At the top of the list of problems is whether any of the wheels is unbalanced. Unbalanced wheels are caused by worn or deflated or underinflated tyres.
Misaligned wheels could also be the cause of your steering wheel shaking so much. Alignment problems could cause damage to your tyres making future drives uncomfortable and irritating.
There is a possibility that one of the side walls of the tyre is damaged. It could either be the front or the rear one depending on whether you have a front wheel driving or rear wheel driving car. The shaking will only be felt if the rack and pinion gear is connected directly to the axle.
A damaged sidewall is incredibly dangerous and you should get a new tyre replacement before you end up in an accident. The sidewall can’t be destroyed and be fixed later on. Once this part is torn, you need to replace it immediately. Unfortunately, because there is so much tension in this part of the tyre it cannot be fixed.
You will also feel the shaking and vibrating if the rack and pinion is damaged or any other parts of the wheel are damaged including the ball bearings, rods and nuts. If any of these components are worn down it will usually feel like the motion factor of the car is about to fall apart with the slightest bump.
If you live in a muddy or snowy area, there are chances that the debris picked up along the way has gotten embedded into the components. This might be the easiest problem to fix as nothing was damaged and your car was manufactured to be prepared for this sort of situation. It may only require a thorough clean.
Also consider whether there are exterior factors that may cause the shaking. This could include underinflated tyres, worn treads or whether the edging of the tyre has been worn out. In that case, you may only need to go to a tyre supplier to have the tyres replaced.
You will only feel the shaking or vibrating of the steering wheel whilst you drive but make sure that you get it checked. It is best to trust the professionals because they will always be able to help you with tasks that you are not familiar with.