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Teng's curve
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JVCSNL
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PostPosted: Tue Jun 14, 2011 3:20 am    Post subject: Reply with quote

Dear Sir,

It would be really great if someone can develop the equation for Teng's curves.  I tried, but ended up developing a numerical method which works for all cases of eccentricities and is unconditional.

Basically, these curves are graphical representation of the result which meets equilibrium condition for footings subjected to large moments in both the directions.

In my earlier post I mentioned that Teng's charts depict the pressure coefficients vary from linear to polynomial for different combinations of eccentricities.  

In Teng's curve:

Zone 1 is a case of linear pressure coefficients and it is nothing but the Kern portion. This case is for loading which do not produce -ve pressure at any of the corners.

Zone 2 is above zone 1 and it is leaf shaped.  The values of X and Y (to calculate uplift area) are given in graphically form and equation is not given for obtaining the same.

Zone 3 is on two sides of zone 2.  The equations given shall be used with appropriate values of ex/Lx and ey/Ly.  The equations given in the book apply only for the one side of zone 3 and other side is mirrored. The equation given is with power 2.   If solution of equation is not possible due to negative roots, just interchange ex/Lx and ey/Ly.

Zone 4 is with values of ex/Lx and ey/Ly > 0.25.  Usually, the foundations in this zone fail in overturning stability check and for all practical reasons, this zone may be ignored.  However, the equation given is pretty simple and straight forward and is based on volume and CG of tetrahedron.

Most of the foundations fall in zone 2 and zone 3 and the behavior of uplift area and pressure coefficient is varying a lot.  Finding the uplift area (x and y) is really a challenge.  Also, engineer has to work on many load combinations where the uplift case will arise.

Since, we are working with some portion of foundation unstressed, the higher level of accuracy shall be sought while analyzing foundations having uplift cases.  Approximation may lead to unsafe foundation design.

Just to add here that the solution adopted by software working on soil as elastic medium like SAFE, also works on iterative procedure to obtain the unstressed zone and modified pressure on the compression side.

Regards,

Jignesh V Chokshi
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k.gangadharan
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PostPosted: Tue Jun 14, 2011 4:12 am    Post subject: Teng's curve Reply with quote

dear I. Barua
Can you please send the Qbasicprogramfor Curve fitting to my email Id with explaations how to do work out it. I shall be greatly thankful to you.
regards
Gangadharan.K
structural consultant
email id assekg1@gmail.com (assekg1@gmail.com)


On Mon, Jun 6, 2011 at 7:37 PM, ibarua <forum@sefindia.org (forum@sefindia.org)> wrote:
[quote]  6th June 2011

The method of 'Least Squares Curve Fitting' is a very useful procedure for obtaining an equation for any curve, given a set of known 'x' and 'y' values.

I had written a Qbasic program for solving this problem, many years ago. I could send it to you if you let me have your e-mail ID.

Indrajit Barua.

On Thu, 02 Jun 2011 08:48:44 +0530 "haridevender" wrote
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vikram.jeet
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PostPosted: Tue Jun 14, 2011 5:14 am    Post subject: Teng's curve Reply with quote

Teng's curves for Biaxial moments on footing causing upliftment

Er Jignesh V Chkshi has given ample information on Teng's charts. Just to add a liitle:-

Case -2 The Uplifted area is triangular and contact area is pentagonal(with five sides
including two complete sides of footing dimension)
This is a case of low moments on footing,though enough to cause upliftment .

Case -3 The Uplifted area is quadrangular and contact area is also quadrangular
( both having four sides including one complete side of footing dimension)
This is a case of high moments on footing .

Case -4 The Uplifted area is pentagonal(with five sides including two complete  
sides of footing dimension) and contact area is triangular This is a case of VERY
HIGH moments on footing enough to cause stability failures and shall be  
avoided by increasing footing size to bring in zone 2 or 3 .

best regards

vikramjeet


Most of the foundations fall in zone 2 and zone 3 and the behavior of uplift area and pressure coefficient is varying a lot. Finding the uplift area (x and y) is really a challenge. Also, engineer has to work on many load combinations where the uplift case will arise.
Since, we are working with some portion of foundation unstressed, the higher level of accuracy shall be sought while analyzing foundations having uplift cases. Approximation may lead to unsafe foundation design.
Just to add here that the solution adopted by software working on soil as elastic medium like SAFE, also works on iterative procedure to obtain the unstressed zone and modified pressure on the compression side.
Regards,

Jignesh V Chokshi

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bijay sarkar
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PostPosted: Tue Jun 14, 2011 7:55 am    Post subject: Reply with quote

Dear Sirs,

Teng's book has  provided the curves as well as the methodology of its solution by trial and error method. If someone minutely goes through the (i) Teng's Chart, (ii) Equations provided (iii) And also the literature portion of the Teng's book, solution by trial & error method is not so hard for all the four cases when computer is in hand.  Everything is already provided in the book.   Methodology described in Teng's book is by "TRANSFORMED AREA METHOD".   However, someone should have programming capability. Considering an initial Neutral Axis and several strips of the compressed area portion parallel to the assumed NA and finding out the load & CG thereof and comparing the same with the location of the actual acting load at the eccentric location. When CG of the compressed area is equal to that of the acting load, your assumed Neutral Axis is correct one. However, you are to study the Teng's curve and equations provided for initial guess of the neutral axis which should be parallel to the actual NA.


regards,


bijay sarkar
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JVCSNL
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PostPosted: Tue Jun 14, 2011 12:42 pm    Post subject: Reply with quote

Dear Er. Bijay Sarkar,

The solution to obtain equilibrium condition is not so easy as it appears to implement on computer.  

Just to share the experience, I was trying to work with ex/Lx = 0.4 and ey/Ly = 0.20, it took almost 318,000 iterations to obtain solution with acceptable error of 0.5%.  However, the moment I interchanged ex/Lx=0.2 and ez/Lz = 0.4, it took only 2500 iterations.  

To obtain the results faster, we can increase the acceptable error limit but in days of computers, we are keen to achieve higher accuracy.  

I recall that long back on SEFI, some one has kept Excel spreadsheet which used Excel add-ins solver to obtain quick solution to the problem.  It may still be on this website.  The roundation was divided in various elements and for each element, the pressure was calculated.  The constraints were assigned in such a manner that the pressure shall be +ve or Zero.  

Please share your views on methodology to be adopted for programming so that the solution converges faster.

My program is based on finding a solution band, which is two extremes of NA within which the iterations shall be done.  However, I am yet to make it faster for the conditions I explained above in this mail.

Regards,

Jignesh V Chokshi
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bijay sarkar
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PostPosted: Tue Jun 14, 2011 1:01 pm    Post subject: Reply with quote

Dear Er Jignesh V Chokshi,

Solution as described by me was done many days back.  Speed of calculation part was not of a "delay type" what i can remember. Actually i am busy with something other. I wish to go through that again and come back. I did not make any chart by the data produced, preparing a chart object by computer takes enough time for its doing everything. I will communicate you what is the iteration number for convergence for its solution and percentage of deviation to this solution.

regards,


bijay sarkar
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jiwaji
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PostPosted: Wed Jun 15, 2011 7:21 am    Post subject: Teng's curve Reply with quote

Dear Shri Sarkar

Would it be possible for you to provide the details of this book - exact title, edition, where it could be purchased, etc? With equations provided, one could develop a trial and error method easily in EXCEL, I think.
Thanks and regards
Jiwaji Desai



"bijay sarkar" <forum@sefindia.org>  
06/15/2011 12:21 PM    Please respond to
general@sefindia.org

To
general@sefindia.org   cc
Subject
[SEFI] Re: Teng's curve




Dear Sirs,

Teng's book has provided the curves as well as the methodology of its solution by trial and error method. If someone minutely goes through the (i) Teng's Chart, (ii) Equations provided (iii) And also the literature portion of the Teng's book, solution by trial & error method is not so hard for all the four cases when computer is in hand. Everything is already provided in the book. Methodology described in Teng's book is by "TRANSFORMED AREA METHOD". However, someone should have programming capability. Considering an initial Neutral Axis and several strips of the compressed area portion parallel to the assumed NA and finding out the load & CG thereof and comparing the same with the location of the actual acting load at the eccentric location. When CG of the compressed area is equal to that of the acting load, your assumed Neutral Axis is correct one. However, you are to study the Teng's curve and equations provided for initial guess of the neutral axis which should be parallel to the actual NA.


regards,


bijay sarkar







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JVCSNL
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PostPosted: Thu Jun 16, 2011 3:52 am    Post subject: Teng's curve Reply with quote

Dear Mr. Jiwaji Desai,

The transformed area method as indicated by Mr. Bijay Sarkar is given in the "Foundation Design" by W C Teng, 1962, Prentice Hall India, on page 131 under the "Eccentric Loading" section.

In the beginning of the explanation of the method, author indicates "The procedure for determination of soil pressure when the load is applied outside the kern is simple in principle but laborious."

Please note that the procedure is given based on integration method. Method also tells about calculating CG of compressed area using card board. We need to appreciate that the method was given in 1962 when the computers were not in use as they are today. The procedure is definitely laborious even today.

For a case of rectangular footing, the problem is simplified as the shape of pressure diagram under compression is tetrahedron. The volume of tetrahedron is 1/6 LBH and CG is 1/4 L and 1/4 B from the corner. Based on this principle one can easily work out the exact location of neutral axis for given eccentricities ex and ey. This procedure is better explained in "Foundation Engineering" by Peck, Hanson and Thornburn (John Wiley), which I used in my work. The charts previously I attached in this forum are based on this principle.

It is amazing to note that the curves originated by W C Teng 50 years before, without using computers, are absolutely perfect and universally accepted. It would be great if someone finds out how he has developed it without using computers.

Similar curves to solve the problem are given in Foundation Design Handbook edited by H F Winterkorn & H Y Fang (Book may be available in India from Galgotia Booksource.. , Delhi) This book provides the graphs to obtain pressure coefficient k and dimensions of footing portion under uplift.


Regards,

Jignesh V Chokshi





Quote:
Quote:
Quote:
forum@sefindia.org 15-06-2011 >>>

Dear Shri Sarkar

Would it be possible for you to provide the details of this book - exact title, edition, where it could be purchased, etc? With equations provided, one could develop a trial and error method easily in EXCEL, I think.
Thanks and regards
Jiwaji Desai

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PostPosted: Thu Jun 16, 2011 2:37 pm    Post subject: Reply with quote

Dear Shri Desai,

Details of Teng's Book :

Foundation Design
Wayne C. Teng
Prentice Hall of India Pvt Ltd
New Delhi - 110001
Sixth Edition - 1979............I dont know the more latest edition, if any. Price was Rs. 20 in India when USA printing price was Rs 197.55 in 1979.

First Printing edition in India is in 1965. First Printing Edition in USA is in 1962 by PH, Inc, Eagleford Cliffs, NJ, USA.

Contact PHI people in Delhi or elsewhere.


regards,

bijay sarkar
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PostPosted: Fri Jun 17, 2011 6:23 am    Post subject: Teng's curve Reply with quote

17th June 2011

Details of Teng's book:

'Foundation Design' by Wayne C. Teng

Prentice Hall of P. India Ltd.,
M-97 Connaught Circus,
New Delhi - 110 001

Indrajit Barua

From: "jiwaji" <forum@sefindia.org> On Wed, 15 Jun 2011 20:12:16
To: general@sefindia.org

           Dear Shri Sarkar

Would it be possible for you to provide the details of this book - exact title, edition, where it could be purchased, etc? With equations provided, one could develop a trial and error method easily in EXCEL, I think.
Thanks and regards
Jiwaji Desai



"bijay sarkar" <forum@sefindia.org>
06/15/2011 12:21 PM Please respond to
general@sefindia.org

To
general@sefindia.org cc
Subject
[SEFI] Re: Teng's curve




Dear Sirs,

Teng's book has provided the curves as well as the methodology of its solution by trial and error method. If someone minutely goes through the (i) Teng's Chart, (ii) Equations provided (iii) And also the literature portion of the Teng's book, solution by trial & error method is not so hard for all the four cases when computer is in hand. Everything is already provided in the book. Methodology described in Teng's book is by "TRANSFORMED AREA METHOD". However, someone should have programming capability. Considering an initial Neutral Axis and several strips of the compressed area portion parallel to the assumed NA and finding out the load & CG thereof and comparing the same with the location of the actual acting load at the eccentric location. When CG of the compressed area is equal to that of the acting load, your assumed Neutral Axis is correct one. However, you are to study the Teng's curve and equations provided for initial guess of the neutral axis which should be parallel to the actual NA.


regards,


bijay sarkar







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