Roll Cage Base Plate FEA?

[gearheadeh]

Is the polyethylene cage made to a particular scale (1/10th or so)?

It is scaled so that the 1/4 inch tube is a scale 1 5/8 or 1 3/4 or what ever size tube I was planning on (simply can't remember now)
If you look closely at the cardboard floor plan on a couple of those pictures you will see scale dimensions.

I "think" I was using 1 mm = 1 inch, which would scale the tubes to 1.5875 diameter. It is not exact but a reasonable approximation of a scale size.
Metric scale in mm at 1 mm=1 inch works nicely because for all practical purposes it is a 1/25 scale (1 inch = 25.4 mm)
To hold some of the tubes in place long enough for the hot melt glue to set, dress maker pins worked nicely to "pin" the end of the tube in place long enough
for the hot melt to cool.

It was fun to build up the cage incrementally, and play with it then add a tube to try to limit a certain weakness and repeat. It is surprising how stiff it becomes with the addition of a couple critical tubes, and very interesting to see where the inherent weak points of a common cage. The most critical weak points in that design were always a front diagonal impact on the drivers side top corner of the windshield, and the middle of the top bar across the front windshield.

I was never really satisfied with how much less force it took to bring that front windshield corner down compared to the main hoop behind the drivers head.
That bar that runs across the top of the door and down the A post of the windshield needs to be a double tube (stacked vertically) to really stiffen it up to that front quartering top inpact.

Larry

Now that is a great idea! as well as the building of a scale model -

[johnneilson]

Of course, you could look at a failure...............
Trees move at a pretty good clip when the car is on its side.

John

[SteveM]

Do you guys think it would be a good idea to tie the A-pillar bars of the cage to the actual A-pillar of the car's structure (maybe by using several short sections of 1/8" thick sheet) to create a truss-like structure?

Steve.

[Seldom Seen Slim]

Trees move at a pretty good clip


How did Lynnard Skynard phrase it -- "Oak tree, get outa my way"?

[Saltfever]

Steve, if you were going to do that one thought might be to use weak materials to try and create a crumple zone to help attenuate the G-force. Although you would not want to do anything that would weaken the integrity of the cage. AFAIK NASCAR doesn't do that and surely they have spent $Ms on testing.

[Saltfever]

edit . . . Like I said earlier, this is not a real world application.. . . This shows a #100 force and failed.

Well John I am not a structures guy so please evaluate my untested hypothesis. While failure is failure it can be either benign or catastrophic. AFAIK a tensile deformation-to-failure is less catastrophic than a shear failure. A design that fails in shear will fail with less force than a design with tensile deformation. When the base plate size changed to ¼” thickness (on very thin sheet metal) it changed the failure mode from tensile deformation to catastrophic shear of the sheet metal. I was hoping FEA would test the truth of that supposition. If true that data (and pictures) could assist in cage design and talks with SCTA tech.

Are those loads correct? #100 caused a failure of the thin sheet metal floor pan!

Thank you for your patience and continued support.

[johnneilson]

Salt,

The application of the 1/4" foot plate is to distribute the tube applied forces to the cars structure without just punching through.
If I am reading the rule correctly, it pertains to bolted application with top and bottom sandwich construction. If this is true, the 1/4" plate thickness is to retain the mounting bolts more than anything else.

Yes, at #100's this is why the test is less than desirable.

In answer to your comment about stitching the cage to the chassis, especially the A pillars, it is done all the time. Look at rally cars and road race cars.

John

[panic]

Tony Foale has some useful hints on his web site http://www.tonyfoale.com/Articles/index.htm, samples from his excellent motorcycle chassis book.

[hotrod]

If the failure mode of the 1/4" base plate is a shear failure the most direct solution would be to increase the perimeter area of the base plate so it has more material to shear. Perhaps the most straight forward solution would be to specify a larger base plate perimeter on unit body vehicle cage base plates or a pair of 16 gauge doubler plates 2x the size of the 1/4" base plate sandwiched between the 1/4" base plate and the body sheet metal and repeat on the bottom backing plate.

Stitch weld those 16 gauge doubler plates to the floor pan and you substantially increase the shear strength of the floor pan in the area of the cage base plates. You would have to do much more work to punch the base plate through that 3 layer sandwich of 16 gauge doubler plates and the floor pan.

Larry

[Saltfever]

John, yes your interpetation is the written part of the rule. However, the “interpretative” part of the rule allows welding a top plate only. Look at my pictures. Those cars have only a welded top plate!  No doubler, repeat . . . no doubler on either the top or bottom. But here is the written rule.

On a unitized construction and monococque cars, the roll cage structure and braces shall have ¼” thick support pads on the top and bottom of the floor (or sill) in a sandwich construction and shall be of sufficient area to support an impact load equal to the weight of the car. For cars weighing . . . over 2500 pounds shall have at least 22 in perimeter.

So model it that way. Bolt two ¼” plates together, squeezing 0.035” sheet metal in the middle, and then load it to the cars weight (4,000 lbs) and show the results.  Assume there is about 6” of fixed sheet metal all around. OK, it is not real world but please tell me if it is in shear or tensile deformation and if it fails, what was the load at failure.

Yes, the rally cages are beautifully engineered structures. I have taped a few programs and am looking for a frame grabber so I can print it out and study it further.

[Interested Observer]

Saltfever and Johnneilson, you guys need to get together on what you consider “failure” to be.

It appears that John’s 100 lb “failure” was so-deemed because most of the thin sheet around the baseplate edges was stressed to the yield point of the material.  Yet, I think we all would agree that if we built an actual version of John’s model and loaded it with 100 pounds, it would probably flex the sheet some, but would not produce a catastrophic failure. 

It would be interesting for John to go ahead and do an elastic-plastic model with a realistic stress-strain curve for the material and see how much more load and deflection could be carried before exceeding the tensile strength.

With the direct downward loading, it is probable that the thicker baseplate detracts slightly from the load carrying capability of the sheet.  However, that may or may not be the case for a bending load like Woody tried earlier.  A number of geometric variables would enter into how that condition would perform for various baseplate thicknesses.  If John has nothing better to do.....

In any case, these investigations show what should be fairly apparent--depending on a thin sheet to provide any substantial structural capability is hopeless.  Roll cage tubulars should be routed to the strongest features of the frame, with spreader plates, gussets, and doublers as needed.  If that location is not as convenient as the floor pan, just remember the 100 pound analysis results.

[johnneilson]

I think the real test is more the one shown on reply #20.

I have 2 pcs of .030 material bent 90° and the vertical pcs directly under the tube loading.
Take a look at the deflection and the loading, it clearly shows that even this simple sheetmetal can hold up to #5k.
Yes, 5000 as compared to the flat sheet at #100.

Is it ideal, no, it shows that the cage must be attached to structure, horizontal as well as vetical.

It sounds like someone doesn't like the 1/4" rule for what ever reason. I think it is irrelevant, if the construction isn't supported it doesn't matter what the foot plate is.

I now need to get some work done.

John

[WOODY@DDLLC]

To my earlier point this is not such a simple problem! When I was working for the man we used to call this project scope creep! The more you discuss it the more everyone wants! 

If you restraint the floor material in the FEA model too close to the base plate then you turn the floor and base plate into a die set and you only shear the floor material. If you move it farther away then you can see the elongation before the floor gets "tight" and then fails. Think trampoline and the circus fat lady if we are going straight down! More stress in tension than in shear! If you look at my earlier shots that's a 500 lbf load on the lever and the material is buckling before it fails in shear.

Saint-Venant's principle says that several characteristic dimensions away from an effect the effect is essentially dissipated. In this case that means that once the base plate is 3~5 times as thick as the floor that's probably as good as it gets! So if the base plate is a little thinner (.12"~.19") then it will deform as well as the floor and help to prohibit the tube from penetrating. Actually a series of thin plates laminated together would probably work even better! When they tested for meteorite penetration on space vehicles they found that a series of thin copper plates worked better than thick armor plate. Each plate stretched then failed until the energy was completely dissipated and the last plate held.

Impact loads are what we really want to know. The peak impact load may be high but as the material stretches it absorbs the energy and the loads go down. Remember it's not the fall that kills you it's the sudden stop! 

Complex crash tests are done in the computer now but with lot's more HP than we have on tap!

Keep talking we may finger this out yet! 

[hotrod]

Keep in mind that by definition any unmoving anchor point will give false results, if the model is too restricting.

In reality, the floor pan forms a sagging sheet with a point load in the center (roll cage base plate in this case).
If you work the geometry the tensile loads on the floor go to infinity as the floor approaches being completely flat.
As soon as the floor sags even slightly those tensile loads drop very rapidly.

It is basically a geometry of the angle problem. If you simplify the situation and represent the sheet metal by a single infinitely rigid cable.
If you specify the "dip angle" as "D" the angle below the horizontal that a cable forms under load (measured at the anchor end), then the tension in the cable is (F/2)/(sin D).

So for a rope or cable stretched between two anchors and loaded in the middle with a force F applied in the center, the tension in the cable will be:

D=5.0 degrees, tension = 11.474 x F
D=4.0 degrees, tension = 14.336 x F
D=3.0 degrees, tension = 19.107 x F
D=2.0 degrees, tension = 28.654 x F
D=1.5 degrees, tension = 38.202 x F
D=1.2 degrees, tension = 45.750 x F
D=1.0 degrees, tension = 57.299 x F
D=0.8 degrees, tension = 71.622 x F
D=0.5 degrees, tension = 114.593 x F
D=0.3 degrees, tension = 190.987 x F

As you can see, as the floor approaches being completely flat the stress in the sheet to support a weight skyrockets until the floor stretches slightly under the load to achieve a dip angle of a few degrees. Even small loads will generate huge stresses until the floor dishes slightly to carry the load.
This is one of the hardest things to model as stresses might be substantially increased or decreased by the stiffness of structure elements far away from the point of load application. One of the reasons this simplified FEA is only a very rough approximation. There are two stresses in the floor sheet metal, a shearing stress at the perimeter of the roll bar support pad that depends only on the perimeter length of the pad, the thickness of the sheet metal and the applied load. The second is a tension stress in the sheet as it sags to carry the weight. It can fail due to either stress.

These are only theoretical values because no real material is infinitely rigid (has no stretch), so even very light loads placed in the center of a sheet of material will stretch the surface so it is never completely flat. It is physically impossible to support the load without developing some dip angle in the surface.


As a rough back of the envelope analysis:
If you apply 5000 # to a plate with a 21 inch perimeter resting on .035 thick steel the shearing stress at the edge of the base plate will be 5000/(21x.035)=6802 psi shear.

Shear strength is commonly about 75% of tensile strength, so an assumption of shear strength of about 25,000 psi - 40,000 psi would be reasonable.
That means in pure shear that 21 inch perimeter base plate would shear the sheet metal at a load of about 18,375 - 29,400 pounds applied load.
On a 5000 pound car slamming down on the roof that would be an impact of 4-5 G's would be enough to blow the base plate through the floor if the full impact was focused on a single base plate due to circumstances of the impact.

Needless to say any side loading that tended to bend the base plate over to the side turning a corner into a can opener and that number drops significantly.

Larry

[superford317]

the best results I have had were with adding a 2x2 square tube welded in a channel cut in the floor to tie the front and rear sub frames together and then weld the ¼ reinforcing base plate for the cage  from the 2x2, to the floor and then to the floor sills. do this for the front and rear mounting points.