Rigid Isolated Rectangular Footing Biaxial Bending Active Area Pressure on Soil

[LiviuM]

Rigid Isolated Rectangular Footing Active Area Maximum Pressure on Soil

This excel file written by myself contains macro (visual basic script) that allows the user to compute maximum pressure and active area (due to detachment) for rectangular rigid isolated footings under compression and biaxial bending.
Calculation assumptions:
- Footing is infinite rigid, no bending

Functions available:
=FootPressMax(Length,Width,N,Mx,My,pX,pY) returns maximum pressure on soil

=FootAActive(Length,Width,N,Mx,My,pX,pY) returns active area

=FootPressure(Length,Width,N,Mx,My,pX,pY) returns matrix with pressures, matrix size is px*py

Length is measured in X direction; Width is measured in Y direction

N - axial force (compression always positive)
Mx - bending moment around x axis
My - bending moment around y axis
pX,pY - number of meshing points 25*25 is most of the time enough

Files included:
Rigid Isolated Footings.xls (Microsoft Office 97-2003)
Rigid Isolated Footings.xlsm (Microsoft Office 2007 or newer versions)
footing.SDB (for verification, SAP2000 V14.2.4)
footing.$2k (for verification, SAP2000 V14.2.4)

Code:

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Code:

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[LiviuM]

This is the first part of the explanation regarding the way the algorithm used in the above excel worksheet macros works.

This part explains the way meshing was done. And the equilibrium equation.
In few words, the footing area is meshed into equivalent joints. By using a loop, iterations are performed until no joint has uplift force (negative value). This way the contact shape is determined step by step. Equilibrium equation is evaluated each step on the contact shape.

For better understanding all calculations were done in 2D, mathcad using both programing and math formulas. Also a sap 14.2.4 model is provided for verification.
Note: Increase mesh, noPoints for closer results to direct formulas. like instead of 9 use 30.

Files included: Isolated Rigid Footing.pdf, Isolated Rigid Footing.xmcd, 1.SDB
The pdf is just a print of xmcd. Mathcad file has 14 version.

0.6 MBytes

Code:

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Pass

Code:

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The second part will cover the biaxial bending, this one doesn't.