## Beam on Elastic Foundations Analysis

A previous post on laterally loaded piles used a finite difference analysis to analyse the deflections and forces in a vertical pile subject to a lateral load at the top.  An alternative approach to the same problem is presented in “Programming the Finite Element Method” by I.M. Smith and D.V. Griffiths, including Fortran code.  The main advantage of their approach is that the pile and soil stiffness values are treated as varying linearly between each node, rather than being constant over each segment.  Also the code provides for up to 6 integration points in each segment, allowing a smooth transition between elements with different properties.

I have converted the Fortran code to VBA, and incorporated it into the LatPile function presented previously.  The spreadsheet also includes a new function, BoEFA, with additional flexibility for specifying node constraints and variable segment lengths, and with sign conventions better suited to horizontal beams.  The spreadsheet, including full open source code, may be downloaded from LatPileB.zip

Screenshots below show typical input and output, including comparison of results of the same analysis in Strand7 FEA software.  Click on any image for a full size view.

LatPileB input and output

LatpileB Bending Moments

LatPileB Shear Forces

LatPileB Deflections

BoEFA Input and Output

BoEFA and Strand7 Deflections

BoEFA and Strand7 Bending Moments

BoEFA and Strand7 Shear Forces

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### 6 Responses to Beam on Elastic Foundations Analysis

1. FM says:

Hello Doug,
I am new here and find this very useful and interesting.
how would the “Beam On Elastic Foundation” Excel sheet behave if there is a load(s) acting “away” from the soil, tending to lift the beam off its foundation. Do the springs tend to hold it down or is it worked out that in a case like that they are ineffective and work in “one direction” only? I can see this not being an issue for the Lateral Pile sheets since piles are surrounded by the supporting medium.

I am trying to put a file together (using stiffness matrix) to analyze a concrete element that would be pushed into soil and/or pulled away from it, in the latter case, the spring contribution to the stiffness must be Zero.

Thank you.

FM

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2. dougaj4 says:

FM – the springs work in both direction. The simplest way to get compreassion only springs would be to update the spring stiffness table on the spreadsheet, either manually or with a formula. You could set the stiffness of springs in tension to zero, and repeat until you get a stable solution (remembering to check each spring to see if it had gone back into compression).

Alternatively you could put a loop in the LatPileB VBA function to do that automatically.

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• FM says:

Many thanks, indeed.
I am trying to put a file together for a “rough” design of buried structures, arch, horse shoe..,etc. elastic supports all around at each joint is where I hit the wall.
Thanks, your work gives me a starting point and an excellent learning tool. It really is not “Just Another Excel Site”

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3. FM says:

I should have used the Frame Analysis Spreadsheet to start my question.
I am basically wondering how to define “Elastic” or “Spring” Supports in, say, fame4.xls
FM

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• dougaj4 says:

You can define springs by inserting a short member perpendicular to the main frame, and restraining the free end against translation, but not rotation. Release the other end (the connection to the frame) against rotation, and give it an axial stiffness according to the required spring stiffness. The bending stiffness doesn’t matter, as it can rotate about both ends.

I’m not a big fan of using “soil springs” for modelling buried frame structures because they don’t interact in the way that soil does, and the appropriate stiffness is difficult to determine; but people do use this method for real designs. If you are designing a real structure I’d suggest getting it reviewed by someone familiar with this type of work.

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