I'm looking for a text book , or any written material in any form, explaining the analysis of the spread footing subjected to biaxial bending, which is causing footing upleft on the far end of the moments. any suggestion please?. Also an advice how to analyze is appreciated.
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Biaxial bending on a spread footing? 3
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The information you desire is in many texts; one that comes to mind is Braja Das' Foundation Engineering. If you have access to AASHTO you could use chapter 4 as it is very similar to the above text.
Basically, you will have to use the old formula, stress = (P\A)+-[MyX/Iy]+-[MxY/Ix] where the small letters x, y represent the axes. Once the maximum stress is known and the eccentricity found you can use the charts in Das or AASHTO to develop the modified bearing values.
Basically, you will have to use the old formula, stress = (P\A)+-[MyX/Iy]+-[MxY/Ix] where the small letters x, y represent the axes. Once the maximum stress is known and the eccentricity found you can use the charts in Das or AASHTO to develop the modified bearing values.
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Thanks QShake for the hint. Currently I do not have an access to AASHTO reference. However my goal is to find out how the analysis is done, manually, and without using any charts or computer programs. Let us look at single moment case, eccentricty e=M/p, we compare this with L/6 value, where L is footing lenght in moment direction. if e<L/6, flexural equation is used (i.e. q=P/A+-M/S). on the other hand if e>L/6 flexural equation shall not be used and the static eqautions must be used (segma V=0, and segma M=0). Two equations for two unknowns, qmax and Leff. Now in the case of the biaxial bending, there are more unkowns than the number of equations you can generate. Any hint. thanks.
We have to find out the location of zero stress line and ignore the
tension area. Normally we get an odd shaped area (rectangle with
a triangular corner chipped off). The new Centre of gravity,
moments of inertia about the two axes will be found. The vertical
loads and moments will be transferred to the new COG. Stresses
at the ends of the zero-stress axis are checked to confirm that
they are very small (very difficult to get zero stresses!). If not,
assume a revised zero-stress line. This is an iterative process.
Once the desired accuracy of the zero stress line is obtained,
Stresses at the corners are computed to check if they are within
allowable limits. My experience is that usually the revised stresses
are slightly less than the original stresses. For documentation,
however, this exercise will be required by the approver of designs.
Good luck,
Hariharan
tension area. Normally we get an odd shaped area (rectangle with
a triangular corner chipped off). The new Centre of gravity,
moments of inertia about the two axes will be found. The vertical
loads and moments will be transferred to the new COG. Stresses
at the ends of the zero-stress axis are checked to confirm that
they are very small (very difficult to get zero stresses!). If not,
assume a revised zero-stress line. This is an iterative process.
Once the desired accuracy of the zero stress line is obtained,
Stresses at the corners are computed to check if they are within
allowable limits. My experience is that usually the revised stresses
are slightly less than the original stresses. For documentation,
however, this exercise will be required by the approver of designs.
Good luck,
Hariharan
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Hi!
See 'Foundation Engineering' by Bowls. Without a computer program or charts, it is almost impossible to perform an accurate analysis for your conditions. As you are dealing with a tension zone on the soil, which is not bearable by it, you have to locate nuetral axis orientation and location using a vertical force equilibrium equation simultaneously with two moment equilibrium equations. For a rectangular shape, this procedure requires a large number of double integrals over odd-shaped regions. Beleive me, no one can solve them analytically in general. Even if you construct such integrals, you will be needing a computer to solve them numerically.
See 'Foundation Engineering' by Bowls. Without a computer program or charts, it is almost impossible to perform an accurate analysis for your conditions. As you are dealing with a tension zone on the soil, which is not bearable by it, you have to locate nuetral axis orientation and location using a vertical force equilibrium equation simultaneously with two moment equilibrium equations. For a rectangular shape, this procedure requires a large number of double integrals over odd-shaped regions. Beleive me, no one can solve them analytically in general. Even if you construct such integrals, you will be needing a computer to solve them numerically.
What you ask will vary substantially for a clayey reactive soil as compared to a stable and granular soil. If you want to address the total question you will need to examine the seasonal and long term soil movement since this interacts (a critical point this) with the footing forces. You can therefore get differing situations in Summer and in Winter and long-term, depending on your local climate.
You could search for work by Peter Mitchell (Mitchell PW) who did a substantial amount of work in Australia on developing just such an interactive method on (principally) reactive soils, and including analysing Raft type footings this way.
Also look for "Reactive Soil" publications by various authors through CSIRO Australia (just use the acronym).
If you reduce your problem just to the action of the footing in isolation then there are any number of structures books which will cover kern area calculations, bending, twisting and deflection of the footing body etc. You have almost certainly covered these things in your studies also ... or you're about too! Anthony Tugwell
Project Director & Consulting Engineer - now in Australia
You could search for work by Peter Mitchell (Mitchell PW) who did a substantial amount of work in Australia on developing just such an interactive method on (principally) reactive soils, and including analysing Raft type footings this way.
Also look for "Reactive Soil" publications by various authors through CSIRO Australia (just use the acronym).
If you reduce your problem just to the action of the footing in isolation then there are any number of structures books which will cover kern area calculations, bending, twisting and deflection of the footing body etc. You have almost certainly covered these things in your studies also ... or you're about too! Anthony Tugwell
Project Director & Consulting Engineer - now in Australia
If anyone is still interested in doing a manual anlysis for this basic problem - seek out a copy of "Civil Engineering" Vol 10, No.3 for March 1940. page 170 (as far as I can read from a very old dog-eared copy).
Under the heading "Engineers' Notebook" ("Ingenious Suggestions and Practical Data Useful in the Solution of a Variety of Engineering Problems" - [a sort of hard copy pre-internet eng-tips series]) you will find a method for "Analyzing Non-Homgeneous Sections Subjected to Bending and Direct Stress" by Willam G.S.Saville, Associate Engineer, Bridge Design Section, Tennessee valley Authority.
This is a successive approximations method which will do an elastic analysis of reinforced concrete sections or spread footings subject to direct load and bi-axial bending. It takes a bit of understanding, but is fairly simple once you get the hang of it.
Under the heading "Engineers' Notebook" ("Ingenious Suggestions and Practical Data Useful in the Solution of a Variety of Engineering Problems" - [a sort of hard copy pre-internet eng-tips series]) you will find a method for "Analyzing Non-Homgeneous Sections Subjected to Bending and Direct Stress" by Willam G.S.Saville, Associate Engineer, Bridge Design Section, Tennessee valley Authority.
This is a successive approximations method which will do an elastic analysis of reinforced concrete sections or spread footings subject to direct load and bi-axial bending. It takes a bit of understanding, but is fairly simple once you get the hang of it.
DaveAtkins
Structural
This does not have to be solved by trial and error. I use a chart in "Foundation Design" by Wayne C. Teng. The chart is on page 133 in my edition. Teng also includes guidance on how to solve the problem by hand, using a graphical approach.
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A simple and straight-forward theoretical solution for finding the zero pressure line and the modified pressure is available in Proceedings of ASCE-Journal of the Structural Division - August-1962. The paper is titled
'Analytical approach to Biaxial Eccentricity'. The author is Mr. E. Cherniak.
I have used this approach very effectively for designing Foundations with biaxial eccentricity and undergoing loss of contact.
'Analytical approach to Biaxial Eccentricity'. The author is Mr. E. Cherniak.
I have used this approach very effectively for designing Foundations with biaxial eccentricity and undergoing loss of contact.
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