We''ll begin by discussing what exactly a chassis is. A chassis is defined as the main structure of a vehicle. This superstructure is the basis for all pieces to be bolted to. Motors, transmissions, suspension, sway bars all bolt into this structure. Rigidity on its face, is important in these structures because all of the components that bolt to it need to retain their dimensions so that the vehicle doesn't collapse under its own weight. Furthermore some areas of the chassis govern elements of handling such as toe, caster, and camber as each suspension component bolts into the chassis.
We should think of a chassis like a piece of paper or cardboard. If we managed to bolt wheels to it, it wouldn't be very fun to roll around while making Subaru noises would it? It would be a floppy mess! But if we make it a little stronger, in the trade this is referred to as "torsional rigidity", it becomes a functional model car. Now lets take that cardboard car and put a big fold in the middle of it running the full length of the "car". The car will have all sorts of issues with wallowing as the fold flexes in and out. This is exactly how your exhaust tunnel impacts handling. Its a natural crease that reduces the chassis strength. By adding some braces to that tunnel we can prevent that crease from flexing and make it more predictable. This is just one type of bracing but the same holds true throughout the vehicle.
Another critical junction in a car is where the subframes bolt into the unibody. Unibodies are the trade term for modern chassis that do not utilize a body on frame construction(like a pickup truck) For our vehicles, Unibodies are the way our cars are built. The subframe is a sub structure that contains the rear suspensions or the front suspension/engine and transmission. Since these components need to be bolted into the unibody for the vehicle to work, there are joints where large bolts fasten the two together. This junction provides a massive weakness for chassis flex. This weakness can give the car a wallowing feeling as you go around a corner and your car rolls over slight road imperfections. If you can bolt a brace across this critical joint and give that area more strength you will effectively reduce the deflection of the two portions of the car and make the vehicle handle in a much more predictable fashion. This increase in predictability will allow the driver to go around corners quicker which we can call an increase in handling!
Yet another area of a chassis that can have a significant weakness is the tops of the strut towers. Strut towers are the area where you coil spring and damper mate with the chassis of the car. This can get a little tricky with multi-link rear suspensions, which I will cover below. In between the front strut towers is where your engine and transmission are carried inside of that subframe we discussed earlier. Since the struts are carrying the full load of the car, it is not uncommon for them to deflect going around a corner. This deflection causes changes in camber, caster and toe as the tower moves about. When these portions of your alignment shift suddenly, the handling is less predictable and thus the car is slower. By running a bar or brace across this gap and linking the strut towers we can reduce this deflection and once again increase predictability and thus handling!
Inside of the vehicles subframe itself is also an area of weakness. LCA's(lower control arms) bolt into the subframe via bushings and bolts. On the horizontal plane of the car, the LCA's mount via an outrigger that comes off the subframe. This region is usually floating out on its own and as such its predisposed to flex. Even more so if this area is on the drive wheels such as a FWD(front wheel drive) car. The rear portion of these LCA's mount via a bushing. When a driver suddenly gets on the throttle or goes into a corner in a spirited way, these areas will deflect, the horizontal mounts shifting in and out ever so slightly and the bushings shifting independent of one another. This movement combined with the sudden changes to toe and caster contribute heavily to wheel hop and torque steer. By locking them down with a brace such as my Traction Bar or Torque Gusset Traction Bar, the driver is able to get on throttle earlier and harder while having less wheel hop and torque steer. Interestingly enough these braces happen to reduce motor mount vibrations by acting as a chassis damper.
So why do we need braces? Didn't the OEM's(manufacturers such as Ford, Mazda or Toyota) design these with teams of engineers to make sure that the chassis is well designed? This is a very good question! Just like power adders, OEM's definitely try their best to give buyers the maximum performance at the best price. However, some areas of the chassis get overlooked just like the engines total power output. Quite honestly the OEM's try their best to make a rigid chassis and each subsequent generation of cars gets even more rigid than the previous but some areas are too costly and would drive up the MSRP to price points not feasible or competitive for consumers. Other areas are not practical from a mass production assembly standpoint. SO while the OEM's are doing a great job on the chassis side of things since the 80's and 90's, there is still a ton of improvement and performance left on the table for consumers to bolt on!