Happy Thursday! This is Back of the Envelope, where we crunch numbers for fun.

In today’s email, I’ll talk about something I learned recently related to “embedded posts and poles.”

• Quick overview: "nonconstrained" & "constrained"

• What exactly is “rigid floor or pavement”?

• Another option for “chain-link fence”

(Estimated reading time = 3 minutes and 10 seconds)

Overview

You’ve probably seen these two goodies:

(Source: UpCodes)

They are equations for “embedded posts and poles” from IBC section 1807.3.

We use them to design pole footings for miscellaneous things that cantilever off the ground (e.g., fence posts and flag poles etc.)

The first equation is for “nonconstrained.” Basically, the top of the footing is surrounded by dirt, so it’s free to move horizontally. (By the way, “nonconstrained” is not an actual word in the dictionary, so I am getting the red squiggly line in Word. Why is it not called “unconstrained”… sorry I digress.)

The second equation is for, you guessed it, “constrained.” The code defines it: “lateral constraint is provided at the ground surface, such as by a rigid floor or pavement.”

Using the constrained equation usually allows the footing embedment depth to be shorter than using the nonconstrained equation (potentially saving you or the owner money.)

“Rigid floor or pavement”

The question is then, what exactly is “rigid floor or pavement”?

Some jurisdictions consider it constrained if the top of footing (or post) is surrounded by a concrete slab.

For example, if the post is in the middle of a slab-on-grade, you are good to go.

On the other hand, certain jurisdictions require the top of the footing to be doweled into the slab. Or you can have bars welded to the steel post with enough length to develop the bars into the slab.

Either way, the code is perhaps being intentionally vague so it’s up to interpretation.

Which got me thinking.

These equations have been around for a long, long time. Where did they come from?

Apparently... from tons of research throughout the years (just skim through some of these titles):

(Source: American Society of Agricultural and Biological Engineers)

After some digging, I found this document called ANSI/ASAE EP486.1 Shallow Post Foundation Design, published by the American Society of Agricultural and Biological Engineers (ASABE).

Say what? Agricultural?

Yeah I imagine they probably build tons of posts out there.

My guess is that ASABE studied the researches and compiled their findings into a detailed document. Then the code writers studied the ASABE document and simplified it down to two easy-to-follow equations so we can all enjoy them (if you happen to know the real history – let me know!)

Anyhow. Back to what is considered “constrained.”

Interestingly… check this out.

ANSI/ASAE EP486.1 actually gives you a formula with a nice picture and everything:

(Source: ANSI/ASAE EP486.1)

(In case you are wondering, “table 1” referenced here is the same as IBC Table 1806.2 Presumptive Load-Bearing Values.)

How cool is that?

Essentially, the report considers the constraint resistance to be based on friction + lateral pressure. Sounds reasonable.

If we do a fun run:

• Say you have 5ft x 5ft x 4” concrete slab (Wd = 1250 lbf)

• S = 150 lbf/ft^3

• k_cs = 0.25

The resulting "lateral resistance of constraint" = 400 lbf.

Not bad. And most likely adequate for things you are using the pole foundation for.

Your miles may vary depending on the jurisdiction, but it’s food for thought.

(By the way, for you die-hard enginerds, there is another related document by ASABE that you can dig into: ASABE Meeting Presentation.)

Chain-link fence

Now, suppose you are just using the footings for a chain-link fence. In that case, there is another goodie you can potentially utilize: ASTM 567-14a(2019) Standard Practice for Installation of Chain-Link Fence.

The standard uses a prescriptive method for the footing, which states (just skim through it):

Let me unwrap that for you.

First, the posts have to be spaced at 10’o.c. or less.

Then,

• If posts are 4” or smaller, footing diameter = 4 x post diameter

• If posts are larger than 4", footing diameter = 3 x post diameter

Now let’s say H = fence height (ft):

• If H is 4’ or less, then footing depth = 24”

• If H is between 4' and 20', then footing depth = 24" + 3" x (H - 4')

In other words, if you have the post size, spacing, and fence height – boom! You get footing size.

You can also go the detailed route and run ASCE 7 wind load + pole footing per 1807.3 -- but if you are in a hurry and need to get something out quickly to the client, this could be helpful.

(Again, mileage may vary depending on the jurisdiction.)

Alright, and that is all for this week. Hopefully it’s helpful – thanks for reading!

Andy Lin
Back of the Envelope/Structural Engineer HQ