Overturning failure of spread footing below grade and connected to frames 4

[LuisUgarte]

Hello!

I am currently working on a PEER review for a steel moment frame building. In the past, I used to check isolated footings against overturning moment, no matter if they are below grade. At this time, there is a dicussion with the EOR, since he thinks that overturning only affects footings that are free to rotate and in our casem every footing is connected to the steel columns of the structure. I´ve been thinking on that and these are my thougths:

- Isolated footings for frames are not subjected to local overturning moment, because they are connected with the rest of the structure and soil below grade makes this difficult, even if grade beams are not present. So, if global building overturning check is satisfied there is no need to check every footing.

-Overturning check is only required for footings of bridge piers, tower tanks or retaining walls where global stability depends on a single footing.

Do you agree with that? What is your opinion? I will appreciate it.

Thank you.

Regards

 

[KootK]

HOWEVER, I'm willing to give you the benefit of the doubt - how is it that you're ending up with net uplift?

That's gracious.

1) For wind, I should restate my prior comment as: when net tension is present in the column, often the remaining net compression at the soil interface is lacking for shear resistance.

2) In high seismic applications, sometimes I'm dealing with foundation systems where rocking is the cap on the seismic demand.

For moment frames, I am a pretty big fan of grade beams connecting all of the participating columns in a line.

I should have expanded upon that. I do it because I have a very strong preference for moving the shear through the foundation of the compression column.

 

[LuisUgarte]

2) Columns that land directly on footings with no intervening piers.

That is very interesting for me, could you please elaborate how piers participate?

Thank you.

Regards

 

[KootK]

That is very interesting for me, could you please elaborate how piers participate?

Elaborate?? I already drew you a picture of it. If you need more than that, you'll have to ask me a more specific question.

 

[LuisUgarte]

Elaborate?? I already drew you a picture of it. If you need more than that, you'll have to ask me a more specific question.

I am sorry about that, at first I did not understand. Now is clear, thanks for your help!

Regards

 

[le99]

For individual footing in a building system, the properly estimated bearing pressure has already incorporated the consideration of uplift and moment from the column, for which the safety factor is at least 1.0. Moreover, the properly designed flooring system (with ties/grade beams) will not allow the individual footing to undergo large displacement/rotation that could lead to overturning similar to the free standing earth retaining structure, or a single pier foundation. Thus, I don't recall I've checked OT stability for individual building foundations. But, if you are not convinced, do check it (the OT stability).

 

[WinelandV]

le99,

If you are not using a hairpin/building tie to remove the shear force from the pier, and if you have high ground bearing pressure values, you can conceivably size a footing that will meet GBP requirements, but fail the OT check.(Please note that I only use ASD for my foundation design, as such I use a minimum FS of 1.5 against OT.)

Normally I don't get such high GBP values, so your statement tends to be true 99% of the time.

 

[phamENG]

properly estimated bearing pressure has already incorporated the consideration of uplift and moment from the column

This may just be a semantic misunderstanding, but isn't this what we're talking about? When designing a column, I don't particularly care what the bearing pressure is. I care about the bearing pressure when I design the column's individual footing. And when designing the footing, I care very much about overturning as that's what's going to create the variable bearing pressure under the footing. A lot of "properly designed floor systems" don't have ties or grade beams, and many are completely independent of the footings. In my region, virtually every first floor is a floating slab, even if the building itself is on piles. That only changes for unique circumstances: really awful soils like sites with deep uncontrolled fill, heavy equipment on the floor, etc. So the only thing to restrain an individual footing is the fixity of the footing achieved by it's width and bearing - maybe some overburden but the footings are usually so shallow relying on it is questionable.

 

[human909]

There is a possibility that you do have good understanding here and we are just all confused about what you are trying to achieve. However many of you comments have left people confused including myself.

I can't see a footing below grade be overturned, before that, soil mass mut be movilized and create a condition free to rotate, which involves that soil pressure reach it's capacity. But if soil pressure check is ok and below it's capacity, how could overturning happen?

I've seen footings below grade undergo rotation when they are not supposed to.

In this case a typical portal frame shed had an end wall mullion without any lateral other than the roof membrane. Storm winds (though nothing close to ultimate winds) blew the wall in buckling the roof members, a large roller door came off its tracks and got blow in relieving the pressure and preventing further damage. There was very observable cracking all around slab that overlaid the foundation as the footing below it had rotated.

For individual footing in a building system, the properly estimated bearing pressure has already incorporated the consideration of uplift and moment from the column

True true... But one of the reason why this thread seems to have gone on for so long is that is hasn't been clear that your ARE designing "a properly designed footing for moment". The diagram you provided below emphasises this as this doesn't LOOK like a column that would effectively be rigid enough to consider it a moment connection between the column and the footing. It looks more like an overturning check or a eccentricity check which does check for 'moment' resistance, but doesn't check appropriate rigidity to be able to assume that the column-footing connection is rigid!

I am a pretty big fan of grade beams connecting all of the participating columns in a line.

Me too.

 

[Celt83]

Simple animation of Foundation pressure increase (red) and rotation (blue) as eccentricity increases:

Generating Code:

import math
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.animation as animation

def animationfunc(frame, P_k, q_1in_ksf, b_f, scale=10):
    
    # Set eccentricity based on the frame number
    # 250 total frames go from 0 to 0.5 ft beyond fnd
    e_ft = (frame/250)*(b_ft/2 + 0.5)
    
    # plot points for the load
    load_x = [b_ft/2+e_ft,b_ft/2+e_ft]
    load_y = [0,P_k]
    
    if e_ft == 0:
        # e=0, bearing pressure = P/A
        ql = P_k/(b_ft*b_ft)
        qr = ql
        
        dl = -1*ql/q_1in_ksf
        dr = -1*qr/q_1in_ksf
        
        brg_x = [0,0,b_ft,b_ft]
        brg_y = [0,-ql,-qr,0]
        
        delta_x = [0,b_ft]
        delta_y = [dl,dr]
        
    elif e_ft <= b_ft/6:
        # e in kern, bearing pressure = P/A +/- M/S
        ql = (P_k*(1-((6*e_ft)/b_ft)))/(b_ft*b_ft)
        qr = (P_k*(1+((6*e_ft)/b_ft)))/(b_ft*b_ft)
    
        dl = -1*ql/q_1in_ksf
        dr = -1*qr/q_1in_ksf
        
        brg_x = [0,0,b_ft,b_ft]
        brg_y = [0,-ql,-qr,0]
        
        delta_x = [0,b_ft]
        delta_y = [dl,dr]
    
    elif e_ft > b_ft/6 and e_ft < b_ft/2:
        # e outside of kern
        # resultant of bearing pressure must align with load point
        # Triangular pressure assumed, no tension allowed
        
        e_prime = (b_ft/2) - e_ft
        
        qr = (2*P_k)/(3*b_ft*e_prime)
        ql = 0
        
        zero_pt = b_ft - (P_k/(0.5*qr*b_ft))
        
        dr = -1*qr/q_1in_ksf
        
        # Technical incorrect method for the settlement/rotation
        # but it illustrates the process well enough
        theta = math.atan2(dr, b_ft - zero_pt)
        
        dl = zero_pt*math.tan(-theta)
        
        brg_x = [0,zero_pt,b_ft,b_ft]
        brg_y = [0,0,-qr,0]
        
        delta_x = [0,b_ft]
        delta_y = [dl,dr]
    
    else:
        
        # e is off the foundation
        brg_x = [b_ft/2 + e_ft,b_ft/2 + e_ft]
        brg_y = [0,-P_k]
        
        delta_x = [b_ft/2,b_ft/2]
        delta_y = [b_ft/2,-b_ft/2]
    

    delta_y = [scale*i for i in delta_y]
    
    l1.set_data(load_x, load_y)
    l2.set_data(brg_x, brg_y)
    l3.set_data(delta_x, delta_y)

# Load
P_k = 100

# pressure associated with 1 inch settlement
q_1in_ksf = 3

# foundation square dimension
b_ft = 6

# foundation line
ftg_x = [0,b_ft]
ftg_y = [0,0]
    
# plot setup
fig, ax = plt.subplots()

ax.set_xlim(-1,b_ft+1)
ax.set_ylim(-P_k,P_k)
ax.plot(ftg_x, ftg_y)

l1, = ax.plot([],[],'g')
l2, = ax.plot([],[],'r')
l3, = ax.plot([],[],'b')

ani = animation.FuncAnimation(fig, animationfunc, frames = np.arange(0,250), fargs=(P_k, q_1in_ksf, b_ft), interval=100)

writergif = animation.PillowWriter(fps=30)

ani.save("eng-tips_p_e_stability.gif",writer= writergif)

plt.show()

I'm making a thing:

http://www.thestructuraltoolbox.com

(It's no Kootware and it will probably break but it's alive!)

 

[LuisUgarte]

I am very sorry if my comments promote confusion. I was trying to understand if footing below grade are really free to rotate and if OT check is required. But, as seen, there are other things to take into account. Sorry if I deviate from the topic, but some replies where very interesting.







Regards

 

[le99]

Bearing pressure fp = V/A +- My/I. For fp(max) <= fa, a safety factor of 1.0 against rotation is achieved without utilizing any external devices, which inevitably will be present in the building system. My understanding is that we are talking about the footing, not the column.

 

[WinelandV]

I suppose if you maintain full contact of the footing against the soil, then yes, you will be safe against overturning.

I'm going to assume I'm not the only designer that allows the heel to come off the soil (which make the V/A +/- M/S equation invalid for your max pressure).

 

[KootK]

Thus, I don't recall I've checked OT stability for individual building foundations. But, if you are not convinced, do check it (the OT stability).

As phamEng suggested, I suspect that this may indeed be just a semantic thing. When I look at your sketch below, and read your description of it, that sounds to me like designing the footing for overturning. Your scheme is, verbatim, how we used to design shear walls for overturning in buildings with basements back before computers were available.

 

[KootK]

I'm going to assume I'm not the only designer that allows the heel to come off the soil (which make the V/A +/- M/S equation invalid for your max pressure).

#MeToo. I can't produce regionally competitive foundation designs if I attempt to keep things in the kern.

 

[le99]

In the modern code in the US, while the 1.5 OT safety factor for retaining walls is mandatory, it is mute on the shallow foundations, which, IMO, is achieved through the use of the proper load combinations in the design (LRFD or the ASD - Basic).

 

[MX Structure]

I can't produce regionally competitive foundation designs if I attempt to keep things in the kern.

In your experience, which percentage of the total area should be in compression?

I have seen designs using only 20-30% as effective bearing area. As a criteria, I think the value should be around 75-50%.

 

[KootK]

In your experience, which percentage of the total area should be in compression?

I adhere to no percentage area limit. If it's a situation where I have a real concern for the serviceability consequences of a high degree of rotation, I'll try to ballpark that rotation based on the strain profile. I even use a rectangular, plastic soil distribution for shear wall footings etc. Everything but the kitchen sink as it were. I've worked for both of the two big-dog architectural SE firms in Canada an they both have this same strategy baked into their design standards. So my options are limited.

 

[Lomarandil]

A few comments late to the party

1. Celt, awesome animation.
2. In my experience, whether active or passive soil pressures are selected, they provide very marginal benefit to the overturning capacity of most shallow foundations. 5-10% boost perhaps.
3. Yes, where we explicitly check overturning resistance of isolated structures, I more often see it considered in connected building foundations by use of the 0.6DL factor load combinations. (That's a whole separate discussion).
4. Absolutely, I'm glad that students are taught to stay inside the kern (given the limited teaching time available), but in the real world I'm outside all the time. Call me cowboy, but some of my designs have 10-20% contact under a wind or seismic event.

----
just call me Lo.

 

[Once20036]

I suppose if you maintain full contact of the footing against the soil, then yes, you will be safe against overturning.
I'm going to assume I'm not the only designer that allows the heel to come off the soil (which make the V/A +/- M/S equation invalid for your max pressure).

For me, it varies with the load combination.
When you`re looking at ASD bearing pressures, there's a 0.6*D+0.6*W load combination. I aim for about 50% soil contact in this scenario.
I think that the 0.6*D is a built in safety factor as my concrete will never weigh 60% of my assumed value.
With 50% bearing under this load combination, I tend to be pretty close to full contact for 1.0*D+0.6*W

In the modern code in the US, while the 1.5 OT safety factor for retaining walls is mandatory, it is mute on the shallow foundations, which, IMO, is achieved through the use of the proper load combinations in the design (LRFD or the ASD - Basic).

Agreed - that 1.5OT FS is based on load combinations where everything get's hit with a 1.0 load factor.
When using the ASD combination, the 0.6DL basically creates the same result.