JP7272142B2 - Seismic performance evaluation method and program - Google Patents

Description

The present invention relates to a seismic performance evaluation method and program.

A well-known method for evaluating the seismic performance of structures (for example, buildings) is to set the seismic performance (strength, deformation performance, etc.) for each layer (each floor) of the structure and evaluate the seismic performance for each layer. there is

"JSCA Performance Design Manual [Seismic Performance] 2017 Edition", Japan Association of Structural Engineers, March 2018

Each layer of the structure is generally composed of a plurality of members. In general, the seismic performances of the members forming the layer are different from each other.

Conventionally, for example, in consideration of safety, the seismic performance of a layer is set according to the member with the lowest seismic performance among the plurality of members constituting the layer. Therefore, in a layer where members with different seismic performance are mixed, the setting of the seismic performance of the layer could not be said to be appropriate, and the seismic performance of the layer could not be evaluated appropriately.

The present invention has been made in view of such problems, and its object is to appropriately evaluate the seismic performance of a structure having a layer composed of a plurality of members with different seismic performances. .

The main invention for achieving the above object is a method for evaluating the seismic performance of a structure having a layer composed of a plurality of members with different seismic performance, wherein the restoring force characteristics and the ultimate story drift angle of the members are set. , based on the restoring force characteristics, obtain the energy absorption amount up to the final story drift angle and the residual energy absorption capacity of the member showing a change according to the story drift angle, and obtain the energy absorption amount and the residual energy a step of performing, for each member, a process for obtaining a relationship between the seismic performance reduction coefficient of the seismic performance reduction coefficient of the member, which is a ratio of the absorption capacity, and the story drift angle; and obtaining a seismic performance residual rate-story drift angle relationship of said layer by weighting and averaging the relationship with the importance coefficient of each member.

Other features of the present invention will become apparent from the description of the specification and accompanying drawings.

ADVANTAGE OF THE INVENTION According to this invention, it becomes possible to evaluate the earthquake-resistant performance of the structure which has the layer comprised by several members with which earthquake-resistant performance differs appropriately.

It is a flow chart of earthquake-resistant performance evaluation concerning this embodiment. It is the figure which graph-ized the restoring force characteristic _Aij . FIG. 10 is a diagram showing the relationship between seismic resistance reduction coefficient η _ij and interstory drift angle δ _i for members of quantity n _i ; It is an explanatory view for explaining seismic performance residual rate _Ri . FIG. 5 is an explanatory diagram for explaining the difference in the critical inter-story drift angle with respect to the degree of damage of members having different earthquake resistance performances; FIG. 10 is an explanatory diagram for explaining a seismic capacity remaining rate R _kii with respect to the degree of damage k _i of the i layer; FIG. 11 is an explanatory diagram for explaining a limit interlayer deformation angle δ _kii with respect to the degree of damage k _i of the i layer; FIG. 4 is a diagram showing restoring force characteristics A _ij and ultimate interlayer deformation angles δ _ui1 to δ _ui3 of members 1 to 3; FIG. 10 is a diagram showing the relationship between seismic resistance reduction coefficients η _i1 to η _i3 and interstory drift angle δ _i . FIG. 10 is a diagram showing proof stress distribution ratios γ _i1 to γ _i3 of members 1 to 3 in five different cases. FIG. 10 is a diagram showing importance coefficients E _ri1 to E _ri3 of members 1 to 3 in five cases; FIG. 10 is a diagram showing the relationship between seismic performance residual rate R _i and inter-story drift angle δ _i for the i-layer according to five cases. FIG. 4 is a diagram showing critical interlayer deformation angles δ _kii1 to δ _kii3 with respect to degree of damage k _i of members 1 to 3; FIG. 3 is a diagram showing seismic performance reduction coefficients η _ki1 to η _ki3 with respect to degrees of damage k _i of members 1 to 3; FIG. 10 is a diagram showing the seismic capacity remaining rate R _kii with respect to the degree of damage k _i of the i layer in five cases. FIG. 10 is a diagram showing the critical inter-story drift angle δ _kii with respect to the degree of damage k _i of the i layer in five different cases. FIG. 10 is a diagram showing a limit inter-story drift angle δ _kii with respect to the degree of damage k _i of the i layer obtained by a conventional method;

At least the following matters will become apparent from the present specification and the accompanying drawings.

A method for evaluating the seismic performance of a structure having a layer composed of a plurality of members with different seismic performance, wherein the restoring force characteristics and the ultimate story drift angle of the members are set, and based on the restoring force characteristics, the ultimate The energy absorption amount up to the story drift angle and the residual energy absorption capacity of the member that changes according to the story drift angle are obtained, and the seismic performance of the member, which is the ratio of the energy absorption amount and the residual energy absorption capacity. A step of performing a process for obtaining a seismic performance reduction coefficient-story drift angle relationship of the reduction coefficient for each member, and weighting the seismic performance reduction coefficient-story drift angle relationship for each member with an importance coefficient for each member. A method for evaluating seismic performance, comprising the step of averaging the relationship between seismic performance remaining ratio and inter-story drift angle of said layer.

According to this seismic performance evaluation method, it is possible to obtain a strict relationship between the seismic performance residual rate of the story and the story drift angle, and to appropriately evaluate the seismic performance of a structure that has a story composed of multiple members with different seismic performance. It is possible to evaluate to

In this seismic performance evaluation method, a limit story drift angle for the damage degree of the member is set for each member, and based on the seismic performance reduction coefficient-story drift angle relationship, the above-mentioned corresponding to the limit story drift angle It is desirable to obtain the value of the seismic performance reduction coefficient for each of the members, and obtain the seismic performance remaining rate with respect to the degree of damage of the layer by weighting and averaging the values acquired for each of the members by the importance coefficient.

According to this seismic performance evaluation method, it is possible to obtain a strict relationship between the degree of damage to a layer and the rate of remaining seismic performance with respect to the degree of damage to a layer. It is possible to appropriately evaluate the seismic performance.

In this seismic performance evaluation method, the value of the story drift angle corresponding to the obtained seismic performance residual rate for the degree of damage of the layer is obtained based on the seismic performance residual rate of the layer - story drift angle relationship. Therefore, it is desirable to obtain the limit inter-story drift angle for the damage degree of the above-mentioned layer.

According to this seismic performance evaluation method, it is possible to obtain a strict relationship between the degree of damage to a story and the critical story drift angle, and to appropriately evaluate the seismic performance of a structure that has a story composed of multiple members with different seismic performance. can be evaluated.

In this seismic performance evaluation method, the plurality of members with different seismic performance are classified according to the degree of seismic performance to form a plurality of member groups, and the plurality of members with different seismic performance are classified into the plurality of members with different seismic performance. It is preferable to evaluate as a group.

According to such an earthquake-resistant performance evaluation method, it is possible to appropriately evaluate the earthquake-resistant performance of a structure having a layer composed of a plurality of member groups with different earthquake-resistant performances.

A computer that evaluates the seismic performance of a structure having a layer composed of a plurality of members with different seismic performance is set with the restoring force characteristics and the ultimate story drift angle of the members, and based on the restoring force characteristics, the ultimate The energy absorption amount up to the story drift angle and the residual energy absorption capacity of the member that changes according to the story drift angle are obtained, and the seismic performance of the member, which is the ratio of the energy absorption amount and the residual energy absorption capacity. A step of performing a process for obtaining a seismic performance reduction coefficient-story drift angle relationship of the reduction coefficient for each member, and weighting the seismic performance reduction coefficient-story drift angle relationship for each member with an importance coefficient for each member. A program for executing a step of averaging the seismic resistance residual rate of the layer - inter-story drift angle relationship.

According to such a program, it is possible to obtain a strict relationship between the seismic performance residual rate of a story and the story drift angle, and to appropriately evaluate the seismic performance of a structure that has a story composed of multiple members with different seismic performance. becomes possible.

===this embodiment===
The seismic performance evaluation method according to the present embodiment is a method for evaluating the seismic performance of a building (corresponding to a structure) having floors (floors) composed of a plurality of members with different seismic performances. A specific description will be given below.

<<<Seismic performance evaluation method>>>
A method for evaluating the seismic performance of an _i- layer composed of ni members will be described below with reference to FIGS. 1 to 7. FIG. FIG. 1 is a flowchart of earthquake resistance performance evaluation according to this embodiment. 2 to 7 will be described later.

First, for a member j (j=1, 2, . . . quantity n _i . That is, member 1, member 2 _{, .} δ _uij indicates the ultimate interlayer deformation angle δ _u of the member j of the i layer (the same applies hereinafter) and the restoring force characteristic A _ij are set (step S1). The ultimate inter-story deformation angle δ _uij is the inter-story deformation angle δ _i at which the member j breaks down, and the larger the value, the higher the deformation performance (the member does not break even when deformed).

The final story drift angle δ _uij is determined based on the toughness index (F value) in the earthquake resistance diagnosis standard (2017 revision of the earthquake resistance diagnosis standard for existing reinforced concrete buildings, same commentary, Japan Building Disaster Prevention Association, 2017.7). However, it is not limited to this.

The restoring force characteristic A _ij is a characteristic of deformation when a load is applied to a member and a deformation return characteristic when the applied load is reduced (unloaded). ), so select and set as appropriate.

Next, the energy absorption amount P _uij and the residual energy absorption capacity P _rij of the i-layer member j are obtained from the ultimate interlayer deformation angle δ _uij and the restoring force characteristic A _ij (step S2). Although the Takeda model and the origin-oriented model are used as the restoring force characteristic A _ij according to the present embodiment, they are not limited to these.

A method of calculating the energy absorption amount P _u and the residual energy absorption capacity P _r when using the Takeda model and the origin-directed model will be described below. FIG. 2 is a graph of the restoring force characteristic A _ij , the left figure shows the Takeda model, and the right figure shows the origin-oriented model.

<Takeda model>
The Takeda model will be described using the symbols shown in the left diagram of FIG. First, the amount of energy absorption P _u (P _r +P _d ) up to the ultimate interlayer deformation angle δ _u is calculated using equations (1) and (2).

γは除荷時剛性低下指数であり、γ＝０．４が一般的に用いられる。

γ is the unloading rigidity reduction index, and γ=0.4 is generally used.

Next, the residual energy absorption capacity _Pr is calculated using the equation (3).

P _r = P _u - P _d (3)
Here, the consumed energy P _d is obtained by comparing the value of the inter-story drift angle δ with the values of the first inter-story drift angle δ _c and the second inter-story drift angle δ _y , and the conditions among the equations (4) to (10) calculated by a formula that fits

・In the case of inter-story drift angle δ<first inter-story drift angle δ _c :
_Pd = 0 (4)
・When first story drift angle δ _c ≤ story drift angle δ < second story drift angle δ _y :

・When second story drift angle δ _y ≤ story drift angle δ:

<Origin-oriented model>
The origin-oriented model will be described using the symbols shown in the right diagram of FIG. First, the energy absorption amount P _u (P _r +P _d ) up to the ultimate interlayer deformation angle δ _u is calculated using the equation (11).

次に、残存エネルギー吸収能力Ｐ_ｒを（１２）式を用いて計算する。

Next, the residual energy absorption capacity _Pr is calculated using the equation (12).

P _r = P _u - P _d (12)
Here, the consumed energy P _d is obtained by comparing the value of the inter-story drift angle δ with the values of the first inter-story drift angle δ _c and the second inter-story drift angle δ _y . calculated by a formula that fits

・In the case of inter-story drift angle δ<first inter-story drift angle δ _c :
P _d =0 (13)

・When first story drift angle δ _c ≤ story drift angle δ < second story drift angle δ _y :

・When second story drift angle δ _y ≤ story drift angle δ:

<Earthquake resistance reduction coefficient η _ij >
Next, from the energy absorption amount P _uij and the residual energy absorption capacity P _rij calculated above, the seismic performance reduction coefficient η _ij - story drift angle δ _i relationship is obtained (step S3). The seismic performance reduction coefficient η _ij is a continuous quantity between 0 and 1, with 1 being no damage and 0 being the ultimate limit, representing the degree of damage (residual seismic performance) of member j in layer i. .

The seismic performance reduction coefficient η _ij is, for example, according to the damage level classification criteria (damage level classification criteria and recovery technical guidelines for earthquake-damaged buildings, Japan Building Disaster Prevention Association, 2016.3), the ultimate interlayer deformation angle δ _uij ( δ _u in FIG. 2) is set, the energy absorption amount P _uij (area where _Pr and _Pd in FIG. 2 are combined) up to the ultimate interlayer deformation angle δ _uij is calculated, and the residual energy with respect to the energy absorption amount P _uij It can be obtained by taking the ratio of absorption capacities P _rij (area of P _r in FIG. 2), and is expressed by Equation (18).

η _ij =P _rij /P _uij (18)
In equation (18), the residual energy absorption capacity _Prij , which is the numerator on the right side, changes according to the interlayer deformation angle _δi . That is, the equation (18) becomes an equation representing the seismic performance reduction coefficient η _ij - story drift angle δ _i relationship.

FIG. 3 is a diagram showing the relationship between the seismic performance reduction coefficient η _ij and the story drift angle δ _i for the number of members n _i . As shown in FIG. 3, the seismic performance reduction coefficient η _ij of all members is expressed as a continuous quantity between 0 and 1, with 1 being no damage and 0 being the ultimate limit, regardless of whether the seismic performance is high or low.

In this embodiment, the seismic performance reduction coefficient η _ij is obtained using the equation (18), but the method for obtaining the seismic performance reduction coefficient η _ij is not limited to this.

<Earthquake-resistant performance residual rate R _i >
Next, the seismic performance reduction coefficient η _ij - story drift angle δ _i relationship of each member is weighted and averaged by the importance coefficient E _rij of each member to obtain the seismic performance residual rate R _i - story drift angle δ _i of the i layer. A relationship is obtained (step S4).

FIG. 4 is an explanatory diagram for explaining the seismic performance residual rate R _i . The left figure shows the seismic performance reduction coefficient η _ij - story drift angle δ _i relationship, and the right figure shows the seismic performance residual rate R _{i .} - story drift angle δ _i relationship. The seismic performance residual rate R _i is an index representing the degree of damage (residual seismic performance) of the i-layer as a continuous quantity between 0 and 1, with 1 being no damage and 0 being the ultimate limit.

The importance coefficient E _rij indicates the importance of the member j in the i layer, and can be obtained, for example, using the equation (19), but is not limited to this.

Ｐ_ｕｉｊ：ｉ層の部材ｊの終局層間変形角δ_ｕｉｊまでのエネルギー吸収量
ｉ層の耐震性能残存率Ｒ_ｉ－層間変形角δ_ｉ関係は、耐震性能低減係数η_ｉｊ－層間変形角δ_ｉ関係を重要度係数Ｅ_ｒｉｊで重み付け平均した関係なので、（２０）式で求めることができる。

P _uij : Energy absorption amount up to the ultimate inter-story drift angle δ _uij of member j in layer i Seismic performance residual rate of i-layer R _i - inter-story drift angle δ _i relationship is seismic performance reduction coefficient η _ij - inter-story drift angle δ _i Since the relationship is weighted and averaged by the importance coefficient E _rij , it can be obtained by equation (20).

ｉ層の耐震性能残存率Ｒ_ｉ－層間変形角δ_ｉ関係は、図４の右図に示すように、グラフ上の１つの曲線で表すことができる。つまり、かかる曲線とｉ層の層間変形角δ_ｉとから、数量ｎ_ｉの部材で構成されたｉ層の耐震性能（残存耐震性能であってｉ層の耐震性能残存率Ｒ_ｉの値）を評価することが可能となる。

The relationship between the seismic performance residual rate R _i of the i-layer and the inter-story drift angle δ _i can be represented by one curve on the graph as shown in the right diagram of FIG. In other words, from this curve and the inter-story deformation angle _δi of the i-layer, the seismic performance of the i-layer (remaining seismic-resistant performance and the value of the seismic performance survival rate _Ri of the i-layer) composed of the number of members n _i can be calculated. can be evaluated.

In the method for evaluating the seismic performance of the i-layer in steps S1 to S4, the restoring force characteristic A _ij and the ultimate inter-story drift angle δ _uij of the member j are set, and based on the restoring force characteristic A _ij , the ultimate inter-story drift angle δ _uij The energy absorption amount P _uij up to and the residual energy absorption capacity P _rij of the member j showing a change according to the interlayer deformation angle _δi are obtained, and the ratio of the energy absorption P _uij and the residual energy absorption capacity P _rij is Seismic performance reduction coefficient η _ij of member j - story drift angle _δ A process for obtaining _the relationship between seismic performance reduction coefficient η _ij and story drift angle δ i for each member, It can also be rephrased as a seismic performance evaluation method _comprising the step of weighting and averaging the i relationship with the importance coefficient E _rij for each member to obtain the seismic performance residual rate R _i -straight drift angle _δi relationship of the i layer.

<Earthquake resistance remaining rate R _kii for degree of damage k _i >
Next, the critical story drift angle δ _kiij is set for the degree of damage k _i of the member j of the i layer (step S5), and the residual rate of seismic performance R _kii for the degree of damage k _i of the i layer is calculated (step S6). .

The degree of damage k _i is, for example, based on “Damage degree classification criteria and recovery technical guidelines for earthquake-damaged buildings, Japan Building Disaster Prevention Association, 2016.3”, in order from the smallest damage to the i layer, no damage It can be classified as light, minor, moderate, and severe damage. For each degree of damage, a corresponding limit story drift angle δ _kiij (minimum story drift angle δ _i at each degree of damage k _i ) is set. In Non-Patent Document 1, for example, the limit inter-story deformation angle δ _kiij is 1/150 (unit: rad) for small damage, 1/100 for medium damage, Wreckage is set to 1/75.

Fig. 5 is an explanatory diagram for explaining the difference in the critical story drift angle with respect to the degree of damage of members with different seismic performance. there is

Comparing the left and right diagrams in FIG. 5, members with lower seismic performance show small, medium, and severe damage with small deformation (interlayer deformation angle δi) and load (shear force Q). In other words, the critical interlaminar drift angle for the degree of damage to the member differs depending on the seismic performance of the member. Therefore, for each of the number n _i of members, a limit interlayer deformation angle δ _kiij is set for the degree of damage k _i of member j.

FIG. 6 is an explanatory diagram for explaining the seismic performance residual rate R _kii with respect to the degree of damage _{k i} of the i layer. _kiij , and the figure on the right shows the seismic performance survival rate _Rkii with respect to the degree of damage _ki of the i layer. In the following figures, regarding the parameters for small damage (medium damage, large damage) of the degree of damage k _i , the limit inter-story deformation angle is δ _{small damage ij} (δ _{medium damage ij} , δ _{large damage ij} ), and the seismic performance reduction coefficient is sometimes expressed as η _{small damage ij} (η _{medium damage ij} , η _{large damage ij} ), and the seismic performance residual rate is expressed as R _{small damage i} (R _{medium damage i} , R _{large damage i} ).

Here, the equation (18) expressing the seismic performance reduction coefficient η _ij of the member j of the i layer can be expressed by the equation (21) as a function of the story drift angle _δi .

g _ij (δ _i )=η _ij (21)
The seismic performance reduction coefficient η _kiij for the degree of damage k _i of the member j in the i layer is the seismic performance reduction coefficient _{η ij} when the inter-story drift angle δ _i coincides with the limit inter-story drift angle δ _kiij for the degree of damage k i. , (21) to (22).

ｉ層の被災度ｋ_ｉに対する耐震性能残存率Ｒ_ｋｉｉは、耐震性能低減係数η_ｋｉｉｊを重要度係数Ｅ_ｒｉｊで重み付け平均した値なので、（２３）式で求めることができる。

Since the seismic performance remaining rate _Rkii for the degree of damage k _i of the i layer is a value obtained by weighting and averaging the seismic performance reduction coefficient η _kiij with the importance coefficient E _rij , it can be obtained by Equation (23).

なお、ステップＳ５、Ｓ６のｉ層の耐震性能評価方法は、部材ｊの被災度ｋ_ｉに対する限界層間変形角δ_ｋｉｉｊを部材毎に設定し、耐震性能低減係数η_ｉｊ－層間変形角δ_ｉ関係に基づいて、限界層間変形角δ_ｋｉｉｊに対応する耐震性能低減係数η_ｋｉｉｊの値を、部材毎に取得し、部材毎に取得された値を重要度係数Ｅ_ｒｉｊで重み付け平均してｉ層の被災度ｋ_ｉに対する耐震性能残存率Ｒ_ｋｉｉを求める耐震性能評価方法、と言い換えることもできる。

In the method for evaluating the seismic performance of the i-layer in steps S5 and S6, the limit inter-story drift angle δ _kiij for the damage degree k _i of the member j is set for each member, and the seismic performance reduction coefficient η _ij - inter-story drift angle δ _i relationship Based on this, the value of the seismic performance reduction coefficient η _kiij corresponding to the limit story drift angle δ _kiij is obtained for each member, and the values obtained for each member are weighted and averaged by the importance coefficient E _rij for the i layer. It can also be rephrased as a seismic performance evaluation method for determining the seismic performance remaining rate R _kii with respect to the degree of damage k _i .

<Limit inter-layer deformation angle δ _kii for i-layer damage degree k _i >
Next, the limit inter-layer deformation angle δ _kii for the degree of damage k _i of the i layer is obtained (step S7). FIG. 7 is an explanatory diagram for explaining the limit inter-story drift angle δ _kii with respect to the degree of damage k _i of the i layer.

The equation (20) expressing the seismic performance residual rate R _i of the i-layer can be expressed by the equation (24) as a function of the story drift angle δ _i .

f _ij (δ _i )=R _i (24)
Since the critical story drift angle δ _kii for the degree of damage k _{i of} the i layer is the story drift angle δ _i when the residual rate of seismic performance Ri coincides with the rate of residual seismic performance R _kii for the degree of damage k _i , (24 ) from the formula (25).

そうしたら、かかる限界層間変形角δ_ｋｉｉを閾値として、ｉ層における被災度クライテリアを定める。すなわち、図７に示すように、ｉ層の層間変形角δ_ｉが、０～δ_小破ｉであれば被災度が無被害・軽微、δ_小破ｉ～δ_中破ｉであれば被災度が小破、δ_中破ｉ～δ_大破ｉであれば被災度が中破、δ_大破ｉ以上であれば被災度が大破、と定める。そうすると、地震により発生したｉ層の層間変形角δ_ｉが、いずれの被災度ｋ_ｉに該当するか確認することが可能となる。

Then, the critical inter-story deformation angle δ _kii is used as a threshold to determine the degree of damage criteria for the i-layer. That is, as shown in FIG. 7, if the inter-layer deformation angle δ _i of the i layer is 0 to δ _{small damage i} , the degree of damage is no damage or light, and if δ _{small damage i} to δ _{medium damage i} , the degree of damage is is minor damage, δ _{medium damage i} to δ _{heavy damage i} is medium damage, and δ _{heavy damage i} or more is heavy damage. Then, it becomes possible to confirm to which degree of damage k _i the interlayer deformation angle _δi of the i-layer caused by the earthquake corresponds.

In step S7, the method for evaluating the seismic performance of the i-layer is to calculate the value of the inter-story drift angle _δi corresponding to the calculated seismic performance residual rate R _kii for the i-layer damage level ki, and the seismic performance residual rate R It can also be rephrased as a seismic performance evaluation method for determining the critical inter-story drift angle δ _kii for the degree of damage k _i of the i-layer by obtaining it based on the relationship between i and the inter _- story drift angle δ _i .

<<<calculation example>>>
Next, an example of calculating the critical inter-story drift angle δ _kii with respect to the degree of damage k _i of the i-layer composed of three types of members with different seismic performance using the earthquake resistance performance evaluation method described above is shown below.

The object of the calculation example is an i-layer composed of two types of bending members and one type of shearing member with different seismic performance (yield strength, deformation performance, etc.) in an RC building. Then, the bending members are set to member 1 and member 2, and the shearing member is set to member 3, and the restoring force characteristics A _i1 to A _i3 and the ultimate interlayer deformation angles δ _ui1 to δ _ui3 of the members 1 to 3 are set. In the present embodiment, when the necessary items for members 1 to 3 (eg, material, evaluation formula) are input to the computer, the computer calculates and sets the restoring force characteristics A _i1 to A _i3 etc. of members 1 to 3 individually. .

FIG. 8 is a diagram showing the restoring force characteristics A _i1 to A _i3 of members 1 to 3 and the ultimate interlayer deformation angles δ _ui1 to δ _ui3 . As the unloading stiffness (K _ruij in FIG. 8) in the restoring force characteristics A _i1 to A _i3 , the Takeda model is used for bending members, and the origin-oriented model is used for shear members.

After setting the restoring force characteristics A _i1 to A _i3 of the members 1 to 3, the seismic performance of the members 1 to 3 is calculated from the restoring force characteristics A _i1 to A _i3 and the ultimate interstory deformation angles δ _ui1 to δ _ui3 of the members 1 to 3. The reduction coefficients η _i1 to η _i3 are obtained from the above equation (18).

FIG. 9 is a diagram showing the relationship between seismic performance reduction coefficients η _i1 to η _i3 and story drift angle δ _i . From FIG. 9, when the story drift angle _δi is the same, member 1 has the largest seismic performance reduction coefficient _ηi1 , member 2 has the second largest seismic performance reduction coefficient _ηi2 , and member 3 has the seismic performance reduction coefficient η. It can be seen that _i3 is the smallest. That is, it can be seen that member 1 has the highest earthquake resistance performance, member 2 has the second highest earthquake resistance performance, and member 3 has the lowest earthquake resistance performance.

Next, the seismic performance reduction coefficient η _i1 to η _i3 - inter-story deformation angle δ _i is weighted and averaged with the importance coefficients E _ri1 to E _ri3 of members 1 to 3, and the seismic performance residual rate R _i of the i-layer - inter-story deformation is calculated. Determine the angle δ _i relation.

In the calculation example according to the present embodiment, the importance coefficients E _ri1 to E _ri3 of the members 1 to 3 are calculated using the proof stress distribution ratios γ _i1 to γ _i3 of the members 1 to 3. The yield strength sharing ratios γ _i1 to γ _i3 are ratios of the yield strength sharing of the member to the yield strength of the entire layer, and are obtained from the formula (26).

Ｑ_ｕｉｊ：ｉ層の部材ｊの耐力
また、この計算例では、耐力分担率γ_i１～γ_i３の割合を変更したケース１～５を設定して５ケース分の耐力分担率γ_i１～γ_i３について計算を行う。図１０は、５ケース別における部材１～３の耐力分担率γ_i１～γ_i３を示した図である。図１０に示すように、５ケースのうちのいずれのケースにおいても、耐力分担率γ_i１～γ_i３の合計が１になる。例えば、ケース１（図の丸印）であれば、部材１のγ_ｉ１が０．９、部材２のγ_ｉ２が０．０７、部材３のγ_ｉ３が０．０３であり、ケース２（図のダイヤ印）であれば、部材１のγ_ｉ１が０．７、部材２のγ_ｉ２が０．２、部材３のγ_ｉ３が０．１である。

Q _uij : Yield strength of member j in layer i In addition, in this calculation example, cases 1 to 5 in which the ratio of the yield strength sharing ratios γ _i1 to γ _i3 are changed are set, and yield strength sharing ratios γ _i1 to γ _i3 for five cases are set. Calculate about FIG. 10 is a diagram showing the proof stress distribution ratios γ _i1 to γ _i3 of members 1 to 3 in five cases. As shown in FIG. 10, the sum of the strength sharing ratios γ _i1 to γ _i3 is 1 in any of the five cases. For example, in case 1 (circled in the figure), _γi1 of member 1 is 0.9, _γi2 of member 2 is 0.07, _γi3 of member 3 is 0.03, and case 2 (circle in the figure) ), _γi1 of member 1 is 0.7, _γi2 of member 2 is 0.2, and _γi3 of member 3 is 0.1.

FIG. 11 shows the calculation of the importance coefficients E _ri1 to E _ri3 of members 1 to 3 in five cases from the yield strength distribution ratios γ _i1 to γ _i3 in the five cases shown in FIG. 10 using equation (19). FIG. 11 is a diagram showing importance coefficients E _ri1 to E _ri3 of members 1 to 3 in five cases.

Once the importance coefficients E _ri1 to E _ri3 are obtained, the seismic resistance reduction coefficient η _i1 to η _i3 - story drift angle δ _i relationship is weighted and averaged by the importance coefficients E _ri1 to E _ri3 , and from the equation (20), i The seismic performance residual rate R _i - story drift angle δ _i relationship of the story is obtained. FIG. 12 is a diagram showing the relationship between the seismic performance residual rate R _i of the i-layer and the inter-story drift angle δ _i .

Next, the limit inter-layer deformation angle δ _kiij for the degree of damage k _i of the member j in the i layer is set. FIG. 13 is a diagram showing the critical interlayer deformation angles δ _kii1 to δ _kii3 with respect to the degree of damage k _i of members 1 to 3. In FIG. Then, the seismic performance reduction coefficient η _kij for the degree of damage k _i of the member j of the i layer is obtained using the equation (22). FIG. 14 is a diagram showing seismic performance reduction coefficients η _ki1 to η _ki3 with respect to degrees of damage k _i of members 1 to 3. In FIG.

Then, weighted averaging of the seismic performance reduction coefficients η _ki1 to η _ki3 for the degree of damage k _i using the importance coefficients E _ri1 to E _ri3 of members 1 to 3 shown in FIG. Determine the seismic performance residual rate R _kii with respect to the degree k _i . FIG. 15 is a diagram showing the seismic capacity remaining rate R _kii with respect to the degree of damage k _i of the i layer.

Then, by substituting the value of the seismic capacity remaining rate R _kii for the damage level k _i of the i-layer into the _equation (25), the limit inter-layer Obtain the deformation angle δ _kii . FIG. 16 is a diagram showing the critical inter-story drift angle δ _kii with respect to the degree of damage k _i of the i layer.

FIG. 17 shows the limit inter-story drift angle δ _kii for the degree of damage k _i of the i-layer obtained by using the conventional method. In the conventional method, even if the yield strength sharing ratios γ _i1 to γ _i3 change, the critical interlaminar deformation angle δ _kii remains constant.

<About calculation method>
In the present embodiment, a computer performs the calculation of the calculation example described above (evaluation of seismic performance of a building having an i-layer composed of a plurality of members with different seismic performance), and the computer has the above-described A program for processing an earthquake resistance performance evaluation method (evaluation method for determining the relationship between the earthquake resistance residual rate Ri of the i-layer and the inter-story drift angle δi) is stored.

That is, the restoring force characteristic A _ij and the ultimate inter-story deformation angle δ _uij of the member j are set in a computer that evaluates the seismic performance of a building having a layer composed of a plurality of members with different seismic performances, and the restoring force characteristic A _ij Based on, the energy absorption amount P _uij up to the final interlayer deformation angle δ _uij and the residual energy absorption capacity P _rij of the member j showing a change according to the interlayer deformation angle δ _i are obtained, and the energy absorption amount P _uij and Seismic performance reduction coefficient η _{ij of} member _j , which is the ratio of residual energy absorption capacity P _rij . a step of weighting and averaging the performance reduction coefficient η _ij - story drift angle δ _i relationship with the importance coefficient E _rij for each member to obtain the seismic performance residual rate R _i - story drift angle δ _i relationship of the i layer. The program was memorized, and the calculation of the example of calculation described above was performed.

<<<Regarding the effectiveness of the method for evaluating seismic performance according to the present embodiment>>>
In this embodiment, the restoring force characteristic A _ij and the ultimate interlayer deformation angle δ _uij of the member j are set, and based on the restoring force characteristic A _ij , the energy absorption amount P _uij up to the ultimate interlayer deformation angle δ _uij and the interlayer The residual energy absorption capacity Prij of the member j that changes according to the deformation angle _δi is obtained, and the seismic performance reduction coefficient η _ij of the member j, which is the ratio of the energy absorption amount P _uij and the _residual energy absorption capacity _Prij , is calculated. A process for _obtaining the seismic performance reduction _coefficient η _ij - story drift angle δ _i relationship for each member, and an importance coefficient E and a step of weighting and averaging by _rij to obtain the seismic performance residual rate R _i - story drift angle δ _i relationship of the i layer. Therefore, it is possible to obtain a strict relationship between the seismic performance residual rate R _i and the story drift angle δ _i of the i-layer, and to appropriately evaluate the seismic performance of a building having an i-layer composed of multiple members with different seismic performance. becomes possible.

Conventionally, for example, in consideration of safety, the seismic performance of a layer is set according to the member with the lowest seismic performance among the plurality of members constituting the layer. For example, when the members in the left and right diagrams of FIG. 5 constitute a layer, the members with low earthquake resistance performance in the right diagram are set as the earthquake resistance performance of the layer. Therefore, in a layer where members with different seismic performance are mixed, the setting of the seismic performance of the layer could not be said to be appropriate, and the seismic performance of the layer could not be evaluated appropriately.

On the other hand, in the present embodiment, the seismic performance reduction coefficient η _ij - story drift angle δ _i relationship is obtained for each member of the i layer, and the seismic performance reduction coefficient η _ij - story drift angle δ _i relationship for each member is calculated. The relationship between seismic performance residual rate R _i and inter-story drift angle δ _i of the i-layer is obtained by weighting and averaging with the importance coefficient E _rij for each layer.

In other words, instead of evaluating the seismic performance of the i-layer using a specific member that composes the i-layer (for example, the member with the lowest seismic performance), the seismic performance of each member that composes the i-layer (seismic performance reduction coefficient η _ij ), and weighted and averaged the seismic performance of each member (seismic performance reduction coefficient η _ij ) by the contribution of each member to the i-layer (importance coefficient E _rij ) to obtain the seismic performance of the i-layer ( It was used as a method of evaluating the seismic performance residual rate R _i ).

According to this seismic performance evaluation method, it is possible to obtain a strict relationship between the seismic performance residual rate R _i and the inter-story drift angle δ _i of the i-layer. It is possible to appropriately evaluate the seismic performance of buildings with

Further, in this embodiment, the critical inter-story drift _angle δ _kiij for the damage degree k _i of the member _j is set for each member, and the critical inter-story drift angle The value of the seismic performance reduction coefficient η _kiij corresponding to δ _kiij is obtained for each member, and the values obtained for each member are weighted and averaged by the importance coefficient E _rij to determine the remaining seismic performance for the damage level _ki of the i layer. It was decided to obtain the rate R _kii .

In other words, instead of setting the seismic performance residual rate _Rkii of the i-layer using the critical interlaminar drift angle _δkiij of a specific member (for example, the member with the lowest seismic performance) that constitutes the i-layer Set the critical story drift angle δ _kiij for each member, obtain the earthquake resistance performance reduction coefficient η _kiij corresponding to the set critical story drift angle δ _kiij for each member, and the contribution of the seismic performance to the i layer for each member (Importance coefficient E _rij ) is a method of obtaining the seismic performance residual rate R _kii of the i layer by weighting and averaging the seismic performance reduction coefficients η _kiij obtained for each member.

According to this seismic performance evaluation method, a strict relationship between the degree of damage k _i of the layer and the survival rate R _kii of the seismic performance of the i-layer can be obtained. It is possible to appropriately evaluate the seismic performance of buildings with

Further, in the present embodiment, the value of the story drift angle δ _i corresponding to the determined seismic performance residual rate R _kii with respect to the degree of damage k _i of the i layer is _calculated as follows: By acquiring based on the _δi relationship, the limit inter-story drift angle _δkii for the degree of damage k _i of the i layer is obtained.

In other words, instead of setting the critical inter-story drift angle δ _{kii of the i-layer using the critical inter-story drift angle δ ki of} a specific member (for example, the member with the lowest seismic performance) that constitutes the i-layer, the above weighted average The inter-story drift angle δ _i corresponding to the seismic performance residual rate R _kii of the i-layer obtained by the above method is used as the limit inter-story drift angle δ _kii of the i-layer.

According to this seismic performance evaluation method, a strict relationship between the damage degree k _i of the story and the inter-story deformation angle δ _i can be obtained. It is possible to appropriately evaluate the seismic performance.

Next, two application examples in which the relationship between the damage degree k _i of the story and the limit story drift angle δ _kii is set based on the present invention and its effectiveness will be shown.

The first case is an example applied to a disaster degree estimation system. By applying the relationship between the degree of damage k _i and the limit interlayer deformation angle δ _kii set based on the present invention to the degree of damage estimation system (for example, JP 2017-194309, JP 5838561), It is possible to set the relationship between the degree of damage k _i and the limit inter-story deformation angle δ _kii of the floors and buildings composed of members having different earthquake resistance performances with high precision and speed. Then, for example, when a large-scale earthquake occurs, the degree of damage k _i can be estimated with high accuracy and speed from the inter-story deformation angle δ _i detected by the building sensor. It is possible to achieve speed and efficiency of

The second is an example of application to earthquake risk assessment. By applying the relationship between the structural damage degree k _i and the limit story drift angle δ _kii set based on the present invention to earthquake risk assessment (for example, Japanese Patent No. 5418038), It is possible to set the relationship between the damage degree k _i of the story and the building and the limit inter-story deformation angle δ _kii with high precision and speed. Then, for example, it becomes possible for a designer or the like to perform performance design with the earthquake risk as a target value.

===Other Embodiments===
The above-described embodiments are intended to facilitate understanding of the present invention, and are not intended to limit and interpret the present invention. The present invention can be modified and improved without departing from its spirit, and it goes without saying that the present invention includes equivalents thereof.

In the above embodiment, the relationship between the seismic performance residual rate R _i and the inter-story drift angle δ _i of the i-layer was determined, and then the limit inter-story drift angle δ _kiij for the damage degree k _i of the member j of the i-layer was set. It is not limited. For example, when setting the ultimate inter-story deformation angle δ _uij and the restoring force characteristic A _ij for the i-layer member j, set the limit inter-story deformation angle δ _kiij for the degree of damage k _i of the i-layer member j at the same time. may

Further, in the above embodiment, the i-layer of the plurality of members j is evaluated for the seismic performance, but the present invention is not limited to this. The i-layer may be evaluated for seismic performance. In other words, even if the plurality of members j with different seismic performance are classified according to the degree of seismic performance to form a plurality of member groups, and the plurality of members j with different seismic performance are evaluated as a plurality of member groups with different seismic performance. good.

Specifically, the members constituting a certain layer are classified into member types having similar deformation performance and failure mode (flexural failure, shear failure, etc.) for each part such as columns, beams, and load-bearing walls.

For example, in an RC building,
・Parts: columns, beams, load-bearing walls ・Member types: member type A, member type B, member type C
Then, the classification table of the members constituting a certain layer is as follows.

ここで、ある層を構成する部材の部材種別への分類方法として、建築基準法の方法がある。柱、梁の種別ならびに耐力壁の種別は、例えば、「建築構造設計指針2019、一般社団法人 東京都建築士事務所協会」に記載の方法で分類される。

Here, as a method for classifying members constituting a certain layer into member types, there is a method according to the Building Standards Law. The types of columns and beams and the types of load-bearing walls are classified, for example, by the method described in "Building Structural Design Guidelines 2019, Tokyo Association of Architectural Firms".

Q Shear force Q _u Ultimate shear force Q _uij Ultimate shear force of i-layer member j P _d Energy consumption P _diji Energy consumption of i-layer member j _Pr Residual energy absorption capacity P _riji Residual energy absorption of i-layer member j Ability _Pu Energy absorption amount up to ultimate inter-story drift _angle P _uij Energy absorption amount up to final inter-story drift angle of member _{j in} layer j Inter-layer drift angle δ _kii Limit inter-layer drift angle δ _kiij Limit inter-layer drift angle for damage degree _ki of i-layer member j Ultimate inter-layer drift angle _{δ uij of} i _- layer member j Ultimate story drift angle η _ij Seismic performance reduction coefficient for i-layer member j η _kiij Seismic performance reduction coefficient for i-layer member j for damage level k _i Seismic performance residual rate for _i -layer damage level k _i Residual rate A _{ij Restoring} force characteristic E _r of i-layer member j Importance coefficient E _riji Importance coefficient of _i- layer member j k _r Unloading stiffness k _rij Unloading stiffness of i-layer member j

Claims (5)

A method for evaluating the seismic performance of a structure having a layer composed of a plurality of members with different seismic performance,
A restoring force characteristic and an ultimate inter-story drift angle of the member are set, and based on the restoring force characteristic, an energy absorption amount up to the final inter-story drift angle and a residual energy absorption of the member showing a change according to the inter-story drift angle. A process of obtaining the capacity and the relationship between the seismic performance reduction coefficient of the member, which is the ratio of the energy absorption amount and the residual energy absorption capacity, and the story drift angle,
performing for each member;
A step of weighting and averaging the seismic performance reduction coefficient-story drift angle relationship for each member with the importance coefficient for each member to obtain the seismic performance residual rate-straight story drift angle relationship of the layer;
A seismic performance evaluation method characterized by having The seismic performance evaluation method according to claim 1,
setting a limit interlaminar deformation angle for each member with respect to the degree of damage of the member;
Based on the seismic performance reduction coefficient-story drift angle relationship, the value of the seismic performance reduction coefficient corresponding to the limit story drift angle is obtained for each of the members,
A method for evaluating seismic performance, wherein the value obtained for each of the members is weighted and averaged by the importance coefficient to obtain a seismic performance remaining rate for the degree of damage of the layer. The seismic performance evaluation method according to claim 2,
By acquiring the value of the story drift angle corresponding to the determined seismic performance residual rate for the degree of damage of the layer based on the relationship between the seismic performance residual rate of the layer and the story drift angle, A seismic performance evaluation method characterized by obtaining a limit interstory drift angle. The seismic performance evaluation method according to any one of claims 1 to 3,
The plurality of members having different seismic performance are classified according to the degree of seismic performance to form a plurality of member groups, and the plurality of members having different seismic performance are evaluated as a plurality of member groups having different seismic performance. Seismic performance evaluation method. A computer that evaluates the seismic performance of structures that have layers composed of multiple members with different seismic performance,
A restoring force characteristic and an ultimate inter-story drift angle of the member are set, and based on the restoring force characteristic, an energy absorption amount up to the final inter-story drift angle and a residual energy absorption of the member showing a change according to the inter-story drift angle. A process of obtaining the capacity and the relationship between the seismic performance reduction coefficient of the member, which is the ratio of the energy absorption amount and the residual energy absorption capacity, and the story drift angle,
performing for each member;
A step of weighting and averaging the seismic performance reduction coefficient-story drift angle relationship for each member with the importance coefficient for each member to obtain the seismic performance residual rate-straight story drift angle relationship of the layer;
A program characterized by causing the execution of

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