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SkyCiv Foundation

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  2. SkyCiv Foundation
  3. 孤立した基礎
  4. 長方形のコンクリートフーチングの下の圧力分布


基礎は、構造の総荷重を地面に伝達および分散することにより、全体的な安定性を提供する構造の不可欠な要素です。. 浅い土台, 長方形または正方形の独立基礎など, are the preferred type of foundation due to the simplicity of their construction and overall cost compared to deep foundations. Estimating the base pressure dramatically affects the design and sizing of the footing. 通常, the utility ratio between the allowable bearing capacity of the soil and the governing base pressure under the footing is the basis of the initial size of the footing. 基礎の初期寸法が設定されたら, 安全性と安定性のためのさらなる設計チェック, 一方向および二方向せん断など, 曲げ能力, および展開長チェック, are checked depending on which design code is used.

When a footing is subjected to a bi-axial bending (Mバツ, M), it is assumed that the axial load (P) is acting on an eccentricity coordinate (eバツ, e) where there is a tendency to rotate from the center. The interaction between the soil and footing mainly depends on the footing dimension and the resultant eccentricity of the applied loads. 結果として生じる偏心の位置に応じて, ベース圧力により、フーチングが完全または部分的に圧縮されます. 実際には, 完全に圧縮されたフーチングを設計することをお勧めします. Partial compression or loss of contact between the soil and footing should not be neglected, but most designers avoid this scenario due to its calculation complexity. 結果として生じる偏心がカーン内またはゾーン C の下にある場合、足場は完全に圧縮されています。. ゾーン C の外側の偏心により、基礎が部分的に圧縮されます. 図 1 長方形のフーチング上のさまざまな指定ゾーンを示しています.

This article shall focus on calculating corner pressures under different zone classifications based on Bellos & 痕跡 (2017) とSS. Ray’s (1995) studies.


The zone classifications of a rectangular footing are derived from multiple studies by different authors to develop a practical approach to estimating the distribution of soil pressure under expected loading conditions. 図に示すように 1, 5つの異なる地域があります (ゾーン A ~ E) depending on the location of resultant eccentricity. Each zone corresponds to a different loading, ベース圧力分布, and deformation. ゾーンC, カーンとも呼ばれる, is the main core. It is the ideal region to design a footing, resulting in full compression on the footing. この領域の次元は 1/6 それぞれの基礎の長さ.

図 1: 直角フーチングのゾーン分類


二次コアは楕円形の領域です (図の破線で囲まれた 1) 長半軸と短半軸が等しい 1/3 それぞれの基礎の長さ. このリージョンは、ゾーン B 全体をカバーします。 & C and some parts of zones D & E. 二次コアにより、基礎が部分的に圧縮されます. 許容できるフーチング設計のために、セカンダリ ゾーン内の離心率を維持することをお勧めします。.

二次ゾーンを超える偏心は、高い二軸負荷の結果です. ゾーン A 全体とゾーン D の残りの部分をカバーします。 & E. 転倒の危険性があるため、これらの領域でのフーチングの設計は避けることをお勧めします。. したがって, it is advisable to redesign the footing dimensions for this loading type.



ゾーンC (メインコア, Full compression zone)

述べたように, this is the most preferred case for designing footings since it is capable of setting the whole base of the footing into compression, 図に示すように 2. This case is represented by small eccentricity within the kern or no eccentricity. 図 2 shows the eccentricity within the kern with its maximum pressure at corners P3 & P4 and minimum pressure at corners P1 & P2.

図 2: Eccentricity (-eバツ, -e) at Zone C & full compression area

Maximum & minimum corner pressures (Bellos & 痕跡, 2017):



Corner pressures based on eccentricity
P1 P2 P3 P4
+eバツ, +e P最高 P最高 P P
+eバツ, -e P最高 P最高 P P
-eバツ, -e P P P最高 P最高
-eバツ, +e P P P最高 P最高

ゾーンA (Triangular compression zone)

This case corresponds to four rectangular areas in every corner of the footing. It usually occurs with large bi-axial eccentricity, imposing a high triangular compressive area in one of the corners, as shown by the shaded region in Figure 3. The remaining corners lose contact with the soil. したがって, this case is not advisable for design.

図 3: Eccentricity (-eバツ, -e) at Zone A & triangular compression area around P3


Maximum pressure (Bellos & 痕跡, 2017):



Corner pressures based on eccentricity
P1 P2 P3 P4
eバツ(+), e(+) P最高 0 0 0
eバツ(+), e(-) 0 P最高 0 0
eバツ(-), e(-) 0 0 P最高 0
eバツ(-), e(+) 0 0 0 P最高

ゾーンD (Trapezoidal compression zone)

Zone D also corresponds to large eccentricities in the areas attached in the x-direction of the footing, 図に示すように 4. The eccentricity in the z-direction (e) is much greater than in the x-direction (eバツ). この場合, two corners of the footing lose contact with soil and produce a trapezoidal compressive area. Compared to zone A, which is entirely outside the secondary zone, a portion of zone D is still covered by the secondary zone.


図 4: Eccentricity (-eバツ, -e) at Zone D & trapezoidal compression area around P3


Maximum & minimum corner pressures (Bellos & 痕跡, 2017):




Vertical heights of the trapezoidal compressive area (Bellos & 痕跡, 2017):





Corner pressures based on eccentricity
P1 P2 P3 P4
eバツ(+), e(+) P最高 0 0 P
eバツ(+), e(-) 0 P最高 P 0
eバツ(-), e(-) 0 P P最高 0
eバツ(-), e(+) P 0 0 P最高


ゾーンE (Trapezoidal compression zone)

Similar to zone D, this case also produces a trapezoidal compressive area but is caused by a large eccentricity in the x-direction(eバツ).

図 5: Eccentricity (-eバツ, -e) at Zone E & trapezoidal compression area around P3


Maximum & minimum corner pressures (Bellos & 痕跡, 2017):




Horizontal bases of the trapezoidal compressive area (Bellos & 痕跡, 2017):





Corner pressures based on eccentricity
P1 P2 P3 P4
eバツ(+), e(+) P最高 P 0 0
eバツ(+), e(-) P P最高 0 0
eバツ(-), e(-) 0 0 P最高 P
eバツ(-), e(+) 0 0 P P最高

ゾーンB (Pentagonal compression zone)

This case occurs when the applied loads on the footings generate a moderate eccentricity within the secondary zone. The areas covered by zone B are bounded by two curved sides and one flat base around the exteriors of zone C. この場合, a pentagonal compressive area is produced, and only a corner of the footing loses contact with the soil. しかしながら, the solutions provided below are slightly complex and require numerical solving methods for the corner pressures and the x & y intercepts of the compressive area.

Corner pressures (Bellos & 痕跡, 2017):




Pentagonal sides of the compressive area (Bellos & 痕跡, 2017):






Corner pressures based on eccentricity
P1 P2 P3 P4
eバツ(+), e(+) P最高 Pq 0 Pp
eバツ(+), e(-) Pp P最高 Pq 0
eバツ(-), e(-) 0 Pp P最高 Pq
eバツ(-), e(+) Pq 0 Pp P最高


あるいは, a more direct solution by S.S. レイ (1995) can be used for the corner pressures and intercepts of the pentagonal compressive zone. The equations are given below:

Corner pressures (S.S. レイ, 1995):





Pentagonal sides of the compressive area (S.S. レイ, 1995):



SkyCivの 基礎設計モジュール is capable of solving the base pressures of a rectangular concrete footing. Additional design checks in accordance with different design codes (ACI 318-14, Australian standard 2009 & 2018, とユーロコード) are also available.


SkyCivのFoundationDesignソフトウェアを試してみたい? Our free tool allows users to perform concrete footing calculations without any download or installation!


  • Bellos, J., 痕跡, N. (2017). Complete Analytical Solution for Linear Soil Pressure Distribution under Rigid Rectangular Spread Footing.
  • それか, B.M. (2007). 基礎工学の原則 (7第版). グローバルエンジニアリング
  • Rawat, S., et. al. (2020). Isolated Rectangular Footings under Biaxial Bending: A Critical Appraisal and Simplified Analysis Methodology.
  • レイ, S.S. (1995). 強化コンクリート. Blackwell Science


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