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Teng's curve
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vikram.jeet
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PostPosted: Mon Apr 19, 2010 7:15 am    Post subject: Teng's curve Reply with quote

Foundation Design by Wayne C Teng

Yes ,This is very good Book. This book has been in use by the designers / structural consultants/Geotech consultants
since long, may be from 50's/60's.Very popular & practical due to availability of curves/tables.
This book ,surely ,enrich the domain of Civil Engg. Libraries .

vikramjeet


Dear Sefians

Foundation design by Wayne C.Teng is a very usefull book on Siol Mechanics and foundation engg and it is woth to buy the book at any cost.

er.Balaji venkateswaran

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haridevender
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PostPosted: Wed Jun 01, 2011 4:53 pm    Post subject: Reply with quote

Dear all, Please anybody can give the mathematical modelling equation for the calculation of x and y, in Zone II.

Hari Devender
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sudhansh09
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PostPosted: Thu Jun 02, 2011 3:51 pm    Post subject: Reply with quote

Dear haridevender,

You might be asking for base pressure redistribution.
Here is table to find out value of k,
from book " Roark's Formulas for stress and strain"


e1=eb/B
e2=el/L 0 0.05 0.1 0.15 0.175 0.2 0.225 0.25 0.275 0.3 0.325 0.35 0.375 0.4
0 1 1.3 1.6 1.9 2.05 2.22 2.43 2.67 2.96 3.33 3.81 4.44 5.33 6.67
0.05 1.3 1.6 1.9 2.21 2.38 2.58 2.81 3.09 3.43 3.87 4.41 5.16 6.17 7.73
0.1 1.6 1.9 2.2 2.56 2.76 2.99 3.27 3.6 3.99 4.48 5.14 5.99 7.16 9
0.15 1.9 2.21 2.56 2.96 3.22 3.51 3.84 4.22 4.66 5.28 6.03 7.04 8.45 10.6
0.175 2.05 2.38 2.76 3.22 3.5 3.81 4.16 4.55 5.08 5.73 6.55 7.66 9.17 11.5
0.2 2.22 2.58 2.99 3.51 3.81 4.13 4.5 4.97 5.54 6.24 7.12 8.33 9.98
0.225 2.43 2.81 3.27 3.84 4.16 4.5 4.93 5.18 6.05 6.83 7.82 9.13 10.9
0.25 2.67 3.09 3.6 4.22 4.55 4.97 5.48 6 6.67 7.5 8.57 10 12
0.275 2.96 3.43 3.99 4.66 5.08 5.54 6.05 6.67 7.41 8.37 9.55 11.1
0.3 3.33 3.87 4.48 5.28 5.73 6.24 6.83 7.5 8.37 9.37 10.8
0.325 3.81 4.41 5.14 6.03 6.55 7.12 7.82 8.57 9.55 10.8
0.35 4.44 5.16 5.99 7.04 7.66 8.33 9.13 10 11.1
0.375 5.33 6.17 7.16 8.45 9.17 9.98 10.9 12
0.4 6.67 7.73 9 10.6 11.5

Thanks & Regards
sudhanshu
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haridevender
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PostPosted: Thu Jun 02, 2011 4:18 pm    Post subject: Reply with quote

Dear Sir,
Thanks for providing the K Values. Please tell me in which chapter, above table has been taken.
But I need of Mathematical modelling equations to find out the x and y values which are zone II of Teng's Curves, to findout the contact area of the footing under the application of eccentric loading in either directions simultaneously.

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ibarua
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PostPosted: Mon Jun 06, 2011 8:57 am    Post subject: Teng's curve Reply with 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" <forum@sefindia.org> wrote
Quote:
           Dear all, Please anybody can give the mathematical modelling equation for the calculation of x and y, in Zone II.

Hari Devender
     
Quote:





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ibarua
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PostPosted: Mon Jun 06, 2011 9:11 am    Post subject: Teng's curve Reply with quote

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/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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jiwaji
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PostPosted: Tue Jun 07, 2011 4:33 am    Post subject: Teng's curve Reply with quote

Dear Sir

Would it possiblefor you to help me find /give me similar equations for a closed solution, for bases subjected to tension uplift due to eccentricties (greater than B/6 and L/6) about both orthogonal axes, ie biaxial bending with tension? I would be grateful for the same.

Thanks and regards

Jiwaji




"ibarua" <forum@sefindia.org>  
06/06/2011 07:41 PM    Please respond to
general@sefindia.org

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




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/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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ibarua
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PostPosted: Wed Jun 08, 2011 6:31 am    Post subject: Teng's curve Reply with quote

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
[quote]           Dear Sir

Would it possiblefor you to help me find /give me similar equations for a closed solution, for bases subjected to tension uplift due to eccentricties (greater than B/6 and L/6) about both orthogonal axes, ie biaxial bending with tension? I would be grateful for the same.

Thanks and regards

Jiwaji




"ibarua" <forum@sefindia.org>
06/06/2011 07:41 PM Please respond to
general@sefindia.org

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




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/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
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PostPosted: Thu Jun 09, 2011 3:21 am    Post subject: Teng's curve Reply with quote

We can not treat the effects of moments in individual direction and then superimpose. The large moments in both the direction is usually a short term loading case (due to EQ force) for many industrial plant structures and tall equipment foundations and hence, we do not align the foundation in the direction of resultant moments as most of the times, these moments would not be present.

To answer Mr. Jiwaji's query, there is no unified equation which can take care of any combination of eccentricity in X and Y direction. It may be possible, but so far I have not seen literature giving these equations. Please note that the moment there is tension (-ve bearing pressure) at any of the corner, one has to analyze the foundation considering the neutral axis which is not orthogonal to any direction.

If you refer to Teng's curve, for eccentricity within the Kern, the pressure distribution is linear (say x to power 1). As eccentricity increases, the behavior starts to become non linear and the power to X increases continuously. In the high eccentricity zones (ex/Lx and ey/Ly more than 0.25), the equation seems to be of power 3 or 4 and reaches to infinity when eccentricity value reaches near the foundation edges.

Since, these equations were not available, I solved the problem with numerical approach and the literature on this is already available on SEFI (may be on page 3 of this topic). You may refer to the same for more about foundations with large moments in both the directions.

Regards,

Jignesh V Chokshi



Quote:
Quote:
Quote:
forum@sefindia.org 08-06-2011 >>>

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
Quote:
Dear Sir

Would it possiblefor you to help me find /give me similar equations for a closed solution, for bases subjected to tension uplift due to eccentricties (greater than B/6 and L/6) about both orthogonal axes, ie biaxial bending with tension? I would be grateful for the same.

Thanks and regards

Jiwaji




"ibarua"
06/06/2011 07:41 PM Please respond to
general@sefindia.org (general@sefindia.org)

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




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/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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jiwaji
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PostPosted: Thu Jun 09, 2011 4:31 am    Post subject: Teng's curve Reply with quote

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" <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
Quote:
Dear Sir

Would it possiblefor you to help me find /give me similar equations for a closed solution, for bases subjected to tension uplift due to eccentricties (greater than B/6 and L/6) about both orthogonal axes, ie biaxial bending with tension? I would be grateful for the same.

Thanks and regards

Jiwaji




"ibarua" <forum@sefindia.org>
06/06/2011 07:41 PM Please respond to
general@sefindia.org

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




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/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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