2001 California Building Code Title 24, Part 2, Volume 2, Paragraph 1806.8.2.1 etal.

[KRB]

Hello,
I’m new to this forum. Please allow me briefly introduce myself. I’m a retired mechanical engineer with a strong DIY skill set for home projects. 20 years ago, after a long search, I landed on the 2001 California Building Code Title 24, Part 2, Volume 2, Paragraph 1806.8.2.1 etal. I was looking for guidance on a pole I was setting. I was thrilled to finally have an equation to derive the footing depth. Over the years, I’ve worked with the equations therein but recently realized I don’t understand how to apply a particular statement in the associated Table 18-I-A (page: 2-50). The Lateral Bearing of Depth Below Grade column in this table cites Footnote 3. The first sentence in that footnote states:
“May be increased the amount of the designated value for each additional foot (305 mm) of depth to a maximum of 15 times the designated value.” In addition to what? I’m unclear about the authors intentions of how to fold that statement into the depth calculations in equations 6-1 (S1) and 6-2 (S2).

I realize this is old, obscure, there are newer versions of the CBC, and other perhaps more complete treatments of this subject. Of note, I’ve found this exact same statement in the 2022 CBC version, Paragraph 1806.3.3. So I would like to understand how to include this statement in my calculations. I would appreciate any and all help.

Thank you,
KRB

 

[Yankee Chronicler]

The starting point is the full section. From the IBC 2021:

1806.3.3 Increase for depth. The lateral bearing pressures
specified in Table 1806.2 shall be permitted to be increased
by the tabular value for each additional foot (305 mm) of
depth to a value that is not greater than 15 times the tabular
value.

The California version is the same:

1806.3.3 Increase for Depth. The lateral bearing pressures
specified in Table 1806.2 shall be permitted to be increased
by the tabular value for each additional foot (305 mm) of
depth to a value that is not greater than 15 times the tabular
value.

Which suggests that we can look at the ICC Commentary for assistance:

The lateral sliding resistance is calculated as the
sum of the lateral bearing and lateral sliding values
from Table 1806.2. The lateral bearing values are
determined as the product of the tabular value and
the depth below natural grade. This section essentially
limits the foundation depth for which the lateral
bearing values can be increased to 15 feet (4572
mm).

The reference is to Table 1806.2. In that table, the third column (lateral bearing pressure) is expressed in pounds per square foot [of lateral resistance] per foot of depth below natural grade. So, basically, you take the lateral bearing pressure for the soil type and multiply it by the depth of the footing below grade to obtain the total lateral bearing capacity of the footing.

Suppose your soil type is sandy gravel and the cross sectional area of one face of the foundation is 10 feet wide. The tabular lateral bearing capacity is 200 psf per foot of depth. So ==> a one-foot deep foundation provides 2,000 pounds of lateral resistance (200 x 10), A two-foot deep foundation provides 4,000 pounds of lateral resistance (200 x 10 x 2). At four feet of depth the lateral bearing capacity increases to 8,000 pounds (200 x 10 x 4).

A quick read of the section and the Commentary suggests that you can multiply the tabular capacity by the depth below grade. I don't think that's what it's saying, but I may be wrong. If you go that route, increasing the foundation depth from one foot to four feet results in a lateral bearing capacity of 32,000 pounds -- essentially increasing the capacity exponentially, since the depth increases the area of the foundation, and then you would also be multiplying the tabular area by the same depth factor. That IS what the commentary says, but I have difficulty accepting that they want us to apply the depth factor twice -- once to increase the tabular load factor, and then again to get the contributing area of the foundation.

I'm not sure. I used to be licensed as an architect in California but I let it lapse years ago because I wasn't using it.

 

[KRB]

Yankee Chronicler,
Thank you for your response!

Digging deeper into this issue than ever before, I learned a variety of things. My confusion with the statement in Footnote 3 in Table 18-I-A in the 2001 CBC stems from it being an odd way of imposing a limitation on the applicability of an analysis. This limitation was presented differently in the 2007 CBC. It went from a depth of 15’ to a depth of 12’ and was stated explicitly in the variable declaration associated with the design equations. These design equations were completely removed beginning with the 2016 CBC. My local building department stated detailed design analysis responsibility was removed from the CBC and now resides with soils/geo engineering fields.

Thank you again for your help.
KRB

 

[Yankee Chronicler]

These design equations were completely removed beginning with the 2016 CBC. My local building department stated detailed design analysis responsibility was removed from the CBC and now resides with soils/geo engineering fields.

That's consistent with the removal of a lot of structural requirements from the code in deference to ASCE-7 for structural design.

 

[KRB]

I believe my desire to fully understand the 2001 CBC, Table 18-I-A, Footnote 3 has turned into obsession. Continued study, now casts doubt on my previous interpretation. It appears my research efforts would be better spent on tracking down the original development from basics. Trying to interpret the summaries presented in the various CBC editions and questionable 3rd party interpretations of them has led to impasse.

 

[wwhitney]

Seems to me 1806.3.3 just means the allowable bearing pressure follows a triangular distribution, increasing with depth. Just like the applied lateral load from retained soil or water increases with depth.

. If you go that route, increasing the foundation depth from one foot to four feet results in a lateral bearing capacity of 32,000 pounds -- essentially increasing the capacity exponentially, since the depth increases the area of the foundation, and then you would also be multiplying the tabular area by the same depth factor.

It's not exponential, it's quadratic--just the area of the triangular distribution.

Cheers, Wayne

 

[KRB]

It turns out, the IBC has the same calculations as the CBC and therefore just as nebulous. Can anyone recommend a post footing calculation that’s reasonably easy to compute with straight forward definitions? I would like to read the development of the final equations.

 

[Paul Sweet]

It turns out, the IBC has the same calculations as the CBC and therefore just as nebulous. Can anyone recommend a post footing calculation that’s reasonably easy to compute with straight forward definitions? I would like to read the development of the final equations.

I have a spreadsheet I developed for a parking lot lighting project a few years ago. PM me and I can e-mail you a copy.

 

[KRB]

Paul,
Thank you for your offer. Unfortunately I don’t know how to private message you. I selected your name on your response above and a “start conversation” screen came up and I responded to it. Is that it?

All I’m really looking for is a reference to the mathematical development from basics of the industry standard for post footings. Something with hole size, soil properties, loads/moments, etc. as inputs and it calculates depth. I can write my own spreadsheet and would enjoy doing so.

KRB

 

[KRB]

I have personally found the nonconstrained & constrained equations as far back as 1970 UBC. I spoke with the structural engineer for the IBC who is approaching retirement. He said he recently investigated these equations for their origin and was unable to determine it. He even spoke to his father, a retired structural engineer, about them. These equation were around during his tenure and he didn’t know where they came from. Therefore, I surmise these equations are perhaps 1940’s vintage or before. This may seem like a ridiculous question at this point, but does anyone know the origin of these equations? They’re continually presented but their history is MIA.
KRB