What is Eccentric Footing?
Em alguns casos, columns lie eccentric to the center of the footing. Footings that are not concentrically loaded are known as “Sapatas Excêntricas”. Além disso, when footings are subjected to an axial load “P” e momento de flexão “M” or lateral force “H”, the footing will experience unbalanced stress distributions along the base of the footing. This can also be achieved with an axial load acting at an eccentricity “e” from the centroid of the footing.
Como um resultado, the total combined stress at the base of the footing is equal to the sum of the stress due to the axial load over footing area (P/A) and the bending moment over section modulus “S” of footing (M/S).
The pressure is assumed to vary linearly, como mostrado na figura 1. This distribution is valid where the axial load falls within the kern of the footing area, enquanto a tensão no aço fs é menor que a tensão de escoamento f, where the eccentricity “e” is less than L/6. The following equations shown in Figure 1 for soil pressure (q) can be used to determine the minimum and maximum pressures at the extreme edges of the footing¹.
Figura 1. Soil pressure distribution of eccentric footing
(uma) eccentric within the kern boundary (b) eccentric within the boundary of the kern (c) eccentric outside the kern boundary
Figure 1A depicts the footing when the eccentricity is located inside of the kern boundary. The entire footing is still in compression and the soil pressure reacts with a trapezoidal distribution where:
qmax = P/A + M/S and qmin = P/A – M/S.
Figure 1B depicts the footing when the eccentricity is located at the kern boundary. The entire footing is still in compression, but the soil pressure now reacts with a triangular distribution where:
qmax = 2P/A.
Figure 1C depicts the footing when the eccentricity is located outside the kern boundary. that when eccentricity is located outside of the kern. The soil pressure still reacts with a triangular distribution, but cannot resist tension (upward movement of footing, or uplift) left of the column boundary. Nesse caso:
qmax = 2P/3(0.5L-e)B
SkyCiv Foundation Design presents great Analytical graphics that make understanding eccentricity a breeze. Figura 2 shows the dynamic Analytical diagram, where soil pressure behaviors are obviously shown.
Figura 2. Fundação SkyCiv – Isolated Footing analytical diagram.
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Engenheiro estrutural, Desenvolvimento de Produto
B.S. Engenharia Civil
- Reinforced Concrete Structures: Analysis and Design, Second Edition. McGraw-Hill Professional.