One question asked about 'harmonics', but flex from road irregularities is the real issue in sissy bar construction.
Here are some basic principles and lessons from experience. Hope this helps you builders out there...
Sissy bars flex forwards and backwards as the rear of the bike bounces up and down over our carefully protected Australian pot holes, corrugations and bumps. A sissy bar on a rigid will flex more than on a chopper with suspension because the movement is sharper, because the springs are not taking up any of the sudden shocks of the bumpy road.
So let's start off with rigids...
The taller the sissy bar, the more it will flex. The steel uprights are bending back and forth at a rapid rate. A stress point (where all the stresses of the steel trying to bend are focussed) is created at the spot where a bar is rigidly mounted. The point cannot move, but the bar above (and please note, also below that point) can and its movement basically HINGES at the fixed point. If there is no hinge, it tries to bend and will eventually crack and break. You've no doubt broken wire using this method. Bend it back and forwards and it will heat up and snap. But the bending (stresses) has to be concentrated on a single point for it to break. See main picture below...
If the stresses on your sissy bar are focussed on a single spot, your sissy bar wants to do the same as the wire. How tall it is, how rigid the bike is how thick and what kind of material it is made of, will determine how quickly it will snap... and I've had a few snap in my time! In one case the passenger went off the back when I did a wheel stand!
Sissy bars also need to be strong especially if a passenger is to be carried (even periodically). No one is silly enough to build a sissy bar out of aluminium tube. Modern aluminium motorcycle frames no matter how heavy seem to be, are quite prone to breaking.
For sissy bars, mild steel and stainless are the two common options.
Stainless work hardens quicker than mild steel. Welded stainless will work harden and snap at the weld rather quickly if the weld is cooled quickly. When welding a stainless sissy bar, any possible stress point (most notably at the rear guard mount) must be cooled very slowly. A pile of dry sand is best for this.
I prefer solid bar for sissy bars because it's strength is less affected by welding. I have used and do sometimes use tube, but only if it is well gusseted and heavy walled... not the thin stuff you buy at the local fence making place!
12.5mm bar is ok for up to 18" above the guard if no one is sitting against it. 16mm bar is the smallest I use if a passenger will be carried and for higher bars.
Gusseting. What does it do? A bar will snap due to stress concentrated at a point. That point on our sissy bars is at the highest fixed point; the rear guard bracket. A gusset is a curved 'triangle' or two 'triangles' that remove the stress point by spreading the stresses (that would cause a crack) over a wider area.
The easiest and neatest way to spread the stresses on a sissy bar is to turn your simple rear guard mounting into a double 'triangle'. As you can see in diagram 'A', that stress point no longer exists. The stresses are now spread over a 40-70mm area. Because the 'triangular' gusset is curved, the stresses are progressively spread to a stronger and stronger section. The strength of the bar is slightly greater at point 'z', stronger at 'y' and stronger again at 'x'. If you make the curve a smooth transition from the ungusseted part or the bar to the strongest section the stresses are spread and basically become non existent and your sissy bar is unlikely to crack. Gusset does not have to be overly thick. 3mm is fine if the gusset is thick enough around the bolt hole.
I often see straight triangular gussets (especially on frames) that don't smoothly change thickness, They are ineffective, because the stresses will locate at the sudden change in thickness anyway. Their only real value is in adding more weld length with will make a stronger joint.
A sissy bar can also be mounted to the top surface of the guard with a welded in cross piece. However once again, the gusset above is needed to prevent cracking at the rigid (stress) point.
This photo shows a gusset as mentioned on a tall stainless sissy bar which is mounted to the top surface of the guard...
Triangulation. What does it do? A triangle is the strongest engineering shape available to us. See diagram 'C'. For it to change shape, one side must actually stretch or break.
You can add some triangulation to your sissy bar to reduce flex and the accompanying stress points. This photo shows very minimal triangulation of the back of this tall sissy bar. The inner pieces of decorative bar sit 10mm behind the main bars (white arrow) and create a very shallow triangle whose top point is at the red arrow. This will not reduce the stresses sufficiently to prevent breakage, but does help. See diagram 'B'. It ideally should be 50mm back and would then be sufficient, but in this instance makes the carrying of gear on the back of the sissy bar a pain.
Triangulation can also be built in using a high back seat (see diagram 'D'. Triangular gusset is at 'J'. 'K' shows where the base of the triangle will try to lift and causes a stress point. Point where the seat back is attached to the top of the sissy bar is the top of the 'triangulation'. Not all that effective unless seat back and base is 3mm steel with some reinforcement, but an alternative all the same especially if your sissy bar is not all that high...
Sissy bars on sprung rears...
Reduced road shock due to rear suspension makes life a lot easier on sissy bars.
If care is taken with welding at bottom mount of sissy bar and 16mm mild steel is used, gusseting is not always needed. Welds and heated bends must still be cooled slowly. Also, don't weld all the way around the bar. Keep the welding to a maximum of half the diameter of the round or square bar. A seat back that is part of the passenger seat and is fixed at the top, will also reduce sissy bar flex. If the number plate is mounted at the bottom of the sissy bar, 5mm plates welded up the sissy bar for the number plate will add some strength; just make sure any welded bracket overlaps one close to it, so you don't create a stress point at the join of the two.
Not high, strong mount reinforced (a little) by number plate brackets, 16mm mild steel...
This sissy bar has done almost 50 years of service. Of 16mm mild steel, it is not overly high, has no gusseting and no lower welds to create stress points and is reinforced by the seat back...
Tall, 16mm. Supported by the seat back. Extra support by widening the bottom of the sissy bar through the bend to 22mm to fit into the frame tubing....
Not supported by the seat/back rest, and fairly tall, so supported by triangulation...
Another method of triangulation, designed to allow an octo strap to fit through the rear triangulated space. The rider did a lot of camping trips, so benefitted from the extra strength imparted to the 16mm stainless bar...
Using proper thickness material and sensible gusseting will allow you to carry loads trouble free. But... still keep an eye out for cracking around possible stress points...
