CN103106304A - Earthquake resistant design method based on condition spectrum harmonic function - Google Patents

Earthquake resistant design method based on condition spectrum harmonic function Download PDF

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CN103106304A
CN103106304A CN2013100360106A CN201310036010A CN103106304A CN 103106304 A CN103106304 A CN 103106304A CN 2013100360106 A CN2013100360106 A CN 2013100360106A CN 201310036010 A CN201310036010 A CN 201310036010A CN 103106304 A CN103106304 A CN 103106304A
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spectrum
condition
earthquake
condition spectrum
earthquake resistant
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刘文锋
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青岛理工大学
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Abstract

The invention belongs to the field of civil construction project engineering, and particularly relates to an earthquake resistant design method based on a condition spectrum harmonic function. The earthquake resistant design method based on the condition spectrum harmonic function comprises the following steps: 1, structuring an earthquake resistant condition spectrum harmonic function expression, 2, inputting different frequencies of harmonic functions of earthquake resistant condition spectrum harmonic function into structural motion differential equation and obtaining structural responses, and 3, solving structural seismic action effect, conducting structural time-procedure analysis and conducting combination according to a square and extraction method, a complete square combination method and a linear combination method and completing the earthquake resistant design. According to the earthquake resistant design method based on the condition spectrum harmonic function, condition spectrum input novel method and a refined performance-based earthquake resistant design novel method are offered.

Description

Seismic Design Method based on condition spectrum hamonic function
Technical field
The invention belongs to civil construction project engineering field, relate in particular to a kind of Seismic Design Method based on condition spectrum hamonic function.
Background technology
From the beginning of the nineties, after performance-based seismic design method proposes, become the advanced subject of international earthquake research.California, USA Institution of Structural Engineers stands up in 1992 year's harvest framework that a 21 century council (Vision 2000 Committee SEAOC) is intended to set up new structural behaviour design system, its research work obtains U.S.'s Natural Science Fund and adds the strong subsidy (SEAOC-VISION2000.Performance Based Seismic Engineering of Buildings.April3,1995) of state government.Emergency relief administration of the United States Federal (FEMA) and NSFC(National Natural Science Foundation of China) (NSF) also subsidize and have carried out an action plan of 6 years by a definite date, and the seismic design in future has been carried out many-sided basic research.Japan has also begun " exploitation of the new building structural system " research project in 3 years by a definite date in nineteen ninety-five under in many ways subsidizing, set up the comprehensive council of new building tectonic system that has prominent domestic scholar to participate in, divided into performance evaluation, target level and social framework three sub-committees.For advancing and coordinating this project process, also set up " Neotectonic Systems promotion meeting ", the work of the face of discussing, plan, coordinate all quarters concerned.Afterwards, the Latin American countries such as European countries, China, New Zealand, Japan, Chile also conduct in-depth research (Moehle J.P.Displacement-based Design of RC Structures.10WCEE to this problem, Mexico, 1992:1576-1574; Liu Wenfeng, king's section. based on the condition spectrum [J] of displacement target. engineering mechanics, 2012,29 (10): 75-81.)
Seismic design based on performance has been the developing direction of countries in the world earthquake resistant design code at present, and FEMAP695 (2009), FEMA440 (2005), Japan " building standard method " (2003), Eurocode 8 (2004), American Architecture and state's earthquake resistant codes such as the performance specification (2009) of facility, Chinese earthquake resistant code (2010) have all begun to adopt the seismic design based on performance.
Seismic design essence based on performance is to hold and control the elastic plastic behavior of large shake, middle shake, little shake structure.Probe into from earthquake response spectrum the importance that the structural elasto-plastic response behavior is earthquake research, also be based on the important tool of the seismic design of performance.The sixties is to the seventies, Veletos, Newmark and Hall (Newmark N M and Hall W J.Earthquake Spectra and Design[R] .Earthquake Engineering Research Institute, University of California at Berkeley, 1982; A.S.Veletos, N.M.Newmark.Effect of Inelastic Behavior on the Response of Simple Systems to Earthquake Motion, 2WCEE[M], 1960:895-912; N.M.Newmark, W.J.Hall, A Rational Approach of Seismic Design Standards for Structures, 5 thWCEE[M], 1975:2266-2277; N.M.Newmark, The trend of Seismic Analysis and Design for tall building.Earthquake Engineering[M], Beijing:Science Press.1978.) proposed to estimate the linear response spectrum of earthquake motion and the method that nonlinearity response is composed.Wang Qianxin (Wang Qianxin etc. the elastoplasticity response spectrum. earthquake engineering research report collection [R], the second collection, Beijing: Science Press, 1965.) propose Elastoplastic Aseismic Design should take maximum displacement response as according to and replenish the idea of the design of considering energy response, and suggestion consideration system when entering plasticity design acceleration should carry out reduction with the ductility factor of system.The eighties, China is comparatively active to the research of ductility spectrum and displacement comparison, and Chen Dan (old engaging. the ductility spectrum of anti-seismic structure. Tsing-Hua University's antidetonation antiknock Engineering Research Report collection [R], publishing house of Tsing-Hua University, 1980; Chen Dan.Ductility Spectra and Collapse Spectra for Earthquake Resistant Structures, Proc.7 thEuropean Conference on Earthquake Engineering[R], 1982) etc. the ductility spectrum of people's research is take ductility factor as spectral coordinate, has proposed the reflection earthquake to structural strength and ductility two aspects require and the nonlinearity response spectrum of the two mutual relationship.The beginning of the nineties, after performance-based seismic design method proposes, static analysis method becomes the main method based on the seismic design of performance, with Fajfar (Fajfar.P.and Fischinger.M.Earthquake Design Spectra Considering Duration Of Ground Motion, Proc.4 thU.S.NCEE.May, 1990, Palm, springs, Cailfornia, Vol.2,15-24; Peter.fajfar, Tomaz Vidic, Consistent Inelastic Design Spectra:Hysteretic and Input Energy, EESD, Vol.23.1994:523-537; Tolis SV and Faccioli E.Displacement Design Spectra[J] .Journal of Earthquake Engineering, Vol.3 (1) .1999:107-125; Krawinkler H, Nassar AA.Seismic design based on ductility and cumulative damage demands and capacities.In:Fajfa P, Krawinkler H, editors.Nonlinear seismic analysis and design of RC buildings.Elsevier; 1992.p.23-39.) etc. people's research typical case the most, their research employing power mostly reduces coefficient, the coefficient of performance or ductility reduction factor carry out reduction to elastic response spectrum, thereby directly obtain the elastoplasticity response spectrum.Krawinkler and Nassar (Peter.fajfar, Tomaz Vidic, Consistent Inelastic Design Spectra:Hysteretic and Input Energy, EESD, Vol.23.1994:523-537.), Jean and Loh (Jean W-Y, Loh C-H.Seismic demand for SDOF system based on structural damage control concept.In:Proceedings of the sixth East Asia-Pacific conference on structural engineering and construction, Taipei, Taiwan, 1998:1633-1638.) etc. the people ductility method such as also pass through and obtain the elastoplasticity response spectrum.The later stage nineties, Chopra (Chopra A.K, Goel R.K.Capacity-Demand-Diagram Method for Estimating Seismic Deformation of Inelastic Structures.University of California, Berkeley, Report No.PEER-1999/0,1999) improvement Capacity spectrum method is to be the elastoplasticity response spectrum with the elastic response spectrum reduction, and is converted into the form of Demand Spectra, and different ductility ratio correspondences different demand curves.2004,2009, Xu Longjun, the gift in token of gratitude are vertical, the people such as Guo Xiaoyun, Zhai Changhai (Xu Longjun, the gift in token of gratitude is vertical. two rule standardizing earthquake ground motion acceleration response spectrums researchs. earthquake engineering and Engineering Vibration, 2004,24 (2): 1-6; Guo Xiaoyun, Zhai Changhai, the gift in token of gratitude is vertical. the earthquake motion accurate velocity response spectrum research of requiring to report his or her problems within a prescribed time and in a prescribed place. and earthquake engineering and Engineering Vibration, 2009,29 (3): 9-14.) proposed two rule standardizing earthquake ground motion accelerations, velocity response spectrum, two rule standardizings have been eliminated Earthquake Intensity to the impact on shape of response spectrum of the impact of response spectrum spectrum value and predominant period, 2008,2010,2012, Liu Wenfeng, king's section, Pan Fu Xing, Chen Gonglian (Liu Wenfeng, king's section. based on the condition spectrum [J] of displacement target. engineering mechanics, 2012,29 (10): 75-81; Liu Wenfeng, Chen Gonglian. definite method [J] of For Performance Spectrum of Aseismatic Buildings. engineering mechanics, 2008,25 (2): 160-167; ] Wenfeng Liu, Xingpan Fu.Seismic Performance Spectra[J] .Advanced Materials Research 2011, Vols.163-167:443-453.) set up antidetonation condition spectrum, the condition spectrum is according to performance objective, seismologic record is input to the structure of different natural vibration periods, in three-dimensional coordinate, set up the funtcional relationship of earthquake demand (assembly average of maximum seismic acceleration) and structural cycle, elastic-plastic behavior, the measurable earthquake demand that reaches performance objective.Adopt hamonic function to express the condition spectrum, be input to the structure motion differential equation, carry out the time-history analysis of structure, complete seismic design, the world does not still exist.
Summary of the invention
In order to make up the deficiencies in the prior art, the invention provides a kind of Seismic Design Method based on condition spectrum hamonic function.
The technical solution used in the present invention is: the Seismic Design Method based on condition spectrum hamonic function comprises the following steps:
1, the structure of antidetonation condition spectrum hamonic function expression formula;
2, antidetonation condition spectrum is adopted the different frequency hamonic function, be input to respectively the structure motion differential equation, obtain structural response;
3, based on structural response, find the solution the structural earthquake action effect, carry out the time-history analysis of structure, make up according to quadratic sum extraction of square root method, fully flat method combined method and LINEAR COMBINATION METHOD, complete seismic design.
The construction method of described antidetonation condition spectrum hamonic function expression formula is:
(1), regard antidetonation condition spectrum as the target spectrum; (2), based target is composed and the transformational relation of power spectrum, by the mode that iterates, has obtained the earthquake motion trigonometric function analytical expression of condition spectrum for the target spectrum; (3), with the earthquake motion trigonometric function analytical expression substitution single dof mobility differential equation of motion of target spectrum, obtain antidetonation condition spectrum hamonic function expression formula.
Described antidetonation condition spectrum refers to the condition spectrum of elasticity or plastic stage.
Seismic Design Method based on condition spectrum hamonic function of the present invention, the new method that provides the condition spectrum to input provides the performance-based that becomes more meticulous new aseismic design method.
Description of drawings
Fig. 1 is the Seismic Design Method process flow diagram based on condition spectrum hamonic function of the present invention.
Embodiment
Embodiment 1 as shown in Figure 1, the present embodiment comprises the following steps: based on the Seismic Design Method of condition spectrum hamonic function
1, the structure of antidetonation condition spectrum hamonic function expression formula
(1) the random ground movement acceleration after adopting the trigonometric series Construction of A Model steadily:
Each component amplitude of its trigonometric series is by given power spectral density function S (ω j) try to achieve:
a j = 4 S ( ω j ) · Δω - - - ( 2 )
Δω = 2 π T ω j = 2 πj T - - - ( 3 )
In formula: when T is always holding of stochastic process a (t).
(2) countries in the world earthquake resistant code design response spectrum (comprising earthquake response spectrum) is regarded as the target spectrum, compose and the transformational relation of power spectrum by target, by the mode that iterates, obtained the earthquake motion trigonometric function analytical expression of design response spectrum (comprising earthquake response spectrum) for the target spectrum.
The transformational relation of response spectrum and power spectrum can be expressed as:
S ( ω j ) = f ( S PS T ( ω j ) ) - - - ( 4 )
In formula Be given target condition spectrum, the various ways such as transformational relation Kaul spectrum, Kanai-Tajimi and Clough-Penzien spectrum of condition spectrum and power spectrum.
By the mode that iterates, obtained the earthquake motion trigonometric function analytical expression of design response spectrum (comprising earthquake response spectrum) for the target spectrum.
(3) the trigonometric function earthquake motion of adopting the target spectrum is as input, and the single-degree-of-freedom system equation of motion is:
Wherein ξ is the damping ratio of system, and ω is the natural frequency of vibration of system, a jWith Be respectively earthquake motion incoming frequency component ω jAmplitude and phase place.
(4) solution of the equation of motion (5) is:
At starting condition x| T=0=x (0)=0, In situation, coefficient A, B, as follows respectively:
A = Σ j = 1 n a j - 2 ξ β j ( 1 - β j 2 ) 2 + ( 2 ξ β j ) 2 - - - ( 7 )
B = Σ j = 1 n a j ω j ( ( 1 - β j 2 ) - 2 ( ξω ) 2 ) ω D ( ( 1 - β j 2 ) 2 + ( 2 ξ β j ) 2 ) - - - ( 8 )
In formula: frequency ratio β j = ω j ω .
(5) the stable state absolute acceleration of elastic stage any time system is counter is:
In formula: R D = Σ j = 1 n 1 ( 1 - β j 2 ) 2 + ( 2 ξ β j ) 2 ; R V = Σ j = 1 n β j ( 1 - β j 2 ) 2 + ( 2 ξ β j ) 2 ; R A = Σ j = 1 n β 2 j ( 1 - β j 2 ) 2 + ( 2 ξ β j ) 2 ; C 1 = Σ j = 1 n - 2 ξ β j 3 ( 1 - β j 2 ) 2 + ( 2 ξ β j ) 2 ; D 1 = Σ j = 1 n 1 - β j 2 + ( 2 ξ β j ) 2 ( 1 - β j 2 ) 2 + ( 2 ξ β j ) 2 ; T R j = Σ j = 1 n 1 + ( 2 ξ β j ) 2 ( 1 - β j 2 ) 2 + ( 2 ξ β j ) 2 , ϵ ′ = Σ j = 1 n tan - 1 2 ξ β j 3 1 - β j 2 + ( 2 ξ β j ) 2 .
Take elastic stage earthquake effect factor alpha as characterizing condition spectrum parameter, antidetonation condition spectrum hamonic function expression formula:
(6) any time plastic stage system the stable state absolute acceleration be instead:
In formula: R PD = Σ j = 1 n 1 ( α - β j 2 ) 2 + ( 2 ξ β j ) 2 ; R PV = Σ j = 1 n β j ( α - β j 2 ) 2 + ( 2 ξ β j ) 2 ; R PA = Σ j = 1 n β 2 j ( α - β j 2 ) 2 + ( 2 ξ β j ) 2 ; C P 1 = Σ j = 1 n - 2 ξ β j 3 ( α - β j 2 ) 2 + ( 2 ξ β j ) 2 ; D P 1 = Σ j = 1 n α - β j 2 + ( 2 ξ β j ) 2 ( α - β j 2 ) 2 + ( 2 ξ β j ) 2 ; TR j ′ = Σ j = 1 n α + ( 2 ξ β j ) 2 ( 1 - β j 2 ) 2 + ( 2 ξ β j ) 2 ; ϵ pj ′ = Σ j = 1 n tan - 1 2 ξβ j 3 α - β j 2 + ( 2 ξ β j ) 2 .
Take plastic stage earthquake effect factor alpha as characterizing condition spectrum parameter, antidetonation condition spectrum hamonic function expression formula:
2, the condition of elasticity or plastic stage is composed the hamonic function of different frequency, the differential equation of motion of input structure:
[ M ] { x · · } + [ C ] { x · } + [ K ] { x } = [ M ] { I } x · · g ( t ) - - - ( 15 )
In formula, [M], [K], [C] they are architecture quality matrix, stiffness matrix, damping matrix, I} is the unit column vector, Be the earthquake ground motion acceleration, { x} is respectively structure with respect to the column vector of acceleration, speed and the displacement on basis, obtains structural response;
3, based on structural response, find the solution structural earthquake action effect (moment of flexure, shearing, axial force, distortion, stress and strain), make up according to quadratic sum extraction of square root method (SRSS), fully flat method combined method (CQC) and LINEAR COMBINATION METHOD, complete seismic design.
Quadratic sum extraction of square root method (SRSS): S = Σ S j 2 - - - ( 16 )
Fully flat method combined method (CQC): S = Σ j = 1 m Σ k = 1 m ρ jk S j S k - - - ( 17 )
ρ jk = 8 ζ j ζ k ( 1 + λ T ) λ T 1.5 ( 1 - λ T 2 ) 2 + 4 ζ j ζ k ( 1 + λ T ) 2 λ T - - - ( 18 )
LINEAR COMBINATION METHOD: S = Σ j = 1 n S j - - - ( 19 )
S-geological process effect; S j, S k-be respectively geological process effect under j, k frequency; ζ j, ζ k-be respectively the damping ratio of j, the k vibration shape; ρ jkThe related coefficient of-j frequency and k frequency; λ T-k, j frequency ratio.
Described structure comprises framed structure, shear wall structure, frame shear wall structure, frame supported shear wall structure, tube-in-tube structure, framework-core wall structure, simply supported slab beam bridge, cantilever glider bridge, continuous bridge, T shape rigid frame bridge, suspension bridge, cable-stayed bridge, suspension bridge, combined system birdge are depending on tower, storage tank, pylon, warehouse, water tower, pond, chimney, tunnel, dam.

Claims (2)

1. based on the Seismic Design Method of condition spectrum hamonic function, it is characterized in that: comprise the following steps:
(1), the structure of antidetonation condition spectrum hamonic function expression formula;
(2), antidetonation condition spectrum is adopted the different frequency hamonic function, be input to respectively the structure motion differential equation, obtain structural response;
(3), based on structural response, find the solution the structural earthquake action effect, carry out the time-history analysis of structure, make up according to quadratic sum extraction of square root method, fully flat method combined method and LINEAR COMBINATION METHOD, complete seismic design.
2. the Seismic Design Method based on condition spectrum hamonic function according to claim 1, it is characterized in that: the construction method of described antidetonation condition spectrum hamonic function expression formula is: (1), regard antidetonation condition spectrum as the target spectrum; (2), based target is composed and the transformational relation of power spectrum, by the mode that iterates, has obtained the earthquake motion trigonometric function analytical expression of condition spectrum for the target spectrum; (3), with the earthquake motion trigonometric function analytical expression substitution single dof mobility differential equation of motion of target spectrum, obtain antidetonation condition spectrum hamonic function expression formula.
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Publication number Priority date Publication date Assignee Title
CN103926836A (en) * 2014-04-18 2014-07-16 郑州大学 Shock absorption control method of aqueduct structure under action of random loads
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CN105550414B (en) * 2015-12-08 2018-06-22 哈尔滨工业大学 A kind of energy spectrum Forecasting Methodology based on main aftershock sequence
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