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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 Xaxis (Ix) and the minimum section modulus (Wxmin) 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.
Let's say, for example, our calculation shows that the required moment of inertia Ix is 75,000 cm^4. We could apply an HEA500; this has an Ix of 86,975 cm^4 and weighs 158 kg/m. The moment of inertia is considerably overdimensioned. A size smaller, however, the HEA450, has an Ix of 63,722 cm^4 and is therefore too light. As an alternative, we could consider an HEB450. The Ix 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 HEA500. The HEM 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 IPE600. 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 IPE550, does not quite fit, with its Ix 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 IPE565, 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.
Another example calculation. Say we need an Ix of 40,000 cm^4. An ordinary rolled IPE500 with its Ix of 48,200 cm^4 would do. This weighs 92.4 kg/m. First, as an alternative, we look at a castellated beam with PeinerSchnittführung, the traditional shape (until now). In this case, a castellated beam IPE400/600 with an Ix of 53,704 cm^4 (taken over the web opening) should be chosen. This weighs 67.6 kg/m. A Peinercastellated beam IPE360/480 comes to an Ix of 37,780 cm^4 and unfortunately that is too small. That's a pity, because our Peiner beam IPE400/600 is considerably overdimensioned and  also not so good  its overall height is no less than 100 mm greater than that of the (heavier) alternative IPE500. 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 Peinercastellated 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 IPE400/530 has an Ix of 42,652 cm^4. This would make the floor height only a little higher than with an IPE500; after all, the castellated beam is only 30 mm deeper than the rolled beam.
There is a second good reason for choosing an IPE400/530 instead of an IPE400/600. 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 PeinerSchnittführung.
Now what is the consequence of choosing a castellated beam with a reduced depth? To assess that, we must look at the Wxmin of the lower and upper edges in the section through the web opening. That is the criterion for this. Well, for an IPE400/600 (Peinerpattern) the Wxmin equals 24 cm^3 while with the IPE400/530 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 IPE400/515, this still will weigh 67.6 kg/m; at 40,190 cm^4. The Ix almost exactly meets the requirement of 40,000 cm^4. And the corresponding Wxmin is 48 cm^3, twice as great as the Wxmin of the Peinercastellated beam IPE400/600! And as a bonus, the castellated beam is no more than 15 mm higher than the rolled IPE ....
All books of tables for castellated beams give data for the Peinertype only. Which means the optimization described above cannot be carried out for want of data.
As it happens, Grünbauer has sophisticated computer programs with which all kinds of different cutting patterns can be calculated quickly and easily.
We have put tables on this website for all the common IPE, HEA, HEB and HEM castellated beams with eight steps in the ratio H/h. You can access these tables HERE. Using our tables, it is possible to arrive at a beam that is very close to the actual optimum castellated beam.
If you'd rather have the best of all possible worlds, you can. Contact Grünbauer  then we'll work out the most favourable geometry and dimensioning together. An email is all it takes to set this process in motion ....
© Johann Grünbauer Tel (+31) (0)20 6990300 Email info@grunbauer.nl  TOP 