JP2016095242A - Method of estimating interlayer displacement of building - Google Patents
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Abstract
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本発明は、地震等の外乱が建物に入力された場合の建物の損傷判断を行うために、外乱が作用している建物の層間変位を推定する建物層間変位推定方法に関する。 The present invention relates to a building interlayer displacement estimation method for estimating an interlayer displacement of a building on which a disturbance is applied in order to determine building damage when a disturbance such as an earthquake is input to the building.
従来、地震により建物が受けた損傷を算出して地震発生後の建物の残余耐震性能を判定する技術が知られている（例えば特許文献１等参照）。
当該技術は、建物の基礎部と最上階とに加速度センサーを設置しておいて、地震時に計測された加速度を２回積分することで計測点の絶対変位を算出し、最上階の絶対変位から基礎部の絶対変位を引いて、基礎部に対する最上階の相対変位を算出する。そして、当該相対変位と建物の振動モード形とに基づいて、各階の相対変位（層間変位）を算出する。また、計測した加速度と振動モード形とに基づいて、各階の絶対加速度を算出する。
そして、各階の相対変位と各階の質量比とにより建物全体の代表変位を算定するとともに、各階の絶対加速度と各階の質量比とにより建物全体の代表加速度を算定し、当該代表変位及び代表加速度を用いて建物の損傷を判定するようにしている。
2. Description of the Related Art Conventionally, there has been known a technique for calculating the residual earthquake resistance performance of a building after the occurrence of an earthquake by calculating the damage received on the building by an earthquake (see, for example, Patent Document 1).
In this technology, acceleration sensors are installed on the foundation and the top floor of the building, and the absolute displacement of the measurement point is calculated by integrating the acceleration measured during the earthquake twice. The absolute displacement of the base part is subtracted to calculate the relative displacement of the top floor relative to the base part. Then, the relative displacement (interlayer displacement) of each floor is calculated based on the relative displacement and the vibration mode shape of the building. Moreover, the absolute acceleration of each floor is calculated based on the measured acceleration and the vibration mode shape.
The representative displacement of the entire building is calculated from the relative displacement of each floor and the mass ratio of each floor, the representative acceleration of the entire building is calculated from the absolute acceleration of each floor and the mass ratio of each floor, and the representative displacement and the representative acceleration are calculated. It is used to judge building damage.
特許文献１では、加速度センサーにより加速度を計測し、地震時に計測された加速度を２回積分することで計測点の絶対変位を算出し、最上階の絶対変位から基礎部の絶対変位を引いて、基礎部に対する最上階の相対変位を算出するようにしている。
特許文献１では、建物の基礎部に設置された加速度センサーによる計測点と建物の最上階に設置された加速度センサーによる計測点とに共通の基準点を設定しなければならない。しかしながら、地震時においては、計測点と基準点とが共に変位するため、絶対変位を正確に算出することが困難となり、基礎部に対する最上階の相対変位を正確に得ることができず、推定した各階の相対変位（層間変位）の精度が得られない。
また、加速度を積分して変位を計算する数値積分は誤差が蓄積しやすい。よって、積分の数値計算においては、誤差の蓄積を少なくするように、波形毎に注意深い検討が必要になる。
本発明は、外乱時において測定される建物最上層の相対変位に基づいて外乱後の建物の層間変位の推定値を算出する場合において、建物最上層の相対変位を正確に得ることができ、算出される層間変位の推定値の精度を向上させることが可能な建物層間変位推定方法を提供するものである。
In
In
In addition, numerical integration that calculates displacement by integrating acceleration tends to accumulate errors. Therefore, in the numerical calculation of integration, careful consideration is required for each waveform so as to reduce the accumulation of errors.
The present invention can accurately obtain the relative displacement of the top layer of the building when calculating the estimated value of the interlayer displacement of the building after the disturbance based on the relative displacement of the top layer of the building measured during the disturbance. The present invention provides a building interlayer displacement estimation method capable of improving the accuracy of the estimated value of the interlayer displacement.
本発明に係る建物層間変位推定方法によれば、評価対象の建物が外乱を受けた際の建物の層間変位を推定する方法であって、評価対象の建物が外乱を受けた際の建物最上層の絶対変位の時刻歴と建物最下層の絶対変位の時刻歴とを計測して、建物最上層の絶対変位の時刻歴から建物最下層の絶対変位の時刻歴を引くことによって建物最上層の相対変位の時刻歴を求める建物最上層相対変位算出ステップと、評価対象の建物の固有周波数と固有振動モードとを求める固有値解析を行う固有値解析ステップと、建物の固有振動モードに基づいて建物の最上層以外の各層の相対変位の時刻歴を算出する各層変位推定ステップと、各層変位推定ステップで求めた各層の相対変位の時刻歴に基づいて建物の層間変位の時刻歴を算出する層間変位推定ステップと、を備え、建物最上層相対変位算出ステップでは、航法衛星システムを用いて、建物最上層の絶対変位の時刻歴と建物最下層の絶対変位の時刻歴とを計測したので、外乱時において測定される建物最上層の相対変位に基づいて外乱後の建物の層間変位の推定値を算出する場合において、建物最上層の相対変位を正確に得ることができ、算出される層間変位の推定値の精度を向上させることができる。
また、建物最上層相対変位算出ステップで得られた建物最上層の相対変位の時刻歴の周波数成分を、建物の２次固有周波数ｆ２よりも低い周波数成分である低周波成分の時刻歴と建物の２次固有周波数ｆ２以上の高周波成分の時刻歴とに分離する周波数成分分離ステップを備え、各層変位推定ステップでは、建物の変形を１次固有振動モードでの相対変位と２次固有振動モードでの相対変位との和とみなし、建物の１次固有振動モードでの建物最上層の相対変位の時刻歴を周波数成分分離ステップで求めた低周波成分の時刻歴とみなして、１次固有振動モードでの建物最上層以外の各層の相対変位の時刻歴を１次固有振動モードに基づいて算出するとともに、建物の２次固有振動モードでの建物最上層の相対変位の時刻歴を周波数成分分離ステップで求めた高周波成分の時刻歴とみなして、２次固有振動モードでの建物最上層以外の各層の相対変位の時刻歴を２次固有振動モードに基づいて算出することによって、建物の各層の相対変位の時刻歴を算出したので、外乱時において測定に基づいて求められた建物最上層の相対変位の時刻歴を用いて建物の層間変位の推定値を算出する場合において、演算負荷を軽減できるとともに、算出される層間変位の推定値の精度を向上させることができる。
また、建物最上層相対変位算出ステップで得られた建物最上層の相対変位の時刻歴の周波数成分を、建物の２次固有周波数ｆ２よりも低い周波数成分である低周波成分の時刻歴と建物の２次固有周波数ｆ２以上の高周波成分の時刻歴とに分離する周波数成分分離ステップを備え、各層変位推定ステップでは、建物の変形を１次固有振動モードでの相対変位と２次固有振動モードでの相対変位との和とみなし、建物の１次固有振動モードでの建物最上層以外の各層の相対変位の時刻歴を算出する第１ステップと、建物の２次固有振動モードでの建物最上層の相対変位の時刻歴を周波数成分分離ステップで求めた高周波成分の時刻歴とみなして、２次固有振動モードでの建物最上層以外の各層の相対変位の時刻歴を２次固有振動モードに基づいて算出する第２ステップとを実施することによって、建物の各層の相対変位の時刻歴を算出し、第１ステップにおいては、建物の静的弾塑性解析を実施し、周波数成分分離ステップで求めた低周波成分の時刻歴の最大値に最も近い変形値が得られた変形性状に基づいて建物の１次固有振動モードでの建物最上層以外の各層の相対変位の時刻歴を算出したので、１次固有振動モードでの層間変位の最大値の推定精度を向上させることができる。
周波数成分分離ステップでは、ローパスフィルターを用いて、建物最上層の相対変位の時刻歴の周波数成分から低周波成分の時刻歴を抽出するとともに、建物最上層の相対変位の時刻歴の周波数成分から低周波成分の時刻歴を引いて、当該低周波成分以外のその他の成分である高周波成分の時刻歴を抽出することとし、ローパスフィルターのカットオフ周波数ｆｃを、(１次固有周波数ｆ１＋２次固有周波数ｆ２)／２としたので、建物最上層の相対変位の時刻歴ＸＲ(t)の周波数成分を、建物の２次固有周波数ｆ２よりも低い周波数成分である低周波成分の時刻歴ＬＸＲ(t)と、建物の２次固有周波数ｆ２以上の高周波成分の時刻歴ＨＸＲ(t)とに、簡単かつ精度良く分離できるとともに、建物の最上層以外の層の１次固有振動モードでの相対変位の時刻歴及び２次固有振動モードでの相対変位の時刻歴の推定精度も良く、かつ、演算負荷も軽減できるようになる。
According to the building interlayer displacement estimation method according to the present invention, it is a method for estimating the interlayer displacement of a building when the evaluation target building is subjected to disturbance, and the building uppermost layer when the evaluation target building receives disturbance The absolute displacement time history of the building and the absolute displacement time history of the bottom layer of the building are measured, and the absolute displacement time history of the bottom layer of the building is subtracted from the absolute displacement time history of the top layer of the building. Relative displacement calculation step for the top layer of the building to obtain the time history of displacement, eigenvalue analysis step to perform eigenvalue analysis to obtain the natural frequency and natural vibration mode of the building to be evaluated, and the top layer of the building based on the natural vibration mode of the building Each layer displacement estimation step for calculating the relative displacement time history of each layer, and the interlayer displacement estimation step for calculating the interlayer displacement time history of the building based on the relative displacement time history obtained in each layer displacement estimation step. In the building top layer relative displacement calculation step, the absolute displacement time history of the building top layer and the absolute displacement time history of the building bottom layer were measured using a navigation satellite system. When calculating the estimated value of the interlayer displacement of the building after the disturbance based on the measured relative displacement of the top layer of the building, the relative displacement of the top layer of the building can be obtained accurately, and the estimated value of the calculated interlayer displacement Accuracy can be improved.
In addition, the frequency component of the time history of the relative displacement of the top layer of the building obtained in the building top layer relative displacement calculation step is used as the time history of the low frequency component that is lower than the secondary natural frequency f 2 of the building and the building. And a frequency component separation step for separating high-frequency components having a frequency higher than or equal to the secondary natural frequency f 2. In each layer displacement estimation step, relative deformation in the primary natural vibration mode and the secondary natural vibration mode are determined in each layer displacement estimation step. 1st natural vibration considering the time history of the relative displacement of the top layer of the building in the primary natural vibration mode of the building as the time history of the low frequency component obtained in the frequency component separation step. Calculates the time history of relative displacement of each layer other than the top layer of the building in the mode based on the primary natural vibration mode, and separates the time history of the relative displacement of the top layer of the building in the secondary natural vibration mode of the frequency component By considering the time history of the relative displacement of each layer other than the top layer of the building in the secondary natural vibration mode as the time history of the high-frequency component obtained in step, by calculating the time history of each layer of the building based on the secondary natural vibration mode Since the time history of relative displacement has been calculated, the calculation load can be reduced when calculating the estimated value of the interlayer displacement of the building using the time history of the relative displacement of the top layer of the building obtained based on the measurement during disturbance. At the same time, the accuracy of the calculated estimated value of the interlayer displacement can be improved.
In addition, the frequency component of the time history of the relative displacement of the top layer of the building obtained in the building top layer relative displacement calculation step is used as the time history of the low frequency component that is lower than the secondary natural frequency f 2 of the building and the building. And a frequency component separation step for separating high-frequency components having a frequency higher than or equal to the secondary natural frequency f 2. In each layer displacement estimation step, relative deformation in the primary natural vibration mode and the secondary natural vibration mode are determined in each layer displacement estimation step. The first step of calculating the time history of relative displacement of each layer other than the top layer of the building in the primary natural vibration mode of the building in the primary natural vibration mode of the building, Considering the time history of the relative displacement of the upper layer as the time history of the high frequency component obtained in the frequency component separation step, the time history of the relative displacement of each layer other than the top layer of the building in the secondary natural vibration mode is changed to the secondary natural vibration mode. Based on The time step of relative displacement of each layer of the building is calculated by performing the second step to calculate, and in the first step, the static elasto-plastic analysis of the building is performed and the low frequency obtained in the frequency component separation step is calculated. Since the time history of the relative displacement of each layer other than the top layer of the building in the primary natural vibration mode of the building was calculated based on the deformation property that obtained the deformation value closest to the maximum value of the time history of the frequency component, the primary The estimation accuracy of the maximum value of the interlayer displacement in the natural vibration mode can be improved.
In the frequency component separation step, the low frequency component time history is extracted from the frequency component of the relative displacement time history of the top layer of the building using a low-pass filter, and the low frequency component is extracted from the frequency component of the relative displacement time history of the top layer of the building. pull the time history of the frequency component, and extracting the time history of the high frequency components are components other than the low frequency components, the cut-off frequency f c of the lowpass filter, (first natural frequency f 1 +2 primary Since the natural frequency is f 2 ) / 2, the frequency component of the time history X R (t) of the relative displacement of the top layer of the building is the time of the low frequency component that is a frequency component lower than the secondary natural frequency f 2 of the building. The history L X R (t) and the time history H X R (t) of the high frequency component higher than the secondary natural frequency f 2 of the building can be easily and accurately separated, and one of the layers other than the top layer of the building In the next natural vibration mode Time history of the relative displacement and the estimation accuracy is good in the time history of the relative displacement in the secondary natural vibration mode, and also to be able to reduce calculation load.
実施形態１
実施形態１による建物の層間変位推定方法は、評価対象の建物が地震等の外乱を受けた際の建物の層間変位を推定する方法であって、建物最上層相対変位取得ステップと、固有値解析ステップと、周波数成分分離ステップと、各層変位推定ステップと、層間変位推定ステップと、を備える。
The building interlayer displacement estimation method according to the first embodiment is a method for estimating the building interlayer displacement when the evaluation target building is subjected to a disturbance such as an earthquake, and includes a building top layer relative displacement acquisition step and an eigenvalue analysis step. And a frequency component separation step, each layer displacement estimation step, and an interlayer displacement estimation step.
建物最上層相対変位取得ステップは、地震時において建物最上層の相対変位の時刻歴ＸＲ(t)を取得するステップである。
建物最上層の相対変位の時刻歴ＸＲ(t)を取得する方法は、図１に示すように、評価対象の建物Ｂ（以下、単に「建物」という）の建物最下層Ｕ（以下、単に「建物最下層」という）又は建物近辺の地上Ｅ（以下、単に「地上」という）と、建物最上層（屋上）Ｒ（以下、単に「建物最上層」という）とに、それぞれＧＮＳＳ（航法衛星システム（ｇｌｏｂａｌ ｎａｖｉｇａｔｉｏｎ ｓａｔｅｌｌｉｔｅ ｓｙｓｔｅｍ））の１つであるＧＰＳ（グローバル・ポジショニング・システム）の受信機（ＧＰＳ受信機）Ｇを１つずつ設置した建物最上層相対変位取得装置を用いる。
当該建物最上層相対変位取得装置を用いて、建物最下層又は建物近辺の地上の絶対変位の時刻歴と、建物最上層の絶対変位の時刻歴とが計測される。
そして、図２に示すように、ＧＰＳにより計測した建物最上層の絶対変位の時刻歴（Ｘ０(t)＋ＸＲ(t)）からＧＰＳにより計測した建物最下層又は建物近辺の地上の絶対変位の時刻歴Ｘ０(t)を引くことにより、建物最上層の相対変位の時刻歴ＸＲ(t)を求める。
The building top layer relative displacement acquisition step is a step of acquiring the time history X R (t) of the relative displacement of the building top layer during an earthquake.
As shown in FIG. 1, the method of acquiring the relative displacement time history X R (t) of the top layer of the building is as shown in FIG. 1. The bottom layer U (hereinafter simply referred to as “building”) of the building B to be evaluated (hereinafter simply referred to as “building”). GNSS (navigation satellites) respectively on the ground E (near the “bottom”) or near the building (hereinafter simply “ground”) and the building top (roof) R (hereinafter simply “top building”) A building top-layer relative displacement acquisition device in which one GPS (global positioning system) receiver (GPS receiver) G, which is one of the systems (global navigation satellite system), is installed.
Using the building top layer relative displacement acquisition device, the time history of the absolute displacement on the ground at the bottom of the building or near the building and the time history of the absolute displacement of the top layer of the building are measured.
Then, as shown in FIG. 2, the absolute displacement of the top floor of the building measured by GPS (X 0 (t) + X R (t)) on the ground at the bottom of the building or near the building measured by GPS. The time history X R (t) of the relative displacement of the top layer of the building is obtained by subtracting the time history X 0 (t).
固有値解析ステップは、固有値解析を行って建物の固有周波数と固有振動モードとを求めるステップである。
例えば、建物が３階建て建物である場合、図３に示すような、３質点系モデルの固有振動モードである１次固有振動モード（以下、「１次モード」という）、２次固有振動モード（以下、「２次モード」という）、３次固有振動モード（以下、「３次モード」という）、及び、建物の１次固有周波数ｆ１（Ｈｚ）、２次固有周波数ｆ２（Ｈｚ）、３次固有周波数ｆ３（Ｈｚ）を得る。
The eigenvalue analysis step is a step of performing eigenvalue analysis to obtain the natural frequency and natural vibration mode of the building.
For example, when the building is a three-story building, a primary natural vibration mode (hereinafter referred to as “primary mode”) that is a natural vibration mode of a three-mass system model as shown in FIG. (Hereinafter referred to as “secondary mode”), third-order natural vibration mode (hereinafter referred to as “third-order mode”), and primary natural frequency f 1 (Hz) of the building, secondary natural frequency f 2 (Hz) A third natural frequency f 3 (Hz) is obtained.
周波数成分分離ステップは、ローパスフィルターを用いて建物最上層の相対変位の時刻歴ＸＲ(t)の周波数成分を２つに分離するステップである。
即ち、図４（ａ）に示すように、ローパスフィルターＬＰを用いて、時刻歴ＸＲ(t)から低周波成分の時刻歴ＬＸＲ(t)を抽出するとともに、図４（ｂ）に示すように、時刻歴ＸＲ(t)から低周波成分の時刻歴ＬＸＲ(t)を引いて、当該低周波成分以外のその他の成分である高周波成分の時刻歴ＨＸＲ(t)を抽出する。即ち、ＸＲ(t)とＬＸＲ(t)との同時刻での値を引き算した値ＨＸＲの時刻歴ＨＸＲ(t)を抽出する。
つまり、図４（ｃ）に示すように、建物最上層の相対変位の時刻歴ＸＲ(t)を低周波成分の時刻歴ＬＸＲ(t)と高周波成分の時刻歴ＨＸＲ(t)とに分ける。
周波数成分分離ステップでは、建物最上層の相対変位の時刻歴ＸＲ(t)の周波数成分を、建物の２次固有周波数ｆ２よりも低い周波数成分である低周波成分の時刻歴ＬＸＲ(t)と建物の２次固有周波数ｆ２以上の高周波成分の時刻歴ＨＸＲ(t)とに分離する。
例えば、ローパスフィルターＬＰのカットオフ周波数ｆｃを、建物の１次固有周波数ｆ１よりも高く、建物の２次固有周波数ｆ２よりも低い周波数とすることで、建物最上層の相対変位の時刻歴ＸＲ(t)の周波数成分を、建物の１次固有周波数ｆ１を含むカットオフ周波数ｆｃよりも低い周波数成分の時刻歴ＬＸＲ(t)と、建物の２次以上の固有周波数を含むカットオフ周波数ｆｃ以上の高周波成分の時刻歴ＨＸＲ(t)と、に分離する。これにより、後述する建物の最上層以外の層の１次モードでの相対変位の時刻歴及び２次モードでの相対変位の時刻歴の推定精度も良く、かつ、演算負荷も軽減できるようになる。
具体的には、ローパスフィルターＬＰのカットオフ周波数ｆｃを、(ｆ１＋ｆ２)／２とすることにより、建物最上層の変位の時刻歴ＸＲ(t)を、(ｆ１＋ｆ２)／２よりも低い低周波成分の時刻歴ＬＸＲ(t)と、(ｆ１＋ｆ２)／２よりも高い高周波成分の時刻歴ＨＸＲ(t)と、に分離する。これにより、建物最上層の相対変位の時刻歴ＸＲ(t)の周波数成分を、建物の２次固有周波数ｆ２よりも低い周波数成分である低周波成分の時刻歴ＬＸＲ(t)と、建物の２次固有周波数ｆ２以上の高周波成分の時刻歴ＨＸＲ(t)とに、簡単かつ精度良く分離できるとともに、後述する建物の最上層以外の層の１次モードでの相対変位の時刻歴及び２次モードでの相対変位の時刻歴の推定精度も良く、かつ、演算負荷も軽減できるようになる。
The frequency component separation step is a step of separating the frequency component of the relative displacement time history X R (t) of the top layer of the building into two using a low-pass filter.
That is, as shown in FIG. 4A, the low-frequency component time history L X R (t) is extracted from the time history X R (t) using the low-pass filter LP, and FIG. as shown, time history X R from (t) by subtracting the low frequency component time history L X R (t), the low non-frequency component of the high frequency component which is the other component time history H X R (t) To extract. That is, the time history H X R (t) of the value H X R obtained by subtracting the value of X R (t) and L X R (t) at the same time is extracted.
That is, as shown in FIG. 4C, the time history X R (t) of the relative displacement of the top layer of the building is changed into the time history L X R (t) of the low frequency component and the time history H X R (t of the high frequency component. ).
In the frequency component separation step, the frequency component of the relative displacement time history X R (t) of the uppermost layer of the building is converted into the time history L X R (low frequency component, which is a frequency component lower than the secondary natural frequency f 2 of the building. t) and the time history H X R (t) of the high frequency component higher than the secondary natural frequency f 2 of the building.
For example, the cut-off frequency f c of the lowpass filter LP, higher than the first natural frequency f 1 of the building, by a frequency lower than the second-order natural frequency f 2 of the building, the time of relative displacement of the building uppermost layer the frequency components of the gravel X R (t), the time history of frequency components lower than the cutoff frequency f c which includes a primary natural frequency f 1 of the building L X R (t), 2-order or higher natural frequency of the building a cut-off frequency f c or more high-frequency components of the time-history H X R (t) including, to separate. Thereby, the estimation accuracy of the relative displacement time history in the primary mode and the relative displacement time history in the secondary mode of the layers other than the uppermost layer of the building to be described later is good, and the calculation load can be reduced. .
Specifically, the cut-off frequency f c of the lowpass filter LP, by a (f 1 + f 2) / 2, the time history of the displacement of the building uppermost X R (t), (f 1 + f 2) The time history L X R (t) of the low frequency component lower than / 2 and the time history H X R (t) of the high frequency component higher than (f 1 + f 2 ) / 2 are separated. As a result, the frequency component of the relative displacement time history X R (t) of the top layer of the building is changed to the time history L X R (t) of the low frequency component which is a frequency component lower than the secondary natural frequency f 2 of the building. In addition, it can be easily and accurately separated from the time history H X R (t) of the high frequency component higher than the secondary natural frequency f 2 of the building, and the relative displacement in the primary mode of the layers other than the uppermost layer of the building described later. The estimation accuracy of the time history and the relative displacement time history in the secondary mode are good, and the calculation load can be reduced.
各層変位推定ステップは、建物最上層以外の各層（各階床）の相対変位の時刻歴であるＸＲ−１(t)、…Ｘ１(t)を、固有振動モードに基づいて求めるステップである。
例えば、建物が３階建て建物である場合、図５（ａ）に示すように、建物の２層目（２階）部分の相対変位の低周波成分の時刻歴ＬＸ２(t)、及び、建物の１層目（１階）部分の相対変位の低周波成分の時刻歴ＬＸ１(t)を、固有値解析で得られた３質点系モデルの１次モードに基づいて算出するとともに、図５（ｂ）に示すように、建物の２層目部分の相対変位の高周波成分の時刻歴ＨＸ２(t)、及び、建物の１層目部分の相対変位の高周波成分の時刻歴ＨＸ１(t)を３質点系モデルの２次モードに基づいて推定する。
Each layer displacement estimation step is a step of obtaining X R-1 (t),... X 1 (t), which is the time history of relative displacement of each layer (each floor) other than the top layer of the building, based on the natural vibration mode. .
For example, when the building is a three-story building, as shown in FIG. 5A, the time history L X 2 (t) of the low frequency component of the relative displacement of the second layer (second floor) portion of the building, and The time history L X 1 (t) of the low frequency component of the relative displacement of the first layer (first floor) part of the building is calculated based on the first mode of the three-mass system model obtained by eigenvalue analysis, As shown in FIG. 5B, the time history H X 2 (t) of the high frequency component of the relative displacement of the second layer portion of the building and the time history H of the high frequency component of the relative displacement of the first layer portion of the building. X 1 (t) is estimated based on the second-order mode of the three-mass system model.
実施形態１では、例えば、建物が３階建て建物である場合、当該建物の変形を固有値解析で得られた１次モードと２次モードとの和と考える。
即ち、図５（ａ）に示すように、１次モードでの建物最上層の相対変位の時刻歴を、測定した時刻歴ＸＲ(t)から抽出した低周波成分の時刻歴ＬＸＲ(t)とみなして、１次モードでの建物最上層以外の層である２層目の相対変位の時刻歴ＬＸ２(t)、及び、１層目の相対変位の時刻歴ＬＸ１(t)を、１次モードに基づいて算出するとともに、図５（ｂ）に示すように、２次モードでの建物最上層の相対変位の時刻歴を、測定した時刻歴ＸＲ(t)から抽出した高周波成分の時刻歴ＨＸＲ(t)とみなして、２次モードでの建物最上層以外の層である２層目の相対変位の時刻歴ＨＸ２(t)、及び、１層目の相対変位の時刻歴ＨＸ１(t)を、質点系モデルの２次モードに基づいて算出することで、建物の最上層以外の層の１次モードでの相対変位の時刻歴及び２次モードでの相対変位の時刻歴を推定する。
In the first embodiment, for example, when a building is a three-story building, the deformation of the building is considered as the sum of the primary mode and the secondary mode obtained by eigenvalue analysis.
That is, as shown in FIG. 5A, the time history L X R (of the low frequency component extracted from the measured time history X R (t) is obtained as the time history of the relative displacement of the top layer of the building in the primary mode. t), the time history L X 2 (t) of the relative displacement of the second layer which is a layer other than the top layer of the building in the primary mode, and the time history L X 1 of the relative displacement of the first layer t) is calculated based on the primary mode, and the time history of the relative displacement of the top layer of the building in the secondary mode is calculated from the measured time history X R (t) as shown in FIG. extracted is regarded as time history H X R of the high frequency component (t), the time history of the building is a layer other than the uppermost layer a second layer of relative displacement in the
次に、建物が３階建て建物である場合において、建物最上層以外の層の１次モードでの相対変位の時刻歴、及び、２次モードでの相対変位の時刻歴を、３質点系モデルに基づいて算出する方法について説明する。
多質点系の振動方程式は次式（１）で示される。
１ｑ、２ｑが求まれば、式（４）のＸ２、Ｘ１、即ち、建物の最上層以外の層の１次モードの変位ＬＸ２、ＬＸ１、及び、建物の最上層以外の層の２次モードの変位ＨＸ２、ＨＸ１を計算でき、建物の最上層以外の層である２層目の相対変位Ｘ２＝ＬＸ２＋ＨＸ２、及び、１層目の相対変位Ｘ１＝ＬＸ１＋ＨＸ１の時刻歴を求めることができる。
Next, when the building is a three-story building, the time history of the relative displacement in the primary mode and the time history of the relative displacement in the secondary mode of the layers other than the top layer of the building are expressed as a three-mass system model. A method of calculating based on the above will be described.
The vibration equation of the multi-mass point system is expressed by the following equation (1).
If 1 q and 2 q are obtained, X 2 and X 1 in Equation (4), that is, displacements L X 2 and L X 1 of the first-order modes of the layers other than the top layer of the building, and the top layer of the building The second-order mode displacements H X 2 and H X 1 of the other layers can be calculated, and the second layer relative displacement X 2 = L X 2 + H X 2 and one layer other than the top layer of the building The time history of the relative displacement of the eyes X 1 = L X 1 + H X 1 can be obtained.
即ち、３質点以上の質点系モデルでは、３つ以上の固有モードが存在するが、実施形態１では、各層の変位を推定する際に、１次モード及び２次モードのみを考慮し、表面上は３次モード以上の高次モードを考慮しない。しかし、測定された２次モード以上の成分は、変形推定において、２次モードとして考慮される。 That is, in the mass system model of three or more mass points, there are three or more eigenmodes. However, in the first embodiment, when estimating the displacement of each layer, only the primary mode and the secondary mode are considered, and on the surface. Does not consider higher order modes beyond the third order mode. However, the components of the measured secondary mode or higher are considered as the secondary mode in the deformation estimation.
層間変位推定ステップは、各層変位推定ステップで求めた建物最上層以外の各層の相対変位の時刻歴ＸＲ−１(t)、…Ｘ１(t)に基づいて、建物の各層間変位の各時刻歴を推定するステップである。
即ち、ＬＸ３、ＨＸ３の時刻歴は測定に基づいて求められており、建物の最上層以外の層の１次モードの相対変位ＬＸ２、ＬＸ１、及び、建物の最上層以外の層の２次モードの相対変位ＨＸ２、ＨＸ１の時刻歴は上述した計算で求まっているので、これら値を次式（７）に代入して層間変位δ３、δ２、δ１（図６参照）を算出し、建物の層間変位の各時刻歴を求めることができる。
That is, the time history of L X 3 and H X 3 is obtained based on the measurement, and the relative displacements L X 2 and L X 1 of the primary mode of the layers other than the top layer of the building and the top layer of the building Since the time histories of the secondary mode relative displacements H X 2 and H X 1 of the layers other than those are obtained by the above-described calculation, these values are substituted into the following equation (7) to obtain interlayer displacements δ 3 , δ 2 , δ 1 (see FIG. 6) is calculated, and each time history of the interlayer displacement of the building can be obtained.
そして、各層間変位の各時刻歴において各層間における層間変位の最大値を抽出し、当該最大値が所定の指標値よりも大きければ該当する層間の損傷の可能性が高いと判断し、最大値が所定の指標値より小さければ該当する層間の損傷の可能性が低いと判断する。
そして、層間の損傷の可能性が高いと判断された場合には、該当する層間の補強対策を検討する。
Then, in each time history of each interlayer displacement, the maximum value of interlayer displacement between each layer is extracted, and if the maximum value is larger than a predetermined index value, it is determined that there is a high possibility of damage between the corresponding layers, and the maximum value Is smaller than a predetermined index value, it is determined that the possibility of damage between the corresponding layers is low.
If it is determined that the possibility of damage between the layers is high, the countermeasures for reinforcing the corresponding layers are examined.
実施形態１の建物層間変位推定方法によれば、地震時において測定に基づいて求められた建物最上層の相対変位の時刻歴ＸＲ(t)を用いて地震後の建物の層間変位を容易に推定できるようになって、推定した層間変位と指標値とを比べて地震後の建物の損傷の可能性が高い個所を推定でき、地震後の建物の耐震補強対策を的確に行えるようになる。 According to the inter-building displacement estimation method of the first embodiment, the inter-displacement displacement of the building after the earthquake can be easily performed using the time history X R (t) of the relative displacement of the uppermost layer of the building obtained based on the measurement during the earthquake. It is possible to estimate the location where the possibility of damage to the building after the earthquake is high by comparing the estimated interlaminar displacement and the index value, so that the seismic reinforcement measures for the building after the earthquake can be accurately performed.
実施形態１によれば、測定に基づいて求められた建物最上層の相対変位の時刻歴ＸＲ(t)の周波数成分を２つに分離し、質点系モデルにおいて３つ以上の固有モードが存在する場合でも、１次モード及び２次モードのみを考慮して、建物最上層以外の各層の変位の時刻歴を推定することで、建物の層間変位を推定するようにしているので、地震時において測定に基づいて求められた建物最上層の相対変位の時刻歴ＸＲ(t)を用いて建物の層間変位の推定値を算出する場合において、演算負荷を軽減できるとともに、算出される層間変位の推定値の精度を向上させることができる。 According to the first embodiment, the frequency component of the time history X R (t) of the relative displacement of the top layer of the building determined based on the measurement is separated into two, and there are three or more eigenmodes in the mass system model Even when doing so, considering only the primary mode and secondary mode, we estimate the displacement history of each layer other than the top layer of the building to estimate the interlayer displacement of the building. When calculating the estimated value of the interlayer displacement of the building using the time history X R (t) of the relative displacement of the top layer of the building obtained based on the measurement, the calculation load can be reduced and the calculated interlayer displacement can be reduced. The accuracy of the estimated value can be improved.
また、ＧＰＳを用いた測定に基づいて地震時における建物最上層の相対変位を求めているので、地震時における建物最上層の相対変位を簡単かつ正確に測定でき、層間変位の推定精度を向上させることができる。 In addition, since the relative displacement of the top layer of the building during an earthquake is obtained based on measurements using GPS, the relative displacement of the top layer of the building during an earthquake can be measured easily and accurately, and the estimation accuracy of interlayer displacement is improved. be able to.
実施形態２
実施形態１では、固有値解析で得られる質点系の固有振動モードに基づいて層間変位を推定したが、静的弾塑性解析（増分解析法）で得られる変形性状を用いて層間変位を推定（算出）してもよい。
建物の各階の床に作用する外力ＰＲ、Ｐ２、Ｐ１を外力ＰＲ、Ｐ２、Ｐ１の比を一定に保ったまま増加していく各ステップ（ｉ，ｉ＋１,…）毎に、図７（ａ）に示すように、各階の変形値ＸＲ、Ｘ２、Ｘ１が得られ、図７（ｂ）に示すように、各ステップ（ｉ，ｉ＋１,…）毎の建物モデルの変形性状が得られる。
そして、ＧＰＳによる測定に基づいて求められた建物最上層の変位の時刻歴ＸＲ(t)から周波数成分分離ステップで求めた低周波成分の時刻歴ＬＸＲ(t)の最大値に最も近い変形値ＸＲが得られたステップ時の建物モデルの変形性状を実施形態１の１次モードの代わりに用いて、上述したように、１次モードでの建物最上層以外の各層の相対変位の最大値を算出して推定値とする。
即ち、実施形態２では、建物の静的弾塑性解析を実施し、周波数成分分離ステップで求めた低周波成分の時刻歴ＬＸＲ(t)の最大値に最も近い変形値が得られた変形性状に基づいて建物の１次固有振動モードでの建物最上層以外の各層の相対変位の最大値を算出する。
尚、２次モードでの層間変位の推定値は、実施形態１で説明した方法で算出する。
In the first embodiment, the interlaminar displacement is estimated based on the natural vibration mode of the mass system obtained by the eigenvalue analysis. However, the interlaminar displacement is estimated (calculated) using the deformation property obtained by the static elastic-plastic analysis (incremental analysis method). )
At each step (i, i + 1,...), The external forces P R , P 2 , P 1 acting on the floor of each floor of the building are increased while keeping the ratio of the external forces P R , P 2 , P 1 constant. 7A, the deformation values X R , X 2 , and X 1 of each floor are obtained. As shown in FIG. 7B, the building model for each step (i, i + 1,...) Is obtained. The deformation property is obtained.
And it is closest to the maximum value of the time history L X R (t) of the low frequency component obtained in the frequency component separation step from the time history X R (t) of the displacement of the top layer of the building obtained based on the measurement by GPS. the deformation properties of building models of the deformation value at X R is obtained step used in place of the first mode of
That is, in the second embodiment, a static elasto-plastic analysis of a building is performed, and a deformation value that is closest to the maximum value of the time history L X R (t) of the low frequency component obtained in the frequency component separation step is obtained. Based on the properties, the maximum relative displacement of each layer other than the top layer of the building in the primary natural vibration mode of the building is calculated.
Note that the estimated value of the interlayer displacement in the secondary mode is calculated by the method described in the first embodiment.
実施形態２によれば、建物の各階の床に作用させる外力分布として、例えば「Ａｉ分布にもとづく外力分布」を用いることによって、１次モードでの層間変位の最大値の推定精度を向上させることができる。 According to the second embodiment, for example, “external force distribution based on the Ai distribution” is used as the external force distribution to be applied to the floor of each floor of the building, thereby improving the estimation accuracy of the maximum value of the interlayer displacement in the primary mode. Can do.
尚、実施形態では、各層の変位を推定する際に、１次モード及び２次モードのみに基づいて層間変位の推定値を算出したが、３次モード以上の高次モードも用いるようにして層間変位の推定値を算出するようにしてもよい。 In the embodiment, when the displacement of each layer is estimated, the estimated value of the interlayer displacement is calculated based only on the primary mode and the secondary mode. An estimated value of displacement may be calculated.
本発明は、建物が地震以外の外乱を受けた場合の建物の損傷判断を行う場合において、外乱後の建物の層間変位を推定する際にも適用可能である。 The present invention can also be applied to estimating the interlayer displacement of a building after a disturbance in the case where the damage of the building is determined when the building receives a disturbance other than an earthquake.
Ｂ 建物、Ｇ ＧＰＳ受信機、ＬＰ ローパスフィルター。
B building, G GPS receiver, LP low pass filter.
Claims (4)
評価対象の建物が外乱を受けた際の建物最上層の絶対変位の時刻歴と建物最下層の絶対変位の時刻歴とを計測して、建物最上層の絶対変位の時刻歴から建物最下層の絶対変位の時刻歴を引くことによって建物最上層の相対変位の時刻歴を求める建物最上層相対変位算出ステップと、
評価対象の建物の固有周波数と固有振動モードとを求める固有値解析を行う固有値解析ステップと、
建物の固有振動モードに基づいて建物の最上層以外の各層の相対変位の時刻歴を算出する各層変位推定ステップと、
各層変位推定ステップで求めた各層の相対変位の時刻歴に基づいて建物の層間変位の時刻歴を算出する層間変位推定ステップと、を備え、
建物最上層相対変位算出ステップでは、航法衛星システムを用いて、建物最上層の絶対変位の時刻歴と建物最下層の絶対変位の時刻歴とを計測したことを特徴とする建物層間変位推定方法。 A method for estimating an interlayer displacement of a building when an evaluation target building is subjected to disturbance,
Measure the absolute displacement time history of the uppermost building and the absolute displacement time history of the lowermost building when the building being evaluated is subject to disturbance. A building top layer relative displacement calculating step for obtaining a time history of relative displacement of the building top layer by subtracting a time history of absolute displacement;
An eigenvalue analysis step for performing eigenvalue analysis to obtain the natural frequency and natural vibration mode of the building to be evaluated;
Each layer displacement estimation step for calculating a time history of relative displacement of each layer other than the top layer of the building based on the natural vibration mode of the building;
An interlayer displacement estimation step that calculates a time history of interlayer displacement of the building based on a time history of relative displacement of each layer obtained in each layer displacement estimation step,
In the building top layer relative displacement calculation step, a building interlayer displacement estimation method characterized in that a time history of absolute displacement of the top layer of the building and a time history of absolute displacement of the bottom layer of the building are measured using a navigation satellite system.
各層変位推定ステップでは、建物の変形を１次固有振動モードでの相対変位と２次固有振動モードでの相対変位との和とみなし、建物の１次固有振動モードでの建物最上層の相対変位の時刻歴を周波数成分分離ステップで求めた低周波成分の時刻歴とみなして、１次固有振動モードでの建物最上層以外の各層の相対変位の時刻歴を１次固有振動モードに基づいて算出するとともに、建物の２次固有振動モードでの建物最上層の相対変位の時刻歴を周波数成分分離ステップで求めた高周波成分の時刻歴とみなして、２次固有振動モードでの建物最上層以外の各層の相対変位の時刻歴を２次固有振動モードに基づいて算出することによって、建物の各層の相対変位の時刻歴を算出したことを特徴とする請求項１に記載の建物層間変位推定方法。 The frequency component of the time history of the relative displacement of the building top layer obtained in the building top layer relative displacement calculation step is the time history of the low frequency component that is a frequency component lower than the secondary natural frequency f 2 of the building and 2 of the building. A frequency component separating step for separating the time history of high frequency components of the second natural frequency f 2 or higher
In each layer displacement estimation step, the deformation of the building is regarded as the sum of the relative displacement in the primary natural vibration mode and the relative displacement in the secondary natural vibration mode, and the relative displacement of the top layer of the building in the primary natural vibration mode of the building The time history of the relative displacement of each layer other than the top layer of the building in the primary natural vibration mode is calculated based on the primary natural vibration mode. In addition, the time history of the relative displacement of the top layer of the building in the secondary natural vibration mode of the building is regarded as the time history of the high frequency component obtained in the frequency component separation step, and other than the top layer of the building in the secondary natural vibration mode. 2. The building interlayer displacement estimation method according to claim 1, wherein the time history of relative displacement of each layer of the building is calculated by calculating the time history of relative displacement of each layer based on the secondary natural vibration mode.
各層変位推定ステップでは、建物の変形を１次固有振動モードでの相対変位と２次固有振動モードでの相対変位との和とみなし、建物の１次固有振動モードでの建物最上層以外の各層の相対変位の時刻歴を算出する第１ステップと、建物の２次固有振動モードでの建物最上層の相対変位の時刻歴を周波数成分分離ステップで求めた高周波成分の時刻歴とみなして、２次固有振動モードでの建物最上層以外の各層の相対変位の時刻歴を２次固有振動モードに基づいて算出する第２ステップとを実施することによって、建物の各層の相対変位の時刻歴を算出し、
第１ステップにおいては、建物の静的弾塑性解析を実施し、周波数成分分離ステップで求めた低周波成分の時刻歴の最大値に最も近い変形値が得られた変形性状に基づいて建物の１次固有振動モードでの建物最上層以外の各層の相対変位の時刻歴を算出したことを特徴とする請求項１に記載の建物層間変位推定方法。 The frequency component of the time history of the relative displacement of the building top layer obtained in the building top layer relative displacement calculation step is the time history of the low frequency component that is a frequency component lower than the secondary natural frequency f 2 of the building and 2 of the building. A frequency component separating step for separating the time history of high frequency components of the second natural frequency f 2 or higher
In each layer displacement estimation step, the deformation of the building is regarded as the sum of the relative displacement in the primary natural vibration mode and the relative displacement in the secondary natural vibration mode, and each layer other than the top layer of the building in the primary natural vibration mode of the building. The first step of calculating the time history of the relative displacement of the building, and the time history of the relative displacement of the top layer of the building in the secondary natural vibration mode of the building is regarded as the time history of the high frequency component obtained in the frequency component separating step. Calculate the time history of relative displacement of each layer of the building by performing the second step of calculating the relative displacement time history of each layer other than the top layer of the building in the secondary natural vibration mode based on the secondary natural vibration mode And
In the first step, a static elasto-plastic analysis of the building is carried out, and the building 1 is determined based on the deformation property obtained from the deformation value closest to the maximum value of the time history of the low frequency component obtained in the frequency component separation step. The building interlayer displacement estimation method according to claim 1, wherein a time history of relative displacement of each layer other than the top layer of the building in the next natural vibration mode is calculated.
In the frequency component separation step, the low frequency component time history is extracted from the frequency component of the relative displacement time history of the top layer of the building using a low-pass filter, and the low frequency component is extracted from the frequency component of the relative displacement time history of the top layer of the building. pull the time history of the frequency component, and extracting the time history of the high frequency components are components other than the low frequency components, the cut-off frequency f c of the lowpass filter, (first natural frequency f 1 +2 primary The building interlayer displacement estimation method according to claim 2 or 3, wherein the natural frequency is f 2 ) / 2.
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