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Nowadays it is possible for castellated beams to be designed to exactly fit the occurring load. By choosing the cutting pattern and the ratio H/h correctly, we can make the beam meet all technical requirements (according to the situation: bending strength; deflection; transverse shearing; and/or buckling of the web). Overdimensioning of the beam is no longer necessary. And that saves money! Or floor height!

The calculation of a castellated beam for a given situation is followed by requirements with regard to (among other things) the moment of inertia about the X-axis (I-x) and the minimum section modulus (W-x-min) of the lower and upper edges on the web opening, respectively. Castellated beams are used, in particular, for slender beams with large spans and an evenly divided load. In these cases, permissible deflection is usually the criterion. Obviously a check must be carried out to make sure that no impermissible stress concentrations occur as a result of transverse forces, particularly at the points of support.

How do you optimize an ordinary hot-rolled section?

Let's say, for example, our calculation shows that the required moment of inertia I-x is 75,000 cm^4. We could apply an HEA-500; this has an I-x of 86,975 cm^4 and weighs 158 kg/m. The moment of inertia is considerably overdimensioned. A size smaller, however, the HEA-450, has an I-x of 63,722 cm^4 and is therefore too light. As an alternative, we could consider an HEB-450. The I-x of this comes well within the requirement, with 79,887 cm^4. But this beam weighs 174.4 kg/m and that is far less favourable than the HEA-500. The HE-M is definitely not suitable.

Now we could of course also consider an IPE. Would this be better suited for our purpose? In our case we would have to chose an IPE-600. True, the moment of inertia of this is even more oversized - it's no less than 92,080 cm^4 - but the beam is lighter, i.e. 124.8 kg/m. It is a pity that one size smaller, an IPE-550, does not quite fit, with its I-x of 67,120 cm^4. It would weigh only 107.5 kg/m. But - too light is too light! If there had been a beam of about IPE-565, we could have had the best of both worlds. But that beam does not exist and that's all there is to it. That's why very little actually comes of our "optimization".

So is there no answer to this? Do we just have to put up with this overdimensioning caused by a really very limited range of rolled sections? No way! Because we can opt for a castellated beam. And cut this to precisely the right size.

How do you optimize a castellated beam?

Another example calculation. Say we need an I-x of 40,000 cm^4. An ordinary rolled IPE-500 with its I-x of 48,200 cm^4 would do. This weighs 92.4 kg/m. First, as an alternative, we look at a castellated beam with Peiner-Schnittführung, the traditional shape (until now). In this case, a castellated beam IPE-400/600 with an I-x of 53,704 cm^4 (taken over the web opening) should be chosen. This weighs 67.6 kg/m. A Peiner-castellated beam IPE-360/480 comes to an I-x of 37,780 cm^4 and unfortunately that is too small. That's a pity, because our Peiner- beam IPE-400/600 is considerably overdimensioned and - also not so good - its overall height is no less than 100 mm greater than that of the (heavier) alternative IPE-500. Presumably the reduction in weight (67.6 kg/m instead of 92.4 kg/m) does not outweigh the increased floor height.

But why should we take a Peiner-castellated beam at all? Because this is the traditional shape? Rubbish! We would do much better using a castellated beam with a smaller ratio H/h. It won't make any difference to the weight, that will remain 67,6 kg/m. We could get by with a ratio H/h of, say, 1.33. The resulting castellated beam IPE-400/530 has an I-x of 42,652 cm^4. This would make the floor height only a little higher than with an IPE-500; after all, the castellated beam is only 30 mm deeper than the rolled beam.

There is a second good reason for choosing an IPE-400/530 instead of an IPE-400/600. For that we must look at the transverse force calculation. Since their webs are full of openings, castellated beams must always be checked for transverse force. Doing so, they often turn out to be too weak locally (at the points of support). Then they must be reinforced at these points, for example by filling one opening with a plate welded in. That costs money: inserting a plate in a web opening requires as much weld length as the welding of six teeth. In our experience, filler plates are quite often necessary in castellated beams with Peiner-Schnittführung.

Now what is the consequence of choosing a castellated beam with a reduced depth? To assess that, we must look at the W-x-min of the lower and upper edges in the section through the web opening. That is the criterion for this. Well, for an IPE-400/600 (Peiner-pattern) the W-x-min equals 24 cm^3 while with the IPE-400/530 it is no less than 43 cm^3. Consequently, the expensive reinforcement of the castellated beam can be omitted and - bearing in mind welding costs - that's a big advantage.

The direction of the optimization of the castellated beam is now becoming clear. We must aim for the minimum ratio H/h. If we specify a castellated beam IPE-400/515, this still will weigh 67.6 kg/m; at 40,190 cm^4. The I-x almost exactly meets the requirement of 40,000 cm^4. And the corresponding W-x-min is 48 cm^3, twice as great as the W-x-min of the Peiner-castellated beam IPE-400/600! And as a bonus, the castellated beam is no more than 15 mm higher than the rolled IPE ....

Practical problem?

All books of tables for castellated beams give data for the Peiner-type only. Which means the optimization described above cannot be carried out for want of data.

Oh no!

As it happens, Grünbauer has sophisticated computer programs with which all kinds of different cutting patterns can be calculated quickly and easily.

So where is this data?