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Ann-Kathrin Dannwerth, B.Sc.

2024-07-11

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Loads with Large Eccentricities

EN 1997-1: Highly Eccentric Loads

According to EN 1997-1 [1] 6.5.4, no special precautions are required if the following generally applies to a rectangular base area:

e_{x,max} = \frac{w_{x}}{3}

e_{y,max} = \frac{w_{y}}{3}

Loads with Large Eccentricities According to EN 1997-1 6.5.4

The formulas refer to the limitation of the 2nd core width, which is elliptical. The eccentricities e_x and e_y are considered separately.

For rectangular foundations, the eccentricity of the load resultant must therefore not exceed 1/3 of the side length; for circular foundations, it must not exceed 0.6 of the radius. If the eccentricity exceeds these specified limit values, special provisions must be made in accordance with Section 2.4.2.

A technical illustration to explain the maximum allowable eccentricities for maintaining the core widths for geotechnical design.

Illustration of 1st and 2nd Core Widths

Marking 1 : The limitation of the 1st core width is represented by a rhombus.

Marking 2 : The limitation of the 2nd core width is represented by an ellipse.

Marking 3 : The point of application of the resultant is the point where the total resultant load acts on the foundation base.

IBC 2021 / ACI 318-19 (ASD): Loads with Large Eccentricities

Purpose of Verification

The verification for loads with large eccentricities checks whether the resultant vertical load remains within the permissible eccentricity limits of the foundation base. This ensures that the resultant force lies within the core section of the foundation and full-surface contact between the foundation and subsoil is maintained.

General Procedure

The verification is performed separately for both principal directions of the foundation. The eccentricities of the resultant vertical load result from the acting bending moments and the total vertical load:

\begin{matrix} e_{x} = \frac{M_{y}}{P} \\ e_{y} = \frac{M_{x}}{P} \end{matrix}

e_x, e_y	Eccentricity of the resulting vertical load [ft]
M_y, M_x	bending moments at the foundation base [kipft]
P	entire vertical load on the foundation [kip]

Eccentricity of the resulting vertical load

Eccentricity Limits

The permissible eccentricities are determined based on the foundation dimensions:

\begin{matrix} e_{x, \max} = \frac{B}{6} \\ e_{y, \max} = \frac{L}{6} \end{matrix}

B, L	Foundation dimensions in x and y direction [ft]

Eccentricity Limits

Verification

The governing condition results from the larger normalized eccentricity:

η = \max (\frac{| e_{x} |}{e_{x, \max}}; \frac{| e_{y} |}{e_{y, \max}}) \leq 1.0

Utilization ratio – loads with large eccentricities

If the resultant lies outside the core section of the foundation, a partial loss of contact occurs, and the assumption of a linear stress distribution is no longer valid.

Software Configuration

The verification is automatically performed for all defined load combinations. The bending moments and vertical forces are taken from the selected load cases and load combinations. The foundation dimensions required to determine the eccentricity limits are taken from the defined foundation geometry.

References

European Committee for Standardization (CEN). (2014). Eurocode 7: Geotechnical Design – Part 1: General Rules, EN 1997-1:2014-03. Berlin: Beuth Verlag GmbH.

Parent Chapter

External stability - Geotechnical design