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"BOEF" is a spreadsheet program written in MS-Excel for the purpose of analysis a finite length beam with free ends supported continuously on an elastic foundation.  This program is ideally suited for analyzing a soil supported beam, a combined footing, or a strip of a slab or a mat.  Specifically, the beam shear, moment, deflection, and soil bearing
pressure are calculated for 100 equal beam segments, as well as the maximum values.  Plots of both the shear, moment, and soil bearing pressure diagrams are produced, as well as a tabulation of the shear, moment, deflection, and bearing pressure for the beam.

This program is a workbook consisting of three (3) worksheets, described as follows:

Doc - documentation sheet
Beam on Elastic Fdn. (English) - Beam on elastic foundation analysis (English units)
Beam on Elastic Fdn. (metric) - Beam on elastic foundation analysis (metric units)

Program Assumptions and Limitations:

1. The following reference was used in the development of this program (see below):
    "Formulas for Stress and Strain" - Fifth Edition
    by Raymond R. Roark and Warren C. Young, McGraw-Hill Book Company (1975), pages 128 to 146.
2. This program uses the equations for a "finite-length" beam in the analysis.  This usually gives very similar to exact results for a "semi-infinite" beam which has had end-corrections applied to "force" the moment and shear values to be equal to zero at the ends.  (Note: a "semi-infinite" beam is defined as one that has a  b*L value > 6.)
3. This program uses the five (5) additional following assumptions as a basis for analysis:
    a.  Beam must be of constant cross section (E and I are constant for entire length, L).
    b.  Beam must have both ends "free".  ("Pinned" or "fixed" ends are not permitted.)
    c.  Elastic support medium (soil) has a constant modulus of subgrade, K, along entire length of beam.
    d.  Applied loads are located in the center of the width, B, of the beam and act along a centroidal line of the beam-soil contact area.
    e.  Bearing pressure is linearly proportional to the deflection, and varies as a function of subgrade modulus, K.
4. This program can handle up to twelve (12) concentrated (point) loads, a full uniformly distributed load with up to six (6) additional full or partial uniformly distributed loads, and up to four (4) externally applied moments.  
5. Beam self-weight is NOT automatically included in the program analysis, but may be accounted for as a full uniformly distributed applied load.  Beam self-weight will only affect the deflection and bearing pressure, and not the moment or shear.
6. This program will calculate the maximum positive and negative shears, the maximum positive and negative moments, the maximum negative deflection, and the maximum soil bearing pressure.  The calculated values for the maximum shears, maximum moments, deflection, and bearing pressure are determined from dividing the beam into 100 equal segments with 101 points, and including all of the point load and applied moment locations as well.  
7. The user is given the ability to input four (4) specific locations from the left end of the beam to calculate the shear, moment, deflection, and bearing pressure.
8. The plots of the shear, moment, and bearing pressure diagrams as well as the displayed tabulation of shear, moment, deflection, and bearing pressure are based on the beam being divided up into 100 equal segments with 101 points.
9. This program contains numerous “comment boxes” which contain a wide variety of information including explanations of input or output items, equations used, data tables, etc.  (Note:  presence of a “comment box” is denoted by a “red triangle” in the upper right-hand corner of a cell.  Merely move the mouse pointer to the desired cell to view the contents of that particular "comment box".)

Calculation Reference
Beam Analysis
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Roark's Formulas for Stress and Strain
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| Find on | Find on | Find on | Find on | Find on |

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Submitted On:
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#9 Jake.B 2014-11-20 11:19
Excellent, well thought out spreadsheet. The detailed comments and references are evidence of a well experienced, competent engineer. Thank you.
#8 hades3 2013-12-02 16:08
#7 ATomanovich 2011-08-05 13:50
To help clarify the use of the "BOEF.xls" program, let me demonstrate with a simple example problem and compare results with my "FOOTINGS.xls" program.
In the "BOEF" workbook (English units worksheet) use the following input:
L = 8, B = 3, T = 2.25, E = 3600, K = 100, no full uniform or distributed loads, for point load a = 4 and P = 40, and for concentrated moment c= 4 and M = -70.
Now in the "FOOTINGS" workbook (8 net pier loads worksheet) use the following input: L = 8, B = 3, T = 2.25, assume soil and concrete unit weights = 0, Q = 0, pier is concentric on footing base, Load Pz = -40, and My = 70.
Per "FOOTINGS" program, results are:
pressures P1 = P2 = 3.951, and P3 = P4 = 0, with 84.38% of footing length in bearing.
Per "BOEF" program, results are:
maximum pressure = 3.840, with about 88% of footing length in bearing.
From these results, you see that even though the "BOEF" program solution depicts soil in tension (not really possible), the error in brearing pressure is still less than 3%. What I believe this says that as long as the the vast majortiy of the footing base (say 85%) is in bearing the "BOEF" program will still give very acceptable results.
Sorry for the "long winded" reply, but I thought this simple example would help.
#6 ATomanovich 2011-08-05 12:42
No, there really is no error as far as the solution used per "Formulas for Stress and Strain" by Raymond Roark is concerned. Keep in mind that this solution has its limitations and there are no soil "springs", and as we all know the soil cannot take tension, only bearing. When you see "negative" bearing pressure results at the ends of the beam, footing, mat, mat strip, etc. it's a matter of proper interpretation. What this is telling you is that you really are way too flexible and not getting much distribution of the load, and thus you should increase the thickness. When you do increase the thickness, you will see that soil tension problem go away. This workbook is a GREAT tool for the structural engineer to quickly determine just how rigid or flexible the particular element is. Way too often the engineer, for simplicity sake, blindly assumes full theoretical rigidity in an analysis, where that may not be the case at all. Also, this workbook will help the engineer determine the shear and moment for combined footings (with say 2 piers) that can be used in the concrete design.
In closing, this workbook is certainly not intended nor capable of being a subsitute for a much more sophisticated analysis such as FEM or finite differences. But as I said, when it is used properly, the results and limitations are understood and properly interpreted, it can be a very efficient and timely tool.
#5 jnazal 2011-08-05 05:02
Hi... there is something that may be an error. When the sheet calculates bearings on soil shouldn't consider that soil is having negative pressure. Soil just doesn't work in traction so in the equilibrium this must not be considered. Is this sheet considering this?.

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