Help on equations necessary for staircase support bolt design (Junior Engineer) 3

[Alessandro Morelli]

Hi! My name is Aless, I am a Colombian Junior Mechatronic Engineer. I have a passion for CAD design and applied for my first job in the matter.
I got hired by a company, however, they want to test my design knowledge.
So I was given this problem of a staircase that the company produces by blocks of 6 stairs, the way they do bigger stairs is by connecting these 6 stair blocks in series by a joint in the middle using bolts (in the first image, the bolts are in the positions of the red lines drawn over the model, there are 8 of them holding the 3 pieces).
I was asked to design 4 possible variants of this joint in the 3D software, and point which bolts are under the biggest stress and give the stress numbers.
I have read the normativity, calculated dead stress and live stress on the staircase and have already calculated which distributed load the stairs should be able to withstand and under what safety factor.

Once I have the bolt forces calculated I know I will be able to calculate stress and design variants in no time, however, the knowledge of how to find the forces in the first place escapes my memory.
They are implying this is a very simple calculation that is done by an experienced engineer in under 2 hours by hand and they won't allow me to use the software's built-in finite element analysis tool
Perhaps I just don't know which equations should be used in the first place.
I have tried free force diagram by separating the distributed load into 2 punctual forces (Fko1 and Fko2) and calculating for the 3 parts but it gives me a system of 16 equations and 16 variables (forces in X and Y for 8 bolts), which I doubt can be done in so little time by hand and no matrix calculator.
I have also looked into Bolt Group Calculations using the elastic method, however, the books I found only go as deep as having only one set of fixed grouped bolts on one side.
I would be forever thankful if there is an experienced engineer in the matter that could simply tell me which equations might be of interest to me in this case.
Or even a book I could look into.
I already know how to use the 3D software for design and simulation, I think that once I understand this calculation I will be able to do a great job at the company, if I manage to keep it...
Thanks a lot for reading and for the invaluable help, and have a nice day!

 

[chris3eb]

I got hired by a company, however, they want to test my design knowledge.

Your company is giving you a test to determine what level of guidance/oversight you will need. It doesn't help you or your company if you try to get others to help you with the test. You should just tell them the steps that you took and let them know where you got stuck.

 

[Alessandro Morelli]

Your company is giving you a test to determine what level of guidance/oversight you will need.

Sorry, I explained it poorly. By the way they talk, pointing expected time frame and so on, it seems to me that on this depends my stay on the company or not, they added me two days for the paperwork but if I cant do this they will most possibly kick me out...

 

[Settingsun]

You're generally better off doing a hierarchy of analyses, starting with a global model that's less detailed, then taking the results of that to look in more detail at specific areas such as connections or stress concentrations.

In this case, start by assuming the middle splice is rigid, so you can treat the stairs as a beam spanning from support to support. Treat the supports as pins/rollers/fixed - your judgment on what to do there. Calculate support reactions, and bending moments and shear forces at points of interest (the connections in this case). Then move to free body diagrams locally at the connections.

Don't change the load. Leave it as a distributed load - it's simple enough when you start with a global analysis.

 

[rb1957]

I think you're going at this the wrong way.

You show one way to join the two pieces of stair together.
Ok, what loads are reacted at your joint ? Not detail individual bolt loads, but loadpaths ?

what's another design approach that's different to bolting the last treads ?

MOST important ... show you can attack the problem from a consistent direction.
First applied loads, good, got them.
Next, reactions ... draw a free body diagram.
Now, you can calculate the loads at the joint.
Assume simple loadpaths ... fasteners carry shear, tension if they have to, and rarely bending.

Are they looking to see how creative you are (coming up with solutions), or whether you are analytical, or good at driving CAD ? (or all three ??)

another day in paradise, or is paradise one day closer ?

 

[XR250]

They are implying this is a very simple calculation that is done by an experienced engineer in under 2 hours by hand and they won't allow me to use the software's built-in finite element analysis tool

They are correct and for good reason. If you cannot solve this problem by hand (or get a reasonable estimate of the forces in the bolts), you have no business using FEA to solve it (or any other structural problem). Sorry to sound harsh.

 

[rb1957]

sorry to echo that comment ... they are giving you days to do it. "playing" with FEA is too damn dangerous. You need a firm foundation as you start your career.

The number of 4th year grads who couldn't solve a simply supported beam is truly distressing ...

another day in paradise, or is paradise one day closer ?

 

[human909]

Despite the bluntly true comments above I've decided for some reason to be generous. This generosity might not last.

The first step in challenging any problem is appropriately simplifying it and modelling it. They will want to see this. It seems you are struggling with this bit. I'd suggest asking yourself how can this be simplified?

Also a quick question is that triangle piece in the middle a 'support' as you mention in one spot or a joining piece that simply joins the two stair stringers. Your comments imply the latter but your diagram implies the former.

 

[XR250]

This may be the basis for a another thread, but it seems there are a lot of posts recently from folks who seem to be able to use software but are pretty weak in fundamentals. I am a mechanical engineer by training so I don't know the typical CE or SE curriculum, but I received solid training in statics and mechanics of materials (this was 1982). Software was not a big thing back then and we had to write our own FEA solver to run on the UNIVAC. I even had some professors who did not let us use calculators. They said if the problem is not working out nicely, then you are doing it wrong.

Is the modern CE education getting diluted by pushing the learning of particular software packages rather then focusing on fundamentals?

 

[phamENG]

That wasn't my experience. When I went back to school in the late '00s/early '10s we didn't touch analysis software. Wasn't until I took a few masters courses that we had to run seismic simulations in SAP.

However...a lot of the really useful design methods weren't taught either. I got a lot of theoretical knowledge, but had to learn to apply it all (whether by hand or with software) on my own after graduation.

 

[rb1957]

"I got a lot of theoretical knowledge, but had to learn to apply it" ...

I thought that was the point ... learn theoretical foundational knowledge in school, then 10+ years learning how to apply what you've learnt ?

I don't think you can understand the rules of thumb or very typical good design is the way it is without the foundation.

another day in paradise, or is paradise one day closer ?

 

[human909]

Is the modern CE education getting diluted by pushing the learning of particular software packages rather then focusing on fundamentals?

I can't speak about other localities but here in Australia we focus extensively on the fundamental calculation (IMO too much). But being able to calculate an exam problem is one thing, being about to problem solve suitably is harder to teach and in general not taught. I think this is exhibited in the case of this post, Alessandro has done an excellent job of blindly applying loads and considering all reaction points. A+ for following the recipes universities teach. D- for thinking about the problem in a wholistic sense.

Regarding software I thought we used FAR too little. We did zero courses that covered any sort of drawing which really should be at least one semester. Even my father half a century ago was doing this for chemical engineer. Though that was a drawing board an pencils not CAD obviously.

Compared to many of the experienced engineers here I am fresh face I didn't do my degree that long ago. I would say my calculative ability is fairly poor (despite having done a undergrad in mathematics) and very rusty. I lean heavily on software packages when and where I can. But I can at least problem solve. I can't even write out bending moment formula and beam formula from memory! But if I had to I could derive the from first principles.

I think the general calibre of students coming out of engineering schools are now no longer the brightest 1-3% of the population they are instead the 15-20% of the population. So there is that aspects of things.

I thought that was the point ... learn theoretical foundational knowledge in school, then 10+ years learning how to apply what you've learnt ?

I don't think you can understand the rules of thumb or very typical good design is the way it is without the foundation.

The foundations are important, but there is a whole lot that is covered in excess beyond that. Not covered is plenty of basic knowledge that can help students and engineers apply that knowledge in practice. At least how I learn, if I can't apply something in context I will forget it and not properly understand it.

I've been training up a student of a similar aptitude of what we've describe here. Coming in with almost zero knowledge of the fundamentals and very little ability to think about the bigger picture. Though give him a computer program and he'll run wild. I've made reasonable progress I believe, his work ethic is good and I've taught him alot. Still to be seen on how much he can fully stand on his own feet.

 

[phamENG]

rb - yes, that is the point of university. My point was that the problem is less a reliance on software and more, as human909 put it rather nicely, a lack of problem solving ability. For some people it comes naturally and they can see through a problem no matter the nature of it, others need to be taught. The former tend to shine in our profession while the latter may struggle unless they work their way into a pigeon hole, learn it really well, and stay there.

human909 - let's not get started on the quality of students going into and leaving universities...

I think the tendency to rely on computers is something of a natural progression. In many ways they are the nomographs of old. Why solve anything directly when you can look a chart that tells you what the answer is? Well...why calculate anything directly when the computer will do it for you? There are obvious differences, but as I said I think it's a natural progression. Every generation, engineers are seeking ways to make their work more efficient. With every efficiency improvement there is an opportunity for misuse. I can learn how to design something by hand and it'll take me a week, or I can look at this neat chart, get the right answer (probably/maybe) and move on. Not much different than "I can build a quick model and it'll tell me the forces." The new version is more powerful and, therefore, more prone to misuse. The consequences can also be more severe since the software often looks like it's filling in the steps in between with decisions and judgement.

 

[XR250]

I think the tendency to rely on computers is something of a natural progression. In many ways they are the nomographs of old. Why solve anything directly when you can look a chart that tells you what the answer is? Well...why calculate anything directly when the computer will do it for you? There are obvious differences, but as I said I think it's a natural progression.

I think that is fine but you outta be able to use fundamentals to approximately check your software output.

 

[phamENG]

I agree. Just like the engineers of yester-year should have been able to create the nomographs they were using, we should be able to perform the design and analysis the computer is doing for us.

Now where is KootK and his doomsday visions of AI structural engineering replacing us all by 2030?

 

[Alessandro Morelli]

Thank you for the comments, guys. You have been very helpful in the process and I have been using it to solve the problem.

Don't change the load. Leave it as a distributed load - it's simple enough when you start with global analysis.

Thanks for the help, this did make the problem solving much easier.

Sorry to sound harsh.

It's ok, I understand, it's just the truth. No problem, I'll just learn. Even though, yes, I can remember clearly now that they did teach me this, it just has been almost 6 years already with 0 use of that knowledge so I guess it had started kinda fading away. But as I read what you guys say I go like "ahh yes, yes, I remember that part", hahaha.

I am a mechanical engineer by training so I don't know the typical CE or SE curriculum, but I received solid training in statics and mechanics of materials (this was 1982).

That's cool!
Perhaps if I might give some information about myself, I am a mechatronic engineer, which means the focus of my career was about 75% electronics and 15% mechanics because it's focused on robot programming, mainly. I have mostly worked on code and doing a master's in Data Science, which is an entirely different world than this sort of design... To decide that 3d design was my passion is something I chose with the limited knowledge that I can remember about static design. This, I suspect, it's not a problem. It took me a day to remember with the help of this thread I should simplify the problems and how to do so, so...I don't think the lack of the knowledge required to be creative in the first place may last long... Still, thanks for your comment!

I entered college at 12 and finished at 17 (college is 5 years here), however, to put it bluntly, the pay in Colombia for a Mechanic Engineer with 3 years of experience is, to be exact, 456 USD, per month. Perhaps if you are a senior with 30 years of experience then you might be able to make up to 2000 USD a month if you are VERY lucky. That's depressing, I sorta need to eat, so I've had to pick jobs I don't like to win more money in the first place. So, I came to Russia where they accepted me to study for my master's. Let's hope the Russians give me an opportunity! Because returning to America is not a possibility, and I, like, REALLY need to eat, and I have 200 dollars left, AND there are no flights out of here anymore
Sometimes you just get unlucky like that...anyway

joining piece that simply joins the two stair stringers.

Yes, more like a joining piece, I suppose. Poor wording on my part. I did the simplifying and it became more understandable indeed.
The 3%, 20% of population thing...well, maybe, there IS more people now, though, so more Engineers are needed, so...it's all welcomed to me. As far as I'm concerned, everybody should get taught static design, why not?
However, I do feel the need to point out that how creative you are, is modeled primarily by your knowledge and then by your intelligence and so on.
Like, if I just don't know that simplifying in such manner is even possible then the idea might never come to my head. I suspect you are assuming that it is a core concept that I already had within me and wasn't applying but...no, I just didn't know. It is like that sometimes when you get into a new sphere of knowledge. Imagine getting into, I don't know, music, so late into your career, and the teacher getting mad because you are not applying the knowledge about octaves properly (you had no idea).
You get me?

 

[human909]

I think that is fine but you outta be able to use fundamentals to approximately check your software output.

I'm going to play a bit of devils advocate here.

I would argue that you don't need to calculatively 'use the fundamentals' to approximately check software output but I do agree that you need adopt a rational approach to sanity check software and in fact ALL output.

The question can arise, how far back to first principles does our understanding need to go? Do we need to be able to derive beam formula? Do we need to be able to show mathematical proofs of the various calculus rules? Because as you go back down the line you either stop somewhere or required a deep knowledge of mathematics which most engineers don't have.

For example is it worth my time to be able to calculate the effective lengths of my columns in a moment frame when my software package does it for me? Yes I do check that the output is reasonable and appropriate and within the bounds on what is expected. But I don't check it and I would need to do a fair bit of reading before I could suitable hand calculate out the answer.


I'm someone who leans heavily on software. But I always gain confidence in my application of the software by considering in the context of who should be expected from traditional approaches or referring to actual physical research. I recently spent far too long working and reviewing bolt prying forces using a software package. But the time was well spent as I am now confident that I can suitably construct a model that does cater for the effects of bolt prying in calculated the loads on bolts.

 

[human909]

Hi Alessandro Morelli,

Just for some context. This forums gets lots of people clearly out of their depth posting and asking for extensive help. This has been particularly common in the recent weeks and some regular members are likely sick of it. So replies to you may be more rude and less helpful that at other times. That

It's ok, I understand, it's just the truth. No problem, I'll just learn. Even though, yes, I can remember clearly now that they did teach me this, it just has been almost 6 years already with 0 use of that knowledge so I guess it had started kinda fading away.

6 years is a long time. You have some catching up to do.

I entered college at 12 and finished at 17 (college is 5 years here), however, to put it bluntly

If you completed college by the time you were 17 years old then that is impressive and likely puts you in the top 1%. Congratulations. But as you are now finding out it is easy to forget as time passes no matter how skilled you are.

So, I came to Russia where they accepted me to study for my master's. Let's hope the Russians give me an opportunity! peace Because returning to America is not a possibility, and I, like, REALLY need to eat, and I have 200 dollars left, AND there are no flights out of here anymore neutral.

Probably one of the last countries I would choose! But like you say we all need to eat. I have Colombian friends who have moved into my country. You need to chase the opportunities.


~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Okay... Enough chit chat I'll give you a rough guide of how I would approach the problem. Note that I'm not perfect so sanity check all responses.

1. Decide on whether the end connections are pinned or moment connection. This is a choice and likely 2 of the variants you mention.

2. Transform the vertical load into one that is perpendicular and parallel to the stairway. Ignore the parallel load to begin with.

3. Calculate the bending moments and shear forces for the ends and centre of the WHOLE stairway using a simply supported beam foruma or a fixed end beam formula.

Congratulations you now have the key loads you need to deal with to calculate the forces in the bolts!

4. Calculate the forces in the central bolts by considering the moment transfer required through the connection.

5. Calculate the shear demands on the bolts by resolving the end shear demands of the stairway beam.

6. Add back in the loads parallel to the stairway beam.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

I probably screw up somewhere there or handwaved away some of the complexities but that is a start.

 

[XR250]

I would argue that you don't need to calculatively 'use the fundamentals' to approximately check software output

In my mind, Statics is fundamental. Def. was not thinking of deriving formulas!

 

[rb1957]

my 2c ...

1) this is like "draw a free body diagram". Decide on how you want the structure to interface with the "rest of the world". There are minimal solutions that satisfy the equations of equilibrium, called statically determinate. Figure out why we put a roller support at one end of simply supported beam. If you don't provide enough loadpaths then the structure is a mechanism (not what you want !). For example you typically have two reactions in the Z directions ... one for Fz equilibrium, and the 2nd for Mx (this is simply supported); or you can use 1 Fz reaction and one Mx (like a cantilever). These choices influence the internal loads in your structure. This is possibly the most important link between "learning from a book" and "applying that learning to the real world".

2) this is like "calculate the reactions", the loads your structure applies to the "rest of the world".

3) sure use "canned" solutions for internal but if you're "remembering/relearning" this I'd like to think you could go back and derive things ... it should all come back.

my other 2c ... these guys are expecting a lot from you. It should be apparent from your CV and your immediate reaction to this problem that you haven't done calcs in some years, possibly never, and so stumbling when applying "book learning" to real world problems/structures shouldn't be surprising. The absolutely key things are i) do you have the foundation analytical skills (or at least the analytical bent to take this on), and ii) do you learn (or repeat the same stumbles) ?

another day in paradise, or is paradise one day closer ?