Good morning! This is Back of the Envelope – the place to learn structural engineering in tiny bites .

In today’s article, I will talk about how to do a quick-n-dirty preliminary check to make sure your composite steel deck meets the fire rating requirement.

This is something that confuses me almost all the time… but there are some rule of thumb that could be applied for back-of-the-envelope checks.

Let’s dive in.

(Estimated read time = 1 minute and 30 seconds — I told you, tiny bites)

By the way, this is a rehash of an article I wrote in my weekly newsletter, “Back of the Envelope” — where I teach you SE-related things in 5 minutes (or less), once a week.

What is the fire rating requirement?

The first step is to obtain the structure’s required fire rating from the client/architect. This is based on the type of building and other goodies per IBC Table 601.

Spray-applied fire resistive material underside of deck?

Once you know the required rating, you should then find out if “spray-applied fire resistive materials” (SFRM) will be applied to the underside of the deck.

(Some people refer to the SFRM using the product name Monokote).

Rule of thumb

Now here comes the rule of thumb:

If SFRM will be applied to the underside of the deck, then the concrete thickness above the deck would generally be 2-1/2” thick.

And it can be either normal weight or lightweight.

You’ll achieve a 1 to 4-hour rating with most UL assemblies (the architect and/or fire protection engineer need to detail that).

(source: Verco Deck Binder)

On the other hand, if SFRM will NOT be applied to the underside of the deck, then the thickness of the concrete varies depending on the required rating.

The legacy Verco catalog had this handy table below (it’s a rough generalization of all the UL assemblies):

(source: legacy Verco catalog)

For example, the thinnest configuration to get a 1-hour rating would be using 2-1/2” lightweight concrete over 1-1/2” deck (watch out for unshored span though – topic for another email).

A very common 2-hour rating configuration that I have seen is 3-1/4” lightweight concrete over 3” deck.

And there you have it. Hope that all makes sense.

Now you should be able to come up with a preliminary concrete thickness based on the required rating.

You could then move on to figure out the other design requirements (e.g., unshored span, vertical capacity, diaphragm capacity…etc.). We'll save those for another email.

Thanks for reading and enjoy the rest of your week!

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In today's post, 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)

Good morning. Andy here from Back of the Envelope — the place to be for all your p-delta soul-crushing info.

Just kidding. No but seriously. Over the weekend, as I was working on a RISA Floor/3d model for a looming deadline, I repeatedly ran into the dreaded “P-delta diverging” error. It drove me crazy.

So today, I am going to cover:

• What is P-delta
• Why it is important
• What is “P-delta divergence”
• Why it happens and how to resolve it

(Estimated reading time = 4 minutes and 30 seconds)

What is P-delta

Quick refresher.

Say you have a column.

“P” is the axial load applied to the column.

“Delta” is the lateral displacement on one end of the column (caused by whatever reason. E.g., earthquake load or miscellaneous small displacement that just happens in a complex 3d model).

P-delta effect is essentially the extra (aka secondary) moment and shear due to this displacement.

Here is a nice picture from RISA explaining it:

Why is P-delta important?

Because if we don’t account for that secondary moment in the design, we could be under-designing the column.

For example, if your DC ratio for axial load is already high, a little extra moment can put your column into the overstress territory, which is obviously not good.

What is P-delta divergence?

As you can see from the picture above, the secondary shear will cause more lateral displacement, which means… more p-delta effect.

In other words:

Lateral displacement -> secondary shear -> more lateral displacement -> and so on

In practical terms, if we were to do this by hand (don’t):

1/ Apply the load and apply a displacement

2/ Determine the secondary shear caused by p-delta

3/ Apply that shear and determine the new displacement and new secondary shear

4/ Rinse and repeat until the new displacement is so small that it won’t make any more difference — aka the solution converges.

RISA does all this for you in the backend.

But it gets tricky (and soul-crushing) when the solution cannot converge. In other words, the “new displacement” in step 3 is not getting any smaller on each iteration – hence the “P-delta divergence” error.

Why does it happen

Because you screwed up, and your model is broken.

Jk, but actually, yes the model is broken-ish. But how?

If you think about it: What could cause the new displacement to get larger at each iteration?

One reason could be that the column is not restrained by other members. So one end of the column is either moving or rotating out whack — aka “instability.”

Another reason could be because the applied load is causing the member to buckle (remember Euler’s formula from school?). So a solution literally cannot be derived because the column is unstable.

How to resolve it

“How do I get rid of this error asap so I can move on with the rest of my life!” I asked myself.

RISA has a few helpful info to help you debug this (link here and here and here).

They created all of these because, apparently, it is a very common issue.
(“I know I’m not the only one,” sings Sam Smith when he found out that other people were also having p-delta divergence issues).

Long story short, there are 3 steps:

1/ Run the load combination without p-delta and see what happens to the deflected shape (difficulty = easy-ish)

This helped me find my first issue.

The top of my columns did not have rotation stiffness since it’s pinned all around.

The result = whacky deflected shape.

(See the long lines at the bottom? Those are some beams deflecting miles into the center of earth.)

Easy fix — go back to RISA Floor and change the top of columns to “fixed”. This will hopefully resolve the entire issue.

If not, move on to step 2.

2/ Turn on p-delta, but run load combo with only a fraction of the load (difficulty = medium)

In other words, to debug: Create a self-weight dead-load-only combo. Change the load factor to something small like 0.1 to see if the divergence error goes away.

If it does, then it means there is a buckling issue somewhere.

You can potentially find this by looking at the deflected shape in the plan view.

For example, here is a top view of a truss buckling out-of-plane:

3/ Look at the coordinate of the error and hypothesize (difficulty = sucks)

Sometimes the lateral displacement is so tiny that the deflected shape from steps 1 or 2 tells you literally nothing.

And because you know nothing at this point, Jon Snow, the only thing you could really do is locate the coordinate (RISA tells you where it is) and just “look around it” to see if you can figure out what’s wrong.

Luckily for me, after fidgeting for hours with this, I was able to see that one of my columns in the area was not restrained in one of the directions.

Adding a beam where my arrow is showing resolved the issue. And the soul has been uncrushed, for now.

And that’s all – thanks for reading! 

Hope this is helpful (at least maybe someday).

If p-delta divergence ever occurs to you… good luck, but never give up, never surrender. You got this.

The post P-delta diverging error was literally crushing my soul appeared first on Structural Engineer HQ.

Steel is actually one of my favorite structural materials. For some reason, the design outlined by AISC just seems much more straightforward compared to other materials (e.g. concrete). Perhaps I just had a really good professor in college… (thanks Professor Uang!)

Anyways, if you are planning to take the PE or the SE but have very limited knowledge or experience with structural steel design, my goal is to be able to teach you 70% of what you need to know (for gravity design) with the least amount of effort.

I intend to cover these topics below in a number of posts (I'll start from the top down and if people find them useful, I'll continue. If not, perhaps I'll move on to talk about something else instead):

• Design strengths
• Load combinations
• Shapes and materials
• Flexural design
• Shear design
• Compression design
• Tension design
• Bolted connections
• Welded connections
• Composite beam design

…so hopefully by the end, you will know a thing or two about steel!

Let's get started with design strengths (this may be pretty basic to most of you out there, but we have to start somewhere).

Required Strength vs. Nominal Strength vs. Allowable Strength vs. Design Strength???

If you are new to “strength” design, all of these different terminologies may sound confusing to you. Let me just clear that up by using a simple diagram.

We'll start from the top. Basically, you have the demand, which is the required strength. This can be either ASD () or LRFD () depending on which load combination you are using (we'll talk about ASD & LRFD load combinations in another post).

In the manual, the subscript for required strength is “a”. Personally I find that slightly confusing so when I do my calculations, I like to write “req” as the subscript instead. Like this: .

Next, you have the nominal capacity (or nominal strength) which is the “unfactored” capacity. Meaning you basically calculate this out using the formulas in the manual for axial (), moment (), or shear () without applying the resistance factor or safety factor (more on this below).

ASD

From the nominal capacity, if you divide it by Ω, you end up with the allowable strength (e.g. . I like to call this ).

Ω is the safety factor which is always greater than or equal to one.

Note that for for seismic design, there is a thing called the overstrength factor which uses the symbol . This has nothing to do with the safety factor Ω that we use here, so make sure you don't get those two confused.

So now you got your demand and capacity, you can check to see if your design is “OK” or “No Good (NG)” (e.g. if , OK, otherwise NG).

LRFD

Similarly, you do the same thing for LRFD.

From the nominal capacity, you would multiply by to obtain the design strength (e.g. ).

 is the resistance factor and it's always less than or equal to one.

From there you check your demand vs capacity (e.g. if , OK, otherwise NG).

The End

From time to time, in the PE or the SE exam, there may be questions that specifically use the word “nominal” and then asks you to calculate some stuff out. By knowing the difference between these 4 different “strength” terminologies, you should have no problem understanding what you have to do.

Hopefully you find this helpful. Next up: load combinations.

Stay tuned.

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