# Stuck with steel sizing

#### angelboy

I'm planning an outdoor gazebo with concrete filled brick pillars (450 x 450) and a clay tiled roof and I'm struggling to work out what beam size I need for the spans between the pillars.

The span between the pillars are 4400 so allowing a 150 bearing (on 3 engineering bricks) the steel size would be 4700 - around the opening of a double garage really.

So far, I've worked out that the roof weight is 3100kg, so there would be a UDL of 1550kg along one steel and then a point load of 775kg (each roof gable ends supporting the ridge beam).

I have formulas from Chudleys but I'm running round in circles pumping out figures that have no meaning.

I'd read from a BC guide (san't get my hands on it now) that a 5m span 178x102x19 UB can take the weight of a 2.4m block wall - so even with a 14kg block that's a UDL of nearly 1700kg.

Would this beam be OK?

Download a copy of super beam if you are sure you can do this yourself. Deflection limits of typically 1/200 will give you what you need.

A 7" x 4" would be OK.

A 7" x 4" would be OK.

Really? A timber beam would be OK?

I'd much rather build it out of timber and I suppose if I were putting shakes on the roof then I wouldn't be concerned, but the weight of the tiles concerned me, especially at the gable end where the point load is.

This sketchup drawing gives you a rough idea of what I'm planning.

Download a copy of super beam if you are sure you can do this yourself. Deflection limits of typically 1/200 will give you what you need.

I've looked at super beam but to be honest, it's still beyond me. I've seen a thread http://www.greentram.com/forums/showthread.php?t=1950
that says it's a GIGO program (garbage in, garbage out) and that it's really to streamline long-hand calculations.

Reading back my notes, which look foreign to me even though I did them, I'd calculated the roof area to be either 38.8m2 or 32m2. The reason being was that I read that you only take the direct vertical load rather than the actual area of the roof which includes the pitch. With this in mind I'd come to he conclusion that 32m2 equated to 0.9375kN/m2 and with a 1.5kN/m2 snow load would mean that I would have 2.4kN/m2 loading. Each pillar would then (rounded up) have a load of 20kN which would also be the point load for the beam.

Does this sound right or am I a million miles away?

Crudely then shows formulas for bending, shear and deflection.

Bending for point loads was BM=WL/4

So for a 4700 beam the distributed load would be W - total load (20kN but 2.5kN/m2) x span (4.7m) = 11.75/8 = 1.469kNm

Then,
Z=M/f

So (this is where it's not explained to me)
Z, section/elastic modulus
M, movement or resistance (max bending moment)
f, fibre stress of the material (normal 165N/mm2)

Z = 1.496 x 10(6) why this number I don't know = 14960000/165 = 90666.66 or 90.7cm

So looking at BS 4.1 the steel would be - 152x89x16

Does this all sound right so far?

You don't need a steel on the gable ends as that could be made as a truss.

I also suspect that you can't use the factors for a fully restrained beam in a building, as wind will be trying to twist that structure all over the place. So you need to use different factors, and think about the piers too.

It seems that two or three 50mm joists bolted to form a beam would be better and easier all round, Whether that's 175, 200 or 225mm deep would need working out. But 2 x 50x200 would seem likely.

I also suspect that you can't use the factors for a fully restrained beam in a building, as wind will be trying to twist that structure all over the place. So you need to use different factors, and think about the piers too.

What would you suggest?

The pad foundation for the piers will have a basic rebar frame tied into 3 vertical lengths. The concrete will be poured for the pads, the brick work completed then more concrete poured into the piers. The pads will be connected by a 100mm ground beam with more rebar installed to 'hopefully' tie the foundations and piers together.

I was going to brick in the beams and strap down the rear wall plate along the back wall. I'll also strap across 3 rafter spans along the full length of the roof. The rafters will be toe-nailed and I'll put in rafter clips for added security.

The gable ends will stay open - what else could I do to protect against wind?

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There are a couple of engineering types on here who do this thing for a living so they may be able to check your calcs, so I would not really want to get involved in doing that.

But in general it seem like you have thought about everything, and its probably just the size of those beams and whether to use steel or timber.

If you are designing to BS5950, or Eurocode 3, then there are different factors to use depending on the use of the beam - restraint and deflection come to mind. So if you are doing this properly, then using the correct factors would help.

The only other thing that you might need to look at, is the racking (twisting) resistance of the roof. What will stop the rafters or the whole roof from moving sideways at the ridge and toppling over? It might be OK, but it needs considering.

Thanks for that.

@ OP; no, I meant a 178 x 102 steel (ie 7x4 in old money).

But as above, a (deeper) timber beam would probably be OK.

@ OP, just a few suggestions on your figures:

If designing in steel using BS 5950, you need to 'factor-up' the loads (x by 1.4 for dead loads and 1.6 for live loads.

Max bending moment is WL/4 for the point load (on the gable ends) and WL/8 for the uniform load on the side beams.

For the rest, you really need the tables to check maximum permissible stress, and from that, you check the maximum buckling-resistance moment of your chosen beam for your span. Admittedly not easy if you don't know where to look; there is also deflection to consider.

But aside from all this figures-nonsense, why not do it the old way in timber, as ^W^ suggests? Two (or possibly 3) 2x9s should do it, and easier to fix your rafters as well.

I think you might be right, three 2x9s bolted together. I'm waiting for a price for a single 150x225 beam but I think it might be silly. Other than that I might go for the 178x102 UB.

If you go with timber, three 50x225s would be stronger than one 150x225.

If you go with timber, three 50x225s would be stronger than one 150x225.

Right. If I make sure the middle one has grains in the opposite direction shouldn't it be even stronger?

The grains in each piece will always run in the same direction!

Generally, in using two or more pieces, you will be at least 10% stronger than an equivalent solid piece.

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