HW11-CE357-Stress Distribution and Settlement

1 The University of Texas at Austin CE 357 Department of Civil, Architectural Geotechnical Engineering And Environmental Engineering Prof. El Mohtar Homework No. 11 – Stress Distribution and Settlement 1. [40 Points] As depicted below, a column imparts a 500 kip load (1 kip = 1000 lbs) to the top of a concrete footing on the ground surface. The footing is rectangular, measuring 5 ft by 8 ft in plan. Assume the footing distributes the column load uniformly to the soil (imparts a uniform pressure to ground surface). 2. (a.) Compute the change in vertical stress below the center of the footing (point A). Plot the change in vertical stress from the ground surface to a depth of 20 ft. Use two methods to compute the change in vertical stress: • 2:1 (vertical:horizontal) approximate load distribution • Boussinesq’s solution ( Use any of the stress distribution chart solutions that you find best.). Plot the results from both methods on the same graph, with stresses on the horizontal axis and depth on the vertical axis. (b.) Now, using only Boussinesq’s solution, plot the change in vertical stress from the ground surface down to 20 ft below the center (A), corner (B), and the mid-point of one edge (C) of the footing as shown in the sketch. 2. [30 Points] A new hotel is shown below in plan and cross section. The hotel has a 5-story structure along with a 10-story tower. Construction of the hotel imparts a uniform increase in pressure of 500 psf and 1000 psf as indicated. Find the increase in vertical stress at 50 ft below the ground surface at points A, B, and C. Use any of the stress distribution chart solutions that you find best. Elevation Plan View q=500 psf q=1000 psf 100 ft 50 ft 60 ft 60 ft A B C 1 ft 8 ft 4 ft B C A Soil:  T = 110 pcf 500 kips 2.5 ft 5 ft