Chapter 7, Problem 7.23QPP

Three columns, A, B, and C, are collinear, 500 mm in diameter, and 2.0 m on-center. They have unfactored vertical downward loads of 1,000,550, and 700 kN, respectively, and are to be supported on a single, 1.0 m deep rectangular combined footing. The soil beneath this proposed footing has the following properties: $\gamma =19.5{\text{kN/m}}^{\text{3}},c\text{'}=10\text{kPa,}$ and $\varphi \text{'}=31°.$ The groundwater table is at a depth of 25 m below the ground surface.

1. using ASD, determine the minimum footing length, L, and the placement of the columns on the footing that will place the resultant load at the centroid of the footing. The footing must extend at least 500 mm beyond the edges of columns A and C.
2. Using the results from part (a), determine the minimum footing width, B, that will maintain a factor of safety of 2.5 against a bearing capacity failure. Show the final design in a sketch.

Hint: Assume a value for B, compute the allowable bearing capacity, then solve for B. Repeat this process until the computed B is approximately equal to the assumed B.