The question that this begs to be asked, of course, is 'Why do it?'
If you have the technology and money to build infinitely high from the earth, then why not start from scratch and build an infinitely large space station?
The advantages of such is that, building on earth, you have the problem of earth's mass creating a large gravitational pull with no contribution to 'inhabitable' area. If you start from scratch, the entire volume is inhabitable from the very center out, and all of the mass that results in a gravitational pull is structurally integrated into the design. Thus, stress is not directed all to the center, but is diffused throughout. This is the 'Christmas ornament' ball effect. The 'Death Star' in Starwars.
Of course, you can make the planet as big as you want, if it is one solid mass and not 'habitable' except for 'tunnels' throughout it. You just end up with a bigger planet.
If you use the 'Christmas bulb ornament' idea, why even encase the earth in the first place? Why not just encase a large volume of space?
What would the purpose of having an earth at the center be?
And, of course, there is the problem of materials. To build such a huge structure, one would need to use up the material in the earth to do so. That is, you would have to 'hollow out' the earth. This creates an interesting conundrum - gravity 'pulls' everything, not to the center, but to the center of gravity. If in building such a large construct, and you did so lopsidedly, you moved the center of gravity towards one side or the other. A person might actually be pulled 'up' from the center of what is now the earth, if the structure were really lop-sided. To ensure the center of the earth remained the center of gravity, the construction would have to be symmetrical.
And, of course, if the outer shell were rotated at a sufficient speed, the outer surface would attain escape velocity, and would 'pull' everything outwards, much like spinning a bucket of water around at a sufficient velocity causes it to pull the rope away from you (the concept of anchoring the other end of a space elevator). Thus, the structural design of the enclosure would be in tension, not compression.
But two more much more germane contributing arguments to the 'why?' question.
One is the effect that such a structure would have not just on the earth's rotation around itself, but of the earth's rotation around the sun, and the effect on the distance from the sun to the earth. Bringing in materials from off-planet means the total weight of the earth is increasing. That effects the total gravitational mass of the earth, and thus its rotational speed and velocity. With sufficient gravity, of course, the moon would eventually be pulled into the earth (if it were not completely consumed in the quest for construction materials).
Secondly, the velocity at the surface of a spinning ball increases for the same rotational speed, the further out you get. Eventually, with a large enough construction, either the earth would have to slow down in its rotation, or an object at the outer surface would be exceeding the escape velocity of the earth (the bucket-on-a-string example - at sufficient velocity of the bucket, if there is nothing holding the bucket to the earth, will 'escape' earth's gravity.
This, of course, begs another question be asked "How high up does a structure need to be built on earth, before the centrifugal force (speed) is sufficient to propel a standing human into space?'