the same as above
(1) objective function
Taking the cost of the column body material and the template as the objective function.
(2) Constraints
â‘ maximum bending compression strength.
a) Large eccentricity (ie ξ b).
b) small eccentricity, ie ξ ξb).
â‘¡ maximum shear strength.
â‘¢ longitudinal bar minimum, maximum reinforcement rate.
â‘£ Minimum cross-section height requirements.
⑤ structural requirements minimum cross-sectional area of ​​steel.
(3) Optimization methods and steps
The optimization method and procedure are basically the same as the bias slats.
Third, optimize the design process
The overall layout of the caisson structure pump house structure is generally controlled by the process flow and construction requirements. Structural design is to meet the technical requirements and construction requirements under the conditions of the layout of a reasonable structure, and in accordance with the design of the size of the components. However, the span of the plate and the width of the beam and column are often also dependent on the process or construction requirements. Thus, the main task of structural optimization is to optimize the plate thickness and beam and column section height.
Optimization program based on the previous idea: the frozen internal force method combined with the 0.618 method, the optimal design of the caisson structure of the pump room.
Specific steps are as follows:
(1) The initial value X0 of the thickness of each plate, the height of the beam section and the height of the column section is prepared; the internal force analysis of the structure under various working conditions is carried out according to the geometrical dimensions of the initially proposed structure; Calculate the internal forces generated under various load conditions, and select the most unfavorable internal force of each component as the internal force for optimal calculation in the next step.
â‘¡ With 0.618 method for each pure curved slats, bias slats, beams, column components to optimize, obtain the optimal cross-section height of each component X and the corresponding rebar area. Calculate the objective function of each structure.
C = Ci
In this step, it is considered that the internal force of each component is unchanged, that is, the internal force of each component obtained by the previous structural analysis is frozen.
â‘¢ Performing internal force reanalysis - Perform internal force reanalysis using the X? Of each component as the new XO.
â‘£ The re-analysis of the internal force frozen into the second step.
⑤ check before and after the two iterative results are fully close to meet the requirements of the end of the calculation, optimization tasks completed.