JP2017125742A - Mass/rigidity distribution setup method for determining soundness of building and mass/rigidity distribution setup system for determining soundness of building - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a mass/rigidity distribution setup method and mass/rigidity distribution setup system for determining soundness of a building, capable of easily acquiring the mass/rigidity distribution as initial information of a building model for determining the soundness of the building, without requiring a special dynamic analysis model.SOLUTION: A first natural period of a building is acquired by an eaves height of a building and a regression equation of an experimental equation. A mass of each story of the building is set to a fixed mass, and a first rigidity in the first natural period is calculated. When a top story of the building is 1 and a lowest story is N-times as much as a rigidity distribution factor of the top story, a trapezoidal-shaped first rigidity distribution is formed by multiplying the whole by the first rigidity, and a second natural period is calculated from a mass distribution and the first rigidity distribution. A second rigidity distribution is calculated by multiplying the first rigidity distribution by a value obtained by squaring a correction factor of the second natural period/first natural period. A third natural period and a stimulus function are calculated from the mass distribution and the second rigidity distribution. When the third natural period accords with the first natural period, the mass distribution and the second rigidity distribution are defined as the mass distribution and the rigidity distribution.SELECTED DRAWING: Figure 9

Description

  The present invention is for building health judgment that makes it possible to easily obtain the mass and stiffness distribution of the initial information of a building model for judging the health of the building without requiring a special dynamic analysis model. The present invention relates to a mass / rigidity distribution setting method and a mass / rigidity distribution setting system for determining the soundness of a building.

  Sensors have been installed in buildings and civil engineering structures, and structural health monitoring has been attracting attention, as it determines the degree of damage to structures (buildings) based on information from these sensors, and detects damage and evaluates soundness of structures. Yes. In particular, in a multi-layered building such as an office building or an apartment building, when an earthquake occurs, it is required to determine (confirm, grasp, evaluate) the state of the damage early and accurately.

  In addition, a technique for detecting damage (including damage due to deterioration) from a change in vibration characteristics of a target structure using a vibration sensor is a technique for directly detecting damage using a sensor that measures deformation, distortion, and the like. Compared to the above, it is excellent in that the sensor installation position does not have to be the same as the damaged part. For this reason, it can be said that it is a damage detection method suitable for a building / civil engineering structure in which the target structure is large and it is difficult to predict and specify the place where damage occurs in advance.

  If a large number of sensors are installed for each level of the building, it is possible to accurately grasp the response of each floor (layer) of the building and the overall response of the building during an earthquake (see, for example, Patent Document 1). In this case, a large number of sensors are connected to one data recording processing device by cables (wiring), and the detection information (data) of each sensor is collected in one place for detailed analysis. The response acceleration and displacement during an earthquake are detected by a number of sensors installed at each level of the building in this way, and the soundness and damage status (damage, safety, etc.) of the structure is determined from the recorded acceleration waveform information. Sex).

  On the other hand, a sensor is installed in the observation layer of an arbitrarily set building, and based on the response information of the observation layer acquired by the sensor at the time of an earthquake, the model of the building is calculated using Bayes' theorem (learning type response estimation function / Bayes update). The initial parameter (initial information) is corrected to an optimum value, and the response of each layer of the building is estimated using the parameters of the corrected model. (Building health check system for earthquakes (Structural health monitoring system / (For example, see Patent Document 2).

  In this method, in the event of an earthquake, the building design model information (parameters) is corrected (updated) based on the earthquake response information obtained from the sensors installed in a limited observation layer. The response of each layer (each floor) of the building is estimated using the corrected model information. This makes it possible to accurately estimate the response of each layer of the building with a small number of sensors, and perform highly reliable soundness and earthquake resistance evaluation.

JP 2011-132680 A JP 2013-195354 A

  Here, for example, in the structural health monitoring system having the learning type response estimation function (Bayes update) described above, it is necessary to set the building model as initial information, and when setting this initial information (parameter), Generally, a building is treated as a mass system analysis model, and mass and stiffness distributions are used.

  In the past, structural designers set the distribution of mass and stiffness from the design information of the dynamic analysis model that is used in building structure design, and it is necessary to judge the set values by advanced design by experts. ing. As a result, this system itself cannot be applied to buildings where dynamic analysis information is not obtained, and it is difficult to apply this system to many buildings.

  In view of the above circumstances, the present invention makes it possible to easily obtain the mass and stiffness distribution of the initial information of the building model for determining the soundness of the building without requiring a special dynamic analysis model. It is an object of the present invention to provide a mass / rigidity distribution setting method for building health judgment and a mass / rigidity distribution setting system for building health judgment.

  In order to achieve the above object, the present invention provides the following means.

The mass / rigidity distribution setting method for determining the soundness of a building according to the present invention includes a building structure input process for inputting the structure type of the building, the number of building levels, and the stiffness distribution coefficient N at the lowest layer of the building, The first eigenperiod calculation step of obtaining the eave height of the building from the number and the standard floor height, and obtaining the first eigenperiod of the building by the regression equation of the eave height and the empirical formula obtained in advance, and the mass of each level of the building Is set to a constant mass, and the first stiffness calculation step of obtaining the first stiffness k ₁ in the first natural period by k ₁ = m × (2π / T ₁ ) ² , the top layer of the building is 1, the bottom layer A first rigidity distribution creating step of creating a trapezoidal first rigidity distribution obtained by multiplying the rigidity distribution coefficient of the uppermost layer by N times, and multiplying the first rigidity by the whole, a constant mass distribution of the building, and the first rigidity distribution 2nd natural period calculation process to obtain the 2nd natural period from eigenvalue analysis A correction coefficient calculating step of calculating the second natural period / the first natural period to obtain a correction coefficient; and multiplying the first rigidity distribution by a value obtained by squaring the correction coefficient to obtain the second rigidity distribution. A second stiffness distribution calculation step to be obtained; a third natural cycle / stimulus function calculation step to obtain a third natural cycle and a stimulus function by eigenvalue analysis from the constant mass distribution of the building and the second stiffness distribution; and When the period is compared with the first natural period, and the third natural period is coincident with the first natural period, the constant mass distribution and the second rigidity distribution of the building are used to determine the soundness of the building. A mass determination / stiffness distribution determining step for determining soundness, which is determined as a mass distribution and a stiffness distribution.

  The mass / rigidity distribution setting system for determining the soundness of a building according to the present invention includes a building eave height calculation means for obtaining an eave height from the number of building floors and a standard floor height, and A first natural period calculating means for obtaining a first natural period of a building from an empirical regression equation indicating a relation between natural periods; a first rigidity calculating means for calculating a first rigidity in the first natural period; and a mass of the building A second natural period calculating means for obtaining a second natural period of the building by eigenvalue analysis from the distribution and the distribution of the first stiffness, and a correction coefficient calculating for calculating a correction coefficient by calculating the second natural period / the first natural period A second stiffness distribution calculating means for obtaining a second stiffness distribution by multiplying the first stiffness distribution by a value obtained by squaring the correction coefficient, and a third value by eigenvalue analysis from the mass distribution of the building and the second stiffness distribution. Find natural period and stimulus function A third natural period / stimulus function calculating means; a third natural period / first natural period comparing means for comparing the third natural period and the first natural period; and the third natural period is the first natural period. Soundness determination mass distribution / stiffness distribution for determining the building's mass distribution and the second rigidity distribution as the building's soundness determination mass distribution and rigidity distribution when they coincide with each other And a determining means.

  In the mass / rigidity distribution setting method for building soundness judgment and the mass / rigidity distribution setting system for building soundness judgment according to the present invention, no special dynamic analysis model is required, and From the information, the building mass and stiffness distribution as the initial model information of the building can be automatically created.

It is a figure which shows the mass point system analysis model in the soundness confirmation method of the building which concerns on one Embodiment of this invention. It is a figure which shows the soundness confirmation method (Structural health monitoring system which has a learning type | mold response estimation function (Bayes update)) concerning one Embodiment of this invention. It is a figure which shows the regression formula (empirical formula) used with the mass / rigidity distribution setting method for the soundness determination which concerns on one Embodiment of this invention, (a) is a regression formula of S building, (b) is RC / The regression formula of the SRC building is shown. It is a figure which shows the model image of the initial information used with the soundness confirmation method (structural health monitoring system which has a learning type | mold response estimation function (Bayes update)) concerning one Embodiment of this invention. First-order natural frequency (1-layer to S-building model of initial information used in building health check method (structural health monitoring system having learning type response estimation function (Bayes update)) according to an embodiment of the present invention 100 layers), (a) shows before correction, and (b) shows after correction. First natural frequency (1) of RC / SRC building model of initial information used in building health check method (structural health monitoring system having learning type response estimation function (Bayes update)) according to one embodiment of the present invention (A) to (100)), (a) shows before correction, and (b) shows after correction. It is a figure which shows the mass distribution (a), rigidity distribution (b), and stimulus function (up to the fifth order) (c) of the 20-layer building model automatically created from the floor number. It is a figure which shows the mass distribution (a), rigidity distribution (b), and stimulus function (up to the fifth order) (c) of the 40-layer building model automatically created from the floor number. It is a flowchart which shows the soundness confirmation method of the building which concerns on one Embodiment of this invention. It is a figure which shows the mass distribution (a) and rigidity distribution (b) which were calculated | required with the analysis and the soundness confirmation method of the building which concerns on one Embodiment of this invention. It is the result of the simulation which performed the mass distribution and rigidity distribution which were calculated | required with the analysis and the soundness confirmation method of the building which concerns on one Embodiment of this invention as an initial condition, The maximum acceleration distribution (a) of a strong nonlinear response, and the maximum speed It is a figure which shows distribution (b) and maximum displacement distribution (c). It is the result of the simulation performed using the analysis and the mass distribution and rigidity distribution obtained by the building soundness confirmation method according to one embodiment of the present invention as initial conditions, and the maximum acceleration distribution (a) of the linear response and the maximum velocity distribution It is a figure which shows (b) and maximum displacement distribution (c). First-order natural frequency (1-layer to S-building model of initial information used in building health check method (structural health monitoring system having learning type response estimation function (Bayes update)) according to an embodiment of the present invention 100 layers), (a) shows before correction, and (b) shows after correction.

  Hereinafter, a mass / rigidity distribution setting method for building soundness determination and a mass / rigidity distribution setting system for building soundness determination according to an embodiment of the present invention will be described with reference to FIGS. 1 to 13.

Here, in this embodiment, when confirming, grasping, and evaluating (determining) the soundness of multi-layered buildings such as office buildings and apartments using a structural health monitoring system having a learning type response estimation function (Bayes update) The building mass and stiffness distribution as initial information of the building model necessary for the building is set by the mass / rigidity distribution setting method for building soundness judgment according to the present invention.
The mass / rigidity distribution setting method for building soundness determination according to the present invention can also be used when other structural health monitoring systems are applied.

  First, in the building health check method (structural health monitoring system having a learning type response estimation function) according to the present embodiment, as shown in FIGS. 1 and 2, it is installed in a limited observation layer during a certain earthquake. Based on the earthquake response information of the building acquired by the sensor, the building design model information (parameters) is corrected (updated) by learning, and the response of each layer (each floor) of the building using the corrected model information. presume.

Specifically, in the building soundness confirmation method of the present embodiment, first, a mass matrix M, an attenuation coefficient matrix C, and a stiffness matrix K of a design model are given, and the general eigenvalue problem shown in Equation (1) is solved. A j-th order natural angular frequency w _j and a stimulation function φ _j are obtained.

Here, in the “structural health monitoring system having a conventional learning type response estimation function (building soundness confirmation method)”, a function Δk (θ) for correcting the stiffness distribution k is introduced. Thereby, the stiffness distribution is corrected to k ′ = k + Δk (θ), and the stiffness matrix K is corrected to K ′ (θ) correspondingly. At this time, the model parameter is a random variable as shown in Expression (2) (n _p is the number of parameters).

On the other hand, the building response absolute acceleration y _p (θ) of the sensor installation floor (observation layer) is expressed by Equation (3), and the probability model of this building response absolute acceleration can be expressed by Equation (4).

n _s (except those for ground motion measurement) The number of sensors installed in a building, y p _(^ (hat) on) (theta) is defined M, C, in K '(theta) This is the absolute response acceleration of the sensor installation floor at each time when the observed ground motion u is input to the modified design model, and shows that it is normally distributed independently with the same variance σ _y ² as the expected value. Yes.

  Then, when observation data D represented by Equation (5) is obtained during an earthquake, the posterior distribution of θ is obtained by Equation (6) according to Bayes' theorem.

  Here, p (θ) is a prior distribution, and is a uniform distribution that is independent from each other and has an average of 0 as in Expression (7). Further, p (D | θ) is a likelihood function, and is obtained by Expression (8).

Thus posteriori obtained distribution p | When the theta maximizing _{(θ D) θ MAP (^} ( hat) above), theta _MAP (^) is modified by a stiffness matrix K '(θ _MAP ( From ^)), the same eigenvalue problem as in equation (1) is solved to obtain the corresponding stimulus function φ _j ′.

  This means that the design model, which is prior information, has been updated to be closer to reality based on actual observation data. The updated posterior distribution p (θ | D) may be used as a prior distribution for the next earthquake so that continuous learning may be performed.

And if the mode which has a dominant influence on the response of a building is 1 to _nm , the response absolute acceleration on the sensor installation floor can be approximated by equation (9).

D is D = [1... 1] ^T ∈ R ^ns , and Ф _p is a matrix obtained by extracting the row corresponding to the sensor installation floor from Ф = [φ ₁ '... Φ _nm ']. , q is _{q = [q 1 (t)} ··· q nm (t)] 1~n m order mode response relative acceleration vector represented by ^T. Then, the observed response acceleration waveform y _p estimate of modal response relative acceleration from _(~ (tilde) above) q (^) is obtained by Equation (10).

Ф _p ⁺ is a generalized inverse matrix of _{ｐ p} . Thereby, the response y∈R ^nf (n _f is the number of building layers) of all layers can be estimated by the equation (11).

Note that D ′ = [1... 1] ^T ∈ R ^nf . Further, by using the generalized inverse matrix in Expression (10), the number of main modes used for estimation can be arbitrarily set.

  On the other hand, in the present embodiment, the soundness of multi-layered buildings such as office buildings and apartments is confirmed and grasped by the above-described soundness confirmation method (structural health monitoring system having a learning type response estimation function (Bayes update)). The mass distribution m and stiffness distribution k of the building as initial information of the building model required for evaluation (determination) are set by the mass / rigidity distribution setting method for building soundness judgment of the present embodiment shown below. I tried to do it.

  Specifically, the mass / rigidity distribution setting method for building soundness determination according to the present embodiment does not require information on the dynamic analysis model of structural design by an expert, and automatically calculates the rigidity distribution according to the natural period of the building. It is a method to create with.

  In this mass / rigidity distribution setting method for determining the soundness of a building, an empirical formula (regression formula) for the primary period T1 for building design is obtained in advance.

  As shown in FIG. 3, the empirical formula is divided according to the structural type (S structure, RC / SRC structure), and the eigen height of the eave height in the actual building and the primary natural period obtained from the vibration measurement in the building. A regression equation showing the relationship is used. Moreover, as a regression formula of this empirical formula, for example, as shown in FIG. 3, a primary regression formula, a quadratic regression formula, and a logarithmic regression formula are selectively used.

  The log-log regression equation has a high correlation (fitness) from low-rise to high-rise buildings. The primary regression equation has a high correlation at the middle and high layers, the correlation is low at the low layer, and the secondary regression equation tends to have a high correlation at the high layer and a low correlation at the low layer.

If a log-logarithmic regression equation having good compatibility from a low-rise building to a super-high-rise building is used, this regression equation becomes an equation (12) for the S structure and an equation (13) for the RC / SRC structure. T ₁ represents the primary natural period (s), and H represents the eave height (m).

  Next, in the mass / rigidity distribution setting method for building soundness determination according to the present embodiment, only the number of floors of the building is given as information, and the eave height is determined from the standard floor height. In addition, the standard floor height is 4.0 m for S and 3.3 m for RC / SRC.

  In the mass system model, the mass m of each layer is a constant 1.0 t so that the natural period of the building is based on the number of stories, and the rigidity of each layer is 1 for the top layer and N times (for example, 4 times) the stiffness distribution coefficient for the bottom layer. Given as a trapezoidal distribution.

  Note that the rigidity distribution of the building model can be created with an arbitrary trapezoidal distribution, and a trapezoidal distribution other than 4k (N = 4) may be set. At this time, it is preferable to set the trapezoidal distribution in a range of 2 to 5 times (N = 2 to 5), for example.

  Further, the rigidity (stiffness of the first degree of freedom system) k is multiplied by the rank by using a value obtained from the expression (15) obtained by converting the following expression (14) which is the natural period of the one degree of freedom system. Shall.

  A model image of the initial information in the present system obtained by the above calculation is shown in FIG.

  FIG. 5 (a) shows the change in the natural frequency (reciprocal of the natural period) in an S-structure building of 1 to 100 layers (1 floor to 100 floors) of the model obtained by this calculation. .

Here, in FIG. 5A, the abscissa represents the natural frequency to be set, the ordinate represents the natural frequency in the mass system model, and a circle represents a change.
Further, the x-rays indicate the coefficient value (correction magnification) of the natural frequency necessary for the correction because there is a deviation in the natural frequency in the actual calculation.

  And in this embodiment, it correct | amends with the coefficient value for every natural frequency, and corrects the rigidity of an analysis model. FIG. 5B shows the relationship of the natural frequency in the finally corrected mass system model. As shown in FIG. 5B, the relationship of the natural frequency is almost 1, and each layer has The stiffness distribution when the mass is 1.0 t can be determined.

  6 (a) and 6 (b) show the natural frequency distribution before and after the correction of the RC / SRC building, and the mass of each layer is the same as that of the S building. This shows that the rigidity distribution can be determined when 1.0 t is set.

  Next, FIG. 7 (20th floor) and FIG. 8 (40th floor) show examples of building models that are automatically created by designating the number of levels as 20 and 40. In both examples, the shape of the stimulus function is similar because the rigidity of the same trapezoidal distribution is created.

  Here, the mass / rigidity distribution setting method for determining the soundness of the building and the mass / rigidity distribution setting system for determining the soundness of the building are summarized as shown in FIG.

  That is, when the building structure type (S structure, RC / SRC structure), the number of building floors, and the stiffness distribution coefficient N in the lowest layer are input (Step 1: building structure input process), the mass / rigidity distribution for building soundness judgment The eave height is obtained from the building floor height and the standard floor height by the building eave height calculating means of the setting system, and the first natural period calculating means calculates the eave height from the eave height and the regression equation of the empirical formula obtained in advance. One natural period is calculated (Step 2: first natural period calculating step).

  Then, the mass of each level of the building is set to a predetermined constant mass (1 ton), and the first stiffness calculation means calculates the first stiffness in the first natural period using the formula (15) (Step 3: First) Rigidity calculation step). Also, the first layer 1 and the bottom layer are set to N times the stiffness distribution coefficient, and the first stiffness distribution calculating means creates a trapezoidal first stiffness distribution obtained by multiplying the entire first stiffness (Step 4: Create first stiffness distribution) Step / see FIG. 4).

  Next, the second natural period calculation means obtains the second natural period from the mass distribution (all layers 1 ton) and the first stiffness distribution by eigenvalue analysis (Step 5: second natural period calculation step). Further, the correction coefficient calculation means calculates the second natural period / first natural period and sets it as a correction coefficient (Step 6: correction coefficient calculation step / see FIGS. 5A and 6A).

  Next, the second stiffness distribution calculating means obtains the second stiffness distribution by multiplying the first stiffness distribution by the value obtained by squaring the correction coefficient based on the equation (15) (Step 7: second stiffness distribution calculating step). Further, the third natural period / stimulus function calculating means obtains a third natural period and a stimulus function from the mass distribution (1 ton) and the second stiffness distribution by eigenvalue analysis (Step 8: third natural period / stimulus function calculating step).

  Next, it is confirmed by the third natural period / first natural period comparison means that the third natural period coincides with the first natural period (see Step 9 / FIG. 5 (b) and FIG. 6 (b)). . When the soundness determination mass distribution / rigidity distribution determining means confirms that the third natural period coincides with the first natural period, the mass distribution and the second rigidity distribution that become the first natural period are obtained. It can be determined as the mass distribution and rigidity distribution for building soundness determination (Step 10: soundness determination mass / rigidity distribution determining step / see FIG. 4).

  The mass distribution and stiffness distribution obtained by the mass / rigidity distribution setting method for building soundness judgment according to the present embodiment as described above are used as initial information of the building model, and are applied to a 24-story S building model. And the simulation result which performed the response estimation by the soundness confirmation method (structural health monitoring system which has a learning type response estimation function (Bayes update)) of this embodiment is demonstrated.

  In this simulation, acceleration sensors were installed on the 1st, 9th, 17th and 24th floors of a multi-layered building, and the responses of all floors were estimated from these four acceleration waveforms.

  Then, the ground motion was input to the building model, the response analysis was performed, and the absolute acceleration response of each layer was calculated as the true value. Moreover, using the waveform of only the sensor installation floor acquired by the sensor, the absolute acceleration waveform of all layers is obtained by the mass / rigidity distribution setting method for building soundness judgment of the present invention and the building soundness confirmation method of this embodiment. We estimated and compared the true value with the estimated value of all layers.

First, FIG. 10 shows the mass distribution and rigidity distribution obtained by the analysis and the present invention.
FIG. 11 shows a result of comparing the analysis in the strong nonlinear response with the maximum acceleration distribution, the maximum velocity distribution, the maximum displacement distribution, and the maximum interlayer displacement distribution according to the present invention.
FIG. 12 shows the result of comparing the analysis in the linear response with the maximum acceleration distribution, the maximum velocity distribution, the maximum displacement distribution, and the maximum interlayer displacement distribution according to the present invention.

  From these results, it was confirmed that even when the mass / rigidity distribution setting method for determining the soundness of a building according to the present invention was used, the response estimation results of acceleration, velocity, and displacement almost coincided with the analysis. . In addition, when the present invention is used for the inter-layer displacement (displacement difference between adjacent floors: relative displacement), an error of about 10% is recognized at the maximum point of inter-layer displacement for the analysis, but the maximum response is generally good. It was confirmed that it can be estimated.

  Therefore, according to the mass / rigidity distribution setting method for building soundness determination and the mass / rigidity distribution setting system for building soundness determination according to the present embodiment, the structural design movement by an expert in the building model setting. It is possible to create a stiffness distribution that matches the natural period of the building without the need for information on the dynamic analysis model.

  Moreover, when setting the building model used for response estimation, setting information can be easily created by the number of floors and the structure type (S structure, RC / SRC structure).

  Further, the mass and stiffness distribution in the building model obtained by the mass / rigidity distribution setting method for building soundness determination and the mass / rigidity distribution setting system for building soundness determination according to the present embodiment is a normal vibration. It can also be used as a parameter of an analysis model (linear model).

  Here, an example of calculation in the linear regression equation is shown. From FIG. 3, the first-order regression equations are the following equation (16): S structure, and equation (17): RC / SRC structure. T1 represents the primary natural period (s), and H represents the eave height (m).

FIG. 13 (a) shows changes in the natural frequency (reciprocal of the natural period) from the first layer to the 100th layer (from the first floor to the 100th floor) of the model obtained by this regression equation (S structure: Expression (16)). Shown in The horizontal axis indicates the natural frequency to be set, the vertical axis indicates the natural frequency in the mass system model, and the change is indicated by a circle.
In the actual calculation, there is a deviation in the natural frequency, and the coefficient value (correction magnification) of the natural frequency necessary for the correction is indicated by x-rays.

The stiffness of the analysis model is corrected by correcting with the coefficient value for each natural frequency.
FIG. 13B shows the relationship of the natural frequency in the finally corrected mass system model.

  From these results, it is possible to cope with this embodiment even if the regression equation is different, and it is possible to set the optimal primary natural frequency and set the initial information of the building model. I understand.

  However, the regression equation shown in this example shows a tendency for the number of building floors to be lower than the actual one in the lower floors (because the regression equation is highly correlated in buildings with higher floors), It is important to select the optimal regression equation.

  Although one embodiment of the mass / rigidity distribution setting method for building soundness determination and the mass / rigidity distribution setting system for building soundness determination according to the present invention has been described above, the present invention is based on the above embodiment. It is not limited and can be changed as appropriate without departing from the spirit of the invention.

Claims (2)

A building structure input process for inputting the structure type of the building, the number of floors of the building, and the stiffness distribution coefficient N in the lowest layer of the building;
A first eigenperiod calculation step of obtaining the eave height of the building from the number of building hierarchies and the standard floor height, and obtaining the first eigenperiod of the building by a regression equation of the eave height and a predetermined experimental formula;
A first stiffness calculation step of setting a mass of each level of the building to a constant mass, and obtaining a first stiffness k ₁ in the first natural period by k ₁ = m × (2π / T ₁ ) ² ;
A first stiffness distribution creating step of creating a trapezoidal first stiffness distribution in which the top layer of the building is 1 and the bottom layer is N times the stiffness distribution coefficient of the top layer and is multiplied by the first stiffness;
A second natural period calculation step of obtaining a second natural period from the constant mass distribution of the building and the first rigidity distribution by eigenvalue analysis;
A correction coefficient calculation step of calculating a correction coefficient by calculating the second natural period / the first natural period;
A second stiffness distribution calculating step of obtaining a second stiffness distribution by multiplying the first stiffness distribution by a value obtained by squaring the correction coefficient;
A third natural period / stimulus function calculating step of obtaining a third natural period and a stimulus function by eigenvalue analysis from the constant mass distribution of the building and the second stiffness distribution;
The third natural period and the first natural period are compared, and when the third natural period matches the first natural period, the constant mass distribution and the second rigidity distribution of the building are A mass / rigidity distribution setting method for building soundness determination, comprising: a soundness determination mass / rigidity distribution determining step for determining soundness determination mass distribution and rigidity distribution. Building eaves height calculation means for obtaining eave height from the number of building floors and standard floor height,
A first natural period calculating means for obtaining a first natural period of the building from the regression equation of an empirical formula indicating a relationship between the eave height and the eave height obtained in advance and the natural period of the building;
First stiffness calculating means for calculating the first stiffness in the first natural period;
Second natural period calculating means for obtaining a second natural period of the building by eigenvalue analysis from the mass distribution of the building and the distribution of the first rigidity;
Correction coefficient calculation means for calculating the second natural period / the first natural period to obtain a correction coefficient;
Second stiffness distribution calculating means for obtaining a second stiffness distribution by multiplying a value obtained by squaring the correction coefficient by the first stiffness distribution;
A third natural period / stimulus function calculating means for obtaining a third natural period and a stimulus function by eigenvalue analysis from the mass distribution of the building and the distribution of the second stiffness;
A third natural period / first natural period comparing means for comparing the third natural period and the first natural period;
When the third natural period coincides with the first natural period, the mass distribution and the second stiffness distribution of the building that become the first natural period are represented by the mass distribution and the stiffness distribution for building soundness determination. A mass / rigidity distribution setting system for determining the soundness of a building, comprising: a mass distribution / rigidity distribution determining means for determining soundness determined as:

Images