JP2015010459A - Buckling bearing force calculation method - Google Patents
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- 238000004364 calculation method Methods 0.000 title claims abstract description 34
- 239000004567 concrete Substances 0.000 claims abstract description 45
- 230000035882 stress Effects 0.000 claims abstract description 20
- 230000008646 thermal stress Effects 0.000 claims abstract description 8
- 238000005452 bending Methods 0.000 claims description 23
- 230000001052 transient effect Effects 0.000 claims description 9
- 239000011150 reinforced concrete Substances 0.000 description 6
- 238000010438 heat treatment Methods 0.000 description 5
- 238000000034 method Methods 0.000 description 3
- 230000007423 decrease Effects 0.000 description 2
- 230000003014 reinforcing effect Effects 0.000 description 2
- 230000008602 contraction Effects 0.000 description 1
- 230000000694 effects Effects 0.000 description 1
- 238000002474 experimental method Methods 0.000 description 1
- 239000011372 high-strength concrete Substances 0.000 description 1
- 230000002787 reinforcement Effects 0.000 description 1
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Abstract
Description
本発明は、コンクリート柱の火災時の座屈耐力算定方法に関する。 The present invention relates to a method for calculating the buckling strength of a concrete column during a fire.
従来の鉄筋コンクリート柱の構造設計では、地震時等の外力に対して十分な耐力を発現し得るコンクリート強度や配筋量について検討するものの（例えば、特許文献１参照）、軸力に対する座屈破壊の検討を行うことは一般的ではなかった。 In the conventional structural design of reinforced concrete columns, although concrete strength and the amount of reinforcement that can express sufficient strength against external force during an earthquake, etc. are examined (for example, see Patent Document 1), buckling failure of axial force is considered. Consideration was not common.
これは、建築基準法施行令第７７条第５号によって、径長さ比（柱高さ／断面の小径）が１５以下に制限されていたため、柱高さ（柱の長さ）に対して十分な大きさの断面寸法（太さ）を有しており、座屈破壊に対して十分な耐力を備えていると考えられていたためである。 This is because the length-to-length ratio (column height / small diameter of the cross section) was limited to 15 or less by the Building Standards Law Enforcement Ordinance Article 77 No. 5, so the column height (column length) This is because the cross-sectional dimension (thickness) is sufficiently large, and it was considered that it had sufficient strength against buckling failure.
平成２３年の建築基準法の法改正により、鉄筋コンクリート柱に座屈が発生しないことが確認されれば、径長さ比を１５以上にすることが可能となった。なお、圧縮力を負担する部材の座屈耐力の算定式としては、オイラー座屈の式が知られている。 If it was confirmed that the reinforced concrete columns would not buckle due to the 2011 revision of the Building Standards Law, the diameter-to-length ratio could be increased to 15 or more. As a formula for calculating the buckling strength of a member that bears a compressive force, the Euler buckling formula is known.
ところが、火災等により加熱されると、ヤング係数が低下するため、座屈しないように設計されたコンクリート柱でも、座屈の発生が懸念される。
一方、コンクリート柱の火災時の座屈耐力を算定する手法は確立されていない。
However, since the Young's modulus decreases when heated by a fire or the like, buckling is a concern even with concrete columns that are designed not to buckle.
On the other hand, no method has been established for calculating the buckling strength of concrete columns during a fire.
本発明は、前記の問題点を解決するためになされたものであって、コンクリート柱の火災時の座屈耐力算定方法を提案することを課題とする。 The present invention has been made to solve the above-described problems, and an object thereof is to propose a method for calculating the buckling strength at the time of fire of a concrete column.
前記の課題を解決するために、本発明は、火災時のコンクリート柱の座屈耐力を算定する座屈耐力算定方法であって、火災時におけるコンクリート柱の断面の温度分布を把握する温度把握作業と、前記コンクリート柱の断面を複数の要素の集合体にモデル化するモデル化作業と、前記各要素の瞬間ヤング係数を算出するヤング係数算出作業と、前記瞬間ヤング係数に断面二次モーメントを乗じて算出された曲げ剛性を断面全体で積分することで前記断面全体の曲げ剛性である全体曲げ剛性を算出する曲げ剛性算出作業と、前記全体曲げ剛性をオイラー座屈の式に代入して座屈耐力を算出する座屈応力算出作業とを備え、火災時の熱膨張により前記要素に発生する熱膨張ひずみおよび火災時の圧縮力と温度により前記要素に発生する過渡ひずみのうちの少なくとも一方を、前記コンクリート柱に作用する軸力により前記要素に発生する軸力ひずみに加えたひずみを全ひずみとし、前記ヤング係数算出作業では、前記各要素の全ひずみが等しくなると仮定して熱応力解析を行うことで、前記各要素の軸力ひずみを算出し、当該軸力ひずみに対応する瞬間ヤング係数を算出することを特徴としている。
ここで、「軸力ひずみ」は、要素に発生する弾性ひずみと塑性ひずみの和である。
In order to solve the above-mentioned problem, the present invention is a buckling strength calculation method for calculating the buckling strength of a concrete column at the time of fire, and grasps the temperature distribution of the cross section of the concrete column at the time of fire. Modeling work for modeling the section of the concrete column into an assembly of a plurality of elements, Young's modulus calculation work for calculating the instantaneous Young's modulus of each element, and multiplying the instantaneous Young's modulus by the sectional second moment The bending stiffness is calculated by integrating the calculated bending stiffness over the entire cross section to calculate the total bending stiffness, which is the bending stiffness of the entire cross section, and the total bending stiffness is substituted into the Euler buckling formula. A buckling stress calculation work for calculating a proof stress, thermal expansion strain generated in the element due to thermal expansion during a fire, and transient strain generated in the element due to compressive force and temperature during a fire Assuming that at least one of them is the total strain that is added to the axial force strain generated in the element by the axial force acting on the concrete column, the total strain of each element is assumed to be equal in the Young's modulus calculation operation. Then, by performing thermal stress analysis, the axial force strain of each element is calculated, and the instantaneous Young's modulus corresponding to the axial force strain is calculated.
Here, “axial strain” is the sum of elastic strain and plastic strain generated in the element.
なお、前記軸力と前記座屈耐力とを比較し、前記座屈耐力が前記軸力以下である場合に前記コンクリート柱が座屈で破壊すると認定すればよい。 In addition, what is necessary is just to certify that the said concrete pillar will break by buckling, when the said axial force and the said buckling strength are compared and the said buckling strength is below the said axial force.
かかる座屈耐力算定方法によれば、火災時に部材内部に発生する熱応力の影響を考慮したコンクリート柱の座屈耐力を算定することができるため、火災が生じた場合であっても、安全な建物を提供することが可能となる。 According to such a buckling strength calculation method, it is possible to calculate the buckling strength of a concrete column in consideration of the effect of thermal stress generated inside the member in the event of a fire. It becomes possible to provide buildings.
また、コンクリート柱の径長さ比が大きな長柱であっても、当該コンクリート柱に作用する軸力に対して安全性を確保した設計をすることが可能である。 Moreover, even if the concrete column is a long column having a large diameter-to-length ratio, it is possible to design with safety secured against the axial force acting on the concrete column.
本発明の座屈耐力算定方法によれば、コンクリート柱の火災時の座屈耐力を検証し、火災が起きた場合であっても安全な建物を提供することが可能となる。 According to the buckling strength calculation method of the present invention, it is possible to verify the buckling strength of a concrete column at the time of a fire and to provide a safe building even when a fire occurs.
本実施形態では、径長さ比が１５を超える鉄筋コンクリート長柱の火災時の座屈耐力を算定する場合について説明する。
本実施形態の座屈耐力算定方法は、温度把握作業Ｓ１と、モデル化作業Ｓ２と、ヤング係数算出作業Ｓ３と、曲げ剛性算出作業Ｓ４と、座屈応力算出作業Ｓ５とを備えている。
This embodiment demonstrates the case where the buckling proof strength at the time of the fire of the reinforced concrete long column whose diameter length ratio exceeds 15 is calculated.
The buckling strength calculation method according to the present embodiment includes a temperature grasping operation S1, a modeling operation S2, a Young's modulus calculating operation S3, a bending stiffness calculating operation S4, and a buckling stress calculating operation S5.
温度把握作業Ｓ１では、火災時におけるコンクリート柱の断面の温度分布を把握する。
例えば、コンクリート柱の外周囲が同じ温度により加熱された場合について熱伝導解析や実験を行うことで、温度分布の経時変化を把握する。
In the temperature grasping operation S1, the temperature distribution of the cross section of the concrete column during a fire is grasped.
For example, the temporal change of the temperature distribution is grasped by conducting a heat conduction analysis or experiment when the outer periphery of the concrete column is heated at the same temperature.
上記の条件でコンクリート柱を加熱すると、図２の（ａ）に示すように、コンクリート柱の表面側の温度が高く、断面中央部の温度が低い状態となる。そして、さらに加熱を続けると、図２の（ｂ）に示すように、断面中央部の温度も上昇する。 When the concrete column is heated under the above conditions, as shown in FIG. 2 (a), the temperature on the surface side of the concrete column is high, and the temperature at the center of the cross section is low. When the heating is further continued, as shown in FIG. 2B, the temperature at the center of the cross section also increases.
モデル化作業Ｓ２では、図３に示すように、コンクリート柱１の断面を複数の要素の集合体にモデル化する。このとき、各要素の断面形状は同一形状にする。 In the modeling operation S2, as shown in FIG. 3, the cross section of the concrete pillar 1 is modeled into an aggregate of a plurality of elements. At this time, the cross-sectional shape of each element is the same.
本実施形態では、コンクリート柱１の断面を９つに区分する。なお、図３では、９つに区分された要素を火災時の温度分布に応じて三種類に分類し、比較的高温になりやすい部位（二辺が外面に露出する部位）を要素Ａ、温度上昇が中庸な部位（一辺が外面に露出する部位）を要素Ｂ、比較的低温になる部位（外面に露出しない部位）を要素Ｃとした場合について説明する。
なお、モデル化作業Ｓ２は、温度把握作業Ｓ１の前に行ってもよい。また、断面の分割数は限定されるものではない。
In this embodiment, the concrete pillar 1 is divided into nine sections. In FIG. 3, the nine elements are classified into three types according to the temperature distribution at the time of the fire, and the part that tends to be relatively high temperature (part where two sides are exposed to the outer surface) is the element A, the temperature A description will be given of a case where a portion where the rise is moderate (a portion where one side is exposed to the outer surface) is element B and a portion where the temperature is relatively low (a portion which is not exposed to the outer surface) is element C.
The modeling operation S2 may be performed before the temperature grasping operation S1. Further, the number of divisions of the cross section is not limited.
ヤング係数算出作業Ｓ３では、想定される軸力が与えられたコンクリート柱１の熱応力解析を行い、加熱開始後の時刻ｔにおける各要素Ａ〜Ｃの瞬間ヤング係数を算出する。
図４に示す通り、外力として軸力が与えられたコンクリート柱１における軸応力とひずみ（軸力ひずみεσ）の関係は、温度毎に異なる。
In Young's modulus calculation operation S3, thermal stress analysis of the concrete column 1 to which an assumed axial force is applied is performed, and instantaneous Young's modulus of each element A to C at time t after the start of heating is calculated.
As shown in FIG. 4, the relationship of strain and axial stress in the axial force concrete column 1 given as the external force (axial force strain epsilon sigma) it is different for each temperature.
また、コンクリート柱１には、熱膨張に伴う熱膨張ひずみεth（図５参照）と、単位応力あたりの収縮ひずみである過渡ひずみεtr（図６参照）が生じる。
なお、過渡ひずみεtrは、例えば、４００℃のとき、単位応力あたりの収縮ひずみは約１．５×１０２μ／（Ｎ／ｍｍ２）であるので、軸応力が２０Ｎ／ｍｍ２であれば、１．５×１０２×２０＝３．０×１０３μとなる。
Further, in the concrete column 1, a thermal expansion strain ε th (see FIG. 5) accompanying thermal expansion and a transient strain ε tr (see FIG. 6) which is a contraction strain per unit stress are generated.
For example, when the transient strain ε tr is 400 ° C., the shrinkage strain per unit stress is about 1.5 × 10 2 μ / (N / mm 2 ), so that the axial stress is 20 N / mm 2 . For example, 1.5 × 10 2 × 20 = 3.0 × 10 3 μ.
時刻ｔにおける各要素Ａ〜Ｃの温度が異なるので、時刻ｔにおける各要素（要素Ａ〜Ｃ）の応力と軸力ひずみεσとの関係は、図７の（ａ）のようになる。 The temperature of each element A through C at time t is different, the relationship between the stress and the axial force strain epsilon sigma of each element (Element A through C) at time t is as shown in FIG. 7 (a).
本実施形態では、軸力（応力）とひずみの関係から得られる軸力ひずみεσに、火災時の熱膨張により要素に発生する熱膨張ひずみεthおよび火災時の圧縮力と温度により要素に発生する過渡ひずみεtrを加えたひずみを全ひずみεtotとする（式１）。 In this embodiment, the axial force strain ε σ obtained from the relationship between the axial force (stress) and strain, the thermal expansion strain ε th generated in the element due to thermal expansion at the time of fire, and the compressive force and temperature at the time of the fire The total strain ε tot is the sum of the generated transient strain ε tr (Equation 1).
なお、軸力ひずみεσに熱膨張ひずみεthを加えると全体のひずみ量は増加し、過渡ひずみεtrを加えると全体のひずみ量は減少するため、各要素Ａ〜Ｃの全ひずみεtotは、ひずみ軸に沿って平行移動する形となり、図７の（ｂ）のように表わすことができる。
図７の（ｂ）から分かるように、火災時の軸力ひずみεσは、要素Ａ〜Ｃで同じにならず、要素Ｃに発生する軸力ひずみεσが最も大きくなる。
If the thermal expansion strain ε th is added to the axial force strain ε σ , the total strain amount increases, and if the transient strain ε tr is added, the total strain amount decreases, so the total strain ε tot of each element A to C Is parallel to the strain axis and can be expressed as shown in FIG.
As can be seen from FIG. 7 (b), the axial force strain epsilon sigma of a fire, not the same for elements A through C, axial strain force generated in the element C epsilon sigma is maximized.
続いて、各要素の全ひずみεtotが等しくなる（平面保持）と仮定して、時刻ｔにおける熱応力解析を行うことで各要素Ａ〜Ｃの軸力ひずみεσを算出し、当該軸力ひずみεσに対応する瞬間ヤング係数ＥＡ(t)〜ＥＣ(t)を算出する。熱応力解析を行う際には、温度把握作業Ｓ１で求めたデータを使用する。
瞬間ヤング係数ＥＡ(t)〜ＥＣ(t)は、応力とひずみとの関係により求まる曲線との接線勾配により求める（図７の（ｂ）参照）。
Subsequently, assuming that the total strain ε tot of each element becomes equal (plane holding), the thermal stress analysis at time t is performed to calculate the axial force strain ε σ of each element A to C, and the axial force calculating the instantaneous Young's modulus E a (t) ~E C ( t) corresponding to the strain epsilon sigma. When performing the thermal stress analysis, the data obtained in the temperature grasping operation S1 is used.
The instantaneous Young's modulus E A (t) to E C (t) is obtained from a tangential gradient with respect to a curve obtained from the relationship between stress and strain (see FIG. 7B).
曲げ剛性算出作業Ｓ４では、各要素Ａ〜Ｃの曲げ剛性を断面全体で積分することで断面全体の曲げ剛性である全体曲げ剛性Ｅ(t)・Ｉを算出する。 In the bending stiffness calculation operation S4, the total bending stiffness E (t) · I, which is the bending stiffness of the entire cross section, is calculated by integrating the bending stiffness of each element A to C over the entire cross section.
曲げ剛性は、各要素Ａ〜Ｃの瞬間ヤング係数ＥＡ(t)〜ＥＣ(t)に、断面全体の図心軸に関する断面二次モーメントＩを乗じることで算出する。 The bending stiffness is calculated by multiplying the instantaneous Young's modulus E A (t) to E C (t) of each element A to C by the sectional secondary moment I related to the centroid axis of the entire section.
各要素Ａ〜Ｃの曲げ剛性ＥＡ(t)・Ｉ〜ＥＣ(t)・Ｉを算出したら、式２を用いて断面全体で積分することで、時刻ｔにおける全体曲げ剛性を算出する。 After calculating the bending stiffness E A (t) · I to E C (t) · I of each element A to C, the entire bending stiffness at time t is calculated by integrating the entire cross section using Equation 2.
座屈応力算出作業Ｓ５では、全体曲げ剛性Ｅ(t)・Ｉを式３に示すオイラー座屈の式に代入して時刻ｔにおける座屈耐力ＰＥ(t)を算出する。
座屈耐力ＰＥ(t)は、全体曲げ剛性Ｅ(t)・Ｉと設計で想定される座屈長さｌkを用いて算出する。
In buckling stress calculation operations S5, it calculates the overall flexural rigidity E (t) · I a seat at time t into Equation Euler buckling shown in Equation 3 Buckling force P E (t).
The buckling strength P E (t) is calculated using the total bending stiffness E (t) · I and the buckling length l k assumed in the design.
座屈耐力ＰＥ(t)を算出したら、コンクリート柱に作用する軸力と座屈耐力ＰＥ(t)とを比較する。 When the buckling strength P E (t) is calculated, the axial force acting on the concrete column is compared with the buckling strength P E (t).
必要に応じて、ヤング係数算出作業Ｓ３と、曲げ剛性算出作業Ｓ４と、座屈応力算出作業Ｓ５を、所定時間毎に繰り返し実施することで、座屈耐力の経時変化を算出する。
そして、座屈耐力ＰＥ(t)が軸力と等しくなるときの時刻が、鉄筋コンクリート柱が座屈で破壊する時刻となり、加熱開始から座屈破壊するまでの時刻がコンクリート柱の耐火時間となる。
If necessary, the Young's modulus calculation work S3, the bending rigidity calculation work S4, and the buckling stress calculation work S5 are repeatedly performed at predetermined time intervals, thereby calculating the change over time of the buckling strength.
The time when the buckling strength P E (t) becomes equal to the axial force is the time when the reinforced concrete column is broken due to buckling, and the time from the start of heating to the buckling failure is the fire resistance time of the concrete column. .
なお、コンクリート柱に付加する軸力を変化させて、ヤング係数算出作業Ｓ３と、曲げ剛性算出作業Ｓ４と、座屈応力算出作業Ｓ５を繰り返し実施すれば、コンクリート柱の導入軸力と耐火時間の関係を得ることができる。 If the axial force applied to the concrete column is changed and the Young's modulus calculation operation S3, the bending stiffness calculation operation S4, and the buckling stress calculation operation S5 are repeated, the introduction axial force of the concrete column and the fire resistance time can be reduced. You can get a relationship.
以上、本実施形態の座屈耐力算定方法によれば、火災時に部材内部に発生する熱応力の影響を考慮したコンクリート柱の座屈耐力を算定することができる。
そのため、本実施形態の座屈耐力算定方法を利用して、径長さ比が大きな（１５を超える）鉄筋コンクリート長柱の断面設計を行うことで、火災が生じた場合であっても座屈することのない長柱を設計することが可能となる。ゆえに、建物の空間設計の自由度が向上する。
As described above, according to the buckling strength calculation method of the present embodiment, it is possible to calculate the buckling strength of a concrete column in consideration of the influence of thermal stress generated inside the member during a fire.
Therefore, using the buckling strength calculation method of this embodiment, buckling even if a fire occurs by designing a cross section of a reinforced concrete long column with a large diameter-to-length ratio (exceeding 15) It becomes possible to design a long pillar without any. Therefore, the degree of freedom in building space design is improved.
火災により部材の曲げ剛性が低下する鉄筋コンクリート柱について、所望の耐火時間を確保した設計を行うことができる。 About the reinforced concrete column in which the bending rigidity of a member falls by a fire, the design which ensured the desired fireproof time can be performed.
以上、本発明の実施形態について説明したが、本発明は前記の実施形態に限られず、本発明の趣旨を逸脱しない範囲で適宜変更が可能である。
例えば、前記実施形態では、軸力ひずみに熱膨張ひずみおよび過渡ひずみを加えて全ひずみを算出するものとしたが、全ひずみは、軸力ひずみに熱膨張ひずみおよび過渡ひずみのうちのいずれか一方を加えたものとしてもよい。
As mentioned above, although embodiment of this invention was described, this invention is not restricted to the said embodiment, In the range which does not deviate from the meaning of this invention, it can change suitably.
For example, in the embodiment, the total strain is calculated by adding the thermal expansion strain and the transient strain to the axial force strain, but the total strain is one of the thermal expansion strain and the transient strain to the axial force strain. May be added.
また、コンクリート柱を構成するコンクリートは、高強度コンクリートであってもよいし、普通コンクリートであってもよい。
また、鉄筋等の補強材の配筋は適宜行えばよい。
The concrete constituting the concrete pillar may be high-strength concrete or ordinary concrete.
Further, reinforcing bars such as reinforcing bars may be appropriately arranged.
１ コンクリート柱
Ａ〜Ｃ 要素
Ｓ１ 温度把握作業
Ｓ２ モデル化作業
Ｓ３ ヤング係数算出作業
Ｓ４ 曲げ剛性算出作業
Ｓ５ 座屈応力算出作業
1 Concrete Column A to C Element S1 Temperature Grasping Work S2 Modeling Work S3 Young's Modulus Calculation Work S4 Bending Rigidity Calculation Work S5 Buckling Stress Calculation Work
Claims (2)
火災時におけるコンクリート柱の断面の温度分布を把握する温度把握作業と、
前記コンクリート柱の断面を複数の要素の集合体にモデル化するモデル化作業と、
前記各要素の瞬間ヤング係数を算出するヤング係数算出作業と、
前記瞬間ヤング係数に断面二次モーメントを乗じて算出された曲げ剛性を断面全体で積分することで前記断面全体の曲げ剛性である全体曲げ剛性を算出する曲げ剛性算出作業と、
前記全体曲げ剛性をオイラー座屈の式に代入して座屈耐力を算出する座屈応力算出作業と、を備え、
火災時の熱膨張により前記要素に発生する熱膨張ひずみおよび火災時の圧縮力と温度により前記要素に発生する過渡ひずみのうちの少なくとも一方を、前記コンクリート柱に作用する軸力により前記要素に発生する軸力ひずみに加えたひずみを全ひずみとし、
前記ヤング係数算出作業では、前記各要素の全ひずみが等しくなると仮定して、熱応力解析を行うことで、前記各要素の軸力ひずみを算出し、当該軸力ひずみに対応する瞬間ヤング係数を算出することを特徴とする、座屈耐力算定方法。 A buckling strength calculation method for calculating the buckling strength of a concrete column during a fire,
Temperature grasping work to grasp the temperature distribution of the cross section of the concrete pillar at the time of fire,
Modeling work for modeling the cross section of the concrete column into an aggregate of a plurality of elements;
A Young's modulus calculation operation for calculating an instantaneous Young's modulus of each element;
Bending stiffness calculation work for calculating the overall bending stiffness that is the bending stiffness of the entire cross section by integrating the bending stiffness calculated by multiplying the instantaneous Young's modulus by the cross sectional second moment over the entire cross section;
A buckling stress calculating operation for calculating the buckling strength by substituting the total bending stiffness into the Euler buckling formula,
At least one of thermal expansion strain generated in the element due to thermal expansion during fire and transient strain generated in the element due to compressive force and temperature during fire is generated in the element due to axial force acting on the concrete column. The total strain is the strain applied to the axial force strain
In the Young's modulus calculation work, assuming that the total strain of each element is equal, the thermal stress analysis is performed to calculate the axial force strain of each element, and the instantaneous Young's modulus corresponding to the axial strain is calculated. A buckling strength calculation method characterized by calculating.
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| CN111985027A (en) * | 2020-08-13 | 2020-11-24 | 宁波大学 | Method for calculating bending resistance bearing capacity of composite beam |
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