Uniformly Loaded Rectangular Area
Many structural foundations are rectangular or approximately rectangular in shape. The increases in stresses below the corner of a rectangular area of width B and length L are
These equations can be written as
where I denotes the infl uence factor. The infl uence factor for the vertical stress is
where m 5 B/z and n 5 L/z. You can program your calculator or use a spreadsheet program to fi nd Iz. You must be careful in the last term (tan21) in programming. If m2 1 n2 1 1 , m2n2, then you have to add p to the bracketed quantity in the last term. The distribution of vertical stress below a uniformly loaded square foundation is shown in Figure . The increase in vertical stress is about 10% below a depth of 2B; B is the diameter of the foundation. The vertical stress decreases from the center of the foundation outward, reaching a value of about 10% at a horizontal distance of B/2 from the edge at a depth of B. A chart for Iz for the corner of rectangular loaded area is shown in Figure 7.24 on page 172. You would have to calculate m 5 B/z and n 5 L/z and read Iz from the chart; m and n are interchangeable. In general, the vertical stress increase is less than 10% of the surface stress when z . 2B.
where Is is a settlement infl uence factor that is a function of the L/B ratio (L is length and B is width). Setting js 5 L/B, the equations for Is are
At center of a rectangle (Giroud, 1968):
At corner of a rectangle (Giroud, 1968):