JP6798732B2 - Multimodal performance-oriented seismic design method based on performance bispectrum - Google Patents
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- 238000000034 method Methods 0.000 title claims description 38
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Description
本発明は耐震設計の技術分野に関し、具体的には性能双スペクトルに基づくマルチモーダル性能指向型耐震設計方法に関するものである。 The present invention relates to a technical field of seismic design, specifically to a multimodal performance-oriented seismic design method based on performance bispectral.
中国の耐震規範（ＧＢ ５００１１−２０１６）では、耐震設計震度（地震動パラメーター）による耐震設計が行われている。５０年超過確率１０％、６３％及び２％の地震動強さをそれぞれ小地震、中地震及び大地震の震度とし、小震不壊、中震可修、大震不倒の３レベルに基づく対策が採用されている。また２段階法が採用されており、第１段階は弾性設計、第２段階は弾塑性設計となっている。第１段階は、小地震の作用下において弾性設計を採用し、２次元の弾性地震応答スペクトルに基づき、モーダルアナリシス法又はＥｑｕｉｖａｌｅｎｔ Ｂａｓｅ Ｓｈｅａｒ法を用いて地震作用を計算し、小地震による構造物の変位を計算した上で、重力などの他の荷重と組み合わせて、構造の内力を求める。第２段階は、大地震下の弾塑性変形の検証であり、構造の変形が規範で定められた変形の許容値を超えないことが要求され、これによって大震不倒の要求を満たしており、特定の構造については、２次元の弾性地震応答スペクトルに基づき、簡略化された方法で大地震による構造物の変位を計算している。 According to China's seismic code (GB 50011-2016), seismic design is carried out based on seismic design seismic intensity (seismic dynamic parameters). The seismic intensities of 10%, 63%, and 2% with a probability of exceeding 50 years are set as the seismic intensities of small earthquakes, medium earthquakes, and large earthquakes, respectively. It has been adopted. In addition, a two-step method is adopted, the first step is elastic design, and the second step is elasto-plastic design. The first stage adopts elastic design under the action of a small earthquake, calculates the seismic action using the modal analysis method or the Equivalent Base Shear method based on the two-dimensional elastic seismic response spectrum, and calculates the seismic action of the structure due to the small earthquake. After calculating the displacement, combine it with other loads such as gravity to obtain the internal force of the structure. The second stage is the verification of elasto-plastic deformation under a large earthquake, and it is required that the deformation of the structure does not exceed the allowable deformation value stipulated in the norm, thereby satisfying the requirement of unyielding large earthquake. For a specific structure, the displacement of the structure due to a large earthquake is calculated by a simplified method based on the two-dimensional elastic seismic response spectrum.
米国のＡＳＣＥ７、ＩＢＣでは、２レベルの対策に基づく変換を行い、最大想定地震（中国の規範でいう「大地震」に相当する）の２／３を設計用地震動（中国の規範でいう「中地震」に相当する）に変換し、単一段階設計で耐震強度の検算を行い、構造物が弾塑性状態にあると仮定した上で、応答スペクトルに基づいて静的設計のＥｑｕｉｖａｌｅｎｔ Ｂａｓｅ Ｓｈｅａｒ法（等価水平力法）及び動的設計のモーダルアナリシス法を採用し、構造物の調整係数Ｒにより様々な構造別変形性能を考慮した上で設計用地震動を弾性範囲に換算し、内力耐荷力の検算及び変位の計算を行い、構造物の変位増幅係数Ｃｄを弾塑性変形に換算することで構造物の剛性を計算し、Ｐ−デルタ分析を行うかどうか判断している。欧州の耐震基準は米国と似ており、設計用地震動における設計用地震力の換算は、性能係数ｑにより、設計用応答スペクトル中でｑの陽関数形式で表し、内力耐荷力の検算及び変位の計算を行い、構造物の変位増幅係数ｑｅを用いて弾塑性変形を計算している。 At ASCE7 and IBC in the United States, conversion is performed based on two-level measures, and two-thirds of the maximum assumed earthquake (corresponding to "major earthquake" in Chinese norms) is used for design seismic motion ("middle" in Chinese norms). Converted to "earthquake"), calculated the seismic strength in a single-stage design, assumed that the structure is in an elasto-plastic state, and then based on the response spectrum, the Equivalent Base Shear method of static design (equivalent to earthquake). Equivalent horizontal force method) and modal analysis method of dynamic design are adopted, and the seismic motion for design is converted into the elastic range after considering various deformation performances by structure by the adjustment coefficient R of the structure, and the internal force load bearing capacity is calculated. And the displacement is calculated, and the rigidity of the structure is calculated by converting the displacement amplification coefficient Cd of the structure into elasto-plastic deformation, and it is determined whether or not to perform the P-delta analysis. European seismic standards are similar to those in the United States, and the conversion of design seismic force in design seismic motion is expressed in the explicit function form of q in the design response spectrum by the performance coefficient q, and the internal force load bearing capacity is checked and displaced. The calculation is performed, and the elasto-plastic deformation is calculated using the displacement amplification coefficient qe of the structure.
上記の事実は、中国、米国、欧州の基準がいずれも設計震度（地震動パラメーター）下の設計用応答スペクトルによって性能指向型耐震設計を行っていることを示している。しかし、唐山（中国、１９７６）、ノースリッジ（米国、１９９４）、神戸（日本、１９９５）、集集（中国台湾、１９９９）、スマトラ−アンダマン（インドネシア、２００４）、ペルー （ペルー、２００７）、ブン川（中国、２００８）、ポルトープランス（ハイチ、２０１０）、コンセプシオン（チリ、２０１０）、玉樹（中国、２０１０）、日本東北太平洋海域（日本、２０１１）などの地震は、設計震度（地震動パラメーター）の基準をはるかに上回っていた。設計震度（地震動パラメーター）で耐震設計を行った場合、設計震度（地震動パラメーター）と最終的な破壊状態との関連性がはっきりしないため、設計震度（地震動パラメーター）を上回る地震が発生した場合、工程の損壊程度を把握することは不可能である。そのため、設計震度（地震動パラメーター）に基づく性能指向型耐震設計は改良する必要があった。 The above facts indicate that the standards of China, the United States, and Europe all carry out performance-oriented seismic design based on the design response spectrum under the design seismic intensity (earthquake motion parameter). However, Tangshan (China, 1976), North Ridge (USA, 1994), Kobe (Japan, 1995), Gathering (China Taiwan, 1999), Sumatra-Andaman (Indonesia, 2004), Peru (Peru, 2007), Bun Earthquakes such as rivers (China, 2008), Port-au-Prince (Haiti, 2010), conceptions (Chile, 2010), Tamaki (China, 2010), and the Japan Northeast Pacific Ocean (Japan, 2011) have design seismic intensity (seismic motion parameters). It was well above the standard. When seismic design is performed with the design seismic intensity (earthquake motion parameter), the relationship between the design seismic intensity (earthquake motion parameter) and the final state of destruction is not clear. It is impossible to know the degree of damage to the earthquake. Therefore, it was necessary to improve the performance-oriented seismic design based on the design seismic intensity (seismic motion parameter).
本発明は、以上のような技術的課題に鑑み、性能双スペクトルに基づくマルチモーダル性能指向型耐震設計方法を提供するが、それは定量化した性能レベルに基づいてそのまま耐震設計を行う方法であり、従来の設計震度（地震動パラメーター）に基づく性能指向型耐震設計よりもさらに科学的で、構造物の耐震挙動を制御することが可能である。 In view of the above technical issues, the present invention provides a multimodal performance-oriented seismic design method based on performance bispectral, which is a method of performing seismic design as it is based on a quantified performance level. It is more scientific than the performance-oriented seismic design based on the conventional design seismic intensity (earthquake motion parameters), and it is possible to control the seismic behavior of structures.
上記目的を達成するために、本発明は以下の技術案を提供する。性能双スペクトルに基づくマルチモーダル性能指向型耐震設計方法は、以下の工程を含む。 In order to achieve the above object, the present invention provides the following technical proposals. The multimodal performance-oriented seismic design method based on the performance bispectrum includes the following steps.
第１工程：１組の異なる性能双スペクトルの仮想構造物の最上層における特性変位角ρｏｂｊ−ｍ（ｄ）を設定し、性能双スペクトルの１自由度弾塑性構造系、及び性能双スペクトルの１自由度系の変位性能レベルを構築する。 First step: Set the characteristic displacement angle ρ obj-m (d) in the uppermost layer of a set of different performance bispectral virtual structures, and set the performance bispectral one-degree-of-freedom elasto-plastic structural system and the performance bispectral. Build a displacement performance level for one degree of freedom system.
第２工程：耐震設計場所の地震環境特性に基づき、１組の地震動記録を選択し、性能双スペクトルの１自由度弾塑性微分方程式中に入力して、地震動記録における加速度のピーク値の最小値、平均値及び最大値、及び性能双スペクトルの１自由度弾塑性構造系における地震応答の絶対加速度のピーク値の最小値、平均値及び最大値を得る。 Second step: Based on the seismic environmental characteristics of the seismic design site, select a set of seismic motion records and input them into the one-degree-of-freedom elasto-plastic differential equation of the performance dual spectrum, and the minimum value of the acceleration peak value in the seismic motion record. , Mean and maximum, and performance The minimum, mean and maximum values of the peak values of the absolute acceleration of the seismic response in a bi-spectral one-degree-of-freedom elasto-plastic structure system are obtained.
第３工程：同じ構造物周期において、１組の異なる２本折れ線弾塑性モデルの第２剛性を設定し、第２工程を繰り返す。 Third step: In the same structure period, the second stiffness of one set of different two-line elasto-plastic models is set, and the second step is repeated.
第４工程：実際の必要を考慮しつつ、耐震基準に基づいて設計する構造物の耐震性能レベルを設定し、それには耐震性能レベルの変位角
、構造物の高さ
を含める。
Fourth step: Set the seismic performance level of the structure designed based on the seismic standards while considering the actual needs, and set the displacement angle of the seismic performance level.
, Structure height
Include.
第５工程：設計構造物に基づき、異なる振動モードにおける構造物周期、振動モード及びモード刺激係数を計算する。 Fifth step: Based on the design structure, the structure period, vibration mode and mode stimulation coefficient in different vibration modes are calculated.
第６工程：任意の応答量に対し、異なる振動モードの寄与係数を計算し、寄与閾値εを設定して、必要な振動モードの個数を求める。 Sixth step: Contribution coefficients of different vibration modes are calculated for an arbitrary response amount, a contribution threshold value ε is set, and the number of required vibration modes is obtained.
第７工程：第１構造物周期を標準１自由度弾塑性構造系として設定し、標準１自由度弾塑性構造系を基に構造物の耐震応答効果を合成する。 Seventh step: The first structure period is set as a standard 1-degree-of-freedom elasto-plastic structure system, and the seismic response effect of the structure is synthesized based on the standard 1-degree-of-freedom elasto-plastic structure system.
第８工程：構造物の耐震応答効果を設定した構造物の耐震性能レベルと等しくさせて、標準１自由度弾塑性構造系における耐震性能レベルを得る。 Eighth step: The seismic response effect of the structure is made equal to the set seismic performance level of the structure to obtain the seismic performance level in the standard 1 degree of freedom elasto-plastic structural system.
第９工程：設計構造物をＰｕｓｈｏｖｅｒ解析し、構造物の耐力曲線（ｐｕｓｈｏｖｅｒ ｃｕｒｖｅ）を対応する標準１自由度弾塑性構造系加速度−変位関係曲線に変換する。 9th step: Pushover analysis of the design structure is performed, and the force curve (pushover curve) of the structure is converted into the corresponding standard 1-degree-of-freedom elasto-plastic structural system acceleration-displacement relationship curve.
第１０工程：標準１自由度弾塑性構造系を性能双スペクトルの１自由度弾塑性構造系と等価にして、第１構造物周期に基づき、性能双スペクトルの１自由度弾塑性構造系から直接地震動記録における加速度のピーク値の最小値、平均値及び最大値、及び標準１自由度弾塑性構造系における地震応答の絶対加速度のピーク値の最小値、平均値及び最大値を得る。 Step 10: Equivalent the standard 1-degree-of-freedom elasto-plastic structure system to the 1-degree-of-freedom elasto-plastic structure system with performance dual spectra, and based on the first structural period, directly from the 1-degree-of-freedom elasto-plastic structure system with performance dual spectra. The minimum, mean and maximum values of the peak values of acceleration in the seismic motion record, and the minimum, mean and maximum values of the peak values of the absolute acceleration of the seismic response in the standard 1-degree-of-freedom elasto-plastic structure system are obtained.
第１１工程：標準１自由度弾塑性構造系における地震応答の絶対加速度のピーク値の最小値、平均値及び最大値に基づき、耐震性能レベル下での構造物の耐震応答効果の最小値ｒｍｉｎ、平均値ｒａｖｅ及び最大値ｒｍａｘを計算する。 11th step: Minimum value of seismic response effect of structures under seismic performance level r min based on minimum, mean and maximum peak values of absolute acceleration of seismic response in standard 1 degree of freedom elasto-plastic structural system , Mean r- ave and maximum r- max .
さらに、第１工程において、性能双スペクトルの１自由度系の変位性能レベルの計算式は以下の通りである。 Further, in the first step, the calculation formula of the displacement performance level of the one-degree-of-freedom system of the performance dual spectrum is as follows.
そのうち、Ｈは構造物の仮想の高さであり、
であり、χ及びＣｒは経験係数であり、経験式で得る。Ｄｏｂｊ−ｍは性能双スペクトルの構造物の頂点変位性能値であり、
であり、仮想構造物の地震応答のモード制御については、モード形状ベクトルと高さは正比例の関係をなし、即ち
であり、ｈｉは第ｉ層の層間高さであり、Ｈｉは第ｉ層の構造物の高さであり、ｍｉは第ｉ層の質量である。
Of these, H is the virtual height of the structure,
, And χ and Cr are empirical coefficients, which are obtained by empirical formulas. Obj-m is the vertex displacement performance value of the performance bispectral structure.
Therefore, regarding the mode control of the seismic response of the virtual structure, the mode shape vector and the height have a direct proportional relationship, that is,
And a, h i is the interlayer height of the i-layer, H i is the height of the structure of the i layer, m i is the mass of the i-th layer.
さらに、第２工程において、地震環境特性は、マグニチュード、断層メカニズム、断層距離及び土地条件を含む。 In addition, in the second step, seismic environmental characteristics include magnitude, fault mechanism, fault distance and land conditions.
さらに、第２工程において、選択した地震動記録を性能双スペクトルの１自由度弾塑性微分方程式中に入力し、地震動記録の大きさを繰り返し調整して、性能双スペクトルの１自由度弾塑性系の変位応答ピーク値が性能双スペクトルの１自由度系の耐震性能レベルに達するようにして、地震動記録における加速度のピーク値の最小値、平均値及び最大値、及び前記性能双スペクトルの１自由度弾塑性構造系における地震応答の絶対加速度のピーク値の最小値、平均値及び最大値を得る。 Further, in the second step, the selected seismic motion record is input into the one-degree-of-freedom elasto-plastic differential equation of the performance dual spectrum, and the size of the seismic motion record is repeatedly adjusted to obtain the one-degree-of-freedom elasto-plastic system of the performance dual spectrum. Make sure that the displacement response peak value reaches the seismic performance level of the one-degree-of-freedom system of the performance dual spectrum, and the minimum, mean and maximum values of the acceleration peak value in the seismic motion record, and the one-degree-of-freedom bullet of the performance dual spectrum. Obtain the minimum, mean, and maximum values of the peak values of the absolute acceleration of the seismic response in the plastic structure system.
さらに、第５工程において、動特性方程式を用いて設計構造物の動特性解析を行うが、動特性方程式は、 Further, in the fifth step, the dynamic characteristic analysis of the design structure is performed using the dynamic characteristic equation.
そのうち、ｋは構造物自体の剛性マトリクスであり、
は第ｎ次振動モードのモードであり、ωｎは第ｎ次振動モードの構造物振動数であり、第ｎ次振動モードの構造物周期は
であり、第ｎ次振動モードのモード刺激係数は
であり、そのうちＮは構造物の振動モードの合計次数であり、振動モードの総数でもある。ｍｊは構造物の第ｊ層の質量である。
は構造物の第ｊ層の振動モードである。
Of these, k is the stiffness matrix of the structure itself.
Is the mode of the nth vibration mode, ω n is the structure frequency of the nth vibration mode, and the structure period of the nth vibration mode is.
And the mode stimulation coefficient of the nth vibration mode is
Of which, N is the total order of the vibration modes of the structure and is also the total number of vibration modes. m j is the mass of the j-th layer of the structure.
Is the vibration mode of the jth layer of the structure.
さらに、第７工程において、平方及び平方根を求める方法又は完全二次結合法を用いて、構造物の耐震応答効果を合成する。 Further, in the seventh step, the seismic response effect of the structure is synthesized by using the method of determining the square and the square root or the perfect secondary coupling method.
さらに、第１０工程において、標準１自由度弾塑性構造系における耐震性能レベルと性能双スペクトルの１自由度系の性能レベルが一致しない場合には、近接する２つの性能双スペクトルの１自由度系の性能レベルの間で内挿法を用いて確定することができる。また標準１自由度弾塑性構造系の第２剛性係数と性能双スペクトルの１自由度弾塑性構造系における２本折れ線弾塑性モデルの第２剛性係数が一致しない場合には、近接する２つの性能双スペクトルの１自由度系の性能レベルの間で内挿法を用いて確定することができる。 Further, in the tenth step, if the seismic performance level in the standard one-degree-of-freedom elasto-plastic structure system and the performance level of the one-degree-of-freedom system of the performance dual spectrum do not match, the one-degree-of-freedom system of two adjacent performance twin spectra Can be determined using the interpolation method between the performance levels of. If the second rigidity coefficient of the standard 1-degree-of-freedom elasto-plastic structure system and the second rigidity coefficient of the two-fold line elasto-plastic model in the double-spectrum 1-degree-of-freedom elasto-plastic structure system do not match, the two performances are close to each other. It can be determined using the interpolation method between the performance levels of a bimodal one-degree-of-freedom system.
さらに、第１１工程において、平方及び平方根を求める方法又は完全二次結合法を用いて、耐震性能レベル下での構造物の耐震応答効果の最小値ｒｍｉｎ、平均値ｒａｖｅ及び最大値ｒｍａｘを計算する。 Further, in the eleventh step, the minimum value r min , mean value r ave and maximum value r max of the seismic response effect of the structure under the seismic performance level are used by the method of obtaining the square and the square root or the perfect secondary coupling method. To calculate.
本発明の性能双スペクトルに基づくマルチモーダル性能指向型耐震設計方法は、定量化した性能レベルに基づいてそのまま耐震設計を行う方法であり、性能レベルに基づいて耐震設計を行う方法では最終的な破壊状態を耐震設計の基礎とするため、設計震度（地震動パラメーター）を上回る地震が発生したとしても、構造物の耐震性能を制御することが可能である。明らかに、本件特許出願は、従来の設計震度（地震動パラメーター）に基づく性能指向型耐震設計よりもさらに科学的で、構造物の耐震挙動を制御することが可能である。 The multimodal performance-oriented seismic design method based on the performance bispectrum of the present invention is a method of performing seismic design as it is based on the quantified performance level, and the method of performing seismic design based on the performance level is the final destruction. Since the state is the basis of seismic design, it is possible to control the seismic performance of structures even if an earthquake that exceeds the designed seismic intensity (seismic dynamics parameter) occurs. Obviously, the patent application is more scientific than traditional performance-oriented seismic design based on design seismic intensity (earthquake motion parameters) and can control seismic behavior of structures.
本発明の目的、技術案及び優位点をより明解にするため、以下で実施例と合わせて本発明についてより詳細に説明する。ここに記述された具体的な実施例は本発明を説明するためのものに過ぎず、本発明を限定するものでは決してないことを理解されたい。 In order to clarify the object, the technical proposal and the superiority of the present invention, the present invention will be described in more detail below together with Examples. It should be understood that the specific examples described herein are merely for explaining the present invention and are by no means limiting to the present invention.
本発明の性能双スペクトルに基づくマルチモーダル性能指向型耐震設計方法は、以下の工程を含む。 The multimodal performance-oriented seismic design method based on the performance bispectrum of the present invention includes the following steps.
第１工程：１組の異なる性能双スペクトルの仮想構造物の最上層における特性変位角ρｏｂｊ−ｍ（ｄ）を設定し、性能双スペクトルの１自由度弾塑性構造系、及び性能双スペクトルの１自由度系の変位性能レベルを構築する。 First step: Set the characteristic displacement angle ρ obj-m (d) in the uppermost layer of a set of different performance bispectral virtual structures, and set the performance bispectral one-degree-of-freedom elasto-plastic structural system and the performance bispectral. Build a displacement performance level for one degree of freedom system.
性能双スペクトルの１自由度弾塑性動的微分方程式は以下の通りである。 The one-degree-of-freedom elasto-plastic dynamic differential equation of the performance bispectrum is as follows.
そのうち、ωは構造物の固有振動数を表しており、周期は
であり、ξは減衰比であり、Ｄは１自由度系の変位であり、
は既知の地震励振であり、Ｆは標準の２本折れ線弾塑性モデルであり、標準の２本折れ線弾塑性モデルＦｉの第２剛性係数ψＦｉを規定する。
Of these, ω represents the natural frequency of the structure, and the period is
, Ξ is the damping ratio, D is the displacement of one degree of freedom system,
Is a known seismic excitation, F is a standard two polygonal elasto-plastic model, defining a second stiffness coefficient PusaiF i standard two polygonal elasto-plastic model F i.
性能双スペクトルのｏｂｊ−ｍ個の構造物の最上層における特性変位角ρｏｂｊ−ｍ（ｄ）を設定し、構造物の高さは経験式に基づいて構造物の周期で表す。例えば、仮想構造物の高さは； The characteristic displacement angle ρ obj-m (d) in the uppermost layer of the obj-m structure of the performance bispectrum is set, and the height of the structure is expressed by the period of the structure based on the empirical formula. For example, the height of the virtual structure is;
そのうち、χ及びＣｒは経験係数であり、経験式で得る。 Among them, χ and Cr are empirical coefficients, which are obtained by an empirical formula.
性能双スペクトルの構造物の頂点変位性能値Ｄｏｂｊ−ｍは； Performance The vertex displacement performance value obj-m of the bispectral structure is;
仮想構造物の地震応答のモード制御については、モード形状ベクトルと高さは正比例の関係をなしており、 Regarding the mode control of the seismic response of the virtual structure, the mode shape vector and the height are in a direct proportional relationship.
そのうち、ｈｉは第ｉ層の層間高さであり、Ｈｉは第ｉ層の構造物の高さであり、ｍｉは第ｉ層の質量である。 Among them, h i is the interlayer height of the i-layer, H i is the height of the structure of the i layer, m i is the mass of the i-th layer.
性能双スペクトルの１自由度系の変位性能レベル； Performance Bispectral displacement performance level of one degree of freedom system;
第２工程：耐震設計場所の地震環境特性に基づき、１組の地震動記録を選択し、性能双スペクトルの１自由度弾塑性微分方程式中に入力して、地震動記録における加速度のピーク値の最小値、平均値及び最大値、及び性能双スペクトルの１自由度弾塑性構造系における地震応答の絶対加速度のピーク値の最小値、平均値及び最大値を得る。 Second step: Based on the seismic environmental characteristics of the seismic design site, select a set of seismic motion records and input them into the one-degree-of-freedom elasto-plastic differential equation of the performance dual spectrum, and the minimum value of the acceleration peak value in the seismic motion record. , Mean and maximum, and performance The minimum, mean and maximum values of the peak values of the absolute acceleration of the seismic response in a bi-spectral one-degree-of-freedom elasto-plastic structure system are obtained.
そのうち、地震環境特性は、マグニチュード、断層メカニズム、断層距離及び土地条件を含む。 Among them, seismic environmental characteristics include magnitude, fault mechanism, fault distance and land conditions.
第２工程において、選択した地震動記録を性能双スペクトルの１自由度弾塑性微分方程式中に入力し、地震動記録の大きさを繰り返し調整して、性能双スペクトルの１自由度弾塑性系の変位応答ピーク値が性能双スペクトルの１自由度系の耐震性能レベルに達するようにして、地震動記録における加速度のピーク値の最小値、平均値及び最大値、及び前記性能双スペクトルの１自由度弾塑性構造系における地震応答の絶対加速度のピーク値の最小値、平均値及び最大値を得る。 In the second step, the selected seismic motion record is input into the one-degree-of-freedom elasto-plastic differential equation of the performance dual spectrum, and the magnitude of the seismic motion record is repeatedly adjusted to change the displacement response of the one-degree-of-freedom elasto-plastic system of the performance dual spectrum. The minimum, mean and maximum values of the peak values of acceleration in the seismic motion record, and the one-degree-of-freedom elasto-plastic structure of the performance-bispectral, so that the peak value reaches the seismic performance level of the one-degree-of-freedom system of the performance bispectral. Obtain the minimum, mean, and maximum values of the peak values of the absolute acceleration of the seismic response in the system.
第３工程：同じ構造物周期において、１組の異なる２本折れ線弾塑性モデルの第２剛性を設定し、第２工程を繰り返す。 Third step: In the same structure period, the second stiffness of one set of different two-line elasto-plastic models is set, and the second step is repeated.
第４工程：実際の必要を考慮しつつ、耐震基準に基づいて設計する構造の耐震性能レベルを設定し、それには耐震性能レベルの変位角
、構造の高さ
を含める。
Step 4: Set the seismic performance level of the structure designed based on seismic standards, taking into account actual needs, and set the displacement angle of the seismic performance level.
, Structural height
Include.
第５工程：設計した構造物に基づき、異なる振動モードにおける構造物周期、振動モード及びモード刺激係数を計算する。 Fifth step: Based on the designed structure, the structure period, vibration mode and mode stimulation coefficient in different vibration modes are calculated.
第５工程において、動特性方程式に基づき、異なる振動モードにおける構造物周期、振動モード及びモード刺激係数を求めるが、動特性方程式は以下の通りである。 In the fifth step, the structure period, the vibration mode, and the mode stimulation coefficient in different vibration modes are obtained based on the dynamic characteristic equations. The dynamic characteristic equations are as follows.
そのうち、ｋは構造物自体の剛性マトリクスであり、
は第ｎ次振動モードのモードであり、ωｎは第ｎ次振動モードの構造物振動数であり、第ｎ次振動モードの構造物周期は
であり、第ｎ次振動モードのモード刺激係数は
であり、そのうちＮは構造物の振動モードの合計次数であり、振動モードの総数でもある。ｍｊは構造物の第ｊ層の質量である。
は構造物の第ｊ層の振動モードである。
Of these, k is the stiffness matrix of the structure itself.
Is the mode of the nth vibration mode, ω n is the structure frequency of the nth vibration mode, and the structure period of the nth vibration mode is.
And the mode stimulation coefficient of the nth vibration mode is
Of which, N is the total order of the vibration modes of the structure and is also the total number of vibration modes. m j is the mass of the j-th layer of the structure.
Is the vibration mode of the jth layer of the structure.
第６工程：任意の応答量に対し、異なる振動モードの寄与係数を計算し、寄与閾値εを設定して、必要な振動モードの個数を求める。 Sixth step: Contribution coefficients of different vibration modes are calculated for an arbitrary response amount, a contribution threshold value ε is set, and the number of required vibration modes is obtained.
外力Ｓによって引き起こされる構造物ｒの静的値はｒｓｔで設定し、第ｎ次振動モードにおける静的値は
であり、第ｎ次振動モードのｒｓｔに対する貢献度は
で設定し、
The static value of the structure r caused by the external force S is set by r st , and the static value in the nth vibration mode is
And the contribution of the nth vibration mode to r st is
Set with
を解き、必要な振動モードの個数を得る。 To obtain the required number of vibration modes.
第７工程：第１構造物周期を標準１自由度弾塑性構造系として設定し、標準１自由度弾塑性構造系を基に構造物の耐震応答効果を合成する。 Seventh step: The first structure period is set as a standard 1-degree-of-freedom elasto-plastic structure system, and the seismic response effect of the structure is synthesized based on the standard 1-degree-of-freedom elasto-plastic structure system.
第１工程において選択した耐震性能レベルが変位であることに対応して、ここで選択する構造物の耐震応答効果も変位とする。 Corresponding to the seismic performance level selected in the first step being displacement, the seismic response effect of the structure selected here is also displacement.
第ｎ次振動モードにおける静的値は
であり、第ｎ次振動モードにおける変位は
であり；
The static value in the nth vibration mode is
And the displacement in the nth vibration mode is
Is;
そのうち、Ｓａｎは設計地震動の加速度応答スペクトルにおける第ｎ構造物周期のスペクトル値であり、Ｄ１は性能双スペクトルの１自由度弾塑性構造系中でω１に対応する応答値であり； Of these, San is the spectral value of the nth structure period in the acceleration response spectrum of the design seismic motion, and D 1 is the response value corresponding to ω 1 in the one-degree-of-freedom elasto-plastic structural system of the performance dual spectrum;
とすれば、 given that,
第７工程において、平方及び平方根を求める方法又は完全二次結合法を用いて、構造物の耐震応答効果、即ち変位を合成する。 In step 7, the seismic response effect of the structure, i.e., displacement, is synthesized using the method of determining squares and square roots or the perfect secondary coupling method.
そのうち、平方及び平方根は以下の通りである。 Among them, the square and the square root are as follows.
そのうち、完全二次結合法は以下の通りである。 Among them, the perfect secondary bond method is as follows.
ρｉｎはモード結合係数であり、 ρ in is the mode coupling coefficient
そのうち、ζｉ、ζｎはそれぞれ第ｉ及び第ｎモードの減衰比であり、ρｉｎは第ｉ構造物振動数と第ｎ構造物振動数の相関係数であり、λＴは第ｉ構造物振動数と第ｎ構造物振動数の比率である。 Of these, ζ i and ζ n are the damping ratios of the i and nth modes, respectively, ρ in is the correlation coefficient between the i-th structure frequency and the nth structure frequency, and λ T is the i-th structure. It is the ratio of the object frequency and the nth structure frequency.
第８工程：構造物の耐震応答効果を設定した構造物の耐震性能レベルと等しくさせて、標準１自由度弾塑性構造系における耐震性能レベルを得る。即ち； Eighth step: The seismic response effect of the structure is made equal to the set seismic performance level of the structure to obtain the seismic performance level in the standard 1 degree of freedom elasto-plastic structural system. That is;
として、標準１自由度弾塑性構造系における耐震性能レベルの変位を求める。 As a result, the displacement of the seismic performance level in the standard 1 degree of freedom elasto-plastic structure system is obtained.
第９工程：設計構造物をＰｕｓｈｏｖｅｒ解析し、構造物の耐力曲線（ｐｕｓｈｏｖｅｒ ｃｕｒｖｅ）を対応する標準１自由度弾塑性構造系加速度−変位関係曲線に変換する。 9th step: Pushover analysis of the design structure is performed, and the force curve (pushover curve) of the structure is converted into the corresponding standard 1-degree-of-freedom elasto-plastic structural system acceleration-displacement relationship curve.
変換式は以下の通りである。 The conversion formula is as follows.
そのうち、
は第１振動モード等価質量であり、Γ１は第１振動モード刺激係数である。
は第１振動モード頂点ベクトルである。ｕｒｎは構造物の頂点の変位である。Ｖｂは構造物のベースシアであり、これにより構造物の第１モードにおける弾塑性折れ線モデルの第２剛性係数
を得る。
Of which
Is the first vibration mode equivalent mass, and Γ 1 is the first vibration mode stimulation coefficient.
Is the first vibration mode vertex vector. run is the displacement of the apex of the structure. V b is the base shear of the structure, thereby the second stiffness coefficient of the elasto-plastic line model in the first mode of the structure.
To get.
第１０工程：標準１自由度弾塑性構造系を性能双スペクトルの１自由度弾塑性構造系と等価にして、第１構造物周期に基づき、性能双スペクトルの１自由度弾塑性構造系から直接地震動記録における加速度のピーク値の最小値、平均値及び最大値、及び標準１自由度弾塑性構造系における地震応答の絶対加速度のピーク値の最小値、平均値及び最大値を得る。 Step 10: Equivalent the standard 1-degree-of-freedom elasto-plastic structure system to the 1-degree-of-freedom elasto-plastic structure system with performance dual spectra, and based on the first structural period, directly from the 1-degree-of-freedom elasto-plastic structure system with performance dual spectra. The minimum, mean and maximum values of the peak values of acceleration in the seismic motion record, and the minimum, mean and maximum values of the peak values of the absolute acceleration of the seismic response in the standard 1-degree-of-freedom elasto-plastic structure system are obtained.
標準１自由度弾塑性構造系における耐震性能レベルと性能層スペクトルの１自由度形の整能レベルが一致しない場合には、近接する２つの性能双スペクトルの１自由度系の性能レベルの間で内挿法を用いて確定することができる。また標準１自由度弾塑性構造系の第２剛性係数と性能双スペクトルの１自由度弾塑性構造系における２本折れ線弾塑性モデルの第２剛性係数が一致しない場合には、近接する２つの性能双スペクトルの１自由度系の性能レベルの間で内挿法を用いて確定することができる。 If the seismic performance level in the standard one-degree-of-freedom elasto-plastic structure system and the one-degree-of-freedom constitutive level in the performance layer spectrum do not match, between the performance levels in the one-degree-of-freedom system with two adjacent performance dual spectra. It can be determined using the interpolation method. If the second rigidity coefficient of the standard 1-degree-of-freedom elasto-plastic structure system and the second rigidity coefficient of the two-fold line elasto-plastic model in the double-spectrum 1-degree-of-freedom elasto-plastic structure system do not match, two performances in close proximity It can be determined using the interpolation method between the performance levels of a bimodal one-degree-of-freedom system.
第１１工程：標準１自由度弾塑性構造系における地震応答の絶対加速度のピーク値の最小値、平均値及び最大値に基づき、平方及び平方根を求める方法又は完全二次結合法を用いて、耐震性能レベル下での構造物の耐震応答効果の最小値ｒｍｉｎ、平均値ｒａｖｅ及び最大値ｒｍａｘを計算する。 Step 11: Seismic resistance using the method of finding squares and square roots or the perfect secondary coupling method based on the minimum, mean and maximum peak values of the absolute acceleration of seismic response in standard 1 degree of freedom elasto-plastic structures. Calculate the minimum value r min , mean value r ave and maximum value r max of the seismic response effect of the structure under the performance level.
そのうち、平方及び平方根を求める方法は以下の通りである。 Among them, the method of finding the square and the square root is as follows.
そのうち、完全二次結合法は以下の通りである。 Among them, the perfect secondary bond method is as follows.
本発明の性能双スペクトルに基づくマルチモーダル性能指向型耐震設計方法は、定量化した性能レベルに基づいてそのまま耐震設計を行う方法であり、最初に１つの性能双スペクトルの１自由度弾塑性構造系を人為的に仮定し、構造物の最上層における特性変位角ρｏｂｊ−ｍ（ｄ）及び２本折れ線弾塑性モデルの第２剛性を調整して、それらを標準１自由度弾塑性構造系と等しくさせることにより、耐震性能レベルにおける構造物の耐震応答効果を求めるものである。本発明の性能レベルに基づいて耐震設計を行う方法では、最終的な破壊状態を耐震設計の基礎とするため、設計震度（地震動パラメーター）を上回る地震が発生したとしても、構造物の耐震性能を制御することが可能である。明らかに、本件特許出願は、従来の設計震度（地震動パラメーター）に基づく性能指向型耐震設計よりもさらに科学的で、構造物の耐震挙動を制御することが可能である。 The multimodal performance-oriented seismic design method based on the performance bispectral of the present invention is a method of performing seismic design as it is based on the quantified performance level. First, a one-degree-of-freedom elasto-plastic structure system of one performance bispectral system. Artificially assume that the characteristic displacement angle ρ obj-m (d) in the top layer of the structure and the second stiffness of the two-fold line elasto-plastic model are adjusted to make them a standard 1-degree-of-freedom elasto-plastic structure system. By making them equal, the seismic response effect of the structure at the seismic performance level is obtained. In the method of seismic design based on the performance level of the present invention, the final fracture state is the basis of seismic design. Therefore, even if an earthquake exceeding the designed seismic intensity (seismic motion parameter) occurs, the seismic performance of the structure is improved. It is possible to control. Obviously, the patent application is more scientific than traditional performance-oriented seismic design based on design seismic intensity (earthquake motion parameters) and can control seismic behavior of structures.
なお、当業者であれば上述の説明に基づいて改良又は変換を行うことができ、それらの改良及び変換はすべて本発明が添付する特許請求の範囲の保護範囲に属することを理解されたい。 It should be understood that those skilled in the art can make improvements or conversions based on the above description, and all of these improvements and conversions fall within the scope of the claims attached to the present invention.
Claims (6)
前記性能双スペクトルの１自由度系の変位性能レベルの計算式は：
そのうち、Ｈは前記設計構造物の仮想の高さであり、
であり、χ及びＣｒは経験係数であり、経験式で得て、Ｄｏｂｊ−ｍは、性能双スペクトルの前記設計構造物の頂点変位性能値であり、
であり、前記設計構造物の地震応答のモード制御については、モード形状ベクトルと高さは正比例の関係をなし、即ち
であり、ｈｉは第ｉ層の層間高さであり、Ｈｉは第ｉ層の前記設計構造物の高さであり、ｍｉは第ｉ層の質量であり；
耐震設計場所の地震環境特性に基づき、１組の地震動記録を選択し、性能双スペクトルの１自由度弾塑性微分方程式中に入力して、地震動記録における加速度のピーク値の最小値、平均値及び最大値、及び前記性能双スペクトルの１自由度弾塑性構造系における地震応答の絶対加速度のピーク値の最小値、平均値及び最大値を得る第２工程と、
同じ構造物周期において、１組の異なる２本折れ線弾塑性モデルの第２剛性を設定し、第２工程を繰り返す第３工程と、
実際の必要性を考慮しつつ、耐震基準に基づいて前記設計構造物の耐震性能レベルを設定し、前記耐震性能レベルの変位角
、前記設計構造物の高さ
を含める第４工程と、
前記設計構造物に基づき、異なる振動モードにおける構造物周期、振動モード及びモード刺激係数を計算し；動特性方程式を用いて前記設計構造物の動特性解析を行うが、動特性方程式は：
そのうち、ｋは前記設計構造物自体の剛性マトリクスであり、
は第ｎ次振動モードのモードであり、ωｎは第ｎ次振動モードの構造物振動数であり、第ｎ次振動モードの構造物周期は
であり、第ｎ次振動モードのモード刺激係数は
であり、そのうちＮは前記設計構造物の振動モードの合計次数であり、振動モードの総数でもあり、ｍｊは前記設計構造物の第ｊ層の質量であり、
は前記設計構造物の第ｊ層の振動モードである第５工程と、
任意の応答量に対し、前記異なる振動モードの寄与係数を計算し、寄与閾値εを設定して、必要な振動モードの個数を求める第６工程と、
第１構造物周期を標準１自由度弾塑性構造系として設定し、前記標準１自由度弾塑性構造系を基に前記設計構造物の耐震応答効果を合成し；前記設計構造物の耐震応答効果は変位とし、
第ｎ次振動モードにおける静的値は
であり、第ｎ次振動モードにおける変位は
であり；
そのうち、Ｓａｎは設計地震動の加速度応答スペクトルにおける第ｎ構造物周期のスペクトル値であり、Ｄ１は性能双スペクトルの１自由度弾塑性構造系中でω１に対応する応答値であり；
とすれば、
となる第７工程と、
前記設計構造物の耐震応答効果を設定した前記設計構造物の前記耐震性能レベルと等しくさせて、前記標準１自由度弾塑性構造系における耐震性能レベルを得る第８工程と、
前記設計構造物をＰｕｓｈｏｖｅｒ解析し、前記設計構造物の耐力曲線（ｐｕｓｈｏｖｅｒ ｃｕｒｖｅ）を対応する標準１自由度弾塑性構造系加速度−変位関係曲線に変換する第９工程と、
前記標準１自由度弾塑性構造系を前記性能双スペクトルの１自由度弾塑性構造系と等価にして、第１構造物周期に基づき、前記性能双スペクトルの１自由度弾塑性構造系から直接地震動記録における加速度のピーク値の最小値、平均値及び最大値、及び前記標準１自由度弾塑性構造系における地震応答の絶対加速度のピーク値の最小値、平均値及び最大値を得る第１０工程と、
前記標準１自由度弾塑性構造系における地震応答の絶対加速度のピーク値の最小値、平均値及び最大値に基づき、前記耐震性能レベル下での前記設計構造物の耐震応答効果の最小値ｒｍｉｎ、平均値ｒａｖｅ及び最大値ｒｍａｘを計算する第１１工程、を含むことを特徴とする、性能双スペクトルに基づくマルチモーダル性能指向型耐震設計方法。 In order to obtain the displacement performance level of the one-degree-of-freedom system of the performance dual spectrum, the characteristic displacement angle ρobj-m (d) in the uppermost layer of the design structure of one set of different performance dual spectrum is set, and one freedom of the performance dual spectrum is set. The first step of constructing the elasto-plastic structural system and
The formula for calculating the displacement performance level of the one-degree-of-freedom system of the performance bispectrum is:
Of these, H is the virtual height of the design structure .
Χ and Cr are empirical coefficients, and obtained by the empirical formula, Dobj-m is the apex displacement performance value of the design structure in the performance bispectrum.
Therefore, regarding the mode control of the seismic response of the design structure , the mode shape vector and the height have a direct proportional relationship, that is,
, Hi is the height between layers of layer i, Hi is the height of the design structure of layer i, and mi is the mass of layer i;
Based on the seismic environment characteristics of the seismic design site, a set of seismic motion records is selected and input into the one-degree-of-freedom elasto-plastic differential equation of the performance dual spectrum, and the minimum, mean, and mean values of the peak acceleration values in the seismic motion records are selected. The second step of obtaining the minimum value, the average value, and the maximum value of the peak value of the absolute acceleration of the seismic response in the one-degree-of-freedom elasto-plastic structure system of the performance dual spectrum and the maximum value, and
In the same structure period, the second step of setting the second rigidity of one set of different two-line elasto-plastic models and repeating the second step, and the third step.
Taking into account the actual needs, set the seismic performance level of the design features based on seismic standards, displacement angle of the seismic performance level
, Height of the design structure
4th step including
Based on said design feature, structure cycle in different vibration modes, calculated vibration modes and modal participation factor; performs the dynamic characteristic analysis of the design features with the dynamic characteristic equation, the dynamic characteristic equation:
Among them, k is the rigidity matrix of the design structure itself.
Is the mode of the nth vibration mode, ωn is the structure frequency of the nth vibration mode, and the structure period of the nth vibration mode is.
And the mode stimulation coefficient of the nth vibration mode is
In and of which N is the total order of the vibration mode of the design features, is also the total number of vibrational modes, mj is the mass of the j-th layer of the design features,
Is the fifth step, which is the vibration mode of the j-th layer of the design structure , and
In the sixth step, the contribution coefficients of the different vibration modes are calculated for an arbitrary response amount, the contribution threshold value ε is set, and the number of required vibration modes is obtained.
Set the first structure period as a standard one degree of freedom elastic-plastic structural system, by combining the seismic response effect of the design features based on the standard one-degree-of-freedom elastic-plastic structural system; Seismic response effect of the design features Is a displacement
The static value in the nth vibration mode is
And the displacement in the nth vibration mode is
Is;
Of these, San is the spectral value of the nth structure period in the acceleration response spectrum of the design seismic motion, and D1 is the response value corresponding to ω1 in the one-degree-of-freedom elasto-plastic structure system of the performance dual spectrum;
given that,
The 7th process and
Wherein by equal seismic performance level of the design features that set the seismic response effect of the design features, and the eighth step to obtain the seismic performance level in the standard one-degree-of-freedom elastic-plastic structural system,
The ninth step of performing Pushover analysis of the design structure and converting the force curve (pushover curve) of the design structure into the corresponding standard 1-degree-of-freedom elasto-plastic structure system acceleration-displacement relationship curve.
The standard one-degree-of-freedom elasto-plastic structure system is equivalent to the one-degree-of-freedom elasto-plastic structure system of the performance twin spectrum, and the seismic motion is directly from the one-degree-of-freedom elasto-plastic structure system of the performance twin spectrum based on the first structure period. The tenth step of obtaining the minimum value, the average value and the maximum value of the peak value of the acceleration in the recording, and the minimum value, the average value and the maximum value of the absolute acceleration value of the seismic response in the standard one-degree-of-freedom elasto-plastic structure system. ,
Based on the minimum, mean and maximum values of the peak values of the absolute acceleration of seismic response in the standard 1 degree of freedom elasto-plastic structure system, the minimum value rmin of the seismic response effect of the designed structure under the seismic performance level, A multimodal performance-oriented seismic design method based on performance bispectrum, comprising the eleventh step of calculating the mean value rave and the maximum value rmax.
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