# Calculation of the strength of a wooden beam

I'm designing a wooden structure for Shibari purpose and I need to calculate the maximum load capacity of a beam at the midpoint. I've tried using various calculators, but I don't fully understand all the parameters. Could someone explain or point me to a place where I can easily calculate the maximum load?

The data for my calculations looks like this:

• Type of wood: spruce
• Class: C24
• Lenght: 3000 mm
• h: 95 mm
• b: 45 mm

The beam is supported at both ends. The main force will be placed in a single point middle of the beam (hanging on a rope). What's the maximum weight I can put on such beam without it breaking or getting damaged from the bend?

• Hi, welcome to Woodworking. There are a few points you need that are key to understanding how the wood will behave. You'll get much better performance if the ends of the beam aren't merely supported, but are instead locked solidly in place (same as shelves perform far better with joints at each end versus merely sitting on shelf supports/pins). And if you can spread the load so that instead of one or two rope thicknesses the force is spread over a wider area (e.g. by attaching a steel plate) it would be better. Edit: is there a total span of unsupported beam that you need? Feb 1, 2023 at 15:09
• Beyond that, it may help you to consider what a pull-up bar/chinning bar has to withstand, which is far beyond the static load of a person hanging in place. Also, I presume there are many photos online of other people's shibari setups? There could be a wealth of details available in those if you examine them closely. Feb 1, 2023 at 15:15
• Seems like a 9' 2x4. construction grade. I had to look up shibari, Lets say I would want to have at least 2 of those for my weight, and I'd tend to go for 2 2x6's for that span. Feb 1, 2023 at 15:40
• @Graphus i was not clear, by supported I mean they will be mounted on outer beam hangers and secured with screws to prevent any movements. As for the setups, usually they are made on dedicated constructions (which I can not do inside the room) or using chemical anchors on celling (can not be used because of building type) Feb 1, 2023 at 16:19
• There are quite a collection of "Will this `<item>` support `<weight>`" where `<weight>` includes pull-up bars, heavy bags, etc. over at Home Improvement. That would be an excellent place to browse for the type of answer that this deserves. If you're not satisfied with any of the answers you've found, ask a question there (and explain which answers you've looked at and found lacking). Feb 3, 2023 at 19:31

The answer to your question is not as simple as it may first appear. You propose using a 45x95mm (2x4") piece of lumber spanning 3000mm (10') with a person suspended at mid-point. The amount it will support is substantially greater than even a heavier person would present. However, there are several problems to consider.

1. As you apply weight the beam will tend to sag. How much sag are you willing to accept?
2. The amount of bearing and the means of connecting the beam at the ends is important. You want to prevent twist at the ends to maintain secure connections at the bearing points. You must also consider that the load is not static. The person will move and this will introduce lateral loads that make the stresses on the beam more than just vertical causing the beam to twist.
3. As the beam sags more, it will have a tendency to twist. In doing so, the vertical profile of the beam decreases and so too does its capability to support the person. It will then have a tendency to twist more and sag further. (Hence the need to properly secure the ends.)
4. Your span is significant, and this reduces the load it can carry and its ability to resist the tendency to twist under load. The shorter the span the better it will perform.

My instincts tell be that the size of your beam is inadequate. I would be inclined to suggest increasing the depth to 6" or 8" and doubling its width. Of course, the best answer is not in calculation but by testing the set-up before actually using it.

• Thanks you for your insights. as for your points: 1. i dont mind sagging as long as it doesn't damage the the beam 2. it will be secured to the wall with outer beam hanger, and the beam to hanger will be secured with wood screws to prevent any movements 4. there is no possibility to shorten the span unfortunately. Feb 1, 2023 at 16:15
• Good answer, but I disagree with that last line about the best answer not being from a calculation. If someone builds a bridge, drives a bunch of trucks over it to test, and declares "yup, that's not going anywhere..." would you feel confident in its safety? While testing is important, I'd want to know that the bridge was engineered to withstand loads up to some multiple (the safety factor) of the largest expected load. Feb 1, 2023 at 16:34
• @Caleb. I would generally agree with you, but this is a single beam with a lot of unusual /eccentric loads. It would take a structural engineer to really address the overall structural issues and we are dealing with a very small scale problem. I suspect the engineer would be more inclined to simply over size the beam and call it done.
– Ashlar
Feb 1, 2023 at 21:59
• @Cynizm Using a joist hanger will help reduce the possibility of twisting. Consistent with my answer I would suggest using a double joist hanger and use a 4"x6" piece of lumber. The difference in cost is minimal. Remember to test it out before using it.
– Ashlar
Feb 1, 2023 at 22:02
• @Ashlar The whole question is really more a structural engineering question than a woodworking one, and for that reason possibly off topic, perhaps better suited to DIY. Honestly, considering that safety is at issue here, I think the OP would be a fool to rely on any answer here, no matter how thorough, for the same reason one shouldn't seek legal or medical advice from Internet forums. Feb 1, 2023 at 22:07