Footing Soil Pressure from Biaxial Loading
A symmetrical isolated rectangular footing with centered biaxial overturning develops soil pressure that shifts to counter balance the loads. The highest soil pressure is at a corner. The objective of this paper is to extend the uniaxial soil pressure solution to include biaxial loads and to document a simple and understandable way to directly calculate the shape of the soil pressure distribution. Another objective is to make the solution suitable for automation. In uniaxial overturning there are two transition shapes, trapezoidal and triangular. In biaxial overturning there are three transition shapes and they form 4, 5 & 6 sided polyhedrons. This analysis calculates those volumes and compares them to the design vertical load to determine the characteristic shape of the soil pressure distribution. The calculation then proceeds to converge on the precise shape and calculate its centroid and moment capacity. Assemblies of tetrahedrons are used to model all of the soil pressure shapes. The advantage of this methodology is that matrix algebra can be used to organize the calculations and make them computationally efficient. The assumed soil pressure and footing dimensions can be adjusted until the calculated moment capacity matches the overturning moment.
Peck, Ralph Brazelton, Walter Edmund Hanson, and Thomas Hampton Thornburn. Foundation engineering. Vol. 10. New York: Wiley, 1974.
McCormac, Jack C., and Russell H. Brown. Design of reinforced concrete. John Wiley & Sons, 2015.
CHibbeler, R. "Engineering Mechanics: Statics." (1986).
Paré, Eugene G. Descriptive Geometry: Worksheets with Computer Graphics. Simon & Schuster Books for Young Readers, 1990.
Young, W. (1989). Elastic stability formulas for stress and strain. Roark’s Formulas for Stress and Strain, 6th ed. McGraw-Hill, New York, NY, USA, 688.
Bellos, John, and Nikolaos P. Bakas. “High Computational Efficiency through Generic Analytical Formulation for Linear Soil Pressure Distribution of Rigid Spread Rectangular Footings.” Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016) (2016). doi:10.7712/100016.2015.5100.
Luiz de França Filho, Wanderson, Roberto Chust Carvalho, André Luís Christoforo, and Francisco Antonio Rocco Lahr. “Dimensioning of Isolated Footing Submitted to the Under Biaxial Bending Considering the Low Concrete Consumption.” International Journal of Materials Engineering 7, no. 1 (February 1, 2017): 1–11. doi:10.5923/j.ijme.20170701.01.
Rodriguez-Gutierrez, J. A., and J. Dario Aristizabal-Ochoa. “Rigid Spread Footings Resting on Soil Subjected to Axial Load and Biaxial Bending. I: Simplified Analytical Method.” International Journal of Geomechanics 13, no. 2 (April 2013): 109–119. doi:10.1061/(asce)gm.1943-5622.0000218.
Burkardt, John. "Computational Geometry Lab: TRIANGLES." (2010).
Savov, Ivan ”N0 BS Guide to Linear Algebra” (2018).
Wylie, Clarence Raymond. Plane trigonometry. McGraw-Hill, 1955.
Ray, J. “Calculating the Centroid of Compound Shapes Using the Method of Geometric Decomposition”. Available online: https://owlcation.com/stem/How-to-Solve-Centroids-of-Compound-Shapes, (accessed on 1 May 2018).
- There are currently no refbacks.
Copyright (c) 2019 Christopher Moffitt
This work is licensed under a Creative Commons Attribution 4.0 International License.