CN106372324A - Structural seismic sensitivity optimizing method based on seismic shear coefficient constraint - Google Patents

Abstract

The invention relates to a structural seismic sensitivity optimizing method based on seismic shear coefficient constraint. The structural seismic sensitivity optimizing method comprises the steps: (1) setting a lateral resistant component into multiple optimization groups; (2) carrying out modal analysis, determining a modal number required to be considered by analysis, calculating each modal amplitude, and extracting a bottom modal shear force; (3) carrying out response spectrum analysis, thus obtaining a bottom shear force; (4) respectively applying virtual unit horizontal forces defined as a working situation 1, ... and a working situation M (M is the total number of floors) to all floors; (5) calculating a sensitivity coefficient of the volume of each component or the material cost of each component on a seismic shear coefficient; (6) carrying out volume weighted average on all optimization groups, thus obtaining the sensitivity coefficient of all optimization groups on the seismic shear coefficient; (7) increasing the volume of each component in the optimization groups with large sensitivity coefficients, and reducing the volume of the components with small sensitivity coefficients. Compared with the prior art, the structural seismic sensitivity optimizing method disclosed by the invention has the advantages of cost saving and the like.

Description

Structural seismic sensitivity optimization method based on seismic shear restricted coefficients of equation

Technical field

The present invention relates to technical field of structural engineering, especially relate to a kind of structure based on seismic shear restricted coefficients of equation and resist Shake sensitivity optimization method.

Background technology

Raising due to the demand of Economization on land, the development of high-strength light material, technique of design and construction in urban construction And people are for the serious hope of superelevation landmark, high-rise building more and more occurs.The super-high building structure cycle Partially long, little with the counted geological process of mode-shape decomposition response spectrum, lead to seismic shear coefficient to be difficult to meet the requirement of specification.

The super-high building structure scale of construction is huge, long construction period, and structural cost is high and the fund period of investment return is long.Relevant house is made Valency as shown by data, structural cost accounts for 25% about that peace total cost is built in house, and its ratio is in close relations with building height.To superelevation For layer building, structural cost ratio may be up to 30%-35%.Carry out structure optimization and can save structural cost, lift structure warp Ji property.Structure design personnel generally utilize concept and the engineering experience of conventional structure, manually adjust tentative calculation repeatedly, this process is time-consuming Arduously, generally also cannot get optimal solution.By the rational reallocation to material of sensitivity analyses result, not only can subtract Few material usage, lift structure economy is moreover it is possible to improve the overall performance of structure.

Sensitivity coefficient is an important parameter in structure optimization, represents the sensitivity with regard to optimized variable for the constraints. Constraints is the structural earthquake coefficient of shear, and when optimized variable is component volume, sensitivity coefficient represents that component volume change is right The impact of the structural earthquake coefficient of shear.Increase the scantling sensitive to the earthquake coefficient of shear, reduce to the earthquake coefficient of shear not Sensitive scantling, can reasonable redistribution material, meet the constraints of the earthquake coefficient of shear using minimum component volume.

Mostly super high rise structure is Steel-concrete Composite, and its cost of different materials differs greatly, and with structural volume is Optimized variable not necessarily obtains the optimum result of structural cost.Available sensitivity coefficient represents the structural earthquake coefficient of shear with regard to structure The sensitivity of part material cost.Increase the scantling sensitive to the earthquake coefficient of shear, reduce unwise to the earthquake coefficient of shear Sense scantling, can reasonable redistribution material, meet the constraints of the earthquake coefficient of shear using minimum structural cost.

The static(al) operating mode lower member volume such as equivalent static wind load can be set with general to the sensitivity of story drift at present Meter software is analyzed, but rarely has the sensitivity to constraintss such as story drift, seismic shear coefficients for the geological process lower member Journal of Sex Research.Dynamic performances method lower member volume, construction material cost are to the sensitivity analyses of the earthquake coefficient of shear relatively For numerous and diverse, need to consider earthquake load effects combination.

Content of the invention

The purpose of the present invention is exactly to overcome the defect of above-mentioned prior art presence to provide one kind to be based on seismic shear The structural seismic sensitivity optimization method of restricted coefficients of equation, obtains structure lateral resistant member volume under dynamic performances method Change or structure lateral resistant member change the impact to the earthquake coefficient of shear by the material cost that change in volume causes, and to difference Type component, same type different cross section component are compared.In further optimization process, can be tied according to sensitivity analyses Fruit carries out redistribution to structural material, under the conditions of being met seismic shear restricted coefficients of equation with structural volume or structural cost is The Optimal Distribution of each construction material of structure of optimization aim.The present invention is applied to any structure, is particularly well-suited to optimize space relatively Big super-high building structure.

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

A kind of structural seismic sensitivity optimization method based on seismic shear restricted coefficients of equation, including step:

1) lateral resistant member each in high-rise building is set to multiple optimization groups, and extracts each component in each optimization group Sectional dimension and material behavior；

2) carry out model analyses, determine that analysis needs the mode number n considering, calculate each order mode state amplitude λ_j(j=1, 2 ..., n), extract bottom mode shearing f_j(j=1,2 ..., n)；

3) carry out spectrum method, extract bottom shearing f；

4) apply virtual unit level power respectively in all floors and be defined as operating mode 1～operating mode m (m is floor sum)；

5) calculate the sensitivity coefficient to the earthquake coefficient of shear for each component volume:

sc^k=g₁ ^k(ω)+g₂ ^k(φ)

In formula, sc^kFor the sensitivity coefficient to the earthquake coefficient of shear for the component k volume, g₁ ^k(ω) it is component k volume to earthquake The periodic term of the sensitivity coefficient of the coefficient of shear, g₂ ^k(φ) it is component k volume shaking to the sensitivity coefficient of the earthquake coefficient of shear Type item.

Or the calculating sensitivity coefficient to the earthquake coefficient of shear for each construction material cost:

${\left({\mathrm{sc}}^k\right)}_{cost}=\frac{{\mathrm{sc}}^k}{c^k}$

In formula, (sc^k)_costFor the sensitivity coefficient to the earthquake coefficient of shear for the component k material cost, c^kUnit for component k Volume material cost；

6) each component sensitivity coefficient in each optimization group is made with the weighted average of volume, obtains each optimization group and earthquake is cut The sensitivity coefficient of force coefficient；

7) sensitivity coefficient according to each optimization group optimizes the volume of each component, specifically, it is big to increase sensitivity coefficient Each component volume in optimization group, reduces each component volume in the little optimization group of sensitivity coefficient.

Described step 1) in optimization group set the condition of process as:

A) different classes of component is set as different groups；

B) same category but the different component of sectional dimension is set as different groups；

C) same category, sectional dimension identical but in further optimization process its sectional dimension the structure of difference occurs Part is set as different groups.

Described step 5) specifically include step:

51) extract each component internal force of j first order mode under mode operating mode, and each component internal force under virtual unit level power, Obtain each component volume to the sensitivity coefficient periodic term of the earthquake coefficient of shear and vibration shape item；

52) each component volume is sued for peace and obtained each component to the sensitivity coefficient periodic term of the earthquake coefficient of shear, vibration shape item The sensitivity coefficient to the earthquake coefficient of shear for the volume；

53) each component volume, to the sensitivity coefficient of the earthquake coefficient of shear divided by this component unit volume material cost, obtains To the sensitivity coefficient to the earthquake coefficient of shear for each construction material cost.

Under srss modal combination rule, component volume to the sensitivity coefficient periodic term of the earthquake coefficient of shear particularly as follows:

${c_1}^k\left(\mathrm{\ω}\right)=\frac{1}{g}\·\underset{j=1}{\overset{n}{\σ}}\{\frac{f_j}{f}\·(-\frac{\mathrm{\π}}{{\mathrm{\ω}}_j^3}\·\frac{{\mathrm{da}}_j}{dt})\·\[\frac{\∂e_{w_j}^k}{\∂v^k}-2{\mathrm{\ω}}_j^2\·\underset{i=1}{\overset{m}{\σ}}(m_i{x}_{ji}\·\frac{\∂e_{x_{ji}}^k}{\∂v^k})\]\·{\mathrm{\γ}}_j^2\}$

In formula, g is structure representative value of gravity load, and j numbers for mode, and n is the mode sum considering, f is corresponding to water The bottom shearing of flat characteristic value of earthquake action, f_jFor bottom shearing j rank modal components, ω_jFor j rank circular frequency, a_jFor the j rank cycle Corresponding aseisimc design acceleration, t is structural cycle, w_jThe virtual work done in j first order mode by j rank modal forces,For component k pair Answer w_jInternal force virtual work, v^kFor the volume of component k, i is floor number, and m is floor sum, m_iFor i-th layer of concentration matter of floor Amount, x_jiFor the horizontal relative displacement in x direction for the j first order mode i layer barycenter,Correspond to h for component k_i·x_jiInternal force virtual work, h_i·x_jiFor i layer virtual unit level power h_iThe virtual work done in j first order mode, γ_jParticipate in coefficient for j first order mode.

Under cqc modal combination rule, component volume to the sensitivity coefficient periodic term of the earthquake coefficient of shear particularly as follows:

${c_1}^k\left(\mathrm{\ω}\right)=\frac{1}{g}\·\underset{j=1}{\overset{n}{\σ}}\{\frac{\underset{n=1}{\overset{n}{\σ}}\left({\mathrm{\ρ}}_{jn}{f}_n\right)}{f}\·(-\frac{\mathrm{\π}}{{\mathrm{\ω}}_j^3}\·\frac{{\mathrm{da}}_j}{dt})\·\[\frac{\∂e_{w_j}^k}{\∂v^k}-2{\mathrm{\ω}}_j^2\·\underset{i=1}{\overset{m}{\σ}}(m_i{x}_{ji}\·\frac{\∂e_{x_{ji}}^k}{\∂v^k})\]\·{\mathrm{\γ}}_j^2\}$

In formula, ρ_jnFor mode correlation coefficient, f_nFor bottom shearing n rank modal components.

Under srss modal combination rule, component volume to the sensitivity coefficient vibration shape item of the earthquake coefficient of shear particularly as follows:

$g_2^k\left(\mathrm{\φ}\right)=\frac{1}{g}\·\underset{j=1}{\overset{n}{\σ}}\{\frac{f_j}{f}\·\underset{i=1}{\overset{m}{\σ}}\[m_i\·(1-{\mathrm{\γ}}_j{x}_{ji})\·\frac{\∂e_{x_{ji}}^k}{\∂v^k}\]\·2a_j{\mathrm{\γ}}_j\}$

In formula, g is structure representative value of gravity load, and j numbers for mode, and n is the mode sum considering, f is corresponding to water The bottom shearing of flat characteristic value of earthquake action, f_jFor bottom shearing j rank modal components, i is floor number, and m is floor sum, m_i For i-th layer of lumped mass of floor, γ_jParticipate in coefficient, x for j first order mode_jiFor the level phase in x direction for the j first order mode i layer barycenter To displacement,Correspond to h for component k_i·x_jiInternal force virtual work, h_i·x_jiFor i layer virtual unit level power h_iDone in j first order mode Virtual work, v^kFor the volume of component k, a_jFor j rank cycle corresponding aseisimc design acceleration.

Under cqc modal combination rule, component volume to the sensitivity coefficient vibration shape item of the earthquake coefficient of shear particularly as follows:

$g_2\left(\mathrm{\φ}\right)=\frac{1}{g}\·\underset{j=1}{\overset{n}{\σ}}\{\frac{\underset{n=1}{\overset{n}{\σ}}\left({\mathrm{\ρ}}_{jn}{f}_n\right)}{f}\·\underset{i=1}{\overset{m}{\σ}}\[m_i\·(1-{\mathrm{\γ}}_j{x}_{ji})\·\frac{\∂e_{x_{ji}}^k}{\∂v^k}\]\·2a_j{\mathrm{\γ}}_j\}$

In formula, ρ_jnFor mode correlation coefficient, f_nFor bottom shearing n rank modal components.

When component k is frame unit, component k corresponds to w_jInternal force virtual work particularly as follows:

$e_{w_j}^k=\underset{0}{\overset{l^k}{\&integral;}}(\frac{{\left(f_{{\mathrm{\φ}}_{j}x}^k\right)}^2}{{\mathrm{ea}}_x}+\frac{{\left(f_{{\mathrm{\φ}}_{j}y}^k\right)}^2}{{\mathrm{ga}}_y}+\frac{{\left(f_{{\mathrm{\φ}}_{j}z}^k\right)}^2}{{\mathrm{ga}}_z}+\frac{\left(m_{{\mathrm{\φ}}_{j}x}^k\right)}{{\mathrm{gi}}_x}+\frac{{\left(m_{{\mathrm{\φ}}_{j}y}^k\right)}^2}{{\mathrm{ei}}_y}+\frac{{\left(m_{{\mathrm{\φ}}_{j}z}^k\right)}^2}{{\mathrm{ei}}_z})dx$

In formula, l^kFor the length of component k, e is elastic modelling quantity, and g is modulus of shearing, a_xFor axially loaded area, a_yFor y to The section of shear, a_zFor z to the section of shear, i_xFor torsional moment of inertia, i_yFor y to bending the moment of inertia, i_zFor z to bending the moment of inertia,Mode internal force for component k.

When component k is shell unit, component k corresponds to w_jInternal force virtual work particularly as follows:

$\begin{array}{c}{e}_{w_j}^k=\underset{0}{\overset{h^k}{\&integral;}}\underset{0}{\overset{d^k}{\&integral;}}\{\frac{1}{e}\[\frac{{\left(f_{{\mathrm{\φ}}_{j}11}^k\right)}^2}{b}+\frac{{\left(f_{{\mathrm{\φ}}_{j}22}^k\right)}^2}{b}+\frac{12{\left(m_{{\mathrm{\φ}}_{j}11}^k\right)}^2}{b^3}+\frac{12{\left(m_{{\mathrm{\φ}}_{j}22}^k\right)}^2}{b^3}-v\frac{2f_{{\mathrm{\φ}}_{j}11}^k{f}_{{\mathrm{\φ}}_{j}22}^k}{b}-v\frac{24m_{{\mathrm{\φ}}_{j}11}^k{m}_{{\mathrm{\φ}}_{j}22}^k}{b^3}\]\\ +\frac{1}{g}\[\frac{{\left(f_{{\mathrm{\φ}}_{j}12}^k\right)}^2}{b}+\frac{12{\left(m_{{\mathrm{\φ}}_{j}12}^k\right)}^2}{b^3}\]+\frac{6}{5g}\[\frac{{\left(v_{{\mathrm{\φ}}_{j}23}^k\right)}^2+{\left(v_{{\mathrm{\φ}}_{j}13}^k\right)}^2}{b}\]\}{\mathrm{dx}}_1{\mathrm{dx}}_2\end{array}$

In formula, h^k、d^k, b be respectively the height of component k, width, thickness, ν is material Poisson's ratio, Mode internal force for component k.

When component k is frame unit, component k corresponds to h_i·x_jiInternal force virtual work be specially (h_i·x_jiFor the virtual list of i layer Position horizontal force h_iThe virtual work done in j first order mode):

$e_{x_{ji}}^k=\underset{0}{\overset{l^k}{\&integral;}}(\frac{f_{{\mathrm{\φ}}_{j}x}^k{f}_{h_{i}x}^k}{{\mathrm{ea}}_x}+\frac{f_{{\mathrm{\φ}}_{j}y}^k{f}_{h_{i}y}^k}{{\mathrm{ga}}_y}+\frac{f_{{\mathrm{\φ}}_{j}z}^k{f}_{h_{i}z}^k}{{\mathrm{ga}}_z}+\frac{m_{{\mathrm{\φ}}_{j}x}^k{m}_{h_{i}x}^k}{{\mathrm{gi}}_x}+\frac{m_{{\mathrm{\φ}}_{j}y}^k{m}_{h_{i}y}^k}{{\mathrm{ei}}_y}+\frac{m_{{\mathrm{\φ}}_{j}z}^k{m}_{h_{i}z}^k}{{\mathrm{ei}}_z})dx$

In formula, l^kFor the length of component k, e is elastic modelling quantity, and g is modulus of shearing, a_xFor axially loaded area, a_yFor y to The section of shear, a_zFor z to the section of shear, i_xFor torsional moment of inertia, i_yFor y to bending the moment of inertia, i_zFor z to bending the moment of inertia,Mode internal force for component k, For internal force under i layer virtual unit level power for the component k,

When component k is shell unit, component k corresponds to h_i·x_jiInternal force virtual work be specially (h_i·x_jiFor the virtual unit of i layer Horizontal force h_iThe virtual work done in j first order mode):

$\begin{array}{c}{e}_{x_{ji}}^k=\underset{0}{\overset{h^k}{\&integral;}}\underset{0}{\overset{d^k}{\&integral;}}\{\frac{1}{e}\[\frac{f_{{\mathrm{\φ}}_{j}11}^k{f}_{h_{i}11}^k}{b}+\frac{f_{{\mathrm{\φ}}_{j}22}^k{f}_{h_{i}22}^k}{b}+\frac{12m_{{\mathrm{\φ}}_{j}11}^k{m}_{h_{i}11}^k}{b^3}+\frac{12m_{{\mathrm{\φ}}_{j}22}^k{m}_{h_{i}22}^k}{b^3}-v\frac{f_{{\mathrm{\φ}}_{j}11}^k{f}_{h_{i}22}^k}{b}\\ -v\frac{12m_{{\mathrm{\φ}}_{j}11}^k{m}_{h_{i}22}^k}{b^3}-v\frac{f_{{\mathrm{\φ}}_{j}22}^k{f}_{h_{i}11}^k}{b}-v\frac{12m_{{\mathrm{\φ}}_{j}22}^k{m}_{h_{i}11}^k}{b^2}\]+\frac{1}{g}\[\frac{f_{{\mathrm{\φ}}_{j}12}^k{f}_{h_{i}12}^k}{b}+\frac{12m_{{\mathrm{\φ}}_{j}12}^k{m}_{h_{i}12}^k}{b^3}\]\\ +\frac{6}{5g}\[\frac{v_{{\mathrm{\φ}}_{j}23}^k{v}_{h_{i}23}^k+v_{{\mathrm{\φ}}_{j}13}^k{v}_{h_{i}13}^k}{b}\]\}{\mathrm{dx}}_1{\mathrm{dx}}_2\end{array}$

In formula, h^k、d^k, b be respectively the height of component k, width, thickness, ν is material Poisson's ratio, Mode internal force for component k, For internal force under i layer virtual unit level power for the component k.

Compared with prior art, the invention has the advantages that

1) sensitivity analyses to the earthquake coefficient of shear for each component volume of structure under dynamic performances method are realized, In further optimization process, redistribution can be carried out to structural material according to sensitivity analyses result, be met seismic shear The Optimal Distribution of each construction material of the structure with structural volume as optimization aim under the conditions of restricted coefficients of equation.

2) realize structure each construction material cost under dynamic performances method the sensitivity of the earthquake coefficient of shear is divided Analysis, in further optimization process, can carry out redistribution according to sensitivity analyses result to structural material, be met earthquake The Optimal Distribution of each construction material of the structure with structural cost as optimization aim under coefficient of shear constraints.

3) by component volume or material cost, the impact to the earthquake coefficient of shear quantifies, and comparable each group component sensitivity is big Little, increase the scantling sensitive to the earthquake coefficient of shear, reduce the scantling insensitive to the earthquake coefficient of shear, can be reasonable Reallocation material, need not manually adjust tentative calculation repeatedly, waste time and energy and hardly result in optimal solution.

4) instruct optimization process using the present invention, material usage not only can be reduced, lift structure economy is moreover it is possible to improve The overall performance of structure.

Brief description

Fig. 1 is the flow chart of the present invention；

Fig. 2 is frame unit internal force of the present invention, the schematic diagram of moment of flexure；

Fig. 3 is the schematic diagram of shell unit internal force of the present invention；

Fig. 4 is the schematic diagram of shell unit moment of flexure of the present invention；

Fig. 5 is the schematic diagram that the present invention applies virtual unit level power；

Fig. 6 is the schematic diagram of embodiment of the present invention lateral resistant member；

Fig. 7 is the schematic diagram of embodiment of the present invention semi-girder truss；

Fig. 8 is the schematic diagram of embodiment of the present invention peripheral support；

Fig. 9 is the schematic diagram of embodiment of the present invention combined steel and concrete column；

Figure 10 is the schematic diagram of embodiment of the present invention shear wall；

Figure 11 is that embodiment of the present invention component unit volume illustrates to the sensitivity coefficient of the earthquake coefficient of shear；

Figure 12 is that embodiment of the present invention component unit cost illustrates to the sensitivity coefficient of the earthquake coefficient of shear；

In formula, 1, semi-girder truss, 2, shear wall, 3, combined steel and concrete column, 4, peripheral diagonal brace.

Specific embodiment

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 implemented, give detailed embodiment and specific operating process, but protection scope of the present invention be not limited to Following embodiments.

A kind of structural seismic sensitivity optimization method based on seismic shear restricted coefficients of equation, as shown in figure 1, including step:

1) lateral resistant member each in high-rise building is set to multiple optimization groups, and extracts each component in each optimization group Sectional dimension and material behavior, optimization group can be single component it is also possible to be grouped component according to following condition:

A) different classes of component is set as different groups；

B) same category but the different component of sectional dimension is set as different groups；

C) same category, sectional dimension identical but in further optimization process its sectional dimension the structure of difference occurs Part is set as different groups, and same category, sectional dimension identical component, because of component aspect constraint bar in initial designs The redundancy difference of part (as the stress ratio of steel beam column, axial compression ratio of shear wall etc.) is more or quick to the earthquake coefficient of shear Perception difference larger (before sensitivity analyses, tentatively can be judged by component present position, if position apart from each other it is believed that quick Perception difference is larger), in further optimization process, its sectional dimension is likely to occur difference, and these components are set as difference Group, such as the support of not same district, may be identical in initial designs middle section size, but due to the sensitivity to the earthquake coefficient of shear Difference, is likely to be of different sectional dimensions after optimization, specifically, the knowledge that those skilled in the art are grasped according to itself Can voluntarily judge whether same category, sectional dimension identical component can occur in sectional dimension in follow-up optimization process Difference.

2) carry out model analyses, determine that analysis needs the mode number n considering, mode number n to take accumulated quality to participate in coefficient and reaches To more than 90% front n order mode state, calculate each order mode state amplitude λ_j(j=1,2 ..., n), extract bottom mode shearing f_j(j=1, 2,…,n)；

3) carry out spectrum method, extract bottom shearing f；

4) apply virtual unit level power respectively in all floors and be defined as operating mode 1～operating mode m (m is floor sum)；

5) calculate the sensitivity coefficient to the earthquake coefficient of shear for each component volume, the Earthquake occurrence control coefficient of shear of structure is often Occur in the bottom of structure, definition bottom seismic shear coefficient:

μ=f/g (1)

In formula, μ is structure bottom seismic shear coefficient, and f is the bottom shearing corresponding to horizontal earthquake action standard value, g For structure representative value of gravity load, due to the impact to the overall representative value of gravity load of structure for the partial component stereomutation very Little it is believed that g does not change with the change in volume of structural elements.

The component k change impact to bottom seismic shear coefficient μ for the unit volume can use sensitivity coefficient to represent:

${\mathrm{sc}}^k=\frac{\∂\mathrm{\μ}}{\∂v^k}=\frac{1}{g}\·\frac{\∂f}{\∂v^k}---\left(2\right)$

In formula, sc^kFor the sensitivity coefficient to component k change in volume for the seismic shear coefficient, v^kVolume for component k.

Under srss modal combination rule, bottom shearing f is by bottom shearing j rank modal components f_jCombine and obtain:

$f=\sqrt{\underset{j=1}{\overset{n}{\σ}}{f}_j\·f_j}---\left(3\right)$

In formula, j numbers for mode, and n needs the mode sum considering, f for mode-shape decomposition response spectrum_jFor bottom shearing j Rank modal components.

Under cqc modal combination rule, bottom shearing f is calculated by following formula:

$f=\sqrt{\underset{j=1}{\overset{n}{\σ}}\underset{m=1}{\overset{n}{\σ}}{\mathrm{\ρ}}_{jm}\·f_j\·f_m}---\left(4\right)$

In formula, j, m number for mode, and n needs the mode sum considering, ρ for mode-shape decomposition response spectrum_jmRelated for mode Coefficient, f relevant with the ratio of structural damping ratio, j rank, m first order mode circular frequency_jFor bottom shearing j rank modal components, f_mCut for bottom Power m rank modal components.

Bottom shearing j rank modal components f_jCan be by j order mode state bottom shearing f_j, mode amplitude λ_jRepresent.

f_j=λ_j·f_j(5)

${\mathrm{\λ}}_j=a_j{\mathrm{\γ}}_j/{\mathrm{\ω}}_j^2---\left(6\right)$

$f_j={\mathrm{\ω}}_j^2\·\underset{i=1}{\overset{m}{\σ}}\left(m_i{x}_{ji}\right)---\left(7\right)$

In formula, λ_jFor j order mode state amplitude, f_jFor j order mode state bottom shearing, a_jAccelerate for j rank cycle corresponding aseisimc design Degree, ω_jFor j rank circular frequency, i is floor number, and m is all numbers of floor levels, m_iFor the lumped mass of the i-th floor layer, x_jiFor the j vibration shape The horizontal relative displacement in x direction for the i layer barycenter, γ_jParticipate in coefficient, when only taking x direction geological process, γ for j first order mode_jCan Represented with following formula:

In formula, y_jiFor the horizontal relative displacement in y direction for the j vibration shape i layer barycenter,For the relative torsional angle of j vibration shape i layer, r_iFor the i layer radius of gyration.

Formula (6)～formula (8) is substituted into formula (5), bottom shearing j rank modal components f_jIt is represented by

Assume that earthquake act as x direction, because partial component stereomutation affects very little on y to the vibration shape, torsion vibration mode, recognize For y_ji、Do not change with the change in volume of structural elements.For setting up the relation of component and bottom shearing, by formula (3), formula (4), formula (9) understands should set up component and j rank circular frequency ω respectively_j(j rank seismic acceleration a_jIt is j rank circular frequency ω_jLetter Number), j first order mode x_jiRelation.

By Rayleigh's principle, j rank circular frequency squareIt is represented by

${\mathrm{\ω}}_j^2={\mathrm{\φ}}_j^t{\mathrm{k\φ}}_j/{\mathrm{\φ}}_j^t{\mathrm{m\φ}}_j=w_j/{\mathrm{\φ}}_j^t{\mathrm{m\φ}}_j---\left(10\right)$

In formula, φ_jRepresent j first order mode, k is structural stiffness matrix, m is architecture quality matrix, w_jFor j rank modal forces in j rank The virtual work that the vibration shape is done, by principle of virtual work w_jIt is represented by:

$w_j=\underset{k=1}{\overset{p}{\σ}}{e}_{w_j}^k---\left(11\right)$

In formula, p represents component sum,Represent that component k corresponds to w_jInternal force virtual work, to frame unit and shell unit, Can be expressed as formula (12), formula (13):

$e_{w_j}^k=\underset{0}{\overset{l^k}{\&integral;}}(\frac{{\left(f_{{\mathrm{\φ}}_{j}x}^k\right)}^2}{{\mathrm{ea}}_x}+\frac{{\left(f_{{\mathrm{\φ}}_{j}y}^k\right)}^2}{{\mathrm{ga}}_y}+\frac{\left(f_{{\mathrm{\φ}}_{j}z}^k\right)}{{\mathrm{ga}}_z}+\frac{\left(m_{{\mathrm{\φ}}_{j}x}^k\right)}{{\mathrm{gi}}_x}+\frac{{\left(m_{{\mathrm{\φ}}_{j}y}^k\right)}^2}{{\mathrm{ei}}_y}+\frac{{\left(m_{{\mathrm{\φ}}_{j}z}^k\right)}^2}{{\mathrm{ei}}_z})dx---\left(12\right)$

In formula, l^kRepresent the length of component k, e is elastic modelling quantity, g is modulus of shearing, a_xFor axially loaded area, a_yFor y To the section of shear, a_zFor z to the section of shear, i_xFor torsional moment of inertia, i_yFor y to bending the moment of inertia, i_zFor z to bending the moment of inertia,Mode internal force for component k, the interior force direction of frame unit is as shown in Figure 2.

$\begin{array}{c}{e}_{w_j}^k=\underset{0}{\overset{h^k}{\&integral;}}\underset{0}{\overset{d^k}{\&integral;}}\{\frac{1}{e}\[\frac{{\left(f_{{\mathrm{\φ}}_{j}11}^k\right)}^2}{b}+\frac{{\left(f_{{\mathrm{\φ}}_{j}22}^k\right)}^2}{b}+\frac{12{\left(m_{{\mathrm{\φ}}_{j}11}^k\right)}^2}{b^3}+\frac{12{\left(m_{{\mathrm{\φ}}_{j}22}^k\right)}^2}{b^3}-v\frac{2f_{{\mathrm{\φ}}_{j}11}^k{f}_{{\mathrm{\φ}}_{j}22}^k}{b}-v\frac{24m_{{\mathrm{\φ}}_{j}11}^k{m}_{{\mathrm{\φ}}_{j}22}^k}{b^3}\]\\ +\frac{1}{g}\[\frac{{\left(f_{{\mathrm{\φ}}_{j}12}^k\right)}^2}{b}+\frac{12{\left(m_{{\mathrm{\φ}}_{j}12}^k\right)}^2}{b^3}\]+\frac{6}{5g}\[\frac{{\left(v_{{\mathrm{\φ}}_{j}23}^k\right)}^2+{\left(v_{{\mathrm{\φ}}_{j}13}^k\right)}^2}{b}\]\}{\mathrm{dx}}_1{\mathrm{dx}}_2\end{array}---\left(13\right)$

In formula, h^k、d^k, b be respectively the height of component k, width, thickness, ν is material Poisson's ratio, The mode internal force of component k, interior force direction such as Fig. 3 of shell unit, Shown in Fig. 4.For thin shell element, do not consider v₁₃、v₂₃The deformation causing.

When component volume minor variations, component internal force can regard constant as, and formula (12), formula (13) are considered as with regard to component The function of k volume.

By the principle of virtual work, j first order mode i layer horizontal relative displacement x_jiCan be write as:

$h_i\·x_{ji}=\underset{k=1}{\overset{p}{\σ}}{e}_{x_{ji}}^k---\left(14\right)$

In formula, h_iRepresent the virtual unit level power being added in i layer, as shown in figure 5,Correspond to h for component k_i·x_jiInterior Power virtual work.To frame unit and shell unit,Can be expressed as formula (15), formula (16):

$e_{x_{ji}}^k=\underset{0}{\overset{l^k}{\&integral;}}(\frac{f_{{\mathrm{\φ}}_{j}x}^k{f}_{h_{i}x}^k}{{\mathrm{ea}}_x}+\frac{f_{{\mathrm{\φ}}_{j}y}^k{f}_{h_{i}y}^k}{{\mathrm{ga}}_y}+\frac{f_{{\mathrm{\φ}}_{j}z}^k{f}_{h_{i}z}^k}{{\mathrm{ga}}_z}+\frac{m_{{\mathrm{\φ}}_{j}x}^k{m}_{h_{i}x}^k}{{\mathrm{gi}}_x}+\frac{m_{{\mathrm{\φ}}_{j}y}^k{m}_{h_{i}y}^k}{{\mathrm{ei}}_y}+\frac{m_{{\mathrm{\φ}}_{j}z}^k{m}_{h_{i}z}^k}{{\mathrm{ei}}_z})dx---\left(15\right)$

In formula,For component k under i layer virtual unit level power Internal force.

$\begin{array}{c}{e}_{x_{ji}}^k=\underset{0}{\overset{h^k}{\&integral;}}\underset{0}{\overset{d^k}{\&integral;}}\{\frac{1}{e}\[\frac{f_{{\mathrm{\φ}}_{j}11}^k{f}_{h_{i}11}^k}{b}+\frac{f_{{\mathrm{\φ}}_{j}22}^k{f}_{h_{i}22}^k}{b}+\frac{12m_{{\mathrm{\φ}}_{j}11}^k{m}_{h_{i}11}^k}{b^3}+\frac{12m_{{\mathrm{\φ}}_{j}22}^k{m}_{h_{i}22}^k}{b^3}-v\frac{f_{{\mathrm{\φ}}_{j}11}^k{f}_{h_{i}22}^k}{b}\\ -v\frac{12m_{{\mathrm{\φ}}_{j}11}^k{m}_{h_{i}22}^k}{b^3}-v\frac{f_{{\mathrm{\φ}}_{j}22}^k{f}_{h_{i}11}^k}{b}-v\frac{12m_{{\mathrm{\φ}}_{j}22}^k{m}_{h_{i}11}^k}{b^3}\]+\frac{1}{g}\[\frac{f_{{\mathrm{\φ}}_{j}12}^k{f}_{h_{i}12}^k}{b}+\frac{12m_{{\mathrm{\φ}}_{j}12}^k{m}_{h_{i}12}^k}{b^3}\]\\ +\frac{6}{5g}\[\frac{v_{{\mathrm{\φ}}_{j}23}^k{v}_{h_{i}23}^k+v_{{\mathrm{\φ}}_{j}13}^k{v}_{h_{i}13}^k}{b}\]\}{\mathrm{dx}}_1{\mathrm{dx}}_2\end{array}---\left(16\right)$

In formula,Virtual in i layer for component k Internal force under unit level power.

When component volume minor variations, component internal force can regard constant as, and formula (15), formula (16) are considered as with regard to component The function of k volume.

By formula (10)～formula (16), j rank circular frequency squareComponent k volume derivation is represented by:

$\frac{\∂{\mathrm{\ω}}_j^2}{\∂v^k}=\[\frac{\∂e_{w_j}^k}{\∂v^k}-2{\mathrm{\ω}}_j^2\·\underset{i=1}{\overset{m}{\σ}}(m_i{x}_{ji}\·\frac{\∂e_{x_{ji}}^k}{\∂v^k})\]/{\mathrm{\φ}}_j^t{\mathrm{m\φ}}_j---\left(17\right)$

By formula (14)～formula (16), j first order mode x_jiComponent k volume derivation is represented by:

$\frac{\∂x_{ji}}{\∂v^k}=\frac{\∂e_{x_{ji}}^k}{\∂v^k}---\left(18\right)$

It is assumed that modal mass is 1 under srss modal combination rule, the sensitivity system to bottom coefficient of shear μ for the component k volume Number sc^kCan be represented by the formula

${\mathrm{sc}}^k=\frac{1}{g}\·\frac{\∂f}{\∂v^k}=\frac{1}{g}\·\underset{j=1}{\overset{n}{\σ}}(\frac{f_j}{f}\·\frac{\∂f_j}{\∂v^k})---\left(19\right)$

$\frac{\∂f_j}{\∂v^k}=\frac{\∂a_j}{\∂v^k}\·{{\mathrm{\γ}}_j}^2+\underset{i=1}{\overset{m}{\σ}}\[m_i\·(1-{\mathrm{\γ}}_j{x}_{ji})\·\frac{\∂x_{ji}}{\∂v^k}\]\·2a_j{\mathrm{\γ}}_j---\left(20\right)$

Formula (17), (18), (20) are substituted into formula (19), sc^kIt is represented by:

sc^k=g₁(ω)+g₂(φ) (21)

$g_1\left(\mathrm{\ω}\right)=\frac{1}{g}\·\underset{j=1}{\overset{n}{\σ}}\{\frac{f_j}{f}\·(-\frac{\mathrm{\π}}{{\mathrm{\ω}}_j^3}\·\frac{{\mathrm{da}}_j}{dt})\·\[\frac{\∂e_{w_j}^k}{\∂v^k}-2{\mathrm{\ω}}_j^2\·\underset{i=1}{\overset{m}{\σ}}(m_i{x}_{ji}\·\frac{\∂e_{x_{ji}}^k}{\∂v^k})\]\·{\mathrm{\γ}}_j^2\}---\left(22\right)$

$g_2\left(\mathrm{\φ}\right)=\frac{1}{g}\·\underset{j=1}{\overset{n}{\σ}}\{\frac{f_j}{f}\·\underset{i=1}{\overset{m}{\σ}}\[m_i\·(1-{\mathrm{\γ}}_j{x}_{ji})\·\frac{\∂x_{ji}}{\∂v^k}\]\·2a_j{\mathrm{\γ}}_j\}---\left(23\right)$

In formula, sc^kFor the sensitivity coefficient to the earthquake coefficient of shear for the component k volume, g₁ ^k(ω) it is component k volume to earthquake The periodic term of the sensitivity coefficient of the coefficient of shear, g₂ ^k(φ) it is component k volume shaking to the sensitivity coefficient of the earthquake coefficient of shear Type item, t is structural cycle；

Formula (22) is periodic term in sensitivity coefficient, represents the impact to the earthquake coefficient of shear for the cyclomorphosis, and formula (23) is Vibration shape item in sensitivity coefficient, represents that the vibration shape changes the impact to the earthquake coefficient of shear.

It is assumed that modal mass is 1 under cqc modal combination rule, the sensitivity system to bottom coefficient of shear μ for the component k volume Number sc^kCan be represented by the formula:

${\mathrm{sc}}^k=\frac{1}{g}\·\frac{\∂f}{\∂v^k}=\frac{1}{g}\·\underset{j=1}{\overset{n}{\σ}}(\frac{\underset{n=1}{\overset{n}{\σ}}{\mathrm{\ρ}}_{jn}\·f_n}{f}\·\frac{\∂f_j}{\∂v^k})---\left(24\right)$

Formula (17), (18), (20) are substituted into above formula, sc^kIt is represented by:

sc^k=g₁(ω)+g₂(φ) (25)

$g_1\left(\mathrm{\ω}\right)=\frac{1}{g}\·\underset{j=1}{\overset{n}{\σ}}\{\frac{\underset{n=1}{\overset{n}{\σ}}\left({\mathrm{\ρ}}_{jn}{f}_n\right)}{f}\·(-\frac{\mathrm{\π}}{{\mathrm{\ω}}_j^3}\·\frac{{\mathrm{da}}_j}{dt})\·\[\frac{\∂e_{w_j}^k}{\∂v^k}-2{\mathrm{\ω}}_j^2\·\underset{i=1}{\overset{m}{\σ}}(m_i{x}_{ji}\·\frac{\∂e_{x_{ji}}^k}{\∂v^k})\]\·{\mathrm{\γ}}_j^2\}---\left(26\right)$

$g_2\left(\mathrm{\φ}\right)=\frac{1}{g}\·\underset{j=1}{\overset{n}{\σ}}\{\frac{\underset{n=1}{\overset{n}{\σ}}\left({\mathrm{\ρ}}_{jn}{f}_n\right)}{f}\underset{i=1}{\overset{m}{\σ}}\[m_i\·(1-{\mathrm{\γ}}_j{x}_{ji})\·\frac{\∂x_{ji}}{\∂v^k}\]\·2a_j{\mathrm{\γ}}_j\}---\left(27\right)$

Formula (26) is periodic term in sensitivity coefficient, and formula (27) is vibration shape item in sensitivity coefficient.

Component volume change can cause the change of construction material cost, the shadow to bottom coefficient of shear μ for the component k material cost Ring available sensitivity coefficient to represent:

${\left({\mathrm{sc}}^k\right)}_{cost}=\frac{\∂\mathrm{\μ}}{\∂{\mathrm{co}}^k}=\frac{\∂\mathrm{\μ}}{\∂v^k}\·\frac{\∂v^k}{\∂{\mathrm{co}}^k}=\frac{{\mathrm{sc}}^k}{c^k}---\left(28\right)$

In formula, (sc^k)_costFor the sensitivity coefficient to bottom seismic shear coefficient for the component k material cost, co^kRepresent component K material cost, c^kRepresent component k unit volume material cost, i.e. material unit price.

Based on above-mentioned derivation, design procedure 5) concrete steps:

51) extract each component internal force of j first order mode under mode operating mode, and each component internal force under virtual unit level power, Obtain each component volume to the sensitivity coefficient periodic term of the earthquake coefficient of shear and vibration shape item；

52) each component volume is sued for peace and obtained each component to the sensitivity coefficient periodic term of the earthquake coefficient of shear, vibration shape item The sensitivity coefficient to the earthquake coefficient of shear for the volume；

53) each component volume, to the sensitivity coefficient of the earthquake coefficient of shear divided by this component unit volume material cost, obtains To the sensitivity coefficient to the earthquake coefficient of shear for each construction material cost:

${\left({\mathrm{sc}}^k\right)}_{cost}=\frac{{\mathrm{sc}}^k}{c^k}$

In formula, (sc^k)_costFor the sensitivity coefficient to the earthquake coefficient of shear for the component k material cost, c^kUnit for component k Volume material cost；

6) each component sensitivity coefficient in each optimization group is made with the weighted mean of volume, obtains each optimization group to earthquake The sensitivity coefficient of the coefficient of shear；

7) sensitivity coefficient according to each optimization group optimizes the volume of each component, specifically, it is big to increase sensitivity coefficient Each component volume in optimization group, reduces each component volume in the little optimization group of sensitivity coefficient.Specifically, for different buildings Structure, the sensitivity coefficient difference calculating is larger, and sensitivity coefficient herein is big and little to be for same structure different component For.Those skilled in the art can select a variety of standards according to practical situation and be determined, for example, if optimization group a is sensitive Property coefficient absolute value sc is more than remaining optimization group sensitivity coefficient absolute value, if the sensitivity coefficient absolute value of certain optimization group is more than The 30% of sc is it is believed that sensitivity coefficient is larger；If the sensitivity coefficient absolute value of certain optimization group is less than the 30% of sc it is believed that sensitive Property coefficient is less.

Hereinafter choosing certain building function is to integrate the comprehensive high-rise building of business, office and hotel.Building Height 468m, totally 101 layers；Main Lateral Resistant System adopts Core Walls Structure-stiff steel reinforced column-overhanging arm system；Seismic fortification intensity For 7 degree, know that seismic influence coefficient maximum is 0.1147 by Seismic Safety Assessment Report, Characteristic Site Period is 0.5s, many Meeting earthquake damping ratio is 4%, seismic shear coefficient limit value 1.38%g.Result of calculation shows that x to seismic shear coefficient is 1.43%g, y are 1.42%g to seismic shear coefficient.Seismic shear coefficient meets code requirement, and y is to seismic shear coefficient more Close to Criterion restriction.

In figure 6, choose lateral resistant member: semi-girder truss 1, peripheral diagonal brace 4, combined steel and concrete column 3, shear wall 2 are carried out Optimize.

As shown in fig. 7, structure has three road semi-girder truss 1, it is arranged in 23-26 layer (semi-girder 1), 47-50 layer (semi-girder 2), 98-100 layer (semi-girder 3).Because the interior semi-girder truss 1 that buries is less on the impact of overall Lateral Resistant System, the present embodiment is only to overhanging Arm truss 1 is optimized.Overhanging arm truss 1 is divided into upper and lower chord member a, diagonal web member c, diagonal web member to prop up according to the difference of position Support d.Semi-girder truss 1 is set as 9 groups, the upper and lower chord member of 23-26 layer: o1a, 23-26 layer diagonal web member: o1c, 23-26 layer diagonal web member Support: o1d；The upper and lower chord member of 47-50 layer: o2a, 47-50 layer diagonal web member: o2c, 47-50 layer diagonal web member supports: o2d；98-100 The upper and lower chord member of layer: o3a, 98-100 layer diagonal web member: o3c, 98-100 layer diagonal web member supports: o3d.

As shown in figure 8, structure overall height arrangement herringbone rectangle tube section huge periphery diagonal brace 4, peripheral diagonal brace 4 is pressed vertical Height different set is 12 groups.

As shown in figure 9, combined steel and concrete column 3 is divided into z1 and two kinds of forms of z2 by the difference at angle of inclination, by z1, z2 respectively It is divided into 9 groups by vertical height difference.

As shown in Figure 10,2 points of abdomen walls of shear wall and aileron.Aileron is divided into 8 groups by vertical height difference, abdomen wall is pressed perpendicular It is divided into 7 groups to highly difference.

Extract mode operating mode go to the bottom story shear, component internal force when consider front 15 first order modes.

Figure 11, Figure 12 represent respectively component volume to y to the sensitivity coefficient of seismic shear coefficient, construction material cost pair Y is to the sensitivity coefficient of seismic shear coefficient.C, d represent z1, z2 of combined steel and concrete column 3 respectively；F represents Core Walls Structure aileron, w Represent Core Walls Structure abdomen wall；O represents overhanging arm truss 1；B represents peripheral diagonal brace 4.The sensitivity to the earthquake coefficient of shear for the component volume Coefficient sorts: semi-girder truss 1 > peripheral diagonal brace 4 > shear wall 2 > combined steel and concrete column 3.Consider unit volume concrete material, steel The difference of material cost, construction material cost sorts to the sensitivity coefficient of the earthquake coefficient of shear: shear wall 2 > combined steel and concrete column 3 > semi-girder truss 1 > peripheral diagonal brace 4.

With the minimum optimization aim of structural cost, should preferentially optimize to the earthquake coefficient of shear less component, optimization order: Peripheral diagonal brace 4, semi-girder truss 1, combined steel and concrete column 3, shear wall 2.

Before and after optimization, the sectional dimension of peripheral diagonal brace 4 is as shown in table 1.Through statistics, optimize peripheral diagonal brace 4 and reduce steel using amount 1306t.

Table 1

Before and after optimization, the sectional dimension of semi-girder truss 1 is as shown in table 2.Through statistics, optimize semi-girder truss 2 and reduce steel using amount 323t.

Table 2

Except the steel ratio of 1-51 layer z1 is that in addition to 6%, the steel ratio of remaining combined steel and concrete column 3 reaches 4% lower limit.Keep The steel ratio of post is constant, reduces column cross-section size.Before and after optimization, the sectional dimension of combined steel and concrete column 3 is as shown in table 3.Through system Meter, optimizes combined steel and concrete column 3 and reduces steel using amount 574t, reduce concrete 1750m³.

Table 3

Before and after optimization, the sectional dimension of shear wall 2 is as shown in table 4.Through statistics, optimize shear wall 2 and reduce concrete 2844m³.

Table 4

The present embodiment scantling is optimized, altogether Saving steel amount 2203t, concrete 4594m³, saving construction cost altogether 1285.26 ten thousand yuan, as shown in table 5.

Table 5

Note: the Freight Basis of steel using amount per ton are 5000 yuan/t, the Freight Basis of every cubic meter of concrete are 400 yuan/m³.

After optimization, y is 1.40%g to seismic shear coefficient.

Claims (7)

1. a kind of structural seismic sensitivity optimization method based on seismic shear restricted coefficients of equation is it is characterised in that include step:

1) lateral resistant member each in high-rise building is set to multiple optimization groups, and extracts each member section in each optimization group Size and material behavior；

2) carry out model analyses, determine that analysis needs the mode number n considering, calculate each order mode state amplitude λ_j, wherein, j=1, 2 ..., n, extract bottom mode shearing f_j, wherein, j=1,2 ..., n；

3) carry out spectrum method, extract bottom shearing f；

4) apply virtual unit level power in all floors；

5) calculate the sensitivity coefficient to the earthquake coefficient of shear for each component volume:

sc^k=g₁ ^k(ω)+g₂ ^k(φ)

In formula, sc^kFor the sensitivity coefficient to the earthquake coefficient of shear for the component k volume, g₁ ^k(ω) it is component k volume to seismic shear The periodic term of the sensitivity coefficient of coefficient, g₂ ^k(φ) for the vibration shape item of the sensitivity coefficient to the earthquake coefficient of shear for the component k volume,

Or the calculating sensitivity coefficient to the earthquake coefficient of shear for each construction material cost:

${\left({\mathrm{sc}}^k\right)}_{cost}=\frac{{\mathrm{sc}}^k}{c^k}$

In formula, (sc^k)_costFor the sensitivity coefficient to the earthquake coefficient of shear for the component k material cost, c^kUnit volume for component k Material cost；

6) each component sensitivity coefficient in each optimization group is made with the weighted average of volume, obtains each optimization group to seismic shear system The sensitivity coefficient of number；

7) sensitivity coefficient according to each optimization group optimizes the volume of each component, specifically, increasing the big optimization of sensitivity coefficient Each component volume in group, reduces each component volume in the little optimization group of sensitivity coefficient.

2. a kind of structural seismic sensitivity optimization method based on seismic shear restricted coefficients of equation according to claim 1, its Be characterised by, described step 1) in optimization group set the condition of process as:

A) different classes of component is set as different groups；

B) same category but the different component of sectional dimension is set as different groups；

C) same category, sectional dimension identical but in further optimization process its sectional dimension occur that the component of difference sets It is set to different groups.

3. a kind of structural seismic sensitivity optimization method based on seismic shear restricted coefficients of equation according to claim 1, its It is characterised by, described step 5) specifically include step:

51) extract each component internal force of j first order mode under mode operating mode, and each component internal force under virtual unit level power, obtain Each component volume is to the sensitivity coefficient periodic term of the earthquake coefficient of shear and vibration shape item；

52) each component volume is sued for peace and obtained each component volume to the sensitivity coefficient periodic term of the earthquake coefficient of shear, vibration shape item Sensitivity coefficient to the earthquake coefficient of shear；

53) each component volume, to the sensitivity coefficient of the earthquake coefficient of shear divided by this component unit volume material cost, obtains each The sensitivity coefficient to the earthquake coefficient of shear for the construction material cost.

4. a kind of structural seismic sensitivity optimization method based on seismic shear restricted coefficients of equation according to claim 1, its Be characterised by, under srss modal combination rule, component volume to the sensitivity coefficient periodic term of the earthquake coefficient of shear particularly as follows:

${g_1}^k\left(\mathrm{\ω}\right)=\frac{1}{g}\·\underset{j=1}{\overset{n}{\σ}}\left\{\frac{f_j}{f}\·\left(-\frac{\mathrm{\π}}{{\mathrm{\ω}}_j^3}\·\frac{{\mathrm{da}}_j}{dt}\right)\·\[\frac{\∂e_{w_j}^k}{\∂v^k}-2{\mathrm{\ω}}_j^2\·\underset{i=1}{\overset{m}{\σ}}\left(m_i{x}_{ji}\·\frac{\∂e_{x_{ji}}^k}{\∂v^k}\right)\]\·{\mathrm{\γ}}_j^2\right\}$

In formula, g is structure representative value of gravity load, and j numbers for mode, and n is the mode sum considering, f is corresponding to flatly The bottom shearing of shake characteristic value of action, f_jFor bottom shearing j rank modal components, ω_jFor j rank circular frequency, a_jCorrespond to for the j rank cycle Aseisimc design acceleration, t be structural cycle, w_jThe virtual work done in j first order mode by j rank modal forces,Correspond to w for component k_j Internal force virtual work, v^kFor the volume of component k, i is floor number, and m is floor sum, m_iFor i-th layer of lumped mass of floor, x_ji For the horizontal relative displacement in x direction for the j first order mode i layer barycenter,Correspond to h for component k_i·x_jiInternal force virtual work, h_i·x_jiFor I layer virtual unit level power h_iThe virtual work done in j first order mode, γ_jParticipate in coefficient for j first order mode,

Under cqc modal combination rule, component volume to the sensitivity coefficient periodic term of the earthquake coefficient of shear particularly as follows:

${g_1}^k\left(\mathrm{\ω}\right)=\frac{1}{g}\·\underset{j=1}{\overset{n}{\σ}}\left\{\frac{\underset{n=1}{\overset{n}{\σ}}\left({\mathrm{\ρ}}_{jn}{f}_n\right)}{f}\·\left(-\frac{\mathrm{\π}}{{\mathrm{\ω}}_j^3}\·\frac{{\mathrm{da}}_j}{dt}\right)\·\[\frac{\∂e_{w_j}^k}{\∂v^k}-2{\mathrm{\ω}}_j^2\·\underset{i=1}{\overset{m}{\σ}}\left(m_i{x}_{ji}\·\frac{\∂e_{x_{ji}}^k}{\∂v^k}\right)\]\·{\mathrm{\γ}}_j^2\right\}$

In formula, ρ_jnFor mode correlation coefficient, f_nFor bottom shearing n rank modal components.

5. a kind of structural seismic sensitivity optimization method based on seismic shear restricted coefficients of equation according to claim 1, its Be characterised by, under srss modal combination rule, component volume to the sensitivity coefficient vibration shape item of the earthquake coefficient of shear particularly as follows:

$g_2^k\left(\mathrm{\φ}\right)=\frac{1}{g}\·\underset{j=1}{\overset{n}{\σ}}\{\frac{f_j}{f}\·\underset{i=1}{\overset{m}{\σ}}\[m_i\mathrm{\δ}\·(1-{\mathrm{\γ}}_j{x}_{ji})\·\frac{\∂e_{x_{ji}}^k}{\∂v^k}\]\·2a_j{\mathrm{\γ}}_j\}$

In formula, g is structure representative value of gravity load, and j numbers for mode, and n is the mode sum considering, f is corresponding to flatly The bottom shearing of shake characteristic value of action, f_jFor bottom shearing j rank modal components, i is floor number, and m is floor sum, m_iFor building The lumped mass of i-th layer of layer, γ_jParticipate in coefficient, x for j first order mode_jiFor j first order mode i layer barycenter x direction level of relative position Move,Correspond to h for component k_i·x_jiInternal force virtual work, h_i·x_jiFor i layer virtual unit level power h_iThe void done in j first order mode Work(, v^kFor the volume of component k, a_jFor j rank cycle corresponding aseisimc design acceleration,

Under cqc modal combination rule, component volume to the sensitivity coefficient vibration shape item of the earthquake coefficient of shear particularly as follows:

$g_2\left(\mathrm{\φ}\right)=\frac{1}{g}\·\underset{j=1}{\overset{n}{\σ}}\{\frac{\underset{n=1}{\overset{n}{\σ}}\left({\mathrm{\ρ}}_{jn}{f}_n\right)}{f}\·\underset{i=1}{\overset{m}{\σ}}\[m_i\·(1-{\mathrm{\γ}}_j{x}_{ji})\·\frac{\∂e_{x_{ji}}^k}{\∂v^k}\]\·2a_j{\mathrm{\γ}}_j\}$

In formula, ρ_jnFor mode correlation coefficient, f_nFor bottom shearing n rank modal components.

6. a kind of structural seismic sensitivity optimization method based on seismic shear restricted coefficients of equation according to claim 4, its It is characterised by, when component k is frame unit, component k corresponds to w_jInternal force virtual work particularly as follows:

$e_{w_j}^k=\underset{0}{\overset{l^k}{\&integral;}}(\frac{{\left(f_{{\mathrm{\φ}}_{j}x}^k\right)}^2}{{\mathrm{ea}}_x}+\frac{{\left(f_{{\mathrm{\φ}}_{j}y}^k\right)}^2}{{\mathrm{ga}}_y}+\frac{{\left(f_{{\mathrm{\φ}}_{j}z}^k\right)}^2}{{\mathrm{ga}}_z}+\frac{{\left(m_{{\mathrm{\φ}}_{j}x}^k\right)}^2}{{\mathrm{gi}}_x}+\frac{{\left(m_{{\mathrm{\φ}}_{j}y}^k\right)}^2}{{\mathrm{gi}}_y}+\frac{{\left(m_{{\mathrm{\φ}}_{j}z}^k\right)}^2}{{\mathrm{gi}}_z})dx$

In formula, l^kFor the length of component k, e is elastic modelling quantity, and g is modulus of shearing, a_xFor axially loaded area, a_yFor y to shearing Area, a_zFor z to the section of shear, i_xFor torsional moment of inertia, i_yFor y to bending the moment of inertia, i_zFor z to bending the moment of inertia,Mode internal force for component k,

When component k is shell unit, component k corresponds to w_jInternal force virtual work particularly as follows:

$\begin{array}{c}{e}_{w_j}^k=\underset{0}{\overset{h^k}{\&integral;}}\underset{0}{\overset{d^k}{\&integral;}}\{\frac{1}{e}\[\frac{{\left(f_{{\mathrm{\φ}}_{j}11}^k\right)}^2}{b}+\frac{{\left(f_{{\mathrm{\φ}}_{j}22}^k\right)}^2}{b}+\frac{12{\left(m_{{\mathrm{\φ}}_{j}11}^k\right)}^2}{b^3}+\frac{12{\left(m_{{\mathrm{\φ}}_{j}22}^k\right)}^2}{b^3}-v\frac{2f_{{\mathrm{\φ}}_{j}11}^k{f}_{{\mathrm{\φ}}_{j}22}^k}{b}-v\frac{24m_{{\mathrm{\φ}}_{j}11}^k{m}_{{\mathrm{\φ}}_{j}22}^k}{b^3}\]\\ +\frac{1}{g}\[\frac{{\left(f_{{\mathrm{\φ}}_{j}12}^k\right)}^2}{b}+\frac{12{\left(m_{{\mathrm{\φ}}_{j}12}^k\right)}^2}{b^3}\]+\frac{6}{5g}\[\frac{{\left(v_{{\mathrm{\φ}}_{j}23}^k\right)}^2+{\left(v_{{\mathrm{\φ}}_{j}13}^k\right)}^2}{b}\]\}{\mathrm{dx}}_1{\mathrm{dx}}_2\end{array}$

In formula, h^k、d^k, b be respectively the height of component k, width, thickness, ν is material Poisson's ratio, Mode internal force for component k.

7. a kind of structural seismic sensitivity optimization method based on seismic shear restricted coefficients of equation according to claim 4 or 5, It is characterized in that, when component k is frame unit, component k corresponds to h_i·x_jiInternal force virtual work be specially (h_i·x_jiEmpty for i layer Quasi-simple position horizontal force h_iThe virtual work done in j first order mode):

$e_{x_{ji}}^k=\underset{0}{\overset{l^k}{\&integral;}}(\frac{f_{{\mathrm{\φ}}_{j}x}^k{f}_{h_{i}x}^k}{{\mathrm{ea}}_x}+\frac{f_{{\mathrm{\φ}}_{j}y}^k{f}_{h_{i}y}^k}{{\mathrm{ga}}_y}+\frac{f_{{\mathrm{\φ}}_{j}z}^k{f}_{h_{i}z}^k}{{\mathrm{ga}}_z}+\frac{m_{{\mathrm{\φ}}_{j}x}^k{m}_{h_{i}x}^k}{{\mathrm{gi}}_x}+\frac{m_{{\mathrm{\φ}}_{j}y}^k{m}_{h_{i}y}^k}{{\mathrm{ei}}_y}+\frac{m_{{\mathrm{\φ}}_{j}z}^k{m}_{h_{i}z}^k}{{\mathrm{ei}}_z})dx$

In formula, l^kFor the length of component k, e is elastic modelling quantity, and g is modulus of shearing, a_xFor axially loaded area, a_yFor y to shearing Area, a_zFor z to the section of shear, i_xFor torsional moment of inertia, i_yFor y to bending the moment of inertia, i_zFor z to bending the moment of inertia,Mode internal force for component k, For internal force under i layer virtual unit level power for the component k,

When component k is shell unit, component k corresponds to h_i·x_jiInternal force virtual work be specially (h_i·x_jiFor the virtual unit level of i layer Power h_iThe virtual work done in j first order mode):

$\begin{array}{c}{e}_{x_{ji}}^k=\underset{0}{\overset{h^k}{\&integral;}}\underset{0}{\overset{d^k}{\&integral;}}\{\frac{1}{e}\[\frac{f_{{\mathrm{\φ}}_{j}11}^k{f}_{h_{i}11}^k}{b}+\frac{f_{{\mathrm{\φ}}_{j}22}^k{f}_{h_{i}22}^k}{b}+\frac{12m_{{\mathrm{\φ}}_{j}11}^k{m}_{h_{i}11}^k}{b^3}+\frac{12m_{{\mathrm{\φ}}_{j}22}^k{m}_{h_{i}22}^k}{b^3}-v\frac{f_{{\mathrm{\φ}}_{j}11}^k{f}_{h_{i}22}^k}{b}\\ -v\frac{12m_{{\mathrm{\φ}}_{j}11}^k{m}_{h_{i}22}^k}{b^3}-v\frac{f_{{\mathrm{\φ}}_{j}22}^k{f}_{h_{i}11}^k}{b}-v\frac{12m_{{\mathrm{\φ}}_{j}22}^k{m}_{h_{i}11}^k}{b^3}\]+\frac{1}{g}\[\frac{f_{{\mathrm{\φ}}_{j}12}^k{f}_{h_{i}12}^k}{b}+\frac{12m_{{\mathrm{\φ}}_{j}12}^k{m}_{h_{i}12}^k}{b^3}\]\\ +\frac{6}{5g}\[\frac{v_{{\mathrm{\φ}}_{j}23}^k{v}_{h_{i}23}^k+v_{{\mathrm{\φ}}_{j}13}^k{v}_{h_{i}13}^k}{b}\]\}{\mathrm{dx}}_1{\mathrm{dx}}_2\end{array}$

In formula, h^k、d^k, b be respectively the height of component k, width, thickness, ν is material Poisson's ratio, Mode internal force for component k, For internal force under i layer virtual unit level power for the component k.