# RSJ size

still waiting for help on the following problem?
I have a lounge floor 16 X 12 feet wide which has 5" X 2" joists at 11" centres along the width (12 feet).I have removed a toilet and pantry underneath, the walls of which helped to support the floor in question.The floor is ok but a bit bouncy,since it should really have 7" joists.I intend to put a 16 foot RSJ underneath at 7 feet along the width.Any help in calculating the size of the RSJ? How thin can get away with,bearing in mind that anything would improve the situation? Hope all this makes sense! Any help greatly appreciated!
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I like http://www.torfaen-fighttheplan.org.uk

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johncol wrote:

Lounge, lounge. What is it? Have you bought an ex-public house? Anyway, a little more detail on what's been removed, and the general structure, would be helpful - photos to a website near you if poss.
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johncol wrote:

It is quite some time since I had dealings with RSJs, but will try to help. You may have more of a problem here than it looks at first sight. It may be you appreciate that as you say you want the RSJ as thin as possible (by which you mean short vertically, I presume?). So I will start by taking a few steps back to survey your problem.
Taking a stab in the dark I'd guess the 5m (16ft) span needs a 200 x 100 (ie 8in x 4 in) RSJ or possibly a size up or down. NB This is just an aid to visualise the problem NOT the final answer.
A 5m I beam (ie shape of a capital letter I aka RSJ) this size will sag (deflect) quite considerably just under its own weight, and will have quite a tense springiness. Despite its apparent strength in the vertical direction it is only a tenth or so as strong in the horizontal direction. What it adds up to is that an effective solution to your floor problem by this method will need adequately tieing-in vertically and horizontally to the existing floor. Unless that is done it would be quite likely that movement and vibration between the beam and the existing floor would conflict in an unnerving way. You might find installing this RSJ properly would be more trouble than it looks at first sight.
Have you considered other options? If you were building this floor for the first time it's likely that either deeper joists (7 or 8inch as you suggest) would be used to span the 12ft direction; or an RSJ would have been put across in the middle at 8ft to support 8ft joists supported in the RSJ flanges (giving you two half floors of 12ft x 8 ft). IMHO reconstructing the floor along either method is worth considering before going down the long beam route.
BTW you'd be well advised to use only metric units (metres & millimetres, Kilograms [mass] & Newtons [weight]): all the data in the tables you'll need are in these units & as NASA knows too well Mixed Measurements Miss Mars.
Considering the first option could you raise the floor and/or lower the ceiling under by a total of 50mm (75mm would be better)? Is it feasible to remove the floor and or ceiling? If so you could glue and nail strips to the top and/or underside of the timber joists to make a compound joist. You have to use full length strips and a good quality water resistant glue (eg Evostik W). It isn't absolutely necessary for the strips to go into the wall, though that might be better, but it is essential the glued bond is good and the strip is unbroken for the full width of the span. NB The strips need to be cut from joist quality certified/graded timber. That way you'll end up with a sound floor on 7 or 8 inch joists. My guess is that this would prove the most satisfactory & cost effective solution: you should be able to rescue enough of the floor boards & plasterboard is cheap enough.
If you want to explore the second option of a short RSJ and 8ft joists, this would be much more of a rebuild, but it might be possible to rescue & reuse the existing 5in joists. Even so you might find 5in joists just too near the limit - IMHO joists sizes in the Bldg Regs near the span limit tend to be a tad too small for a really satisfactory floor.
Another option is to consider putting down a secondary floor of 25mm T&G plywood on top of the existing. It would have to be well bonded by nails or screws. It's an iffy option - it puts extra load on the 5in joists but against that weakening you'd be hoping added stiffness of the floor would counterbalance that. Before going down this route seek advice from an experienced builder or structural engineer who can view the floor.
If none of the above options are feasible, and you still wish to put in the long RSJ, here's how to go about the calculations.
You'll need an up to date table of standard I beams showing size, Iyy and mass per unit length, published by BSI IIRC or ask your steel stockist or search the web.
The key to working out the size of a beam out is that a steel RSJ is allowed to deflect (sag) by 1/300th of its clear span. More cautious people use 1/360, but this not a fixed number but the larger you allow the sag the more you eat into the safety margin before the beam fails.
There are standard formulae for the sag for different types of loading and fixing of the beam. The formulae are mostly similar and in the form
d [ie deflection or sag]= k * [W * (L ^ 3)]/[E * I].
Assuming the beam is to rest at each end on (sound) 100mm walls, there's possibly only 2 values for k you'll need to get started - a point load in the middle of the beam, k=1/48 & for an evenly distributed load k = 5/384. For other load configurations you'll need to look up the formulae in a mechanical engineers ref book or textbook.
W is the total load (in Newtons =9.81 * Kilograms). L is the clear span of the beam in metres. E is Young's modulus for steel - 207 * 10^9 is a typical value. Iyy is the moment of inertia of the beam on the vertical axis - in Pascals (aka Newtons/m^2)
You make the above calculation using the appropriate formula for each load. Then add the calculated sags together. The resulting total must not exceed the calculated max sag (1/300). Note (assuming you are working in metres/newtons) the formulae yield d in metres not mm.
1. Its own self weight: take from the BSI table
2. An evenly distributed deadload due to weight of the floor boards, timber joists, and plastered ceiling under + any other similar load. You'll need to calculate this by measuring the size of each component & working out the total mass/weight - look on the web for typical densities. The area the beam is to support is a central band 16 ft x 6ft. (The side strips 16ft x 3ft against each wall are supported by the wall via the joists and so don't enter the calcs.)
3. A standard live load due to occupation (people + furniture) - IIRC the Bldg regs indicate a minimum of 1.44kN/m^2 should be used. Again this is only over the 16ft x 6 ft area the beam is to support.
4. If you are ultra cautious you might like to consider the effect of a 1000Kg (eg a medium size car) load placed in the middle of the floor. This on the basis that if I could park a car in my living room alongside all my normal gear, the floor will support anything or anyone likely to call on me.
Calculating the sags for a range of beam sizes should provide a feel for the sizes of RSJ feasible. The choice is then yours. However if the result is significantly different from 200 x 100, I'd look very carefully at the calcs & may be run through them in 2 or 3 different ways & ask someone else to repeat the calcs & check the formulae 'blindfold' - ie without your help. IIRC some steel stockists/suppliers will do the calcs for you, though IMHO you'd still do best making an independant check yourself.
Lastly about your requirement for a 'thin' RSJ. The slenderness ratio of a beam is an important part of its strength in the vertical direction. The shape of a steel RSJ is the key to its strength. By robbing mass from the sides the beam is made lighter. It won't sag so much under its own weight, but weakens it sideways - so it ideally needs some lateral restraint. In other words a squatter RSJ is weaker vertically than a narrow tall one. In other words your requirement may be awkward to meet.
HTH, sorry its such a long response & much delayed. BTW you must proceed on the assumption that I'm rusty in this area AND DEFINITELY more idiotic and stupid than you: everything needs independant checking before spending or doing anything irreversible.
In days of yore there were a fair number of posters on uk.d-i-y who'd toss their penny's worth into a posting like this. Where are you all now? Not killed off by 2 Jag's building police state I hope?
Good luck. Please post again if any queries. I'd be interested to hear what you decide (and how it works out).
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I had a couple of attempts at drafting an answer for the op before giving up on the basis that my info was 40 years out of date and my practical experience of the relevant calculations of similar vintage.
Just to now add my tuppenceworth.
AFAIK new RSJs have not been available for decades and any secondhand stuff would now be at least getting on for 40 years old (just like my information). The modern equivalents are Universal Beams and Columns which have thinner sections and are wider relative to their depth than RSJs. As the name suggests UCs are intended to be used vertically but where depth of a beam is an issue ISTR that it might be more advantageous to use a column as a beam.
On a practical note I have a 30 foot by 8 foot barn where the original hayloft has been replaced and that floor is now supported by 2 transverse 8" x 4" RSJs with a clear span of 18 feet. That shows no sign of collapsing and the deflection is not immediately apparent to the naked eye.
I have a 1965 Collins Architects Diary that has tables for both RSJS and the Universal Beams and Columns available at the time. That suggests that 8" x 4" RSJ would have a safe distributed load of 4.5 tons for a 16 foot span (3.6 at 18 feet) but that buckling might be an issue without adequate lateral support.
Tables for Universal Beams only go down to 8" x 5.25" but that is significantly stronger than the same depth RSJ at 5.7 or 4.7 tons (depending on weight of beam) SDL at 16 Foot span.
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Roger Chapman

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