CN104820762A - Method for optimized design of high-rise building frame structure containing concrete filled steel tubular column - Google Patents
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Abstract
The invention discloses a method for optimized design of a high-rise building frame structure containing a concrete filled steel tubular column. According to the method, the cross section of the concrete filled steel tubular column is selected to serve as an optimization variable, the internal force of each rod piece of a frame structure under the load effect is obtained through equivalent conversion of the concrete filled steel tubular column by utilizing a finite element method, the explicit function relation between the optimization variable and a displacement constrain condition is built through the utilization of the internal force according to the virtual work principle, and iteration optimization operation is conducted for the optimization variable within the boundary condition range of the optimization variable by matching an objective function of one optimization problem that the construction cost of the whole structure is the lowest, so that the optimum cross section of the concrete filled steel tubular column is obtained, the optimum total cost can be obtained, the consumption of materials is ensured to be low, and the top displacement and the story displacement of the optimized high rise building frame structure are ensured to meet design requirements of relevant specifications. The method for optimized design of the high-rise building frame structure can reduce the consumption of building materials, and the optimized cross section size can meet the building and construction requirements.
Description
Technical Field
The invention relates to the technical field of building structures, in particular to an optimization design method for a high-rise building frame structure containing a steel pipe concrete column.
Background
When the lateral force resistance (wind load, earthquake load and the like) optimization design of the high-rise building frame structure is carried out, an objective function and constraint conditions need to be explicitly expressed by related variables, so that the structure optimization problem is mathematically modeled into a function extreme value problem with constraint conditions, and then optimization iterative solution is carried out. The inventor finds that in the related art of the high-rise building wind-resistant or earthquake-resistant optimization method, most of display expressions of displacement constraint conditions of members are directed to simple rectangular-section single-material members, in actual projects, most of high-rise or super-high-rise building structures with the height exceeding 150m use the steel pipe concrete columns as important pressure-bearing and lateral-force-resistant members, and the lack of the lateral-force-resistant optimization design method for the high-rise building frame structure containing the steel pipe concrete columns causes that the common optimization design method cannot be applied to the actual projects containing the steel pipe concrete columns.
Disclosure of Invention
The invention aims to avoid the defects in the prior art and provides a method for optimally designing a high-rise building frame structure containing a concrete-filled steel tubular column.
The purpose of the invention is realized by the following technical scheme:
the method for optimally designing the high-rise building frame structure containing the steel pipe concrete columns is provided, the high-rise building frame structure comprises the steel pipe concrete columns, and the method comprises the following steps:
1) establishing a frame structure model for the high-rise building frame structure, wherein the frame structure model is a finite element model, a plurality of units are divided on the finite element model, and unit nodes are formed among the units;
2) the method comprises the steps of equivalence of the steel tube concrete column into a plain concrete column by adopting a rigidity equivalence method, calculating the equivalent diameter of the plain concrete column expressed by the section of the steel tube concrete column serving as an optimized variable display, and assigning the equivalent diameter and the optimized variable to a frame structure model by adopting a finite element analysis method;
3) applying an external load to the element nodes of the assigned frame structure model by adopting a finite element analysis method, and solving the internal force of the frame structure model under the external load; then respectively applying unit virtual loads to all unit node positions with displacement constraint one by one, taking the unit virtual loads applied each time as an independent working condition, and reading the internal force of the frame structure model under each independent working condition after carrying out structure analysis;
4) based on the virtual work principle and the internal force of the frame structure model obtained by the analysis in the step 3) under the action of the external load and the unit virtual load, calculating the top displacement and the interlayer lateral displacement of the frame structure model, and explicitly expressing the top displacement and the interlayer lateral displacement by optimizing variables;
5) and establishing an objective function for optimizing the total construction cost of the structural material by taking the top displacement and the interlayer lateral displacement as constraint conditions and the lowest overall construction cost, and performing iterative optimization on the optimized variables within the boundary condition range of the optimized variables according to the constraint conditions and the objective function to obtain the final section of the concrete-filled steel tubular column.
In the step 2), the optimization variables are specifically the outer diameter D and the thickness-diameter ratio v of the section of the steel tube concrete column, wherein v is t/D, and t is the wall thickness of the steel tube.
Wherein, the equivalent diameter expression in the step 2) is as follows:
in the formula, DeDenotes the equivalent diameter of the concrete-filled steel tube, EsIs the modulus of elasticity of the steel pipe, EcThe modulus of elasticity of the concrete in the steel tube; gsShear modulus of steel pipe, GcThe shear modulus of the concrete in the steel tube.
Wherein, the internal force of the frame structure model under the action of the external load and the unit virtual load comprises: axial force of the steel tube concrete column in the x-axis direction generated under the action of external loadAnd shear force in y-axis and z-axis directionsTorque about the x-axisAnd bending moments around the y-axis and the z-axisAnd axial force f of the steel tube concrete column in the x-axis direction when unit virtual load is applied to the corresponding displacement positionxjShear force f in the y-axis and z-axis directionsyj、fzjTorque m about the x-axisxjAnd bending moment around the y-axis and the z-axis, myj、mzj。
Wherein, the specific expression of the constraint condition is as follows:
in the formula,is a standard displacement limit; diIs the outer diameter v of the ith steel pipe concrete columniThe thickness-diameter ratio of the ith concrete-filled steel tube column is; n is a radical ofi1The number of the steel tube concrete columns is shown, wherein each coefficient expression is as follows:
wherein L isiThe length of the ith concrete filled steel tube column.
The objective function is specifically as follows:
wherein T represents the total cost of the structural material; n is a radical of1Representing the number of types of the concrete filled steel tubular columns; a. b is the price of the steel pipe and the concrete in unit volume respectively; a. thei1、Ai2The sectional area of the steel pipe and the sectional area of concrete in the steel pipe are respectively; ki1The number of the i-type steel tube concrete columns is represented; linThe length of the nth class i steel tube concrete column.
In the step 5), in the iterative optimization process of the optimization variable, the absolute value of the relative error of the optimization variable between the iteration step v +1 and the iteration step v is used as a convergence condition, and the specific expression is as follows:
the method is characterized in that the value of an optimized variable of the ith concrete-filled steel tube column in the iteration step v is shown, and e is a preset minimum constant;
when in useAndand when the convergence condition is not met, taking a new optimization variable to perform iterative optimization from the step 2) to the step 5) again until the convergence condition is met.
Wherein e is recommended to be 0.001 in engineering applications.
The high-rise building frame structure further comprises a rectangular section beam, and the optimization variables further comprise section width B and section height H of the rectangular section beam;
the constraint expression is extended to:
in the formula, BiIs the cross section width H of the ith rectangular section beamiThe section height of the ith rectangular section beam is high; n is a radical ofi2Is rectangular
The number of the section beams, wherein each coefficient is expressed as follows:
wherein L isiIs a momentLength of the cross-section beam;
the high-rise building frame structure further comprises a rectangular section beam, and the optimization variables further comprise section width B and section height H of the rectangular section beam; the objective function is extended to:
wherein N is2The number of beams with rectangular cross sections is shown; b isi、HiThe width and the height of the ith rectangular section beam are respectively; ki2The number of the i-type rectangular section beams is represented; l in the second formulainThe length of the nth class i steel tube concrete column; l in the third formulainThe length of the nth i-type rectangular section beam.
The above extends the method for optimally designing a framework structure of a story building which also comprises rectangular section beams, and if other types of section beams are also included, such as i-shaped section beams or circular tube section beams, the formula can be extended by a similar method.
And additionally, the external load in the step 4) comprises a wind load, and the wind load is according to the high-rise building frame structure
The basic wind pressure of the location is calculated by the following formula:
ωk＝βzμsμzω0
in the formula, ωkIs the standard value of wind load (KN/m)2)；βzIs the wind vibration coefficient at height z; mu.ssIs the wind load figure coefficient; mu.szIs the wind pressure height variation coefficient; omega0Refers to the basic wind pressure (KN/m)2)。
The beneficial effects created by the invention are as follows:
the invention provides an optimized design method of a high-rise building frame structure containing a steel pipe concrete column, which selects the section of the steel pipe concrete column, specifically, the outer diameter and the thickness-diameter ratio of the section of the steel pipe concrete column as optimized variables, by equivalent conversion of the steel pipe concrete column and endowing the frame structure model established in the finite element analysis software, the internal force born by the frame structure model is obtained by using a finite element analysis method, and then the internal force is utilized, according to the virtual work principle, the relationship between the optimization variable and the displacement constraint condition is established, and the objective function of the total construction cost optimization of the structural material established by the lowest overall construction cost is matched, iteratively optimizing the optimized variables within the boundary condition range of the optimized variables to obtain the optimal section of the concrete-filled steel tubular column, and then obtain the optimum total cost, when guaranteeing that the material quantity is few, guarantee that the top displacement of structure and interlayer sidesway satisfy relevant standard's requirement. The relation between the optimization variable and the displacement constraint condition is obtained by matching a section rigidity formula of the concrete-filled steel tube column with a virtual work principle and simultaneously deducing internal force obtained by utilizing finite element analysis software, is specially used for displaying an expression aiming at the displacement constraint condition of a common component of the concrete-filled steel tube in a high-rise building structure, and is used for optimizing the high-rise building frame structure by matching an objective function, so that the more excellent outer diameter and thickness-diameter ratio of the section of the concrete column can be obtained, and the optimization iteration process can be rapidly and stably converged.
Drawings
The invention is further described with the aid of the accompanying drawings, in which, however, the embodiments do not constitute any limitation to the invention, and for a person skilled in the art, without inventive effort, further drawings may be derived from the following figures.
FIG. 1 is a graph showing the ratio of the equivalent diameter to the outer diameter as a function of the thickness to diameter ratio for three equivalent methods.
Fig. 2 is a schematic structural view of a framework model.
Fig. 3(a) is a schematic diagram of an iterative process for optimizing the outer diameter of the steel pipe in the working condition 1.
Fig. 3(b) is a schematic diagram of an iterative process for optimizing the aspect ratio of the operating condition 1.
Fig. 3(c) is a schematic diagram of an iterative process for optimizing the beam width and the beam height under the working condition 1.
FIG. 3(d) is a schematic diagram of an optimization iteration process of the optimization objective for condition 1.
Fig. 4(a) is a schematic diagram of an iterative process for optimizing the outer diameter of the steel pipe in the working condition 2.
Fig. 4(b) is a schematic diagram of an iterative process for optimizing the aspect ratio of the operating condition 2.
Fig. 4(c) is a schematic diagram of an iterative process for optimizing the beam width and the beam height in the working condition 2.
FIG. 4(d) is a schematic diagram of an optimization iteration process of the optimization objective for condition 2.
FIG. 5 is a schematic diagram of horizontal y-direction displacement under condition 1.
FIG. 6 is a schematic diagram of y-direction layer sideshift under condition 1.
FIG. 7 is a schematic diagram of horizontal y-displacement under condition 2.
FIG. 8 is a schematic diagram of y-direction layer sideshift under condition 2.
Detailed Description
The invention will be further described with reference to the following examples.
The high-rise building frame structure comprises a steel tube concrete column 1 and a rectangular section beam 2, firstly, optimization variables are selected, the outer diameter D and the thickness-diameter ratio v of the section of the steel tube concrete column 1, and the section width B and the section height H of the rectangular section beam 2 are selected as the optimization variables, wherein v is t/D, and t is the wall thickness of the steel tube.
Establishing a frame structure model in SAP2000 according to the high-rise building frame structure, wherein the frame structure model is a finite element model, a plurality of units are divided on the finite element model, unit nodes are formed among the units, the steel pipe concrete column 1 is equivalent to a plain concrete column by adopting a rigidity equivalent method, the equivalent diameter of the plain concrete column is calculated, the equivalent diameter is displayed and expressed by an optimized variable, and after calculation, the equivalent diameter and the optimized variable are assigned to the frame structure model. Wherein the equivalent diameter expression is as follows:
in the formula, DeDenotes the equivalent diameter of the concrete-filled steel tubular column 1, EsIs the modulus of elasticity of the steel pipe, EcThe modulus of elasticity of the concrete in the steel tube; gsShear modulus of steel pipe, GcThe shear modulus of the concrete in the steel tube.
The steel pipe concrete column 1 is composed of two materials, namely a steel pipe and concrete, and only one material can be used for assigning a value to a section through SAP2000API, so that the steel pipe concrete column 1 needs to be equivalent to a concrete column, the inventor researches rigidity equivalence, strength equivalence and shearing equivalence methods, and equivalent diameter expressions of the three equivalence methods are as follows:
strength equivalence:
shearing equivalence:
rigidity equivalence:
the thickness-diameter ratio gama is taken as an abscissa, the ratio of the equivalent diameter to the outer diameter is taken as an ordinate to draw a graph, and the trend of the ratio of the three equivalent diameters to the outer diameter along with the change of the gama value is shown in figure 1.
Since the influence of the shear strength on the displacement value is small, it can be known from fig. 1 that the rigidity equivalence principle is safe and conservative, and the smaller the thickness-diameter ratio is, the equivalent diameter is close to the actual outer diameter value, so the rigidity equivalence method is selected.
Then, applying external load to the unit nodes of the frame structure model in SAP2000, and calculating the internal force of the frame structure model under the external load; and then respectively applying unit virtual loads to all the unit node positions with displacement constraint one by one, wherein the unit virtual loads are applied each time to serve as an independent working condition, and after structural analysis is carried out, reading the internal force of the frame structure model under each independent working condition. Wherein, the external load is wind load, the wind load is calculated according to the basic wind pressure of the high-rise building frame structure, the calculation formula is: omegak＝βzμsμzω0. And the internal force includes: axial force of the steel tube concrete column 1 in the x-axis direction generated under the action of external loadAnd shear force in y-axis and z-axis directionsTorque about the x-axisAnd bending moments around the y-axis and the z-axisAnd applying unit dummy load to the corresponding displacementAxial force f of the concrete column 1 in the x-axis directionxjShear force f in the y-axis and z-axis directionsyj、fzjBending moment m around x-axis and y-axisxj、myjTorque m about the z-axiszj
After the internal force is obtained, the relation between the optimized variable and the displacement constraint condition can be established, and the specific expression of the constraint condition is as follows:
in the formula,is a standard displacement limit; diIs the outer diameter v of the ith steel pipe concrete columniThe thickness-diameter ratio of the ith concrete-filled steel tube column 1 is shown; n is a radical ofi1The number of the steel tube concrete columns 1, BiIs the cross section width H of the ith rectangular section beam 2iThe section height of the ith rectangular section beam 2 is high; n is a radical ofi2Is a rectangular sectionThe number of the face beams 2; wherein each coefficient expression is as follows:
wherein L of the above four formulaeiThe length of the ith concrete filled steel tubular column 1.
Wherein, the three formulas LiThe length of the rectangular section beam 2.
The derivation process of the specific expression of the constraint condition is as follows:
the specific expression of the constraint condition is deduced according to the virtual work principle, and the displacement of a certain node of the framework structure model under the action of external load is as follows:
as known from the technical specification of the steel pipe concrete structure (CECS28:2012), when calculating the elastic internal force and displacement of the steel pipe concrete structure, the section stiffness of the steel pipe concrete column 1 can be calculated according to the following formula:
EA＝EsAs+EcAc
EI＝EsIs+EcIc
GI＝GsIs1+GcIc1
GA＝GsAs+GcAc
in the formula, EA, EI, GA and GI respectively refer to the section compressive stiffness, the section bending stiffness, the section shearing stiffness and the section torsional stiffness of the steel pipe concrete column 1; es、EcRespectively steel pipe and steelThe modulus of elasticity of the concrete in the pipe; gs、GcThe shear modulus of the steel pipe and the shear modulus of the concrete in the steel pipe are respectively; a. thes、AcThe cross-sectional areas of the steel pipe and the concrete in the steel pipe are respectively; i iss、IcThe section inertia moment of the steel pipe and the section inertia moment of the concrete in the steel pipe are respectively; i iss1、Ic1Respectively the polar inertia moment of the steel pipe and the concrete in the steel pipe.
On the other hand
The cross section area of the steel pipe is as follows:
As＝π(Dt-t2)＝π(D2ν-D2ν2)＝πD2ν(1-ν)
concrete cross-sectional area:
moment of inertia of the steel pipe:
polar moment of inertia of steel pipe:
moment of inertia of concrete:
the ratio of the cross-sectional area of the steel pipe to the cross-sectional area of the concrete is represented by α:
the ratio of the steel pipe moment of inertia to the concrete moment of inertia is represented by beta:
the coefficients alpha, beta, n1、n2Substituting into formula As＝π(Dt-t2)＝π(D2ν-D2ν2)＝πD2ν (1- ν), the calculation expression of the section rigidity of the concrete filled steel tube can be written as:
in the formula Ix isTorsional moment of inertia, I, of the concrete-filled steel tubular column 1 about the x-axisy、Iz is respectivelyThe bending moment of inertia of the steel tube concrete column 1 around the y axis and the z axis.
Substituting the four formulas into a displacement expression of a certain node of the frame structure model under the action of external load, and obtaining a concrete expression of the constraint condition of the concrete-filled steel tubular column 1:
similarly, a specific expression of the constraint condition of the rectangular section beam 2 can be obtained, and the sum of the two expressions is the expression of the constraint condition of the high-rise building frame structure comprising the concrete-filled steel tubular column 1 and the rectangular section beam 2.
Finally, establishing an objective function of total cost optimization of the structural material with the lowest overall structure cost; the objective function is specifically:
wherein T represents the total cost of the structural material, i.e., the objective function of the optimization problem; n is a radical of1The number of types of the concrete filled steel tubular columns 1 is shown; a. b is the price of the steel pipe and the concrete in unit volume respectively; a. thei1、Ai2The sectional area of the steel pipe and the sectional area of concrete in the steel pipe are respectively; ki1The number of the i-type steel pipe concrete columns 1 is represented; linThe length of the nth type i concrete filled steel tubular column 1.
After the constraint condition and the objective function are determined, the optimization variables are subjected to iterative optimization within the boundary condition range of the optimization variables according to the two expressions, and the optimal total manufacturing cost is obtained.
Specifically, in the iterative optimization process of the optimization variable, the absolute value of the relative error of the optimization variable in the iteration step v +1 and the iteration step v is used as a convergence condition, and the specific expression is as follows:
for the optimized variable value of the ith concrete-filled steel tube column 1 in the iteration step v, e is a preset minimum constant, and the value range is preferably 0.001.
When in useAndand when the convergence condition is not met, taking a new optimization variable to continue iterative optimization from the calculation of the equivalent diameter again until the convergence condition is met.
In order to verify whether the adopted equivalent diameter is reasonable or not, the thickness-diameter ratio is 0.03, the formula equivalent diameter expression is substituted into the constraint condition expression, a corresponding displacement calculation program is compiled, the internal force of each component of the equivalent model is read through the SAP2000API function, and the displacement value of each layer is u1(ii) a Directly programming according to the constraint conditional expression, reading the internal force of each component of the actual model through an SAP2000API function, and calculating the displacement value u of each layer2(ii) a The displacement value of each layer obtained after running and analyzing the actual model through SAP2000 is u3. The 19 th floor to the top floor displacement of the building is compared, as shown in table 1, and the result shows that the displacement u of each floor is equivalent to the displacement u of each floor of the model with equivalent diameter1Displacement u of each layer from the actual model2Substantially identical, and both approximate the displacement value u obtained by running and analyzing the actual model with SAP20003It is stated that a stiffness equivalent approach is feasible.
TABLE 1 v Displacement values for three algorithms at 0.03
In order to more intuitively highlight the optimization effect of the optimization design method for the high-rise building frame structure containing the concrete filled steel tubular column 1, an example of a specific iterative optimization process of a frame structure model established by using specific numerical values is given below, and the remarkable technical effect of the method can be verified through data comparison before and after optimization.
Aiming at the cross section size optimization of a reinforced concrete high-rise building with a 24-layer frame structure under the action of wind load, a corresponding wind-resistant structure optimization mathematical model is established, namely a frame structure model, the beam of the frame structure model is a concrete beam with a rectangular cross section 2, the column of the frame structure model is a steel pipe concrete with a circular cross section 1, and the frame structure model is as shown in figure 2, the layer height is 3.3 meters, and the single span is 6 meters. Corresponding basic wind load values are respectively applied to the top nodes of the 1 st to 24 th floors on the left side, the top displacement of the building structure in the y direction of the top-floor mass center under the action of the basic wind load and the interlayer lateral displacement of each floor are mainly considered, and the top displacement and the interlayer lateral displacement of each floor are used as optimization constraint conditions, and according to the limit value requirement of the technical regulation of high-rise building concrete structures (JGJ3-2010) on the difference between the horizontal displacement and the interlayer displacement of the frame structure: the limit of the ratio of top displacement to building height is 1/550, and the limit of the ratio of maximum floor-to-floor lateral displacement to floor height is 1/550. The total construction cost of a frame structure model is taken as an objective function, the optimized objective is that the overall structure construction cost is the lowest, the outer diameter D and the thickness-diameter ratio v of the section of the steel tube concrete column 1, the section width B and the section height H of the rectangular section beam 2 are taken as optimized variables, the initial outer diameter of the column is set to be 0.7 m, and the thickness-diameter ratio is 0.03.
In order to investigate whether the optimal criterion method and the initial state of the strength of the design variable affect the convergence of the iterative process, the example is subjected to optimization analysis according to three working conditions shown in table 2. Boundary values of design variables of the working condition 1 and the working condition 2 are completely the same, initial design values are different (the initial structure design of the working condition 1 is weak, the initial structure design of the working condition 2 is strong), and convergence stability of an optimal criterion method can be investigated by comparing and analyzing optimization calculation results of the working condition 1 and the working condition 2; in order to illustrate the effectiveness of the relaxation processing method adopted when the design variables are out of bounds, the initial values of the design variables of the working condition 1 and the working condition 3 are completely the same, and the boundary values are different, wherein the upper limit and the lower limit of v are determined according to the specification, so that the upper limit and the lower limit of v are not changed.
TABLE 2 analysis of the operating conditions
Table 3 and fig. 3(a) to 3(d) show the optimization iteration process of the design variables and the objective function of the operating condition 1, table 4 and fig. 4(a) to 4(d) show the optimization iteration process of the design variables and the objective function of the operating condition 2, and table 5 shows the optimization iteration process of the design variables and the objective function of the operating condition 3. As can be seen from tables 3 and 4, under the condition that the given objective function, constraint condition and boundary condition are the same, no matter whether the structure is designed to be stronger or weaker, the optimization process can obtain the same optimal solution, and the design variables and optimization target of the iterative process can be converged quickly and stably. Tables 3 and 5 show that the width and height of the rectangular-section beam 2 can always reach the upper limit and the price of concrete is low, so that the larger the rectangular-section beam 2 is, the more advantageous the optimization object is, but the larger the rectangular-section beam 2 is, the more the aesthetic appearance is affected and the use function is affected, the less the space used by the building is, and therefore, the size of the rectangular-section beam 2 needs to be limited by setting the upper and lower limit values.
TABLE 3 optimized iterative procedure for Condition 1
TABLE 4 optimized iterative procedure for Condition 2
TABLE 5 optimized iterative procedure for Condition 3
The difference between the horizontal displacement in the y direction and the horizontal displacement between layers before and after the optimization of the working condition 1 is respectively given by fig. 5 and fig. 6, and whether the optimized structure meets the requirement of the constraint condition can be judged. As can be seen from fig. 5, the structure meets the requirements of the constraint conditions only in the y-direction of the layer 1 before optimization, but does not meet the requirements of other layers, and the displacements of the optimized layers meet the requirements of the constraint conditions; as can be seen from fig. 6, most floors before optimization cannot meet the requirement of the specification on the interlayer displacement difference, and the interlayer displacement difference after optimization is obviously improved, and only the interlayer displacement difference at the 7 th floor is very close to the constraint limit.
The horizontal displacement in the y direction and the interlayer lateral displacement before and after the optimization of the working condition 2 are respectively given by the graph in fig. 7 and 8, and whether the optimized structure meets the requirement of the constraint condition can be judged. As can be seen from fig. 7, the y-direction horizontal displacements of the respective floors can meet the requirements of the constraint conditions, and the displacement values of the optimized respective floors are reduced from the 18 th floor to the top floor as compared with those before the optimization, and are increased at other floors, but all meet the requirements of the constraint conditions; it can be seen from fig. 8 that the structure cannot meet the requirements of the specification on the interlayer displacement difference between the 8 th layer and the 12 th layer before optimization, and only the interlayer displacement difference between the 7 th layer is very close to the constraint limit value after optimization, which proves that the optimization result reaches the optimal solution under the condition of just meeting the constraint condition. Fig. 7 and 8 show that when the initial values of the set structural design variables are appropriate, the top displacement can already satisfy the constraint condition of the horizontal displacement before optimization, so that the interlayer displacement difference is used as the control condition of the optimization iteration process in the whole optimization process of the structure.
Finally, it should be noted that the above embodiments are only used for illustrating the technical solutions of the present invention, and not for limiting the protection scope of the present invention, although the present invention has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that modifications or equivalent substitutions can be made on the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention.
Claims (10)
1. The optimization design method of the high-rise building frame structure containing the steel tube concrete column is characterized by comprising the following steps of:
1) establishing a frame structure model for the high-rise building frame structure, wherein the frame structure model is a finite element model, a plurality of units are divided on the finite element model, and unit nodes are formed among the units;
2) the method comprises the steps of equivalence of the steel tube concrete column into a plain concrete column by adopting a rigidity equivalence method, calculating the equivalent diameter of the plain concrete column expressed by the section of the steel tube concrete column serving as an optimized variable display, and assigning the equivalent diameter and the optimized variable to a frame structure model by adopting a finite element analysis method;
3) applying an external load to the element nodes of the assigned frame structure model by adopting a finite element analysis method, and solving the internal force of the frame structure model under the external load; then respectively applying unit virtual loads to all unit node positions with displacement constraint one by one, taking the unit virtual loads applied each time as an independent working condition, and reading the internal force of the frame structure model under each independent working condition after carrying out structure analysis;
4) based on the virtual work principle and the internal force of the frame structure model obtained by the analysis in the step 3) under the action of the external load and the unit virtual load, calculating the top displacement and the interlayer lateral movement of the frame structure model, and explicitly expressing the top displacement and the interlayer lateral movement by optimizing variables;
5) and establishing an objective function for optimizing the total construction cost of the structural material by taking the top displacement and the interlayer lateral displacement as constraint conditions and the lowest overall construction cost, and performing iterative optimization on the optimized variables within the boundary condition range of the optimized variables according to the constraint conditions and the objective function to obtain the final section of the concrete-filled steel tubular column.
2. The method of claim 1 for optimally designing a frame structure of a high-rise building including the concrete-filled steel tubular column, wherein the method comprises the following steps: in the step 2), the optimization variable is the outer diameter D and the thickness-to-diameter ratio v of the section of the steel tube concrete column, wherein v is t/D, and t is the wall thickness of the steel tube.
3. The method of claim 2, wherein the method comprises the steps of: the expression of the equivalent diameter in the step 2) is as follows:
wherein,
in the formula, DeDenotes the equivalent diameter of the concrete-filled steel tube, EsIs the modulus of elasticity of the steel pipe, EcThe modulus of elasticity of the concrete in the steel tube; gsShear modulus of steel pipe, GcThe shear modulus of the concrete in the steel tube.
4. The method of claim 3, wherein the method comprises the steps of: the internal force of the frame structure model under the action of external load and unit virtual load comprises: axial force of the steel tube concrete column in the x-axis direction generated under the action of external loadAnd shear force in y-axis and z-axis directions Torque about the x-axisAnd bending moments around the y-axis and the z-axis And axial force f of the steel tube concrete column in the x-axis direction when unit virtual load is applied to the corresponding displacement positionxjShear force f in the y-axis and z-axis directionsyj、fzjTorque m about the x-axisxjAnd bending moment around the y-axis and the z-axis, myj、mzj。
5. The method of claim 4, wherein the method comprises the steps of: the specific expression of the constraint condition is as follows:
in the formula,is a standard displacement limit; diIs the outer diameter v of the ith steel pipe concrete columniFor the ith steel pipe
The thickness-diameter ratio of the column is determined; n is a radical ofi1The number of the steel tube concrete columns is shown, wherein each coefficient expression is as follows:
wherein L isiThe length of the ith concrete filled steel tube column.
6. The optimum design method of a high-rise building frame structure containing a steel tubular concrete column according to claim 1 or 2, characterized in that: the objective function is specifically:
wherein T represents the total cost of the structural material; n is a radical of1Representing the number of types of the concrete filled steel tubular columns; a. b is the price of the steel pipe and the concrete in unit volume respectively; a. thei1、Ai2The sectional area of the steel pipe and the sectional area of concrete in the steel pipe are respectively; ki1The number of the i-type steel tube concrete columns is represented; linThe length of the nth class i steel tube concrete column.
7. The method of claim 5, wherein the method comprises the steps of: in the step 5), in the iterative optimization process of the optimization variables, the absolute value of the relative error of the optimization variables in the iteration step v +1 and the iteration step v is used as a convergence condition, and the specific expression is as follows:
the optimization variable value of the ith concrete-filled steel tube column in the iteration step v is changed, and e is a preset minimum constant; when in useAndand when the convergence condition is not met, taking a new optimization variable to perform iterative optimization from the step 2) to the step 5) again until the convergence condition is met.
8. The method of claim 7, wherein the method comprises the steps of: the preset minimum constant is 0.001.
9. The method of claim 5, wherein the method comprises the steps of: the high-rise building frame structure further comprises a rectangular section beam, and the optimization variables further comprise the section width B and the section height H of the rectangular section beam;
the constraint expression is extended to:
in the formula, BiIs the cross section width H of the ith rectangular section beamiThe section height of the ith rectangular section beam is high; n is a radical ofi2The number of the beams with the rectangular cross sections is shown, wherein each coefficient is expressed as follows:
wherein L isiThe length of a beam of rectangular cross section.
10. The method of claim 6, wherein the method comprises the steps of: the high-rise building frame structure further comprises a rectangular section beam, and the optimization variables further comprise the section width B and the section height H of the rectangular section beam; the objective function is extended to:
wherein N is2The number of beams with rectangular cross sections is shown; b isi、HiThe width and the height of the ith rectangular section beam are respectively; ki2The number of the i-type rectangular section beams is represented; l in the second formulainThe length of the nth class i steel tube concrete column; l in the third formulainThe length of the nth i-type rectangular section beam.
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Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106909735A (en) * | 2017-02-24 | 2017-06-30 | 广州市建筑科学研究院有限公司 | A kind of method for designing and design system for Optimizing construction shuttering supporting body |
| CN109682557A (en) * | 2018-12-03 | 2019-04-26 | 北京市市政工程研究院 | A kind of overpass rail structure load carrying capacity test assessment method |
| CN110309605A (en) * | 2019-07-05 | 2019-10-08 | 北京交通大学 | Curve steel-Combined concrete box beam one-dimensional beam element model method for building up |
| CN111382910A (en) * | 2020-03-16 | 2020-07-07 | 上海大学 | Analysis method of optimization model based on club-footed uplift pile |
Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2004310376A (en) * | 2003-04-04 | 2004-11-04 | Canon Inc | Optimum design of structure |
| CN102147597A (en) * | 2010-02-10 | 2011-08-10 | 广州大学 | Health monitoring system for structures of great building and bridge |
| CN102392422A (en) * | 2011-11-26 | 2012-03-28 | 广州大学 | Reinforcement structure of single-cable-plane cable-stayed bridge |
-
2015
- 2015-05-22 CN CN201510268993.5A patent/CN104820762B/en not_active Expired - Fee Related
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2004310376A (en) * | 2003-04-04 | 2004-11-04 | Canon Inc | Optimum design of structure |
| CN102147597A (en) * | 2010-02-10 | 2011-08-10 | 广州大学 | Health monitoring system for structures of great building and bridge |
| CN102392422A (en) * | 2011-11-26 | 2012-03-28 | 广州大学 | Reinforcement structure of single-cable-plane cable-stayed bridge |
Non-Patent Citations (2)
| Title |
|---|
| MP LI ETC.: "Association of platelet ITGA2B and ITGB3 polymorphisms with ex vivo antiplatelet effect of ticagrelor in healthy Chinese male subjects", 《INTERNATIONAL JOURNAL OF HEMATOGOGY》 * |
| 高炜文等: "群体高层建筑风效应的数值模拟", 《广州大学学报(自然科学版)》 * |
Cited By (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106909735A (en) * | 2017-02-24 | 2017-06-30 | 广州市建筑科学研究院有限公司 | A kind of method for designing and design system for Optimizing construction shuttering supporting body |
| CN109682557A (en) * | 2018-12-03 | 2019-04-26 | 北京市市政工程研究院 | A kind of overpass rail structure load carrying capacity test assessment method |
| CN109682557B (en) * | 2018-12-03 | 2020-11-10 | 北京市市政工程研究院 | Method for evaluating bearing capacity test of pedestrian overpass railing structure |
| CN110309605A (en) * | 2019-07-05 | 2019-10-08 | 北京交通大学 | Curve steel-Combined concrete box beam one-dimensional beam element model method for building up |
| CN110309605B (en) * | 2019-07-05 | 2020-10-16 | 北京交通大学 | Method for establishing one-dimensional beam unit model of curved steel-concrete combined box beam |
| CN111382910A (en) * | 2020-03-16 | 2020-07-07 | 上海大学 | Analysis method of optimization model based on club-footed uplift pile |
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