Zero Cost Modelling of Space-Frames

This article was first published in 2009.

These days, engineers use finite element analysis (FEA) software when working out the stresses in structures. This gives accurate, quantifiable results. But what if you don’t have access to such programs, or the training that needs to go with that access?

If the structure consists of individual members – eg a tubular space-frame – there is an incredibly simple way of assessing the relative level of the stresses undergone by each member in the structure. By using this technique, you can quickly work out which members need to be the strongest, especially in bending (eg when failing in compression).  In addition, the technique will show where along the length of the member the stress is greatest. Finally, you’ll also be able to quickly and easily test the relative merits of alternative design configurations. 

And all you need is some copper wire and a soldering iron...

Let’s apply the technique to the design of the front suspension member in a recumbent, pedal-powered trike. This is a difficult design because an extremely high strength-to-weight ratio is needed and so the design has to be spot-on if it isn’t to be either heavy or weak – or both! Furthermore, three quite different stressing exercises need to be undertaken – maximum braking, and the forces introduced by two suspension springs placed well apart. The suspension arm will be made from thin-wall chrome-moly 4130 steel tube.

Design Starting Points

This is a sketch of the overall proposed design for the recumbent trike. The front and rear suspension members are coloured red. (The full design of this machine will be covered in detail in an upcoming AutoSpeed series called ‘Chalky’.)

This diagram shows just the proposed suspension arm. Note how the suspension pivot is located on the bottom right corner of the assembly. So what loads is this arm to be subjected to? 

Braking Forces

The biggest load that occurs on the suspension arm is in braking. If the machine is imagined to have the front wheel locked, and the rear wheels just coming off the road, a very large force (depicted by the ‘braking’ arrow) is fed into the front suspension arm.  This could be expected to place the top tube in extension, the bottom tube in compression, and the far right tube in extension. The remaining brace – is that in compression or extension? It’s hard to tell. 

And where in the tubes are the forces the greatest – that is, at what points along their length will these tubes fail? 

(Note: the front forks are being ignored in this scenario; at this stage I am trying to find the best design of the arm itself.)

Using 1.35mm copper wire and a soldering iron, I built a model of the proposed design. The copper wire was a single strand taken from a multi-strand cable used in industrial electrical wiring. The insulation on the cable was stripped, the individual strands separated and then stretched a little by using pliers and a vice. This gave straight pieces of copper wire. (The thickness isn’t critical, and any old off-cut of cable from a building site will probably be fine.)

The front suspension design was then printed out on paper and the copper wire placed on top to get the correct scaling and angles.  The wire was soldered at the joins. 

To replicate the force being fed into the assembly by braking, long nose pliers were used to grip the ‘headstock’ area (ie for the purposes of the model, this is regarded as being rigid) and then, by moving the handle of the pliers in the direction of the arrow, feed in the correct tension and compression loads. The model was held at the suspension pivot point.

Braking Results

The model before braking stress was applied.

The model immediately and dramatically failed – and in an area that I didn’t expect. (Yes, it’s easy to be wise after the event – “Of course it will fail there!” – but I certainly didn’t pick it prior to the test.) Note also how the member has bent close to each of the soldered joins. (This is one reason why using the copper wire is much better than using – say – wooden toothpicks. You can clearly see at what points the material fails –  it continues to bear witness to the failure mode.)

I straightened the bent wire and then added this cross-brace.

This time, the newly added cross-brace failed, right at its middle. (It’s bent up straight towards the camera.) So, of all the pieces of tube making up the front suspension arm, during braking this piece is being subjected to the most stress. Considering how short it is, it’s an amazing failure (in compression, you’d normally expect the longer tubes to fail first).

So, was the big diagonal brace (green) really needed when the assembly was undergoing braking forces? I removed it and re-tested....

...to find out that, oh boy, was it ever required! It’s also interesting to also note how the distribution of bending forces in the lower wire has given gentler radius bends.

I went back to the ‘two diagonal braces’ design, and this time when I simulated braking forces, a solder join broke before any member failed. Note that while I didn’t measure the required input forces before failure (this could be done with weights, levers, etc), in the different configurations the force to cause failure varied from being trivial to being quite a major effort needed with the pliers – I’d guess at least a ratio of 10:1!

Work Hardening and Fatigue? Copper will initially work-harden (get stronger as it is ‘worked’, eg by being bent) and then subsequently will weaken as fatigue sets in. To avoid this, always make a new model to check final configurations, ensuring it behaves in the same way as earlier iterations.

Front Spring Forces

In addition to braking forces, what other forces need to be catered for in this recumbent trike design? The front suspension arm has two springs. The position of the front spring is shown here as the unfilled arrow – it feeds loads, at an angle of 20 degrees, into the bottom longitudinal in the suspension member. The two forces acting the other way are effectively pushing-up at the suspension pivot and the wheel. So how would the developed model cope with these forces? Again the results were fascinating.

This time the testing was done on a flat surface, and by placing the assembly against nails driven into a panel. These nails represented the upwards forces of the wheels and suspension pivot. The downwards force of the spring was achieved by pulling on the correct part of the assembly with long-nosed pliers. 

This time the upper longitudinal member failed spectacularly. 

As it happens, the proposed design calls for this member to actually comprise two tubes that are curved around the spring that has its seat on the lower member. Therefore, I doubled the upper member by adding another copper wire to the assembly.

This time in front spring testing, the forward diagonal failed – the very same member that failed under braking forces! So the testing has shown that this is a very heavily stressed member. I then doubled the strength of this member by adding another copper strand in parallel.

And this time the solder connections broke pretty well at the same time as the diagonal brace failed.  

Centre Spring Forces

The forces resulting from the second spring could now be tested. As this diagram shows in blue, the upper member and leading diagonal are now double-strength. The second spring feeds in forces as shown by the upper right arrow. (The suspension system uses interconnected front/rear suspension systems: this force represents that connecting spring.)

Testing was carried out in a way that subjected the model to forces in the correct directions. (This pic is actually of a second test, so explaining the fact that some wires are no longer dead straight!)

Both the doubled top member and the largest diagonal failed – but a lot of force was applied before failure occurred. In fact, so much force that I decided not to strengthen things further.

All the Forces Together? Testing in this way does one configuration at a time – braking, then one spring, then the other.  Where a particular member is subjected to greatest forces in more than one configuration, it could be expected to fail in each of those individual tests. So for example, the front small diagonal failed when both testing the braking forces and the forces of the front spring. The top longitudinal failed when testing both the front spring and the rear spring.  But in actuality, some forces will add to each other, and others will subtract from each other. Most importantly, if a single part fails in two different tests, and those forces occur simultaneously, that member will be subjected to greater total loads. I did one test where both spring forces were applied simultaneously - and here is the result. But before it failed like this, the effort required with the pliers was very large indeed.

Outcomes

As I said in the introduction, by using this modelling technique you can very quickly work out:

• Which members need to be the strongest, especially in compressive bending (this type of bending is the most common failure mode of an ‘ideal’ space-frame)
• Exactly where along their length the members need to be strongest
• The relative strengths of different designs of space-frames

After weeks of on-paper examination of the proposed front suspension design, I had decided that:

- The lower longitudinal would need to be a stronger member than the others

- A member parallel to the front spring would probably be needed (primarily to distribute the spring’s load into both upper and lower longitudinals)

However, I certainly did not realise that the lower longitudinal had to be strong only for one short section near the front, or that a short diagonal brace near the front would be an absolute essential (let alone one of double strength!)

Bigger Structures

The tests conducted here have been done on only a very simple space-frame – just seven members. But exactly the same approach can be taken with space-frames as complex as you like. 

You can model - and then test to failure - a space-frame being subject to torsion, bending or tension. You can model the affect of changing suspension spring motion ratios, altering where the greatest weights are located in the vehicle, and so on. The more complex the space-frame, the longer it will take you to model it – but then again, that’s an encouragement to start with the simplest possible structure...

Conclusion

I think this approach beats everything except a full FEA analysis of stresses. Unlike drawings on paper, you don’t need to mentally (or mathematically) work out the complex load paths taken in real structures – just model it, then see what bends, and where it bends. The approach has given me much greater confidence that I can develop a light, strong structure that doesn’t unduly stress any one part. 

If you are making anything that needs to be light and strong, and uses individual load-bearing members, do it!

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