Has anyone studied tube/roll bar geometry for strength/rigidity vs. weight

[240260280z]

This is done all the time with bike frames, I wonder if anyone has done an actual study for Z cages?

The strength/rigidity to weight would be optimized by Tube dia. vs wall thickness vs geometry for a z.

I think once an optimized basic design/configuration is found for these two items (strength & weight) then this basic structure can be tweaked for:

1. compliance with rules

2. ergonomics

3. safety

I started looking at images of cages online but so many break fundamental engineering rules of "static structures" that I decided to post this question. I guess another option would be to clone BRE and BSR designs but I assume computer modelling has come along way to better their designs? (It certainly has for bikes).

[Jeff G 78]

Not a bad idea. My take on the BRE/BSR cage designs is that they are likely outdated and wouldn't be compliant, so I doubt you could gain much info from them. As for tube diameter vs. wall thickness, it is generally believed that the larger tube with the thinner wall is stronger, but I don't know if one is lighter than the other. The thing with cages is that more bars will usually increase the safety and stiffness of the chassis, so saving a bit of weight is usually secondary to making the car as safe as possible. That said, I'm sure there is room for optimization.

[John Coffey]

I started looking at images of cages online but so many break fundamental engineering rules of "static structures"

I'm not going to let this assumption pass. Where and in what way does current roll cage design violate what static fundamental engineering rule(s) within the confines of a moving vehicle and the requirements of the driver to operate the vehicle?

EDIT: And keep in mind that you have no idea where the load is coming from, what the load will be when it arrives, or how many times the structure will receive a random load during an incident.

Edited May 29, 2012 by John Coffey

[26th-Z]

Roll bar steel specification, tube diameter and wall thickness would be specified as part of the General Competiton Rules, I believe. I would have to do some contemporary research, but back in the day (BRE and BSR) the racing sanctioning body (in this case, the SCCA) specified design and construction of required roll over protection. I recall those specifications for steel grade, tube diameter and wall thickness. A hole was required in the main hoop so that wall thickness could be measured and verified.

This could be an interesting conversation given the level of engineering you are discussing.

[240260280z]

Hi John,

I was referring to simply looking at what others are doing via online pictures. The fundamental static engineering rules I refer too are what one learns in an entry level engineering course: loads, torques, etc. in bridges, trusses, towers, etc. The general rules are: straight sub-members and triangle geometry whenever possible.

In looking at online photos of other's work, I saw things like a crossbeam through the dash is not one piece but rather complicated into two that were angled where butt-joined, I have seen many "almost triangles", overly complicated dips in door areas, over gusseted, non-gusseted, too many sub-members, not-enough sub-members. I know it all depends on the application, rules, and personal taste however, it got me thinking that there must be an ideal optimized configuration to start from.

I just went through this page and it seems to parallel with the core of my question however they show many cat's to skin:

http://www.erareplicas.com/misc/stress/deslogic.htm

Here is another easier question: "What is the best design for an off-the-shelf engine compartment reinforcement assembly?"

Here are some examples, however which gives?

1. Most stiffening

2. Lightest weight

3. Best stiffening to weight trade-off

and

How does tube diameter, tube wall thickness, internal butting, and mounting point method affect stiffening and weight. The best geometry may be useless if it attaches in a weak manner or in an inappropriate location.

A

Lightest, no curve in cross member

B

Big gussets, almost triangle, cross member curved in middle to clear motor,small strut-tower mounting plate

C

Little gussets, two little triangles, cross member curved near ends to clear motor, large strut-tower mounting plate

D

No gussets, three triangles,no curve in cross member

Edited May 29, 2012 by Blue

[240260280z]

In racing bicycle metal tube design, studies found that tubes can be thinner in the middle of a span to save weight and not sacrifice rigidity and strength in a significant manner, as well, some designs had the main tubes of aluminum and the rear triangle and forks out of chromoly steel to maximize strength. Some early aluminum bikes has all aluminum components but flexed like crazy and broke, later designs used larger diameter tubes to increase strength. I assume the same studies and experiments must be done for automobile tube implementations but it is hard to dig up.

[John Coffey]

If you're designing the roll cage structure for chassis reinforcement then the loads and load paths are known. Ideally you wouldn't even use round tubing. An engineered "I" beam is far stronger in bending and square tubes are better in tension/compression.

If you're designing the roll cage structure for safety, then the big mystery is the load, load frequency, and load path. A 3,200 lb. A Sedan Mustang traveling at 80mph and hitting the driver's door at a 24 degree angle is far different then the car rolling onto the left "C" pillar at 40 mph with a rotational rpm of 60. Round tubing is the preferred material because it can handle loads of many different directions better then square tubing or "I" beams.

Also, roll cage design is by necessity prescriptive design, not an engineered design. The FIA Group 5 ruleset is the most closely "engineered" rule set but again its very prescriptive.

Edited May 29, 2012 by John Coffey

[Jeff G 78]

Blue, like John stated, roll cage loading could come from any direction, so it's much more difficult to optimize than a bicycle. On a bike, there are only a few load paths. You have the rider's weight on the pedals and/or seat and bars, and loads going through the tires from various angles. In a race car, you could be hit from any direction and in infinite concentrations. If stiffness was the ONLY concern, it would be simple to model.

If you are just looking at front end stiffness, yes, that could easily be modeled. Again though, it depends if you are building to a rulebook or just for personal use. Some sanctioning bodies allow the cage to be tied into the chassis and others don't. You also have ease of service to consider. In your options above, "A" sucks for stiffness, but it's the only one that can be swung out of the way to remove the valve cover. "B" requires very little modification to the car, while "C" connects to the rails, requiring more extensive mods. The car in picture "D" doesn't use the OE hood latch and the brace appears to diagonal down in front of the short V8, so it's not a fair comparison. If none of that matters, "D" would probably be the stiffest from what I can tell looking at small pictures.

[Zedyone_kenobi]

It often goes back to rules requirements. I designed the roll cage/frame in our baja car in college. We had a specific moment of inertia requirement against bending. The rest of the choice was due to weight, ease of fabrication, price, etc.