CN103729526B - A kind of high-rise building boom truss component cross-sectional size optimization method - Google Patents

Abstract

The present invention relates to a kind of high-rise building boom truss component cross-sectional size optimization method, on the premise of determination in semi-girder truss position and number of channels, by optimizing the sectional dimension of boom truss component based on the optimized algorithm of the principle of virtual work and Sequential Quadratic Programming method.Compared with prior art, the present invention is for optimizing distribution on boom truss component for the material, makes structure under conditions of meeting story drift and cycle constraint, and material usage is minimum, and the sectional dimension after optimization can meet building and construction requirement.

Description

A kind of high-rise building boom truss component cross-sectional size optimization method

Technical field

The present invention relates to technical field of structural engineering, especially relate to a kind of high-rise building boom truss component cross section chi Very little optimization method.

Background technology

Due to the demand of Economization on land in urban construction, the development of high-strength light material, the raising of technique of design and construction And people more and more occur for the serious hope of superelevation landmark, high-rise building.Super-high building structure build Elongated, there is height, soft feature, due to overall structure Gao Rou, the size of main member is usually stiffness reliability.At wind load and Under geological process, high-rise building needs control structure or component to produce excessive deformation, it is to avoid the exterior wall that thus causes, exterior The damage of exterior material.Free vibration period of structure is also the important parameter of Architectural Structure Design, and bigger building structure natural vibration period is not Will result only in the deformation under normal operating condition and comfortableness problem, also can increase the possibility that structure is destroyed under wind action Property.In order to reduce the illeffects that long period causes, it is common practice that the cycle that arranges in Designing Structures of High Rising Buildings limits.For It is effectively increased the rigidity of structure, thus reduce story drift and the cycle of super-high building structure, structural engineer Chang She Standby layer and refuge story space arrange the bigger semi-girder truss of rigidity, to strengthen contacting of Core Walls Structure and peripheral frame, composition anti-side The higher structural system of efficiency.Semi-girder truss has good effect to increasing the rigidity of structure, but boom truss component size is relatively Greatly, general section height is about 1m, and steel using amount is huge.If distribution on semi-girder truss for the material can be optimized, material is made to obtain Sufficiently utilize, be then possible not only to reduce material usage, increase the economical of structure, moreover it is possible to improve the overall performance of structure.Stretch The optimization design of arm trussmember size can carry out increasing to story drift and cycle influences bigger by following measures The size of component, reduces to story drift and cycle influences compared with the size of primary structural component.

Current sectional dimension of members optimization can use some to have the professional software optimizing analytic function, but, above-mentioned soft Part applies in general to small-scale structure or mechanical component, and the result optimizing may not necessarily be used for PRACTICE OF DESIGN, therefore, in actual work Application in journey is relatively fewer；When more, structure designer is by utilizing the concept of conventional structure and engineering experience, Manually adjust tentative calculation repeatedly, laborious during this process, generally also cannot get optimal solution.

Content of the invention

Defect that the purpose of the present invention is contemplated to overcome above-mentioned prior art to exist and provide a kind of material usage few, excellent Sectional dimension after change can meet the high-rise building boom truss component cross-sectional size optimization method of building and construction requirement.

The purpose of the present invention can be achieved through the following technical solutions:

A kind of high-rise building boom truss component cross-sectional size optimization method, comprises the steps:

1) high-rise building is divided along short transverse in units of district, the semi-girder truss arranging in each district is set to many Individual optimization group, the sectional dimension of the inner member of each group is identical；

2) selected optimized variable in each group；

3) with story drift as constraints, setting up optimized variable and the relation of story drift constraint, this relation can Being realized by the principle of virtual work, expression is:

${\mathrm{\δ}}_s=\frac{L^{\left(m\right)}}{6Q_s}\underset{m=1}{\overset{N}{\mathrm{\Σ}}}\left(\left[F_i^{\left(m\right)}{F}_j^{\left(m\right)}\right]\left[\begin{array}{cc}{2K}_e^{\left(m\right)}& K_e^{\left(m\right)}\\ K_e^{\left(m\right)}& {2K}_e^{\left(m\right)}\end{array}\right]\left[\begin{array}{c}{\left[f_i^{\left(m\right)}\right]}^T\\ {\left[f_j^{\left(m\right)}\right]}^T\end{array}\right]\right)\≤\left[\mathrm{\δ}\right]$

In formula, δ_sFor the story drift of s layer, Q_sFor acting on the virtual couple of s layer, N is number of components, L^(m)For component The length of m, N is component number,It is vectorial for the nodal force in design load operating mode lower member m node i,For in design The nodal force vector of load case lower member m node j,For virtual load operating mode lower member m node i nodal force to Amount,It is vectorial for the nodal force at virtual load operating mode lower member m node j,For the diagonal angle stiffness matrix of component m, right On linea angulata, element is followed successively by, 1/EA, 1/GA_Y、1/GA_Z、1/GI_X、1/EI_YAnd 1/EI_Z, A is member section area, A_YAnd A_ZFor dividing Wei be along the section of shear of y-axis and z-axis, I_X、I_YAnd I_ZBeing respectively the cross sectional moment of inertia around x-axis, y-axis and z-axis, E is construction material Elastic modelling quantity, G is the modulus of shearing of construction material, and [δ] is the story drift limit value of structure；

With the first natural vibration period of structure as constraints, setting up the relation of optimized variable and cycle constraint, this relation can be led to Cross the principle of virtual work and Rayleigh method realizes, particularly as follows:

$W=L^{\left(m\right)}\underset{m=1}{\overset{N}{\mathrm{\Σ}}}\left(\left[F_i^{\left(m\right)}{F}_j^{\left(m\right)}\right]\left[\begin{array}{cc}{2K}_e^{\left(m\right)}& K_e^{\left(m\right)}\\ K_e^{\left(m\right)}& {2K}_e^{\left(m\right)}\end{array}\right]\left[\begin{array}{c}{\left[F_i^{\left(m\right)}\right]}^T\\ {\left[F_j^{\left(m\right)}\right]}^T\end{array}\right]\right)=w^2\≤W^U$

In formula, W is modal forces work,It is vectorial for the nodal force in modal forces operating mode lower member m node i, For the nodal force vector at modal forces operating mode lower member m node j, w is Structural Eigenvalue, W^U=(T^U/T⁰)²W⁰=4 π²(T^U/T⁰ )²/(T⁰)², T⁰And T^UFor structure initial first natural vibration period and target period, W⁰Strain energy for initial configuration；

4) the dimensionally-optimised object function of boom truss component is set up with semi-girder truss volume minimum, particularly as follows:

$\begin{array}{cc}\mathrm{Min}& V=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{L}_i{A}_i\end{array}$

In formula, A_iAnd L_iIt is respectively area of section and the length of component i；

5) according to step 3) constraints and step 4) object function, use Sequential Quadratic Programming method carry out component chi Very little optimization, it is thus achieved that optimum boom truss component sectional dimension.

Described step 3) in, when calculating story drift, choosing the floor between adjacent twice semi-girder truss is control Layer, the maximum story drift of key-course is the maximum story drift of structure.

The maximum story drift of a certain floor is the story drift at control point, checks according to FEM model, described Control point be normally on floor Core Walls Structure angle point and exterior frame column node.

Compared with prior art, the invention have the advantages that

1st, the present invention optimizes distribution on boom truss component for the material, makes structure meet story drift and cycle about Under conditions of bundle, material usage is minimum；

2nd, the present invention is applicable to large scale structure, such as high-rise building, and optimize after sectional dimension can meet building and Construction requirement.

Brief description

Fig. 1 is cantilever truss structure schematic diagram of the present invention；

Fig. 2 is structure and the semi-girder truss schematic diagram of the present invention；

Fig. 3 is the changing trend diagram of case semi-girder truss volume of the present invention and the first natural vibration period of structure；

Fig. 4 is story drift change before and after case key-course x direction of the present invention optimizes；

Fig. 5 is story drift change before and after case key-course y direction of the present invention optimizes；

Fig. 6 is that case of the present invention boom truss component cross section in the 1st time, the 4th and last iteration is high.

Detailed description of the invention

The present invention is described in detail with specific embodiment below in conjunction with the accompanying drawings.The present embodiment is with technical solution of the present invention Premised on implement, give detailed embodiment and concrete operating process, but protection scope of the present invention be not limited to Following embodiment.

A kind of high-rise building boom truss component cross-sectional size optimization method, comprises the steps:

1st, high-rise building build is elongated, rigidity is more weak, often arranges semi-girder truss at mechanical floor overall just to increase structure Degree, thus reduce floor story drift and structural cycle.High-rise building generally divides work(along short transverse in units of district Energy range, semi-girder is generally located on the mechanical floor in district.As it is shown in figure 1, position pressed by component in semi-girder truss, can be divided into and winding up Rod member 4 in bar the 1st, lower boom the 2nd, diagonal web member 3 and shear wall.On the premise of determination in semi-girder truss position and number of channels, before optimization Phase, in the top boom of Xu Jiangge district semi-girder truss, lower boom, diagonal web member and shear wall, rod member sets in groups, cutting of group inner member Face is equivalently-sized, as shown in Figure 2.As certain Super High is provided with semi-girder in 5 districts, all boom truss components can be set as 20 Group.

2nd, after setting optimization group, optimized variable need to be selected in each group.Member section is high to story drift and week The impact of phase is relatively big, a height of optimized variable in general optional cross section, and other sizes of cross section may be set to the high a certain multiple in cross section, Or it is set to definite value.

3rd, dimensionally-optimised with story drift for the boom truss component of constraint, optimized variable and story drift need to be set up Relation, this relation can be realized by the principle of virtual work, shown in expression such as formula (1):

${\mathrm{\δ}}_s=\frac{L^{\left(m\right)}}{6Q_s}\underset{m=1}{\overset{N}{\mathrm{\Σ}}}\left(\left[F_i^{\left(m\right)}{F}_j^{\left(m\right)}\right]\left[\begin{array}{cc}{2K}_e^{\left(m\right)}& K_e^{\left(m\right)}\\ K_e^{\left(m\right)}& {2K}_e^{\left(m\right)}\end{array}\right]\left[\begin{array}{c}{\left[f_i^{\left(m\right)}\right]}^T\\ {\left[f_j^{\left(m\right)}\right]}^T\end{array}\right]\right)---\left(1\right)$

In formula, δ_sFor the story drift of s layer, Q_sFor acting on the virtual couple of s layer, N is number of components, L^(m)For component The length of m, N is component number,It is vectorial for the nodal force in design load operating mode lower member m node i,For in design The nodal force vector of load case lower member m node j,For virtual load operating mode lower member m node i nodal force to Amount,It is vectorial for the nodal force at virtual load operating mode lower member m node j,For the diagonal angle stiffness matrix of component m, right On linea angulata, element is followed successively by, 1/EA, 1/GA_Y、1/GA_Z、1/GI_X、1/EI_YAnd 1/EI_Z, A is member section area, A_YAnd A_ZFor dividing Wei be along the section of shear of y-axis and z-axis, I_X、I_YAnd I_ZBeing respectively the cross sectional moment of inertia around x-axis, y-axis and z-axis, E is construction material Elastic modelling quantity, G is the modulus of shearing of construction material.

When calculating story drift, the floor chosen between adjacent twice semi-girder truss is key-course, the maximum of key-course Story drift is the maximum story drift of structure.The maximum story drift of a certain floor is the relative storey displacement at control point Angle, described control point is positioned on floor Core Walls Structure angle point and exterior frame column node.

The story drift of structure need to be less than limit value [δ], according to existing " Concrete Structures of Tall Building technical specification " (JGJ3-2010), maximum under the wind action of frequently occurred earthquake or fundamental wind pressure for the super-high building structure more than 250m Story drift need to be less than 1/500.Therefore need to meet formula (2):

${\mathrm{\δ}}_s=\frac{L^{\left(m\right)}}{6Q_s}\underset{m=1}{\overset{N}{\mathrm{\Σ}}}\left(\left[F_i^{\left(m\right)}{F}_j^{\left(m\right)}\right]\left[\begin{array}{cc}{2K}_e^{\left(m\right)}& K_e^{\left(m\right)}\\ K_e^{\left(m\right)}& {2K}_e^{\left(m\right)}\end{array}\right]\left[\begin{array}{c}{\left[f_i^{\left(m\right)}\right]}^T\\ {\left[f_j^{\left(m\right)}\right]}^T\end{array}\right]\right)\≤\left[\mathrm{\δ}\right]---\left(2\right)$

Dimensionally-optimised with the cycle for the boom truss component of constraint, the relation in optimized variable and cycle need to be set up, this relation The principle of virtual work can be passed through and Rayleigh method realizes.

w²=φ^TKφ/φ^TM φ=φ^TF/φ^TM φ=W/ φ^TM φ=4 π²/T² (3)

By mode normalization, formula (4) can be obtained:

w²=4 π²/T²=φ^TF/φ^TM φ=φ^TF=W (4)

Under modal forces effect, external work is equal to internal strength, can try to achieve formula (5):

$W=L^{\left(m\right)}\underset{m=1}{\overset{N}{\mathrm{\Σ}}}\left(\left[F_i^{\left(m\right)}{F}_j^{\left(m\right)}\right]\left[\begin{array}{cc}{2K}_e^{\left(m\right)}& K_e^{\left(m\right)}\\ K_e^{\left(m\right)}& {2K}_e^{\left(m\right)}\end{array}\right]\left[\begin{array}{c}{\left[F_i^{\left(m\right)}\right]}^T\\ {\left[F_j^{\left(m\right)}\right]}^T\end{array}\right]\right)=w^2---\left(5\right)$

In formula, W is modal forces work,It is vectorial for the nodal force in modal forces operating mode lower member m node i,For At the nodal force vector of modal forces operating mode lower member m node j, K is structure Bulk stiffness matrix, and M is structure total quality matrix, W is Structural Eigenvalue, and T is the first natural vibration period of structure.

In the iterative process of each circulation, it is believed that the quality of structure and the internal force of component temporarily keep constant.For Reduction natural vibration period, it is necessary to increase the rigidity of structure, i.e. increase the sectional dimension of component, this is also equivalent to reduce structure Strain energy W.So, the constraints of free vibration period of structure is converted into the constraints of strain energy, as shown in formula (6):

$W=L^{\left(m\right)}\underset{m=1}{\overset{N}{\mathrm{\Σ}}}\left(\left[F_i^{\left(m\right)}{F}_j^{\left(m\right)}\right]\left[\begin{array}{cc}{2K}_e^{\left(m\right)}& K_e^{\left(m\right)}\\ K_e^{\left(m\right)}& {2K}_e^{\left(m\right)}\end{array}\right]\left[\begin{array}{c}{\left[F_i^{\left(m\right)}\right]}^T\\ {\left[F_j^{\left(m\right)}\right]}^T\end{array}\right]\right)\≤W^U---\left(6\right)$

In formula, W^U=(T^U/T⁰)²W⁰=4 π²(T^U/T⁰)²/(T⁰)², T⁰And T^UFor structure initial first natural vibration period and target Cycle, W⁰Strain energy for initial configuration.

When the 4th, calculating the story drift of a certain layer by the principle of virtual work, virtual operating mode need to be applied to this layer, extract void respectively Intend the internal force of operating mode and design load operating mode lower member, calculate this layer of story drift by formula (1).Due to high-rise building component Numerous, the virtual work calculating all components is computationally intensive.In each circulation that component optimizes, it is believed that the internal force of component is temporary transient Keep constant.Due to the sectional dimension change of only boom truss component in circulation, therefore the virtual work of only semi-girder truss is sent out Give birth to change.Therefore, the external member of semi-girder truss virtual work and for story drift under design load operating mode for this layer with stretch The difference of arm trussmember virtual work.For this layer of story drift limit value, semi-girder truss need to meet the constraint bar of formula (7)～(8) Part:

δ_s=W_Acti+W_Inacti≤[δ] (7)

$W_{\mathrm{Acti}}\≤\left[\mathrm{\δ}\right]-({\mathrm{\δ}}_s^0-W_{\mathrm{Acti}}^0)---\left(8\right)$

In formula, W_ActiFor virtual work under virtual operating mode effect for the boom truss component, W_InactiFor semi-girder truss with external member Virtual work under virtual operating mode effect and δ⁰For optimizing front story drift under design conditions effect for the floor,For optimizing Virtual work under virtual operating mode effect for the lead arm trussmember.

5th, when with the first natural vibration period of structure for constraints, the internal force of modal forces effect lower member need to be extracted, by terms of Calculate the virtual work under modal forces effect.Owing to assuming in cyclic process that internal force is constant, the only cross section of semi-girder truss changes, because of This, the only virtual work of semi-girder truss there occurs change.For all duration value of structure, semi-girder truss need to meet formula (9)～(10) Constraints:

w²=W_Acti+W_Inacti≤W^U (9)

$W_{\mathrm{Acti}}\≤W^U-({\left(w^0\right)}^2-W_{\mathrm{Acti}}^0)---\left(10\right)$

In formula, W_ActiFor virtual work under modal forces operating mode effect for the boom truss component and W_InactiFor non-semi-girder truss structure Virtual work under modal forces operating mode effect for the part and w⁰For optimizing the characteristic value of front corresponding first natural vibration period,Before optimizing Boom truss component virtual work under modal forces operating mode effect.

6th, the dimensionally-optimised target of boom truss component is that semi-girder truss volume is minimum, and semi-girder truss volume can be cut by component Face area and length represent, as shown in formula (11):

$V=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{L}_i{A}_i---\left(11\right)$

7th, on the basis of establishing optimized variable with semi-girder volume and constraint conditional relationship, Sequential Quadratic Programming method is used Carry out the optimization of scantling, and design semi-girder truss with the scantling after optimizing, can reach the few advantage of material usage.Sequence One of row quadratic programming maximally effective algorithm being to solve for general nonlinearity optimization problem.Its basic thought is: change each Ride instead of walk and established the descent direction of design variable by solving a quadratic programming subproblem, obtain step to reduce object function Long, repeat these steps until desired value difference is less than required precision.Sequential Quadratic Programming method is ripe optimized algorithm, some Programming software exists compiling complete program, can directly quote.The present invention solves the sequence of multiple constraint nonlinear problem Shown in the Mathematical Modeling of row quadratic programming such as formula (12):

Min V (X)=(x₁, x₂... x_n)

Find X=(x₁, x₂... x_n)^T∈Rⁿ (12)

δ (X)=g_δ(x₁, x₂... x_n)≤[δ]

T (X)=g_T(x₁, x₂... x_n)≤T

In formula, V is that the volume of boom truss component is with x is the optimized variable of boom truss component；δ is structure sheaf meta Moving angle value, T is the first natural vibration period of structure, can be set up the relation with x by formula (1) and formula (5) respectively.

Choosing certain building function is to integrate the comprehensive high-rise building in business, office and hotel；Structure height 600m, totally 140 layers, whole building is close to circular arrangement, and architectural plane is along height indentation；Employing mega-frame-annulus truss-stretch Arm truss-core wall structure system；High building arranges 5 road semi-girder truss along height, and (1st～2 district and 8～9 district's boundarys, truss is single Direction；5～6,6～7 and 7～8 district's boundarys, truss is twocouese) and 9 road annulus truss (1～9 district's boundary) with 9 road rings Band truss is boundary, and along height, high building is divided into 9 districts, and 1st district includes 1～12 floor, and 2nd district include 13～28 floor, and 3rd district include 29～44 Layer, 4th district include 45～60 floor, and 5th district include 61～76 floor, and 6th district include 77～92 floor, and 7th district include 93～107 floor, and 8th district include 108～123 layers, 9th district include 124～138 floor.Semi-girder truss along height distribution and numbering as shown in Figure 2.This case initial Maximum story drift occurs at 116 layers, is 1/523；Initial first natural vibration period is 9.52s.The target of this case is: adjust Boom truss component sectional dimension, makes semi-girder truss be less than 9.50s's at satisfied maximum story drift less than the 1/500th, the cycle Under the conditions of material usage minimum.Optimized variable is semi-girder truss cross section height t₃, limiting value for sectional dimension such as table 1 institute during optimization Show.

Table 1

The process that case is implemented is as follows:

1) respectively 1～No. 5 boom truss component is set as group, per pass semi-girder truss press top boom, lower boom, diagonal web member and In shear wall, rod member is grouped.The initial cross-section of boom truss component is as shown in table 2.

Table 2

2) execute virtual operating mode to floor, run FEM model, extract each layer relative storey displacement and floor floor height, calculate each building The story drift of layer.

4) design conditions, the internal force of boom truss component under modal forces operating mode and each virtual operating mode effect, meter are extracted respectively Calculate virtual work under design conditions and modal forces operating mode for the semi-girder truss.Set up optimized variable and layer according to formula (8) and (10) respectively Between angle of displacement constraint and the relation of cycle constraint.

5) extract the length of boom truss component from FEM model, formula (11) is set up design variable and semi-girder joist body Relation between Ji.

6) relation based on optimized variable and constraints and semi-girder volume, utilizes Sequential Quadratic Programming method to be optimized change The optimization of amount.

Present case boom truss component size has been carried out 8 take turns circulation thickness, semi-girder Volume Changes meet required precision, follow Result output during ring is as shown in table 3～table 14 and shown in Fig. 3～6.Wherein, table 3 is initially high for boom truss component M (), table 4 is that the 1st to take turns circulation boom truss component high (m), and table 5 is that the 2nd to take turns circulation boom truss component high (m), and table 6 is the 3rd Wheel circulation boom truss component is high (m), and table 7 is that the 4th to take turns circulation boom truss component high (m), and table 8 is the 5th to take turns circulation semi-girder purlin Frame member high (m), table 9 is that the 6th to take turns circulation boom truss component high (m), and table 10 is that the 7th to take turns circulation boom truss component high (m), Table 11 is that the 8th to take turns circulation boom truss component high (m), and table 12 is the change of key-course x direction story drift, and table 13 is key-course The story drift change of y direction, table 14 is the first natural vibration period of structure and semi-girder truss Volume Changes.

Table 3

Table 4

Table 5

Table 6

Table 7

Table 8

Table 9

Table 10

Table 11

Table 12

Note: iteration step 0 represents that structure is in original state.

Table 13

Table 14

From table 12 and table 13, x direction and y direction story drift are not up to limit value, from table 14, structure first Natural vibration period reaches limit value, and therefore the Optimum cross section size of semi-girder truss is by cycle constraint control.The volume of semi-girder truss reduces 153.159m³, steel density is 7.85t/m³, semi-girder truss steel using amount reduces 1202t.

Claims (3)

1. a high-rise building boom truss component cross-sectional size optimization method, it is characterised in that comprise the steps:

1) high-rise building is divided along short transverse in units of district, the semi-girder truss arranging in each district is set to multiple excellent Change group, the sectional dimension of the inner member of each group is identical；

2) selected optimized variable in each group；

3) with story drift as constraints, setting up optimized variable and the relation of story drift constraint, this relation can be passed through The principle of virtual work realizes, expression is:

${\mathrm{\δ}}_s=\frac{L^{\left(m\right)}}{6Q_s}\underset{m=1}{\overset{N}{\Σ}}\left(\left[\begin{array}{cc}{F}_i^{\left(m\right)}& F_j^{\left(m\right)}\end{array}\right]\left[\begin{array}{cc}2K_e^{\left(m\right)}& K_e^{\left(m\right)}\\ K_e^{\left(m\right)}& 2K_e^{\left(m\right)}\end{array}\right]\left[\begin{array}{c}{\[f_i^{\left(m\right)}\]}^T\\ {\[f_j^{\left(m\right)}\]}^T\end{array}\right]\right)\≤\[\mathrm{\δ}\]$

In formula, δ_sFor the story drift of s layer, Q_sFor acting on the virtual couple of s layer, N is number of components, L^(m)For component m's Length,It is vectorial for the nodal force in design load operating mode lower member m node i,For at design load operating mode lower member m The nodal force vector of node j,It is vectorial for the nodal force in virtual load operating mode lower member m node i,For virtual lotus Carry the nodal force vector of operating mode lower member m node j,For the diagonal angle stiffness matrix of component m, on diagonal, element is followed successively by, 1/EA、1/GA_Y、1/GA_Z、1/GI_X、1/EI_YAnd 1/EI_Z, A is member section area, A_YAnd A_ZFor respectively along y-axis and z-axis The section of shear, I_X、I_YAnd I_ZBeing respectively the cross sectional moment of inertia around x-axis, y-axis and z-axis, E is the elastic modelling quantity of construction material, and G is structure The modulus of shearing of part material, [δ] is the story drift limit value of structure；

With the first natural vibration period of structure as constraints, setting up the relation of optimized variable and cycle constraint, this relation can be by void Work(principle and Rayleigh method realize, particularly as follows:

$W=L^{\left(m\right)}\underset{m=1}{\overset{N}{\Σ}}\left(\left[\begin{array}{cc}{F}_i^{\left(m\right)}& F_j^{\left(m\right)}\end{array}\right]\left[\begin{array}{cc}2K_e^{\left(m\right)}& K_e^{\left(m\right)}\\ K_e^{\left(m\right)}& 2K_e^{\left(m\right)}\end{array}\right]\left[\begin{array}{c}{\[F_i^{\left(m\right)}\]}^T\\ {\[F_j^{\left(m\right)}\]}^T\end{array}\right]\right)=w^2\≤W^U$

In formula, W is modal forces work, and w is Structural Eigenvalue, W^U=(T^U/T⁰)²W⁰=4 π²(T^U/T⁰)²/(T⁰)², T⁰And T^UFor Structure initial first natural vibration period and target period, W⁰Strain energy for initial configuration；

4) the dimensionally-optimised object function of boom truss component is set up with semi-girder truss volume minimum, particularly as follows:

$\begin{array}{cc}Min& V=\underset{i=1}{\overset{N}{\Σ}}{L}_i{A}_i\end{array}$

In formula, A_iAnd L_iIt is respectively area of section and the length of component i；

5) according to step 3) constraints and step 4) object function, use Sequential Quadratic Programming method carry out scantling Optimize, it is thus achieved that optimum boom truss component sectional dimension.

2. a kind of high-rise building boom truss component cross-sectional size optimization method according to claim 1, its feature exists In described step 3) in, when calculating story drift, the floor chosen between adjacent twice semi-girder truss is key-course, control The maximum story drift of preparative layer is the maximum story drift of structure.

3. a kind of high-rise building boom truss component cross-sectional size optimization method according to claim 2, its feature exists In the maximum story drift of a certain floor is the story drift at control point, and described control point is positioned at floor Core Walls Structure angle On point and exterior frame column node.