Compressor-Turbine: Why a shaft and not kind of a "rotating drum"? I'm studying the fundamentals of jet propulsion and its applications. I really have this next question and haven't found an answer yet: why do jets use a shaft (or more) to connect the turbine(s) to the compressor device(s), but not a "rotating drum" instead?

What I call a "rotating drum" (I sketched it below) is a thin, rotating cylinder that has built-in rotor blades at the beginning and exit.

I'd like to know if this is a feasible arrangement, and what would be the disadvantages of it. I think this might be unfeasible because:


There would be a lot of thermal stress at the middle of the drum.


But if we were to overcome this drawback somehow, I think we would benefit in the following ways:


Less weight, I think, with respect the traditional shaft system.
More internal space (no hollow) for other demanding components, like the combustor. The combustor could be made a bit larger, thus increasing the burning efficiency (more reaction time for reactants, ...).




I don't know how correct/wrong I am. This is a question out of pure curiosity and I wanted to get some feedback on it. Should I go ahead and start working on a small scale prototype of it? Hope my question here is not too basic.

PS: The sketch I made is just that: a sketch. Therefore, important things like the relative number of stages compressor-turbine, or the increasing/decreasing areas for each of those two components, do not appear.
There are a few very practical reasons why turbine engines use inner shafts/spools. 

First, jet engine spools are very high speed rotating parts, this means they are subjected to high amounts of centripetal force. Centripetal force is calculated by $F=mr\omega ^2$ were F is Force, m is mass, r is radius of gyration and $\omega$ is angular velocity. So obviously the larger the radius of gyration the higher the forces that the rotors must carry. To reduce the radius of gyration manufacturers try to push the mass of the rotors as close to the centerline of the engine as possible. In the picture below (source) I have circled the HPC, HPT and LPT rotors. You can see how they are very thin under the blades and then have a large bulb very close to the engine centerline. Moving all of this mass towards the centerline, lowers the radius of gyration, and thus reduces the centripetal force. By reducing the centripetal force, you can reduce the strength of the rotors as well, since they don't have to carry as much load. This allows you to remove mass from the rotors, further reducing the centripetal force and overall weight of the engine. 



Next, you want the bearings to be as small as possible. This is because as the radius of a bearing increases the linear velocity of it also increases, via this equation: $v=\omega r$. The faster the linear velocity the higher the wear, the greater the friction and greater the heat generation. So there is a push to make the bearings as small as possible given other constraints. In the image below I have circled the bearings, the red circles are on the low pressure spool bearings, while the blue circles are the high pressure spool bearings. This isn't always done, but it is becoming very common for the aft high pressure bearing to actual ride on the low pressure shaft. Typically these shafts spin in the same direction, so the bearing speed is reduced by this equation $\omega_{AftHPbearing}=\omega_{HP}-\omega_{LP}$. Bearing friction reduces the efficiency of the engine, and bearing wear is a significant maintenance driver. 



(This is getting long so I am going to truncate the rest) There would be many other issues as well, such of blade mounting (dovetails in compression instead of tension), blade design (compression instead of tension), possible increase in leakage paths, containment, stator structure design (now all of your stators are attached to a stationary shaft that can only be supported at the ends), control of variable stator vanes, getting the fuel into the combustor, how do mount the engine, etc.

Edit: Just reread the question and realized you were also talking about making the combustor bigger. Modern combustors are getting smaller and are much smaller than they were in the original jet engines. You can also see in the pictures above, they already don't use all of the space available to them and if they needed more space the arm (shaft) connecting the HPT and HPC could be lowered some more.