Tube Frame Analysis
How to score some tube frame design points (and save some frustration).
Frame designers on the teams in my bay asked me what analyses I expected to see. Different design judges have different expectations. While it’s useful for me to compare cars by their calculated and measured torsional stiffness, this is not the most important load case for the design of a frame. This advice is for those building a tube-frame car - monocoques are designed in a different way once the loads are selected.
This is a long post to say "I don't want to see just a fixed-bulkhead-to-fixed-bulkhead torsional load case on only the frame design that you'd already sent out to the tube cutter." Most FSAE frames should be analyzed for stresses, stiffnesses, and directions of deflection under:
Torsion, either from the front suspension pickup points to the rear suspension pickup points, or (better) from the wheelrim to the wheelrim through the outboard assemblies and links
Maximum braking at the same time as maximum chain tension applied on the driven side. Bonus points for using a kinetic energy analysis to determine what the loads are and what components are most and least stiff!
Maximum acceleration at the same time as maximum chain tension applied on the driving side. Does your chain jump off if you dump the clutch uphill?
Maximum cornering in the fastest (highest-wing-load) corner you anticipate - remember that you need both loads applied at the tires and loads at the wings
One-wheel bump with a simultaneous cornering load
A false-static analysis of the forces in a 20g front crash
List THE Loads
The first step is to list out the loads to be applied, looking out for ones that have to be applied simultaneously. A good example is the reaction load at the rocker pivot and the transverse load at the end of the spring and damper unit when a wheel goes over a bump. A more complex case is a front crash, with the impact attenuator's compression load on the frontal bulkhead, the driver's tension load on the seatbelts, and the engine's load on its mounts. A list of the loads on your frame will help you find the important ones by magnitude and by the inconvenience of reacting them to frame members. A classic case of the latter is compression in the outside upper control arm - the arm is nearly at a right angle to the tubes it is pushing on.
DESIGN THE LOAD PATHS AND STRUCTURE
Apply the principles of Strong, Stiff, and Light Structures (especially sections 3 and 4) to the concept before starting the Finite Element Analysis (FEA) process. Steel tubes are a light way to carry a load in tension, but a heavy way to carry one in bending. The nodes between long, thin tubes are used as examples for sum-of-forces-equal-zero calculations in freshman statics for a reason.
Clean UP THE CAD
Second, make sure you have a clean CAD model. Trimming every single tube so that there are no gaps or overlaps is necessary to get them cut to size by your vendor. It is also a lot less frustrating than individually tracing every can't-mesh-won't-mesh error in your analysis software. Necessary features to generate in CAD include the details of your load application points. Applying the load uniformly to the lap belt tabs will not tell you whether the tabs themselves will fail, and will hide any moment you've put on the weld - but if you're analyzing several frame concepts you can put a split surface for it now and return later for the detail design. Splitting surfaces to allow you to select only the area that'll actually have load or constraint applied to it is necessary.
Mesh Model
Third, go build a mesh for your model in your analysis program. Analysis programs are all accurate, some run faster, some have features that allow you to find and fix model errors easily. Computing power is cheap - simplifications used by experts in the past to reduce element counts needed at the expense of accuracy are obsolete. I'd rather have you run a couple fewer iterations that accurately show local deflections and stress concentrations than get the last 20 lb*ft/deg gain you could've found. I recommend starting with 5.1 mm second-order shell elements for the simple reason that you get 5 of them around a one-inch tube, so you can see which part of the joints are most heavily stressed. An advantage of using shell elements for broad analysis is that you won’t have to remesh if you want to change a wall thickness, so that troubleshooting doesn’t have to be repeated.
Make sure every element is at least high enough quality to be calculated here. Most programs will have a cutoff threshold of how far a tetrahedron can be distorted from equilateral and still transmit stress flux to the elements it intersects. Use beam elements only if you've got an automated system to set up and run a large number of configurations and are only using it to see which gives the least deflection under a load.
constrain and Load
Now you are ready for constraints. Lock down only the degrees of freedom that actually are either fixed or reacting the load beyond the frame. The torsion test should only constrain six degrees of freedom - if you’ve chosen two points to lock against translation in three directions you’ve prevented all free rotations. A front braking load should induce a moment that the rear control arm, spring, and rocker mounts have to react. If you overconstrain the model it will appear to be stiffer than it really is, as movement that can happen doesn’t.
Loads come next. Apply them in a physically reasonable way. A bolt in double shear will apply its load to the tab sides on the area clamped under its head - unless it is so heavily loaded that it exceeds its clamping force, slips, and applies the load to the faces of the bolt hole. If you have an asymmetric frame and symmetrical loads that can go either direction, make sure you don’t end up with driver complaints that it turns differently left from right!
Minimal torsion test constraints at rear damper / rocker mounts:
Fixed vertical position on both sides.
Fixed longitudinal position and fixed longitudinal axis moment, one side.
Fixed lateral position and fixed lateral axis moment, opposite side.
Equal and opposite vertical loads at the front damper / rocker mounts.
Simulate, Analyze, Iterate
Finally, assign the material, choose the solver parameters, and run the simulation. If it succeeds, start looking out for too-big elements. If stress changes more than 40% between adjacent elements you have enough discretization error to need to refine the mesh in that area to get accurate stresses. Your stress results near a sharp corner or at a tube intersection will be lower than actual unless a fillet is provided to eliminate the singularity. Luckily, you're going to make a fillet there by adding welding wire to the pool of the steel that was already there. Finding these areas is where the pretty colors of a results plot come in handy.
Once you have the results, decide what changes you will make. A plot of the local strains from the load application point to the constraints will show the places where added material will increase stiffness most efficiently. A plot of the total deflection in torsion will allow you to identify which "bay" of the chassis is weakest - or if one of your loads is not triangulated properly and is causing deflection to be dominated by local bending. Your stress plots will show what areas require careful detail design of the joints, or a tube that needs to be larger or thicker.
If you don't want to redesign the whole frame because your analysis showed one tube well over the stress limit you set, and it's impractical to increase its size or wall thickness, consider choosing a different tube alloy and joining process for it. At the far extreme is silver-brazing in a 4130 tube that you have heat-treated so that you have its elevated strength and no heat-affected zones in its joints, but brazing is not allowed for the regulated structure in FSAE for 2023. Other solutions to consider include TIGing one 4130 tube in a MIGed 1018 or 1026 frame using an ER70S-2 wire, or calling out a visually-perfect-weld requirement on the drawing. If your team becomes the first team to heat treat their chassis after welding, let me know how much it distorted during hardening.