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DESIGN OF STRIP FOOTING (BEAM-SLAB TYPE)
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Anagha
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PostPosted: Fri Jan 19, 2018 6:47 am    Post subject: DESIGN OF STRIP FOOTING (BEAM-SLAB TYPE) Reply with quote

Dear Engineers,
     While designing strip footing for 3 columns, I calculated bending moment at each supports and mid span points, by considering loads on left of the section and then from right of the section. But got different values of moment at the same point. which should I select?
loads considered are,
column loads (downwards), soil pressure(udl acting upwards)
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Abishek_Siingh
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PostPosted: Fri Jan 19, 2018 3:05 pm    Post subject: Reply with quote

Care to upload calculations?
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es_jayakumar
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PostPosted: Sun Jan 21, 2018 7:14 am    Post subject: Reply with quote

The doubt raised by Er.Anagha looks quite genuine ! Please see the attached example taken from a text book. This is the case of a strip footing for 4 columns. If you work out the BM at 2nd and 3rd column points from either side, you wil not get the matching moment. I hope, this is due to the high degree of simplification involved in the analysis. Maybe, the set of loads that would satisfy the static equilibrium of BM is the reactions obtained by analysing the system as a continuous beam. The method being very rude, we could have even taken M= wl2/10 as the probable maximum moment, provided the length of the spans do not vary much. However, the Shear Force will keep its balance, since the total upward reaction is equal to the total downward reaction .
     Textbooks indicate that the results of the simplified method vary drastically from those obatained by the more rational methods such as beam on elastic foundations. We can also try the same by giving spring supports to represent the flexibility of the soil-foundation system in STAAD or other software.

E S Jayakumar



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samirbendre1
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PostPosted: Mon Jan 22, 2018 11:50 am    Post subject: Reply with quote

uniform upward pressure is a approximation. if the location of resultant of downward forces is worked out and upward pressures are adjusted as pmax and pmin , then this problem will not happen
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es_jayakumar
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PostPosted: Mon Jan 22, 2018 3:06 pm    Post subject: Reply with quote

In the given example, the length of the strip footing is so chosen that the centres of gravity of the load group and geometry of the footing coincide. This will produce uniform soil pressure under the footing. Even then, the mismatch of the BMs calculated from the either side occurs. If the loading is symmetrical, then this error tends to reduce.
It will be a fair idea to use the average of these two moments. In the example from the text book, please note that the BM under the load 1350 kN (F-G) is 157 kNm, and not 15.7 kNm, as shown in the BMD. Analysis using Software will render more realistic results.

E S Jayakumar
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Abishek_Siingh
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PostPosted: Tue Jan 23, 2018 5:50 am    Post subject: Reply with quote

Dear Jayakumar ji,

As far as I know, bending moment diagram is unique for a given loading no matter which direction we calculate from.

All this confusion came up because I think that the calculation of bending moment in the textbook page you uploaded is wrong. Could you kindly see whether what I did in the attachment is fine?

I have put in the exact cantilever dimension that is 838 and 1162 in place of 840 and 1160 because the squared function makes all the difference.

Thanks and Regards,

Abhishek



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knsheth123
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PostPosted: Tue Jan 23, 2018 2:12 pm    Post subject: Reply with quote

Dear Sefian,

The simplified approximation of the continuous footing with more than two columns satisfy Equilibrium equation for V-Loads only, equilibrium for sum of moments-M = 0 is not satisfied.

The analysis when carried out as a continuous beam subjected to UDL will give support reactions at column points required to satisfy equilibrium. The results will indicate the reactions and column loads are not the same. The difference can be calculated as moment shear force (difference of moment on either side support divided by span).

As the column loads are from structure itself and can not be altered, the pressure distribution could not remain uniform and has to be adjusted as uniformly varying to obtain support reaction as column loads. The method of obtaining linearly varying pressure distribution is called soil line method.
(Ref. : Ana. & dsn of Fdn & Retaining str - Samsher Prakash, Gopal Ranjan and Swami Saran.)

Presently we use modulus of subgrade reaction method. I am attaching a brief presentation for the same. It can easily be handled using Staad or Etabs by dividing footing in small length and applying nodal Springs.

This attachment will also show that uniform pressure approach is crude and to be updated.

With Regards

Prof. K. N. Sheth
D. D. University, Nadiad.



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Soil Structure Interaction for Foundations (Beams & Plates) supported on on Winkler's Spring Bed.

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es_jayakumar
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PostPosted: Tue Jan 23, 2018 3:44 pm    Post subject: Reply with quote

As suggested by Er.Sheth, the strip footing is anaysed in STAAD Pro, by supprting it at several nodes with spring supports assigned to each node, to represent the flexibility of soil. The results are compared with those of uniform pressure approach. Please see the attachment for the details (in MS Word) & the STAAD file.

E S Jayakumar



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knsheth123
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PostPosted: Wed Jan 24, 2018 2:18 pm    Post subject: Reply with quote

Dear Er. Jayakumar,

I Very much appreciate your efforts to solve the problem in Staad for comparison of results with the earlier solution.

Empirical guidelines for Modulus of subgrade reaction can be obtained from IS 2950/Fdn. Engg. by J. E. Bowles/ Substructure Analysis by Swami saran etc. The values are given for plate size 300x300. It has to be corrected for width, shape and placement depth of footing.

A simplified approach is to consider SBC of soil as soil pressure "p" divided by settlement corresponding to this pressure obtained from soil report.
In the solved problem, for loading of 4350 kN (1000+2000+1350) the fdn provided is 13.8 x 2.00m. It gives bearing pressure of 157.60 kN/m2. Considering 50mm allowable settlement for sand, K = 157.60 / 0.050 = 3152 kN/m2/m.

The value of spring constant is in empirical state yet, hence the solution is obtained for 3 to four values from 0.5 times above mentioned value upto max. 2 times the same.

Then envelope values at all critical section shall be used for design. This approach works well for the routine practice.

With Regards,

K. N. Sheth
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es_jayakumar
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PostPosted: Thu Jan 25, 2018 2:52 am    Post subject: Reply with quote

Dear Prof.Sheth,
Thanks for your vaulable guidance. I adopted the Modulus of Subgarde Reaction value tentatively from Table 1 of IS 2950, for medium sand. Is the method proposed by you being used in design office generally ? Similar to this, can we work out the spring value of a friction pile by dividing its safe load capacity with permissible settelment (12mm) ?

Regards,
E S Jayakumar
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