Stress Increase Under Circular Loaded Area

Hi arjan, let's solve this geotechnics problem where we calculate the stress increase beneath a flexible circular loaded area using Boussinesq's theory.

Let's list the given parameters first. We have a uniformly distributed load, lowercase q, of one hundred fifty kilonewtons per square meter.

The diameter is two meters, which means the radius R of the circular area is one meter. We are looking for the stress increase delta sigma at a depth z of three meters.

According to Boussinesq's solution for a circular area, the vertical stress increase depends on the ratios of radius over depth and radial distance over depth. We define two non-dimensional parameters, capital A and capital B.

For points not at the center, we use influence charts or updated formulas involving ratios. Here, r is the horizontal distance from the center. Let's calculate the common ratio r over z for each case.

We also need the ratio R over z, which is constant for all points in this problem.