Stress under circular loads

[sofiecv]

Hello,

I need to calculate the vertical stresses under a circular uniform load (a reactor) but I need to do this for random points. So I cannot use the Boussinesq formula as it refers only to points below the circle axis.

Also, since I need to do this for almost 2,500 points, I cannot use diagrams and tables. Is there any analytical solution, some equation or anything else I can use in Excel?

Thanks

 

[JedClampett]

Newmark's Influence Chart?

 

[aeoliantexan]

Perhaps you could use the Boussinesq equation for vertical stress due to a vertical point load. Sigma z = (3Pz^3)/(2 Pi R^5). Please look it up and verify it. z is the depth to the point, and R is the straight-line distance from the load to the point. R^2 =x^2+y^2+z^2. My style would be to draw the circle to scale on a one-foot grid, write equations for x, y and z for the center of each square as well as the center of the point in question, calculate the contribution of each square, and total them.

If you can use charts or tables, Elastic Solutions for Soil and Rock Mechanics by Poulos and Davis has good ones and is available free online.

Boussinesq is for a uniform pressure on a semi-infinite isotropic medium, of course. Your reactor foundation is probably pretty rigid, and your soil layer is not semi-infinite (there is rock down there somewhere). So you results can be mathematically correct, but far from the truth. Be especially careful about the pressures near the edge of a rigid foundation, which can be very high. The above book has useful solutions for rigid foundations and infinite thicknesses of soil.

 

[BigH]

. . . And do elastic stress distributions really exist?

 

[sofiecv]

Thank you for your replies - this is not something I need for a professional issue so it is ok to work with some assumptions I guess.

My problem is the following:

I have a rectangular raft foundation which also carries one extra uniformly loaded rectangular load and one circular. The foundation level is 9 meters from the ground level and the water table is 3 meters from the ground level. I have created a spreadsheet that calculates the vertical stress caused by each of the three loads but I am confused about which is the q included in the equations; I have read that it is the load applied by the structures minus the weight of the excavated soil. By ''weight of the excavated soil'' it is meant the effective stress at foundation level (3*γb+6*γsat-6*γwater) ??

Also, since I am not familiar with the term:

which one is the average gross effective foundation pressure?

I would appreciate very much your help since it has been a long time that I have not dealt with geotechnical issues.