Eccentric Footing e>L/6, Formula for Moment calculation? 5

[ak.t]

Hi All,

The footing size is (1.4 x 1.75)m (Fig. attached) & the SBC is 110 kN/m2

I get e> L/6 condition, Hence, I applied the 2P/BL' to calculate pressure max;
where L' is the bearing length = 3* (0.5L-e)

Thus, Qu = 2P/BL' = 102.6 kNm2

L' = 1.55 m ; P = 111.6 kN(Factored, Calculated) ;
M = 39.856 kNm (Factored, Calculated)
L = 1.75 m ; e = 0.357 m


How do I calculate moment for reinforcement from this triangular pressure profile ?
In report i found that Moment is 4.62 kNm. But I could not get the same.
Thank you.

 

[RPMG]

Take the sum of all forces (volume of a wedge) and multiply it by the distance to the centroid (b/3). Or it can be designed for the maximum bearing pressure, conservatively.

 

[ChipB]

Well, it's not a confidential client, so I assume I can share my calculations.
See attached. I hope it helps.

 

[JLNJ]

Footings with the load way out on the edge present serious design issues and difficulties.

Sketch the soil pressure profile and upload it for us. I think it will be very telling.

 

[r13]

Agree with JLNJ.

How you make moment connection between two precast members?

 

[civeng80]

Also Agree with JLNJ.

Have seen a lot of damage to buildings because of this especially when soil on the edge gets wet. This occurs even when bearing pressure is well below the safe value.

 

[ak.t]

Dear RPMG,ChipB,JLNJ, retired13 &civeng80,

Thank you for your valuable kind response and time. I attached the calculations that made for the same. Kindly let me know how to solve, if incorrect.

Thank you.

Dear ChipB,

Thank you so much for the attached file and your time.
In your calculations, I'd see that has trapezoidal pressure distribution. I will keep this for my reference for that particular case. Here i get triangular distribution and also its e> L/6; footing bearing area is less.

 

[r13]

AkshikaS,

Put pressure, due to soil weight, surcharge, and weight of the base slab, back to your stress diagram, then take moment about the wall.

You still need to assure the full rigidity (fixed joint) can be achieved at the wall-base slab connection, as you are designing a cantilever retaining wall. Also, it is paramount to check safety against rotation instability (overturning).

No file is attached.

 

[ak.t]

Dear retired13, I think, I dint mention it clearly. It is not the retaining wall. This is the r.c precast boundary wall panel sandwiched into I-shaped precast columns that are supported by eccentric footing.

Yes. Could not see the attached file. Sorry for that. I will attach the drawings and calculations that are made for the same.

Thank you so much for your kind response.

 

[r13]

AkshikaS,

Don't be discouraged by my comment towards you at the other thread. I assume your wall won't see much of lateral load, except wind and earthquake cases. If necessary, you can,

1) thicken the slab,
2) slopping the bottom of slab to add weight, and improve lateral load resistance, also save some concrete, and
3) add turn down at the free end of slab.

All 3 suggestions might bot be simple for precast member though.

Do you have free room in front of the wall (toe)? Extend the slab beyond the toe may help a lot.

 

[r13]

AkshikaS,

I've retracted my comment on the other thread. Please go check the correct method offered by BAretired. Sorry, if I have misled you.

 

[BAretired]

The footing size is (1.4 x 1.75)m (Fig. attached) & the SBC is 110 kN/m2

I get e> L/6 condition, Hence, I applied the 2P/BL' to calculate pressure max;
where L' is the bearing length = 3* (0.5L-e)

Thus, Qu = 2P/BL' = 102.6 kNm2

L' = 1.55 m ; P = 111.6 kN(Factored, Calculated) ;
M = 39.856 kNm (Factored, Calculated)
L = 1.75 m ; e = 0.357 m

What is SBC, Soil Bearing Capacity? Is that factored or unfactored?
If P and M are factored, bearing capacity should also be factored, but it is more usual to work with unfactored values for determining soil pressures.

If all values are factored and if e = 0.357 m, then Qu of 102.6 kPa is correct...BUT

...the column has an eccentricity of 1750/2 = 875 mm, so how do you get e = 357 mm? Are you considering the weight of footing and soil overburden? If so, that is not the usual practice.

How did you arrive at the plan dimensions of the footing? They do not make sense unless there is another column or wall adding load to the footing or perhaps a moment applied to the footing.

How do I calculate moment for reinforcement from this triangular pressure profile?
In report i found that Moment is 4.62 kNm. But I could not get the same.

Report? What report?

The moment at any point in the footing may be calculated in the usual way using statics. The load causing bending in the footing is equal to the ordinate of the triangular pressure diagram less the downward load such as column reaction and weight of footing.

The distribution of downward load has not been made clear in the original post.

BA

 

[JLNJ]

If you place a book on the floor and stand on one edge, the pressure under the book where your foot is is very high. Choosing a book larger in plan doesn't help the pressure under your foot. The force resultant is still right under your foot. The footing (in this case the book) doesn't really distribute the load beyond your footprint.

The only way to move the resultant away from the edge is to have the footing's self weight plus overburden weight be large. If your column load is 150,000# and your footing weighs 5,000#, then the resultant is still close to the edge and the pressures will be too high.

You might need a 50,000# footing for a 150,000# column load to help move the resultant.

If the column load is large, there may be no way to make it work. Just because the footing can be sketched doesn't necessarily mean there is an engineered solution to make the sketch work.

 

[civeng80]

A strap or cantilever beam may also be a solution to this high pressure.

 

[ak.t]

Dear All,

Thank you for your response.

retired13, the time u spent on explaining itself much appreciable. so It is okay
Yes, I have gone through other thread and responded.

JLNJ, Thank you for explaining the concept in the simpler way. This way is much easier to understand.

Civeng80 & BAretired,

Yes, It is L shaped boundary wall. This project was an executed one. I just got to see only the results in the report, provided with drawings.
Since , I am a learner , trying to understand the concept and preparing elaborate (trying my level best ) calculations in excel.

Kindly see attached the excel (calculation for your kind review. I have got confusion in calculating Flexural moment.

 

[r13]

AkshikaS,

1) Per the data you provided previously, using the method BA & JLNJ provided, I found your toe pressure is somewhere around 144 kN/m²/m_{of wall}. You may want to go back and check it.

2) Below is a suggestive diagram for flexural design (focusing on the slab). As noted before, once you obtained soil pressure, you need to place all loads, that causing the P and M in the analysis, back on the member to perform the flexural calculation, assuming members are cantilevers. The usual governing cases: A) completed structure, and B) construction condition.

load combinations:

A) w_conc + w_soil + Surcharge or LL + Earth Pressure + Wind or Earthquake (EQ)
B) w_conc + Earth Pressure + Wind or Earthquake

Note for each combination, depending on the loads involved, the diagram will look differently.

Errata & Omissions:
1. Fixity shall be assumed at the wall-slab joint, not as shown on face of the toe.
2. Surcharge and LL are not shown, but may need to be considered.
3. Lateral soil pressure on wall is not shown.

 

[r13]

Additional note:

For each load combination case, there could be several subset analyses, that with some loads removed or added to make the worst case for flexural design - shear, positive and negative moments, also soil pressure, sliding and overturning.

 

[ak.t]

Dear retired13,
I have done those cals. Kindly see the sketch below.

The report submitted to us shows 4.62 kN-m. (Loads, moments, combinations, conditions shown are same).
But I get 30.165 kNm (Kindly, refer the above sketch).
I am not sure which is correct. I don’t know how did they arrive that value?

 

[r13]

So far, the reported moment is correct. Remember that you need to put all loads back?!

w_u2 = 1.2*(0.25*25)*1.4 = 10.5 kN/m (uniform downward pressure due to self weight of concrete slab)
w_u3 = 1.2*(0.75*18)*1.4 = 22.68 kN/m (uniform downward pressure due to soil weight above slab)

Loaded span length x = 1.75-0.3 = 1.45 m (distance from heel to face of column)

Mu₂₊₃ = (w_u2+w_u3)*x²/2 = (10.5+22.68)*1.45²/2 = 34.88 kN-m (counter-clockwise)
Mu_b = 30.165 kN-m (clockwise)

Mu_net = 34.88-30.165 = 4.72 kN-m (counter-clockwise, slab top in tension)

The minor difference (4.62 vs 4.72) is due to difference in calculation of the soil pressure.

 

[r13]

Was shear in the concrete slab checked? You shall use the same loadings to check shear at a distance d from the column face.