Floor loading understanding check please (long(ish) & maths content)

[dnb]

I have become a little concerned that I don't fully understand how floor loading calculations work. I've got a whole lot of calculations from the SE and everyone is happy with them, but I would like to make sure I don't do anything silly when heavy things start to arrive in the house (I like books for one thing... And wasn't planning to have a ground floor library this time).

 

So as with engineers everywhere I set out to create a model of the problem to see if that helped. It hasn't much, but if I can explain it here and get some feedback there's a good chance of either knowing not worrying more or averting a disaster by reconsidering the library before I have to ask my very busy SE any more questions.

 

For info, the floors are all implemented with mostly Steico I beam joists with the odd LVL or steelwork for key structural parts (stairs, supporting roof structures etc..) The LVLs and steels aren't involved in the area I am thinking about. The floor design loadings seem typical 1.5kN/m^2 live loads, 0.5kN/m^2 dead loads and 0.25kN/m^2 for partitions.  So my understanding is that since the floor is 100m^2 it would support 15 tonnes and only deflect by the designed amount if evenly loaded throughout. (It would probably support more but the deflection would exceed the requirement and this isn't good, so let's not let this happen.) OK so far, I don't have *that* many books. The thing is that book cases, are usually tall thin things, so then we come to point loads, and the structural calculations as written down are far less clear as to what I can do and what I need to worry about. Taking an absurd example, putting the 15 tonnes of books on 50m^2 of the floor all on one side probably wouldn't be good, but 0.5m^2 piles of the same weight of books over the whole floor might well be OK.

 

The following should be an example that can apply "just too much" loading (unrelated to books) from a limited distributed load sat in one part of the floor to check I am understanding how this works. Let's assume a 650kg distributed mass. To be within the 1.5kN/m^2 live loading simple mathis indicates it would need to be squashed to occupy 4.25m^2. Let's assume my heavy thing is 2.1m long, so would therefore need to be 2m wide. But I've learned over the years that simple often doesn't tell the whole story - joists only go one way for a start. So I tried to simplify it all to a beam loading calculation in 1 dimension because this seems to be what mech engineers try to do... (I do physics based work, so I like point sources and vacuums - who am I to criticise? 😉 ).

 

I set up a 4m long beam to represent the 22mm floorboards and then put supports at 600mm intervals to represent the joists viewed end-on.  I added a 2.1 metre long distributed load across the middle 4 "joists" of 3kN/m. The reaction forces at the supports should represent the forces applied to the joists (albeit with a sign change). The 4 numbers come out as 1kN, 1.97kN, 1.88kN and 1.6kN. Can I translate this back to a 3d reality by assuming that if my 2.1 metre distributed load were 1.6 metres wide (1.6m * 0.6m = 1m^2) then I could approximate the loading across the "heavy thing" as a maximum of 1.97kN/m^2 approximately in the centre? So in this case it exceeds the live loading in 3 of 4 cases.

Given the area occupied by the "heavy thing" in this case works out to only 3.36m^2 we expect a problem since the simple case above also would have indicated a problem.

 

Now if said "heavy thing" were squashed to be 3.2m wide then the approximation of maximum loading would be halved to 0.985kN/m^2, and this is well within the live load for all 4 points so all is fine. But of course the squashed heavy thing is now taking up 6.72m^2 of space. So the simple case again predicts that things are OK, although it would under-estimate the area required for achieving this loading as 6.47m^2 (because it has essentially averaged the load out) indicating that the original 4.25m^2 may also be an under-estimate and the heavy thing really needs to be squashed to at least 2.2m wide rather than 2m so consume at least 4.6m^2 for all 4 of my sample points to be at or below the live loading requirement.

 

I think the take-home here is that working near the limits is best avoided...

 

Now to start weighing the books...  Paper is 1200kg/m^3!

[Marvin]

Hi @dnb

 

Your calculating ability far exceeds mine, however my thoughts are:

 

In a home it would make a difference as to where the floor load-bearing supports are. Towards the ends of the joists the limiting calculations may become the crushing strength of the joists the point load capability of the flooring and the load bearing capasity of the supporting wall below.

 

Most people load books around the edges of rooms.

 

The UDL figures you quote seem standard loading design figures. So no more than a typical house with typical contents. 

 

However if anyone knows otherwise, I'm sure they will let you know.

 

M

 

[SteamyTea]

7 hours ago, dnb said:

I think the take-home here is that working near the limits is best avoided...

Yes, double it then round up.

Or halve it and round down.

 

Remember Young's Modulus, only true within the elastic limits of the material.

[markc]

Floor loadings are often mis understood or applied. I have countless arguments with engineers who simply quote figures but don’t really understand the mechanics. We sell access platforms, majority on stabiliser legs and floors and nearly always xKN/m2 which is fine for general use but when it comes to non pedestrian traffic then you need to look deeper. 
point loads and distributed loads a 50kg person in high heals is  a 50kg/cm2 load while walking which is a high point load but low imposed or distributed load while a 1000kg standard pallet (1200x1000) is only 0.083 kg/cm2

so the question comes down to what is under the floor.

a thick concrete slab on spindle columns can withstand a very high point load but little distributed load while a tarmac surface over sand or gravel is useless for point loads but good for very high distributed loads.

I have positioned and operated 5t+ machines on floors designed for light pedestrian traffic (5KN/m2)

[dnb]

11 hours ago, markc said:

Floor loadings are often mis understood or applied. I have countless arguments with engineers who simply quote figures but don’t really understand the mechanics.

This is exactly what I am trying to do - gain some understanding of the mechanics so I am sufficiently armed to ask the right questions.

 

11 hours ago, SteamyTea said:

Remember Young's Modulus, only true within the elastic limits of the material.

Foremost in my mind. The elastic limit on a Steico joist is closer than one may think. Or so I am told.

 

11 hours ago, markc said:

the question comes down to what is under the floor

At least the answer to that is easy. Steico joists in hangers on to 217mm SIPS panels.

 

11 hours ago, Marvin said:

The UDL figures you quote seem standard loading design figures.

Yes, the design figures are not unusually high or low.

 

Thank you all. Nobody has said the maths is wrong yet, so that's a good start.  So it looks like I plan to spread the books out on half height shelves. This works well for the room since it has a vaulted ceiling and short walls.

 

 

[Marvin]

9 minutes ago, dnb said:

So it looks like I plan to spread the books out on half height shelves. This works well for the room since it has a vaulted ceiling and short walls.

Hopefully across the joists and not along the joists....

[SteamyTea]

2 hours ago, dnb said:

So it looks like I plan to spread the books out on half height shelves.

Or PDF them and get a 30 quid Kindle.  What I have basically done.

[SimonD]

Well, it's Friday night and this thread caught my eye. How many books have you actually got?

 

I haven't sat down and done any math on this one as my main thought was that my dad has a lot of books, a lot of them. My sister

also has a lot of books currently on bookshelves on a floor that's been around for nearly 100 years now. There's never been a problem with floors coping with the load from the bookshelves, even in the last place where my dad had them in a loft converted into a library. In my current house, the SE didn't design the floor according to minimum BR load requirements, but to a higher standard to reduce deflection, which in theory is going to mean the capacity to deal with a greater load. I'll report back when I get my library out of storage and onto the bookshelves ☺️

 

22 hours ago, dnb said:

Can I translate this back to a 3d reality by assuming that if my 2.1 metre distributed load were 1.6 metres wide (1.6m * 0.6m = 1m^2) then I could approximate the loading across the "heavy thing" as a maximum of 1.97kN/m^2 approximately in the centre? So in this case it exceeds the live loading in 3 of 4 cases.

 

If my very rusty engineering brain remembers correctly, this is only one way of calculating your loading which is in effect the resultant force of the load. However, this is a simplified approach. For a uniformly distributed load you may need to think as if it's pressure against the surface which would calculate the pressure over an area - think for example snow load. In this instance you'd be looking at load per unit area, or in more simply terms load per unit length. This way you get a better idea of the distribution of the load which is more accurate because in your case, you wouldn't in reality see the resultant force on one joist with less or nothing on the others. But also, because the floor structure ties the floor together your loading will be distributed across a wider area of the floor than just the joists below the bookshelf - try walking across a load of joists without noggings, then add the noggings, and then add your osb/chipboard floor and in each case there will be a very obvious difference in the floor's behaviour and how it feels underfoot.

 

Like @markc has also clearly experimented, I've driven and used a mini digger on a floor with only 4inch joists.

 

But maybe I've had too much beer....

[dnb]

51 minutes ago, SimonD said:

How many books have you actually got?

There are 4 full height book cases full at home, 1 partially filled case and many boxes squirrelled in places that are now sounding in some cases like a bad place to have a lot of mass. Would guess at somewhere around 2.5 tonnes of books. I'm not a horder, honestly!

 

54 minutes ago, SimonD said:

...a very obvious difference in the floor's behaviour and how it feels underfoot.

That's true. The new house floors are wildly stiffer than the current house. The comparison between 6" timber with dodgy 1980s plumbing notches to 300mm I beam joists is telling.

 

So to check my (similarly alchohol fuelled) undersanding, what you are saying is that I should consider the bonded floorboards + noggins etc as a more efficient load spreader than my calculation would suggest.  So a certain amount of "averaging" will happen provided that I steer clear of very pointy books. And since your Dad hasn't yet ended up with escaped books and my 1980s house hasn't yet fallen down it's all probably OK. 😉

[Bonner]

6 hours ago, dnb said:

undersanding

That’s me after a glass of wine, no undersanding

Problem I find with tall bookcases is wobble. No matter how little deflection in the joists, a tall piece of furniture will move to some degree. I always secure them to the wall for security, thereby sharing the load with the wall.

[SteamyTea]

I think a sketch may be helpful.

https://www.engineeringtoolbox.com/beam-stress-deflection-d_1312.html

 

[Mr Punter]

Often the floor calcs will include the allowable line loads for parallel and transverse to the joists.  Meant for partitions but I guess would work for bookcases.

[Gus Potter]

On 30/09/2022 at 00:40, dnb said:

I have become a little concerned that I don't fully understand how floor loading calculations work. I've got a whole lot of calculations from the SE and everyone is happy with them, but I would like to make sure I don't do anything silly when heavy things start to arrive in the house (I like books for one thing...

Hi dnb and all.

 

I'm a bit late to the table with this but will have a go at exploring as this kind of thing drives early design decisions / cost analysis / cost curves when you are planning your self build, extension or just renovating part of the house.

 

Firstly have enjoyed reading all the other posts. Everyone makes great points.

 

I'm going to have a go what goes on behind the scenes first then touch on some of the in's and outs.

 

Ok you are doing a domestic dwelling, you get some calcs from the SE that reference various design codes. Could be Bristish Standard 5268 or Eurocode EC5. Both these design codes (as are nearly all design codes) are based on the probability of a loading event occuring. For example lets take snow loading on a roof.

 

In the UK we design houses for a snow loading that has a recurrance / return probability period of 50 years. But we could get two snow events two winters in a row that may meet the maximum predicted fall over the next 50 years and then nothing for the next two hundred years. But if we design for a longer return period say snow in two hundered years then houses would become so expensive that we could not afford to build them. Also we need to look at the overall risk over the whole UK and what would be the potential loss of life and balanced that against the benefit to society of taking a pragmatic approach to how we calculate loadings. We may of course not get anywhere near the design snow fall. All I would say is go back and look at the last time all the farm buildings collapsed, they were designing these on a two year snow return period and had got away with it until they didn't. That was a main driver behind changes to the argicultural snow design part of the code.

 

@dnb The floor loadings of 1.5 kN/m^2 ( about 150 kg/sq metre) roughly equates to a value of what has been deemed on basis of probability to be a reasonably safe figure given normal human behaviour in a house.

 

What Engineers then do is to say.. lets put a factor of safety on this loading to account for the fact that folk may a bit daft and have a big party. Lets also add a factor of safety to the materials in case the timber joists you have may include one or two that have a load of knots or just be a bit of duff timber. Also lets say the floor may not be truly uniformly loaded. But we then say.. the floor boards will mitigate by spreading and sharing the load out a bit so we add a bit back in.

 

Now you'll often hear a builder saying.. I have been doing this for years..etc and nothing has fallen down.. I say.. not yet.

 

What SE's (unless you have briefed them) don't do is start out by saying.. someone is going to not use their common sense, go nuts and turn a domestic floor into a library floor. The codes prescribe different loadings for libraries and storage areas and they are much more onerous. I think you may need to come clean with your SE!

 

For all. Here you need to be careful when doing your research (delving into structural design) as the BS code is what we call a permissible stress code. The factors of safety on the loading are all lumped together and not immediately apparent, but the EC codes split this out between a visible load factor and a material factor of safety. In summary though design to the two codes gives pretty similar results, there are caveats but for another day.

 

A big elephant in the room here is that while you may get away with a big stack of book shelves on a house with solid timber floor joists it won't fly with engineered joists as they often buckle and crush at the supports unless you have designed in end struts and so on.. and if they do buckle / crush so will anything else that is relying on them for support also fail! Big trouble. What happens is that one end of the joists get much more heavily loaded in shear even though the overall load on the floor has not increased. @SteamyTea

 

Below is copied a bit out of the BS 6399 part 1 code for loadings.. you can split hairs here but you can see that you may have a "reading room" case thus your 1.5 kN/m^2 live floor loading now jumps to 4.0 kN/m^2 or 2.4 kN/m^2 for each available vertical metre of storage height.

 

 

You can see that you are treading on thin ice here!

 

That's my thoughts so far folks but if there is any interest then I'll do another bit on defections, preliminary sizing and costing.. the other things you need to think about when you are embarking on your journey.

 

To finish @markc makes some good points about concentrated loading.. but the first thing to do is to get the general concept sorted and then you deal with the concentrated loads (see table above) and check something won't punch through the flooring locally. Once you have done this you go back and check the whole design again as a complete system.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

[saveasteading]

I hadn't seen this discussion so I am late joining too. Very good points throughout. May I recommend a book to you....'why you don't fall through the floor.' If you can't find it then I can try harder with the title.  

Re builders thinking they know better than Engineers.....they don't generally know about the safety factors, and there is another one for build quality. Also they are usually long gone when any problems present themselves, and never hear of problems let alone have to resolve them.

Safety factors for office blocks were revised down a few years ago,  on the basis that not all rooms are stationery stores. The cost saving is huge. But in a big office loads are spread whereas in a house they usually apply room by room.

 

 

[George]

Bookcases around the edge of a room wouldn't concern me,  particularly - certainly not if the joists are perpendicular. 

 

Bookcases placed in the centre of a room I'd like to know about. It's unlikely to have a strength failure (due to slight overdesign, load sharing and safety factors), but could certainly affect serviceability (deflection), especially with timber as load duration is a factor. 

Edited October 7, 2022 by George

[SteamyTea]

A few years ago, the company next to us had some external claddings fitted. I noticed that one of our cupboard doors was stuck. This was right under where the work was done.

Transpired that it was nothing to do with the work, just that the company had rearranged thier office space above.

This included some racks to put files on. 

They moved them pretty quickly to a proper external wall, problem sorted.

 

Edited October 7, 2022 by SteamyTea