Apr 2021 - Beam Calculations (for above the doors)
I spent way too long looking into different options for door headers. I was a little paranoid about deflection as I didn't want to have any problems with the doors working properly over time. I have heard of a few people that have had issues with bifold doors and the root cause seems to come back to a combination of:
1. the door header not being suitable for the door span + roof loads
2. the sensitivity of the door to vertical deflection (but reason 1 seems to be the big one)
In addition to this, changes in the weather through the seasons can (I have heard) cause flex and movement which can lead to issues. My doors are alu so that means theoretically more stability versus PVC, and hopefully less issues, but the main reason I selected alu was for the sharper looks (if I'm honest). So... operating from the assumption that vertical deflection is the true nemesis of bifolds this became the factor which I needed to focus on and my mind was set on giving my lovely new doors a stress free life via a suitably deluxe door header experience. This meant doing a bit of research into what my best options were.
Results from my research
Unfortunately, most of the good guidance I found was for multi storey buildings and hence they were often coming up with solutions that would be not be suitable for a garden room. For my particular application, these recommendations would be either:
1. overengineered in terms of strength and cost
2. cause me issues on overall building height
3. or both
Mildly relevant distraction #1:
Regarding the height thing, when working within permitted development you need to keep everything under 2.5m (when building within 2m of the boundary) and for that reason you really need to think about what you are doing every step of the way. For example, assuming 2000mm for your door height, that leaves only half a metre for the base, the headers and the roof (not to mention the air gap under the building, and possibly even your floor boards depending on how you build it).
Anyway, I'm getting distracted, the point is the only other guidance I found for header selection / header design was pretty anecdotal and didn't seem to have any theory behind it. That isn't necessarily a problem, but on this occasion it wasn't giving me enough confidence to make a decision, considering the potential impact of getting it wrong (fiddly / sticky doors of annoyance).
The cunning plan
So... logically, I decided that I would leverage my complete lack of structural engineering knowledge to manually calculate the beam deflections for all of the options available. So here are the options I considered:
1. Doubled up 6 x 2, C24 timber
2. Flitch beam (C24 timber and steel 'flitch plate' sandwiched together)
3. I beam (sometimes known as a H beam or a 'universal beam')
4. RHS (rectangular hollow section)
Note: I did not include concrete lintel or glulam beam, for reasons which I honestly cannot remember, and there may be other options which I dont even know about, that I am hoping people will point out to me.
My plan was to use the below formula to calculate the maximum deflection on the beam. I would still of course have the problem of not knowing how much deflection was acceptable for my particular bifold door, hmmmm... HOWEVER I would be able to COMPARE them all
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Mildly relevant distraction #2:
I did contact some of the door manufactures to find out what sort of deflection they think their products could handle, or even what headers they recommended for different spans - but alas, nobody wanted to commit to anything specific, other than to say "computer says no" or "zero deflection required" which is of course theoretically impossible, even if I made it from diamond.
Note: making it from diamond would represent a significant cost save for the build, considering how much I'm planning to spend on materials and 'essential' tools so far)
Mildly relevant distraction #3:
Note that there are lots of different formulas for this sort of thing, but the one above should represent worst case for my door header because it assumes the beam is simply supported at either end (in reality it has lots of engineering screws holding it in place along some of its length and also has the roof load partially distributed either side of the 'fulcrum' too, which I imagine restricts the movement - not that I know what I am talking about). Oh yeah, please note that I am absolutely NOT qualified in this topic, and everything I say should be considered as science fiction, even the science part is pushing it a bit.
I will point out though that I am lucky enough to know somebody that does know what he is talking about, and he checked this over for me and helped me with some of the calcs, so it isn't completely worthless. As a minimum I think it gives a good indication of how the options stack up against one another. Worst case its a bit of fun, and a good opportunity for everybody to laugh at my mistakes.
Variables
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The legend in the pictures explains what the variables are, so I wont double explain those, but it is worth noting that the values for youngs modulus for each material can be found online in the so called 'blue book', as can the values for moment of inertia (which is specific to each shape / cross section) - you can calculate this if you want to, but its easier to look it up. I vaguely remember us covering how to do this in my mech eng degree, but that was 20 years ago and I was rubbish at it then and suspect even crapper now so much prefer standing on the shoulders of giants. Oh yeah, 'w' or roof load is the other funny one. I think for that one I calculated the weight of my entire roof (timber, insulation, EPDM, chipboard) and then added some for static snow load, and finally I think some for dynamic load for people / person (me) walking on there. I also divided the numbers by two because (approx.) half the load is on the front wall and the other half is on the back wall (my side walls do not support any load) Honestly can't remember exactly how I got that number, but as I say all my assumptions are clearly shown in the workings so as not to mislead anybody into how I got the overall deflection results. Looking at these numbers now, we have 14 N/cm which is 1.4kg per cm, which is 140kg per metre - so that 'feels' in the right ball park for the amount of load along that beam.
Finally, regarding variables, you will notice the slightly hilarious use of 'cm' as a unit. I am advised that the golden rule with SE calcs is to pick one unit and stick with it, and because a lot of the numbers provided for free in the blue book are in 'cm' it makes sense to use cm throughout.
How I will contextualise the results
Seeing as I don't know how much deflection is tolerable by the doors, due to the fact it is a secret (not disclosed by the door manufacturers), I need a way to contextualise any numbers that pop out of the calculations. I am clutching at straws a little here, but I did find some rough guidelines that I think could help put the deflection values into context: I understand that some people work the following rule:
• <2m span = doubled up 2 x 6 timber is ok
• >2m span = metal beam required (or you could use thicker timber, but you can't simply add in 9x2 headers when you only have 2.5m overall building height to play with - so we end up in metal beam territory once a 6 x 2 isn't strong enough)
So, I will use a doubled up 6 x 2 timber as a sort of baseline solution that is 'probably' acceptable for a 2 metre span. Considering my span is 2.4m, I know that any alternative designs only need to be say 20% stronger, for the same constrained / max 150mm header thickness. (I think I mentioned this already, but I cannot just simply add thicker timbers and be done with it, due to the 2.5m building height restriction. That in itself is the ONLY reason for doing all this faffing around - I am fixed with 150mm max for my header)
The results
I will include some extracts below from my summaries for each of the 4 options so that you can see my assumptions (mistakes) in all their glory. As you can see, the timber option (for my 2.4m wide bifold) gives 3.4mm deflection (in the middle), and the metal options are far stiffer ranging from 0.71mm to 0.34mm deflection.
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Below are the full workings in excel.
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The decision
So to cut a long story short (oops too late for that) I have decided to use doubled up 6 x 2 timber for above the french doors which have only a 1.6m span, and a flitch beam for above the bifold door which has a 2.4m span.
Factors influencing the decision:
COST
From a cost perspective timber is cheapest (about £50), and all the metal options work out in a similar same ball park, although flitch was cheaper than the other two metal options by about 30 or 40%
STRENGTH
Again, all the metal options are basically the same - as a minimum they are 4 times stiffer than timber, and if we work from the assumption that the timber option is good enough for a 2m span, then we can conclude from the numbers that the metal options are all way stronger than needed for my 2.4m. So, for my span, strength is not really a factor when choosing between the metal options.
WORKABILITY
the primary reason for choosing flitch beam over i beam or RHS was the fact that the flitch beam gave me a timber surface on both sides, which is nicer to work with (attaching cladding on outside or plasterboard on inside). I dare say flitch beam is slightly more hassle to erect than RHS or I beam because you have to drill holes in the timber and bolt it all together, which takes time, but its probably 2 hours of work to construct and install a flitch beam versus 1 hour to install RHS or I beam so probably not significant in the grand scheme of things.
Mildly relevant distraction #4: I just checked with future self, and I / he has confirmed that the flitch beam did take about 2 hours, not including the 30 minutes spent staring at it proudly afterwards, or the 15 minutes spent explaining it to my (completely uninterested) wife
Summary
Overall I believe flitch beam to be the best option for this application, but I reserve the right to change my mind later, probably when its too late. See below for some top secret pictures which I took from the future.
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Cost wise we are looking at about £100 for the flitch plate, which then gets sandwiched between two timbers to create a flitch beam. Note that the delivery costs for these things are huge (prohibitively so), so I picked mine up in my A-team van as the place was only about 40 minutes away. You will also need some bolts too. And wood. Under £200 'all in' I guess, which feels like good value if it keeps the doors working properly.
I am sorry for the length of that post, I find it hard to filter and I also find it hard and distinguish between useful and useless information. But, one man's trash is another man's treasure. Maybe that means my garden room could actually be worth something in the future.... :-D
Martin