Best angle and length for a diagonal wood support for a pull-up bar

Question

I want to construct a freestanding pull-up bar like the one described here.

But I was wondering what would be the best angle for a diagonal support considering that the things I care are:

1. That it doesn't fall over when doing a muscle-up or swinging from the bar.
2. That it uses the least amount of floor space, i.e. a diagonal support attached at a height of 4 feet at 45 degrees needs a base of 4 feet but a diagonal support at the same height but 30 degrees from the column that holds the bar (or 60 degrees form the base) only needs a base of 2.3 feet. By base, I mean the horizontal beam that closes the triangle between the vertical column and the diagonal support. So I prefer a base of 2.3 feet because it uses less floor space.

So I'm trying to develop an equation with variable angle and height to minimize base length but that it can support the forces for muscle-ups or swinging from the bar. I weight between 130-140 pound and I don't foresee anyone over 200 pound using it.

It's been a long time since I've done any static/dynamic analysis, so I don't really know where to start.

Answer 1

In any product design, there are lots of variables. The angle (or more specifically base width in this case) determines how eccentric the load can be and will not make a huge difference on the total vertical load as that is limited by vertical 2x4.

A lot of product design involves prototyping and measuring that prototype, then using engineering to optimize what you have measured. The trade offs in this application are basically "how stable do you want it to be" vs a smaller foot print. The easiest way to optimize this would be to make a foldable version.

I think the linked design will work well. One thing I would change is to make sure the horizontal supports(where your feet will be) are against the floor; in their current state they are a trip hazard.

Answer 2

I think @ericnutsch's design analysis is slightly oversimplified for your purpose. Plus, you both omitted a key factor in the successful construction of your design — your fastening scheme!

Design Analysis

As ericnutsch correctly points out:

• Your design is about making tradeoff decisions
• One tradeoff is: base width vs eccentric load carrying capacity

However, I disagree and doubt you will want to go with a foldable version. There are too many barriers to that solution from a design, construction and usage standpoint. I think you can construct a perfectly acceptable and functional static (non-folding) solution.

His analysis, however, fails to take into account a key design variable you have at your disposal — the diagonal angle of the support. In other words, how far up the vertical column to connect the diagonal strut. Given that you want to make this in one shot and don't want to make a career out of it, you pretty much want to get this pretty close to correct on the first try.

The tradeoffs, therefore, are as follows. As the height of the connection point increases:

• You use more construction material (i.e., wood in this case)
• Your horizontal stabilization decreases (beyond a certain point of optimization, let's call this the sweet spot)

Here's where it gets tricky. The sweet spot will vary depending on the amount of eccentricity of the load. In other words, the sweet spot will equate the angle of the truss with the angle of the horizontal component of the load it's carrying. This is obviously true in the case when the horizontal load is zero. Increasing the eccentricity angle will increase the angle of the sweet spot. Which is, as previously mentioned, variable.

So, you will have to make your best guess based on how you plan to use the thing as to what the optimal angle is. In this case, I would say the 60 degree angle as you have shown in your design drawings is close enough.

Fastening Scheme

Simply put. You want the highest fastener tension you can get without compromising the structural integrity of the wood. Therefore, I would do the following:

1. Make the largest possible counterbores in the wood.
2. Use washers (that fit the counterbores) to distribute the load normal to the fastened surfaces.
3. Use the longest possible wrench (to give you maximum leverage for torque) when tightening your bolts.
4. Consider trying to find some washers with teeth in them (or leaf spring) to grip the wood so they don't spin radially (about their center axis).