Cross-sectional area and wood quality are the parameters. I'll have to think about it a bit.
The tensile strength of wood is quite high, especially when it comes to knot-free timber. No one knows the quality of your beams, but I think it's reasonable to assume it at least corresponds to C 24. Then the tensile strength can be set to 14.4 MPa (Megapascal). Steel also comes in different strength qualities. If you choose S355, the tensile strength (yield strength) is precisely 355 MPa. This means the steel in this example is 25 times as effective as the wooden beam. If the wooden beam's cross-sectional area is 225 cm2, the steel should be 9 cm2, i.e., have a diameter of about 35 mm. This is just a calculation example but can perhaps serve as a starting point for the discussion. Steel is not my favorite material, so there might be others with more experience with steel who think differently.
Interesting! It feels like the beam's dimension is oversized for the tensile strength needed. The sizing is probably done based on the vertical force from the hayloft. I thought I would take some measurements tonight to get an idea of the actual tensile strength required. In another thread where you did the calculations, I saw that you need the snow zone, roof angle, span, distance between trusses, and the roof's own weight. Is that correct? I saw that you used 0.5 kN/m² as a standard amount for the roof's own weight. Can that be used in this calculation as well (eternittak with raw board underneath)?
I also believe that the beam is over-dimensioned with regard to tensile load. However, not as a floor beam. Surely, no one calculated this before the building was erected. One should still have respect for older techniques, there was a lot of experience involved. Yes, one needs to know "snow zone, roof angle, span, distance between trusses, and the roof's own weight." It's probably best to specifically check the roof's own weight in this case. How thick are the roof boards?
I've measured now. The span is 8.4 meters. Roof angle 45 degrees. Snow zone 1.5. Distance between trusses 1.2 meters. The roof boards are 21mm thick and the trusses are 150*150mm. Found a number on träguiden for roof tiles with underlayment and it is 0.9 kN/m2. I have used 1.0 kN in the calculation below:
Snow load 4.20x1.2x1.5=7.56kN
4.20/cos 45 degrees=5.94 meters
5.94x1.2x1.0=7.13kN
7.56+7.13=14.69kN
Could that be correct?
Snow load 4.20x1.2x1.5=7.56kN
4.20/cos 45 degrees=5.94 meters
5.94x1.2x1.0=7.13kN
7.56+7.13=14.69kN
Could that be correct?
Yes, that must be correct. You can count, and I appreciate that! It is also correct that the snow load is calculated in the horizontal plane. If you divide the roof load of 14.69 kN into two components, one perpendicular and one in the direction of the roof slope, both will be 14.69/square root of 2 = 10.4 kN. If you further divide this force into a horizontal and a vertical part, both will be approximately 7.4 kN. So, it is a horizontal force of 7.4 kN that causes the tensile stress in the beam/brace. In this context, it's a fairly negligible magnitude since S355 steel can handle 35.5 kN/cm2. Even if you go down to S235 steel, a larger diameter is not needed to handle the tensile force. Probably, other considerations will determine the sizing.
Which is preferable, steel rods or wire? I would think wire is more economical. I haven't found prices for steel tie rods online.Mathematics is the foundation for most things. Personally, I only went through the old school system where memorization was central, which I'm grateful for today. Round steel in quality S235 with a 20 mm diameter weighs 2.47 kg/m. With 9 meters and 25 SEK/kg including VAT, it becomes just over 500 SEK per rod. Tibnor has a construction chart for steel online that you can download. It includes most of what you need to know. Wire will probably be cheaper and simpler, but it must have sufficient diameter.