Redistribution of Base Pressure

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vikram.jeetGeneral Sponsor

Joined: 26 Jan 2003Posts: 2212

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 footingshaving 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/2-e)] - - - -considering uniaxial mo along L

Actual Contact length along B direction =y= = 3*[L/2-e')] - - - -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
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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/2-e)

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...


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=5 420 &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:

[email protected] 10-06-2011 >>>

The method described by respected Sh Barua sir is in wide use for footings

having appreciable moment along with vertical load causing part of




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3/15






by Sh Barua sahab.






We may take






or





best regds

vikramjeet

6th June 2011







B = width of fdn.

e = M/W

Indrajit Barua.

--

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JVCSNL...


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5/15



Joined: 26 Jan 2003Posts: 134 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



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=5 420 &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:


The method described by respected Sh Barua sir is in wide use for footings

having appreciable moment along with vertical load causing part of








by Sh Barua sahab.






We may take






or

http://www.sefindia.org/forum/viewtopic.php?t=5420&postdays=0&postorder=asc&start=20


6/15






best regds

vikramjeet

6th June 2011







B = width of fdn.

e = M/W

Indrajit Barua.

--

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vikram.jeetGeneral Sponsor



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 sp-16 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


Considering one moment at a time in respective direction and then superimposing them to know actual unstressed

zone h as many assumptions and limitations. As far as uniaxial moment is considered, we just consider force



a complex problem

--
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hemal...

Joined: 01 Apr 2008Posts: 109

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 wrote:

Quote:

From: vikram.jeet Subject: [SEFI] Re: Teng's curveTo: [email protected]: Friday, 10 June, 2011, 12:08 AM

The method described by respected Sh Barua sir is in wide use for footingshaving appreciable moment along with vertical load causing part offooting to leave contact with base ( i.e. upliftment condition) under theaction of unidirectional moment

Teng's curves also provide upliftment area for footings under action of biaxial momentand gives max base pressure .The use is very common in bridge foundations - -open typegenerally in hilly areas where good rock is available at base.One way is that the two moments can be converted into resultant alongdiagonal and footing could be aligned along diagonal direction as suggestedby Sh Barua sahab.But in actuality, the alignment of footing along diagonal is not in practice .


Just a vague approach - - very approxAn approximate method for such biaxial case can be thought of adoptinglaw of superpositionWe may takeActual Contact length along L direction x= = 3*[L/2-e)] - - - -considering uniaxial mo along LActual Contact length along B direction =y= = 3*[L/2-e')] - - - -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


Max Base pressure(redistributed) =[2*W/{x*Y1} +2*W/{X1*y1}] * 85%orMax Base pressure(redistributed) =[2*W/{X1*y} +2*W/{x*Y1}] * 85%


I think results may be within digestible range , though not exact.Probably some sefi member maycome out with exact algorithm

best regds

vikramjeet

6th June 2011Re.: 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/2-e)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/WIndrajit Barua.--
mailto:[email protected]://www.sefindia.org/forum/posting.php?mode=quote&p=37475http://www.sefindia.org/forum/viewtopic.php?p=37475#37475http://www.sefindia.org/forum/privmsg.php?mode=post&u=1752http://www.sefindia.org/forum/profile.php?mode=viewprofile&u=1752


8/15



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JVCSNL...

Posted: Sun Jun 12, 2011 5:19 am Post subject:
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9/15




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

Back to top

hemal...

Joined: 01 Apr 2008Posts: 109

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 wrote:

Quote:

From: JVCSNL Subject: [SEFI] Re: Teng's curveTo: [email protected]: 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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ibaruaGeneral Sponsor


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/2-e[L], y2 = B/2-e

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" 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, tie-beams 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

[email protected]

To

[email protected] cc

Subject

[SEFI] Re: Teng's curve
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11/15



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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ibaruaGeneral Sponsor


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.


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, tie-beams 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"


[email protected]

To

[email protected] cc

Subject
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12/15




8th June 2011




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


Indrajit Barua.


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JVCSNL...


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,
http://www.sefindia.org/forum/posting.php?mode=quote&p=37556http://www.sefindia.org/forum/viewtopic.php?p=37556#37556http://www.sefindia.org/forum/privmsg.php?mode=post&u=627http://www.sefindia.org/forum/profile.php?mode=viewprofile&u=627


13/15



Jignesh V Chokshi

Quote:

Quote:

Quote:


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.


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 isinclined 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, tie-beams 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"


[email protected] ([email protected])

To

[email protected] ([email protected]) cc

Subject


8th June 2011




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.
mailto:[email protected]:[email protected]


14/15



Indrajit Barua


Indrajit Barua.


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Documents

Redistribution of Base Pressure