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vikram.jeet General Sponsor
Joined: 26 Jan 2003 Posts: 3896

Posted: Thu Jun 09, 2011 10:05 am Post subject: Teng's curve 


The method described by respected Sh Barua sir is in wide use for footings
having appreciable moment along with vertical load causing part of
footing to leave contact with base ( i.e. upliftment condition) under the
action of unidirectional moment
Teng's curves also provide upliftment area for footings under action of biaxial moment
and gives max base pressure .The use is very common in bridge foundations  open type
generally in hilly areas where good rock is available at base.
One way is that the two moments can be converted into resultant along
diagonal and footing could be aligned along diagonal direction as suggested
by Sh Barua sahab.
But in actuality, the alignment of footing along diagonal is not in practice .
There is no quick method to check the base pressures other than Teng's curves
Just a vague approach   very approx
An approximate method for such biaxial case can be thought of adopting
law of superposition
We may take
Actual Contact length along L direction x= = 3*[L/2e)]    considering uniaxial mo along L
Actual Contact length along B direction =y= = 3*[L/2e')]    considering uniaxial mo alongB
(But if above value yield the value x>L due to less Mo along L dir , the x shall be restricted
equal to L and similarily if y>B, then y shall be restricted to B )
Max Base pressure(redistributed) =[2*W/{x*Y1} +2*W/{X1*y1}] * 85%
or
Max Base pressure(redistributed) =[2*W/{X1*y} +2*W/{x*Y1}] * 85%
Y1 is least of( y or B )and X1 is least of (x or L)
I think results may be within digestible range , though not exact.Probably some sefi member may
come out with exact algorithm
best regds
vikramjeet
6th June 2011
Re.: query about Teng's curve
In case of foundations subject to uplift, use may be made of the method prescribed in 'Steel Designers' Manual', explained briefly here as follows:
Loaded length = 3*y = 3*(L/2e)
Maximum edge pressure, p(max) = 2*W/(3*B*y),
where: W = total axial load on foundation including self wt. of fdn.
B = width of fdn.
e = M/W
Indrajit Barua.
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JVCSNL ...
Joined: 26 Jan 2003 Posts: 169

Posted: Fri Jun 10, 2011 7:13 am Post subject: Teng's curve 


Dear Mr. Vikramjeet,
Considering one moment at a time in respective direction and then superimposing them to know actual unstressed zone has many assumptions and limitations. As far as uniaxial moment is considered, we just consider force equilibrium for applied load and reaction from soil for compression zone. Hence, the equation is simple to obtain. However, for biaxial moment case having load point out side kern, the equilibrium behavior is completely different is a complex problem.
As mentioned in my earlier post, it is difficult to obtain one single equation catering all the combinations of eccentricities.
To see the behavior of shift of neutral axis from original position (i.e. when some corners are experiencing ve bearing presure) to actual position (where there is no ve bearing pressure on soil), refer the document uploaded on http://www.sefindia.org/forum/viewtopic.php?t=5420&postdays=0&postorder=asc&start=20. Last two pages of the document shows the actual bearing pressure variation and shift of NA for different cases of ex and ey.
As can be seen, the shift of NA depends on the amount of eccentricity in both the direction and hence, the superposition from individual axis will not meet equilibrium requirements.
The uploaded document describes the step by step numerical approach that can be easily implemented through programming.
For the benefit of the members, I am attaching two pictures showing the pressure coefficient (k) for various eccentricity and unstressed area (called uplift). This was developed through the numerical approach with a tangible accuracy of 99.9%.
Regards,
Jignesh Chokshi
Quote:  Quote:  Quote:  forum@sefindia.org 10062011 >>>



The method described by respected Sh Barua sir is in wide use for footings
having appreciable moment along with vertical load causing part of
footing to leave contact with base ( i.e. upliftment condition) under the
action of unidirectional moment
Teng's curves also provide upliftment area for footings under action of biaxial moment
and gives max base pressure .The use is very common in bridge foundations  open type
generally in hilly areas where good rock is available at base.
One way is that the two moments can be converted into resultant along
diagonal and footing could be aligned along diagonal direction as suggested
by Sh Barua sahab.
But in actuality, the alignment of footing along diagonal is not in practice .
There is no quick method to check the base pressures other than Teng's curves
Just a vague approach   very approx
An approximate method for such biaxial case can be thought of adopting
law of superposition
We may take
Actual Contact length along L direction x= = 3*[L/2e)]    considering uniaxial mo along L
Actual Contact length along B direction =y= = 3*[L/2e')]    considering uniaxial mo alongB
(But if above value yield the value x>L due to less Mo along L dir , the x shall be restricted
equal to L and similarily if y>B, then y shall be restricted to B )
Max Base pressure(redistributed) =[2*W/{x*Y1} +2*W/{X1*y1}] * 85%
or
Max Base pressure(redistributed) =[2*W/{X1*y} +2*W/{x*Y1}] * 85%
Y1 is least of( y or B )and X1 is least of (x or L)
I think results may be within digestible range , though not exact.Probably some sefi member may
come out with exact algorithm
best regds
vikramjeet
6th June 2011
Re.: query about Teng's curve
In case of foundations subject to uplift, use may be made of the method prescribed in 'Steel Designers' Manual', explained briefly here as follows:
Loaded length = 3*y = 3*(L/2e)
Maximum edge pressure, p(max) = 2*W/(3*B*y),
where: W = total axial load on foundation including self wt. of fdn.
B = width of fdn.
e = M/W
Indrajit Barua.
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JVCSNL ...
Joined: 26 Jan 2003 Posts: 169

Posted: Fri Jun 10, 2011 7:23 am Post subject: Teng's curve 


Dear Mr. Vikramjeet,
Considering one moment at a time in respective direction and then superimposing them to know actual unstressed zone has many assumptions and limitations. As far as uniaxial moment is considered, we just consider force equilibrium for applied load and reaction from soil for compression zone. Hence, the equation is simple to obtain. However, for biaxial moment case having load point out side kern, the equilibrium behavior is completely different is a complex problem.
As mentioned in my earlier post, it is difficult to obtain one single equation catering all the combinations of eccentricities.
To see the behavior of shift of neutral axis from original position (i.e. when some corners are experiencing ve bearing presure) to actual position (where there is no ve bearing pressure on soil), refer the document uploaded on http://www.sefindia.org/forum/viewtopic.php?t=5420&postdays=0&postorder=asc&start=20. Last two pages of the document shows the actual bearing pressure variation and shift of NA for different cases of ex and ey.
As can be seen, the shift of NA depends on the amount of eccentricity in both the direction and hence, the superposition from individual axis will not meet equilibrium requirements.
The uploaded document describes the step by step numerical approach that can be easily implemented through programming.
For the benefit of the members, I am attaching two pictures showing the pressure coefficient (k) for various eccentricity and unstressed area (called uplift). This was developed through the numerical approach with a tangible accuracy of 99.9%.
Regards,
Jignesh Chokshi
Quote:  Quote:  Quote:  forum@sefindia.org 10062011 >>>



The method described by respected Sh Barua sir is in wide use for footings
having appreciable moment along with vertical load causing part of
footing to leave contact with base ( i.e. upliftment condition) under the
action of unidirectional moment
Teng's curves also provide upliftment area for footings under action of biaxial moment
and gives max base pressure .The use is very common in bridge foundations  open type
generally in hilly areas where good rock is available at base.
One way is that the two moments can be converted into resultant along
diagonal and footing could be aligned along diagonal direction as suggested
by Sh Barua sahab.
But in actuality, the alignment of footing along diagonal is not in practice .
There is no quick method to check the base pressures other than Teng's curves
Just a vague approach   very approx
An approximate method for such biaxial case can be thought of adopting
law of superposition
We may take
Actual Contact length along L direction x= = 3*[L/2e)]    considering uniaxial mo along L
Actual Contact length along B direction =y= = 3*[L/2e')]    considering uniaxial mo alongB
(But if above value yield the value x>L due to less Mo along L dir , the x shall be restricted
equal to L and similarily if y>B, then y shall be restricted to B )
Max Base pressure(redistributed) =[2*W/{x*Y1} +2*W/{X1*y1}] * 85%
or
Max Base pressure(redistributed) =[2*W/{X1*y} +2*W/{x*Y1}] * 85%
Y1 is least of( y or B )and X1 is least of (x or L)
I think results may be within digestible range , though not exact.Probably some sefi member may
come out with exact algorithm
best regds
vikramjeet
6th June 2011
Re.: query about Teng's curve
In case of foundations subject to uplift, use may be made of the method prescribed in 'Steel Designers' Manual', explained briefly here as follows:
Loaded length = 3*y = 3*(L/2e)
Maximum edge pressure, p(max) = 2*W/(3*B*y),
where: W = total axial load on foundation including self wt. of fdn.
B = width of fdn.
e = M/W
Indrajit Barua.
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vikram.jeet General Sponsor
Joined: 26 Jan 2003 Posts: 3896

Posted: Fri Jun 10, 2011 9:51 am Post subject: Teng's curve 


Dear Er Jignesh Chowkshi ji
I agree with you that it is a complex problem.However for quick check ,if some
approx approach is developed(may be 10% off) , it may help save time of
designers. Not out of context to mention that Column design by reading
the sp16 charts is very time consuming ,but here on sefi ,a veteran designer
Sh RG Gupta has developed MAGIC equations which were posted on
forum. A similar approach is needed for this problem too though I fully agree
it is not easy.
thanks and regards
vikramjeet
Dear Mr. Vikramjeet,
Considering one moment at a time in respective direction and then superimposing them to know actual unstressed zone has many assumptions and limitations. As far as uniaxial moment is considered, we just consider force equilibrium for applied load and reaction from soil for compression zone. Hence, the equation is simple to obtain. However, for biaxial moment case having load point out side kern, the equilibrium behavior is completely different is a complex problem
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hemal ...
Joined: 01 Apr 2008 Posts: 129

Posted: Sat Jun 11, 2011 4:07 am Post subject: Teng's curve 


Dear Sefi Members,
Foundation design module (FOUND) of STRAP software provides options to control uplift. Plz find attached some screenshots to clarify the topic.
Regards
Hemal Mistry
Surat
On Fri, 10/6/11, vikram.jeet <forum@sefindia.org> wrote:
Quote: 
From: vikram.jeet <forum@sefindia.org>
Subject: [SEFI] Re: Teng's curve
To: general@sefindia.org
Date: Friday, 10 June, 2011, 12:08 AM
The method described by respected Sh Barua sir is in wide use for footings
having appreciable moment along with vertical load causing part of
footing to leave contact with base ( i.e. upliftment condition) under the
action of unidirectional moment
Teng's curves also provide upliftment area for footings under action of biaxial moment
and gives max base pressure .The use is very common in bridge foundations  open type
generally in hilly areas where good rock is available at base.
One way is that the two moments can be converted into resultant along
diagonal and footing could be aligned along diagonal direction as suggested
by Sh Barua sahab.
But in actuality, the alignment of footing along diagonal is not in practice .
There is no quick method to check the base pressures other than Teng's curves
Just a vague approach   very approx
An approximate method for such biaxial case can be thought of adopting
law of superposition
We may take
Actual Contact length along L direction x= = 3*[L/2e)]    considering uniaxial mo along L
Actual Contact length along B direction =y= = 3*[L/2e')]    considering uniaxial mo alongB
(But if above value yield the value x>L due to less Mo along L dir , the x shall be restricted
equal to L and similarily if y>B, then y shall be restricted to B )
Max Base pressure(redistributed) =[2*W/{x*Y1} +2*W/{X1*y1}] * 85%
or
Max Base pressure(redistributed) =[2*W/{X1*y} +2*W/{x*Y1}] * 85%
Y1 is least of( y or B )and X1 is least of (x or L)
I think results may be within digestible range , though not exact.Probably some sefi member may
come out with exact algorithm
best regds
vikramjeet
6th June 2011
Re.: query about Teng's curve
In case of foundations subject to uplift, use may be made of the method prescribed in 'Steel Designers' Manual', explained briefly here as follows:
Loaded length = 3*y = 3*(L/2e)
Maximum edge pressure, p(max) = 2*W/(3*B*y),
where: W = total axial load on foundation including self wt. of fdn.
B = width of fdn.
e = M/W
Indrajit Barua.
 ญญ

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JVCSNL ...
Joined: 26 Jan 2003 Posts: 169

Posted: Sun Jun 12, 2011 5:19 am Post subject: 


Dear Mr. Hemal,
Does the software perform this for biaxial moment case also?
If so, what approach the program is using and how it is validated.
Regards,
Jignesh V Chokshi


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hemal ...
Joined: 01 Apr 2008 Posts: 129

Posted: Sun Jun 12, 2011 5:02 pm Post subject: Teng's curve 


Dear Mr. Jignesh,
Yes, you can also have biaxial moment. Actually, as i mentioned earlier, this FOUNDATION DESIGN MODULE IS INBUILT MODULE OF STRAP, which is well recognized general structural design software (www.atirsoft.com), and you can generally expect biaxial moments in a footing of space structure.
You can also have eccentricity ex and/or ey which may be there between c.g. of footing and center of column due geometric restraint, in addition to actual biaxial moments from column.
It provides check for permissible base pressure, one way shear and two way shear. It provides footing dimensions and depth (if possible) such that uplift parameters as specified are satisfied along with usual checks.
Plz find attached screen shots for more details.
Regards
Hemal Mistry
Surat
On Sun, 12/6/11, JVCSNL <forum@sefindia.org> wrote:
Quote: 
From: JVCSNL <forum@sefindia.org>
Subject: [SEFI] Re: Teng's curve
To: general@sefindia.org
Date: Sunday, 12 June, 2011, 12:19 AM
Dear Mr. Hemal,
Does the software perform this for biaxial moment case also?
If so, what approach the program is using and how it is validated.
Regards,
Jignesh V Chokshi

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ibarua General Sponsor
Joined: 26 Jan 2003 Posts: 1039

Posted: Mon Jun 13, 2011 7:49 am Post subject: Teng's curve 


13th June 2011
If 'e' in each of the two orthogonal directions exceeds 1/6*(respective length in that direction), then you could try computing the effects from the two directions as in the following:
y1 = L/2e[L], y2 = B/2e
p(max)[L] = 2*W/(3*B*y1)
p(max) =2*W/(3*L*y2)
It may be noted that p[max] resulting from these computations are not at the same point, and therefore the 2 values cannot be added together to get a result.
As far as Teng's curves are concerned, I'm a bit unsure as to what curve's exactly you are referring to. The version of Teng's 'Foundation Design' I have is quite old (1962, with 8th reprint in March, 1981). Would you please clarify this aspect of the matter?
We can develop equations for any curve provided we have certain sets of 'x' and 'y' values, by the method of 'Least Squares Curve Fitting Routine'. Generally, a polynomial of the third degree yields satisfactory results. The resulting coefficients could be embedded in an Excel worksheet for our purposes.
Of course, we cannot be very sure that Mother Nature would obey the diktats of the mathematical model developed.by us Therefore, the explanation of any curves developed by Teng (or for that matter, by anyone else) should be available to us for our understanding of the matter.
Indrajit Barua.
On Thu, 09 Jun 2011 14:43:11 , "jiwaji" <forum@sefindia.org> wrote
Sir
The equations given by you hold only ecc less than 1/6 th the respective base directions, as full area is assumed in contact in their derivation. My query was for when the only when a part of the area is in contact, ie the NA is inclined to the principal directions of moments, and inside the footing area.
These equations may be the basis of Teng's charts, and one would like to use them for developing EXCEL or mathcad sheets.
Sir, these situations ar often encountered when diect loadings are relatively light, dominant horizontal thrusts (specified by vendors in a variety of combinations) are to be resisted, tiebeams are a luxury and column locations are guided by technological inputs, ie irregular mechanical layouts resulting in high biaxial eccentricities. One is often called upon to locate such additional columns in an existing Plant for various reasons, where choice of location by structural engineer is unthinkable.
I would be grateful any information on such equations, based is made available.
Regards
Jiwaji Desai
"ibarua" <forum@sefindia.org>
06/08/2011 09:23 PM Please respond to
general@sefindia.org
To
general@sefindia.org cc
Subject
[SEFI] Re: Teng's curve
8th June 2011
You could perhaps treat the actions in the two cases separately and then superimpose the results.
Generally, for a loading eccentric about both axes:
If 'eL' and 'eB' are the eccentricities of the load 'W' with regard to 'L' and 'B' respectively, then:
p(max) = W/(B*L) *(1+ 6*eL/L + 6*eB/B)
p(min) = W/(B*L) *(1 6*eL/L  6*eB/B)
Another way could be to compute the resultant moment and align the foundation in the direction of the resultant moment.
Indrajit Barua
However, I have not yet come across a situation when a foundations has uplifts in two directions.
Indrajit Barua.
On Tue, 07 Jun 2011 11:58:39 +0530 "jiwaji" <forum@sefindia.org> wrote
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ibarua General Sponsor
Joined: 26 Jan 2003 Posts: 1039

Posted: Mon Jun 13, 2011 8:27 am Post subject: Teng's curve 


13th June 2011
Sequel to my earlier post:
After some search, I've been able to locate Teng's curves you have referred to (on page 133 of 'Foundation Design' by Teng). I leave it to you to interpret the chart. If some sets of data as 'x' and 'y' can be gleaned from this chart, then I could possibly run the program to determine the coefficients of the polynomial to generate the curves. These coefficients can then be embedded in an Excel worksheet to make a program for analysis and design.
Indrajit Barua.
On Thu, 09 Jun 2011 14:43:11 , "jiwaji" <forum@sefindia.org> wrote
Sir
The equations given by you hold only ecc less than 1/6 th the respective base directions, as full area is assumed in contact in their derivation. My query was for when the only when a part of the area is in contact, ie the NA is inclined to the principal directions of moments, and inside the footing area.
These equations may be the basis of Teng's charts, and one would like to use them for developing EXCEL or mathcad sheets.
Sir, these situations ar often encountered when diect loadings are relatively light, dominant horizontal thrusts (specified by vendors in a variety of combinations) are to be resisted, tiebeams are a luxury and column locations are guided by technological inputs, ie irregular mechanical layouts resulting in high biaxial eccentricities. One is often called upon to locate such additional columns in an existing Plant for various reasons, where choice of location by structural engineer is unthinkable.
I would be grateful any information on such equations, based is made available.
Regards
Jiwaji Desai
"ibarua" <forum@sefindia.org>
06/08/2011 09:23 PM Please respond to
general@sefindia.org
To
general@sefindia.org cc
Subject
[SEFI] Re: Teng's curve
8th June 2011
You could perhaps treat the actions in the two cases separately and then superimpose the results.
Generally, for a loading eccentric about both axes:
If 'eL' and 'eB' are the eccentricities of the load 'W' with regard to 'L' and 'B' respectively, then:
p(max) = W/(B*L) *(1+ 6*eL/L + 6*eB/B)
p(min) = W/(B*L) *(1 6*eL/L  6*eB/B)
Another way could be to compute the resultant moment and align the foundation in the direction of the resultant moment.
Indrajit Barua
However, I have not yet come across a situation when a foundations has uplifts in two directions.
Indrajit Barua.
On Tue, 07 Jun 2011 11:58:39 +0530 "jiwaji" <forum@sefindia.org> wrote
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JVCSNL ...
Joined: 26 Jan 2003 Posts: 169

Posted: Mon Jun 13, 2011 2:02 pm Post subject: Teng's curve 


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 direction.
In my earlier post I mentioned that Teng's charts depict the pressure coefficients vary from linear to polynomial for different combinations of eccentricities.
Zone 1 is a case of linear pressure coefficients and it is nothing but the Kern portion.
Zone 2 is above zone 1 and it is leaf shaped. The values of X and Y are given in graph and equation is not given for it.
Zone 3 is on two sides of zone 2. The equations given shall be used with appropriate values of ex and ey. The equations apply only for the one side and other side is mirrored. The equation given is with power 2. If solution of equation is not available, just interchange ex and ey and lx and ly.
Zone 4 is with values of ex/lx and ey/ly > 0.25. Usually, the foundations in this zone fail in overturning check and for all practical reasons, this zone may be ignored. However, the equation is pretty simple and straight forward and is based on tetrahedron.
Most of the foundations fall in zone 2 and zone 3 category 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.
Just to add the solution adopted by other software working on soil as elastic medium, like SAFE also works on iterative procedure to obtain the foundation in compression only.
Regards,
Jignesh V Chokshi
Quote:  Quote:  Quote:  forum@sefindia.org 13062011 >>>



13th June 2011
Sequel to my earlier post:
After some search, I've been able to locate Teng's curves you have referred to (on page 133 of 'Foundation Design' by Teng). I leave it to you to interpret the chart. If some sets of data as 'x' and 'y' can be gleaned from this chart, then I could possibly run the program to determine the coefficients of the polynomial to generate the curves. These coefficients can then be embedded in an Excel worksheet to make a program for analysis and design.
Indrajit Barua.
On Thu, 09 Jun 2011 14:43:11 , "jiwaji" wrote
Sir
The equations given by you hold only ecc less than 1/6 th the respective base directions, as full area is assumed in contact in their derivation. My query was for when the only when a part of the area is in contact, ie the NA is inclined to the principal directions of moments, and inside the footing area.
These equations may be the basis of Teng's charts, and one would like to use them for developing EXCEL or mathcad sheets.
Sir, these situations ar often encountered when diect loadings are relatively light, dominant horizontal thrusts (specified by vendors in a variety of combinations) are to be resisted, tiebeams are a luxury and column locations are guided by technological inputs, ie irregular mechanical layouts resulting in high biaxial eccentricities. One is often called upon to locate such additional columns in an existing Plant for various reasons, where choice of location by structural engineer is unthinkable.
I would be grateful any information on such equations, based is made available.
Regards
Jiwaji Desai
"ibarua"
06/08/2011 09:23 PM Please respond to
general@sefindia.org (general@sefindia.org)
To
general@sefindia.org (general@sefindia.org) cc
Subject
[SEFI] Re: Teng's curve
8th June 2011
You could perhaps treat the actions in the two cases separately and then superimpose the results.
Generally, for a loading eccentric about both axes:
If 'eL' and 'eB' are the eccentricities of the load 'W' with regard to 'L' and 'B' respectively, then:
p(max) = W/(B*L) *(1+ 6*eL/L + 6*eB/B)
p(min) = W/(B*L) *(1 6*eL/L  6*eB/B)
Another way could be to compute the resultant moment and align the foundation in the direction of the resultant moment.
Indrajit Barua
However, I have not yet come across a situation when a foundations has uplifts in two directions.
Indrajit Barua.
On Tue, 07 Jun 2011 11:58:39 +0530 "jiwaji" wrote
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