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It includes the design of concrete spread footings based on the latest ACI provisions. This article discusses the complexities inherent to the design of spread footings when subjected to a combination of vertical and horizontal loads, and biaxial bending. For a simple spread footing with a vertical concentric compression load, the resulting bearing pressure is uniform and the shear and bending can be calculated easily by hand. If the column is at the corner of a building, then biaxial moments could be transferred to the footing.
Additional moments are produced if the column is placed eccentrically on the footing, or due to the horizontal loads applied at the top of the pedestals. The images below show the general case of a rectangular spread footing with an offset column subject to a vertical load, two horizontal loads, and two bending moments around the orthogonal axes.
What makes biaxial bending so complex? For biaxial bending, the maximum bearing pressure occurs at one corner of the footing, and the minimum pressure at the corner diagonally opposite. The kern is represented by the triangular area in the right image below. As the eccentricities increase and fall outside the kern, the calculations become quite complex, mainly because the tensile resistance of the soil is negligible, and therefore a portion of the footing needs to be ignored in the analysis Types II to IV.
The first difficulty is then determining the shape and size of the remaining effective portion of the footing. Depending on the location of the resultant, this shape in plan view could vary from a full rectangle Type I , through a pentagon Type II , through a trapezoid Type III , to a triangle Type IV , as the blue areas shown above.
Obviously in a perfect world all footings would be Type I, but the reality is that in practice we may have existing footings or other obstructions in the area, or underground piping, or a property line nearby, or probably you need to check an existing footing for higher loads.
In such cases the other footing types may be an option. How do you calculate the shears in the footing? The shear is produced by the soil bearing pressure acting upwards on the footing. If the pressure is uniform, or if the entire footing is under compression, this force can be easily calculated as the volume of the parallelogram delimited by the critical section, the footing edges, and the bearing pressure.
Try to visualize the resulting irregular shape formed in this scenario, as shown in the images below in lighter blue. You still need to calculate the volume of these irregular solids formed by inclined and vertical planes that look like stalactites, but now the calculation is substantially harder to accomplish.
The screen shots above show the factored shear forces of a typical footing under biaxial bending as a result of partial bearing. Note the different hatch representing the effective shear areas in both directions. Similar calculations are required to find the punching shear. Are the bending moments easier to calculate? No, the calculation is actually even more difficult.
The bearing diagram exerts an upward pressure against the footing, but this force acts through the centroid of the solid described above, and produces a moment with respect to the critical section. The footing bending moment is therefore the volume of the solid, multiplied by the centroid with respect to the face of the column. The calculation of the centroid of this irregular body is therefore another required step. Once the bending moments are found, the reinforcing steel may be designed per the concrete design theory.
It should be noted that the bearing pressures are calculated using service loads, but both shears forces and bending moments must be calculated by applying the factored loads. Takeaway The design of spread footings subject to biaxial bending may be cumbersome and time-consuming, particularly for partial bearing conditions. In such cases the calculation of bearing pressures, shears, and moments may become very complex. Best regards,.
Biaxial Footing Design
And the pressure on the design sheet is updated automatically. Life Story of a Structural Engineer. Biaxial Footing Design Posted April 14th, by admin. But sheet1 supplies the max bearing pressure and sheet2 supplies isolsted maximum effective pressure.
DESIGN OF ISOLATED FOOTING WITH BIAXIAL MOMENT PDF